Communications: Survival of the fittest: Accelerating convergence in full configuration-interaction quantum Monte Carlo

Cleland, Deidre; Booth, George H.; Alavi, Ali

doi:10.1063/1.3302277

Cited by 410 publications

(611 citation statements)

References 8 publications

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“…We note that the recent FCI-QMC method of Alavi et al [9,10] uses essentially the same idea, except that in CIPSI the selection is done deterministically instead of stochastically.…”

Section: Summary and Some Perspectivesmentioning

confidence: 99%

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Using CIPSI Nodes in Diffusion Monte Carlo

Caffarel

Applencourt

Giner

et al. 2016

ACS Symposium Series

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Several aspects of the recently proposed DMC-CIPSI approach consisting in using selected Configuration Interaction (SCI) approaches such as CIPSI (Configuration Interaction using a Perturbative Selection done Iteratively) to build accurate nodes for diffusion Monte Carlo (DMC) calculations are presented and discussed. The main ideas are illustrated with a number of calculations for diatomics molecules and for the benchmark G1 set.

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“…We note that the recent FCI-QMC method of Alavi et al [9,10] uses essentially the same idea, except that in CIPSI the selection is done deterministically instead of stochastically.…”

Section: Summary and Some Perspectivesmentioning

confidence: 99%

“…[8] CIPSI being our working algorithm for generating CI expansions, a brief description is given here. It is noted that the recent FCI-QMC method of Alavi et al [9,10] is essentially a SCI approach, except that selection of determinants in FCI-QMC is done stochastically instead of deterministically.…”

Section: Introductionmentioning

confidence: 99%

Using CIPSI Nodes in Diffusion Monte Carlo

Caffarel

Applencourt

Giner

et al. 2016

ACS Symposium Series

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“…This problem is commonly treated with brute force full configuration interaction (FCI), 13 which is practical for up to approximately 16 active orbitals. However, recently significant progress has been made with alternative methods to FCI; in particular, due to developments in the density matrix renormalization group (DMRG) algorithm, FCI Quantum Monte Carlo (FCIQMC), [14][15][16] and selected configuration interaction approaches [17][18][19] , static correlation can now be treated accurately in much larger active spaces. We here focus on DMRG, 20,21 a variational method which minimizes the energy of a wavefunction parametrized as a matrix product state (MPS).…”

Section: Introductionmentioning

confidence: 99%

“…For evaluating the commutator in Eq (14), only up to three-body RDMs are needed. Using similar procedures, IC equations for the other classes in Table I can be derived; the maximum order RDM required in these equations is shown in column 6.…”

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confidence: 99%

Combining Internally Contracted States and Matrix Product States To Perform Multireference Perturbation Theory

Sharma

Knizia

Guo

et al. 2017

J. Chem. Theory Comput.

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We present two efficient and intruder-free methods for treating dynamic correlation on top of general multi-configuration reference wave functions-including such as obtained by the density matrix renormalization group (DMRG) with large active spaces. The new methods are the second order variant of the recently proposed multi-reference linearized coupled cluster method (MRLCC) [S. Sharma, A. Alavi, J. Chem. Phys. 143, 102815 (2015)], and of N-electron valence perturbation theory (NEVPT2), with expected accuracies similar to MRCI+Q and (at least) CASPT2, respectively. Great efficiency gains are realized by representing the first-order wave function with a combination of internal contraction (IC) and matrix product state perturbation theory (MPSPT). With this combination, only third order reduced density matrices (RDMs) are required. Thus, we obviate the need for calculating (or estimating) RDMs of fourth or higher order; these had so far posed a severe bottleneck for dynamic correlation treatments involving the large active spaces accessible to DMRG. Using several benchmark systems, including first and second row containing small molecules, Cr2, pentacene and oxo-Mn(Salen), we shown that active spaces containing at least 30 orbitals can be treated using this method. On a single node, MRLCC2 and NEVPT2 calculations can be performed with over 550 and 1100 virtual orbitals, respectively. We also critically examine the errors incurred due to the three sources of errors introduced in the present implementation -calculating second order instead of third order energy corrections, use of internal contraction and approximations made in the reference wavefunction due to DMRG.

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“…FCI Quantum Monte Carlo and its 'initiator' adaptation (i-FCIQMC) are novel methods developed in a series of recent papers [11][12][13][14][15][16] in which the FCI equations are simulated by representing the determinant coefficients as a set of walkers evolving over discretized imaginary time. This allows much larger Hilbert spaces to be studied, with the largest space accurately sampled to date being 10 108 , in a previous study of the 54-electron gas 16 .…”

Section: Introductionmentioning

confidence: 99%

Investigation of the full configuration interaction quantum Monte Carlo method using homogeneous electron gas models

Shepherd

Booth

Alavi

2012

The Journal of Chemical Physics

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107

143

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Using the homogeneous electron gas (HEG) as a model, we investigate the sources of error in the 'initiator' adaptation to Full Configuration Interaction Quantum Monte Carlo (i -FCIQMC), with a view to accelerating convergence. In particular we find that the fixed shift phase, where the walker number is allowed to grow slowly, can be used to effectively assess stochastic and initiator error. Using this approach we provide simple explanations for the internal parameters of an i -FCIQMC simulation. We exploit the consistent basis sets and adjustable correlation strength of the HEG to analyze properties of the algorithm, and present finite basis benchmark energies for N = 14 over a range of densities 0.5 ≤ rs ≤ 5.0 a.u. A single-point extrapolation scheme is introduced to produce complete basis energies for 14, 38 and 54 electrons. It is empirically found that, in the weakly correlated regime, the computational cost scales linearly with the plane wave basis set size, which is justifiable on physical grounds. We expect the fixed shift strategy to reduce the computational cost of many i -FCIQMC calculations of weakly correlated systems. In addition, we provide benchmarks for the electron gas, to be used by other quantum chemical methods in exploring periodic solid state systems.

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Communications: Survival of the fittest: Accelerating convergence in full configuration-interaction quantum Monte Carlo

Abstract: Unbiased reduced density matrices and electronic properties from full configuration interaction quantum Monte

Cited by 410 publications

References 8 publications

Using CIPSI Nodes in Diffusion Monte Carlo

Using CIPSI Nodes in Diffusion Monte Carlo

Combining Internally Contracted States and Matrix Product States To Perform Multireference Perturbation Theory

Investigation of the full configuration interaction quantum Monte Carlo method using homogeneous electron gas models

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