Monte Carlo Methods in Ab Initio Quantum Chemistry

Hammond, B. L.; Lester, William A.; Reynolds, Peter J.

doi:10.1142/9789814317245

Cited by 402 publications

(227 citation statements)

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“…4,5,6,7 QMC methodology has an important virtue that it enables us to test and employ variety of many-body wave functions (WFs) with explicit electron-electron correlation. This opens a possibility to explore wave functions, which are very difficult to use with traditional methods based on one-particle basis expansions and on orthogonality of one-particle orbitals.…”

Section: Introductionmentioning

confidence: 99%

Pfaffian pairing and backflow wavefunctions for electronic structure quantum Monte Carlo methods

et al. 2008

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We investigate pfaffian trial wave functions with singlet and triplet pair orbitals by quantum Monte Carlo methods. We present mathematical identities and the key algebraic properties necessary for efficient evaluation of pfaffians. Following upon our previous study, 1 we explore the possibilities of expanding the wave function in linear combinations of pfaffians. We observe that molecular systems require much larger expansions than atomic systems and linear combinations of a few pfaffians lead to rather small gains in correlation energy. We also test the wave function based on fully-antisymmetrized product of independent pair orbitals. Despite its seemingly large variational potential, we do not observe additional gains in correlation energy. We find that pfaffians lead to substantial improvements in fermion nodes when compared to Hartree-Fock wave functions and exhibit the minimal number of two nodal domains in agreement with recent results on fermion nodes topology. We analyze the nodal structure differences of Hartree-Fock, pfaffian and essentially exact large-scale configuration interaction wave functions. Finally, we combine the recently proposed form of backflow correlations 2,3 with both determinantal and pfaffian based wave functions.

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Section: Introductionmentioning

confidence: 99%

Pfaffian pairing and backflow wavefunctions for electronic structure quantum Monte Carlo methods

et al. 2008

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“…On the other hand, the quantum Monte Carlo (QMC) method allows direct solution of the many-body problem of interacting electrons using stochastic techniques [3][4][5][6] . In fact, the local density approximation is based on QMC calculations of the homogeneous electron gas 7 (HEG).…”

Section: Pacs Numbersmentioning

confidence: 99%

Simple impurity embedded in a spherical jellium: Approximations of density functional theory compared to quantum Monte Carlo benchmarks

et al. 2011

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We study the electronic structure of a spherical jellium in the presence of a central Gaussian impurity. We test how well the resulting inhomogeneity effects beyond spherical jellium are reproduced by several approximations of density functional theory (DFT). Four rungs of Perdew's ladder of DFT functionals, namely local density approximation (LDA), generalized gradient approximation (GGA), meta-GGA and orbital-dependent hybrid functionals are compared against our quantum Monte Carlo (QMC) benchmarks. We identify several distinct transitions in the ground state of the system as the electronic occupation changes between delocalized and localized states. We examine the parameter space of realistic densities (1 ≤ rs ≤ 5) and moderate depths of the Gaussian impurity (Z < 7). The selected 18 electron system (with closed-shell ground state) presents 1d → 2s transitions while the 30 electron system (with open-shell ground state) exhibits 1f → 2p transitions. For the former system, the accuracy for the transitions is clearly improving with increasing sophistication of functionals with meta-GGA and hybrid functionals having only small deviations from QMC. However, for the latter system, we find much larger differences for the underlying transitions between our pool of DFT functionals and QMC. We attribute these failures to an insufficiently accurate treatment of exchange by these functionals. Additionally, we amplify the inhomogeneity effects by creating the system with spherical shell which leads to even larger errors in DFT approximations.

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“…In the other limit, one must also mention Quantum Monte Carlo approach [181][182][183], the aim of which is to compute the total energy via stochastic sampling of the electronic wavefunction and integrals (properties) as mean values. The non ab-initio methods, much faster from the computer-time point of view, may offer proper tools (still within quantum framework for electrons) in intensive simulations of the dynamics of complex systems with numerous atomic degrees of freedom.…”

Section: Outlook and Further Developmentsmentioning

confidence: 99%

Perspectives from Quantum Chemistry for molecules and nanograins with astrophysical Interest

Spiegelman

Rapacioli

Simon

2011

EPJ Web of Conferences

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Abstract. Quantum Chemistry methods offer powerful tools for the computation of various properties of molecules and nanoparticles or clusters such as structure, thermodynamics, infrared and electronic spectroscopy, in some cases on a routine basis. However, neither the accuracy nor the applicability of the various methods are uniform, and may depend strongly on the nature and the size of the compounds and the desired properties. The ab initio methods for approaching electronic structure can be classified into two classes. The first class includes wavefunction-based methods, namely post-Hartree Fock schemes in the framework of Configuration Interaction or Coupled Cluster schemes which can now be used for molecules containing up to a few ten atoms (for single geometry calculations) and are likely to provide accurate results whenever applicable. The second class of methods is that of density-based methods which cover systems between a few tens up to a few hundreds of atoms. It is often of broad applicability and satisfactorily accurate in many cases. For more extended systems or extensive calculations, tight-binding type approximations or evolved force-fields (based on bond-orders for instance) are also quite promising. In this overview, we will briefly remind the basics of standard Quantum Chemistry methods and provide a survey of present trends which should be of interest for astrochemistry simulations at the atomic scale.

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Monte Carlo Methods in Ab Initio Quantum Chemistry

Cited by 402 publications

References 0 publications

Pfaffian pairing and backflow wavefunctions for electronic structure quantum Monte Carlo methods

Pfaffian pairing and backflow wavefunctions for electronic structure quantum Monte Carlo methods

Simple impurity embedded in a spherical jellium: Approximations of density functional theory compared to quantum Monte Carlo benchmarks

Perspectives from Quantum Chemistry for molecules and nanograins with astrophysical Interest

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