Efficient formulation of full configuration interaction quantum Monte Carlo in a spin eigenbasis via the graphical unitary group approach.
06 Sep 2019-Journal of Chemical Physics (AIP Publishing LLCAIP Publishing)-Vol. 151, Iss: 9, pp 094104
TL;DR: In this article, a spin-adapted formulation of the FCIQMC algorithm, based on the Graphical Unitary Group Approach (GUGA), is proposed, which enables the exploitation of SU(2) symmetry within this stochastic framework.
Abstract: We provide a spin-adapted formulation of the Full Configuration Interaction Quantum Monte Carlo (FCIQMC) algorithm, based on the Graphical Unitary Group Approach (GUGA), which enables the exploitation of SU(2) symmetry within this stochastic framework. Random excitation generation and matrix element calculation on the Shavitt graph of GUGA can be efficiently implemented via a biasing procedure on the branching diagram. The use of a spin-pure basis explicitly resolves the different spin-sectors and ensures that the stochastically sampled wavefunction is an eigenfunction of the total spin operator S^2. The method allows for the calculation of states with low or intermediate spin in systems dominated by Hund's first rule, which are otherwise generally inaccessible. Furthermore, in systems with small spin gaps, the new methodology enables much more rapid convergence with respect to walker number and simulation time. Some illustrative applications of the GUGA-FCIQMC method are provided: computation of the 2F - 4F spin gap of the cobalt atom in large basis sets, achieving chemical accuracy to experiment, and the Σg+1, Σg+3, Σg+5, and Σg+7 spin-gaps of the stretched N2 molecule, an archetypal strongly correlated system.
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TL;DR: An overview of the variational and diffusion quantum Monte Carlo methods as implemented in the casino program is presented, describing state-of-the-art quantum Monte Monte Carlo algorithms and software and discussing their strengths and weaknesses.
Abstract: We present an overview of the variational and diffusion quantum Monte Carlo methods as implemented in the casino program. We particularly focus on developments made in the last decade, describing state-of-the-art quantum Monte Carlo algorithms and software and discussing their strengths and weaknesses. We review a range of recent applications of casino.
84 citations
TL;DR: In this article, the acceptance probability (pacc) of a noninitiator determinant has been used to unbias the initiator bias, in a simple and accurate manner, by reducing the applied shift to the non-initiators proportionately to pacc.
Abstract: We identify and rectify a crucial source of bias in the initiator full configuration interaction quantum Monte Carlo algorithm. Noninitiator determinants (i.e., determinants whose population is below the initiator threshold) are subject to a systematic undersampling bias, which in large systems leads to a bias in the energy when an insufficient number of walkers are used. We show that the acceptance probability (pacc), that a noninitiator determinant has its spawns accepted, can be used to unbias the initiator bias, in a simple and accurate manner, by reducing the applied shift to the noninitiator proportionately to pacc. This modification preserves the property that in the large walker limit, when pacc → 1, the unbiasing procedure disappears, and the initiator approximation becomes exact. We demonstrate that this algorithm shows rapid convergence to the FCI limit with respect to the walker number and, furthermore, largely removes the dependence of the algorithm on the initiator threshold, enabling highly accurate results to be obtained even with large values of the threshold. This is exemplified in the case of butadiene/ANO-L-pVDZ and benzene/cc-pVDZ, correlating 22 and 30 electrons in 82 and 108 orbitals, respectively. In butadiene 5 × 107 and in benzene 108 walkers suffice to obtain an energy within a millihartree of the coupled cluster singles doubles triples and perturbative quadruples [CCSDT(Q)] result in Hilbert spaces of 1026 and 1035, respectively. Essentially converged results require ∼108 walkers for butadiene and ∼109 walkers for benzene and lie slightly lower than CCSDT(Q). Owing to large-scale parallelizability, these calculations can be executed in a matter of hours on a few hundred processors. The present method largely solves the initiator-bias problems that the initiator method suffered from when applied to medium-sized molecules.
60 citations
TL;DR: The core functionalities of NECI are described, including the capabilities to calculate ground and excited state energies, properties via the one- and two-body reduced density matrices, as well as spectral and Green's functions for ab initio and model systems.
Abstract: We present NECI, a state-of-the-art implementation of the Full Configuration Interaction Quantum Monte Carlo (FCIQMC) algorithm, a method based on a stochastic application of the Hamiltonian matrix on a sparse sampling of the wave function. The program utilizes a very powerful parallelization and scales efficiently to more than 24 000 central processing unit cores. In this paper, we describe the core functionalities of NECI and its recent developments. This includes the capabilities to calculate ground and excited state energies, properties via the one- and two-body reduced density matrices, as well as spectral and Green’s functions for ab initio and model systems. A number of enhancements of the bare FCIQMC algorithm are available within NECI, allowing us to use a partially deterministic formulation of the algorithm, working in a spin-adapted basis or supporting transcorrelated Hamiltonians. NECI supports the FCIDUMP file format for integrals, supplying a convenient interface to numerous quantum chemistry programs, and it is licensed under GPL-3.0.
60 citations
Journal Article•
TL;DR: In this article, an algorithm for sampling many-body quantum states in Fock space was proposed, with probability approximately proportional to an arbitrary function of the second-quantized Hamiltonian matrix element connecting the sampled state to the current state.
Abstract: We introduce an algorithm for sampling many-body quantum states in Fock space The algorithm efficiently samples states with probability approximately proportional to an arbitrary function of the second-quantized Hamiltonian matrix element connecting the sampled state to the current state We apply the new sampling algorithm to the recently developed semistochastic full configuration interaction quantum Monte Carlo (S-FCIQMC) method, a semistochastic implementation of the power method for projecting out the ground state energy in a basis of Slater determinants Our new sampling method requires modest additional computational time and memory compared to uniform sampling but results in newly spawned weights that are approximately of the same magnitude, thereby greatly improving the efficiency of projection A comparison in efficiency between our sampling algorithm and uniform sampling is performed on the all-electron nitrogen dimer at equilibrium in Dunning's cc-pVXZ basis sets with X ∈ {D, T, Q, 5}, demonstrating a large gain in efficiency that increases with basis set size In addition, a comparison in efficiency is performed on three all-electron first-row dimers, B2, N2, and F2, in a cc-pVQZ basis, demonstrating that the gain in efficiency compared to uniform sampling also increases dramatically with the number of electrons
45 citations
TL;DR: NECI as discussed by the authors is a state-of-the-art implementation of the Full Configuration Interaction Quantum Monte Carlo algorithm, a method based on a stochastic application of the Hamiltonian matrix on a sparse sampling of the wave function.
Abstract: We present NECI, a state-of-the-art implementation of the Full Configuration Interaction Quantum Monte Carlo algorithm, a method based on a stochastic application of the Hamiltonian matrix on a sparse sampling of the wave function The program utilizes a very powerful parallelization and scales efficiently to more than 24000 CPU cores In this paper, we describe the core functionalities of NECI and recent developments This includes the capabilities to calculate ground and excited state energies, properties via the one- and two-body reduced density matrices, as well as spectral and Green's functions for ab initio and model systems A number of enhancements of the bare FCIQMC algorithm are available within NECI, allowing to use a partially deterministic formulation of the algorithm, working in a spin-adapted basis or supporting transcorrelated Hamiltonians NECI supports the FCIDUMP file format for integrals, supplying a convenient interface to numerous quantum chemistry programs and it is licensed under GPL-30
39 citations
References
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TL;DR: In this paper, a direct difference method for the computation of molecular interactions has been based on a bivariational transcorrelated treatment, together with special methods for the balancing of other errors.
Abstract: A new direct difference method for the computation of molecular interactions has been based on a bivariational transcorrelated treatment, together with special methods for the balancing of other errors. It appears that these new features can give a strong reduction in the error of the interaction energy, and they seem to be particularly suitable for computations in the important region near the minimum energy. It has been generally accepted that this problem is dominated by unresolved difficulties and the relation of the new methods to these apparent difficulties is analysed here.
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TL;DR: A description of the ab initio quantum chemistry package GAMESS, which can be treated with wave functions ranging from the simplest closed‐shell case up to a general MCSCF case, permitting calculations at the necessary level of sophistication.
Abstract: A description of the ab initio quantum chemistry package GAMESS is presented. Chemical systems containing atoms through radon can be treated with wave functions ranging from the simplest closed-shell case up to a general MCSCF case, permitting calculations at the necessary level of sophistication. Emphasis is given to novel features of the program. The parallelization strategy used in the RHF, ROHF, UHF, and GVB sections of the program is described, and detailed speecup results are given. Parallel calculations can be run on ordinary workstations as well as dedicated parallel machines. © John Wiley & Sons, Inc.
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Abstract: In der Anwendung der Quantentheorie auf die Molekeln kann man folgende Entwicklungsstufen unterscheiden: Das erste Stadium1) ersetzt die zweiatomige Molekel durch das Hantelmodell, das als einfacher „Rotator“ behandelt wird. Mehratomige Molekeln werden in entsprechender Weise als starre „Kreisel“ angesehen.2) Dieser Standpunkt erlaubt es, die einfachsten Gesetze der Bandenspektren und der spezifischen Warme mehratomiger Gase zu erklaren. Das nachste Stadium1) last die Annahme starrer Verbindungen zwischen den Atomen fallen und berucksichtigt die Kernschwingungen, zunachst als harmonische Schwingungen; dabie ergenben sich nach Sponer3) und Kratzer4) Zusammenhange zwischen den einzelnen Banden eines Bandensystems.
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TL;DR: In this paper, the Fock-type one-electron operator was extended by allowing the zeroth-order Hamiltonian to have nonzero elements also in nondiagonal matrix blocks.
Abstract: The recently implemented second‐order perturbation theory based on a complete active space self‐consistent field reference function has been extended by allowing the Fock‐type one‐electron operator, which defines the zeroth‐order Hamiltonian to have nonzero elements also in nondiagonal matrix blocks. The computer implementation is now less straightforward and more computer time will be needed in obtaining the second‐order energy. The method is illustrated in a series of calculations on N2, NO, O2, CH3, CH2, and F−.
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TL;DR: Molpro (available at http://www.molpro.net) is a general-purpose quantum chemical program as discussed by the authors, which uses local approximations combined with explicit correlation treatments, highly accurate coupled-cluster calculations are now possible for molecules with up to approximately 100 atoms.
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