Update README.md

README.md

@@ -25,28 +25,93 @@ Legendre quadrature (200 radial points) and Lebedev quadrature (noted as 031, 35
 ```shell
 # 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
+$ 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
+$ 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,
+$ cd ../eneden/
+$ chmod +x eneden.sh
+$ ./eneden.sh ch4 # Here STDOUT will give the values of summing up of the energy density,
                 # 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
+$ 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)
+```bash
+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**
+
+```shell
+# 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)
+```bash
+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**.
+
+
+