Phaseless auxiliary-field quantum Monte Carlo calculations with plane waves and pseudopotentials: Applications to atoms and molecules

The Journal of Chemical Physics

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.

Section: Introductionmentioning

confidence: 99%

“…The recently developed phaseless auxiliary-field quantum Monte Carlo (AFQMC) method 9,10,11,12 is an orbital-based alternative many-body approach. AFQMC can be expressed with respect to any chosen single-particle basis (e.g., gaussians, planewaves, Wannier, etc.…”

Section: Introductionmentioning

confidence: 99%

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

Purwanto

The Journal of Chemical Physics

Krakauer

2009

Self Cite

114

“…[22][23][24][25] We first describe exact free-projection (FP) AFQMC calculations, where we release the usual phaseless approximation, 22 which is used to control the phase/sign problem. 25 The results are then extrapolated to the CBS limit using a combination of phaseless and exact AFQMC calculations.…”

mentioning

confidence: 99%

“…AFQMC obtains ground-state properties by stochastically sampling the many-body ground-state wave function in the space of Slater determinants, expressed in a chosen oneparticle basis. [22][23][24][25] It has modest polynomial scaling with system size M [O M 3 or O M 4 ] rather than the exponen-tial scaling of CI calculations, or the high-order polynomial scaling of typical quantum chemistry many-body methods. The FP AFQMC, 26,27 which leaves the fermion sign/phase problem uncontrolled, 25 is exact but has exponential scaling due to rapidly increasing stochastic noise with projection imaginary-time.…”

mentioning

confidence: 99%

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An auxiliary-field quantum Monte Carlo study of the chromium dimer

Purwanto

The Journal of Chemical Physics

Krakauer

2015

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The chromium dimer (Cr2) presents an outstanding challenge for many-body electronic structure methods. Its complicated nature of binding, with a formal sextuple bond and an unusual potential energy curve, is emblematic of the competing tendencies and delicate balance found in many strongly correlated materials. We present a nearexact calculation of the potential energy curve (PEC) and ground state properties of Cr2, using the auxiliary-field quantum Monte Carlo (AFQMC) method. Unconstrained, exact AFQMC calculations are first carried out for a medium-sized but realistic basis set. Elimination of the remaining finite-basis errors and extrapolation to the complete basis set (CBS) limit is then achieved with a combination of phaseless and exact AFQMC calculations. Final results for the PEC and spectroscopic constants are in excellent agreement with experiment. The chromium dimer is a strongly correlated molecule which poses a formidable challenge to even the most accurate many-body methods. It features a formal sextuple bond, with a weak binding energy (∼ 1.5 eV), a short equilibrium bond length (∼ 1.7Å), and an unusual "shoulder" structure in its potential energy curve (PEC). [1][2][3] The ground state of Cr 2 is highly multiconfigurational, and proper theoretical description requires an accurate treatment of the strong 3d electron correlations (both static and dynamic). The nature of the PEC in Cr 2 is representative of the competing tendencies separated by small energy differences seen in many strongly correlated materials. Because of the fundamental and technological significance of such materials, improving our abilities for accurate calculations in strongly correlated systems is one of the most pressing needs in condensed matter physics and quantum chemistry.Standard quantum chemistry methods, such as density functional theory (DFT), Hartree-Fock (HF), and post-HF methods such as single-reference second-order Møller-Plesset perturbation theory (MP2) and single-reference coupled cluster with singles, doubles, and perturbative triples [CCSD(T)], all fail to describe the correct binding of Cr 2 . Representative standard quantum chemistry results are shown in Fig. 1. As often is the case, the DFT results vary greatly, depending on the choice of exchange-correlation functional. There have also been numerous attempts to calculate the PEC of Cr 2 using sophisticated multireference quantum chemistry methods, 4-9 including the complete active space second-order perturbation theory (CASPT2) 10-12 and, more recently, CASPT2 based on a large density matrix renormalization group (DMRG) reference wave function (DMRG-CASPT2). 13 These calculations obtain qualitatively correct binding, but the results are sensitive to choice of active space and/or basis set. Standard quantum Monte Carlo (QMC) approaches 14,15 have also been severely challenged. A recent fixed-node diffusion Monte Carlo (DMC) study, which examined the use of a variety of single-and multi-determinant trial wave functions, did not obtain satisfactory binding (i...

Ab initio computations of molecular systems by the auxiliary‐field quantum Monte Carlo method

Motta

2018

WIREs Comput Mol Sci

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133

215

The auxiliary-field quantum Monte Carlo (AFQMC) method provides a computational framework for solving the time-independent Schrödinger equation in atoms, molecules, solids, and a variety of model systems. AFQMC has recently witnessed remarkable growth, especially as a tool for electronic structure computations in real materials. The method has demonstrated excellent accuracy across a variety of correlated electron systems. Taking the form of stochastic evolution in a manifold of nonorthogonal Slater determinants, the method resembles an ensemble of density-functional theory (DFT) calculations in the presence of fluctuating external potentials. Its computational cost scales as a low-power of system size, similar to the corresponding independentelectron calculations. Highly efficient and intrinsically parallel, AFQMC is able to take full advantage of contemporary high-performance computing platforms and numerical libraries. In this review, we provide a self-contained introduction to the exact and constrained variants of AFQMC, with emphasis on its applications to the electronic structure of molecular systems. Representative results are presented, and theoretical foundations and implementation details of the method are discussed. This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods Structure and Mechanism > Computational Materials Science Computer and Information Science > Computer Algorithms and Programming K E Y W O R D S ab initio methods, auxiliary-field quantum Monte Carlo, back-propagation, computational quantum chemistry, constrained path approximation, electronic structure, importance sampling, phase problem, phaseless approximation, quantum many-body computation, quantum Monte Carlo methods, sign problem 1 | INTRODUCTIONA central challenge in the fields of condensed matter physics, quantum chemistry (QC), and materials science is to determine the quantum mechanical behavior of many interacting electrons and nuclei. Often relativistic effects and the coupling between the dynamics of electrons and nuclei can be neglected, or treated separately. Within this approximation, the many-electron wave function can be found by solving the time-independent Schrödinger equation for the Born-Oppenheimer Hamiltonian