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• meta_descriptionThis is the personal website of Ivo Filot. Ivo Filot is a theoretical chemist originating from the Netherlands.
• meta_keywordsIvo Filot, Personal website, Fischer-Tropsch, Microkinetic Modeling
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      • id36
      • titleAnimated gifs of molecular orbitals of CO
      • content# Introduction The electron density of a molecular orbital is basically a three-dimensional scalar field which can be visualized using both [contour plots](http://www.itl.nist.gov/div898/handbook/eda/section3/contour.htm) as well as [isosurfaces](https://en.wikipedia.org/wiki/Isosurface). Typically, we see that isosurfaces are being employed, as they more clearly show the three-dimensional character of the molecular orbital. However, such isosurfaces are nothing more than those [set of points in 3D space which have the same value](http://paulbourke.net/geometry/polygonise/). Thus in some sense, there is loss of information, especially if there are interesting features within the three-dimensional object spanned by the isosurface. # Animated gifs A very simple way to resolve this, is to use contour plots. As mentioned, the downside of using contour plots though is that we are no longer able to effectively show the three-dimensional character as we are simply [projecting planes within the scalar field](http://paulbourke.net/papers/conrec/) and colorizing each point on the plane based on the value of that point in the scalar field. We are able to generate a series of contour plots for a set of relevant planes within the three-dimensional space. Using the [previously demonstrated EDP program](http://www.ivofilot.nl/posts/view/27/Visualising+the+electron+density+of+the+binding+orbitals+of+the+CO+molecule+using+VASP), we are able to efficiently create this contour plots using the command line. In turn, using [Imagemagick](https://www.imagemagick.org) and a small Python script as shown below, we are able to construct [animated gifs](https://en.wikipedia.org/wiki/GIF) that loop over the generated set of contour plots. <pre> <code class="python"> #!/usr/bin/env python from subprocess import call import numpy # input file identifier filestr = "CO_5SIGMA" # output file name output = "co_5sigma" # generate slices and create contour plot for z in numpy.linspace(2.0, 8.0, 50): filename = "%s_%f.png" % (filestr, z) call(["/home/ivo/Documents/PROGRAMMING/CPP/edp/build/edp", "-i", "/scratch/ivo/vasp/CO/PARCHG_5SIGMA", "-s", "100", "-v", "1,0,0", "-w", "0,0,1", "-p", "0,%f,0" % z, "-o", filename]) call(["convert", filename, "-resize", "25%", filename.replace(".png",".gif")]) # combine everything inside a single animated gif call(["convert", "-delay", "0", "-loop" , "0", "%s*.gif" % filestr, "%s.gif" % output]) </code> </pre> # Showcase As usual, we use the electron density of the binding molecular orbitals of CO to demonstrate the tool. Below, you can see that the animated gifs loop over a set of contour planes. One of the things that are now easily visible are the regions of near-zero electron density at the center of the 1π and 5σ orbitals, which would normally not be visible when using isosurfaces. <table class="table"> <tr> <td> <b>3σ</b><br> <img src="http://www.ivofilot.nl/images/38/co_3sigma.gif"> </td> <td> <b>4σ</b><br> <img src="http://www.ivofilot.nl/images/39/co_4sigma.gif"> </td> </tr> <tr> <td> <b>1π</b><br> <img src="http://www.ivofilot.nl/images/40/co_1pi.gif"> </td> <td> <b>5σ</b><br> <img src="http://www.ivofilot.nl/images/41/co_5sigma.gif"> </td> </tr> </table> What other molecular orbitals would you like to see? Share your thoughts in the comments!
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      • id35
      • titleEfficient compression of CHGCAR and LOCPOT files
      • content<div class="alert alert-info" role="alert"><i class="fa fa-github"></i> Looking for the Github repository of den2bin?<br><i class="fa fa-link"></i> <a href="https://github.com/ifilot/den2bin">https://github.com/ifilot/den2bin</a> </div> # Introduction I was recently involved in a research endeavor where we had to generate and analyze a substantial amount of [CHGCAR](https://cms.mpi.univie.ac.at/vasp/vasp/CHGCAR_file.html) and [LOCPOT](https://cms.mpi.univie.ac.at/vasp/vasp/LOCPOT_file.html) files. Each of these are relatively big in size (~150MB) and were consuming a lot of free space on our hard drives. Since we employ periodic back-upping of our data; you can imagine that things started to pile up and clutter. We looked into [BZIP2](http://www.bzip.org/) and [ZIP](https://en.wikipedia.org/wiki/Zip_(file_format)) to reduce the size, but found out early on that we only obtained [compression ratios](https://en.wikipedia.org/wiki/Data_compression_ratio) of about 3 (i.e. the zip-archive is only three times smaller than the original file). In this blogpost, I will show you the steps we took to get improved compression ratios. Using [lossy compression](https://en.wikipedia.org/wiki/Lossy_compression), we were able to get compression ratios of over 30 with decent accuracy of the original data. # From human-readable to binary As mentioned in the intro, we did not gain much by simply storing the CHGCAR or LOCPOT files in an archive. Since these files are human-readable, we can easily get better compression results by storing the values in binary format. If we for instance consider the following lines inside the CHGCAR file: <pre> <code class="bash"> 112 128 288 0.46419088767E-03 0.22525899949E-02 0.39391537405E-03 -.28562888829E-02 0.43623947025E-02 0.50580398663E-02 0.31440260409E-02 -.60090684201E-04 0.66497361263E-03 0.25302278248E-02 0.52120528002E-02 0.50812471621E-02 -.19041084105E-02 -.10359924871E-02 0.23382124189E-02 </code> </pre> we can see that each line contains 5 floating point values. Each of these floating point values takes about 18 bytes of storage. If we would store the human-readable number as a `float`, it would only take up 4 bytes of storage, a reduction of almost a factor of 5. In turn, if we do this for all the numbers inside the CHGCAR file and then compress the binary file, we were able to obtain compression ratios of ~10. But can we do better? # Discrete Cosine Transform So far, we have only considered storing the density files in a lossless format. This means that we do not loose any information upon compression and decompression of the data. The opposite is to store data in a lossy fashion, wherein the decompressed data is no longer identical to the original. [JPEG](https://en.wikipedia.org/wiki/JPEG) is an example of such a lossy compression technique. The underlying algorithm behind JPEG is a [Discrete Cosine Transformation (DCT)](https://en.wikipedia.org/wiki/Discrete_cosine_transform), which is really well explained in this [Computerphile YouTube movie](https://www.youtube.com/watch?v=Q2aEzeMDHMA). What the DCT does is fit the finite sequence of data points in terms of a sum of cosine functions oscillating at different frequencies. For example, if we have a set of 64 data points, then the DCT gives us a set of 64 coefficients corresponding to the cosines at different frequencies. The DCT can be done one-dimensional, two-dimensional in the case of images, three-dimensional in our case and in theory even beyond three-dimensional. The DCT itself is lossless, that is, from the set of coefficients, using a inverse discrete cosine transformation, the original data set can be obtained. The way we can employ this algorithm to obtain increased compression, is to drop the higher order frequencies in the DCT, similarly to how higher order frequencies are dropped in an [MP3](https://en.wikipedia.org/wiki/MP3). Let's exemplify this. Assume that we have 3D dataset of 2x2x2 grid points (8 grid points in total) with the values <pre> <code class="bash"> d[0][0][0] = 0.84 d[0][0][1] = 0.39 d[0][1][0] = 0.78 d[0][1][1] = 0.80 d[1][0][0] = 0.91 d[1][0][1] = 0.20 d[1][1][0] = 0.34 d[1][1][1] = 0.77 </code> </pre> The discrete cosine transformation in three dimensions of this dataset gives the following coefficients: <pre> <code class="bash"> c[0][0][0] = 0.63 c[0][0][1] = 0.13 c[0][1][0] = -0.06 c[0][1][1] = 0.40 c[1][0][0] = 0.11 c[1][0][1] = 0.04 c[1][1][0] = -0.09 c[1][1][1] = -0.24 </code> </pre> Let us now set the last coefficient to zero and perform a inverse DCT. We obtain the following values: <pre> <code class="bash"> d[0][0][0] = 0.93 d[0][0][1] = 0.31 d[0][1][0] = 0.70 d[0][1][1] = 0.88 d[1][0][0] = 0.83 d[1][0][1] = 0.28 d[1][1][0] = 0.42 d[1][1][1] = 0.68 </code> </pre> Despite that these values are off, they qualitatively resemble the original data. This example teaches illustrates the trade-off: we are able to increase compression performance but we have to pay in terms of accuracy. # The mathematics Given a cubic block of NxNxN grid points, then each DCT coefficient is calculated using the formula below $$ c\_{i,j,k} = s\_{i,j,k} \sum\_{l=0}^{N-1} \sum\_{m=0}^{N-1} \sum\_{n=0}^{N-1} d\_{l,m,n} \cdot \cos \left( \frac{\pi}{N} (i + \frac{1}{2}) l \right) \cdot \cos \left( \frac{\pi}{N} (j + \frac{1}{2}) m \right) \cdot \cos \left( \frac{\pi}{N} (k + \frac{1}{2}) n \right) $$ wherein $s\_{i,j,k}$ is a scaling constant and $d\_{l,m,n}$ is the value at grid point (l,m,n). Thus, for each coefficient (of which there are $N^{3}$), we have to loop over all the $N^{3}$ data points. The scaling constant is given by $$ s\_{i,j,k} = s\_{i} \cdot s\_{j} \cdot s\_{k} $$ where $$ s\_{i} = \begin{cases} \frac{1}{N},& \text{if } i\geq 0 \\ \frac{2}{N},& \text{otherwise} \end{cases} . $$ This scaling is in principle arbitrary, but we introduce it to ensure that the inverse discrete cosine transformation is given by $$ d\_{i,j,k} = \sum\_{i=0}^{N-1} \sum\_{j=0}^{N-1} \sum\_{k=0}^{N-1} c\_{l,m,n} \cdot \cos \left( \frac{\pi}{N} (l + \frac{1}{2}) i \right) \cdot \cos \left( \frac{\pi}{N} (m + \frac{1}{2}) j \right) \cdot \cos \left( \frac{\pi}{N} (n+ \frac{1}{2}) k \right) . $$ # Block size and quality The above DCT transformation can be done for any size $N$, but it turns out that performing the transformation on typical data sets of 300x300x300 grid points is very expensive. So instead of calculating the DCT for the whole grid, we divide the grid into smaller chunks. This strategy is similar to that employed in JPEG compression, but instead of having 2D chunks, we have 3D chunks. These chunks are called blocks and it turns out that for CHGCAR and LOCPOT files, blocks of 4x4x4 turn out to give the best results (see below for the results). Each (4x4x4) block thus contains 64 values and the corresponding DCT contains 64 coefficients. We can now drop a number of coefficients corresponding to the higher frequencies of the DCT. To formalize this, let us introduce the concept of a quality value. A quality value of `q` means that all coefficients corresponding to those triplet of cosines which frequencies where `i+j+k <= q` holds, are kept and all other coefficients are dropped. This means that the quality values are not transferable between block sizes as the block size determines the maximum values of `i,j,k`. # The algorithm and the code The whole procedure can be summarized in the following six steps: 1. Read in the CHGCAR / LOCPOT 2. Divide the large grid into smaller chunks 3. Perform the DCT on each of these chunks 4. Drop the higher order coefficients based on the `quality` parameter 5. Store the other coefficients in binary format 6. Compress the final result I have written a small C++ program called [den2bin](https://github.com/ifilot/den2bin) that allows you to perform compression and decompression on CHGCAR and LOCPOT files. The program depends on the following development packages: [boost](http://www.boost.org/), [bz2](http://www.bzip.org/), [glm](https://glm.g-truc.net/) and [tclap](http://tclap.sourceforge.net/), which are typically readily available by your package manager. Also, you need to have CMake and the GNU compiler installed. On Ubuntu or Debian, you can get these as follows: <pre> <code class="bash"> sudo apt-get install build-essential cmake libboost-all-dev libbz2-dev libglm-dev libtclap-dev </code> </pre> To compile the code, simply clone the repository and compile it using CMake: <pre> <code class="bash"> git clone https://github.com/ifilot/den2bin cd den2bin mkdir build cd build cmake ../src make -j5 </code> </pre> The code checks if your compiler supports [OpenMP](https://en.wikipedia.org/wiki/OpenMP) for shared memory multiprocessing. If so, the program automatically makes use of all the available cores in your machine. Use the following commands to compress and decompress using the DCT: <pre> <code class="bash"> # to pack (note the "-l") ./den2bin -i *DENSITY_FILENAME* -o *BINARY_FILENAME* -m *MESSAGE_HEADER* -l -b *BLOCKSIZE* -q *QUALITY* # to unpack (same as for the lossless version) ./den2bin -x -i *BINARY_FILENAME* -o *DENSITY_FILENAME* </code> </pre> In the [README.md in the Github repository](https://github.com/ifilot/den2bin/blob/master/README.md), detailed information about all the program option and directives is provided. If you do not like to compile the program yourself, there is also the option to download the binary from the repository [by following these instructions](https://github.com/ifilot/den2bin/blob/master/README.md#obtaining-den2bin-from-the-repository). # Results To get an idea of the capabilities of our tool, I have compressed a CHGCAR file corresponding to the 1PI orbital of CO based on my [previous blog post on visualizing the electron density of the binding orbital of CO](http://www.ivofilot.nl/posts/view/27/Visualising+the+electron+density+of+the+binding+orbitals+of+the+CO+molecule+using+VASP). We are going to compare the compression ratios and data loss (purely qualitatively by looking at a contour plot) as a function of blocksize and quality. In this comparison, we have used cubic blocks of 2x2x2, 4x4x4, 8x8x8 and 16x16x16 grid points. The results are visualized in Figure 1. A high resolution PNG version of this image [can be found here](http://www.ivofilot.nl/images/33/1pi.png). From Figure 1, it can be seen that when using a quality of 1 (i.e. only a single DCT coefficient), we obtain a kind of down-scaling of the image as a single DCT coefficient only contains the average value for the whole data block. Increasing the quality factor decreases the compression ratio but increases the data quality (and hence the contour plot). Similar to JPEG, there is an optimum for the block size. Whereas this optimum is [8x8 for JPEG](https://stackoverflow.com/questions/10780425/why-jpeg-compression-processes-image-by-8x8-blocks), I would say the sweet spot for VASP density files is using a block size of 4x4x4 and a quality of 4. Nevertheless, do not take my word for it but test it for yourself. <img src="http://www.ivofilot.nl/images/32/1pi.jpg" width="100%" class="img img-responsive"> __Figure 1__: *Compression factor versus Blocksize and quality for the 1PI orbital of CO.* # Closing remarks If you like the program, feel free to [star the repository](https://help.github.com/articles/about-stars/) on Github. Bug reports or other comments to improve the program are always highly appreciated. Please use the [Issues](https://github.com/ifilot/den2bin/issues) functionality of Github for that. I am also interested in hearing your experience with the program. Feel free to share in the [comments](http://www.ivofilot.nl/posts/view/35/Efficient+compression+of+CHGCAR+and+LOCPOT+files#comments) where you have used the program for and at what block size and quality settings you found the compression to be ideal for your branch of work. # Bonus: more examples Below are some additional examples to illustrate the correlation between compression efficiency and data set accuracy. <img src="http://www.ivofilot.nl/images/29/chgcar.jpg" width="100%" class="img img-responsive"> __Figure 2__: *Compression factor versus Blocksize and quality for a CHGCAR file.* <img src="http://www.ivofilot.nl/images/28/locpot.jpg" width="100%" class="img img-responsive"> __Figure 3__: *Compression factor versus Blocksize and quality for a LOCPOT file.*
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      • id33
      • titleHow to compile VASP 5.4.1 on a MacBook running OS X El Capitan
      • contentThis tutorial will explain how to install [VASP](https://www.vasp.at/) 5.4.1 on a MacBook. As a small warning, note that this procedure will take quite some time, so make sure you do not need your MacBook for a couple of hours. # Step 0: Directories and settings We are going to compile the source in the ```/Users/<username>/Downloads``` folder and install everything in ```/Users/<username>/vaspbuild```. Note that you need to change <username> with your current login (i.e. the name of your user account). Feel free to change any of these paths to suit your needs. Furthermore, in this tutorial, I will embed the [ScaLAPACK](http://www.netlib.org/scalapack/), [OpenBLAS](http://www.openblas.net/) and [FFTW](http://www.fftw.org/) libraries in the executable. # Step 1: Installing the tool-chain To install VASP, we are going to use [MacPorts](https://www.macports.org) for our tool-chain. First, install MacPorts. On their website, they provide a [set of instructions](https://www.macports.org/install.php). Thereafter, run the following command to install GCC 4.9 with gfortran. ``` sudo port install gcc49 +gfortran ``` and install cmake as well as we are going to use it for building ScaLAPACK. ``` sudo port install cmake ``` # Step 2: OpenMPI Next, we are going to install OpenMPI. Go to [their website](https://www.open-mpi.org/software/ompi) and pick the latest version. At the time of this writing, this is version 1.10.3 and can be downloaded using [this link](https://www.open-mpi.org/software/ompi/v1.10/downloads/openmpi-1.10.3.tar.bz2). Extract the archive ``` tar -xvjf openmpi-1.10.3.tar.bz2 ``` go to the folder and configure it ``` cd openpmi-1.10.3 ``` ``` ./configure --prefix=/Users/<username>/vaspbuild/openmpi-1.10.3 ``` and compile and install it ``` make -j5 && make -j5 install ``` To use this version of OpenMPI for the compilation of VASP and ScaLAPACK, execute the following two commands ``` export PATH=/Users/<username>/vaspbuild/openmpi-1.10.3/bin:$PATH ``` ``` export LD_LIBRARY_PATH=/Users/<username>/vaspbuild/openmpi-1.10.3/lib:$LD_LIBRARY_PATH ``` # Step 3: OpenBLAS Go to the website of [OpenBLAS](http://www.openblas.net/) and download the latest version. At the time of this writing, this is version 0.2.18. Unzip the archive ``` unzip OpenBLAS-0.2.18.zip ``` and go to the folder ``` cd OpenBLAS-0.2.18 ``` and compile the library with ``` make USE_THREAD=0 ``` and install it ``` make PREFIX=/Users/<username>/vaspbuild/openblas-0.2.18 install ``` More information about compiling and installing OpenBLAS can be found [here](https://github.com/xianyi/OpenBLAS/wiki/User-Manual). # Step 4: ScaLAPACK <div class="alert alert-info alert-hover">Note: Make sure you have adjusted your `$PATH` and `$LD_LIBRARY_PATH` to use the version of OpenMPI we just built.</div> Download the latest version of ScaLAPACK from [their website](http://www.netlib.org/scalapack/) and extract the tarball. ``` tar -xvzf scalapack.tgz ``` Create a seperate build folder ``` mkdir spbuild && cd spbuild ``` and execute cmake ``` cmake ../scalapack-2.0.2 ``` We need to make a few adjustments to `CMakeCache.txt`: On line 18, replace <pre> <code class="cmake"> BLAS_Accelerate_LIBRARY:FILEPATH=/System/Library/Frameworks/Accelerate.framework </code> </pre> with <pre> <code class="cmake"> BLAS_Accelerate_LIBRARY:FILEPATH=/Users/<username>/vaspbuild/openblas-0.2.18/lib/libopenblas.dylib </code> </pre> and as well around line 253 we have to replace, <pre> <code class="cmake"> LAPACK_Accelerate_LIBRARY:FILEPATH=/System/Library/Frameworks/Accelerate.framework </code> </pre> with <pre> <code class="cmake"> LAPACK_Accelerate_LIBRARY:FILEPATH=/Users/<username>/vaspbuild-openblas/0.2.18/lib/libopenblas.dylib </code> </pre> Now we are ready to compile ``` make -j5 ``` We are manually installing the library by copying it to an installation folder ``` mkdir -pv /Users/<username>/vaspbuild/scalapack-2.0.2/lib ``` ``` cp -v lib/libscalapack.a /Users/<username>/vaspbuild/scalapack-2.0.2/lib ``` # Step 5: FFTW The last library we need to compile is FFTW. The procedure is fairly similar to how we compiled OpenMPI. As usual, go to [the website of FFTW](http://www.fftw.org/download.html) and download the latest version. Extract the archive ``` tar -xvzf fftw-3.3.4.tar.gz ``` and go to the folder. Therein, configure, build and install the library ``` ./configure --prefix=/Users/<username>/vaspbuild/fftw-3.3.4 ``` ``` make -j5 && make -j5 install ``` # Step 6: VASP <div class="alert alert-info alert-hover">Note: Make sure you have adjusted your `$PATH` and `$LD_LIBRARY_PATH` to use the version of OpenMPI we just built.</div> Extract the VASP tarball, go to the source folder and copy the makefile.include for gfortran ``` cp arch/makefile.include.linux_gfortran makefile.include ``` We need to adjust part of the `makefile.include` so that it looks as follows: <pre> <code class="makefile"> BLAS = LAPACK = /Users/<username>/vaspbuild/openblas-0.2.18/lib/libopenblas.a BLACS = SCALAPACK = /Users/<username>/vaspbuild/scalapack-2.0.2/lib/libscalapack.a OBJECTS = fftmpiw.o fftmpi_map.o fftw3d.o fft3dlib.o \ /Users/<username>/vaspbuild/fftw/3.3.4/lib/libfftw3.a INCS =-I/Users/<username>/vaspbuild/fftw/3.3.4/include </code> </pre> The first two references ensure that our recently built versions of OpenBLAS and ScaLAPACK are used to build VASP and the last few lines grab the header and library files from FFTW. To compile the standard version (non-gamma-point version, run) ``` make std ``` For the gamma point version, you need to run ``` make gam ``` The binary files are written in the `bin` folder. To check that our VASP executable only depend on OpenMPI, run `otool -L bin/vasp_std` and/or `otool -L bin/vasp_gam`. For me, the result looks like this: <pre> <code lang="bash"> My-MacBook-Air:vasp.5.4.1 ivofilot$ otool -L bin/vasp_std bin/vasp_std: /Users/ivofilot/vaspbuild/openmpi-1.10.3/lib/libmpi_usempif08.11.dylib (compatibility version 13.0.0, current version 13.1.0) /Users/ivofilot/vaspbuild/openmpi-1.10.3/lib/libmpi_mpifh.12.dylib (compatibility version 13.0.0, current version 13.1.0) /Users/ivofilot/vaspbuild/openmpi-1.10.3/lib/libmpi.12.dylib (compatibility version 13.0.0, current version 13.3.0) /opt/local/lib/libgcc/libgfortran.3.dylib (compatibility version 4.0.0, current version 4.0.0) /usr/lib/libSystem.B.dylib (compatibility version 1.0.0, current version 1226.10.1) /opt/local/lib/libgcc/libgcc_s.1.dylib (compatibility version 1.0.0, current version 1.0.0) /opt/local/lib/libgcc/libquadmath.0.dylib (compatibility version 1.0.0, current version 1.0.0) </code> </pre> Let's place the VASP executable in the `vaspbuild` folder as well ``` cp -v bin/vasp_* /Users/<username>/vaspbuild/ ``` In order to run and test VASP, create a seperate folder wherein your place the `INCAR`, `POTCAR`, `POSCAR` and `KPOINTS` files. From within that folder you run VASP (in this example using four threads) like so ``` mpirun -np 4 /Users/<username>/vaspbuild/vasp_std ```
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      • id31
      • titleHow to compile VASP 5.4.1 for Linux Debian using the GNU compiler
      • contentThis tutorial will explain how to install VASP 5.4.1 on a Linux Debian system. The developers of VASP have completely remade the compilation procedure. Personally, I believe they have done a marvelous job and the new compilation system will make compiling VASP significantly easier. <i class="fa fa-info-circle"></i> For installing VASP 4.6.38, you can refer to [my previous blogpost](http://www.ivofilot.nl/posts/view/21/How+to+build+VASP+4.6.38+using+the+GNU+compiler). <i class="fa fa-info-circle"></i> If you are interested in compiling VASP 5.3.5 using the old procedure, have a look at [this tutorial](http://www.ivofilot.nl/posts/view/28/How+to+build+VASP+5.3.5+using+the+GNU+compiler+on+Linux+Ubuntu+14.04+LTS). # Step 1: Acquiring the necessary packages <pre> <code class="bash"> sudo apt-get install build-essential libopenmpi-dev libfftw3-dev libblas-dev liblapack-dev libscalapack-mpi-dev libblacs-mpi-dev </code> </pre> # Step 2: Extracting the VASP source tarball Extract the VASP sources and go to the root directory of the VASP package. <pre> <code class="bash"> tar -xvzf vasp.5.4.1.tar.gz cd vasp.5.4.1 </code> </pre> # Step 3: Setting the build procedure You need to copy the makefile corresponding to your build architecture. Here, I assume we are going to use the GNU compiler, so you need to copy the makefile for gfortran: <pre> <code class="bash"> cp -v arch/makefile.include.linux_gfortran makefile.include </code> </pre> # Step 4: Configuring the makefile You need to tweak some directives in the Makefile to point the compiler to the right libraries and header files. For my Linux Debian system, I have used the following directives: <pre> <code class="makefile"> # Precompiler options CPP_OPTIONS= -DMPI -DHOST=\"IFC91_ompi\" -DIFC \ -DCACHE_SIZE=4000 -Davoidalloc \ -DMPI_BLOCK=8000 -DscaLAPACK -Duse_collective \ -DnoAugXCmeta -Duse_bse_te \ -Duse_shmem -Dtbdyn CPP = gcc -E -P -C $*$(FUFFIX) >$*$(SUFFIX) $(CPP_OPTIONS) FC = mpif90 FCL = mpif90 FREE = -ffree-form -ffree-line-length-none FFLAGS = OFLAG = -O2 OFLAG_IN = $(OFLAG) DEBUG = -O0 LIBDIR = /usr/lib/x86_64-linux-gnu BLAS = -L$(LIBDIR) -lblas LAPACK = -L$(LIBDIR) -llapack BLACS = -L$(LIBDIR) -lblacs-openmpi -lblacsCinit-openmpi SCALAPACK = -L$(LIBDIR) -lscalapack-openmpi $(BLACS) OBJECTS = fftmpiw.o fftmpi_map.o fftw3d.o fft3dlib.o \ /usr/lib/x86_64-linux-gnu/libfftw3.a INCS =-I/usr/include LLIBS = $(SCALAPACK) $(LAPACK) $(BLAS) OBJECTS_O1 += fft3dfurth.o fftw3d.o fftmpi.o fftmpiw.o chi.o OBJECTS_O2 += fft3dlib.o # For what used to be vasp.5.lib CPP_LIB = $(CPP) FC_LIB = $(FC) CC_LIB = gcc CFLAGS_LIB = -O FFLAGS_LIB = -O1 FREE_LIB = $(FREE) OBJECTS_LIB= linpack_double.o getshmem.o # Normally no need to change this SRCDIR = ../../src BINDIR = ../../bin </code> </pre> # Step 5: Compiling You are now ready to compile VASP! <pre> <code class="bash"> make std </code> </pre> # Troubleshooting When compiling, I encountered the same error as for VASP 5.3.5 relating to the `us.f90`. <pre> <code class="bash"> us.f90:1403.10: USE us 1 Error: 'setdij' of module 'us', imported at (1), is also the name of the current program unit </code> </pre> The way to resolve this error, is by changing the names. The way we are going to do that, is by applying a patch to this file. You can download the patch file [here](http://www.ivofilot.nl/downloads/vasp535.patch). The patch was created for VASP 5.3.5, but works fine for VASP 5.4.1. Just place it in the same directory as where the VASP sources reside (`src`) and apply the patch by typing: <pre> <code class="bash"> wget http://www.ivofilot.nl/downloads/vasp535.patch patch -p0 < vasp535.patch </code> </pre> This will change the names automatically. You will receive a message such as <pre> <code class="makefile"> patching file us.F </code> </pre> Upon typing `make`, the compilation will resume.
      • watched17522
      • active(true)
      • created2015-11-03 12:00:00
      • modified2018-01-08 18:14:25
    • Comment(array)
      • 0(array)
        • emailnone@none.de
        • commentYou need also in step 1 libscalapack-mpi-dev
        • id52
        • post_id31
        • created2016-06-28 15:34:07
      • 1(array)
        • emailb.zijlstra@tue.nl
        • commentThis is a significant improvement compared to the compilation of previous versions. I did have some trouble linking the libraries, but I worked around that by running: sudo ln -s /usr/lib/libscalapack-openmpi.so.1 /usr/lib/libscalapack-openmpi.so sudo ln -s /usr/lib/libblacs-openmpi.so.1 /usr/lib/libblacs-openmpi.so sudo ln -s /usr/lib/libblacsCinit-openmpi.so.1 /usr/lib/libblacsCinit-openmpi.so
        • id57
        • post_id31
        • created2016-07-19 11:30:35
      • 2(array)
        • emaildimov@cm.kyushu-u.ac.jp
        • commentYou saved my life! Thanks a lot! Looks like these links resolve the difference between debian and ubuntu.
        • id60
        • post_id31
        • created2016-12-14 10:19:04
      • 3(array)
        • emailivo@ivofilot.nl
        • commentI found out that you need to install libblacs-mpi-dev and libscalapack-mpi-dev as well to have those symbolic links. I have changed this in the blog post for convenience.
        • id66
        • post_id31
        • created2018-01-08 18:15:27
      • 4(array)
        • emailme@jessequinn.info
        • commentWith VASP 5.4.4 and lapack i had to modify several key files namely: ./src/symbol.inc ./src/lib/lapack_atlas.f ./src/lib/lapack_double.f ./src/lib/lapack_double_1.1.f ./src/broyden.F ./src/dynbr.F due to a DGEGV misrefernce. Files need to be updated to DGGEV. Otherwise worked nicely on my manjaro build.
        • id67
        • post_id31
        • created2018-05-17 16:39:56
      • 5(array)
        • emailme@jessequinn.info
        • commentWith VASP 5.4.4 and lapack i had to modify several key files namely: ./src/symbol.inc ./src/lib/lapack_atlas.f ./src/lib/lapack_double.f ./src/lib/lapack_double_1.1.f ./src/broyden.F ./src/dynbr.F due to a DGEGV misrefernce. Files need to be updated to DGGEV. Otherwise worked nicely on my manjaro build.
        • id68
        • post_id31
        • created2018-05-17 16:40:11
      • 6(array)
        • emailme@jessequinn.info
        • commentWith VASP 5.4.4 and lapack i had to modify several key files namely: ./src/symbol.inc ./src/lib/lapack_atlas.f ./src/lib/lapack_double.f ./src/lib/lapack_double_1.1.f ./src/broyden.F ./src/dynbr.F due to a DGEGV misrefernce. Files need to be updated to DGGEV. Otherwise worked nicely on my manjaro build.
        • id69
        • post_id31
        • created2018-05-17 16:40:27
      • 7(array)
        • emailme@jessequinn.info
        • commentWith VASP 5.4.4 and lapack i had to modify several key files namely: ./src/symbol.inc ./src/lib/lapack_atlas.f ./src/lib/lapack_double.f ./src/lib/lapack_double_1.1.f ./src/broyden.F ./src/dynbr.F due to a DGEGV misrefernce. Files need to be updated to DGGEV. Otherwise worked nicely on my manjaro build.
        • id70
        • post_id31
        • created2018-05-17 16:40:58
    • Tag(array)
      • 0(array)
        • id22
        • nameVASP
        • iconfa fa-cog
        • colordefault
      • 1(array)
        • id23
        • nameComputational Chemistry
        • iconfa fa-cogs
        • colorinfo
  • 4(array)
    • Post(array)
      • id29
      • titleIntroduction to Electronic Structure Calculations: The variational principle
      • content# Introduction to Electronic Structure Calculations: The variational principle ## Introduction This post is the first part in an upcoming series explaining how to perform electronic structure calculations. The focus of this series is how to set-up an electronic structure calculation from scratch. We are not going to use any of the available quantum chemical codes, but write our very own code. This way, we will obtain a better understanding of how quantum chemical calculations are being performed. The way I am going to present the topic is by first providing the underlying theory and then further explaining the theory by giving a set of examples. The outline of this series is as follows: We start of with explaining some basics such as the (linear) variational principle, the Hartree product and the Slater determinant. From there on, we derive the Hartree-Fock equations and show how to set-up a simple calculation for the H₂ molecule. Next, we explain about basis sets, Gaussian integrals and the Hartree-Fock self-consistent field procedure. Finally, we talk about atomic and molecular orbitals, the construction of MO diagrams and the visualization of orbitals. For this series, I am going to assume that you have a basic understanding of quantum mechanics. You know what a wave function is and its statistical interpretation. Furthermore, I assume that you have passed introductory courses in calculus and linear algebra. ## The variational principle Given a normalized wave function $\lvert\phi\rangle$ that satisfies the appropriate boundary conditions, then the expectation value of the Hamiltonian is an upper bound to the exact ground state energy. In other words, the lowest energy we can find, gives us the best wave function. Thus, if $ \langle \phi \rvert \phi \rangle=1 $, then $ \langle \phi \lvert \hat{H} \rvert \phi \rangle \geq E_{0} $. <div class="bs-callout bs-callout-primary"> <h4>Example 1: The energy of the 1s orbital in hydrogen</h4> Let's exemplify this by providing an example. In the following example, we wish to obtain the best value for $ \alpha $ for the trial function $ \lvert \phi \rangle = N \exp \left( - \alpha r^{2} \right) $ (where $N$ is a normalization constant) that describes the 1s orbital in the H-atom. The Hamiltonian for the H-atom in <a href="https://en.wikipedia.org/wiki/Atomic_units">atomic units</a> is: $$ \hat{H} = -\frac{1}{2} \nabla^{2} - \frac{1}{r}. $$ The first step is to find $E$ as a function of $\alpha$. Therefore, we need to evaluate the following integral $$ E = \langle \phi \lvert \hat{H} \rvert \phi \rangle = \int_{0}^{\infty} \textrm{d}r \int_{0}^{2\pi} \textrm{d} \theta \int_{0}^{\pi} \textrm{d} \varphi \, r^{2} \sin \varphi N \exp \left( - \alpha r^{2} \right) \left[ -\frac{1}{2} \nabla^{2} - \frac{1}{r} \right] N \exp \left( - \alpha r^{2} \right) .$$ Note that because we are integrating in <a href="http://mathworld.wolfram.com/SphericalCoordinates.html">spherical coordinates</a>, we have introduced the <a href="http://mathworld.wolfram.com/Jacobian.html">Jacobian</a> $$ J = r^{2} \sin \varphi .$$ Furthermore, the radial part of the <a href="http://mathworld.wolfram.com/Laplacian.html">Laplacian</a> $\nabla^{2}$ in spherical coordinates has the following form: $$ \nabla^{2} = r^{-2} \frac{\textrm{d}}{\textrm{d} r} \left( r^{2} \frac{\textrm{d}}{\textrm{d} r} \right)$$ (we can ignore the angular parts of the Laplacian, because the 1s trial wave function is spherically symmetrical)<br><br> The above integral can be divided into two seperate integrals of the following forms $$ I_1 = - \left( \frac{4 \pi N^{2}}{2} \right) \int_0^\infty r^2 \exp \left( -\alpha r^2 \right) \left[ r^{-2} \frac{\textrm{d}}{\textrm{d} r} \left( r^{2} \frac{\textrm{d}}{\textrm{d} r} \right) \exp \left( -\alpha r^2 \right) \right] \textrm{d}r $$ and $$ I_2 = - \left( \frac{4 \pi N^{2}}{2} \right) \int_0^\infty r^2 \exp \left( -\alpha r^2 \right) \frac{1}{r} \exp \left( -\alpha r^2 \right) \textrm{d}r .$$ Since the wavefunction has no angular dependencies, the azimuthal ($\theta$) and polar ($\varphi$) parts have already been integrated in the above equations. These give the factor \pi$. To solve the first integral ($I_{1}$), we need to apply the Laplacian. This gives $$ I_1 = - \left( \frac{4 \pi N^{2}}{2} \right) \int_0^\infty \exp \left( -\alpha r^2 \right) \left[ -6 \alpha^{2} + 4 \alpha^{2}r^{4} \right] \exp \left( -\alpha r^2 \right) \textrm{d}r .$$ Slightly rearranging this equation gives us $$ I_1 = - 2 \pi N^{2} \int_0^\infty \left( 4 \alpha^{2}r^{4} -6 \alpha^{2} \right) \exp \left( -2 \alpha r^2 \right) \textrm{d}r .$$ This integral can be solved by performing <a href="https://en.wikipedia.org/wiki/Integration_by_parts">integration by parts</a>, but here we will use just use the following general formulas: $$\int_{0}^{\infty} \textrm{d}r \, r^{2m} \exp \left(-\alpha r^{2} \right) = \frac{(2m)!\pi^{1/2}}{2^{2m+1}m!\alpha^{m+1/2}} $$ and $$\int_{0}^{\infty} \textrm{d}r \, r^{2m+1} \exp \left(-\alpha r^{2} \right) = \frac{m!}{2\alpha^{m+1}} .$$ Applying these formulas for $I_1$ yields $$I_{1} = -2 \pi N^{2} \left[ 4 \alpha^{2} \frac{4! \pi^{1/2}}{2^5 2! (2 \alpha)^{5/2}} - 6 \alpha \frac{2!\pi^{1/2}}{2^3 1! (2\alpha)^{3/2}} \right] = N^{2} \frac{3 \pi^{3/2}} {4 \sqrt{2\alpha}} $$ and for $I_{2}$: $$I_{2} = -4 \pi N^{2} \int_{0}^{\infty} r \exp \left( -2 \alpha r^{2} \right) \textrm{d}r = -4 \pi N^{2} \frac{1}{4 \alpha} = \frac{-\pi}{\alpha} N^{2} .$$ Summing these two parts gives $$\langle \phi \lvert H \rvert \phi \rangle = I_1 + I_2 = N^2 \left( \frac{3 \pi ^{3/2}}{4 \sqrt{2 \alpha}} - \frac{\pi}{\alpha} \right) .$$ Using the same procedure, we can also evaluate the integral $ \langle \phi \rvert \phi \rangle $. $$ \langle \phi \rvert \phi \rangle = 4 \pi N^{2} \int_{0}^{\infty} r^2 \exp \left( -2 \alpha r^2 \right) \textrm{d}r = N^{2} \frac{\pi^{3/2}}{2 \sqrt{2}\alpha^{3/2}} $$ In order to evaluate the expectation value for the energy $E$ for the trial wave function $\lvert \varphi \rangle$, we need to evaluate $$ E = \frac{\langle \phi \lvert \hat{H} \rvert \phi \rangle }{\langle \phi \rvert \phi \rangle} = \frac{3 \alpha}{2} - \frac{2 \sqrt{2} \alpha ^{1/2}}{\pi ^{1/2}} .$$ The reason we need to divide by $\langle \phi \rvert \phi \rangle$ is because $\lvert \phi \rangle$ is not normalized yet. If $\lvert \phi \rangle$ would be normalized, then the integral $\langle \phi \rvert \phi \rangle$ would be equal to one and thus drop out. The best value for $\alpha$ can then be found by differentiating $E$ with respect to $\alpha$ and finding that value for $\alpha$ where the differential is zero. $$ \frac{\textrm{d}E}{\textrm{d}\alpha} = 0 .$$ Thus $$ \frac{\textrm{d}E}{\textrm{d}\alpha} = \frac{3}{2} - \frac{\sqrt{2}}{\pi ^{1/2} \alpha^{1/2}} $$ and $$ \alpha = \frac{8}{9 \pi}.$$ This gives us the following upper bound for the energy $E$: $$E = \frac{3}{2} \frac{8}{9 \pi} - \frac{2 \sqrt{2} \left( \frac{8}{9 \pi} \right)^{1/2}}{\pi ^{1/2}} = -\frac{4}{3 \pi} \approx -0.4244 .$$ </div> The exact energy for the 1s orbital in hydrogen is -0.5 HT with the corresponding wave function $\lvert \phi \rangle = \frac{1}{\sqrt{\pi}} \exp \left( - r \right)$. ## The linear variational principle Although the exact answer to the energy of the 1s orbital in hydrogen is known, let us assume that we do *not* know it and would like to obtain it. One way is to pick various trial wave functions with one independent variable and optimize that variable. The lowest energy we are going to find gives us then the best approximation of the ground state wave function. This approach would be quite tedious (and how would you know what trial wave function to choose in the first place anyway?). It would be nice if we could have just a single trial wave function that has a lot of 'variational freedom'. Here, I propose to use a trial wave function that is a linear set of fixed wave function like so: $$ \lvert \phi \rangle = \sum\_{i=1}^N c_{i} \lvert \psi\_{i} \rangle $$ If we can assume that the wave functions $\lvert \psi\_i \rangle$ are orthonormal in the sense that $\langle \psi\_i \lvert \psi\_j \rangle = \delta\_{ij}$, then the energy is $$E = \sum\_{ij} \langle \psi\_i \lvert \hat{H} \rvert \psi\_j \rangle = \sum_{ij} c\_{i}c\_{j} H\_{ij}$$ and we are tasked with finding the best set of coefficients $c_{i}$ that minimizes $E$. It are exactly these coefficients (and accompanying wave functions) that provide us with the necessary variational freedom. (Note that $H\_{ij} = \langle \psi\_i \lvert \hat{H} \rvert \psi\_j \rangle$) The procedure to find this set is by using [Langrange's method of undetermined multiplies](https://en.wikipedia.org/wiki/Lagrange_multiplier). Herein $$L \left( c\_1, c\_2, \cdots, E \right) = \langle \phi \lvert \hat{H} \rvert \phi \rangle - E \left(\langle \phi \lvert \phi \rangle - 1 \right) $$ and we need to find that particular set of $c\_k$ where $$ \frac{\partial L}{\partial c\_{k}} = 0 $$ for each $k$. For each $k$, this gives the following equation $$ \sum\_{j} c\_j H\_{kj} + \sum\_i c\_i H\_{ik} - 2 E c\_{k} = 0 $$. Since $\langle \psi\_a \lvert \hat{H} \rvert \psi\_b \rangle = \langle \psi\_b \lvert \hat{H} \rvert \psi\_a \rangle = H\_{ab} = H\_{ba}$, we can simplify the above equation to $$ \sum\_{j} H\_{ij} c\_j - E c\_{i} = 0. $$ The above expression is just the matrix expression $$ H\vec{c} = E\vec{c} .$$ This last equation looks probably very familiar to you and relates to the [matrix eigenvalue problem](http://mathworld.wolfram.com/Eigenvalue.html). It is a very typical problem in linear algebra. To solve the matrix eigenvalue problem, one needs to diagonalize the $H$ matrix. This gives a set of eigenvalues and corresponding eigenvalues. The eigenvector corresponding to the lowest eigenvalue is the best set of $c\_k$ we are interested in. <div class="bs-callout bs-callout-primary"> <h4>Example 2: The 2x2 linear variational problem for finding the energy of the 1s orbital of hydrogen </h4> To illustrate the above procedure, we are going to find the best solution for the 1s orbital in the hydrogen atom using a trial wave function that is a linear combination of two orthonormal wave functions. The two orthonormal wave functions are $$\psi_{1} = \frac{2}{\pi^{3/4}} \exp \left( -r^2 / 2 \right)$$ and $$\psi_{2} = \frac{2\pi^{1/4}r - 4/\pi^{1/4}}{\sqrt{2\pi(3\pi-8)}} \exp \left( -r^2 / 2 \right).$$ And because of the orthonormality condition, the following integrals hold $$\langle \psi_{1} \lvert \psi_{2} \rangle = 0$$ and $$\langle \psi_{1} \lvert \psi_{1} \rangle = \langle \psi_{2} \lvert \psi_{2} \rangle = 1.$$ Applying the Hamiltonian to these wave functions, we can obtain the following 2x2 H-matrix: $$H = \begin{bmatrix} \langle \psi_{1} \lvert \hat{H} \rvert \psi_{1} \rangle & \langle \psi_{1} \lvert \hat{H} \rvert \psi_{2} \rangle \\langle \psi_{2} \lvert \hat{H} \rvert \psi_{1} \rangle & \langle \psi_{2} \lvert \hat{H} \rvert \psi_{2} \rangle\end{bmatrix} = \begin{bmatrix} -0.378379 & -0.0185959 \ -0.0185959 & 1.09531 \end{bmatrix}$$ Note that the H-matrix is symmetric. This is because we can exchange $\lvert \psi_{1} \rangle$ and $\lvert \psi_{2} \rangle$ and obtain the same result. Furthermore, note that although $\langle \psi_{1} \lvert \psi_{2} \rangle = 0$, this does not mean that the integral is also zero when the Hamiltonian operator is applied to either of the wave functions.<br><br> In order to find the best energy and approximation to the ground state wave function, we need to diagonalize the H-matrix. This can be easily done by hand, or using the <a href="https://www.wolframalpha.com/input/?i=Diagonalize%5B%7B%7B-0.378379%2C+-0.0185959%7D%2C+%7B-0.0185959%2C+1.09531%7D%7D%5D">very handy Wolfram Alpha website</a>. The result we obtain is $$D = \begin{bmatrix} 1.09554 & 0 \ 0 & -0.378614 \end{bmatrix}$$ for the diagonal (eigenvalue) matrix with corresponding $$X = \begin{bmatrix} -0.0126156 & -0.99992 \ 0.99992 & -0.0126156 \end{bmatrix}$$ for the eigenvector matrix. The first column of $X$ contains the coefficients corresponding to the first eigenvalue (energy) of the $D$-matrix and the second column of $X$ for the second eigenvalue. Since the second eigenvalue is lower ($-0.378614 < 1.09554$), the second column of $X$ contains the coefficients we are looking for. Thus, the best approximation to the ground state wave function is: $$\lvert \phi \rangle = c_{1} \lvert \psi_{1} \rangle + c_{2} \lvert \psi_{2} \rangle = -0.99992 \lvert \psi_{1} \rangle - 0.0126156 \lvert \psi_{2} \rangle.$$ The corresponding energy for this wave function is -0.378614 HT. This result is actually worse than what we obtained using the procedure of example 1 (which was -0.4244 HT). The reason for this is that the variational freedom using a linear combination of only two wave functions is actually less than one where we can vary a coefficient inside an exponent. To get better results, we would need to use a larger set of wave functions in the linear combination. </div> In Example 2 it was shown how we can obtain the best energy given a trial wave function which is a linear combination of a set of wave functions. Let us call these wave functions in the linear combination the basis functions. In order for the procedure in example 2 to work, the basis functions need to be orthonormal to each other. Finding a set of orthonormal functions by hand is somewhat tedious (try it for yourself if you do not believe me!). It would therefore be very handy if we could apply the above methodology (albeit somewhat changed) using a set of non-orthonormal basis functions. I already showed you how you can use Lagrange's method of undetermined multipliers in order to derive the matrix equation $Hc = Ec$. When the basis functions are no longer orthonormal, this matrix equation changes slightly and becomes $$ H\vec{c} = ES\vec{c}.$$ Herein, $S$ is termed the overlap matrix where each term in the matrix is $$ S\_{ij} = \langle \psi\_{i} \lvert \psi\_{j} \rangle.$$ The introduction of the overlap matrix $S$ makes the matrix diagonalization a tiny bit more complicated. There are several procedures for obtaining the eigenvalues and -vectors. The procedure we are going to use follows the canonical orthogonalization scheme. It works as follows 1. Construct the overlap matrix $S$. 2. Diagonalize the overlap matrix $S$ to obtain the eigenvalues of the overlap matrix and its corresponding eigenvector matrix $U$. 3. Construct a transformation matrix $X = U s^{-1/2}$. 4. Transform the Hamiltonian matrix to the canonically orthonormalized basis set $H' = X^{\dagger} H X$. 5. Diagonalize the transformed Hamiltonian matrix to obtain $D$ and $C'$ (where C' are the transformed coefficients). 6. Obtain the coefficients of the original basis by calculating $C = XC'$. The above probably looks a bit complicated, but really, it is not. Let me elaborate by showing you another example. <div class="bs-callout bs-callout-primary"> <h4>Example 3: Finding the energy of the 1s orbital of hydrogen using a non-orthonormal set of basis functions </h4> The two functions we are going to use are $$\psi_{1} = \exp \left( -r^{2} / 2 \right) $$ and $$\psi_{2} = r \exp \left( -r^{2} / 2 \right).$$ (<b>Step 1</b>)Their corresponding overlap matrix is $$S = \begin{bmatrix} \langle \psi_{1} \lvert \psi_{1} \rangle & \langle \psi_{1} \lvert \psi_{2} \rangle \\langle \psi_{2} \lvert \psi_{1} \rangle & \langle \psi_{2} \lvert \psi_{2} \rangle\end{bmatrix} = \begin{bmatrix} 5.56833 & 6.2832 \ 6.2832 & 8.35249 \end{bmatrix}.$$ From this matrix we can clearly see that these functions are neither orthogonal to each other nor normalized. <br><br>(<b>Step 2</b>)Diagonalizing the overlap matrix yields the following diagonal and eigenvector matrices $$D' = \begin{bmatrix} 13.396 & 0 \ 0 & 0.524846 \end{bmatrix}.$$ and $$ U = \begin{bmatrix} 0.625975 & -0.779843 \ 0.779843 & 0.625975 \end{bmatrix}.$$ (<b>Step 3</b>)We can obtain the transformation matrix by calculating $$X = U s^{-1/2} = \begin{bmatrix} 0.625975 & -0.779843 \ 0.779843 & 0.625975 \end{bmatrix} \begin{bmatrix} 1/\sqrt{13.396} & 0 \ 0 & 1/\sqrt{0.524846} \end{bmatrix} = \begin{bmatrix} 0.171029 & -1.07644 \ 0.213069 & 0.864054 \end{bmatrix}.$$ The Hamiltonian matrix is $$ H = \begin{bmatrix} \langle \psi_{1} \lvert \hat{H} \rvert \psi_{1} \rangle & \langle \psi_{1} \lvert \hat{H} \rvert \psi_{2} \rangle \\langle \psi_{2} \lvert \hat{H} \rvert \psi_{1} \rangle & \langle \psi_{2} \lvert \hat{H} \rvert \psi_{2} \rangle\end{bmatrix} = \begin{bmatrix} -2.10694 & -2.42674 \ -2.42674 & -1.4109 \end{bmatrix}.$$ Because our wave function $\lvert \psi_{1} \rangle$ in this example differs only by a normalization constant to the wave function $\lvert \psi_{1} \rangle$ in example 2, the value for the Hamiltonian element $H_{00}$ should only differ by a factor equal to the square of the normalization constant. In other words, if we divide $H_{00}$ by the value for $S_{00}$ (which represents that difference), we obtain the value of $H_{00}$ in example 2. The same applies of course for $H_{11}$. We can obtain the value in example 1 by calculating $H_{11} / S_{11}$.<br><br> (<b>Step 4</b>)And applying the transformation matrix to the Hamiltonian matrix gives $$ H' = X^{\dagger} H X = \begin{bmatrix} 0.171029 & 0.213069 \ -1.07644 & 0.864054 \end{bmatrix} \begin{bmatrix} -2.10694 & -2.42674 \ -2.42674 & -1.4109 \end{bmatrix} \begin{bmatrix} 0.171029 & -1.07644 \ 0.213069 & 0.864054 \end{bmatrix}$$ $$ H' = X^{\dagger} H X = \begin{bmatrix} -0.302548 & 0.32611 \ 0.32611 & 1.01951 \end{bmatrix}.$$ (<b>Step 5</b>)Diagonalizing the transformed Hamiltonian matrix gives $$ D = \begin{bmatrix} 1.09557 & 0 \ 0 & -0.378614 \end{bmatrix}$$ with corresponding eigenvector matrix $$C' = \begin{bmatrix} 0.227151 & -0.973859 \ 0.973859 & 0.227151 \end{bmatrix}.$$ (<b>Step 6</b>)Finally, in order to get the coefficients in the original basis, we need to calculate $$ C = XC' = \begin{bmatrix} 0.171029 & -1.07644 \ 0.213069 & 0.864054 \end{bmatrix} \begin{bmatrix} 0.227151 & -0.973859 \ 0.973859 & 0.227151 \end{bmatrix} = \begin{bmatrix} -1.00945 & -0.411073 \ 0.889866 & -0.0112284 \end{bmatrix}.$$ The lowest eigenvalue found from the diagonal matrix $D$ is -0.378614 HT. The corresponding wave function can be found by taking the coefficients of the corresponding column vector, thus giving $$\lvert \phi \rangle = -0.411073 \cdot \exp \left(-r^2 / 2 \right) - 0.0112284 \cdot r \exp \left(-r^2 / 2 \right).$$ This is effectively the same answer as found in example 2 as can be seen from the radial distribution plot (below)! This is of course not very surprising. The variation used in both approximations was by taking different polynomials in front of the exponent. Both attempts at finding the best wave function (example 2 as well as this example) use a zeroth and first order polynomial in front of the exponent. If we compare the radial distribution function of the wave function here and the one obtained in example 2, we can see that these functions overlap.<br><br> <img src="http://www.ivofilot.nl/images/24/bp_qc1_fig1.png"><br><br> This does not necessarily imply that the underlying contributions of the basis functions are the same. If you would examine the coefficients and the corresponding basis functions, you would notice a particular difference. The contribution of each basis functions in each set is visualized in the graph below. We can clearly see that the contributions differ.<br><br> <img src="http://www.ivofilot.nl/images/25/bp_qc1_fig2.png"><br><br> If we now sum up the contributions of the two basis functions for each linear combination, we note that the two wave functions in example 2 and this example are in principle the same.<br><br> <img src="http://www.ivofilot.nl/images/26/bp_qc1_fig3.png"><br><br> Thus, we obtain the same result for each wave function. </div> Although we have now the tools to find the best approximation of the ground state energy and its corresponding wave function using any set of basis functions, the result so far was not very satisfactory. Using only a single trial wave function as for instance given in example 1 gave better results. In order to improve on the previous results, we need to expand our set of basis functions. A larger basis set should in principle give a better result. <div class="bs-callout bs-callout-primary"> <h4>Example 4: The energy of the 1s orbital of hydrogen using a basis set including polynomials up to 4th order</h4> For our basis set, we are going to use the following set of basis functions: $$ \lvert \psi_{i} \rangle = r^{i} \exp \left( -r^2/2 \right) $$ for $i = 0,1,2,3,4$. The overlap matrix $S$ then looks like: $$ S = \begin{bmatrix} 5.56833 & 6.28319 & 8.35249 & 12.5664 & 20.8812 \ 6.28319 & 8.35249 & 12.5664 & 20.8812 & 37.6991 \ 8.35249 & 12.5664 & 20.8812 & 37.6991 & 73.0843 \ 12.5664 & 20.8812 & 37.6991 & 73.0843 & 150.796 \ 20.8812 & 37.6991 & 73.0843 & 150.796 & 328.879 \end{bmatrix} $$ and the hamiltonian matrix $H$ is $$ H = \begin{bmatrix} -2.10694 & -2.42674 & -4.19506 & -8.35249 & -17.7867 \ -2.42674 & \ -1.4109 & -2.06931 & -5.25794 & -14.598 \ -4.19506 & -2.06931 & -1.08169 & \ -2.03167 & -8.98742 \ -8.35249 & -5.25794 & -2.03167 & 1.45319 & 2.31392 \ -17.7867 & -14.598 & -8.98742 & 2.31392 & 22.7788 \end{bmatrix} $$ Using the same procedure as in example 3, we obtain for the lowest eigenvalue of the transformed hamiltonian matrix the energy of <b>-0.487773 HT</b>. This result is a significant improvement and comes very close to the exact energy of -0.5HT! <br><br> Further improvement by expanding the basis set to 10 basis functions gives a result of -0.498481 HT. </div> ## Summary In this blogpost I have shown you that in order to find the best approximation to the ground state energy, the variational principle can be employed. By introducing some kind of variety in a trial wave function and then minimizing its corresponding energy, gives the best approximation to the ground state energy can be found. In the linear variational method, the variational freedom is provided by the specific set of basis functions used. In this method, the best coefficients in the linear combination of said basis functions that minimize the energy can be found. Here, I have shown that a sufficiently large set of basis functions composed of a Gaussian part (the exponent) multiplied with a polynomial of increasing order is able to approach the true ground state energy of the hydrogen atom. ### Acknowledgements Finally, I would like to acknowledge <a href="https://www.linkedin.com/pub/bart-zijlstra/74/682/29b/de">Bart Zijlstra</a> for thoroughly proofreading this post and pointing out the mistakes.
      • watched12513
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      • id28
      • titleHow to build VASP 5.3.5 using the GNU compiler on Linux Ubuntu 14.04 LTS
      • contentThis tutorial will explain how to install VASP 5.3.5 on a Linux Ubuntu system. I used the latest version at hand (14.04 LTS) and started with a fresh install (in a Virtualbox environment). This tutorial is to a large extend based [on the previous work of Peter Larsson](https://www.nsc.liu.se/~pla/blog/2013/11/05/compile-vasp-on-ubuntu/). This tutorial also works for Debian 8. For Debian 7, you need to use different packages in step 1, but the same procedure holds. For installing VASP 4.6.38, you can refer to [my previous blogpost](http://www.ivofilot.nl/posts/view/21/How+to+build+VASP+4.6.38+using+the+GNU+compiler). In that post, I got some comments regarding how to install VASP 5, this post is therefore also (more-or-less) an answer to these questions. This tutorial proceeds in 4 steps: * <a href="#step1">Installing the necessary packages</a> * <a href="#step2">Building OpenBLAS</a> * <a href="#step3">Building ScaLAPACK</a> * <a href="#step4">Building VASP</a> <a name="step1"></a> # Step 1: Installing the necessary packages <pre> <code class="bash"> sudo apt-get install build-essential gfortran libopenmpi-dev libopenmpi1.6 openmpi1.6 libfftw3-double3 libfftw3-single3 libfftw3-dev git </code> </pre> <a name="step2"></a> # Step 2: Building OpenBLAS From here on, I will assume that everything is compiled in its own build directory. For convenience, let's declare a variable to hold this path. <pre> <code class="bash"> export BUILDPATH=$HOME/vaspbuild mkdir $BUILDPATH cd $BUILDPATH </code> </pre> The latest version of OpenBLAS can be readily obtained via the command below: <pre> <code class="bash"> git clone https://github.com/xianyi/OpenBLAS.git --depth 1 </code> </pre> To compile OpenBLAS run: <pre> <code class="bash"> cd $BUILDPATH/OpenBLAS make FC=gfortran CC=gcc USE_THREAD=0 </code> </pre> This will generate a file called <b>libopenblas.a</b>. We will use this file for the compilation of scaLAPACK as well as VASP. <a name="step3"></a> # Step 3: Building ScaLAPACK <pre> <code class="bash"> cd $BUILDPATH wget http://www.netlib.org/scalapack/scalapack-2.0.2.tgz tar -xvzf scalapack-2.0.2.tgz cd $BUILDPATH/scalapack-2.0.2 cp SLmake.inc.example SLmake.inc </code> </pre> We are going to make a few modifications to SLmake.inc in order to properly link everything to our version of OpenBLAS. To do so, let BLASLIB refer to our OpenBLAS library. Because OpenBLAS also contains LAPACK routines, refer LAPACKLIB to BLASLIB. <pre> <code class="bash"> BLASLIB = -L/home/$USER/vaspbuild/OpenBLAS -lopenblas LAPACKLIB = $(BLASLIB) LIBS = $(LAPACKLIB) $(BLASLIB) </code> </pre> Then, in order to compile everything, simply type <pre> <code class="bash"> make </code> </pre> This will generate a library file called <b>libscalapack.a</b>. Now, we have everything to build VASP. <a name="step4"></a> # Step 4: Building VASP I assume you have extracted the two VASP packages (vasp5.lib.tar.gz and vasp5.tar.gz) in the build folder. Compiling the library part of VASP is easy. <pre> <code class="bash"> cd $BUILDPATH/vasp.5.lib cp Makefile.linux_gfortran Makefile make </code> </pre> Building the other part is somewhat more difficult and requires a bit of tweaking and fixing some things. Start by copying the template makefile. <pre> <code class="bash"> cd $BUILDPATH/vasp.5.3 cp Makefile.linux_gfortran Makefile </code> </pre> Next, we are going to change some directives in the makefile. Open the Makefile with your favorite text editor. First, remove the <i>-C</i> part from the CPP line, like so: <pre> <code class="makefile"> CPP_ = ./preprocess <$*.F | /usr/bin/cpp -P -traditional >$*$(SUFFIX) </code> </pre> Next, we are going to comment the last line of the FPP block. <pre> <code class="makefile"> # this release should be fpp clean # we now recommend fpp as preprocessor # if this fails go back to cpp # CPP_=fpp -f_com=no -free -w0 $*.F $*$(SUFFIX) </code> </pre> Scroll down to the FFLAGS directive and change it to: <pre> <code class="makefile"> FFLAGS =-ffree-form -ffree-line-length-0 </code> </pre> <b>Note that there has to be a space after the 0!!</b> Now scroll further down to the part mentioning <b>MPI section</b>. Uncomment the FC and FCL line and change <i>mpif77</i> to <i>mpif90</i>, like so: <pre> <code class="makefile"> FC=mpif90 FCL=$(FC) </code> </pre> Uncomment the whole block for CPP and add <i>-DMPI</i> and <i>-DscaLAPACK</i> to the block, like so: <pre> <code class="makefile"> CPP = $(CPP_) -DHOST=\"gfortran\" \ -DCACHE_SIZE=4096 -DMINLOOP=1 -DNGZhalf \ -DMPI_BLOCK=8000 -DMPI -DscaLAPACK </code> </pre> Add our version of scaLAPACK to the SCA variable and create a reference to our version of BLAS and LAPACK: <pre> <code class="makefile"> SCA=/home/$USER/vaspbuild/scalapack-2.0.2/libscalapack.a BLAS=/home/$USER/vaspbuild/OpenBLAS/libopenblas.a LAPACK=/home/$USER/vaspbuild/OpenBLAS/libopenblas.a </code> </pre> Uncomment the lines for the LIB and the (second!) FFT3D variables in the <b>libraries for MPI</b> block. Refer to the fftw3 library of the OS. (last part of the FFT3D line) <pre> <code class="makefile"> LIB = -fall-intrinsics \ -L../vasp.5.lib -ldmy \ ../vasp.5.lib/linpack_double.o $(LAPACK) \ $(SCA) $(BLAS) # FFT: fftmpi.o with fft3dlib of Juergen Furthmueller # FFT3D = fftmpi.o fftmpi_map.o fft3dfurth.o fft3dlib.o # alternatively: fftw.3.1.X is slighly faster and should be used if available FFT3D = fftmpiw.o fftmpi_map.o fftw3d.o fft3dlib.o /usr/lib/x86_64-linux-gnu/libfftw3.a </code> </pre> When you would now start to compile VASP by typing `make`, you would encounter an error like the following: <pre> <code class="bash"> us.f90:1403.10: USE us 1 Error: 'setdij' of module 'us', imported at (1), is also the name of the current program unit </code> </pre> The way to resolve this error, is by changing the names. The way we are going to do that, is by applying a patch to this file. You can download the patch file [here](http://www.ivofilot.nl/downloads/vasp535.patch). Just place it in the same directory as where the VASP sources reside and apply the patch by typing: <pre> <code class="bash"> wget http://www.ivofilot.nl/downloads/vasp535.patch patch -p0 < vasp535.patch </code> </pre> This will change the names automatically. You will receive a message such as <pre> <code class="makefile"> patching file us.F </code> </pre> Upon typing `make`, the compilation will resume. The next error we are going to encounter is <pre> <code class="bash"> fftmpiw.f90:70: Error: Can't open included file 'fftw3.f' </code> </pre> The way to resolve this error is by copying our system's version of fftw3.h to the source folder like so <pre> <code class="bash"> cp /usr/include/fftw3.f . </code> </pre> (note that all .f files get removed after a `make clean`) Now, everything should compile perfectly. Type `make` again and the `vasp` executable will be generated.
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        • emailroad309@naver.com
        • commentDear Ivo, Thanks for your kind instructions. Unfortunately, I encountered error message as below, although I followed all the procedures. Would you please give me some solution? - from Yong ====== Error: Syntax error in argument list at (1) bse_te.f90:510.102: ECTORELEMENTS(1,IDIR), MATDIM_NODE(NODE_ME), MPI_COMPLEX, VECTOR_D(1,IDIR),&1 Error: Syntax error in argument list at (1) Makefile:324: recipe for target 'bse_te.o' failed make: *** [bse_te.o] Error 1 ====
        • id43
        • post_id28
        • created2015-08-19 13:06:13
      • 1(array)
        • emailxuwenwu1115@hotmail.com
        • commentI had exactly the same problem about bse_te.f90 error...
        • id44
        • post_id28
        • created2016-02-24 07:17:57
      • 2(array)
        • emailivo@ivofilot.nl
        • commentIt's hard to find out what went wrong with so little details to go on. Furthermore, this version of VASP is outdated and VASP 5.4.x has a completely new build system. Better try that out. (more information can be found in my other blog post)
        • id45
        • post_id28
        • created2016-02-25 12:41:09
      • 3(array)
        • emailkhanhbinh183@yahoo.com
        • commentThank you very much for your guidance. I've installed VASP successfully. But when I run VASP, the percentage of 1 cpu can increase up to 400% and it slows down all of my system. I think that is the OpenMPI problem but I don't know how to fix it. Do you have any suggestion. Thank you very much!
        • id47
        • post_id28
        • created2016-05-01 10:23:58
      • 4(array)
        • emailkhanhbinh183@yahoo.com
        • commentThank you for your response. I've already fixed the problem. I'm not sure about the it. This is probably because that the hyper-threading is enable in my cluster. By adding the flag "-x OMP_NUM_THREADS=1" (or 2), the problem is fixed.
        • id50
        • post_id28
        • created2016-05-04 07:59:37
      • 5(array)
        • emailivo@ivofilot.nl
        • commentThis is indeed most likely caused by a problem with how you use OpenMPI. Regrettably, I cannot give a straight answer how to resolve it as I cannot reproduce the problem you have. Relevant questions for you are: How do you run VASP? (e.g. mpirun -np 4 ./vasp) How did you obtain OpenMPI? My suggestion is to look into the manual pages of OpenMPI and especially the mpirun command. Alternatively, you could try to manually compile OpenMPI yourself and see if that resolves your problem.
        • id49
        • post_id28
        • created2016-05-03 08:03:16
      • 6(array)
        • emailmudra.msu@gmail.com
        • commentHi, i am having same problem, can you please help and share how did you resolved it?
        • id54
        • post_id28
        • created2016-07-11 15:20:15
      • 7(array)
        • emailivo@ivofilot.nl
        • commentLike I said below, it is very hard to give an answer to such questions with so little to go on. I never encountered this problem and it is very hard to reproduce without having some more details. My best guess is that you look into the GCC compilers and make sure you use a recent version. (> 4.9)
        • id55
        • post_id28
        • created2016-07-11 15:46:18
      • 8(array)
        • emailswangi@outlook.com
        • commentChange GCC to 4.9 didn't change the error. I found one solution is to delete '&' symbols in the lines (for instance, bse_te.f90:510.102), and make sure all values in the function in one line.
        • id58
        • post_id28
        • created2016-09-29 19:51:30
      • 9(array)
        • emailjyothigsit26@gmail.com
        • commentHi, I have one problem like AS you mention above Error: 'setdij' of module 'us', imported at (1), is also the name of the current program unit i tried to attach patch file but it showing can't find file to patch at input line 3 Perhaps you used the wrong -p or --strip option? The text leading up to this was: -------------------------- |--- us.F |+++ us.F -------------------------- File to patch: Would you please give me some solution? from Jyothi
        • id61
        • post_id28
        • created2016-12-28 16:46:18
      • 10(array)
        • emailngoctri2990@gmail.com
        • commentDear Ivo, Thank you very much for your instruction. Could you please help me to fix this problem: mpif90 -ffree-form -ffree-line-length-0 -O3 -c symmetry.f90 symmetry.f90:1567:10: USE spinsym 1 Fatal Error: Can't open module file ‘spinsym.mod’ for reading at (1): No such file or directory compilation terminated. makefile:320: recipe for target 'symmetry.o' failed make: *** [symmetry.o] Error 1 Thanks so much!
        • id63
        • post_id28
        • created2017-04-12 02:59:04
      • 11(array)
        • emailbafekry.asad@gmail.com
        • commentHi dears please help me to fix this problem: mpif90 -ffree-form -ffree-line-length-0 -O3 -c symmetry.f90 symmetry.f90:1567:10: USE spinsym 1 Fatal Error: Can't open module file ‘spinsym.mod’ for reading at (1): No such file or directory compilation terminated. makefile:320: recipe for target 'symmetry.o' failed make: *** [symmetry.o] Error 1 Thanks
        • id64
        • post_id28
        • created2017-08-23 06:23:58
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      • id27
      • titleVisualising the electron density of the binding orbitals of the CO molecule using VASP
      • content<div class="alert alert-info" role="alert"><i class="fa fa-github"></i> Looking for the Github repository of EDP?<br><i class="fa fa-link"></i> <a href="https://github.com/ifilot/edp">https://github.com/ifilot/edp</a> </div> # 1. Introduction Let us start by stating what we would like to obtain. We wish to visualise the electron density of the molecular orbitals of CO using VASP. We wish to create a surface cut rather than generating a 3D image containing an isosurface, as the former more clearly conveys the electron density distribution. In this short tutorial, I will show you how to create the image below: <img src="http://www.ivofilot.nl/images/19/CO_molecular_orbitals_plot.jpg" class="img img-responsive img-rounded"> <b>Figure 1:</b> <i>The electron density plots of the molecular orbitals of CO. The yellow line in the lower-left image is added to indicate the nodal plane.</i> The molecular orbitals of CO are formed from the atomic orbitals of C and O. The molecular orbitals of CO can be identified from the molecular orbital diagram of CO as shown below. Each of these orbitals have specific symmetry characteristics and these symmetry characteristics give rise to the name of the molecular orbitals. The molecular orbital lowest in energy, which is a non-bonding molecular orbital that only contains core electrons, is termed the 1σ orbital. The σ denotes the symmetry characteristics of the orbital. σ-symmetry means that the orbital can be rotated arbitrarily around the bonding axis of C and O. Hence, there are an infinite number of mirror planes parallel to this rotation axis. The four molecular orbitals lowest in energy all have this particular symmetry. The fifth molecular orbital however, has π- symmetry and is hence denoted as the 1π molecular orbital. π-symmetric orbitals have a nodal plane on the bonding axis and hence only have a C₂ rotation operation. Consequently, they also have only two mirror planes parallel to this bonding axis. The electron density plots shown above are in agreement with these symmetry characteristics. <img src="http://www.ivofilot.nl/images/18/COMOdiagram.jpg"> <b>Figure 2:</b> <i>The occupied orbitals of CO, that are constructed from the valence atomic orbitals of C and O, are in order of low to high energy: 3σ, 4σ, 1π and 5σ.</i> <image here> # 2. VASP calculations In order to construct the electron density, we first have to perform a series of VASP calculations. * Perform a structure optimisation * Perform a single point calculation and calculate the DOS for the final state (printed in DOSCAR) * Identify the molecular orbitals using the DOS plot (select the "energy range") * Perform for each identified molecular orbital another calculation where the partial charge corresponding to the energy range is saved (printed in PARCHG) If you know how to do this, skip to the next section, else continue reading. ## 2.1 POSCAR and INCAR files Our POSCAR files looks as follows: <pre> <code class="text"> CO 1.0000000000000000 10.0000000000000000 0.0000000000000000 0.0000000000000000 0.0000000000000000 10.0000000000000000 0.0000000000000000 0.0000000000000000 0.0000000000000000 10.0000000000000000 1 1 Direct 0.5000000000000000 0.5000000000000000 0.500000 0.5000000000000000 0.5000000000000000 0.617000 </code> </pre> and the INCAR file as: <pre> <code class="text"> SYSTEM = CO LREAL=.FALSE. LWAVE= .TRUE. LCHARG= .TRUE. PREC = normal ENCUT = 400 ISMEAR = 0 SIGMA = 0.05 EDIFF = 1E-5 EDIFFG = -1E-4 NSW = 100 ISIF = 2 IBRION = 2 ISPIN = 1 POTIM = 0.5 IALGO = 38 NELMIN = 6 NELM = 40 EMIN = -30 EMAX = 15 NEDOS = 4500 NGX = 150 NGY = 150 NGZ = 150 </code> </pre> The KPOINTS file specifies the gamma-point (1x1x1 <i>k</i>-points) and the POTCAR file corresponds to one with the potentials of C and O (in that order). I am not going to discuss all the directives in detail (the VASP manual is really good at that), but I will explain a couple of directives. The INCAR file tells the program to optimise the geometry (IBRION = 2). The WAVECAR and CHGCAR files will be generated and a DOSCAR file will be made with a resolution of 4500 data points on the interval [-30 eV;15 eV]. The mesh of the CHGCAR is 150x150x150 grid points. After the optimisation run, change NSW to 0 and set ISTART = 1. Copy the ```CONTCAR``` to ```POSCAR``` and start the calculation again. (this way, we have the DOS of the final state and not an averaged DOS). The generated ```DOSCAR``` file has 6 header lines and then 4500 lines containing the DOS and the integrated DOS as a function of the energy. To extract that part (and ignore the header lines) and save it ```DOS-total```, we run: <pre> <code class="bash"> sed -n '7,4506p' DOSCAR > DOS_total </code> </pre> This file can be readily visualised using your favourite program (Excel, Origin, GnuPlot, your pick...). I chose Origin and made the following graph: <img src="http://www.ivofilot.nl/images/16/CO_dos.jpg"> <b>Figure 3:</b> <i>The density of states (DOS) and integrated DOS of CO. Each of the peaks corresponds to a molecular orbital.</i> In this graph, I have depicted the molecular orbitals 3σ, 4σ, 1π and 5σ. The corresponding energy intervals (in eV) are (roughly): <table class="table table-striped"> <tr> <th>3σ</th> <td>-30</td> <td>-27</td> </tr> <tr> <th>4σ</th> <td>-15</td> <td>-13</td> </tr> <tr> <th>1π </th> <td>-13</td> <td>-10</td> </tr> <tr> <th>5σ</th> <td>-10</td> <td>-5</td> </tr> </table> For each of the energy intervals, we are going to run VASP again with the following example INCAR file. This INCAR file is for the energy interval [-30; -27.5], but you can chose any interval you like. The LPARD directive instructs the program to generate a PARCHG file of the partial charge corresponding to the wavefunctions between -30 and -27.5 eV. <pre> <code class="text"> SYSTEM = CO LREAL=.FALSE. LWAVE= .TRUE. LCHARG= .TRUE. PREC = medium ENCUT = 400 ISMEAR = 0 SIGMA = 0.05 EDIFF = 1E-5 EDIFFG = -1E-4 NSW = 100 ISIF = 2 IBRION = 2 ISPIN = 1 POTIM = 0.5 IALGO = 38 NELMIN = 6 NELM = 40 EMIN = -30 EMAX = 15 NEDOS = 4500 NGX = 150 NGY = 150 NGZ = 150 LPARD = .TRUE. EINT = -30 -27.5 </code> </pre> The resulting PARCHG files are stored separately and will be used for the visualisation in the next section. # 3. Visualising electron density To visualise the electron density, we are going to use the EDP program, which is freely available via [its Github repository](https://github.com/ifilot/edp). You can [compile the program yourself](https://github.com/ifilot/edp/blob/master/README.md#compilation) or [obtain it from the repository (if you are running Debian)](https://github.com/ifilot/edp/blob/master/README.md#obtaining-edp-from-the-repository). ## 3.1 Visualising electron density with EDP To use the mathematical terms, the electron density is a scalar field. In other words, it is a scalar value that depends on the position in the unit cell. Although the electron density is a smooth function, it is stored at particular grid points in the CHGCAR and PARCHG file. The resolution of that grid can be set by specifying NGX, NGY and NGZ in the ```INCAR``` file. The purpose of EDP is to plot the electron density on a so-called cutting plane. The end result is therefore a heat map (as shown above). In order to specify the cutting plane, the user is required to provide two vectors and one point. In our example, CO is placed along the z-axis at the centre of a cubic unit cell of 10x10x10 angstrom. The centre of the unit cell is at position (5.0, 5.0, 5.0). If we want to project the electron density on an (<i>xz</i>)- plane cutting through the point (5.0, 5.0, 5.0), then the command is: <pre> <code class="bash"> ./bin/edp -i path/to/CHGCAR -v 1,0,0 -w 0,0,1 -p 5,5,5 -s 100 -o test.png </code> </pre> The tags `-v` and `-w` specify the vectors and `-p` specifies the point. The `-s` tag is used to set the resolution of the final image. The value of 100 means that the final image has 100px per angstrom. Finally, the `-i` and `-o` tags designate the input (a CHGCAR of PARCHG file) and output files (an .png image file). Maybe you are wondering how the values are generated that do not lie exactly at the grid points specified in the CHGCAR file. To plot such values, a trilinear interpolation scheme is used. A detailed description of that algorithm is given [here](http://en.wikipedia.org/wiki/Trilinear_interpolation). ## 3.2 Plotting the orbitals Plotting the four binding orbitals has now become a simple matter of running the program for each of the PARCHG files corresponding to the molecular orbitals. To exemplify: <pre> <code class="bash"> ./bin/edp -i path/to/PARCHG_3s -v 1,0,0 -w 0,0,1 -p 5,5,5 -s 100 -o 3s.png ./bin/edp -i path/to/PARCHG_4s -v 1,0,0 -w 0,0,1 -p 5,5,5 -s 100 -o 4s.png ./bin/edp -i path/to/PARCHG_1p -v 1,0,0 -w 0,0,1 -p 5,5,5 -s 100 -o 1p.png ./bin/edp -i path/to/PARCHG_5s -v 1,0,0 -w 0,0,1 -p 5,5,5 -s 100 -o 5s.png </code> </pre> Finally, you can collect all images and create a nice compilation in your favourite photo-editing program (such as what I did in Figure 1). ## 3.3 Concluding remarks Obviously, you can use the above procedure to visualise any kind of molecule. Especially simple molecules such as N₂ or H₂ are easy to visualise. Less obvious is that you can also use the above procedure to visualise the molecular orbitals of a substrate adsorbed on a catalytic surface or the electron density difference between CO in its molecular state and C and O in their atomic states. It all depends on the way the CHGCAR and PARCHG files are created. I hope this tutorial was informative. If you have used this tutorial and found it useful for your work, please drop a line or send me an e-mail. Especially if you have made some nice pictures. :-) # 4.Comments [Bart Zijlstra](https://www.linkedin.com/pub/bart-zijlstra/74/682/29b/de) has made a very nice analysis of the results of the electron density visualisation routine as a function of the number of k-points and the smearing value. The result can be seen below. Increasing the number of K-points shows a more detailed result, yet there is no significant change in the characteristic features. <img src="http://www.ivofilot.nl/images/20/elec_dens_analysis.jpg" class="img img-responsive img-rounded" />
      • watched20407
      • active(true)
      • created2015-04-28 12:00:00
      • modified2017-12-31 23:52:34
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      • 0(array)
        • emailzdenko.kolaric@siol.net
        • commentPlease for something similar for SO2 and SO3. Best Regards Zdenko
        • id46
        • post_id27
        • created2016-04-27 19:51:00
      • 1(array)
        • emailjkshenton@gmail.com
        • commentHi! Nice work with edp! I've generated lots of nice pictures using it, but I have one question: How are the saturation levels chosen? I mean, I'd like to plot a colour bar next to it in some units (say eV/bohr^3). How would I go about doing this? Thanks Kane
        • id56
        • post_id27
        • created2016-07-14 11:01:39
      • 2(array)
        • emailyuzihe@usc.edu
        • commentwhen run on a single orbit, why do you still need to move the atoms by setting ISIF = 2 IBRION = 2 ISPIN = 1 POTIM = 0.5
        • id59
        • post_id27
        • created2016-10-27 12:00:21
      • 3(array)
        • emailivo@ivofilot.nl
        • commentThis feels a bit like necroposting. Nevertheless, I have implemented a legend into EDP. You can enable the legend using the "-l" directive and it will show which colors represent which values. It also mentions the units (which are in eV/A^3).
        • id65
        • post_id27
        • created2017-12-31 21:29:24
      • 4(array)
        • emailmlorke@web.de
        • commentI tried to use edp on a supercell calculation and noticed that apparently edp keeps like a small "edge" from the colormap, i.e. if I try to put the picture and its replica side by side to "extent" the supercell it does not fit. Any way around this? Otherwise great work, really helps
        • id71
        • post_id27
        • created2018-06-02 00:06:40
      • 5(array)
        • emailmlorke@web.de
        • commentI tried to use edp on a supercell calculation and noticed that apparently edp keeps like a small "edge" from the colormap, i.e. if I try to put the picture and its replica side by side to "extent" the supercell it does not fit. Any way around this? Otherwise great work, really helps
        • id72
        • post_id27
        • created2018-06-02 00:07:11
      • 6(array)
        • emailmlorke@web.de
        • commentI tried to use edp on a supercell calculation and noticed that apparently edp keeps like a small "edge" from the colormap, i.e. if I try to put the picture and its replica side by side to "extent" the supercell it does not fit. Any way around this? Otherwise great work, really helps
        • id73
        • post_id27
        • created2018-06-02 00:07:51
    • Tag(array)
      • 0(array)
        • id23
        • nameComputational Chemistry
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        • id22
        • nameVASP
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  • 7(array)
    • Post(array)
      • id24
      • titleHow to build VASP 4.6.38 using the Intel compiler
      • content# Introduction In [my previous post](http://www.ivofilot.nl/posts/view/21/How+to+build+VASP+4.6.38+using+the+GNU+compiler), I explained how to build VASP using the GNU compilers. Here, I will show you how you can build VASP using the Intel Compilers. In principle, the Intel Compilers should give better performance for VASP on Intel processors. # Step 0: Install the Intel Compilers Install the Intel Compiler Suite in ```/opt/intel``` (this is the default setting). Please refer to the installation instructions given by Intel. # Step 1: Load the Intel Compilers <pre> <code class="bash"> source /opt/intel/composer\_xe\_2013\_sp1/bin/compilervars.sh intel64 </code> </pre> #Step 2: Compile the Intel FFTW wrappers <pre> <code class="bash"> cd /opt/intel/composer\_xe\_2013_sp1/mkl/interfaces/fftw3xf make libintel64 </code> </pre> #Step 3: Compile the VASP libraries <pre> <code class="bash"> tar -xvzf vasp.4.lib.tar.gz cd vasp.4.lib cp makefile.linux\_ifc\_P4 Makefile </code> </pre> and change the file so that FC is linking to ifort <pre> <code class="makefile"> .SUFFIXES: .inc .f .F #----------------------------------------------------------------------- # Makefile for Portland Group F90/HPF compiler # the makefile was tested only under Linux on Intel platforms # however it might work on other platforms as well # # this release of vasp.4.lib contains lapack v2.0 # this can be compiled with pgf90 compiler if the option -O1 is used # # Mind: one user reported that he had to copy preclib.F diolib.F # dlexlib.F and drdatab.F to the directory vasp.4.4, compile the files # there and link them directly into vasp # for no obvious reason these files could not be linked from the library # #----------------------------------------------------------------------- # C-preprocessor CPP = gcc -E -P -C $*.F >$*.f FC=ifort CFLAGS = -O FFLAGS = -O0 -FI FREE = -FR DOBJ = preclib.o timing_.o derrf_.o dclock_.o diolib.o dlexlib.o drdatab.o </code> </pre> and type <pre> <code class="bash"> make </code> </pre> #Step 4: Compile VASP <pre> <code class="bash"> source /opt/intel/impi/4.1.1.036/bin64/mpivars.sh tar -xvzf vasp.4.6.tar.gz cd vasp.4.6 cp makefile.linux\_ifc\_P4 Makefile </code> </pre> Alter the Makefile on the following points and finally run make <pre> <code class="bash"> make </code> </pre> when you get this error <pre> <code lang="bash"> mpif77 -fc=ifort -FR -names lowercase -assume byterecl -O3 -xAVX -c fftmpiw.f90 fftmpiw.f90(55): error #5102: Cannot open include file 'fftw3.f' include 'fftw3.f' --------------^ fftmpiw.f90(89): error #5102: Cannot open include file 'fftw3.f' include 'fftw3.f' --------------^ fftmpiw.f90(110): error #5102: Cannot open include file 'fftw3.f' include 'fftw3.f' --------------^ fftmpiw.f90(220): error #5102: Cannot open include file 'fftw3.f' include 'fftw3.f' --------------^ compilation aborted for fftmpiw.f90 (code 1) make: *** [fftmpiw.o] Error 1 </code> </pre> copy the header file <pre> <code class="bash"> cp /opt/intel/mkl/include/fftw/fftw3.f . </code> </pre> and run make again <pre> <code class="bash"> make </code> </pre> # Step 5: Testing our compilation and comparing against the GNU compilation We have used three different models to check the computational efficiency of the Intel Compilations versus that of the GNU compilation: * A single CO molecule in a large box (gamma-point calculation) * A bulk Cu system * A Fe₅C₂ (Hagg carbide) system The results are the following: <table class="table"> <thead> <th>System</th> <th>gcc-4.8.4 VASP 4.6.38</th> <th>Intel VASP 4.6.38</th> </thead> <tr> <td>CO</td> <td>240.483</td> <td>240.683</td> </tr> <tr> <td>Cu</td> <td>54.623</td> <td>34.994</td> </tr> <tr> <td>Fe₅C₂</td> <td>907.617</td> <td>656.705</td> </tr> </table> Interestingly, the Intel compiler does not give significantly different result for the gamma-point calculation (CO molecule). However, the speed improvement for the other calculations is **roughly 30%**!
      • watched9316
      • active(true)
      • created2015-03-22 12:00:00
      • modified2015-06-30 17:18:32
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        • emailfiratyilmazz@gmail.com
        • commentThanks fot this clean explanation.
        • id62
        • post_id24
        • created2017-04-07 09:54:43
    • Tag(array)
      • 0(array)
        • id22
        • nameVASP
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      • 1(array)
        • id23
        • nameComputational Chemistry
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  • 8(array)
    • Post(array)
      • id25
      • titleCreating a local queuing system on Linux Debian using Torque
      • content# Introduction Imagine you would like to perform a large series of calculation. Obviously, you would not run the complete series of calculations at the same time. In principle, you would like to start as many jobs as the number of processors on your computer can handle and start the next job in the series when the previous job has finished. You could write your own program for this, but there are many of such programs available. In this blog post, I will show you how to install and use Torque. Although Torque can be set up to run in a computer cluster, I will show you how you can install and use it on just a single machine. This tutorial is written for Linux Debian, but should in principle also work for Linux Ubuntu and with (hopefully) small modifications for the other distributions. # Compiling Torque Download the tarball from the website. Extract, compile and install it on your machine. <pre> <code class="bash"> wget http://www.adaptivecomputing.com/index.php?wpfb_dl=2868 -O torque-5.1.0.tar.gz cd torque-5.1.0 ./configure --prefix=/opt/gcc-4.7.2/torque-5.1.0 make -j5 sudo make install </code> </pre> # Installing the daemons Torque uses four daemons that have to be loaded at boot time. Copy their ```init.d``` scripts to the ```/etc/init.d``` folder like so <pre> <code class="bash"> sudo cp contrib/init.d/debian.trqauthd /etc/init.d/trqauthd sudo cp contrib/init.d/debian.pbs_mom /etc/init.d/pbs_mom sudo cp contrib/init.d/debian.pbs_server /etc/init.d/pbs_server sudo cp contrib/init.d/debian.pbs_sched /etc/init.d/pbs_sched </code> </pre> and add these to the boot procedure <pre> <code class="bash"> sudo update-rc.d pbs_mom defaults sudo update-rc.d pbs_server defaults sudo update-rc.d pbs_sched defaults sudo update-rc.d trqauthd defaults </code> </pre> # Configuring the server and the nodes Next, we would like to set our machine as both the server as well as the (only) node. Start the ```trqauthd``` daemon <pre> <code class="bash"> sudo /etc/init.d/trqauthd start </code> </pre> Log in as root and add the binary folders of Torque to the path. <pre> <code class="bash"> su export PATH=/opt/gcc-4.7.2/torque-5.1.0/sbin:/opt/gcc-4.7.2/torque-5.1.0/bin:$PATH ./torque.setup root </code> </pre> If you get an error like the following <pre> <code class="bash"> qmgr obj= svr=default: Bad ACL entry in host list MSG=First bad host: </code> </pre> check your ```/etc/hosts``` file and change the directives in there. Torque only reads the first two columns to match the hostname with an IP adress. Add your machine to the list of nodes by editing ```/var/spool/torque/server_priv/nodes```. You have to specify the number of cores in your machine after the ```np=``` directive. <pre> <code class="bash"> localhost np=6 </code> </pre> Edit ```/var/spool/torque/mom_priv/config``` and set your machine as the ```$pbsserver```. Also configure the bitmap for the logging events. <pre> <code class="bash"> $pbsserver ST-A1771 $logevent 225 </code> </pre> Please note that in the above file, `ST-A1771` should be replaced by the name of your local machine. Moreover, this name should match an IP address which can be configured in `/etc/hosts`. (thanks to `danielmejia55_at_gmail_dot_com` for mentioning this, see comments below) Start pbs_mom. <pre> <code class="bash"> /etc/init.d/pbs_mom start </code> </pre> In order for every user to submit files to the queuing system and check the current status of the queue, you would like that every user has the ```bin``` folder of Torque in their ```$PATH``` variable. As such, add the Torque binaries folder to the PATH in ```/etc/profile``` <pre> <code class="bash"> echo 'export PATH=/opt/gcc-4.7.2/torque-5.1.0/bin:$PATH' >> /etc/profile </code> </pre> Finally, log out as root (CTRL+D) # Checking the installation To check that everything is correctly configured, run <pre> <code class="bash"> pbsnodes -a </code> </pre> If you do not get something like this, you can try to reset ```pbs_server```. (see below) <pre> <code class="bash"> state = free power_state = Running np = 6 ntype = cluster status = rectime=1424867568,cpuclock=OnDemand:1998MHz,varattr=,jobs=,state=free,netload=6890398942,gres=,loadave=0.00,ncpus=4,physmem=8066840kb,availmem=11324404kb,totmem=11970324kb,idletime=240,nusers=1,nsessions=2,sessions=3336 27395,uname=Linux ST-A1771 3.2.0-4-amd64 #1 SMP Debian 3.2.65-1+deb7u1 x86_64,opsys=linux mom_service_port = 15002 mom_manager_port = 15003 </code> </pre> To reset ```pbs_server```, run <pre> <code class="bash"> sudo /etc/init.d/pbs_server restart </code> </pre> Also start the scheduler <pre> <code class="bash"> sudo /etc/init.d/pbs_sched start </code> </pre> And test a job by running <pre> <code class="bash"> echo "sleep 30" | qsub </code> </pre> When you run <pre> <code class="bash"> qstat </code> </pre> you should see something like <pre> <code class="bash"> Job ID Name User Time Use S Queue ------------------------- ---------------- --------------- -------- - ----- 0.ST-A1771 STDIN ivo 0 R batch </code> </pre> **Note**: `danielmejia55_at_gmail_dot_com` has noted (see comments below) that if you encounter an error that certain queue directives are missing, that you need to set these first. He has kindly provided the settings he has used. # Submission files Below, an example submission file for a multiprocessor job is given. In the submission file, you specify the name of the job after the ```PBS -N``` directive, the number of nodes and the number of processors per node and finally the maximum time the job is allowed to run. Typically, you would like to run the job in the same folder as where the jobfile is residing. To do so, you can use the ```$PBS_O_WORKDIR``` variable. Furthermore, you can use the ```$PBS_NP``` variable to pass the number of processes to the ```mpirun``` program. <pre> <code class="bash"> #!/bin/bash # #This is an example script example.sh # #These commands set up the Torque Environment for your job: #PBS -N TestJob #PBS -l nodes=1:ppn=4,walltime=00:12:00 pwd cd $PBS_O_WORKDIR pwd #print the time and date date mpirun -np $PBS_NP ./testjob #print the time and date again date </code> </pre>
      • watched12335
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      • created2015-03-03 15:50:39
      • modified2015-06-30 17:22:47
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        • emaildanielmejia55@gmail.com
        • commentFirst of all, Thank you for this guide. Though, I've been having some issues with it. * It is worth to mention that the name "ST-A1771 " stands for the name of your local machine, so it must be already defined in the "/etc/hosts" file and in "/var/spool/torque/mom_priv/config" with the same name * When trying to test the installation "echo "sleep 30" | qsub" it notifies that some "queue" directives for the server are missing. Those are implemented with "qmgr servername" and needed to run tests
        • id35
        • post_id25
        • created2015-05-14 01:45:56
      • 1(array)
        • emaildanielmejia55@gmail.com
        • commentThe settings I've used where # qmgr my_torque_server_name Qmgr: create queue batch Qmgr: set queue batch queue_type = Execution Qmgr: set queue batch max_running = 6 Qmgr: set queue batch resources_max.ncpus = 8 Qmgr: set queue batch resources_max.nodes = 1 Qmgr: set queue batch resources_default.ncpus = 1 Qmgr: set queue batch resources_default.neednodes = 1:ppn=1 Qmgr: set queue batch resources_default.walltime = 24:00:00 Qmgr: set queue batch max_user_run = 6 ...
        • id36
        • post_id25
        • created2015-05-14 01:55:09
      • 2(array)
        • emailivo@ivofilot.nl
        • commentHi danielmejia55_at_gmail_dot_com, Thanks you for your comments and helpful suggestions! I didn't get the notification about the missing queue directives. I am not sure why. I will write a small remark in the post to read your nice comments for people who might encounter them. Thanks again!
        • id37
        • post_id25
        • created2015-05-18 11:09:35
    • Tag(array)
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        • id18
        • nameLinux
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  • 9(array)
    • Post(array)
      • id23
      • titleHow to install and use the environment modules system
      • content# Introduction Let us think about the way we run programs from the terminal. If we want to list the content of a directory, we simply type ```ls```. Why does this work? You probably know the answer: Because the program ```ls``` is residing in the ```/bin/ls``` folder and that folder is in the ```$PATH``` variable. In fact, you can check this by typing: <pre> <code class="bash"> which ls </code> </pre> and <pre> <code class="bash"> echo $PATH </code> </pre> What now if we have multiple versions of a particular program. For instance, we could have multiple versions installed of the GNU compiler. How would you then distinguish the programs? One could then append the version number to the binaries, like so: * gcc-4.7.4-i686 * gcc-4.8.4-i686 and place all the folders where these executables reside in , in the ```$PATH``` variable. Let me now propose an alternative, which is often implemented in computational clusters. It is called [Modules Environment](http://modules.sourceforge.net/). Using this tool, you simply type ```module avail``` to check which programs are installed on the system and if you would like to use a particular program, let's say gcc-4.8.4, you would type ```module load gcc-4.8.4```. The Environment Modules tool will then *prepend* the folder where the executables of gcc-4.8.4 reside in to the ```$PATH``` variable so that when you type ```gcc```, you will automatically use *that particular version*. Pretty nifty tool right? Well, you can use it on your local system as well and in this blog post I will explain you how. # Installation Download the tarball <pre> <code class="bash"> wget http://sourceforge.net/projects/modules/files/latest/download?source=files -O modules-3.2.10.tar.gz </code> </pre> and extract it <pre> <code class="bash"> tar -xvzf modules-3.2.10.tar.gz </code> </pre> You need to have the tcl libraries installed, on Debian this can be done via: <pre> <code class="bash"> sudo apt-get install tcl-dev </code> </pre> Next, run ```configure``` like so <pre> <code class="bash"> ./configure --with-module-path=/opt/modulefiles --prefix=/opt/modules-3.2.10 </code> </pre> Feel free to change the paths mentioned above to something suitable for your system. (Though the ```/opt``` folder is meant to place installed programs in. [Read more about the Linux directory structure here](http://www.thegeekstuff.com/2010/09/linux-file-system-structure/)). After configuring, run ```make``` and ```make install```. <pre> <code class="bash"> make sudo make install </code> </pre> Lastly, you need to initialize the Environment Modules every time you load ```bash```. On Debian, this is done by adding two lines to ```/etc/profile``` (a file that is run every time you run ```bash```). Open ```/etc/profile``` <pre> <code class="bash"> sudo nano /etc/profile </code> </pre> and add at the bottom of the file <pre> <code class="bash"> # load the modules source /opt/modules-3.2.10/Modules/3.2.10/init/bash </code> </pre> And you are all set up. If you now log out and back in, and type ```modules avail```, you should see something like this <pre> <code class="bash"> --------- /opt/gcc-4.7.2/modules-3.2.10/Modules/versions --------- 3.2.10 ---- /opt/gcc-4.7.2/modules-3.2.10/Modules/3.2.10/modulefiles ---- dot module-info null module-git modules use.own </code> </pre> # Configuration In the file ```/opt/modules-3.2.10/Modules/3.2.10/init/.modulespath``` a list of directories are given in which ```modules``` will search for module files. Personally, I don't like the default directories given there, and I tend to change it to something like this: <pre> <code class="bash"> # # This file defines the initial setup for the module files search path. # Comments may be added anywhere, which begin on # and continue until the # end of the line # Each line containing a single path will be added to the MODULEPATH # environment variable. You may add as many as you want - just # limited by the maximum variable size of your shell. # /opt/modulefiles </code> </pre> and I then put in ```/opt/modulefiles``` all my module files. To exemplify, let us assume that we have two different versions of gcc installed, being 4.7.2 and 4.8.3. We then need to create two modulefiles as such ```/opt/modulefiles/gnu-gcc-4.7.2``` <pre> <code class="bash"> #%Module1.0##################################################################### ## ## null modulefile ## ## modulefiles/null. Generated from null.in by configure. ## # for Tcl script use only set root /opt/gcc-4.7.2 prepend-path PATH $root/bin prepend-path LD_LIBRARY_PATH $root/lib prepend-path LD_LIBRARY_PATH $root/lib64 </code> </pre> and ```/opt/modulefiles/gnu-gcc-4.8.3``` <pre> <code class="bash"> #%Module1.0##################################################################### ## ## null modulefile ## ## modulefiles/null. Generated from null.in by configure. ## # for Tcl script use only set root /opt/gcc-4.8.3 prepend-path PATH $root/bin prepend-path LD_LIBRARY_PATH $root/lib prepend-path LD_LIBRARY_PATH $root/lib64 </code> </pre> If you would now run ```module avail```, (assuming you have a similar ```.modulespath``` as mine) you would see something like this <pre> <code class="bash"> -------- /opt/modulefiles -------- gnu-gcc-4.7.2 gnu-gcc-4.8.3 </code> </pre> If I would now like to use gcc-4.7.2 to compile, I would type ```module load gnu-gcc-4.7.2``` and have the bin directories of ```gcc-4.7.2``` appended to my ```$PATH``` ensuring that I use the right compiler. More advanced configuration would actually modify the modulefiles in such a way that when gcc-4.7.2 is loaded and you would run ```module load 4.8.3``` that then a conflict error would be given.
      • watched7168
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    • Publication(array)
      • id18
      • titleFirst-Principles-Based Microkinetics Simulations of Synthesis Gas Conversion on a Stepped Rhodium Surface
      • authorsFilot, I.A.W., Broos, R.J.P., van Rijn, J.P.M., van Heugten, G.J.H.A., van Santen, R.A., Hensen, E.J.M.
      • journalACS Catal.
      • year2015
      • volume5
      • issue(null)
      • pagerange5453-5467
      • doi10.1021/acscatal.5b01391
      • graphical_abstract_id1
      • abstractThe kinetics of synthesis gas conversion on the stepped Rh(211) surface were investigated by computational methods. DFT calculations were performed to determine the reaction energetics for all elementary reaction steps relevant to the conversion of CO into methane, ethylene, ethane, formaldehyde, methanol, acetaldehyde, and ethanol. Microkinetics simulations were carried out on the basis of these first-principles data to predict the CO consumption rate and the product distribution as a function of temperature. The elementary reaction steps that control the CO consumption rate and the selectivity were analyzed in detail. Ethanol formation can only occur on the stepped surface, because the barrier for CO dissociation on Rh terraces is too high; step-edges are also required for the coupling reactions. The model predicts that formaldehyde is the dominant product at low temperature, ethanol at intermediate temperature, and methane at high temperature. The preference for ethanol over long hydrocarbon formation is due to the lower barrier for C(H) + CO coupling as compared with the barriers for CHx + CHy coupling reactions. The C(H)CO surface intermediate is hydrogenated to ethanol via a sequence of hydrogenation and dehydrogenation reactions. The simulations show that ethanol formation competes with methane formation at intermediate temperatures. The rate-controlling steps are CO removal as CO2 to create empty sites for the dehydrogenation steps in the reaction sequence leading to ethanol, CHxCHyO hydrogenation for ethanol formation, and CH2 and CH3 hydrogenation for methane formation. CO dissociation does not control the overall reaction rate on Rh. The most important reaction steps that control the selectivity of ethanol over methane are CH2 and CH3 hydrogenation as well as CHCH3 dehydrogenation.
      • submission_date2039-01-01
      • publication_date2015-07-22
      • selected1
      • created2015-08-20 07:13:20
      • modified2019-10-25 19:29:07
    • GraphicalAbstract(array)
      • id1
      • imagecs-2015-01391b_0012.gif
      • image_dir1
      • created2015-08-20 10:02:15
      • modified2015-08-20 10:02:15
  • 1(array)
    • Publication(array)
      • id15
      • titleQuantum chemistry of the Fischer–Tropsch reaction catalysed by a stepped ruthenium surface
      • authorsFilot, I.A.W., van Santen, R.A., Hensen, E.J.M.
      • journalCatal. Sci. Technol.
      • year2014
      • volume4
      • issue(null)
      • pagerange3129-3140
      • doi10.1039/c4cy00483c
      • graphical_abstract_id7
      • abstractA comprehensive density functional theory study of the Fischer–Tropsch mechanism on the corrugated Ru(1121) surface has been carried out. Elementary reaction steps relevant to the carbide mechanism and the CO insertion mechanism are considered. Activation barriers and reaction energies were determined for CO dissociation, C hydrogenation, CHx + CHy and CHx + CO coupling, CHxCHy–O bond scission and hydrogenation reactions, which lead to formation of methane and higher hydrocarbons. Water formation that removes O from the surface was studied as well. The overall barrier for chain growth in the carbide mechanism (preferred path CH + CH coupling) is lower than that for chain growth in the CO insertion mechanism (preferred path C + CO coupling). Kinetic analysis predicts that the chain-growth probability for the carbide mechanism is close to unity, whereas within the CO insertion mechanism methane will be the main hydrocarbon product. The main chain propagating surface intermediate is CH via CH + CH and CH + CR coupling (R = alkyl). A more detailed electronic analysis shows that CH + CH coupling is more difficult than coupling reactions of the type CH + CR because of the σ-donating effect of the alkyl substituent. These chain growth reaction steps are more facile on step-edge sites than on terrace sites. The carbide mechanism explains the formation of long hydrocarbon chains for stepped Ru surfaces in the Fischer–Tropsch reaction.
      • submission_date2014-04-14
      • publication_date2014-06-19
      • selected1
      • created0000-00-00 00:00:00
      • modified2019-10-25 19:37:19
    • GraphicalAbstract(array)
      • id7
      • imageGA.gif
      • image_dir7
      • created2015-08-20 10:18:24
      • modified2015-08-20 10:18:24
  • 2(array)
    • Publication(array)
      • id16
      • titleThe Optimally Performing Fischer-Tropsch Catalyst
      • authorsFilot, I.A.W., van Santen, R.A., Hensen, E.J.M.
      • journalAngew. Chem. Int. Ed.
      • year2014
      • volume53
      • issue47
      • pagerange12746–12750
      • doi10.1002/anie.201406521
      • graphical_abstract_id5
      • abstractMicrokinetics simulations are presented based on DFT-determined elementary reaction steps of the Fischer–Tropsch (FT) reaction. The formation of long-chain hydrocarbons occurs on stepped Ru surfaces with CH as the inserting monomer, whereas planar Ru only produces methane because of slow CO activation. By varying the metal–carbon and metal–oxygen interaction energy, three reactivity regimes are identified with rates being controlled by CO dissociation, chain-growth termination, or water removal. Predicted surface coverages are dominated by CO, C, or O, respectively. Optimum FT performance occurs at the interphase of the regimes of limited CO dissociation and chain-growth termination. Current FT catalysts are suboptimal, as they are limited by CO activation and/or O removal.
      • submission_date2039-01-01
      • publication_date2014-08-28
      • selected1
      • created0000-00-00 00:00:00
      • modified2019-10-25 19:14:18
    • GraphicalAbstract(array)
      • id5
      • imagenfig003.gif
      • image_dir5
      • created2015-08-20 10:14:32
      • modified2015-08-20 10:14:32
  • 3(array)
    • Publication(array)
      • id4
      • titleSize and Topological Effects of Rhodium Surfaces, Clusters and Nanoparticles on the Dissociation of CO
      • authorsFilot, I.A.W., Shetty, S.G., Hensen, E.J.M., van Santen, R.A.
      • journalJ. Phys. Chem. C
      • year2011
      • volume115
      • issue29
      • pagerange14204-14212
      • doi10.1021/jp201783f
      • graphical_abstract_id14
      • abstractThe present density functional theory study provides insight into the reactivity of the surface metal atoms of extended/periodic Rh surfaces, clusters, and nanoparticles toward CO adsorption and dissociation. Our results demonstrate that the defect site in a B5 configuration is the most active one for CO dissociation on all three considered systems. However, the reactivity of the B5 site for CO dissociation depends critically on the size of the system. The barrier for CO dissociation barrier on the B5 site increases for smaller particles. The lowest barrier is found for the B5 site of a stepped Rh (211) surface. CO dissociation on this site occurred with a barrier below the desorption energy of CO.
      • submission_date2039-01-01
      • publication_date2011-06-15
      • selected1
      • created0000-00-00 00:00:00
      • modified2019-10-25 19:31:34
    • GraphicalAbstract(array)
      • id14
      • imagejp-2011-01783f_0009.gif
      • image_dir14
      • created2015-08-20 10:24:14
      • modified2015-08-20 10:24:14
  • 4(array)
    • Publication(array)
      • id49
      • titleA theoretical study of the reverse water-gas shift reaction on Ni(111) and Ni(311) surfaces
      • authorsZhang, M., Zijlstra, B., Filot, I.A.W., Li, F., Wang, H., Li, J., Hensen, E.J.M.
      • journalCan. J. Chem. Eng.
      • year2019
      • volume0
      • issue(null)
      • pagerangeIn Press
      • doi10.1002/cjce.23655
      • graphical_abstract_id(null)
      • abstractIn this study, a systematic comparison study of the surface redox reaction mechanism for reverse water‐gas shift (RWGS) over Ni(111) and Ni(311) surfaces is presented. Specifically, the most stable surface intermediates and the reaction kinetics involved in the direct CO2 activation and water formation steps are computed with density functional theory calculations and compared for the two different Ni surfaces. The results show that CO2, CO, O, H, OH, and H2O species adsorb stronger on Ni(311) than on Ni(111). Compared to Ni(111), the overall barriers for direct CO2 activation and water formation on Ni(311) are lower by 23 kJ/mol and 17 kJ/mol, respectively. These observations indicate that the RWGS reaction through the surface redox mechanism should be preferred on Ni(311).
      • submission_date2019-10-30
      • publication_date2019-10-03
      • selected0
      • created2019-10-30 18:53:02
      • modified2019-10-30 18:53:02
    • GraphicalAbstract(array)
      • id(null)
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    • Publication(array)
      • id49
      • titleA theoretical study of the reverse water-gas shift reaction on Ni(111) and Ni(311) surfaces
      • authorsZhang, M., Zijlstra, B., Filot, I.A.W., Li, F., Wang, H., Li, J., Hensen, E.J.M.
      • journalCan. J. Chem. Eng.
      • year2019
      • volume0
      • issue(null)
      • pagerangeIn Press
      • doi10.1002/cjce.23655
      • graphical_abstract_id(null)
      • abstractIn this study, a systematic comparison study of the surface redox reaction mechanism for reverse water‐gas shift (RWGS) over Ni(111) and Ni(311) surfaces is presented. Specifically, the most stable surface intermediates and the reaction kinetics involved in the direct CO2 activation and water formation steps are computed with density functional theory calculations and compared for the two different Ni surfaces. The results show that CO2, CO, O, H, OH, and H2O species adsorb stronger on Ni(311) than on Ni(111). Compared to Ni(111), the overall barriers for direct CO2 activation and water formation on Ni(311) are lower by 23 kJ/mol and 17 kJ/mol, respectively. These observations indicate that the RWGS reaction through the surface redox mechanism should be preferred on Ni(311).
      • submission_date2019-10-30
      • publication_date2019-10-03
      • selected0
      • created2019-10-30 18:53:02
      • modified2019-10-30 18:53:02
    • GraphicalAbstract(array)
      • id(null)
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      • image_dir(null)
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  • 1(array)
    • Publication(array)
      • id48
      • titleSupramolecular interactions between catalytic species allow rational control over reaction kinetics
      • authorsTeunissen, A.J.P., Paffen, T.F.E., Filot, I.A.W., Lanting, M.D., van der Haas, R.J.C., de Greef, T.F.A., Meijer, E.W.
      • journalChem. Sci.
      • year2019
      • volume10
      • issue(null)
      • pagerange9115-9124
      • doi10.1039/C9SC02357G
      • graphical_abstract_id44
      • abstractThe adaptivity of biological reaction networks largely arises through non-covalent regulation of catalysts' activity. Such type of catalyst control is still nascent in synthetic chemical networks and thereby hampers their ability to display life-like behavior. Here, we report a bio-inspired system in which non-covalent interactions between two complementary phase-transfer catalysts are used to regulate reaction kinetics. While one catalyst gives bimolecular kinetics, the second displays autoinductive feedback, resulting in sigmoidal kinetics. When both catalysts are combined, the interactions between them allow rational control over the shape of the kinetic curves. Computational models are used to gain insight into the structure, interplay, and activity of each catalytic species, and the scope of the system is examined by optimizing the linearity of the kinetic curves. Combined, our findings highlight the effectiveness of regulating reaction kinetics using non-covalent catalyst interactions, but also emphasize the risk for unforeseen catalytic contributions in complex systems and the necessity to combine detailed experiments with kinetic modelling.
      • submission_date2019-05-15
      • publication_date2019-08-14
      • selected0
      • created2019-10-25 19:49:27
      • modified2019-10-25 19:49:27
    • GraphicalAbstract(array)
      • id44
      • imageimg.gif
      • image_dir44
      • created2019-10-25 19:50:09
      • modified2019-10-25 19:50:09
  • 2(array)
    • Publication(array)
      • id47
      • titleEfficient Base-Metal NiMn/TiO2 Catalyst for CO2 Methanation
      • authorsVrijburg, W.L., Moioli, E., Chen, W., Zhang, M., Terlingen, B.J.P., Zijlstra, B., Filot, I.A.W., Zuttel, A., Pidko, E.A., Hensen, E.J.M.
      • journalACS Catal.
      • year2019
      • volume9
      • issue9
      • pagerange7823-7839
      • doi10.1021/acscatal.9b01968
      • graphical_abstract_id43
      • abstractEnergy storage solutions are a vital component of the global transition toward renewable energy sources. The power-to-gas (PtG) concept, which stores surplus renewable energy in the form of methane, has therefore become increasingly relevant in recent years. At present, supported Ni nanoparticles are preferred as industrial catalysts for CO2 methanation due to their low cost and high methane selectivity. However, commercial Ni catalysts are not active enough in CO2 methanation to reach the high CO2 conversion (>99%) required by the specifications for injection in the natural gas grid. Herein we demonstrate the promise of promotion of Ni by Mn, another low-cost base metal, for obtaining very active CO2 methanation catalysts, with results comparable to more expensive precious metal-based catalysts. The origin of this improved performance is revealed by a combined approach of nanoscale characterization, mechanistic study, and density functional theory calculations. Nanoscale characterization with scanning transmission electron microscopy-energy- dispersive X-ray spectroscopy (STEM-EDX) and X-ray absorption spectroscopy shows that NiMn catalysts consist of metallic Ni particles decorated by oxidic Mn2+ species. A mechanistic study combining IR spectroscopy of surface adsorbates, transient kinetic analysis with isotopically labeled CO2, density functional theory calculations, and microkinetics simulations ascertains that the MnO clusters enhance CO2 adsorption and facilitate CO2 activation. A macroscale perspective was achieved by simulating the Ni and NiMn catalytic activity in a Sabatier reactor, which revealed that NiMn catalysts have the potential to meet the demanding PtG catalyst performance requirements and can largely replace the need for expensive and scarce noble metal catalysts.
      • submission_date2019-10-25
      • publication_date2019-07-17
      • selected0
      • created2019-10-25 19:46:45
      • modified2019-10-25 19:46:45
    • GraphicalAbstract(array)
      • id43
      • imagecs-2019-019689_0012.gif
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      • created2019-10-25 19:46:57
      • modified2019-10-25 19:46:57
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