A study of H+H2 and several H-bonded molecules by phaseless auxiliary-field quantum Monte Carlo with plane wave and Gaussian basis sets

Abstract

We present phaseless auxiliary-field (AF) quantum Monte Carlo (QMC) calculations of the ground states of some hydrogen-bonded systems. These systems were selected to test and benchmark different aspects of the new phaseless AF QMC method. They include the transition state of H+H2 near the equilibrium geometry and in the van der Walls limit, as well as H2O, OH, and H2O2 molecules. Most of these systems present significant challenges for traditional independent-particle electronic structure approaches, and many also have exact results available. The phaseless AF QMC method is used either with a planewave basis with pseudopotentials or with all-electron Gaussian basis sets. For some systems, calculations are done with both to compare and characterize the performance of AF QMC under different basis sets and different Hubbard-Stratonovich decompositions. Excellent results are obtained using as input single Slater determinant wave functions taken from independent-particle calculations. Comparisons of the Gaussian based AF QMC results with exact full configuration show that the errors from controlling the phase problem with the phaseless approximation are small. At the large basis-size limit, the AF QMC results using both types of basis sets are in good agreement with each other and with experimental values.

Excited state calculations using phaseless auxiliary-field quantum Monte Carlo: Potential energy curves of low-lying C2 singlet states

“…In this subsection, we present phaseless AFQMC/CASSCF PECs with large basis sets and compare with experimental spectroscopic values. Figure 5 shows AFQMC/CASSCF PECs for the three lowest lying singlet states, using truncated CASSCF (8,16) wave function as |Φ r , in the cc-pVTZ basis set. 26 For comparison, the figure also shows the RCCSD(T) ground state PEC, which was calculated using the NWCHEM 34 computer program.…”

“…As described in Sec. II C, these are truncated CASSCF (8,16) wave functions, with no further optimization. Figure 4 compares the AFQMC/CASSCF and FCI calculated PECs.…”

“…9,29 In previous applications, phaseless AFQMC with a single unrestricted Hartree-Fock (UHF) determinant |Φ UHF r was found to often give better overall and more uniform accuracy than CCSD(T) in mapping PECs. 11,15,16 In some cases, however, such as the BH and N 2 molecules, achieving quantitative accuracy of a few mE h for the entire PEC required multi-determinant |Φ r . 17 We also find this to be true for the C 2 molecule, as discussed below.…”

“…Most of our AFQMC calculations use as |Φ r a truncated CASSCF (8,16) wave function, obtained from the GAMESS quantum chemistry program. 32 The CASSCF wave function is truncated such that the weight (squared coefficient) of the retained determinants is ∼ 97% of the total.…”

“…), and it exhibits favorable O(M 3 -M 4 ) scaling. For ground states, the new AFQMC method has been applied to close to 100 systems, including first-and second-row molecules, 11,12,13 transition metal oxide molecules, 10 simple solids, 9,14 post-d elements, 15 van der Waals systems, 16 and in molecules in which bonds are being stretched or broken. 17,18 In these calculations we have operated largely in an automated mode, inputting only the DFT or Hartree-Fock (HF) solutions as trial wave functions.…”