README.md

Møller–Plesset Correlation Energy Density Generator

This is python code of generating MP2, MP3, and MP4 correlation energy density based on one boby decomposition scheme (https://doi.org/10.1002/qua.22017)

Requirement of python packages:

numpy, scipy, h5py, torch, quadpy, itertools, mmap, tqdm

Optional of python packages:

pycuda, skcuda # if you use GPU for preparing Ajb

Requirement of external packages to run example files:

psi4 # to generate wavefunction and FCIDUMP file
molden2aim # to convert molden format to .WFN

Examples

ch4_200_031

This is to calculate energy density on Carbon and Hydrogen atom of CH4@3-21g with grid settings: Legendre quadrature (200 radial points) and Lebedev quadrature (noted as 031, 350 angular points).

# prepare wavefunction and FCIDUMP files, here we use Psi4 package
# one can also use other packages, e.g. PySCF, OpenMolcas
$ cd examples/ch4_200_031/calcu/
$ psi4 -n 8 -i input.dat -o output.dat

# convert molden format of wavefunction and txt format of FCIDUMP (in Psi 4 is INPDUMP)
# into .npy files
# Note that external package is needed to convert molden to .wfn first, we use molden2aim 
# (https://github.com/zorkzou/Molden2AIM) for example.
$ cd ../prep/
$ chmod +x mlcorr_prep.sh
$ ./mlcorr_prep.sh ch4

# calculate MP2 MP3 MP4 energy density
$ cd ../eneden/
$ chmod +x eneden.sh
$ ./eneden.sh ch4 # Here STDOUT will give the values of summing up of the energy density on each atom,
                # which should equals to MPn correlation energy

# calculate reference value:
$ cd ../ref/
$ psi4 -n 8 -i input.dat -o output.dat # you can find reference MP2, MP3, and MP4
                                     # correlation energy in output.dat

Results: contribution for each atom (Atomic Contribution)

PT2: 
C: -0.0713488682277866
H: -0.0072268498366822
PT3:
C: -0.0056150246921240
H: -0.0019143657456038
PT4:
C: -0.0031286420616285
H: -0.0005634905197682

Combine:
MP2: -0.1002562675745154
MP3: -0.1135287552490546
MP4(SDTQ): -0.1189113593897559

Compare with reference correlation energy:
MP2: -0.099901794206
MP3: -0.113086192916
MP4(SDTQ): -0.118437326291

~0.5 mH deviation is due to the integration issue. One can decrease by further increase the density of quadratures, or redistribute the deviation to each atom.

ch4_50_011

This is to calculate energy density on Carbon and Hydrogen atom of CH4@3-21g with grid settings: Legendre quadrature (50 radial points) and Lebedev quadrature (noted as 011, 50 angular points). Note that this example settings is not recommended for calculation

# First you need to modify:
codes/prep/Becke_grid.py:
qd.line_segment.gauss_legendre(200) -> qd.line_segment.gauss_legendre(50)
qd.sphere.lebedev_031() -> qd.sphere.lebedev_011()

# Others same with ch4_200_031

Results: contribution for each atom (Atomic Contribution)

PT2: 
C: -0.0731792208782222
H: -0.0073744070379437
PT3:
C: -0.0059725794473153
H: -0.0019610653069297
PT4:
C: -0.0032755188689802
H: -0.0005762340521139

Combine:
MP2: -0.102676849029997
MP3: -0.116493689705031
MP4(SDTQ): -0.1220741447824669

Compare with reference correlation energy:
MP2: -0.099901794206
MP3: -0.113086192916
MP4(SDTQ): -0.118437326291

~3.5 mH deviation is too large, so this setting is not recommended.

h2

This is to calculate energy density on Hydrogen atom of H2@cc-pvdz with grid settings: Legendre quadrature (200 radial points) and Lebedev quadrature (noted as 031, 350 angular points).

# prepare wavefunction and FCIDUMP files, here we use Psi4 package
# one can also use other packages, e.g. PySCF, OpenMolcas
$ cd examples/h2/calcu/
$ psi4 -n 8 -i input.dat -o output.dat

# convert molden format of wavefunction and txt format of FCIDUMP (in Psi 4 is INPDUMP)
# into .npy files
# Note that external package is needed to convert molden to .wfn first, we use molden2aim 
# (https://github.com/zorkzou/Molden2AIM) for example.
$ cd ../prep/
$ chmod +x mlcorr_prep.sh
$ ./mlcorr_prep.sh h2

# calculate MP2 MP3 MP4 energy density
$ cd ../eneden/
$ chmod +x eneden.sh
$ ./eneden.sh h2 # Here STDOUT will give the values of summing up of the energy density on each atom,
                 # which should equals to MPn correlation energy

# calculate reference value:
$ cd ../ref/
$ psi4 -n 8 -i input.dat -o output.dat # you can find reference MP2, MP3, and MP4
                                       # correlation energy in output.dat

Results: contribution for each atom (Atomic Contribution)

PT2: 
H: -0.0132622797812593
PT3:
H: -0.0031027482505314
PT4:
H: -0.0007878420821888

Combine:
MP2: -0.0265245595625186
MP3: -0.0327300560635814
MP4(SDTQ): -0.034305740227959

Compare with reference correlation energy:
MP2: -0.026443871885
MP3: -0.032632881103
MP4(SDTQ): -0.034205101033

~0.1 mH deviation.