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Projection Code Instructions and guide lines By BDD 2/25/15

A description of the projection algorithm can be found in: Dunnington and Schmidt, JCTC; 8, 1902-1911 (2012)

This projection code is capable of representing any plane-wave bands output by VASP into any user specified Gaussian type orbital basis set. Such an AO representation is required for the subsequent NBO analysis. The code is set up to then output all information necessary for periodic NBO analysis using the code of JRS and BDD.

BASIC RECIPE*

1. Insert projection_output.F into directory containing VASP source code and apply proj_VASP.patch (alternatively, there is also a patch available for CRYSTAL).

2. Run VASP calculation with LNBO=.TRUE. in INCAR (creates wavefunction.dat)

3. Command to run the projection with optional arguments in brackets ./projection.exe [basis.inp] [wavefunction.dat] [NBO.out] NOTE: basis.inp must obey Gaussian94 format

COMMON PROBLEMS

If the code crashes and prints "Segmentation fault." you need to increase OMP_STACKSIZE.

Make sure the order of atom types in the basis.inp files matches that of the POTCAR file used for the VAsP calculation.

Using diffuse AO-basis functions will cause problems due to the creation of linear dependencies. These functions are not useful for bulk systems and are also incompatible with NBO analysis. A good rule of thumb is no exponents much lower than 0.1 bohr^-2.

Balance is the most important characteristic when determining the quality of a basis set for projecting into. For instance, using a quadruple-zeta basis for atoms in an adosrbate with a double-zeta basis for surface atoms will give artificially polarized results. This means you should be careful when using basis sets for different atom types from different sources.

VASP Modification

VASP must be modified to output the necessary information that can then be read by the projection code. There are two aspects of this modification process:

1. Inclusion of module, 'projection_output.F' This module is included in the tar and needs to be copied into the directory containing the VASP source code. For VASP 4 and VASP 5.3 you will also need to modify the makefile. In the list labelled 'SOURCE' you will need to include 'projection_output.o'at the end of the list. No modification of the makefile is required for VASP 5.4.
2. Apply proj_VASP.patch You will need to apply the appropriate patch based on the version of VASP you are using. The patch is called 'proj_VASP_{version #}.patch'. It can be applied to the VASP source code using the command "patch < proj_VASP_{version #}.patch" This will modify main.F to call our output subroutine as well as create a logical variable that controls printing of the output.

Running VASP*

For VASP to print the necessary output, the line LNBO=.TRUE. must be included in the INCAR. This will produce an unformatted file called wavefunction.dat that can be read by the projection algorithm. There are a few limiations on other parameters of the VASP run as well:

1. ISYM=0 Turning off k-point symmetry is not required for the projection algorithm, as the process is performed uniquely at each k-point. However, if you are interested in performing a real-space analysis, i.e. NBO, k-point symmetry will need to be turned off in the VASP calculatio as our implementation of inverse Fourier Transforms is not compatible with symmetry.
   NOTE: ISYM=-1 is not recommended.

2. Gamma-point containing k-point mesh. To take advantage of the inversion symmetry of the Brillouin zone, the first k-point is assumed to be the gamma point.

3. NPAR must be left at default values.

4. NO ULTRASOFT PSEUDOPOTENTIALS. There is no functional form associated with this pseudopotential and it is therefore impossible to project a correction for the valence electrons' interaction with the core electrons. This means the valence bands will each reprensent a (different) incorrect number of electrons. Norm conserving and PAW type pseudopotentials are compatible with the code.

The algorithm should be compatible with all other VASP options, including spin polarized calculations.

Compiling the Projection*

The makefile contained with this file will produce an executable called 'projection.exe'. The code uses algorithms from BLAS and LAPACK. We have used the MKL versions. Modifications to both linking and the subroutine calls will need to be made if MKL libraries are not available.

Running the Projection*

This executable then runs with three (optional) inputs. They are listed below in order they will be read in by the program, along with the default file name the program will look for in the working directory.

1. Basis set file. 'basis.inp' This should contain all information on the atomic orbital basis set to be used, in the format of Gaussian94. This means any header can be used, but each atom type must begin and end with a line of '****'. Basis set orbital types can include everything up to f-type, including 'sp'-labeling. Order of the atom types must match that of the POTCAR used in the VASP run.

2. VASP output file. 'wavefunction.dat' This file is output from our customized version of VASP as wavefunction.dat and contains all necessary information about the plane-wave output for use in the projection.

3. NBO input file. 'NBO.out' This file contains information, in a readable format, necessary for the periodic NBO code of JRS and BDD. The header of the file contains information on the basis set as well as atoms of the system. It also contains the k-points utilized in the VASP calculation (where the projection has been performed) as well as the indices of the real space unit cells that will be used in the NBO computation. This set of unit cells is only those which are nearset neighbors to the central unit cell. The actual matrices are stored in 'NBO_mat.out'. For each k-point there is an overlap, density and fock matrix (two density and fock for spin polarized calculations). This file is unformatted for memory considerations as well as efficient input/output. The file name of the matrix storage is placed at the end of 'NBO.out' and read from there by the NBO code, so it will have to be changed if the file name is changed.

A few steps in the algorithm parallelized using Open MP. Some of the default environmental variables related to this are not optimal and should be changed:

1. OMP_NUM_THREADS controls how many threads are parallelized over. If this is not set, the code will try to use as many as possible. This should be set to how many processors are actually available. Not a functionality concern, just courteous.

2. OMP_STACKSIZE controls the amount of memory given to each thread of parallelization. The default is way too low. If this is too low, the code will crash and simply display 'Segmentaion fault.' I have found that setting this to 800mb is sufficient for even surface supercells.

Output Files*

The projection code outputs a couple of additional files.

1. 'spillover.out' Contains quantitative information on the quality of the projection. SPILLOVER is defined as in Eq 10 of the periodic NBO paper. For norm-conserving pseudopotentials, this value is rigorously bound by 0 and 1. However, for PAW-type pseudopotentials, approximations are made in calculating atomic orbital-augmenter overlap and this constraint is lifted. As a result the spillover sum includes both positive and negative terms. To account for this we have defined the SPREAD parameter, which is defined the same as spillover, except using the absolute value for all terms within the summation. Both spillover and spread are calculated across all bands, as well as only those that are occupied, and therefore contribute to the density matrix. Additionally, NO norm should be above 1.01 and a tally of occupied bands who breach this limit is included in this file.

   Additionally, atomic weighted spread and spillover are provided based on occupied bands. These are calculated similarly to Eq 10, except there is now a weighting (and normalization factor) calculated as the sum of the squares of the coefficients in the projected band of all basis functions centered on a particular atom.

   Finally is a listing of the occupied band that the AO basis does the worst job in representing, gauged by the spread of that band, for each k-point. These give an upward bound on the error incurred using a projection

2. 'band_spillover.out' This contains the norm of each projected band, for each spin at each k-point. This just gives a more detailed picture of the information summarized in the spillover.out file.

The program also outputs information to the screen. This mainly consists of system information from the VASP wavefunction file. Additionally after the projection the density and fock matrices (in the projected matrices) are checked by calculating the associated observable, number of electrons and sum of orbital eigenvalues respectively. These are also calculated from the VASP input at the beginning of the calculation.

Sample Calculations

Included are three sample systems to run; bulk silicon, magnesium oxide, and nickel.

First I have included a script to run the projection program. Note that two environmental parameters related to Open_MP paralllelization have been set. Both should be set when running the code, especially OMP_STACKSIZE which controls the memory for each thread included. The default is low and even if only one processor is used, the code can crash here. If the code crashes and just prints 'Segmentation fault.' this is the problem. I have found that export OMP_STACKSIZE=800mb is sufficient for most systems.

For each system, I have included 3 of the 4 VASP input files. There are also AO basis sets included for each system.

Si: Standard 3-21G(d) basis set

MgO: 6-311G(d) basis set with outermost valence functions removed.
Linear dependencies arise very easily in periodic systems and any basis function with an exponent below 0.1 bohr^-2 is probably going to cause problem. While the projection code is enabled to deal with these linear dependencies, NBO is not. In general, diffuse AO-functions should always be avoided for periodic systems.

Ni: Modified 6-31G basis set. Details of the modification process can be found in the supporting information of: Journal of Catalysis, 324, 50-58, (2015). The overall strategy is to modulate the sp-functions' exponent to limit linear dependencies, then modify the d-function's exponent to account for the bulk environment. For main group or molecular solids, gas-phase basis sets can often be applied (perhaps requiring trimming). However, bulk transition metals are not represented as well with gas-phase basis sets and requie more involved basis set development.

One final note about basis sets: It should be noted that even though the VASP results only explicitly include valence electrons, the core basis functions remain in all sets. These functions help in capturing the PAW effect's on the orbitals. The core region of the valence orbitals is oscillatory and can in general not be well represented by only the smoothly varying valence like AO-basis functions.

Periodic NBO instructions and guidelines by BDD 2/26/15

A description of the algorithm can be found in: Dunnington and Schmidt, JCTC; 8, 1902-1911 (2012)

This code will calculate the complete set of Natural Bond Orbitals for a periodic system.

BASIC RECIPE*

1. Run an interface code to get NBO.out and NBO_mat.out

2. Command to run NBO analysis with optional arguements in brackets ./nbo.exe NBO.out [nbo.chk]

3. Control calculation parameters via nbo.config file.

COMMON PROBLEMS

If the code crashes and prints "Segmentation fault." you need to increase OMP_STACKSIZE.

Diffuse AO-basis functions are not compatible with NPA and NBO analysis. The definition of 'too diffuse' is more restrictive for bulk systems due to the increased density and number of nearest neighbors.

If you are planning to write a checkpoint file, the name you supply must not match that of an existing file in the working directory. Otherwise, the code will try to read the already existing file as a checkpoint.

*Compiling Periodic NBO

The makefile contained with this file will produce an executable called 'nbo.exe'. The code uses algorithms from BLAS and LAPACK. We have used the MKL versions. Modifications to both linking and the subroutine calls will need to be modified if the MKL libraries are not available.

Running Periodic NBO*

The executable, 'nbo.exe,' runs with two inputs. They are listed below in order they will be read in by the program, along with sample values.

1. System parameters file 'NBO.out' This is a mandatory input and should be the name of the file containing all the necessary information for NBO analysis. This file is produced from the projection code or CRYSTAL interface. The code assumes a specific format and ordering of information in the file. This file does not contain any matrices, which should be stored in a separate unformatted file. The name of the unformatted file should be included here.

2. Checkpoint file 'nbo.chk' The second input is optional and is the name of a checkpoint file. Since performing the transformation into the NAO basis is the rate limiting step of the calculation, the density matrix in this basis can be stored in a checkpoint file so that this step need only be performed once. The code will check to see if the name given matches an existing file in the working directory. If a file with that name does not exist, the code will run the calculation to obtain the NAO basis, then write a checkpoint file with the given name. If a file with that name does exist, the code will try to read it as a checkpoint file instead of calculating the NAO basis.

Output*

Most code output is sent to the screen. This includes:

Natural Population Analysis Natural Atomic Orbital list for all atoms, with occupancy Natural Bond Orbitals -Lone Pairs -Bonds & Anti-Bonds -Rydberg Orbitals w/ Occupancy above 10^-3

For each NBO, the following information is given:

Occupancy Hybridization Coefficients of Natural Hybrid Orbitals in NAO basis. The order is the same as in NAO occupancy listing.

The only output file is nbo_vis.out that contains information that can be used to generate .cube files of each NBO obtained in the analysis. The program capable of

Configuration File*

The nbo.config file is the primary method for controlling parameters in of the calculation. Upon execution of the program, it will look to see if if such a file exists. If the nbo.config file does not exist, default parameters will be used and a new nbo.config file will be produced. If the nbo.config file does exist, parameters will be read in. A given format/ordering of parameters is expected by the code, so modification of an automatically generated nbo.config file is the safest method of creation.

As of now this file controls two things:

1. Occupancy cutoffs used in the NBO search algorithm. The code is setup to perform an NBO search with a hard occupancy cutoff. Different cutoffs can be set for lone pairs and bonds. Use of a checkpoint file is encouraged if you will be varying these cutoffs.
2. Visualization output of NBOs The code can output .cube files containing gridded representations of any desired NBOs. Default is to output nothing, and it is recommended to identify relevant NBOs before creating any .cube files. Visualization will be explained more in its own section.

Visualization Output*

If visualization of the NBOs is desired, the code can generate .cube files of the gridded electron density, or wavefunction of each orbital. Due to periodic boundary conditions the volume of a given orbital need not reside solely in the central unit cell and thus any grid must extend beyond the central unit cell. However an explicit representation of the central unit cell is useful for visualization purpose. TO address this, two types of files are created

1. lattice_vec.cube - This is a cube file containing only atoms, where the a,b,c vectors are the same as the central unit cell. The idea is to have a set of vectors for a single unit cell, but include some atoms from neighboring unit cells.

2. nbo_xxx.cube - This contains an isosurface of the xxxth nbo. The a,b,c vectors used here are defined by the user and may be larger than a standard unit cell and the 'origin' is shifted off of the unit cell's. The ordering of the NBO's is: i. Lone pairs in the order they were printed to the screen. ii. Paired bonds and antibonds in the order they were printed to the screen. Bonds are first. iii. Rydberg orbitals in order of increasing occupancy by atom. The ones printed to the screen had the highest occupancy and are therefore last in a given atom's list.

In addition to whether or not to visualize, a variety of parameters are controlled in the nbo.config file. In order they are:

1. density - [T or F] Whether to grid out the density or the wavefunction.
2. vis_start vis_end - [Two integers] The beginning and end of the range of NBO's to plot.
3. mesh - [Three integers] Resolution of grid point along each lattice direction. Note this is of the larger box.
4. box_int - [Three integers] How many total lattice cell vector lengths to include along each side of the large box for orbital visualization.
5. origin_fact - [One real] How to shift the origin of the large box with respect to the central unit cell origin.

Some useful values for box size: -To include the central unit cell along with half of each surrounding unit cell for orbital visualization: bulk_int = 2 2 2 origin_fact = -0.5 -To only incloud the central unit cell for orbital visualization (useful for VASP supercells): bulk_int = 1 1 1 origin_fact = 0.0