1
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Cheng Y, Ma H. Renormalized-Residue-Based Multireference Configuration Interaction Method for Strongly Correlated Systems. J Chem Theory Comput 2024; 20:1988-2009. [PMID: 38380619 DOI: 10.1021/acs.jctc.3c01247] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/22/2024]
Abstract
The implementation of multireference configuration interaction (MRCI) methods in quantum systems with large active spaces is hindered by the expansion of configuration bases or the intricate handling of reduced density matrices (RDMs). In this work, we present a spin-adapted renormalized-residue-based MRCI (RR-MRCI) approach that leverages renormalized residues to effectively capture the entanglement between active and inactive orbitals. This approach is reinforced by a novel efficient algorithm, which also facilitates an efficient deployment of spin-adapted matrix product state MRCI (MPS-MRCI). The RR-MRCI framework possesses several advantages: (1) It considers the orbital entanglement and utilizes highly compressed MPS structure, improving computational accuracy and efficiency compared with internally contracted (ic) MRCI. (2) Utilizing small-sized buffer environments of a few external orbitals as probes based on quantum information theory, it enhances computational efficiency over MPS-MRCI and offers potential application to large molecular systems. (3) The RR framework can be implemented in conjunction with ic-MRCI, eliminating the need for high-rank RDMs, by using distinct renormalized residues. We evaluated this method across nine diverse molecular systems, including Cu2O22+ with an active space of (24e,24o) and two complexes of lanthanide and actinide with active space (38e,36o), demonstrating the method's versatility and efficacy.
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Affiliation(s)
- Yifan Cheng
- School of Chemistry and Chemical Engineering, Nanjing University, Nanjing, Jiangsu 210023, China
| | - Haibo Ma
- Qingdao Institute for Theoretical and Computational Sciences, School of Chemistry and Chemical Engineering, Shandong University, Qingdao, Shandong 266237, China
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2
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Matoušek M, Pernal K, Pavošević F, Veis L. Variational Quantum Eigensolver Boosted by Adiabatic Connection. J Phys Chem A 2024; 128:687-698. [PMID: 38214999 PMCID: PMC10823474 DOI: 10.1021/acs.jpca.3c07590] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/17/2023] [Revised: 12/28/2023] [Accepted: 12/29/2023] [Indexed: 01/14/2024]
Abstract
In this work, we integrate the variational quantum eigensolver (VQE) with the adiabatic connection (AC) method for efficient simulations of chemical problems on near-term quantum computers. Orbital-optimized VQE methods are employed to capture the strong correlation within an active space, and classical AC corrections recover the dynamical correlation effects comprising electrons outside of the active space. On two challenging strongly correlated problems, namely, the dissociation of N2 and the electronic structure of the tetramethyleneethane biradical, we show that the combined VQE-AC approach enhances the performance of VQE dramatically. Moreover, since the AC corrections do not bring any additional requirements on quantum resources or measurements, they can actually boost the VQE algorithms. Our work paves the way toward quantum simulations of real-life problems on near-term quantum computers.
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Affiliation(s)
- Mikuláš Matoušek
- J.
Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 18223 Prague 8, Czech Republic
- Faculty
of Mathematics and Physics, Charles University, 121 16 Prague, Czech Republic
| | - Katarzyna Pernal
- Institute
of Physics, Lodz University of Technology, ul. Wolczanska 217/221, 93-005 Lodz, Poland
| | | | - Libor Veis
- J.
Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 18223 Prague 8, Czech Republic
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3
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Zhai H, Larsson HR, Lee S, Cui ZH, Zhu T, Sun C, Peng L, Peng R, Liao K, Tölle J, Yang J, Li S, Chan GKL. Block2: A comprehensive open source framework to develop and apply state-of-the-art DMRG algorithms in electronic structure and beyond. J Chem Phys 2023; 159:234801. [PMID: 38108484 DOI: 10.1063/5.0180424] [Citation(s) in RCA: 9] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/09/2023] [Accepted: 11/16/2023] [Indexed: 12/19/2023] Open
Abstract
block2 is an open source framework to implement and perform density matrix renormalization group and matrix product state algorithms. Out-of-the-box it supports the eigenstate, time-dependent, response, and finite-temperature algorithms. In addition, it carries special optimizations for ab initio electronic structure Hamiltonians and implements many quantum chemistry extensions to the density matrix renormalization group, such as dynamical correlation theories. The code is designed with an emphasis on flexibility, extensibility, and efficiency and to support integration with external numerical packages. Here, we explain the design principles and currently supported features and present numerical examples in a range of applications.
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Affiliation(s)
- Huanchen Zhai
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Henrik R Larsson
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Seunghoon Lee
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Zhi-Hao Cui
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Tianyu Zhu
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Chong Sun
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Linqing Peng
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Ruojing Peng
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Ke Liao
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Johannes Tölle
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Junjie Yang
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Shuoxue Li
- 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
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4
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Ugandi M, Roemelt M. A configuration-based heatbath-CI for spin-adapted multireference electronic structure calculations with large active spaces. J Comput Chem 2023; 44:2374-2390. [PMID: 37589287 DOI: 10.1002/jcc.27203] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/16/2023] [Revised: 07/24/2023] [Accepted: 07/27/2023] [Indexed: 08/18/2023]
Abstract
This work reports on a spin-pure configuration-based implementation of the heatbath configuration interaction (HCI) algorithm for selective configuration interaction. Besides the obvious advantage of being spin-pure, the presented method combines the compactness of the configurational ansatz with the known efficiency of the HCI algorithm and a variety of algorithmic and conceptual ideas to achieve a high level of performance. In particular, through pruning of the selected configurational space after HCI selection by means of a more strict criterion, a more compact wavefunction representation is obtained. Moreover, the underlying logic of the method allows us to minimize the number of redundant matrix-matrix multiplications while making use of just-in-time compilation to achieve fast diagonalization of the Hamiltonian. The critical search for 2-electron connections within the configurational space is facilitated by a tree-based representation thereof as suggested previously by Gopal et al. Usage of a prefix-based parallelization and batching during the calculation of the PT2-correction leads to a good load balancing and significantly reduced memory requirements for these critical steps of the calculation. In this way, the need for a semistochastic approach to the PT2 correction is avoided even for large configurational spaces. Finally, several test-cases are discussed to demonstrate the strengths and weaknesses of the presented method.
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Affiliation(s)
- Mihkel Ugandi
- Institut für Chemie, Humboldt-Universität zu Berlin, Berlin, Germany
| | - Michael Roemelt
- Institut für Chemie, Humboldt-Universität zu Berlin, Berlin, Germany
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5
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King DS, Truhlar DG, Gagliardi L. Variational Active Space Selection with Multiconfiguration Pair-Density Functional Theory. J Chem Theory Comput 2023; 19:8118-8128. [PMID: 37905518 DOI: 10.1021/acs.jctc.3c00792] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2023]
Abstract
The selection of an adequate set of active orbitals for modeling strongly correlated electronic states is difficult to automate because it is highly dependent on the states and molecule of interest. Although many approaches have shown some success, no single approach has worked well in all cases. In light of this, we present the "discrete variational selection" (DVS) approach to active space selection, in which one generates multiple trial wave functions from a diverse set of systematically constructed active spaces and then selects between these wave functions variationally. We apply this DVS approach to 207 vertical excitations of small-to-medium-sized organic and inorganic molecules (with 3 to 18 atoms) in the QUESTDB database by (i) constructing various sets of active space orbitals through diagonalization of parametrized operators and (ii) choosing the result with the lowest average energy among the states of interest. This approach proves ineffective when variationally selecting between wave functions using the density matrix renormalization group (DMRG) or complete active space self-consistent field (CASSCF) energy but is able to provide good results when variationally selecting between wave functions using the energy of the translated PBE (tPBE) functional from multiconfiguration pair-density functional theory (MC-PDFT). Applying this DVS-tPBE approach to selection among state-averaged DMRG wave functions, we obtain a mean unsigned error of only 0.17 eV using hybrid MC-PDFT. This result matches that of our previous benchmark without the need to filter out poor active spaces and with no further orbital optimization following active space selection of the SA-DMRG wave functions. Furthermore, we find that DVS-tPBE is able to robustly and effectively select between the new SA-DMRG wave functions and our previous SA-CASSCF results.
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Affiliation(s)
- Daniel S King
- Department of Chemistry, University of Chicago, Chicago, Illinois 60637, United States
| | - Donald G Truhlar
- Department of Chemistry, Chemical Theory Group, and Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455, United States
| | - Laura Gagliardi
- Department of Chemistry, Pritzker School of Molecular Engineering, James Franck Institute, Chicago Center for Theoretical Chemistry, University of Chicago, Chicago, Illinois 60637, United States
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6
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Drwal D, Matousek M, Golub P, Tucholska A, Hapka M, Brabec J, Veis L, Pernal K. Role of Spin Polarization and Dynamic Correlation in Singlet-Triplet Gap Inversion of Heptazine Derivatives. J Chem Theory Comput 2023; 19:7606-7616. [PMID: 37864544 PMCID: PMC10653106 DOI: 10.1021/acs.jctc.3c00781] [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: 07/18/2023] [Indexed: 10/23/2023]
Abstract
The new generation of proposed light-emitting molecules for organic light-emitting diodes (OLEDs) has raised considerable research interest due to its exceptional feature─a negative singlet-triplet (ST) gap violating Hund's multiplicity rule in the excited S1 and T1 states. We investigate the role of spin polarization in the mechanism of ST gap inversion. Spin polarization is associated with doubly excited determinants of certain types, whose presence in the wave function expansion favors the energy of the singlet state more than that of the triplet. Using a perturbation theory-based model for spin polarization, we propose a simple descriptor for prescreening of candidate molecules with negative ST gaps and prove its usefulness for heptazine-type molecules. Numerical results show that the quantitative effect of spin polarization decreases linearly with the increasing highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) exchange integral. Comparison of single- and multireference coupled-cluster predictions of ST gaps shows that the former methods provide good accuracy by correctly balancing the effects of doubly excited determinants and dynamic correlation. We also show that accurate ST gaps may be obtained using a complete active space model supplemented with dynamic correlation from multireference adiabatic connection theory.
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Affiliation(s)
- Daria Drwal
- Institute
of Physics, Lodz University of Technology, ul. Wolczanska 219, 90-924 Lodz, Poland
| | - Mikulas Matousek
- J.
Heyrovský Institute of Physical Chemistry, Academy of Sciences
of the Czech Republic, v.v.i., Dolejškova 3, 18223 Prague 8, Czech Republic
- Faculty
of Mathematics and Physics, Charles University, 12116 Prague, Czech Republic
| | - Pavlo Golub
- J.
Heyrovský Institute of Physical Chemistry, Academy of Sciences
of the Czech Republic, v.v.i., Dolejškova 3, 18223 Prague 8, Czech Republic
| | - Aleksandra Tucholska
- Institute
of Physics, Lodz University of Technology, ul. Wolczanska 219, 90-924 Lodz, Poland
| | - Michał Hapka
- Faculty
of Chemistry, University of Warsaw, ul. L. Pasteura 1, 02-093 Warsaw, Poland
| | - Jiri Brabec
- J.
Heyrovský Institute of Physical Chemistry, Academy of Sciences
of the Czech Republic, v.v.i., Dolejškova 3, 18223 Prague 8, Czech Republic
| | - Libor Veis
- J.
Heyrovský Institute of Physical Chemistry, Academy of Sciences
of the Czech Republic, v.v.i., Dolejškova 3, 18223 Prague 8, Czech Republic
| | - Katarzyna Pernal
- Institute
of Physics, Lodz University of Technology, ul. Wolczanska 219, 90-924 Lodz, Poland
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7
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Phung QM, Nam HN, Saitow M. Unraveling the Spin-State Energetics of FeN 4 Complexes with Ab Initio Methods. J Phys Chem A 2023; 127:7544-7556. [PMID: 37651105 DOI: 10.1021/acs.jpca.3c04254] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/01/2023]
Abstract
A systematic analysis was conducted to explore the spin-state energetics of a series of 19 FeN4 complexes. The performance of a large number of multireference methods was assessed, highlighting the significant challenges associated with accurately describing the spin-state energetics of FeN4 complexes. Most multireference methods were found to be susceptible to errors originating from the reference CASSCF wavefunction, leading to an overstabilization of high-spin states. Nonetheless, a few multireference methods, namely, CASPT2/CC, DSRG-MRPT3, and LDSRG(2), demonstrated promising performance compared to the benchmark CCSD(T) method. Furthermore, our study revealed that FeN4 complexes having a quintet ground state are exceedingly rare. Accordingly, only one specific model (Fe(L2)) and one synthesized complex (Fe(OTBP)) have the quintet ground state among the studied complexes. This scarcity of quintet FeN4 complexes highlights the unique nature of these systems and raises intriguing questions regarding the factors influencing spin states, such as the size of the macrocycle cavity, the introduction of substituents, or the induction of out-of-plane deformation.
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Affiliation(s)
- Quan Manh Phung
- Department of Chemistry, Graduate School of Science, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Aichi 464-8602, Japan
- Institute of Transformative Bio-Molecules (WPI-ITbM), Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Aichi 464-8602, Japan
| | - Ho Ngoc Nam
- Institute of Materials Innovation, Institutes of Innovation for Future Society, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Aichi 464-8601, Japan
| | - Masaaki Saitow
- Department of Chemistry, Graduate School of Science, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Aichi 464-8602, Japan
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8
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Giarrusso S, Pribram-Jones A. Møller-Plesset and Density-Fixed Adiabatic Connections for a Model Diatomic System at Different Correlation Regimes. J Chem Theory Comput 2023; 19:5835-5850. [PMID: 37642270 DOI: 10.1021/acs.jctc.3c00529] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/31/2023]
Abstract
In recent years, adiabatic connection (AC) interpolations developed within density functional theory (DFT) have been found to provide good performances in the calculation of interaction energies when used with Hartree-Fock (HF) ingredients. The physical and mathematical reasons for such unanticipated performance have been clarified, to some extent, by studying the strong-interaction limit of the Møller-Plesset (MP) AC. In this work, we calculate both the MP and the DFT AC integrand for the asymmetric Hubbard dimer, which allows for a systematic investigation of different correlation regimes by varying two simple parameters in the Hamiltonian: the external potential, Δv, and the interaction strength, U. Notably, we find that, while the DFT AC integrand appears to be convex in the full parameter space, the MP integrand may change curvature twice. Furthermore, we discuss different aspects of the second-order expansion of the correlation energy in each AC, and we demonstrate why the derivative of the λ-dependent density in the MP AC at λ = 0 (i.e., at the HF density) is zero in the model. Concerning the strong-interaction limit of both ACs in the Hubbard dimer setting, we show that the asymptotic value of the MP AC, W∞HF, is lower than (or equal to) its DFT analogue, W∞KS, if the two are compared at a given density, just like in real space. However, we also show that this is not always the case if the two quantities are compared at a given external potential.
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Affiliation(s)
- Sara Giarrusso
- Department of Chemistry and Biochemistry, University of California Merced, 5200 North Lake Rd., Merced, California 95343, United States
| | - Aurora Pribram-Jones
- Department of Chemistry and Biochemistry, University of California Merced, 5200 North Lake Rd., Merced, California 95343, United States
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9
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Xu Y, Cheng Y, Song Y, Ma H. New Density Matrix Renormalization Group Approaches for Strongly Correlated Systems Coupled with Large Environments. J Chem Theory Comput 2023. [PMID: 37471519 DOI: 10.1021/acs.jctc.2c01316] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/22/2023]
Abstract
Thanks to the high compression of the matrix product state (MPS) form of the wave function and the efficient site-by-site iterative sweeping optimization algorithm, the density matrix normalization group (DMRG) and its time-dependent variant (TD-DMRG) have been established as powerful computational tools in accurately simulating the electronic structure and quantum dynamics of strongly correlated molecules with a large number (101-2) of quantum degrees of freedom (active orbitals or vibrational modes). However, the quantitative characterization of the quantum many-body behaviors of realistic strongly correlated systems requires a further consideration of the interaction between the embedded active subsystem and the remaining correlated environment, e.g., a larger number (102-3) of external orbitals in electronic structure or infinite condensed-phase phononic modes in nucleus dynamics. To this end, we introduced three new post-DMRG and TD-DMRG approaches, namely (1) DMRG2sCI-MRCI and DMRG2sCI-ENPT by the reconstruction of selected configuration interaction (sCI) type of compact reference function from DMRG coefficients and the use of externally contracted MRCI (multireference configuration interaction) and Epstein-Nesbet perturbation theory (ENPT), without recourse to the expensive high order n-electron reduced density matrices (n-RDMs). (2) DMRG combined with RR-MRCI (renormalized residue-based MRCI), which improves the computational accuracy and efficiency of internally contracted (ic) MRCI by renormalizing the contracted bases with small-sized buffer environment(s) of a few external orbitals as probes based on quantum information theory. (3) HM (hierarchical mapping)-TD-DMRG in which a large environment is reduced to a small number of renormalized environmental modes (which accounts for the most vital system-environment interactions) through stepwise mapping transformation. These advances extend the efficacy of highly accurate DMRG/TD-DMRG computations to the quantitative characterization of the electronic structure and quantum dynamics in realistic strongly correlated systems coupled with large environments and are reviewed in this paper.
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Affiliation(s)
- Yihe Xu
- School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, China
| | - Yifan Cheng
- School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, China
| | - Yinxuan Song
- School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, China
| | - Haibo Ma
- Qingdao Institute for Theoretical and Computational Sciences, Qingdao Institute of Frontier and Interdisciplinary Science, Shandong University, Qingdao 266237, China
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10
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Liao K, Zhai H, Christlmaier EM, Schraivogel T, Ríos PL, Kats D, Alavi A. Density Matrix Renormalization Group for Transcorrelated Hamiltonians: Ground and Excited States in Molecules. J Chem Theory Comput 2023; 19:1734-1743. [PMID: 36912635 DOI: 10.1021/acs.jctc.2c01207] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/14/2023]
Abstract
We present the theory of a density matrix renormalization group (DMRG) algorithm which can solve for both the ground and excited states of non-Hermitian transcorrelated Hamiltonians and show applications in molecular systems. Transcorrelation (TC) accelerates the basis set convergence rate by including known physics (such as, but not limited to, the electron-electron cusp) in the Jastrow factor used for the similarity transformation. It also improves the accuracy of approximate methods such as coupled cluster singles and doubles (CCSD) as shown by recent studies. However, the non-Hermiticity of the TC Hamiltonians poses challenges for variational methods like DMRG. Imaginary-time evolution on the matrix product state (MPS) in the DMRG framework has been proposed to circumvent this problem, but this is currently limited to treating the ground state and has lower efficiency than the time-independent DMRG (TI-DMRG) due to the need to eliminate Trotter errors. In this work, we show that with minimal changes to the existing TI-DMRG algorithm, namely, replacing the original Davidson solver with the general Davidson solver to solve the non-Hermitian effective Hamiltonians at each site for a few low-lying right eigenstates, and following the rest of the original DMRG recipe, one can find the ground and excited states with improved efficiency compared to the original DMRG when extrapolating to the infinite bond dimension limit in the same basis set. An accelerated basis set convergence rate is also observed, as expected, within the TC framework.
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Affiliation(s)
- Ke Liao
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
| | - Huanchen Zhai
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
| | | | - Thomas Schraivogel
- Max Planck Institute for Solid State Research, Heisenbergstrasse 1, 70569 Stuttgart, Germany
| | - Pablo López Ríos
- Max Planck Institute for Solid State Research, Heisenbergstrasse 1, 70569 Stuttgart, Germany
| | - Daniel Kats
- Max Planck Institute for Solid State Research, Heisenbergstrasse 1, 70569 Stuttgart, Germany
| | - Ali Alavi
- Max Planck Institute for Solid State Research, Heisenbergstrasse 1, 70569 Stuttgart, Germany.,Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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11
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Matoušek M, Hapka M, Veis L, Pernal K. Toward more accurate adiabatic connection approach for multireference wavefunctions. J Chem Phys 2023; 158:054105. [PMID: 36754817 DOI: 10.1063/5.0131448] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023] Open
Abstract
A multiconfigurational adiabatic connection (AC) formalism is an attractive approach to compute the dynamic correlation within the complete active space self-consistent field and density matrix renormalization group (DMRG) models. Practical realizations of AC have been based on two approximations: (i) fixing one- and two-electron reduced density matrices (1- and 2-RDMs) at the zero-coupling constant limit and (ii) extended random phase approximation (ERPA). This work investigates the effect of removing the "fixed-RDM" approximation in AC. The analysis is carried out for two electronic Hamiltonian partitionings: the group product function- and the Dyall Hamiltonians. Exact reference AC integrands are generated from the DMRG full configuration interaction solver. Two AC models are investigated, employing either exact 1- and 2-RDMs or their second-order expansions in the coupling constant in the ERPA equations. Calculations for model molecules indicate that lifting the fixed-RDM approximation is a viable way toward improving the accuracy of existing AC approximations.
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Affiliation(s)
- Mikuláš Matoušek
- J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 18223 Prague 8, Czech Republic
| | - Michał Hapka
- Faculty of Chemistry, University of Warsaw, ul. L. Pasteura 1, 02-093 Warsaw, Poland
| | - Libor Veis
- J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 18223 Prague 8, Czech Republic
| | - Katarzyna Pernal
- Institute of Physics, Lodz University of Technology, ul. Wolczanska 217/221, 93-005 Lodz, Poland
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12
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Mutual information prediction for strongly correlated systems. Chem Phys Lett 2023. [DOI: 10.1016/j.cplett.2023.140297] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023]
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13
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Beran P, Pernal K, Pavošević F, Veis L. Projection-Based Density Matrix Renormalization Group in Density Functional Theory Embedding. J Phys Chem Lett 2023; 14:716-722. [PMID: 36648273 PMCID: PMC10017021 DOI: 10.1021/acs.jpclett.2c03298] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/31/2022] [Accepted: 01/11/2023] [Indexed: 06/17/2023]
Abstract
The density matrix renormalization group (DMRG) method has already proved itself as a very efficient and accurate computational method, which can treat large active spaces and capture the major part of strong correlation. Its application on larger molecules is, however, limited by its own computational scaling as well as demands of methods for treatment of the missing dynamical electron correlation. In this work, we present the first step in the direction of combining DMRG with density functional theory (DFT), one of the most employed quantum chemical methods with favorable scaling, by means of the projection-based wave function (WF)-in-DFT embedding. On two proof-of-concept but important molecular examples, we demonstrate that the developed DMRG-in-DFT approach provides a very accurate description of molecules with a strongly correlated fragment.
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Affiliation(s)
- Pavel Beran
- J.
Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 18223Prague 8, Czech Republic
- Faculty
of Mathematics and Physics, Charles University, 121 16Prague, Czech Republic
| | - Katarzyna Pernal
- Institute
of Physics, Lodz University of Technology, ul. Wolczanska 217/221, 93-005Lodz, Poland
| | - Fabijan Pavošević
- Center
for Computational Quantum Physics, Flatiron
Institute, 162 Fifth Avenue, New York, 10010New York, United
States
| | - Libor Veis
- J.
Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 18223Prague 8, Czech Republic
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14
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Lew-Yee JFH, Del Campo JM, Piris M. Electron Correlation in the Iron(II) Porphyrin by Natural Orbital Functional Approximations. J Chem Theory Comput 2023; 19:211-220. [PMID: 36579972 PMCID: PMC9996833 DOI: 10.1021/acs.jctc.2c01093] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022]
Abstract
The relative stability of the singlet, triplet, and quintet spin states of iron(II) porphyrin (FeP) represents a challenging problem for electronic structure methods. While it is currently accepted that the ground state is a triplet, multiconfigurational wave function-based methods predict a quintet, and density functional approximations vary between triplet and quintet states, leading to a prediction that highly depends on the features of the method employed. The recently proposed Global Natural Orbital Functional (GNOF) aims to provide a balanced treatment between static and dynamic correlation, and together with the previous Piris Natural Orbital Functionals (PNOFs), allowed us to explore the importance of each type of correlation in the stability order of the states of FeP with a method that conserves the spin of the system. It is noteworthy that GNOF correlates all electrons in all available orbitals for a given basis set; in the case of the FeP with a double-ζ basis set as used in this work, this means that GNOF can properly correlate 186 electrons in 465 orbitals, significantly increasing the sizes of systems amenable to multiconfigurational treatment. Results show that PNOF5, PNOF7s, and PNOF7 predict the quintet to have a lower energy than the triplet state; however, the addition of dynamic correlation via second-order Møller-Plesset corrections (NOF-MP2) turns the triplet state to be lower than the quintet state, a prediction also reproduced by GNOF that incorporates much more dynamic correlation than its predecessors.
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Affiliation(s)
- Juan Felipe Huan Lew-Yee
- Departamento de Física y Química Teórica, Facultad de Química, Universidad Nacional Autónoma de México, México CityC.P. 04510, México
| | - Jorge M Del Campo
- Departamento de Física y Química Teórica, Facultad de Química, Universidad Nacional Autónoma de México, México CityC.P. 04510, México
| | - Mario Piris
- Kimika Fakultatea, Euskal Herriko Unibertsitatea (UPV/EHU), P.K. 1072, 20080Donostia, Euskadi, Spain.,Donostia International Physics Center (DIPC), 20018Donostia, Euskadi, Spain.,IKERBASQUE, Basque Foundation for Science, 48013Bilbao, Euskadi, Spain
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15
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King DS, Hermes MR, Truhlar DG, Gagliardi L. Large-Scale Benchmarking of Multireference Vertical-Excitation Calculations via Automated Active-Space Selection. J Chem Theory Comput 2022; 18:6065-6076. [PMID: 36112354 PMCID: PMC9558375 DOI: 10.1021/acs.jctc.2c00630] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
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We have calculated state-averaged complete-active-space
self-consistent-field
(SA-CASSCF), multiconfiguration pair-density functional theory (MC-PDFT),
hybrid MC-PDFT (HMC-PDFT), and n-electron valence
state second-order perturbation theory (NEVPT2) excitation energies
with the approximate pair coefficient (APC) automated active-space
selection scheme for the QUESTDB benchmark database of 542 vertical
excitation energies. We eliminated poor active spaces (20–40%
of calculations) by applying a threshold to the SA-CASSCF absolute
error. With the remaining calculations, we find that NEVPT2 performance
is significantly impacted by the size of the basis set the wave functions
are converged in, regardless of the quality of their description,
which is a problem absent in MC-PDFT. Additionally, we find that HMC-PDFT
is a significant improvement over MC-PDFT with the translated PBE
(tPBE) density functional and that it performs about as well as NEVPT2
and second-order coupled cluster on a set of 373 excitations in the
QUESTDB database. We optimized the percentage of SA-CASSCF energy
to include in HMC-PDFT when using the tPBE on-top functional, and
we find the 25% value used in tPBE0 to be optimal. This work is by
far the largest benchmarking of MC-PDFT and HMC-PDFT to date, and
the data produced in this work are useful as a validation of HMC-PDFT
and of the APC active-space selection scheme. We have made all the
wave functions produced in this work (orbitals and CI vectors) available
to the public and encourage the community to utilize this data as
a tool in the development of further multireference model chemistries.
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Affiliation(s)
- Daniel S. King
- Department of Chemistry, University of Chicago, Chicago Illinois 60637, United States
| | - Matthew R. Hermes
- Department of Chemistry, University of Chicago, Chicago Illinois 60637, United States
| | - Donald G. Truhlar
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputng Institute, University of Minnesota, Minneapolis Minnesota 55455-0431, United States
| | - Laura Gagliardi
- Department of Chemistry, Pritzker School of Molecular Engineering, James Franck Institute, Chicago Center for Theoretical Chemistry, University of Chicago, Chicago Illinois 60637, United States
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16
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Abraham V, Mayhall NJ. Coupled Electron Pair-Type Approximations for Tensor Product State Wave Functions. J Chem Theory Comput 2022; 18:4856-4864. [PMID: 35878319 DOI: 10.1021/acs.jctc.2c00589] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Size extensivity, defined as the correct scaling of energy with system size, is a desirable property for any many-body method. Traditional configuration interaction (CI) methods are not size extensive, hence the error increases as the system gets larger. Coupled electron pair approximation (CEPA) methods can be constructed as simple extensions of a truncated CI that ensures size extensivity. One of the major issues with the CEPA and its variants is that singularities arise in the amplitude equations when the system starts to be strongly correlated. In this work, we extend the traditional Slater determinant based coupled electron pair approaches like CEPA-0, averaged coupled-pair functional, and average quadratic coupled-cluster to a new formulation based on tensor product states (TPS). We show that a TPS basis can often be chosen such that it removes the singularities that commonly destroy the accuracy of CEPA based methods. A suitable TPS representation can be formed by partitioning the system into separate disjoint clusters and forming the final wave function as the tensor product of the many body states of these clusters. We demonstrate the application of these methods on simple bond breaking systems such as CH4 and F2 where determinant based CEPA methods fail. We further apply the TPS-CEPA approach to stillbene isomerization and few planar π-conjugated systems. Overall, the results show that the TPS-CEPA method can remove the singularities and provide improved numerical results compared to common electronic structure methods.
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Affiliation(s)
- Vibin Abraham
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Nicholas J Mayhall
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24060, United States
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17
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Stroscio GD, Zhou C, Truhlar DG, Gagliardi L. Multiconfiguration Pair-Density Functional Theory Calculations of Iron(II) Porphyrin: Effects of Hybrid Pair-Density Functionals and Expanded RAS and DMRG Active Spaces on Spin-State Orderings. J Phys Chem A 2022; 126:3957-3963. [PMID: 35674705 DOI: 10.1021/acs.jpca.2c02347] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Iron(II) porphyrins play critical roles in enzymes and synthetic catalysts. Computationally determining the spin-state ordering for even the unsubstituted iron(II) porphyrin (FeP) is challenging due to its large size. Multiconfiguration pair-density functional theory (MC-PDFT), a method capable of accurately capturing correlation with lower cost than comparably accurate methods, was previously used to predict a triplet ground state for FeP across a wide range of active spaces up to (34e, 35o). The purpose of this present MC-PDFT study is to determine the effects of including nonlocal exchange in the energy calculation and of using a larger active space size [DMRG(40e, 42o) and RAS(40, 2, 2; 16, 6, 20)] on the calculated FeP spin-state ordering. The recently developed hybrid MC-PDFT method, which uses a weighted average of the MC-PDFT energy and the energy expectation value of the reference wave function, is applied with a weight of the reference wave function energy of λ. We find that increasing λ stabilizes the quintet relative to the triplets. The hybrid tPBE0 functional (tPBE with λ set to 0.25) consistently predicts a triplet ground state with the quintet lying above by 0.10-0.16 eV, depending on the reference wave function. These values are particularly interesting in light of tPBE0's very strong performance for a diverse set of other systems.
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Affiliation(s)
- Gautam D Stroscio
- Department of Chemistry, Chicago Center for Theoretical Chemistry, Pritzker School of Molecular Engineering, James Franck Institute, University of Chicago, Chicago, Illinois 60637-5418, United States.,Argonne National Laboratory, Lemont, Illinois 60439, United States
| | - Chen Zhou
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United States
| | - Donald G Truhlar
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United States
| | - Laura Gagliardi
- Department of Chemistry, Chicago Center for Theoretical Chemistry, Pritzker School of Molecular Engineering, James Franck Institute, University of Chicago, Chicago, Illinois 60637-5418, United States.,Argonne National Laboratory, Lemont, Illinois 60439, United States
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18
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Drwal D, Beran P, Hapka M, Modrzejewski M, Sokół A, Veis L, Pernal K. Efficient Adiabatic Connection Approach for Strongly Correlated Systems: Application to Singlet-Triplet Gaps of Biradicals. J Phys Chem Lett 2022; 13:4570-4578. [PMID: 35580342 PMCID: PMC9150121 DOI: 10.1021/acs.jpclett.2c00993] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/05/2022] [Accepted: 05/09/2022] [Indexed: 06/15/2023]
Abstract
Strong electron correlation can be captured with multireference wave function methods, but an accurate description of the electronic structure requires accounting for the dynamic correlation, which they miss. In this work, a new approach for the correlation energy based on the adiabatic connection (AC) is proposed. The ACn method accounts for terms up to order n in the coupling constant, and it is size-consistent and free from instabilities. It employs the multireference random phase approximation and the Cholesky decomposition technique, leading to a computational cost growing with the fifth power of the system size. Because of the dependence on only one- and two-electron reduced density matrices, ACn is more efficient than existing ab initio multireference dynamic correlation methods. ACn affords excellent results for singlet-triplet gaps of challenging organic biradicals. The development presented in this work opens new perspectives for accurate calculations of systems with dozens of strongly correlated electrons.
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Affiliation(s)
- Daria Drwal
- Institute
of Physics, Lodz University of Technology, ul. Wolczanska 219, 90-924 Lodz, Poland
| | - Pavel Beran
- J.
Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 18223 Prague 8, Czech Republic
- Faculty
of Mathematics and Physics, Charles University, Ke Karlovu 2027/3, 12116 Prague 2, Czech Republic
| | - Michał Hapka
- Institute
of Physics, Lodz University of Technology, ul. Wolczanska 219, 90-924 Lodz, Poland
- Faculty
of Chemistry, University of Warsaw, ul. L. Pasteura 1, 02-093 Warsaw, Poland
| | - Marcin Modrzejewski
- Faculty
of Chemistry, University of Warsaw, ul. L. Pasteura 1, 02-093 Warsaw, Poland
| | - Adam Sokół
- Institute
of Physics, Lodz University of Technology, ul. Wolczanska 219, 90-924 Lodz, Poland
| | - Libor Veis
- J.
Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 18223 Prague 8, Czech Republic
| | - Katarzyna Pernal
- Institute
of Physics, Lodz University of Technology, ul. Wolczanska 219, 90-924 Lodz, Poland
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19
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Jangrouei MR, Krzemińska A, Hapka M, Pastorczak E, Pernal K. Dispersion Interactions in Exciton-Localized States. Theory and Applications to π-π* and n-π* Excited States. J Chem Theory Comput 2022; 18:3497-3511. [PMID: 35587598 PMCID: PMC9202351 DOI: 10.1021/acs.jctc.2c00221] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
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We address the problem
of intermolecular interaction energy calculations
in molecular complexes with localized excitons. Our focus is on the
correct representation of the dispersion energy. We derive an extended
Casimir-Polder formula for direct computation of this contribution
through second order in the intermolecular interaction operator V̂. An alternative formula, accurate to infinite order
in V̂, is derived within the framework of the
adiabatic connection (AC) theory. We also propose a new parametrization
of the VV10 nonlocal correlation density functional, so that it corrects
the CASSCF energy for the dispersion contribution and can be applied
to excited-state complexes. A numerical investigation is carried out
for benzene, pyridine, and peptide complexes with the local exciton
corresponding to the lowest π–π* or n– π*
states. The extended Casimir-Polder formula is implemented in the
framework of multiconfigurational symmetry-adapted perturbation theory,
SAPT(MC). A SAPT(MC) analysis shows that the creation of a localized
exciton affects mostly the electrostatic component of the interaction
energy of investigated complexes. Nevertheless, the changes in Pauli
repulsion and dispersion energies cannot be neglected. We verify the
performance of several perturbation- and AC-based methods. Best results
are obtained with a range-separated variant of an approximate AC approach
employing extended random phase approximation and CASSCF wave functions.
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Affiliation(s)
- Mohammad Reza Jangrouei
- Institute of Physics, Lodz University of Technology, ul. Wolczanska 217/221, 93-005, Lodz, Poland
| | - Agnieszka Krzemińska
- Institute of Physics, Lodz University of Technology, ul. Wolczanska 217/221, 93-005, Lodz, Poland
| | - Michał Hapka
- Faculty of Chemistry, University of Warsaw, ul. L. Pasteura 1, 02-093, Warsaw, Poland
| | - Ewa Pastorczak
- Institute of Physics, Lodz University of Technology, ul. Wolczanska 217/221, 93-005, Lodz, Poland
| | - Katarzyna Pernal
- Institute of Physics, Lodz University of Technology, ul. Wolczanska 217/221, 93-005, Lodz, Poland
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20
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Rask AE, Zimmerman PM. The many-body electronic interactions of Fe(II)–porphyrin. J Chem Phys 2022; 156:094110. [DOI: 10.1063/5.0079310] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Fe(II)–porphyrin complexes exhibit a diverse range of electronic interactions between the metal and macrocycle. Herein, the incremental full configuration interaction method is applied to the entire space of valence orbitals of a Fe(II)–porphyrin model using a modest basis set. A novel visualization framework is proposed to analyze individual many-body contributions to the correlation energy, providing detailed maps of this complex’s highly correlated electronic structure. This technique is used to parse the numerous interactions of two low-lying triplet states (3A2g and 3Eg) and to show that strong metal d–d and macrocycle π–π orbital interactions preferentially stabilize the 3A2g state. d–π interactions, on the other hand, preferentially stabilize the 3Eg state and primarily appear when correlating six electrons at a time. Ultimately, the Fe(II)–porphyrin model’s full set of 88 valence electrons are correlated in 275 orbitals, showing the interactions up to the 4-body level, which covers the great majority of correlations in this system.
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Affiliation(s)
- A. E. Rask
- Department of Chemistry, University of Michigan, 930 N. University Ave., Ann Arbor, Michigan 48109, USA
| | - P. M. Zimmerman
- Department of Chemistry, University of Michigan, 930 N. University Ave., Ann Arbor, Michigan 48109, USA
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21
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Cheng Y, Xie Z, Ma H. Post-Density Matrix Renormalization Group Methods for Describing Dynamic Electron Correlation with Large Active Spaces. J Phys Chem Lett 2022; 13:904-915. [PMID: 35049302 DOI: 10.1021/acs.jpclett.1c04078] [Citation(s) in RCA: 15] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
The ab initio density matrix renormalization group (DMRG) method has been well-established and has become one of the most accurate numerical methods for the precise electronic structure solution of large active spaces. In the past few years, to capture the missing dynamic correlation, various post-DMRG approaches have been proposed through the combination of DMRG and multireference quantum chemical methods or density functional theory. With this in mind, this work provides a brief overview of ab initio DMRG principles and the new developments within post-DMRG methods. For clarity, post-DMRG methods are classified into two main categories depending on whether high-order n-electron reduced density matrices are used, and their merits and disadvantages are properly discussed. Finally, we conclude by discussing unsolved bottlenecks and giving development perspectives of post-DMRG approaches, which are expected to yield quantitative descriptions of complex electronic structures in large strongly correlated molecules and materials.
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Affiliation(s)
- Yifan Cheng
- School of Chemistry and Chemical Engineering, Jiangsu Key Laboratory of Vehicle Emissions Control, Nanjing University, Nanjing 210023, China
| | - Zhaoxuan Xie
- School of Chemistry and Chemical Engineering, Jiangsu Key Laboratory of Vehicle Emissions Control, Nanjing University, Nanjing 210023, China
| | - Haibo Ma
- School of Chemistry and Chemical Engineering, Jiangsu Key Laboratory of Vehicle Emissions Control, Nanjing University, Nanjing 210023, China
- Chemistry and Biomedicine Innovation Center (ChemBIC), Nanjing University, Nanjing 210023, China
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