Quantum simulations of realistic systems by auxiliary fields

Self Cite

168

We extend the recently introduced phaseless auxiliary-field quantum Monte Carlo (QMC) approach to any single-particle basis, and apply it to molecular systems with Gaussian basis sets. QMC methods in general scale favorably with system size, as a low power. A QMC approach with auxiliary fields in principle allows an exact solution of the Schrödinger equation in the chosen basis. However, the well-known sign/phase problem causes the statistical noise to increase exponentially. The phaseless method controls this problem by constraining the paths in the auxiliary-field path integrals with an approximate phase condition that depends on a trial wave function. In the present calculations, the trial wave function is a single Slater determinant from a Hartree-Fock calculation. The calculated all-electron total energies show typical systematic errors of no more than a few milli-Hartrees compared to exact results. At equilibrium geometries in the molecules we studied, this accuracy is roughly comparable to that of coupled-cluster with single and double excitations and with non-iterative triples, CCSD(T). For stretched bonds in H2O, our method exhibits better overall accuracy and a more uniform behavior than CCSD(T).

Section: Formalismmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Auxiliary-field quantum Monte Carlo calculations of molecular systems with a Gaussian basis

Al-Saidi

Zhang

Krakauer

2006

Self Cite

168

“…), 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.…”

Section: Introductionmentioning

confidence: 99%

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

Purwanto

Zhang

Krakauer

2009

Self Cite

114

We show that the recently developed phaseless auxiliary-field quantum Monte Carlo (AFQMC) method can be used to study excited states, providing an alternative to standard quantum chemistry methods. The phaseless AFQMC approach, whose computational cost scales as M 3 -M 4 with system size M , has been shown to be among the most accurate many-body methods in ground state calculations. For excited states, prevention of collapse into the ground state and control of the Fermion sign/phase problem are accomplished by the approximate phaseless constraint with a trial wave function. Using the challenging C2 molecule as a test case, we calculate the potential energy curves of the ground and two low-lying singlet excited states. The trial wave function is obtained by truncating complete active space wave functions, with no further optimization. The phaseless AFQMC results using a small basis set are in good agreement with exact full configuration interaction calculations, while those using large basis sets are in good agreement with experimental spectroscopic constants.

“…QMC methods rely on the observation that deterministic evolution driven by the family of operators (3) can be mapped onto suitable stochastic processes and solved by randomly sampling appropriate probability distributions. Along with the typical approach in which (4) is associated to a diffusion process in the configurational space of the system [4,5,17], in a class of more recently developed QMC methods, the so-called determinantal [18][19][20][21][22] methods, (4) is mapped onto a stochastic process in the abstract manifold, which we will denote D(N ), of Nparticle Slater determinants.…”

Section: The Phaseless Afqmcmentioning

confidence: 99%

“…[18,[20][21][22]24]. In the present work we consider one of such QMC methods, the phaseless Auxiliary Fields Quantum Monte Carlo (AFQMC) [20,22,25], which is considered less sensitive than FN to the quality of the trial function [29].…”

Section: Introductionmentioning

confidence: 99%

Imaginary time correlations and the phaseless auxiliary field quantum Monte Carlo

Motta

Galli

Moroni

et al. 2014

The phaseless Auxiliary Field Quantum Monte Carlo method provides a well established approximation scheme for accurate calculations of ground state energies of many-fermions systems. Here we apply the method to the calculation of imaginary time correlation functions. We give a detailed description of the technique and we test the quality of the results for static and dynamic properties against exact values for small systems.