1
|
Zhao C, Lee J, Dou W. Stochastic Resolution of Identity to CC2 for Large Systems: Ground State and Triplet Excitation Energy Calculations. J Phys Chem A 2024; 128:9302-9310. [PMID: 39391927 DOI: 10.1021/acs.jpca.4c04264] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/12/2024]
Abstract
An implementation of stochastic resolution of identity to the CC2 (sRI-CC2) ground state energy followed by triplet excitation energy calculations is presented. A set of stochastic orbitals is introduced to further decouple the expensive 4-index electron repulsion integrals on the basis of RI approximation. A Laplace transformation of the orbital energy difference denominators into numerical summations is adopted to obtain a third-order overall scaling. We select a series of hydrogen dimer chains with nearly thousands of electrons, as well as some other molecules, for sRI-CC2 energies and test the accuracy and time consumption in comparison with those of RI-CC2. Our sRI-CC2 results reproduce a modest agreement with the RI-CC2 in Q-Chem program package and it allows a steep scaling reduction from O(N5) to O(N3). Besides, the unrestricted sRI-CC2 calculations also fit well with the restricted results. Thus, our sRI-CC2 implementation of ground state energy and triplet excitation energy provides a cost-efficient alternative approach, especially for some large-sized systems.
Collapse
Affiliation(s)
- Chongxiao Zhao
- Department of Chemistry, Zhejiang University, Hangzhou 310058, China
- Department of Chemistry, School of Science, Westlake University, Hangzhou, Zhejiang, 310024, China
- Institute of Natural Sciences, Westlake Institute for Advanced Study, Hangzhou, Zhejiang, 310024, China
| | - Joonho Lee
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts, 02138, United States
| | - Wenjie Dou
- Department of Chemistry, School of Science, Westlake University, Hangzhou, Zhejiang, 310024, China
- Institute of Natural Sciences, Westlake Institute for Advanced Study, Hangzhou, Zhejiang, 310024, China
| |
Collapse
|
2
|
Zhao C, Ou Q, Lee J, Dou W. Stochastic Resolution of Identity to CC2 for Large Systems: Excited State Properties. J Chem Theory Comput 2024; 20:5188-5195. [PMID: 38842259 DOI: 10.1021/acs.jctc.4c00629] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/07/2024]
Abstract
We apply a stochastic resolution of identity approximation (sRI) to the CC2 method for the excitation energy calculations. A set of stochastic orbitals are employed to decouple the crucial 4-index electron repulsion integrals and optimize the contraction steps in CC2 response theory. The CC2 response for excitations builds upon sRI-CC2 ground-state calculations, which scales as O(N3), where N is a measure for the system size. Overall, the current algorithm for excited states also allows a sharp scaling reduction from original O(N5) to O(N3). We test the sRI-CC2 for different molecular systems and basis sets, and we show that our sRI-CC2 method can accurately reproduce the results of the deterministic CC2 approach. Our sRI-CC2 exhibits an experimental scaling of O(N2.59) for a series of olefin chains, allowing us to calculate systems with nearly thousands of electrons.
Collapse
Affiliation(s)
- Chongxiao Zhao
- Department of Chemistry, Zhejiang University, Hangzhou 310027, China
- Department of Chemistry, School of Science, Westlake University, Hangzhou, Zhejiang 310024, China
- Institute of Natural Sciences, Westlake Institute for Advanced Study, Hangzhou, Zhejiang 310024, China
| | - Qi Ou
- AI for Science Institute, Beijing 100080, China
| | - Joonho Lee
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138, United States
| | - Wenjie Dou
- Department of Chemistry, School of Science, Westlake University, Hangzhou, Zhejiang 310024, China
- Institute of Natural Sciences, Westlake Institute for Advanced Study, Hangzhou, Zhejiang 310024, China
| |
Collapse
|
3
|
Li J, Yang W. Chemical Potentials and the One-Electron Hamiltonian of the Second-Order Perturbation Theory from the Functional Derivative Approach. J Phys Chem A 2024; 128:4876-4885. [PMID: 38842399 DOI: 10.1021/acs.jpca.4c01574] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/07/2024]
Abstract
We develop a functional derivative approach to calculate the chemical potentials of second-order perturbation theory (MP2). In the functional derivative approach, the correlation part of the MP2 chemical potential, which is the derivative of the MP2 correlation energy with respect to the occupation number of frontier orbitals, is obtained from the chain rule via the noninteracting Green's function. First, the MP2 correlation energy is expressed in terms of the noninteracting Green's function, and its functional derivative to the noninteracting Green's function is the second-order self-energy. Then, the derivative of the noninteracting Green's function to the occupation number is obtained by including the orbital relaxation effect. We show that the MP2 chemical potentials obtained from the functional derivative approach agree with that obtained from the finite difference approach. The one-electron Hamiltonian, defined as the derivative of the MP2 energy with respect to the one particle density matrix, is also derived using the functional derivative approach, which can be used in the self-consistent calculations of MP2 and double-hybrid density functionals. The developed functional derivative approach is promising for calculating the chemical potentials and the one-electron Hamiltonian of approximate functionals and many-body perturbation approaches dependent explicitly on the noninteracting Green's function.
Collapse
Affiliation(s)
- Jiachen Li
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States
| | - Weitao Yang
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
| |
Collapse
|
4
|
Hadad RE, Roy A, Rabani E, Redmer R, Baer R. Stochastic density functional theory combined with Langevin dynamics for warm dense matter. Phys Rev E 2024; 109:065304. [PMID: 39020867 DOI: 10.1103/physreve.109.065304] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/24/2024] [Accepted: 05/17/2024] [Indexed: 07/19/2024]
Abstract
This study overviews and extends a recently developed stochastic finite-temperature Kohn-Sham density functional theory to study warm dense matter using Langevin dynamics, specifically under periodic boundary conditions. The method's algorithmic complexity exhibits nearly linear scaling with system size and is inversely proportional to the temperature. Additionally, a linear-scaling stochastic approach is introduced to assess the Kubo-Greenwood conductivity, demonstrating exceptional stability for dc conductivity. Utilizing the developed tools, we investigate the equation of state, radial distribution, and electronic conductivity of hydrogen at a temperature of 30 000 K. As for the radial distribution functions, we reveal a transition of hydrogen from gaslike to liquidlike behavior as its density exceeds 4g/cm^{3}. As for the electronic conductivity as a function of the density, we identified a remarkable isosbestic point at frequencies around 7 eV, which may be an additional signature of a gas-liquid transition in hydrogen at 30 000 K.
Collapse
Affiliation(s)
| | | | - Eran Rabani
- Department of Chemistry, University of California, Berkeley, California 94720, USA; Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA; and The Raymond and Beverly Sackler Center of Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 69978, Israel
| | | | | |
Collapse
|
5
|
Carter-Fenk K, Shee J, Head-Gordon M. Optimizing the regularization in size-consistent second-order Brillouin-Wigner perturbation theory. J Chem Phys 2023; 159:171104. [PMID: 37933781 PMCID: PMC10752296 DOI: 10.1063/5.0174923] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/04/2023] [Accepted: 10/09/2023] [Indexed: 11/08/2023] Open
Abstract
Despite its simplicity and relatively low computational cost, second-order Møller-Plesset perturbation theory (MP2) is well-known to overbind noncovalent interactions between polarizable monomers and some organometallic bonds. In such situations, the pairwise-additive correlation energy expression in MP2 is inadequate. Although energy-gap dependent amplitude regularization can substantially improve the accuracy of conventional MP2 in these regimes, the same regularization parameter worsens the accuracy for small molecule thermochemistry and density-dependent properties. Recently, we proposed a repartitioning of Brillouin-Wigner perturbation theory that is size-consistent to second order (BW-s2), and a free parameter (α) was set to recover the exact dissociation limit of H2 in a minimal basis set. Alternatively α can be viewed as a regularization parameter, where each value of α represents a valid variant of BW-s2, which we denote as BW-s2(α). In this work, we semi-empirically optimize α for noncovalent interactions, thermochemistry, alkane conformational energies, electronic response properties, and transition metal datasets, leading to improvements in accuracy relative to the ab initio parameterization of BW-s2 and MP2. We demonstrate that the optimal α parameter (α = 4) is more transferable across chemical problems than energy-gap-dependent regularization parameters. This is attributable to the fact that the BW-s2(α) regularization strength depends on all of the information encoded in the t amplitudes rather than just orbital energy differences. While the computational scaling of BW-s2(α) is iterative O(N5), this effective and transferable approach to amplitude regularization is a promising route to incorporate higher-order correlation effects at second-order cost.
Collapse
Affiliation(s)
- Kevin Carter-Fenk
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, USA
| | | | | |
Collapse
|
6
|
Van Benschoten W, Petras HR, Shepherd JJ. Electronic Free Energy Surface of the Nitrogen Dimer Using First-Principles Finite Temperature Electronic Structure Methods. J Phys Chem A 2023; 127:6842-6856. [PMID: 37535315 PMCID: PMC10440793 DOI: 10.1021/acs.jpca.3c01741] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/14/2023] [Revised: 07/20/2023] [Indexed: 08/04/2023]
Abstract
We use full configuration interaction and density matrix quantum Monte Carlo methods to calculate the electronic free energy surface of the nitrogen dimer within the free-energy Born-Oppenheimer approximation. As the temperature is raised from T = 0, we find a temperature regime in which the internal energy causes bond strengthening. At these temperatures, adding in the entropy contributions is required to cause the bond to gradually weaken with increasing temperature. We predict a thermally driven dissociation for the nitrogen dimer between 22,000 to 63,200 K depending on symmetries and basis set. Inclusion of more spatial and spin symmetries reduces the temperature required. The origin of these observations is explored using the structure of the density matrix at various temperatures and bond lengths.
Collapse
Affiliation(s)
| | - Hayley R. Petras
- Department
of Chemistry, University of Iowa, Iowa City, Iowa 52242, United States
| | - James J. Shepherd
- Department
of Chemistry, University of Iowa, Iowa City, Iowa 52242, United States
| |
Collapse
|
7
|
Coveney CJN, Tew DP. A Regularized Second-Order Correlation Method from Green's Function Theory. J Chem Theory Comput 2023. [PMID: 37367932 DOI: 10.1021/acs.jctc.3c00246] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/28/2023]
Abstract
We present a scalable single-particle framework to treat electronic correlation in molecules and materials motivated by Green's function theory. We derive a size-extensive Brillouin-Wigner perturbation theory from the single-particle Green's function by introducing the Goldstone self-energy. This new ground state correlation energy, referred to as Quasi-Particle MP2 theory (QPMP2), avoids the characteristic divergences present in both second-order Møller-Plesset perturbation theory and Coupled Cluster Singles and Doubles within the strongly correlated regime. We show that the exact ground state energy and properties of the Hubbard dimer are reproduced by QPMP2 and demonstrate the advantages of the approach for larger Hubbard models where the metal-to-insulator transition is qualitatively reproduced, contrasting with the complete failure of traditional methods. We apply this formalism to characteristic strongly correlated molecular systems and show that QPMP2 provides an efficient, size-consistent regularization of MP2.
Collapse
Affiliation(s)
| | - David P Tew
- Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
| |
Collapse
|
8
|
Carter-Fenk K, Head-Gordon M. Repartitioned Brillouin-Wigner perturbation theory with a size-consistent second-order correlation energy. J Chem Phys 2023; 158:234108. [PMID: 37338032 PMCID: PMC10284609 DOI: 10.1063/5.0150033] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/10/2023] [Accepted: 06/05/2023] [Indexed: 06/21/2023] Open
Abstract
Second-order Møller-Plesset perturbation theory (MP2) often breaks down catastrophically in small-gap systems, leaving much to be desired in its performance for myriad chemical applications such as noncovalent interactions, thermochemistry, and dative bonding in transition metal complexes. This divergence problem has reignited interest in Brillouin-Wigner perturbation theory (BWPT), which is regular at all orders but lacks size consistency and extensivity, severely limiting its application to chemistry. In this work, we propose an alternative partitioning of the Hamiltonian that leads to a regular BWPT perturbation series that, through the second order, is size-extensive, size-consistent (provided its Hartree-Fock reference is also), and orbital invariant. Our second-order size-consistent Brillouin-Wigner (BW-s2) approach can describe the exact dissociation limit of H2 in a minimal basis set, regardless of the spin polarization of the reference orbitals. More broadly, we find that BW-s2 offers improvements relative to MP2 for covalent bond breaking, noncovalent interaction energies, and metal/organic reaction energies, although rivaling coupled-cluster with single and double substitutions for thermochemical properties.
Collapse
Affiliation(s)
- Kevin Carter-Fenk
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, USA
| | | |
Collapse
|
9
|
Weng G, Romanova M, Apelian A, Song H, Vlček V. Reduced Scaling of Optimal Regional Orbital Localization via Sequential Exhaustion of the Single-Particle Space. J Chem Theory Comput 2022; 18:4960-4972. [PMID: 35817013 PMCID: PMC9367006 DOI: 10.1021/acs.jctc.2c00315] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
![]()
Wannier functions have become a powerful tool in the
electronic
structure calculations of extended systems. The generalized Pipek-Mezey
Wannier functions exhibit appealing characteristics (e.g., reaching
an optimal localization and the separation of the σ–π
orbitals) compared with other schemes. However, when applied to giant
nanoscale systems, the orbital localization suffers from a large computational
cost overhead if one is interested in localized states in a small
fragment of the system. Herein, we present a swift, efficient, and
robust approach for obtaining regionally localized orbitals of a subsystem
within the generalized Pipek-Mezey scheme. The proposed algorithm
introduces a reduced work space and sequentially exhausts the entire
orbital space until the convergence of the localization functional.
It tackles systems with ∼10000 electrons within 0.5 h with
no loss in localization quality compared to the traditional approach.
Regionally localized orbitals with a higher extent of localization
are obtained via judiciously extending the subsystem’s size.
Exemplifying on large bulk and a 4 nm wide slab of diamond with an
NV– center, we demonstrate the methodology and discuss
how the choice of the localization region affects the excitation energy
of the defect. Furthermore, we show how the sequential algorithm is
easily extended to stochastic methodologies that do not provide individual
single-particle eigenstates. It is thus a promising tool to obtain
regionally localized states for solving the electronic structure problems
of a subsystem embedded in giant condensed systems.
Collapse
Affiliation(s)
- Guorong Weng
- Department of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106-9510, United States
| | - Mariya Romanova
- Department of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106-9510, United States
| | - Arsineh Apelian
- Department of Materials, University of California, Santa Barbara, California 93106-9510, United States
| | - Hanbin Song
- Department of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106-9510, United States
| | - Vojtěch Vlček
- Department of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106-9510, United States
| |
Collapse
|
10
|
Cruz JC, Garza J, Yanai T, Hirata S. Stochastic evaluation of four-component relativistic second-order many-body perturbation energies: A potentially quadratic-scaling correlation method. J Chem Phys 2022; 156:224102. [DOI: 10.1063/5.0091973] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A second-order many-body perturbation correction to the relativistic Dirac-Hartree-Fock energy is evaluated stochastically by integrating 13-dimensional products of four-component spinors and Coulomb potentials. The integration in the real space of electron coordinates is carried out by the Monte Carlo (MC) method with the Metropolis sampling, whereas the MC integration in the imaginary-time domain is performed by the inverse-CDF (cumulative distribution function) method. The computational cost to reach a given relative statistical error for spatially compact but heavy molecules is observed to be no worse than cubic and possibly quadratic with the number of electrons or basis functions. This is a vast improvement over the quintic scaling of the conventional, deterministic second-order many-body perturbation method. The algorithm is also easily and efficiently parallelized with demonstrated 92% strong scalability going from 64 to 4096 processors for a fixed job size.
Collapse
Affiliation(s)
- J. César Cruz
- Universidad Autónoma Metropolitana-Iztapalapa, Mexico
| | - Jorge Garza
- Departamento de Química, Universidad Autónoma Metropolitana-Iztapalapa, Mexico
| | - Takeshi Yanai
- Institute of Transformative Bio-Molecules, Nagoya University, Japan
| | - So Hirata
- Department of Chemistry, University of Illinois at Urbana-Champaign, United States of America
| |
Collapse
|
11
|
Van Benschoten WZ, Shepherd JJ. Piecewise Interaction Picture Density Matrix Quantum Monte Carlo. J Chem Phys 2022; 156:184107. [DOI: 10.1063/5.0094290] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The density matrix quantum Monte Carlo (DMQMC) set of methods stochastically samples the exact $N$-body density matrix for interacting electrons at finite temperature. We introduce a simple modification to the interaction picture DMQMC method (IP-DMQMC) which overcomes the limitation of only sampling one inverse temperature point at a time, instead allowing for the sampling of a temperature range within a single calculation thereby reducing the computational cost. At the target inverse temperature, instead of ending the simulation, we incorporate a change of picture away from the interaction picture. The resulting equations of motion have piecewise functions and use the interaction picture in the first phase of a simulation, followed by the application of the Bloch equation once the target inverse temperature is reached. We find that the performance of this method is similar to or better than the DMQMC and IP-DMQMC algorithms in a variety of molecular test systems.
Collapse
|
12
|
Baer R, Neuhauser D, Rabani E. Stochastic Vector Techniques in Ground-State Electronic Structure. Annu Rev Phys Chem 2022; 73:255-272. [PMID: 35081326 DOI: 10.1146/annurev-physchem-090519-045916] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
We review a suite of stochastic vector computational approaches for studying the electronic structure of extended condensed matter systems. These techniques help reduce algorithmic complexity, facilitate efficient parallelization, simplify computational tasks, accelerate calculations, and diminish memory requirements. While their scope is vast, we limit our study to ground-state and finite temperature density functional theory (DFT) and second-order perturbation theory. More advanced topics, such as quasiparticle (charge) and optical (neutral) excitations and higher-order processes, are covered elsewhere. We start by explaining how to use stochastic vectors in computations, characterizing the associated statistical errors. Next, we show how to estimate the electron density in DFT and discuss highly effective techniques to reduce statistical errors. Finally, we review the use of stochastic vector techniques for calculating correlation energies within the second-order Møller-Plesset perturbation theory and its finite temperature variational form. Example calculation results are presented and used to demonstrate the efficacy of the methods. Expected final online publication date for the Annual Review of Physical Chemistry, Volume 73 is April 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.
Collapse
Affiliation(s)
- Roi Baer
- Fritz Haber Center of Molecular Dynamics and Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem, Israel;
| | - Daniel Neuhauser
- Department of Chemistry and Biochemistry, University of California, Los Angeles, California, USA;
| | - Eran Rabani
- Department of Chemistry, University of California, Berkeley, California, USA; .,Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California, USA.,The Raymond and Beverly Sackler Center of Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv, Israel
| |
Collapse
|
13
|
Nguyen M, Li W, Li Y, Rabani E, Baer R, Neuhauser D. Tempering stochastic density functional theory. J Chem Phys 2021; 155:204105. [PMID: 34852484 DOI: 10.1063/5.0063266] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We introduce a tempering approach with stochastic density functional theory (sDFT), labeled t-sDFT, which reduces the statistical errors in the estimates of observable expectation values. This is achieved by rewriting the electronic density as a sum of a "warm" component complemented by "colder" correction(s). Since the warm component is larger in magnitude but faster to evaluate, we use many more stochastic orbitals for its evaluation than for the smaller-sized colder correction(s). This results in a significant reduction in the statistical fluctuations and systematic deviation compared to sDFT for the same computational effort. We demonstrate the method's performance on large hydrogen-passivated silicon nanocrystals, finding a reduction in the systematic deviation in the energy by more than an order of magnitude, while the systematic deviation in the forces is also quenched. Similarly, the statistical fluctuations are reduced by factors of ≈4-5 for the total energy and ≈1.5-2 for the forces on the atoms. Since the embedding in t-sDFT is fully stochastic, it is possible to combine t-sDFT with other variants of sDFT such as energy-window sDFT and embedded-fragmented sDFT.
Collapse
Affiliation(s)
- Minh Nguyen
- Department of Chemistry and Biochemistry, University of California at Los Angeles, Los Angeles, California 90095, USA
| | - Wenfei Li
- Department of Chemistry and Biochemistry, University of California at Los Angeles, Los Angeles, California 90095, USA
| | - Yangtao Li
- Department of Chemistry and Biochemistry, University of California at Los Angeles, Los Angeles, California 90095, USA
| | - Eran Rabani
- Department of Chemistry, University of California and Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA and The Raymond and Beverly Sackler Center of Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 69978, Israel
| | - Roi Baer
- Fritz Haber Center of Molecular Dynamics and Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - Daniel Neuhauser
- Department of Chemistry and Biochemistry, University of California at Los Angeles, and California Nanoscience Institute, Los Angeles, California 90095, USA
| |
Collapse
|
14
|
Petras HR, Van Benschoten WZ, Ramadugu SK, Shepherd JJ. The Sign Problem in Density Matrix Quantum Monte Carlo. J Chem Theory Comput 2021; 17:6036-6052. [PMID: 34546738 PMCID: PMC8515812 DOI: 10.1021/acs.jctc.1c00078] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023]
Abstract
Density matrix quantum Monte Carlo (DMQMC) is a recently developed method for stochastically sampling the N-particle thermal density matrix to obtain exact-on-average energies for model and ab initio systems. We report a systematic numerical study of the sign problem in DMQMC based on simulations of atomic and molecular systems. In DMQMC, the density matrix is written in an outer product basis of Slater determinants. In principle, this means that DMQMC needs to sample a space that scales in the system size, N, as O[(exp(N))2]. In practice, removing the sign problem requires a total walker population that exceeds a system-dependent critical walker population (Nc), imposing limitations on both storage and compute time. We establish that Nc for DMQMC is the square of Nc for FCIQMC. By contrast, the minimum Nc in the interaction picture modification of DMQMC (IP-DMQMC) is only linearly related to the Nc for FCIQMC. We find that this difference originates from the difference in propagation of IP-DMQMC versus canonical DMQMC: the former is asymmetric, whereas the latter is symmetric. When an asymmetric mode of propagation is used in DMQMC, there is a much greater stochastic error and is thus prohibitively expensive for DMQMC without the interaction picture adaptation. Finally, we find that the equivalence between IP-DMQMC and FCIQMC seems to extend to the initiator approximation, which is often required to study larger systems with large basis sets. This suggests that IP-DMQMC offers a way to ameliorate the cost of moving between a Slater determinant space and an outer product basis.
Collapse
Affiliation(s)
- Hayley R Petras
- Department of Chemistry, University of Iowa, Iowa City, Iowa 52242-1294, United States
| | | | - Sai Kumar Ramadugu
- Department of Chemistry, University of Iowa, Iowa City, Iowa 52242-1294, United States
| | - James J Shepherd
- Department of Chemistry, University of Iowa, Iowa City, Iowa 52242-1294, United States
| |
Collapse
|
15
|
Doran AE, Qiu DL, Hirata S. Monte Carlo MP2-F12 for Noncovalent Interactions: The C 60 Dimer. J Phys Chem A 2021; 125:7344-7351. [PMID: 34433271 DOI: 10.1021/acs.jpca.1c05021] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
A scalable stochastic algorithm is presented that can evaluate explicitly correlated (F12) second-order many-body perturbation (MP2) energies of weak, noncovalent, intermolecular interactions. It first transforms the formulas of the MP2 and F12 energy differences into a short sum of high-dimensional integrals of Green's functions in real space and imaginary time. These integrals are then evaluated by the Monte Carlo method augmented by parallel execution, redundant-walker convergence acceleration, direct-sampling autocorrelation elimination, and control-variate error reduction. By sharing electron-pair walkers across the supermolecule and its subsystems spanned by the joint basis set, the statistical uncertainty is reduced by one to 2 orders of magnitude in the MP2 binding energy corrected for the basis-set incompleteness and superposition errors. The method predicts the MP2-F12/aug-cc-pVDZ binding energy of 19.1 ± 4.0 kcal mol-1 for the C60 dimer at the center distance of 9.748 Å.
Collapse
Affiliation(s)
- Alexander E Doran
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
| | - David L Qiu
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
| | - So Hirata
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
| |
Collapse
|
16
|
Lupo C, Jamet F, Tse WHT, Rungger I, Weber C. Maximally localized dynamical quantum embedding for solving many-body correlated systems. NATURE COMPUTATIONAL SCIENCE 2021; 1:410-420. [PMID: 38217238 DOI: 10.1038/s43588-021-00090-3] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/08/2020] [Accepted: 05/21/2021] [Indexed: 01/15/2024]
Abstract
Quantum computing opens new avenues for modeling correlated materials, which are notoriously challenging to solve due to the presence of large electronic correlations. Quantum embedding approaches, such as dynamical mean-field theory, provide corrections to first-principles calculations for strongly correlated materials, which are poorly described at lower levels of theory. Such embedding approaches are computationally demanding on classical computing architectures and hence remain restricted to small systems, limiting the scope of their applicability. Hitherto, implementations on quantum computers have been limited by hardware constraints. Here, we derive a compact representation, where the number of quantum states is reduced for a given system while retaining a high level of accuracy. We benchmark our method for archetypal quantum states of matter that emerge due to electronic correlations, such as Kondo and Mott physics, both at equilibrium and for quenched systems. We implement this approach on a quantum emulator, demonstrating a reduction of the required number of qubits.
Collapse
Affiliation(s)
- Carla Lupo
- Theory & Simulation of Condensed Matter, King's College London, London, UK.
- National Physical Laboratory, Teddington, UK.
| | - François Jamet
- Theory & Simulation of Condensed Matter, King's College London, London, UK.
- National Physical Laboratory, Teddington, UK.
| | | | | | - Cedric Weber
- Theory & Simulation of Condensed Matter, King's College London, London, UK.
| |
Collapse
|
17
|
Doran AE, Hirata S. Stochastic evaluation of fourth-order many-body perturbation energies. J Chem Phys 2021; 154:134114. [PMID: 33832241 DOI: 10.1063/5.0047798] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A scalable, stochastic algorithm evaluating the fourth-order many-body perturbation (MP4) correction to energy is proposed. Three hundred Goldstone diagrams representing the MP4 correction are computer generated and then converted into algebraic formulas expressed in terms of Green's functions in real space and imaginary time. They are evaluated by the direct (i.e., non-Markov, non-Metropolis) Monte Carlo (MC) integration accelerated by the redundant-walker and control-variate algorithms. The resulting MC-MP4 method is efficiently parallelized and is shown to display O(n5.3) size-dependence of cost, which is nearly two ranks lower than the O(n7) dependence of the deterministic MP4 algorithm. It evaluates the MP4/aug-cc-pVDZ energy for benzene, naphthalene, phenanthrene, and corannulene with the statistical uncertainty of 10 mEh (1.1% of the total basis-set correlation energy), 38 mEh (2.6%), 110 mEh (5.5%), and 280 mEh (9.0%), respectively, after about 109 MC steps.
Collapse
Affiliation(s)
- Alexander E Doran
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - So Hirata
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| |
Collapse
|
18
|
Quintas-Sánchez E, Dawes R. Spectroscopy and Scattering Studies Using Interpolated Ab Initio Potentials. Annu Rev Phys Chem 2021; 72:399-421. [PMID: 33503385 DOI: 10.1146/annurev-physchem-090519-051837] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
The Born-Oppenheimer potential energy surface (PES) has come a long way since its introduction in the 1920s, both conceptually and in predictive power for practical applications. Nevertheless, nearly 100 years later-despite astonishing advances in computational power-the state-of-the-art first-principles prediction of observables related to spectroscopy and scattering dynamics is surprisingly limited. For example, the water dimer, (H2O)2, with only six nuclei and 20 electrons, still presents a formidable challenge for full-dimensional variational calculations of bound states and is considered out of reach for rigorous scattering calculations. The extremely poor scaling of the most rigorous quantum methods is fundamental; however, recent progress in development of approximate methodologies has opened the door to fairly routine high-quality predictions, unthinkable 20 years ago. In this review, in relation to the workflow of spectroscopy and/or scattering studies, we summarize progress and challenges in the component areas of electronic structure calculations, PES fitting, and quantum dynamical calculations.
Collapse
Affiliation(s)
- Ernesto Quintas-Sánchez
- Department of Chemistry, Missouri University of Science and Technology, Rolla, Missouri 65409, USA;
| | - Richard Dawes
- Department of Chemistry, Missouri University of Science and Technology, Rolla, Missouri 65409, USA;
| |
Collapse
|
19
|
Bircher MP, Villard J, Rothlisberger U. Efficient Treatment of Correlation Energies at the Basis-Set Limit by Monte Carlo Summation of Continuum States. J Chem Theory Comput 2020; 16:6550-6559. [PMID: 32915565 PMCID: PMC7584365 DOI: 10.1021/acs.jctc.0c00724] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/11/2020] [Indexed: 11/28/2022]
Abstract
The calculation of electron correlation is vital for the description of atomistic phenomena in physics, chemistry, and biology. However, accurate wavefunction-based methods exhibit steep scaling and often sluggish convergence with respect to the basis set at hand. Because of their delocalization and ease of extrapolation to the basis-set limit, plane waves would be ideally suited for the calculation of basis-set limit correlation energies. However, the routine use of correlated wavefunction approaches in a plane-wave basis set is hampered by prohibitive scaling due to a large number of virtual continuum states and has not been feasible for all but the smallest systems, even if substantial computational resources are available and methods with comparably beneficial scaling, such as the Møller-Plesset perturbation theory to second order (MP2), are used. Here, we introduce a stochastic sampling of the MP2 integrand based on Monte Carlo summation over continuum orbitals, which allows for speedups of up to a factor of 1000. Given a fixed number of sampling points, the resulting algorithm is dominated by a flat scaling of ∼ O ( N 2 ) . Absolute correlation energies are accurate to <0.1 kcal/mol with respect to conventional calculations for several hundreds of electrons. This allows for the calculation of unbiased basis-set limit correlation energies for systems containing hundreds of electrons with unprecedented efficiency gains based on a straightforward treatment of continuum contributions.
Collapse
Affiliation(s)
- Martin P. Bircher
- Computational
and Soft Matter Physics, Universität
Wien, Sensengasse 8/9, A-1090 Wien, Austria
| | - Justin Villard
- Laboratory
of Computational Chemistry and Biochemistry, Institut des Sciences
et Ingénierie Chimiques, Ecole Polytechnique
Fédérale de Lausanne (EPFL), Av. F.A. Forel 2, CH-1015 Lausanne, Switzerland
| | - Ursula Rothlisberger
- Laboratory
of Computational Chemistry and Biochemistry, Institut des Sciences
et Ingénierie Chimiques, Ecole Polytechnique
Fédérale de Lausanne (EPFL), Av. F.A. Forel 2, CH-1015 Lausanne, Switzerland
| |
Collapse
|
20
|
Doran AE, Hirata S. Convergence acceleration of Monte Carlo many-body perturbation methods by direct sampling. J Chem Phys 2020; 153:104112. [DOI: 10.1063/5.0020583] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Alexander E. Doran
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - So Hirata
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| |
Collapse
|
21
|
Doran AE, Hirata S. Convergence acceleration of Monte Carlo many-body perturbation methods by using many control variates. J Chem Phys 2020; 153:094108. [DOI: 10.1063/5.0020584] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022] Open
Affiliation(s)
- Alexander E. Doran
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - So Hirata
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| |
Collapse
|
22
|
Dou W, Chen M, Takeshita TY, Baer R, Neuhauser D, Rabani E. Range-separated stochastic resolution of identity: Formulation and application to second-order Green’s function theory. J Chem Phys 2020; 153:074113. [DOI: 10.1063/5.0015177] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Wenjie Dou
- Department of Chemistry, University of California Berkeley, Berkeley, California 94720, USA
| | - Ming Chen
- Department of Chemistry, University of California Berkeley, Berkeley, California 94720, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | | | - Roi Baer
- Fritz Haber Center for Molecular Dynamics, Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - Daniel Neuhauser
- Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095, USA
| | - Eran Rabani
- Department of Chemistry, University of California Berkeley, Berkeley, California 94720, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
- The Raymond and Beverly Sackler Center of Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 69978, Israel
| |
Collapse
|
23
|
Lee J, Reichman DR. Stochastic resolution-of-the-identity auxiliary-field quantum Monte Carlo: Scaling reduction without overhead. J Chem Phys 2020; 153:044131. [DOI: 10.1063/5.0015077] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Joonho Lee
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, USA
| | - David R. Reichman
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, USA
| |
Collapse
|
24
|
White AF, Kin-Lic Chan G. Finite-temperature coupled cluster: Efficient implementation and application to prototypical systems. J Chem Phys 2020; 152:224104. [DOI: 10.1063/5.0009845] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023] Open
Affiliation(s)
- Alec F. White
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Garnet Kin-Lic Chan
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| |
Collapse
|
25
|
Brooks J, Weng G, Taylor S, Vlcek V. Stochastic many-body perturbation theory for Moiré states in twisted bilayer phosphorene. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:234001. [PMID: 31958775 DOI: 10.1088/1361-648x/ab6d8c] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
We implement stochastic many-body perturbation theory for systems with 2D periodic boundary conditions. The method is used to compute quasiparticle excitations in twisted bilayer phosphorene. Excitation energies are studied using stochastic [Formula: see text] and partially self-consistent [Formula: see text] approaches. The approach is inexpensive; it is used to study twisted systems with unit cells containing >2700 atoms (>13 500 valence electrons), which corresponds to a minimum twisting angle of [Formula: see text] [Formula: see text]. Twisted bilayers exhibit band splitting, increased localization and formation of localized Moiré impurity states, as documented by band-structure unfolding. Structural changes in twisted structures lift band degeneracies. Energies of the impurity states vary with the twisting angle due to an interplay between non-local exchange and polarization effects. The mechanisms of quasiparticle energy (de)stabilization due to twisting are likely applicable to a wide range of low-dimensional Moiré superstructures.
Collapse
Affiliation(s)
- Jacob Brooks
- Department of Chemical Engineering, University of California, Santa Barbara, CA 93106-9510, United States of America
| | | | | | | |
Collapse
|
26
|
Dong X, Zgid D, Gull E, Strand HUR. Legendre-spectral Dyson equation solver with super-exponential convergence. J Chem Phys 2020; 152:134107. [DOI: 10.1063/5.0003145] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Xinyang Dong
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Dominika Zgid
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Emanuel Gull
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Hugo U. R. Strand
- Department of Physics, Chalmers University of Technology, SE-412 96 Gothenburg, Sweden
- Center for Computational Quantum Physics, The Flatiron Institute, New York, New York 10010, USA
| |
Collapse
|
27
|
Zhang X, Lu G, Baer R, Rabani E, Neuhauser D. Linear-Response Time-Dependent Density Functional Theory with Stochastic Range-Separated Hybrids. J Chem Theory Comput 2020; 16:1064-1072. [DOI: 10.1021/acs.jctc.9b01121] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Xu Zhang
- Department of Physics and Astronomy, California State University Northridge, Northridge, California 91330, United States
| | - Gang Lu
- Department of Physics and Astronomy, California State University Northridge, Northridge, California 91330, United States
| | - Roi Baer
- Fritz Haber Center for Molecular Dynamics, Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - Eran Rabani
- Department of Chemistry, University of California, Berkeley, California 94720, United States
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
- The Raymond and Beverly Sackler Center of Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 69978, Israel
| | - Daniel Neuhauser
- Department of Chemistry and Biochemistry, University of California at Los Angeles, Los Angeles, California 90095, United States
| |
Collapse
|
28
|
Li Z. Stochastic many-body perturbation theory for electron correlation energies. J Chem Phys 2019; 151:244114. [DOI: 10.1063/1.5128719] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Zhendong Li
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China
| |
Collapse
|
29
|
Tuovinen R, Covito F, Sentef MA. Efficient computation of the second-Born self-energy using tensor-contraction operations. J Chem Phys 2019; 151:174110. [DOI: 10.1063/1.5121820] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Riku Tuovinen
- Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Fabio Covito
- Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Michael A. Sentef
- Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761 Hamburg, Germany
| |
Collapse
|
30
|
Dou W, Takeshita TY, Chen M, Baer R, Neuhauser D, Rabani E. Stochastic Resolution of Identity for Real-Time Second-Order Green’s Function: Ionization Potential and Quasi-Particle Spectrum. J Chem Theory Comput 2019; 15:6703-6711. [DOI: 10.1021/acs.jctc.9b00918] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Wenjie Dou
- Department of Chemistry, University of California Berkeley, Berkeley, California 94720, United States
| | - Tyler Y. Takeshita
- Mercedes-Benz Research and Development North America, Sunnyvale, California 94085, United States
| | - Ming Chen
- Department of Chemistry, University of California Berkeley, Berkeley, California 94720, United States
- Materials Sciences Devision, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Roi Baer
- Fritz Haber Research Center for Molecular Dynamics, Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 9190401, Israel
| | - Daniel Neuhauser
- Department of Chemistry and Biochemistry, University of California Los Angeles, Los Angeles, California 90095, United States
| | - Eran Rabani
- Department of Chemistry, University of California Berkeley, Berkeley, California 94720, United States
- Materials Sciences Devision, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
- The Raymond and Beverly Sackler Center of Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 69978, Israel
| |
Collapse
|
31
|
Doran AE, Hirata S. Monte Carlo Second- and Third-Order Many-Body Green’s Function Methods with Frequency-Dependent, Nondiagonal Self-Energy. J Chem Theory Comput 2019; 15:6097-6110. [DOI: 10.1021/acs.jctc.9b00693] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Alexander E. Doran
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
| | - So Hirata
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
| |
Collapse
|
32
|
Takeshita TY, Dou W, Smith DGA, de Jong WA, Baer R, Neuhauser D, Rabani E. Stochastic resolution of identity second-order Matsubara Green's function theory. J Chem Phys 2019; 151:044114. [PMID: 31370516 DOI: 10.1063/1.5108840] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We develop a stochastic resolution of identity representation to the second-order Matsubara Green's function (sRI-GF2) theory. Using a stochastic resolution of the Coulomb integrals, the second order Born self-energy in GF2 is decoupled and reduced to matrix products/contractions, which reduces the computational cost from O(N5) to O(N3) (with N being the number of atomic orbitals). The current approach can be viewed as an extension to our previous work on stochastic resolution of identity second order Møller-Plesset perturbation theory [T. Y. Takeshita et al., J. Chem. Theory Comput. 13, 4605 (2017)] and offers an alternative to previous stochastic GF2 formulations [D. Neuhauser et al., J. Chem. Theory Comput. 13, 5396 (2017)]. We show that sRI-GF2 recovers the deterministic GF2 results for small systems, is computationally faster than deterministic GF2 for N > 80, and is a practical approach to describe weak correlations in systems with 103 electrons and more.
Collapse
Affiliation(s)
- Tyler Y Takeshita
- Mercedes-Benz Research and Development North America, Sunnyvale, California 94085, USA
| | - Wenjie Dou
- Department of Chemistry, University of California Berkeley, Berkeley, California 94720, USA
| | - Daniel G A Smith
- The Molecular Sciences Software Institute, Blacksburg, Virginia 24060, USA
| | - Wibe A de Jong
- Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Roi Baer
- Fritz Haber Center for Molecular Dynamics, Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - Daniel Neuhauser
- Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095, USA
| | - Eran Rabani
- Department of Chemistry, University of California Berkeley, Berkeley, California 94720, USA
| |
Collapse
|
33
|
Zandkarimi B, Alexandrova AN. Surface‐supported cluster catalysis: Ensembles of metastable states run the show. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2019. [DOI: 10.1002/wcms.1420] [Citation(s) in RCA: 25] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/10/2023]
Affiliation(s)
- Borna Zandkarimi
- Department of Chemistry and Biochemistry University of California, Los Angeles Los Angeles California
| | - Anastassia N. Alexandrova
- Department of Chemistry and Biochemistry University of California, Los Angeles Los Angeles California
- California NanoSystems Institute University of California, Los Angeles Los Angeles California
| |
Collapse
|
34
|
Stochastic density functional theory. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2019. [DOI: 10.1002/wcms.1412] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
|
35
|
Affiliation(s)
- Zhu Ruan
- Fritz Haber Center for Molecular Dynamics, Institute of Chemistry, The Hebrew University of Jerusalem , Jerusalem, Israel
| | - Roi Baer
- Fritz Haber Center for Molecular Dynamics, Institute of Chemistry, The Hebrew University of Jerusalem , Jerusalem, Israel
| |
Collapse
|
36
|
Schäfer T, Ramberger B, Kresse G. Laplace transformed MP2 for three dimensional periodic materials using stochastic orbitals in the plane wave basis and correlated sampling. J Chem Phys 2018; 148:064103. [PMID: 29448777 DOI: 10.1063/1.5016100] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We present an implementation and analysis of a stochastic high performance algorithm to calculate the correlation energy of three-dimensional periodic systems in second-order Møller-Plesset perturbation theory (MP2). In particular we measure the scaling behavior of the sample variance and probe whether this stochastic approach is competitive if accuracies well below 1 meV per valence orbital are required, as it is necessary for calculations of adsorption, binding, or surface energies. The algorithm is based on the Laplace transformed MP2 (LTMP2) formulation in the plane wave basis. The time-dependent Hartree-Fock orbitals, appearing in the LTMP2 formulation, are stochastically rotated in the occupied and unoccupied Hilbert space. This avoids a full summation over all combinations of occupied and unoccupied orbitals, as inspired by the work of Neuhauser, Rabani, and Baer [J. Chem. Theory Comput. 9, 24 (2013)]. Additionally, correlated sampling is introduced, accelerating the statistical convergence significantly.
Collapse
Affiliation(s)
- Tobias Schäfer
- Faculty of Physics and Center for Computational Materials Science, University of Vienna, Sensengasse 8/12, A-1090 Vienna, Austria
| | - Benjamin Ramberger
- Faculty of Physics and Center for Computational Materials Science, University of Vienna, Sensengasse 8/12, A-1090 Vienna, Austria
| | - Georg Kresse
- Faculty of Physics and Center for Computational Materials Science, University of Vienna, Sensengasse 8/12, A-1090 Vienna, Austria
| |
Collapse
|