This is an old revision of the document!
In order to go beyond GGA and hybrid DFT, one option is to use wave function correlation methods. Recently, second-order Møller-Plesset perturbation theory (MP2) and random phase approximation (RPA) have been added to CP2K 10.1016/j.cpc.2014.10.021, 10.1021/ct4002202, 10.1021/ct300531w. The implementations are aimed at condensed phase calculations (see e.g. 10.1021/jz401931f and 10.1021/jz501985w), and in the case of MP2 provides energies, forces and stress (see 10.1063/1.4919238 and 10.1021/acs.jctc.6b00015), and electron (spin) densities at O(N^5) cost, while RPA provides energies at O(N^4) or O(N^3) cost.
However, significant computational resources are needed for the condensed phase calculations. Therefore, we will perform the gas phase calculations in this tutorial, even though RI-GPW is not very efficient in this case.
1. Task: Benzene dimer MP2 binding energy
Employ the provided input file to compute the benzene dimer binding energy. The provided dimer geometry is optimized already. To obtain the energy of the monomer, geometry optimization is necessary (or else is not). Perform a few optimization steps to see how much the energy changes and to calculate electron density (saved as .cube files) at the MP2 level.
Topics:
- RI approach (
RI_MP2_GPW
andRI_AUX_BASIS_SET
) - Wavelet solver (
PSOLVER WAVELET
,CENTER_COORDINATES
) - gas phase HFX calculation
- memory issues (
FREE_HFX_BUFFER
)
Required files
input file for an RI-MP2 calculation on a benzene dimer
- benzene_dimer.inp
&GLOBAL PROJECT benzene_dimer RUN_TYPE ENERGY &END GLOBAL &FORCE_EVAL METHOD Quickstep &DFT ! specification of basis and potential files (cp2k/data) BASIS_SET_FILE_NAME HFX_BASIS POTENTIAL_FILE_NAME HF_POTENTIALS ! Wave function restart file to accelerate HF convergence WFN_RESTART_FILE_NAME benzene_dimer.wfn &MGRID CUTOFF 400 &END MGRID &QS METHOD GPW EPS_DEFAULT 1.0E-10 EPS_PGF_ORB 1.0E-8 &END QS ! standard OT &SCF SCF_GUESS ATOMIC EPS_SCF 1.0E-6 MAX_SCF 40 &OT MINIMIZER CG PRECONDITIONER FULL_SINGLE_INVERSE &END &OUTER_SCF EPS_SCF 1.0E-6 MAX_SCF 10 &END &END SCF ! Non periodic calculation needs Poisson solver: use wavelet solver &POISSON PERIODIC NONE PSOLVER WAVELET &END POISSON &XC ! no XC functional &XC_FUNCTIONAL NONE &END XC_FUNCTIONAL ! and 100%HFX &HF FRACTION 1.0 &SCREENING EPS_SCHWARZ 1.0E-9 &END SCREENING &MEMORY MAX_MEMORY 1800 &END &END HF ! with WF correlation &WF_CORRELATION ! use the RI-GPW approach METHOD RI_MP2_GPW &WFC_GPW CUTOFF 200 REL_CUTOFF 50 &END ! block sizes and memory affect parallel efficiency &RI_MP2 BLOCK_SIZE 1 &END MEMORY 1800 NUMBER_PROC 1 &END &END XC &END DFT &SUBSYS ! sufficiently large non-periodic unit cell &CELL ABC [angstrom] 12 12 12 PERIODIC NONE ! Non periodic calculation. &END CELL ! specification of the system with coordinates &COORD H 8.5709951714 6.1617188657 9.1769626364 C 8.0387778483 5.9757981379 8.2528397815 C 6.6427474511 5.9561428224 8.2430496957 H 6.0937543445 6.1249650636 9.1610309894 C 5.9546039990 5.7314555716 7.0475649921 H 4.8717398728 5.7196290593 7.0404902271 C 6.6635660065 5.5279574532 5.8611612413 H 6.1300650069 5.3536860275 4.9350551393 C 8.0615723757 5.5446390494 5.8709776417 H 8.6121087088 5.3836499080 4.9523278088 C 8.7479484762 5.7683467907 7.0666774749 H 9.8306982448 5.7893185194 7.0736980974 H 6.4284687494 8.8405192314 5.8228620343 H 8.9057373702 8.8752743844 5.8387264727 C 6.9607954533 9.0255100555 6.7471184900 C 8.3568440363 9.0439429763 6.7567676586 C 6.2520232187 9.2329626290 7.9335080936 C 9.0454365692 9.2673522387 7.9522880615 H 5.1692478273 9.2131682112 7.9263504668 H 10.1283042427 9.2780238064 7.9594286415 C 6.9387312641 9.4553058890 9.1292884396 C 8.3367433685 9.4704785560 9.1388664843 H 6.3883177411 9.6163935534 10.0479844468 H 8.8703567259 9.6435467092 10.0651664724 &END ! keep atoms away from box borders, ! a requirement for the wavelet Poisson solver &TOPOLOGY &CENTER_COORDINATES &END &END TOPOLOGY ! MP2 needs correlation consistent basis set ! RI-MP2 needs an auxiliary basis set ! We employ HF pseudo potentials &KIND H BASIS_SET cc-TZV2P-GTH RI_AUX_BASIS_SET TZ_fiodena_opt POTENTIAL GTH-HF-q1 &END KIND &KIND C BASIS_SET cc-TZV2P-GTH RI_AUX_BASIS_SET TZ_fiodena_opt POTENTIAL GTH-HF-q4 &END KIND &END SUBSYS &END FORCE_EVAL ! how to propagate the system, selection via RUN_TYPE in the &GLOBAL section &MOTION &GEO_OPT OPTIMIZER BFGS ! Good choice for 'small' systems (use LBFGS for large systems) MAX_ITER 100 MAX_DR [bohr] 0.003 ! adjust target as needed &BFGS &END &END &END
During the optimization of benzene, one will calculate gradient which, in turn, requires density matrices. Hence, one can calculate electronic densities. Add the following to the &GLOBAL section:
&PRINT MEDIUM &END
and the following lines to the &DFT section
&PRINT &E_DENSITY_CUBE MEDIUM &END &END
Importantly, during the force calculations one will have to solve the coupled-perturbed equations invoking exact exchange calculations. If there is enough memory we can reuse the integrals from the HF calculation by setting the following keyword in the &RI_MP2 section:
FREE_HFX_BUFFER .FALSE.