1
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Song C. New physical insights into the supporting subspace factorization of XMS-CASPT2 and generalization to multiple spin states via spin-free formulation. J Chem Phys 2024; 160:124106. [PMID: 38526101 DOI: 10.1063/5.0192478] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/19/2023] [Accepted: 03/07/2024] [Indexed: 03/26/2024] Open
Abstract
This paper introduces a spin-free formulation of the supporting subspace factorization [C. Song and T. J. Martínez, J. Chem. Phys. 149, 044108 (2018)], enabling a reduction in the computational scaling of the extended multi-state complete active space second-order perturbation (XMS-CASPT2) method for arbitrary spins. Compared to the original formulation that is defined in the spin orbitals and is limited to singlet states, the spin-free formulation in this work treats different spin states equivalently, thus naturally generalizing the idea beyond singlet states. In addition, we will present a new way of deriving the supporting subspace factorization with the purpose of understanding its physical interpretation. In this new derivation, we separate the sources that make CASPT2 difficult into the "same-site interactions" and "inter-site interactions." We will first show how the Kronecker sum can be used to remove the same-site interactions in the absence of inter-site interactions, leading to MP2 energy in dressed orbitals. We will then show how the inter-site interactions can be exactly recovered using Löwdin partition, where the supporting subspace concept will naturally arise. The new spin-free formulation maintains the main advantage of the supporting subspace factorization, i.e., allowing XMS-CASPT2 energies to be computed using highly optimized MP2 energy codes and Fock build codes, thus reducing the scaling of XMS-CASPT2 to the same scaling as MP2. We will present and discuss results that benchmark the accuracy and performance of the new method. To demonstrate how the new method can be useful in studying real photochemical systems, the supporting subspace XMS-CASPT2 is applied to a photoreaction sensitive to magnetic field effects. The new spin-free formulation makes it possible to calculate the doublet and quartet states required in this particular photoreaction mechanism.
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Affiliation(s)
- Chenchen Song
- Department of Chemistry, University of California Davis, 1 Shields Ave., Davis, California 95616, USA
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2
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Inai N, Yamaguchi S, Yanai T. Theoretical Insight into the Effect of Phosphorus Oxygenation on Nonradiative Decays: Comparative Analysis of P-Bridged Stilbene Analogs. ACS PHYSICAL CHEMISTRY AU 2023; 3:540-552. [PMID: 38034034 PMCID: PMC10683489 DOI: 10.1021/acsphyschemau.3c00038] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 08/07/2023] [Revised: 09/26/2023] [Accepted: 09/28/2023] [Indexed: 12/02/2023]
Abstract
Incorporation of the phosphorus element into a π-conjugated skeleton offers valuable prospects for adjusting the electronic structure of the resulting functional π-electron systems. Trivalent phosphorus has the potential to decrease the LUMO level through σ*-π* interaction, which is further enhanced by its oxygenation to the pentavalent P center. This study shows that utilizing our computational analysis to examine excited-state dynamics based on radiative/nonradiative rate constants and fluorescence quantum yield (ΦF) is effective for analyzing the photophysical properties of P-containing organic dyes. We theoretically investigate how the trivalent phosphanyl group and pentavalent phosphine oxide moieties affect radiative and nonradiative decay processes. We evaluate four variations of P-bridged stilbene analogs. Our analysis reveals that the primary decay pathway for photoexcited bis-phosphanyl-bridged stilbene is the intersystem crossing (ISC) to the triplet state and nonradiative. The oxidation of the phosphine moiety, however, suppresses the ISC due to the relative destabilization of the triplet states. The calculated rate constants match an increase in experimental ΦF from 0.07 to 0.98, as simulated from 0.23 to 0.94. The reduced HOMO-LUMO gap supports a red shift in the fluorescence spectra relative to the phosphine analog. The thiophene-fused variant with the nonoxidized trivalent P center exhibits intense emission with a high ΦF, 0.95. Our prediction indicates that the ISC transfer is obstructed owing to the relatively destabilized triplet state induced by the thiophene substitution. Conversely, the thiophene-fused analog with the phosphine oxide moieties triggers a high-rate internal conversion mediated by conical intersection, leading to a decreased ΦF.
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Affiliation(s)
- Naoto Inai
- Department
of Chemistry, Graduate School of Science, Nagoya University, Furo-cho,
Chikusa-ku, Nagoya, Aichi 464-8602, Japan
| | - Shigehiro Yamaguchi
- Department
of Chemistry, Graduate School of Science and Integrated Research Consortium
on Chemical Science (IRCCS), 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
| | - Takeshi Yanai
- Department
of Chemistry, Graduate School of Science and Integrated Research Consortium
on Chemical Science (IRCCS), 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
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3
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Eun HJ, Ishiuchi SI, Yoo IT, Heo J, Park JW, Fujii M, Kim NJ. Cryogenic Ion Spectroscopy of Protonated and Sodiated Methyladenine Derivatives. J Phys Chem A 2023; 127:2472-2480. [PMID: 36895090 DOI: 10.1021/acs.jpca.2c09083] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/11/2023]
Abstract
Ultraviolet photodissociation (UVPD) spectra of protonated 9-methyladenine (H+9MA), protonated 7-methyl adenine (H+7MA), protonated 3-methyladenine (H+3MA), and sodiated 7-methyladenine (Na+7MA) near the origin bands of the S0-S1 transition were obtained using cryogenic ion spectroscopy. The UV-UV hole burning, infrared (IR) ion-dip, and IR-UV double resonance spectra showed that all the ions were present as single isomers in a cryogenic ion trap. The UVPD spectrum of H+9MA exhibited only a broad absorption band, whereas the spectra of H+7MA, H+3MA, and Na+7MA displayed moderately or well-resolved vibronic bands. Potential energy profiles were computed to understand the reason for the different bandwidths of the vibronic bands in the spectra. The broadening of the bands was correlated with the slopes between the Franck-Condon point and the conical intersection between the S1 and S0 states in the potential energy profiles, thus reflecting the deactivation rates in the S1 state.
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Affiliation(s)
- Han Jun Eun
- Gas Metrology Group, Division of Chemical and Biological Metrology, Korea Research Institute of Standards and Science (KRISS), Daejeon 34113, Korea
| | - Shun-Ichi Ishiuchi
- Department of Chemistry, Tokyo Institute of Technology, Ookayama 2-12-1, Tokyo 152-8550, Japan
| | - Il Tae Yoo
- Department of Chemistry, Chungbuk National University, Chungbuk 28644, Korea
| | - Jiyoung Heo
- Department of Green Chemical Engineering, Sangmyung University, Chungnam 31066, Korea
| | - Jae Woo Park
- Department of Chemistry, Chungbuk National University, Chungbuk 28644, Korea
| | - Masaaki Fujii
- Laboratory for Chemistry and Life Science, Tokyo Institute of Technology, Nagatsuta-cho, Yokohama 226-8503, Japan
| | - Nam Joon Kim
- Department of Chemistry, Chungbuk National University, Chungbuk 28644, Korea
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4
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Iino T, Shiozaki T, Yanai T. Algorithm for analytic nuclear energy gradients of state averaged DMRG-CASSCF theory with newly derived coupled-perturbed equations. J Chem Phys 2023; 158:054107. [PMID: 36754810 DOI: 10.1063/5.0130636] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022] Open
Abstract
We present an algorithm for evaluating analytic nuclear energy gradients of the state-averaged density matrix renormalization group complete-active-space self-consistent field (SA-DMRG-CASSCF) theory based on the newly derived coupled-perturbed (CP) DMRG-CASSCF equations. The Lagrangian for the conventional SA-CASSCF analytic gradient theory is extended to the SA-DMRG-CASSCF variant that can fully consider a whole set of constraints on the parameters of multi-root canonical matrix product states formed at all the DMRG block configurations. An efficient algorithm to solve the CP-DMRG-CASSCF equations for determining the multipliers was developed. The complexity of the resultant analytic gradient algorithm is overall the same as that of the unperturbed SA-DMRG-CASSCF algorithm. In addition, a reduced-scaling approach was developed to directly compute the SA reduced density matrices (SA-RDMs) and their perturbed ones without calculating separate state-specific RDMs. As part of our implementation scheme, we neglect the term associated with the constraint on the active orbitals in terms of the active-active rotation in the Lagrangian. Thus, errors from the true analytic gradients may be caused in this scheme. The proposed gradient algorithm was tested with the spin-adapted implementation by checking how accurately the computed analytic energy gradients reproduce numerical gradients of the SA-DMRG-CASSCF energies using a common number of renormalized bases. The illustrative applications show that the errors are sufficiently small when using a typical number of the renormalized bases, which is required to attain adequate accuracy in DMRG's total energies.
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Affiliation(s)
- Tsubasa Iino
- Department of Chemistry, Graduate School of Science, Nagoya University, Furocho, Chikusa Ward, Nagoya, Aichi 464-8601, Japan
| | - Toru Shiozaki
- Quantum Simulation Technologies, Inc., Boston, Massachusetts 02135, USA
| | - Takeshi Yanai
- Department of Chemistry, Graduate School of Science, Nagoya University, Furocho, Chikusa Ward, Nagoya, Aichi 464-8601, Japan
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5
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Substitution Effects on the Mechanism of Light-Induced 2,5-Diaryltetrazole-Naphthoquinone 1,3-Dipolar Cycloaddition: A Theoretical Study. COMPUT THEOR CHEM 2023. [DOI: 10.1016/j.comptc.2023.114060] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/08/2023]
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6
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Huang X, Pei Z, Liang W. Analytical derivative couplings within the framework of time-dependent density functional theory coupled with conductor-like polarizable continuum model: Formalism, implementation, and applications. J Chem Phys 2023; 158:044122. [PMID: 36725492 DOI: 10.1063/5.0130617] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023] Open
Abstract
The nonadiabatic phenomena, which are characterized by a strong coupling between electronic and nuclear motions, are ubiquitous. The nonadiabatic effect of the studied system can be significantly affected by the surrounding environment, such as solvents, in which such nonadiabatic process takes place. It is essential to develop the theoretical models to simulate these processes while accurately modeling the solvent environment. The time-dependent density functional theory (TDDFT) is currently the most efficient approach to describe the electronic structures and dynamics of complex systems, while the polarizable continuum model (PCM) represents one of the most successful examples among continuum solvation models. Here, we formulate the first-order derivative couplings (DCs) between the ground and excited states as well as between two excited states by utilizing time-independent equation of motion formalism within the framework of both linear response and spin flip formulations of TDDFT/CPCM (the conductor-like PCM), and implement the analytical DCs into the Q-CHEM electronic structure software package. The analytic implementation is validated by the comparison of the analytical and finite-difference results, and reproducing geometric phase effect in the protonated formaldimine test case. Taking 4-(N,N-dimethylamino)benzonitrile and uracil in the gas phase and solution as an example, we demonstrate that the solvent effect is essential not only for the excitation energies of the low-lying excited-states but also for the DCs between these states. Finally, we calculate the internal conversion rate of benzophenone in a solvent with DC being used. The current implementation of analytical DCs together with the existing analytical gradient and Hessian of TDDFT/PCM excited states allows one to study the nonadiabatic effects of relatively large systems in solutions with low computational cost.
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Affiliation(s)
- Xunkun Huang
- State Key Laboratory of Physical Chemistry of Solid Surfaces, Collaborative Innovation Center of Chemistry for Energy Materials, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, and Department of Chemistry, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, People's Republic of China
| | - Zheng Pei
- State Key Laboratory of Physical Chemistry of Solid Surfaces, Collaborative Innovation Center of Chemistry for Energy Materials, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, and Department of Chemistry, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, People's Republic of China
| | - WanZhen Liang
- State Key Laboratory of Physical Chemistry of Solid Surfaces, Collaborative Innovation Center of Chemistry for Energy Materials, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, and Department of Chemistry, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, People's Republic of China
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7
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Abstract
We develop analytic gradients for selected configuration interaction wave functions. Despite all pairs of molecular orbitals now potentially having to be considered for the coupled perturbed Hartree-Fock equations, we show that degenerate orbital pairs belonging to different irreducible representations in the largest abelian subgroup do not need to be included and instabilities due to degeneracies are avoided. We introduce seminumerical gradients and use them to validate the analytic approach even when near degeneracies are present due to high-symmetry geometries being slightly distorted to break symmetry. The method is applied to carbon monoxide, ammonia, square planar H4, hexagonal planar H6, and methane for a range of bond lengths where we demonstrate that analytic gradients for selected configuration interaction can approach the quality of full configuration interaction yet only use a very small fraction of its determinants.
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8
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Battaglia S, Fransén L, Fdez Galván I, Lindh R. Regularized CASPT2: an Intruder-State-Free Approach. J Chem Theory Comput 2022; 18:4814-4825. [PMID: 35876618 PMCID: PMC9367007 DOI: 10.1021/acs.jctc.2c00368] [Citation(s) in RCA: 13] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
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In this work we present a new approach to fix the intruder-state
problem (ISP) in CASPT2 based on σp regularization. The resulting σp-CASPT2 method is compared to previous techniques, namely, the real
and imaginary level shifts, on a theoretical basis and by performing
a series of systematic calculations. The analysis is focused on two
aspects, the effectiveness of σp-CASPT2 in removing the ISP and the sensitivity of the approach with
respect to the input parameter. We found that σp-CASPT2 compares favorably with respect to previous
approaches and that different versions, σ1-CASPT2
and σ2-CASPT2, have different potential application
domains. This analysis also reveals the unsuitability of the real
level shift technique as a general way to avoid the intruder-state
problem.
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Affiliation(s)
- Stefano Battaglia
- Department of Chemistry─BMC, Uppsala University, P. O. Box 576, SE-75123 Uppsala, Sweden
| | - Lina Fransén
- Department of Chemistry─BMC, Uppsala University, P. O. Box 576, SE-75123 Uppsala, Sweden
| | - Ignacio Fdez Galván
- Department of Chemistry─BMC, Uppsala University, P. O. Box 576, SE-75123 Uppsala, Sweden
| | - Roland Lindh
- Department of Chemistry─BMC, Uppsala University, P. O. Box 576, SE-75123 Uppsala, Sweden
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9
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Nishimoto Y, Battaglia S, Lindh R. Analytic First-Order Derivatives of (X)MS, XDW, and RMS Variants of the CASPT2 and RASPT2 Methods. J Chem Theory Comput 2022; 18:4269-4281. [PMID: 35699280 DOI: 10.1021/acs.jctc.2c00301] [Citation(s) in RCA: 19] [Impact Index Per Article: 9.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Crossings between states involve complex electronic structures, making the accurate characterization of the crossing point difficult. In this study, the analytic derivatives of three complete active space second-order perturbation theory (CASPT2) variants as well as an extension of the restricted active space (RASPT2) are developed. These variants are applied to locating minimum energy conical intersections. Our results demonstrate that the three CASPT2 variants predict qualitatively similar results, but a recently developed variant, the rotated multistate CASPT2 (RMS-CASPT2), is least sensitive to the number of states considered in the calculation. We demonstrate that CASPT2 and the reference self-consistent field calculations predict qualitatively different energetics and bond lengths.
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Affiliation(s)
- Yoshio Nishimoto
- Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
| | - Stefano Battaglia
- Department of Chemistry - BMC, Uppsala University, P.O. Box 576, SE-75123 Uppsala, Sweden
| | - Roland Lindh
- Department of Chemistry - BMC, Uppsala University, P.O. Box 576, SE-75123 Uppsala, Sweden
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10
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Park JW. Analytical Gradient Theory for Spin-Free State-Averaged Second-Order Driven Similarity Renormalization Group Perturbation Theory (SA-DSRG-MRPT2) and Its Applications for Conical Intersection Optimizations. J Chem Theory Comput 2022; 18:2233-2245. [PMID: 35229599 DOI: 10.1021/acs.jctc.1c01150] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Second-order multireference-driven similarity renormalization group perturbation theory (DSRG-MRPT2) provides an efficient means of correcting the dynamical correlation with the multiconfiguration reference function. The state-averaged DSRG-MRPT2 (SA-DSRG-MRPT2) method is the simplest means of treating the excited states with DSRG-MRPT2. In this method, the Hamiltonian dressed with dynamical correlation is diagonalized in the CASCI state subspace (SA-DSRG-MRPT2c) or the configuration subspace (SA-DSRG-MRPT2). This work develops analytical gradient theory for spin-free SA-DSRG-MRPT2(c) with the density-fitting approximation. We check the accuracy of the analytical gradients against the numerical gradients. We present applications for optimizing minimum energy conical intersections (MECI) of ethylene and retinal model chromophores (PSB3 and RPSB6). We investigate the dependence of the optimized geometries and energies on the flow parameters and reference relaxations. The smoothness of the SA-DSRG-MRPT2(c) potential energy surfaces near the reference (complete active space self-consistent field) MECI is comparable to the XMCQDPT2 one. These results render SA-DSRG-MRPT2(c) theory a promising approach for studies of conical intersections.
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Affiliation(s)
- Jae Woo Park
- Department of Chemistry, Chungbuk National University (CBNU), Cheongju 28644, Korea
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11
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Finney BA, Chowdhury SR, Kirkvold C, Vlaisavljevich B. CASPT2 molecular geometries of Fe(II) spin-crossover complexes. Phys Chem Chem Phys 2022; 24:1390-1398. [PMID: 34981806 DOI: 10.1039/d1cp04885f] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022]
Abstract
Using fully internally contracted (FIC)-CASPT2 analytical gradients, geometry optimizations of spin-crossover complexes are reported. This approach is tested on a series of Fe(II) complexes with different sizes, ranging from 13 to 61 atoms. A combination of active space and basis set choices are employed to investigate their role in determining reliable molecular geometries. The reported strategy demonstrates that a wave function-based level of theory can be used to optimize the geometries of metal complexes in reasonable times and enables one to treat the molecular geometry and electronic structure of the complexes using the same level of theory. For a series of smaller Fe(II) SCO complexes, strong field ligands in the LS state result in geometries with the largest differences between DFT and CASPT2; however, good agreement overall is observed between DFT and CASPT2. For the larger complexes, moderate sized basis sets yield geometries that compare well with DFT and available experimental data. We recommend using the (10e,12o) active space since convergence to a minimum structure was more efficient than with truncated active spaces despite having similar Fe-ligand bond distances.
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Affiliation(s)
- Brian A Finney
- University of South Dakota, Department of Chemistry, 414 E Clark St., Vermillion SD, 57069, USA.
| | - Sabyasachi Roy Chowdhury
- University of South Dakota, Department of Chemistry, 414 E Clark St., Vermillion SD, 57069, USA.
| | - Clara Kirkvold
- University of South Dakota, Department of Chemistry, 414 E Clark St., Vermillion SD, 57069, USA.
| | - Bess Vlaisavljevich
- University of South Dakota, Department of Chemistry, 414 E Clark St., Vermillion SD, 57069, USA.
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12
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Wang S, Li C, Evangelista FA. Analytic Energy Gradients for the Driven Similarity Renormalization Group Multireference Second-Order Perturbation Theory. J Chem Theory Comput 2021; 17:7666-7681. [PMID: 34839660 DOI: 10.1021/acs.jctc.1c00980] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We derive analytic energy gradients of the driven similarity renormalization group (DSRG) multireference second-order perturbation theory (MRPT2) using the method of Lagrange multipliers. In the Lagrangian, we impose constraints for a complete-active-space self-consistent-field reference wave function and the semicanonical orthonormal molecular orbitals. Solving for the associated Lagrange multipliers is found to share the same asymptotic scaling of a single DSRG-MRPT2 energy computation. A pilot implementation of the DSRG-MRPT2 analytic gradients is used to optimize the geometry of the singlet and triplet states of p-benzyne. The equilibrium bond lengths and angles are similar to those computed via other MRPT2s and Mukherjee's multireference coupled cluster theory. An approximate DSRG-MRPT2 method that neglects the contributions of the three-body density cumulant is found to introduce negligible errors in the geometry of p-benzyne, lending itself to a promising low-cost approach for molecular geometry optimizations using large active spaces.
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Affiliation(s)
- Shuhe Wang
- Department of Chemistry and Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, United States
| | - Chenyang Li
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China
| | - Francesco A Evangelista
- Department of Chemistry and Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, United States
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13
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Park JW. Analytical Gradient Theory for Resolvent-Fitted Second-Order Extended Multiconfiguration Perturbation Theory (XMCQDPT2). J Chem Theory Comput 2021; 17:6122-6133. [PMID: 34582217 DOI: 10.1021/acs.jctc.1c00613] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022]
Abstract
We present the formulation and implementation of an analytical gradient algorithm for extended multiconfiguration quasidegenerate perturbation theory (XMCQDPT2) with the resolvent-fitting approximation by Granovsky. This algorithm is powerful when optimizing molecular configurations with a moderate-sized active space and many electronic states. First, we present the powerfulness and accuracy of resolvent-fitting approximations compared to canonical XMCQDPT2 theory. Then, we demonstrate the utility of the current algorithm in frequency analyses, optimizing the minimum energy conical intersection geometries of the retinal chromophore model RPSB6 and evaluating nuclear gradients when there are many electronic states. Furthermore, we parallelize the algorithm using the OpenMP/MPI hybrid approach. Additionally, we report the computational cost and parallel efficiency of the program.
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Affiliation(s)
- Jae Woo Park
- Department of Chemistry, Chungbuk National University (CBNU), Cheongju 28644, Korea
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14
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Rousseau P, González-Vázquez J, Piekarski DG, Kopyra J, Domaracka A, Alcamí M, Adoui L, Huber BA, Díaz-Tendero S, Martín F. Timing of charge migration in betaine by impact of fast atomic ions. SCIENCE ADVANCES 2021; 7:eabg9080. [PMID: 34597129 PMCID: PMC10938492 DOI: 10.1126/sciadv.abg9080] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/03/2021] [Accepted: 08/11/2021] [Indexed: 06/13/2023]
Abstract
The way molecules break after ion bombardment is intimately related to the early electron dynamics generated in the system, in particular, charge (or electron) migration. We exploit the natural positive-negative charge splitting in the zwitterionic molecule betaine to selectively induce double electron removal from its negatively charged side by impact of fast O6+ ions. The loss of two electrons in this localized region of the molecular skeleton triggers a competition between direct Coulomb explosion and charge migration that is examined to obtain temporal information from ion-ion coincident measurements and nonadiabatic molecular dynamics calculations. We find a charge migration time, from one end of the molecule to the other, of approximately 20 to 40 femtoseconds. This migration time is longer than that observed in molecules irradiated by ultrashort light pulses and is the consequence of charge migration being driven by adiabatic nuclear dynamics in the ground state of the molecular dication.
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Affiliation(s)
- Patrick Rousseau
- Normandie Univ, ENSICAEN, UNICAEN, CEA, CNRS, CIMAP, 14000 Caen, France
| | - Jesús González-Vázquez
- Departamento de Química, Módulo 13, Universidad Autónoma de Madrid, 28049 Madrid, Spain
- Institute for Advanced Research in Chemical Sciences (IAdChem), Universidad Autónoma de Madrid, 28049 Madrid, Spain
| | - Dariusz G. Piekarski
- Departamento de Química, Módulo 13, Universidad Autónoma de Madrid, 28049 Madrid, Spain
| | - Janina Kopyra
- Faculty of Exact and Natural Sciences, Siedlce University of Natural Sciences and Humanities, 3 Maja 54, 08-110 Siedlce, Poland
| | - Alicja Domaracka
- Normandie Univ, ENSICAEN, UNICAEN, CEA, CNRS, CIMAP, 14000 Caen, France
| | - Manuel Alcamí
- Departamento de Química, Módulo 13, Universidad Autónoma de Madrid, 28049 Madrid, Spain
- Institute for Advanced Research in Chemical Sciences (IAdChem), Universidad Autónoma de Madrid, 28049 Madrid, Spain
- Instituto Madrileño de Estudios Avanzados en Nanociencia (IMDEA Nano), Cantoblanco, 28049 Madrid, Spain
| | - Lamri Adoui
- Normandie Univ, ENSICAEN, UNICAEN, CEA, CNRS, CIMAP, 14000 Caen, France
| | - Bernd A. Huber
- Normandie Univ, ENSICAEN, UNICAEN, CEA, CNRS, CIMAP, 14000 Caen, France
| | - Sergio Díaz-Tendero
- Departamento de Química, Módulo 13, Universidad Autónoma de Madrid, 28049 Madrid, Spain
- Institute for Advanced Research in Chemical Sciences (IAdChem), Universidad Autónoma de Madrid, 28049 Madrid, Spain
- Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, 28049 Madrid, Spain
| | - Fernando Martín
- Departamento de Química, Módulo 13, Universidad Autónoma de Madrid, 28049 Madrid, Spain
- Instituto Madrileño de Estudios Avanzados en Nanociencia (IMDEA Nano), Cantoblanco, 28049 Madrid, Spain
- Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, 28049 Madrid, Spain
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15
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Matsika S. Electronic Structure Methods for the Description of Nonadiabatic Effects and Conical Intersections. Chem Rev 2021; 121:9407-9449. [PMID: 34156838 DOI: 10.1021/acs.chemrev.1c00074] [Citation(s) in RCA: 50] [Impact Index Per Article: 16.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
Abstract
Nonadiabatic effects are ubiquitous in photophysics and photochemistry, and therefore, many theoretical developments have been made to properly describe them. Conical intersections are central in nonadiabatic processes, as they promote efficient and ultrafast nonadiabatic transitions between electronic states. A proper theoretical description requires developments in electronic structure and specifically in methods that describe conical intersections between states and nonadiabatic coupling terms. This review focuses on the electronic structure aspects of nonadiabatic processes. We discuss the requirements of electronic structure methods to describe conical intersections and nonadiabatic couplings, how the most common excited state methods perform in describing these effects, and what the recent developments are in expanding the methodology and implementing nonadiabatic couplings.
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Affiliation(s)
- Spiridoula Matsika
- Department of Chemistry, Temple University, Philadelphia, Pennsylvania 19122, United States
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16
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Nishimoto Y. Analytic gradients for restricted active space second-order perturbation theory (RASPT2). J Chem Phys 2021; 154:194103. [PMID: 34240887 DOI: 10.1063/5.0050074] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023] Open
Abstract
The computational cost of analytic derivatives in multireference perturbation theory is strongly affected by the size of the active space employed in the reference self-consistent field calculation. To overcome previous limits on the active space size, the analytic gradients of single-state restricted active space second-order perturbation theory (RASPT2) and its complete active space second-order perturbation theory (CASPT2) have been developed and implemented in a local version of OpenMolcas. Similar to previous implementations of CASPT2, the RASPT2 implementation employs the Lagrangian or Z-vector method. The numerical results show that restricted active spaces with up to 20 electrons in 20 orbitals can now be employed for geometry optimizations.
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Affiliation(s)
- Yoshio Nishimoto
- Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
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Song C, Neaton JB, Martínez TJ. Reduced scaling formulation of CASPT2 analytical gradients using the supporting subspace method. J Chem Phys 2021; 154:014103. [PMID: 33412861 DOI: 10.1063/5.0035233] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present a reduced scaling and exact reformulation of state specific complete active space second-order perturbation (CASPT2) analytical gradients in terms of the MP2 and Fock derivatives using the supporting subspace method. This work follows naturally from the supporting subspace formulation of the CASPT2 energy in terms of the MP2 energy using dressed orbitals and Fock builds. For a given active space configuration, the terms corresponding to the MP2-gradient can be evaluated with O(N5) operations, while the rest of the calculations can be computed with O(N3) operations using Fock builds, Fock gradients, and linear algebra. When tensor-hyper-contraction is applied simultaneously, the computational cost can be further reduced to O(N4) for a fixed active space size. The new formulation enables efficient implementation of CASPT2 analytical gradients by leveraging the existing graphical processing unit (GPU)-based MP2 and Fock routines. We present benchmark results that demonstrate the accuracy and performance of the new method. Example applications of the new method in ab initio molecular dynamics simulation and constrained geometry optimization are given.
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Affiliation(s)
- Chenchen Song
- Department of Physics, University of California Berkeley, Berkeley, California 94720, USA
| | - Jeffrey B Neaton
- Department of Physics, University of California Berkeley, Berkeley, California 94720, USA
| | - Todd J Martínez
- Department of Chemistry and the PULSE Institute, Stanford University, Stanford, California 94305, USA
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18
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Park JW. Analytical First-Order Derivatives of Second-Order Extended Multiconfiguration Quasi-Degenerate Perturbation Theory (XMCQDPT2): Implementation and Application. J Chem Theory Comput 2020; 16:5562-5571. [PMID: 32786905 DOI: 10.1021/acs.jctc.0c00389] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Analytical gradient theory for the second-order extended multiconfiguration quasi-degenerate perturbation theory (XMCQDPT2), which can be regarded as the multistate version of the multireference second-order Møller-Plesset perturbation theory (MRMP2), is formulated and implemented. The theory is similar to the previous analytical gradient theory for MCQDPT2, but we take into account the intruder state avoidance (ISA) technique and the "extension" of the MCQDPT2 theory by Granovsky. Although the (X)MCQDPT2 theory is not invariant with respect to rotations among the active orbitals, the resulting analytical gradients are accurate. We demonstrate the utility of the current algorithm in optimizing the minimum energy conical intersections (MECIs) of ethylene, butadiene, benzene, the retinal model chromophore PSB3, and the green fluorescent protein model chromophore pHBI. The XMCQDPT2 MECIs are very similar to the XMS-CASPT2 MECIs in terms of molecular conformation and the computed energies. We also discuss possible improvements of the current algorithm.
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Affiliation(s)
- Jae Woo Park
- Department of Chemistry, Chungbuk National University (CBNU), Cheongju 28644, Korea
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19
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Park JW, Al-Saadon R, MacLeod MK, Shiozaki T, Vlaisavljevich B. Multireference Electron Correlation Methods: Journeys along Potential Energy Surfaces. Chem Rev 2020; 120:5878-5909. [PMID: 32239929 DOI: 10.1021/acs.chemrev.9b00496] [Citation(s) in RCA: 54] [Impact Index Per Article: 13.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Abstract
Multireference electron correlation methods describe static and dynamical electron correlation in a balanced way and, therefore, can yield accurate and predictive results even when single-reference methods or multiconfigurational self-consistent field theory fails. One of their most prominent applications in quantum chemistry is the exploration of potential energy surfaces. This includes the optimization of molecular geometries, such as equilibrium geometries and conical intersections and on-the-fly photodynamics simulations, both of which depend heavily on the ability of the method to properly explore the potential energy surface. Because such applications require nuclear gradients and derivative couplings, the availability of analytical nuclear gradients greatly enhances the scope of quantum chemical methods. This review focuses on the developments and advances made in the past two decades. A detailed account of the analytical nuclear gradient and derivative coupling theories is presented. Emphasis is given to the software infrastructure that allows one to make use of these methods. Notable applications of multireference electron correlation methods to chemistry, including geometry optimizations and on-the-fly dynamics, are summarized at the end followed by a discussion of future prospects.
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Affiliation(s)
- Jae Woo Park
- Department of Chemistry, Chungbuk National University, Chungdae-ro 1, Cheongju 28644, Korea
| | - Rachael Al-Saadon
- Department of Chemistry, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208, United States
| | - Matthew K MacLeod
- Workday, 4900 Pearl Circle East, Suite 100, Boulder, Colorado 80301, United States
| | - Toru Shiozaki
- Department of Chemistry, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208, United States.,Quantum Simulation Technologies, Inc., 625 Massachusetts Avenue, Cambridge, Massachusetts 02139, United States
| | - Bess Vlaisavljevich
- Department of Chemistry, University of South Dakota, 414 East Clark Street, Vermillion, South Dakota 57069, United States
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Locating conical intersections using the quasidegenerate partially and strongly contracted NEVPT2 methods. Chem Phys Lett 2020. [DOI: 10.1016/j.cplett.2020.137219] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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Park JW. Analytical Gradient Theory for Quasidegenerate N-Electron Valence State Perturbation Theory (QD-NEVPT2). J Chem Theory Comput 2019; 16:326-339. [DOI: 10.1021/acs.jctc.9b00919] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022]
Affiliation(s)
- Jae Woo Park
- Department of Chemistry, Chungbuk National University (CBNU), Cheongju 28644, Korea
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Tsuchimochi T, Ten-no SL. Second-Order Perturbation Theory with Spin-Symmetry-Projected Hartree–Fock. J Chem Theory Comput 2019; 15:6688-6702. [DOI: 10.1021/acs.jctc.9b00897] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023]
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Nishimoto Y. Analytic first-order derivatives of partially contracted n-electron valence state second-order perturbation theory (PC-NEVPT2). J Chem Phys 2019; 151:114103. [PMID: 31542000 DOI: 10.1063/1.5115819] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023] Open
Abstract
A balanced treatment of dynamic and static electron correlation is important in computational chemistry, and multireference perturbation theory (MRPT) is able to do this at a reasonable computational cost. In this paper, analytic first-order derivatives, specifically gradients and dipole moments, are developed for a particular MRPT method, state-specific partially contracted n-electron valence state second-order perturbation theory (PC-NEVPT2). Only one linear equation needs to be solved for the derivative calculation if the Z-vector method is employed, which facilitates the practical application of this approach. A comparison of the calculated results with experimental geometrical parameters of O3 indicates excellent agreement although the calculated results for O3 - are slightly outside the experimental error bars. The 0-0 transition energies of various methylpyrimidines and trans-polyacetylene are calculated by performing geometry optimizations and seminumerical second-order geometrical derivative calculations. In particular, the deviations of 0-0 transition energies of trans-polyacetylene from experimental values are consistently less than 0.1 eV with PC-NEVPT2, indicating the reliability of the method. These results demonstrate the importance of adding dynamic electron correlation on top of methods dominated by static electron correlation and of developing analytic derivatives for highly accurate methods.
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Affiliation(s)
- Yoshio Nishimoto
- Fukui Institute for Fundamental Chemistry, Kyoto University, 34-4 Takano Nishihiraki-cho, Sakyo-ku, Kyoto 606-8103, Japan
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Park JW. Analytical Gradient Theory for Strongly Contracted (SC) and Partially Contracted (PC) N-Electron Valence State Perturbation Theory (NEVPT2). J Chem Theory Comput 2019; 15:5417-5425. [DOI: 10.1021/acs.jctc.9b00762] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022]
Affiliation(s)
- Jae Woo Park
- Department of Chemistry, Chungbuk National University (CBNU), Cheongju 28644, Korea
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Wang S, Li C, Evangelista FA. Analytic gradients for the single-reference driven similarity renormalization group second-order perturbation theory. J Chem Phys 2019; 151:044118. [PMID: 31370522 DOI: 10.1063/1.5100175] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023] Open
Abstract
We derive and implement analytic energy gradients for the single-reference driven similarity renormalization group second-order perturbation theory (DSRG-PT2). The resulting equations possess an asymptotic scaling that is identical to that of the second-order Møller-Plesset perturbation theory (MP2), indicating that the exponential regularizer in the DSRG equations does not introduce formal difficulties in the gradient theory. We apply the DSRG-PT2 method to optimizing the geometries of 15 small molecules. The equilibrium bond lengths computed with DSRG-PT2 are found similar to those of MP2, yielding a mean absolute error of 0.0033 Å and a standard deviation of 0.0045 Å when compared with coupled cluster with singles, doubles, and perturbative triples.
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Affiliation(s)
- Shuhe Wang
- Department of Chemistry and Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, USA
| | - Chenyang Li
- Department of Chemistry and Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, USA
| | - Francesco A Evangelista
- Department of Chemistry and Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, USA
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