The CASINO forum

Hi all.

There are orbital optimized methods http://www.ncbi.nlm.nih.gov/pubmed/26609985, http://pubs.acs.org/doi/abs/10.1021/ct500231c implemented in ORCA abd PSI4 programs.
The fundamental idea of the OO-MP2 method is to not only minimize the MP2 energy with respect to the MP2 amplitudes but also to minimize the total energy with respect to changes in the orbitals.
It is also known that in DMC when using Slater-Jastrow trial wave functions we can recover about 90-95% of the correlation energy almost universally, in atoms, molecules, solids, quantum liquids, etc.
So I want to find out is orbital optimized trial wave function better than Slater with respect to fixed node errors in DMC because of orbital optimisation.

Using standard methane geometry

C 0.000000 0.000000 0.000000
H 0.629118 0.629118 0.629118
H -0.629118 -0.629118 0.629118
H 0.629118 -0.629118 -0.629118
H -0.629118 0.629118 -0.629118

DLPNO-CCSD(T) http://pubs.acs.org/doi/abs/10.1021/ct501129s gave me the following energies (in au) with respect to basis sets used:
All energies were calculated without FrozenCore approximation using core–valence Gaussian basis sets.

cc-pCVDZ -40.425659323543
cc-pCVTZ -40.486163601621
cc-pCVQZ -40.503576715705
cc-pCV5Z -40.506805310140
extrapolated to CBS -40.5103 +/- 0.001178 // eq. (4) in http://scitation.aip.org/content/aip/jo ... /1.3613639

For DMC trial wave functions I'am using cc-pV6Z basis truncated to g-orbitals because CASINO can't works with orbitals higher than g-orbitals.

Jastrow optimisation were used in casl format with next terms:
Rank [2,0], Order 2
Rank [1,1], Order 2
Rank [2,1], Order 5, only for C-atom

After VMC I've got:

HF trial WFN -40.471(2) ; var = 0.23(1)
OO-MP2 trial WFN -40.471(2) ; var = 0.219(4)

That's almost equal.


DMC with dmc_target_weight=1000, dmc_equil_nstep=1000, dmc_stats_nstep=1000000 and dt=0.003 gave me following energies:

HF trial WFN -40.506079299206 +/- 0.000153569483 +/- 0.000006964038
OO-MP2 trial WFN -40.506538740532 +/- 0.000157445282 +/- 0.000007139797

Сan we assume that orbital-optimized trial wave function is better than Slater?

with respect, Vladimir.

UPD

with OO-MP2 orbitals on cc-pCV6Z truncated up to g-orbitals I've got even better result:

DMC with dmc_target_weight=2000, dmc_equil_nstep=1000, dmc_stats_nstep=1000000 and dt=0.003 gave me following energies:

HF orbitals (cc-pV6Z_truncated) = -40.506027169422 +/- 0.000105457704
OO-MP2 orbitals (cc-pCV6Z_truncated) = -40.506855158744 +/- 0.000106808965