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Sun C, Gao F, Scuseria GE. Selected Nonorthogonal Configuration Interaction with Compressed Single and Double Excitations. J Chem Theory Comput 2024; 20:3741-3748. [PMID: 38640423 DOI: 10.1021/acs.jctc.4c00240] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/21/2024]
Abstract
Addressing both dynamic and static correlations accurately is a primary goal in electronic structure theory. Nonorthogonal configuration interaction (NOCI) is a versatile tool for treating static correlation, offering chemical insights by combining diverse reference states. Nevertheless, achieving quantitative accuracy requires the inclusion of the missing dynamic correlation. This work introduces a framework for compressing orthogonal single and double excitations into a NOCI of a much smaller dimension. This compression is repeated with each Slater determinant in a reference NOCI, resulting in another NOCI that includes all of its single and double excitations (NOCISD), effectively recovering the missing dynamic correlations from the reference. This compressed NOCISD is further refined through a selection process using metric and energy tests (SNOCISD). We validate the effectiveness of SNOCISD through its application to the dissociation of the nitrogen molecule and the hole-doped two-dimensional Hubbard model at various interaction strengths.
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Affiliation(s)
- Chong Sun
- Department of Chemistry, Rice University, Houston, Texas 77005-1892, United States
| | - Fei Gao
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, United States
| | - Gustavo E Scuseria
- Department of Chemistry, Rice University, Houston, Texas 77005-1892, United States
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, United States
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2
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Dutta R, Gao F, Khamoshi A, Henderson TM, Scuseria GE. Correlated pair ansatz with a binary tree structure. J Chem Phys 2024; 160:084113. [PMID: 38421064 DOI: 10.1063/5.0185375] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/30/2023] [Accepted: 02/02/2024] [Indexed: 03/02/2024] Open
Abstract
We develop an efficient algorithm to implement the recently introduced binary tree state (BTS) ansatz on a classical computer. BTS allows a simple approximation to permanents arising from the computationally intractable antisymmetric product of interacting geminals and respects size-consistency. We show how to compute BTS overlap and reduced density matrices efficiently. We also explore two routes for developing correlated BTS approaches: Jastrow coupled cluster on BTS and linear combinations of BT states. The resulting methods show great promise in benchmark applications to the reduced Bardeen-Cooper-Schrieffer Hamiltonian and the one-dimensional XXZ Heisenberg Hamiltonian.
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Affiliation(s)
- Rishab Dutta
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
| | - Fei Gao
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
| | - Armin Khamoshi
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
| | - Thomas M Henderson
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
| | - Gustavo E Scuseria
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
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Dong X, Thompson LM. Time propagation of electronic wavefunctions using nonorthogonal determinant expansions. J Chem Phys 2024; 160:024106. [PMID: 38189613 DOI: 10.1063/5.0179601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/03/2023] [Accepted: 12/15/2023] [Indexed: 01/09/2024] Open
Abstract
The use of truncated configuration interaction in real-time time-dependent simulations of electron dynamics provides a balance of computational cost and accuracy, while avoiding some of the failures associated with real-time time-dependent density functional theory. However, low-order truncated configuration interaction also has limitations, such as overestimation of polarizability in configuration interaction singles, even when perturbative doubles are included. Increasing the size of the determinant expansion may not be computationally feasible, and so, in this work, we investigate the use of nonorthogonality in the determinant expansion to establish the extent to which higher-order substitutions can be recovered, providing an improved description of electron dynamics. Model systems are investigated to quantify the extent to which different methods accurately reproduce the (hyper)polarizability, including the high-harmonic generation spectrum of H2, water, and butadiene.
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Affiliation(s)
- Xinju Dong
- Department of Chemistry, University of Louisville, Louisville, Kentucky 40205, USA
| | - Lee M Thompson
- Department of Chemistry, University of Louisville, Louisville, Kentucky 40205, USA
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Kempfer-Robertson EM, Mahler AD, Haase MN, Roe P, Thompson LM. Nonorthogonal Active Space Decomposition of Wave Functions with Multiple Correlation Mechanisms. J Phys Chem Lett 2022; 13:12041-12048. [PMID: 36541869 DOI: 10.1021/acs.jpclett.2c03349] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/17/2023]
Abstract
The nonorthogonal active space decomposition (NO-ASD) methodology is proposed for describing systems containing multiple correlation mechanisms. NO-ASD partitions the wave function by a correlation mechanism, such that the interactions between different correlation mechanisms are treated with an effective Hamiltonian approach, while interactions between correlated orbitals in the same correlation mechanism are treated explicitly. As a result, the determinant expansion scales polynomially with the number of correlation mechanisms rather than exponentially, which significantly reduces the factorial scaling associated with the size of the correlated orbital space. Despite the nonorthogonal framework of NO-ASD, the approach can take advantage of computational efficient matrix element evaluation when performing nonorthogonal coupling of orthogonal determinant expansions. In this work, we introduce and examine the NO-ASD approach in comparison to complete active space methods to establish how the NO-ASD approach reduces the problem dimensionality and the extent to which it affects the amount of correlation energy recovered. Calculations are performed on ozone, nickel-acetylene, and isomers of μ-oxo dicopper ammonia.
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Affiliation(s)
| | - Andrew D Mahler
- Department of Chemistry, University of Louisville, Louisville, Kentucky40205, United States
| | - Meagan N Haase
- Department of Chemistry, University of Louisville, Louisville, Kentucky40205, United States
| | - Piper Roe
- Department of Chemistry, University of Louisville, Louisville, Kentucky40205, United States
| | - Lee M Thompson
- Department of Chemistry, University of Louisville, Louisville, Kentucky40205, United States
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5
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Lu Y, Zhao R, Zhang J, Liu M, Gao J. Minimal Active Space: NOSCF and NOSI in Multistate Density Functional Theory. J Chem Theory Comput 2022; 18:6407-6420. [DOI: 10.1021/acs.jctc.2c00908] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Yangyi Lu
- Institute of Systems and Physical Biology, Shenzhen Bay Laboratory, Shenzhen518055, China
| | - Ruoqi Zhao
- Institute of Systems and Physical Biology, Shenzhen Bay Laboratory, Shenzhen518055, China
- Institute of Theoretical Chemistry, Jilin University, Changchun, Jilin Province130023, China
| | - Jun Zhang
- Institute of Systems and Physical Biology, Shenzhen Bay Laboratory, Shenzhen518055, China
| | - Meiyi Liu
- Institute of Systems and Physical Biology, Shenzhen Bay Laboratory, Shenzhen518055, China
| | - Jiali Gao
- Institute of Systems and Physical Biology, Shenzhen Bay Laboratory, Shenzhen518055, China
- Department of Chemistry and Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota55455, United States
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Kempfer-Robertson EM, Haase MN, Bersson JS, Avdic I, Thompson LM. Role of Exact Exchange in Difference Projected Double-Hybrid Density Functional Theory for Treatment of Local, Charge Transfer, and Rydberg Excitations. J Phys Chem A 2022; 126:8058-8069. [PMID: 36269072 DOI: 10.1021/acs.jpca.2c04338] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Difference approaches to the study of excited states have undergone a renaissance in recent years, with the development of a plethora of algorithms for locating self-consistent field approximations to excited states. Density functional theory is likely to offer the best balance of cost and accuracy for difference approaches, and yet there has been little investigation of how the parametrization of density functional approximations affects performance. In this work, we aim to explore the role of the global Hartree-Fock exchange parameter in tuning accuracy of different excitation types within the framework of the recently introduced difference projected double-hybrid density functional theory approach and contrast the performance with conventional time-dependent double-hybrid density functional theory. Difference projected double-hybrid density functional theory was demonstrated to give vertical excitation energies with average error and standard deviation with respect to multireference perturbation theory comparable to more expensive linear-response coupled cluster approaches ( J. Chem. Phys.2020, 153, 074103). However, despite benchmarking of local excitations, there has been no investigation of the methods performance for charge transfer or Rydberg excitations. In this work we report a new benchmark of charge transfer, Rydberg, and local excited state vertical excitation energies and examine how the exact Hartree-Fock exchange affects the benchmark performance to provide a deeper understanding of how projection and nonlocal correlation balance differing sources of error in the ground and excited states.
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Affiliation(s)
| | - Meagan N Haase
- Department of Chemistry, University of Louisville, Louisville, Kentucky40205, United States
| | - Jonathan S Bersson
- Department of Chemistry, University of Louisville, Louisville, Kentucky40205, United States
| | - Irma Avdic
- Department of Chemistry, University of Louisville, Louisville, Kentucky40205, United States
| | - Lee M Thompson
- Department of Chemistry, University of Louisville, Louisville, Kentucky40205, United States
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Abstract
We report a rigorous formulation of density functional theory for excited states, providing a theoretical foundation for a multistate density functional theory. We prove the existence of a Hamiltonian matrix functional H[D] of the multistate matrix density D(r) in the subspace spanned by the lowest N eigenstates. Here, D(r) is an N-dimensional matrix of state densities and transition densities. Then, a variational principle of the multistate subspace energy is established, whose minimization yields both the energies and densities of the individual N eigenstates. Furthermore, we prove that the N-dimensional matrix density D(r) can be sufficiently represented by N2 nonorthogonal Slater determinants, based on which an interacting active space is introduced for practical calculations. This work establishes that the ground and excited states can be treated on an equal footing in density functional theory.
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Affiliation(s)
- Yangyi Lu
- Institute of Systems and Physical Biology, Shenzhen Bay Laboratory, Shenzhen 518055, China
| | - Jiali Gao
- Institute of Systems and Physical Biology, Shenzhen Bay Laboratory, Shenzhen 518055, China
- Department of Chemistry and Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455, United States
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Straatsma TP, Broer R, Sánchez-Mansilla A, Sousa C, de Graaf C. GronOR: Scalable and Accelerated Nonorthogonal Configuration Interaction for Molecular Fragment Wave Functions. J Chem Theory Comput 2022; 18:3549-3565. [PMID: 35640094 DOI: 10.1021/acs.jctc.2c00266] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
GronOR is a program package for nonorthogonal configuration interaction calculations. Electronic wave functions are constructed in terms of antisymmetrized products of multiconfiguration molecular fragment wave functions. The computational complexity of the nonorthogonal methodologies implemented in GronOR applied to large molecular assemblies requires a design that takes full advantage of massively parallel supercomputer architectures and accelerator technologies. This work describes the implementation strategy and resulting performance characteristics. In addition to parallelization and acceleration, the software development strategy includes aspects of fault resiliency and heterogeneous computing. The program was designed for large-scale supercomputers but also runs effectively on small clusters and workstations for small molecular systems. GronOR is available as open source to the scientific community.
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Affiliation(s)
- T P Straatsma
- National Center for Computational Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6373, United States.,Department of Chemistry and Biochemistry, University of Alabama, Tuscaloosa, Alabama 35487-0336, United States
| | - R Broer
- Theoretical Chemistry Group, Zernike Institute for Advanced Materials, University of Groningen, 9747 AG Groningen, The Netherlands
| | - A Sánchez-Mansilla
- Department of Physical and Inorganic Chemistry, Universitat Rovira i Virgili, C. Marcel·lí Domingo 1, 43007 Tarragona, Spain
| | - C Sousa
- Department of Physical Chemistry and Institut de Química Teòrica i Computacional, Universitat de Barcelona, 08028 Barcelona, Spain
| | - C de Graaf
- Theoretical Chemistry Group, Zernike Institute for Advanced Materials, University of Groningen, 9747 AG Groningen, The Netherlands.,Department of Physical and Inorganic Chemistry, Universitat Rovira i Virgili, C. Marcel·lí Domingo 1, 43007 Tarragona, Spain.,ICREA, Pg. Lluís Companys 23, 08010 Barcelona, Spain
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