First Principles Methods: A Perspective from Quantum Monte Carlo

Morales, Miguel A.; Clay, Raymond C.; Pierleoni, Carlo; Ceperley, David M.

doi:10.3390/e16010287

Cited by 38 publications

(41 citation statements)

References 122 publications

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“…In fact, all known exact algorithms for classical computers scale exponentially except for a small class of model systems [1][2][3][4][5][6][7][8][9]. In particular, Quantum Monte Carlo (QMC) methods [10][11][12][13], which are able to provide the exact bosonic ground state in polynomial time for a wide range of Hamiltonians, suffer from a sign problem when applied to fermions. In the following we will often refer to the solution of the fermion sign problem, implicitly meaning that the exact fermion ground state is obtained in polynomial time rather than in exponential time with respect to the number of particles.…”

Section: Introductionmentioning

confidence: 99%

Fermion sign problem in imaginary-time projection continuum quantum Monte Carlo with local interaction

Calcavecchia¹,

Holzmann²

2016

Phys. Rev. E

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We use the Shadow Wave Function formalism as a convenient model to study the fermion sign problem affecting all projector Quantum Monte Carlo methods in continuum space. We demonstrate that the efficiency of imaginary time projection algorithms decays exponentially with increasing number of particles and/or imaginary-time propagation. Moreover, we derive an analytical expression that connects the localization of the system with the magnitude of the sign problem, illustrating this behavior through numerical results. Finally, we discuss the computational complexity of the fermion sign problem and methods for alleviating its severity.

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Section: Introductionmentioning

confidence: 99%

Fermion sign problem in imaginary-time projection continuum quantum Monte Carlo with local interaction

Calcavecchia¹,

Holzmann²

2016

Phys. Rev. E

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“…with an obvious correspondence between Equations (1) and (2). The Hamiltonian does not depend on the spin of electrons and nuclei, since we restrict ourselves to the non-relativistic limit, and we do not include any spin-orbit interaction into our Hamiltonian.…”

Section: The Potential Energy Surface (Pes) Of a Many-atom Systemmentioning

confidence: 99%

“…The most ab initio methods, such as those discussed in [2], represent systems as made of electrons and atomic nuclei, and Coulomb's law is sufficient to account for every interaction. In all other cases, particles represent composite objects, such as atoms or atomic nuclei, dressed by core electrons, possibly embedded into a sea of valence electrons described at some approximate level of a many-body theory.…”

Section: Introductionmentioning

confidence: 99%

Modeling Potential Energy Surfaces: From First-Principle Approaches to Empirical Force Fields

Ballone

2013

Entropy

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Explicit or implicit expressions of potential energy surfaces (PES) represent the basis of our ability to simulate condensed matter systems, possibly understanding and sometimes predicting their properties by purely computational methods. The paper provides an outline of the major approaches currently used to approximate and represent PESs and contains a brief discussion of what still needs to be achieved. The paper also analyses the relative role of empirical and ab initio methods, which represents a crucial issue affecting the future of modeling in chemical physics and materials science.

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“…In contrast to quantumchemical methods, where the computational complexity grows rapidly with the number of considered electrons N [7], the formal scaling of quantum Monte Carlo (QMC) methods is similar to those of HF and DFT [8][9][10][11][12]. However, since it typically relies on HF or DFT orbitals to construct the Slater determinant (SD), it only allows to extract the vast majority of dynamic electron correlation, but suffers from exactly the same static correlation error that is characteristic for single-reference electronic structure methods [13].…”

mentioning

confidence: 99%

On fermionic shadow wave functions for strongly correlated multi-reference systems based on a single Slater determinant

Calcavecchia¹,

Kühne²

2015

EPL

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-We demonstrate that extending the Shadow Wave Function to fermionic systems facilitates to accurately calculate strongly-correlated multi-reference systems such as the stretched H2 molecule. This development considerably extends the scope of electronic structure calculations and enables to efficiently recover the static correlation energy using just a single Slater determinant.Introduction. -One of the most outstanding problems of computational physics and quantum chemistry is the ability to devise a quantitatively precise, yet computationally tractable, method to accurately break a chemical bond across an entire reaction coordinate. A particularly simple example is the H 2 molecule, in particular when the covalent bond between the H atoms is stretched. Effective single-particle theories, such as the widely employed Hartree-Fock (HF) or Density Functional Theory (DFT) methods, describe the covalent bond well, but the energy is severely overestimated upon dissociation [1]. This wellknown problem is attributed to the multi-reference character of the stretched H 2 molecule, or static electron correlation that arises in situations with degeneracy or neardegeneracy, as in transition metal chemistry and stronglycorrelated systems in general [2]. As a consequence, the stretched H 2 molecule and similar problems are typically dealt with using multi-determinant wave functions [3]. However, for larger systems with many degeneracies, the number of determinants quickly becomes unfeasible [4,5].

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First Principles Methods: A Perspective from Quantum Monte Carlo

Cited by 38 publications

References 122 publications

Fermion sign problem in imaginary-time projection continuum quantum Monte Carlo with local interaction

Fermion sign problem in imaginary-time projection continuum quantum Monte Carlo with local interaction

Modeling Potential Energy Surfaces: From First-Principle Approaches to Empirical Force Fields

On fermionic shadow wave functions for strongly correlated multi-reference systems based on a single Slater determinant

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