We introduce a black-box auxiliary field quantum Monte Carlo (AFQMC) approach to perform highly accurate electronic structure calculations using configuration interaction singles and doubles (CISD) trial states. This method consistently provides more accurate energy estimates than coupled cluster singles and doubles with perturbative triples (CCSD(T)), often regarded as the gold standard in quantum chemistry. This level of precision is achieved at a lower asymptotic computational cost, scaling as O ( N 6 ) compared to the O ( N 7 ) scaling of CCSD(T). We provide numerical evidence supporting these findings through results for challenging main group and transition metal-containing molecules.
We introduce a black-box auxiliary field quantum Monte Carlo (AFQMC) approach to perform highly accurate electronic structure calculations using configuration interaction singles and doubles (CISD) trial states. This method consistently provides more accurate energy estimates than coupled cluster singles and doubles with perturbative triples (CCSD(T)), often regarded as the gold standard in quantum chemistry. This level of precision is achieved at a lower asymptotic computational cost, scaling as O ( N 6 ) compared to the O ( N 7 ) scaling of CCSD(T). We provide numerical evidence supporting these findings through results for challenging main group and transition metal-containing molecules.
In this work, we develop a size extensive Auxiliary-Field Quantum Monte Carlo (AFQMC) approach that scales as O(N5) for local energy evaluation by treating the Coupled Cluster Singles and Doubles (CCSD) trial wavefunctions perturbatively. Comprehensive numerical examinations, spanning from main-group molecules to 3d transition metal complexes, demonstrate that this perturbative treatment introduces negligible bias. For small systems, our method achieves an accuracy and level of noise comparable to AFQMC with configuration interaction singles and doubles (CISD) trial wavefunctions while outperforming CCSD(T). This size extensivity offers a decisive advantage for large systems, as suggested by the ground state energies of non-interacting monomers and one-dimensional atomic chains. Finally, the numerical simulations of the uniform electron gas (UEG) provide evidence that, unlike the CCSD(T) method, our new approach does not suffer from infrared divergence in the thermodynamic limit (TDL).
In this work, we develop a size-extensive Auxiliary-Field Quantum Monte Carlo (AFQMC) approach that scales as O(N5) for local energy evaluation by perturbatively treating the Coupled Cluster Singles and Doubles (CCSD) trial wavefunctions. Comprehensive numerical examinations, spanning from main-group molecules to 3d transition metal complexes, demonstrate that this perturbative treatment introduces negligible bias. For small systems, our method achieves an accuracy and level of noise comparable to AFQMC with configuration interaction singles and doubles trial wavefunctions while outperforming CCSD(T). This size extensivity offers a decisive advantage for large systems, as suggested by the ground state energies of non-interacting monomers and one-dimensional atomic chains. Finally, the numerical simulations of the uniform electron gas provide evidence that, unlike the CCSD(T) method, our new approach does not suffer from infrared divergence in the thermodynamic limit.
In this work, we present an overview of the phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) approach from a computational quantum chemistry perspective and present a numerical assessment of its performance on main group chemistry and bond-breaking problems with a total of 1004 relative energies. While our benchmark study is somewhat limited, we make recommendations for the use of ph-AFQMC for general main-group chemistry applications. For systems where single determinant wave functions are qualitatively accurate, we expect the accuracy of ph-AFQMC in conjunction with a single-determinant trial wave function to be between that of coupled-cluster with singles and doubles (CCSD) and CCSD with perturbative triples (CCSD(T)). For these applications, ph-AFQMC should be a method of choice when canonical CCSD(T) is too expensive to run. For systems where multireference (MR) wave functions are needed for qualitative accuracy, ph-AFQMC is far more accurate than MR perturbation theory methods and competitive with MR configuration interaction (MRCI) methods. Due to the computational efficiency of ph-AFQMC compared to MRCI, we recommended ph-AFQMC as a method of choice for handling dynamic correlation in MR problems. We conclude with a discussion of important directions for future development of the ph-AFQMC approach.
We systematically investigate the calculation of excited states in quantum chemistry using auxiliary field quantum Monte Carlo (AFQMC). Symmetry allows targeting of the lowest triplet excited states in AFQMC based on restricted open-shell determinants, effectively as a ground-state calculation. For open-shell singlet states, excited-state calculations can be stabilized with the appropriate trial states, but their quality can have a larger effect on the accuracy in AFQMC. We find that active space-based configuration interaction trial states are often not sufficient to obtain accurate results. We instead use truncated equation of motion coupled cluster with single and double excitations (EOM-CCSD) as trial states. We benchmark the performance of these calculations on a set of small and medium molecules and polyacenes, focusing on predominantly single excitations. We find that the AFQMC results, obtained at a per-sample cost scaling of O(N6), are systematically more accurate than those obtained using EOM-CCSD, reducing excitation energy errors by approximately half for open-shell singlets. In regimes where EOM-CC triples are impractical, these results position AFQMC as a scalable, higher-accuracy complement for low-lying excited states.
to develop quantum Monte Carlo (QMC) approaches for excited states and for more systematic and accurate treatment of ground states of strongly correlated sytems and heavier elements. We use the auxiliary-field quantum Monte Carlo (AFQMC) framework, which is a many-body total energy method that looks like many coupled mean-field calculations. I will discuss this method’s relations and dierences with traditional density-functional and quantum chemistry methods, and with other forms of QMC. The AFQMC method uses importance-sampled random walks in the space of nonorthogonal Slater determinants to project out the many-body ground state, or excited state. The random walks are constrained by a trial wave function (TWF) to remove the so-called sign problem, giving approximate (but non-perturbative) results. With singledeterminant TWFs from Hartree-Fock or density-functional theory (DFT), this approach can be thought of as a post-DFT method with no parameter. In this form, the accuracy is typically comparable to the quantum chemistry coupled-cluster CCSD(T) method near equilibrium geometries, and better than CCSD(T) when bonds are stretched. The computational cost of AFQMC scales as N 3 with characteristic size of the system. Its accuracy can be further improved at the cost of increased computing (releasing the constraint) or better TWF. With AFQMC, we can systematically target selected orbitals to correlate. This allows many-body calculations in solids with a frozen core, with down-folded Hamiltonians, or possibly embeded in a DFT calculations to extend scales. Results from a few on-going applications will be presented, including band structures in simple solids, magnetic phases in MnO, and Cobalt adsoption on graphene.
We extend the use of coupled cluster (CC) trial states in the phaseless auxiliary-field quantum Monte Carlo (AFQMC) method beyond single and double excitations to include both triple and quadruple excitations. With this AFQMC/CC hierarchy, we are able to systematically benchmark the method's performance on molecular systems as the quality of the trial is improved. Our results show that the phaseless AFQMC energy improves systematically and is typically significantly more accurate than the energy of the underlying trial state. However, the relative improvement compared to the trial CC energy decreases as we ascend the CC hierarchy. As the CC wavefunction is usually further approximated when used as an AFQMC trial, we also explore the relationship between the components of the CC wavefunction and the resulting AFQMC/CC error. Our results suggest that improving the representation of the CC wave function in the AFQMC trial does not always lower the bias even when it increases the fidelity of the trial with the exact ground state.