1
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Nykänen A, Thiessen L, Borrelli EM, Krishna V, Knecht S, Pavošević F. Toward Accurate Calculation of Excitation Energies on Quantum Computers with ΔADAPT-VQE: A Case Study of BODIPY Derivatives. J Phys Chem Lett 2024; 15:7111-7117. [PMID: 38954795 DOI: 10.1021/acs.jpclett.4c01301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/04/2024]
Abstract
Quantum chemistry simulations offer a cost-effective way to computationally design BODIPY photosensitizers. However, accurate predictions of excitation energies pose a challenge for time-dependent density functional theory and equation-of-motion coupled-cluster singles and doubles methods. By contrast, reliable predictions can be achieved by multireference quantum chemistry methods; unfortunately, their computational cost increases exponentially with the number of electrons. Alternatively, quantum computing holds potential for an exact simulation of the photophysical properties in a computationally more efficient way. Herein, we introduce the state-specific ΔUCCSD-VQE (unitary coupled-cluster singles and doubles-variational quantum eigensolver) and ΔADAPT-VQE methods in which the electronically excited state is calculated via a non-Aufbau configuration. We show for six BODIPY derivatives that the proposed methods predict accurate excitation energies that are in good agreement with those from experiments. Due to its performance and simplicity, we believe that ΔADAPT will become a useful approach for the simulation of BODIPY photosensitizers on near-term quantum devices.
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Affiliation(s)
- Anton Nykänen
- Algorithmiq Ltd., Kanavakatu 3C, FI-00160 Helsinki, Finland
| | | | | | - Vijay Krishna
- Department of Biomedical Engineering, Lerner Research Institute, Cleveland Clinic, Cleveland, Ohio 44195, United States
- Department of Biomedical Engineering, Cleveland Clinic Lerner College of Medicine, Case Western Reserve University, Cleveland, Ohio 44106, United States
| | - Stefan Knecht
- Algorithmiq Ltd., Kanavakatu 3C, FI-00160 Helsinki, Finland
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2
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Hait D, Lahana D, Fajen OJ, Paz ASP, Unzueta PA, Rana B, Lu L, Wang Y, Kjønstad EF, Koch H, Martínez TJ. Prediction of photodynamics of 200 nm excited cyclobutanone with linear response electronic structure and ab initio multiple spawning. J Chem Phys 2024; 160:244101. [PMID: 38912674 DOI: 10.1063/5.0203800] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2024] [Accepted: 05/05/2024] [Indexed: 06/25/2024] Open
Abstract
Simulations of photochemical reaction dynamics have been a challenge to the theoretical chemistry community for some time. In an effort to determine the predictive character of current approaches, we predict the results of an upcoming ultrafast diffraction experiment on the photodynamics of cyclobutanone after excitation to the lowest lying Rydberg state (S2). A picosecond of nonadiabatic dynamics is described with ab initio multiple spawning. We use both time dependent density functional theory (TDDFT) and equation-of-motion coupled cluster singles and doubles (EOM-CCSD) theory for the underlying electronic structure theory. We find that the lifetime of the S2 state is more than a picosecond (with both TDDFT and EOM-CCSD). The predicted ultrafast electron diffraction spectrum exhibits numerous structural features, but weak time dependence over the course of the simulations.
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Affiliation(s)
- Diptarka Hait
- Department of Chemistry and The PULSE Institute, Stanford University, Stanford, California 94305, USA
- SLAC National Accelerator Laboratory, Menlo Park, California 94024, USA
| | - Dean Lahana
- Department of Chemistry and The PULSE Institute, Stanford University, Stanford, California 94305, USA
- SLAC National Accelerator Laboratory, Menlo Park, California 94024, USA
| | - O Jonathan Fajen
- Department of Chemistry and The PULSE Institute, Stanford University, Stanford, California 94305, USA
- SLAC National Accelerator Laboratory, Menlo Park, California 94024, USA
| | - Amiel S P Paz
- Department of Chemistry and The PULSE Institute, Stanford University, Stanford, California 94305, USA
- SLAC National Accelerator Laboratory, Menlo Park, California 94024, USA
| | - Pablo A Unzueta
- Department of Chemistry and The PULSE Institute, Stanford University, Stanford, California 94305, USA
- SLAC National Accelerator Laboratory, Menlo Park, California 94024, USA
| | - Bhaskar Rana
- Department of Chemistry and The PULSE Institute, Stanford University, Stanford, California 94305, USA
- SLAC National Accelerator Laboratory, Menlo Park, California 94024, USA
| | - Lixin Lu
- Department of Chemistry and The PULSE Institute, Stanford University, Stanford, California 94305, USA
- SLAC National Accelerator Laboratory, Menlo Park, California 94024, USA
| | - Yuanheng Wang
- Department of Chemistry and The PULSE Institute, Stanford University, Stanford, California 94305, USA
- SLAC National Accelerator Laboratory, Menlo Park, California 94024, USA
| | - Eirik F Kjønstad
- Department of Chemistry and The PULSE Institute, Stanford University, Stanford, California 94305, USA
- SLAC National Accelerator Laboratory, Menlo Park, California 94024, USA
- Department of Chemistry, Norwegian University of Science and Technology, Trondheim 7491, Norway
| | - Henrik Koch
- Department of Chemistry, Norwegian University of Science and Technology, Trondheim 7491, Norway
| | - Todd J Martínez
- Department of Chemistry and The PULSE Institute, Stanford University, Stanford, California 94305, USA
- SLAC National Accelerator Laboratory, Menlo Park, California 94024, USA
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3
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Culpitt T, Tellgren EI, Pavošević F. Unitary coupled-cluster for quantum computation of molecular properties in a strong magnetic field. J Chem Phys 2023; 159:204101. [PMID: 37991157 DOI: 10.1063/5.0177417] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/21/2023] [Accepted: 10/20/2023] [Indexed: 11/23/2023] Open
Abstract
In truncated coupled-cluster (CC) theories, non-variational and/or generally complex ground-state energies can occur. This is due to the non-Hermitian nature of the similarity transformed Hamiltonian matrix in combination with CC truncation. For chemical problems that deal with real-valued Hamiltonian matrices, complex CC energies rarely occur. However, for complex-valued Hamiltonian matrices, such as those that arise in the presence of strong magnetic fields, complex CC energies can be regularly observed unless certain symmetry conditions are fulfilled. Therefore, in the presence of magnetic fields, it is desirable to pursue CC methods that are guaranteed to give upper-bound, real-valued energies. In this work, we present the first application of unitary CC to chemical systems in a strong magnetic field. This is achieved utilizing the variational quantum eigensolver algorithm applied to the unitary coupled-cluster singles and doubles (UCCSD) method. We benchmark the method on the H2 molecule in a strong magnetic field and then calculate UCCSD energies for the H4 molecule as a function of both geometry and field angle. We show that while standard CCSD can yield generally complex energies that are not an upper-bound to the true energy, UCCSD always results in variational and real-valued energies. We also show that the imaginary components of the CCSD energy are largest in the strongly correlated region. Last, the UCCSD calculations capture a large percentage of the correlation energy.
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Affiliation(s)
- Tanner Culpitt
- Theoretical Chemistry Institute and Department of Chemistry, University of Wisconsin-Madison, 1101 University Ave., Madison, Wisconsin 53706, USA
| | - Erik I Tellgren
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
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4
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Yuwono SH, Cooper BC, Zhang T, Li X, DePrince AE. Time-dependent equation-of-motion coupled-cluster simulations with a defective Hamiltonian. J Chem Phys 2023; 159:044113. [PMID: 37497820 DOI: 10.1063/5.0157852] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2023] [Accepted: 07/11/2023] [Indexed: 07/28/2023] Open
Abstract
Simulations of laser-induced electron dynamics in a molecular system are performed using time-dependent (TD) equation-of-motion (EOM) coupled-cluster (CC) theory. The target system has been chosen to highlight potential shortcomings of truncated TD-EOM-CC methods [represented in this work by TD-EOM-CC with single and double excitations (TD-EOM-CCSD)], where unphysical spectroscopic features can emerge. Specifically, we explore driven resonant electronic excitations in magnesium fluoride in the proximity of an avoided crossing. Near the avoided crossing, the CCSD similarity-transformed Hamiltonian is defective, meaning that it has complex eigenvalues, and oscillator strengths may take on negative values. When an external field is applied to drive transitions to states exhibiting these traits, unphysical dynamics are observed. For example, the stationary states that make up the time-dependent state acquire populations that can be negative, exceed one, or even complex-valued.
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Affiliation(s)
- Stephen H Yuwono
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, USA
| | - Brandon C Cooper
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, USA
| | - Tianyuan Zhang
- Department of Chemistry, University of Washington, Seattle, Washington 98195, USA
| | - Xiaosong Li
- Department of Chemistry, University of Washington, Seattle, Washington 98195, USA
| | - A Eugene DePrince
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, USA
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5
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Jagau TC. Theory of electronic resonances: fundamental aspects and recent advances. Chem Commun (Camb) 2022; 58:5205-5224. [PMID: 35395664 DOI: 10.1039/d1cc07090h] [Citation(s) in RCA: 17] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/21/2023]
Abstract
Electronic resonances are states that are unstable towards loss of electrons. They play critical roles in high-energy environments across chemistry, physics, and biology but are also relevant to processes under ambient conditions that involve unbound electrons. This feature article focuses on complex-variable techniques such as complex scaling and complex absorbing potentials that afford a treatment of electronic resonances in terms of discrete square-integrable eigenstates of non-Hermitian Hamiltonians with complex energy. Fundamental aspects of these techniques as well as their integration into molecular electronic-structure theory are discussed and an overview of some recent developments is given: analytic gradient theory for electronic resonances, the application of rank-reduction techniques and quantum embedding to them, as well as approaches for evaluating partial decay widths.
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Affiliation(s)
- Thomas-C Jagau
- Department of Chemistry, KU Leuven, Celestijnenlaan 200F, B-3001 Leuven, Belgium.
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6
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Liu J, Matthews DA, Cheng L. Quadratic Unitary Coupled-Cluster Singles and Doubles Scheme: Efficient Implementation, Benchmark Study, and Formulation of an Extended Version. J Chem Theory Comput 2022; 18:2281-2291. [PMID: 35312299 DOI: 10.1021/acs.jctc.1c01210] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
An efficient implementation of the quadratic unitary coupled-cluster singles and doubles (qUCCSD) scheme for calculations of electronic ground and excited states using an unrestricted molecular spin-orbital formulation and an efficient tensor contraction library is reported. The accuracy of the qUCCSD scheme and the efficiency of the present implementation are demonstrated using extensive benchmark calculations of excitation energies and an application to S0 → S1 vertical excitation energies for cis- and trans-4a,4b-dihydrotriphenylene. The qUCCSD scheme has been shown to provide improved excitation energies compared with the UCC3 scheme formulated based on perturbation theory. A UCC truncation scheme that can provide excitation energies correct through the fourth order is also presented to further improve the accuracy of the qUCCSD scheme.
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Affiliation(s)
- Junzi Liu
- School of Chemistry and Biological Engineering, University of Science and Technology Beijing, Beijing, 100083, China
| | - Devin A Matthews
- Department of Chemistry, Southern Methodist University, Dallas, Texas 75275, United States
| | - Lan Cheng
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, United States
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7
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Hohenstein EG, Yu JK, Bannwarth C, List NH, Paul AC, Folkestad SD, Koch H, Martínez TJ. Predictions of Pre-edge Features in Time-Resolved Near-Edge X-ray Absorption Fine Structure Spectroscopy from Hole-Hole Tamm-Dancoff-Approximated Density Functional Theory. J Chem Theory Comput 2021; 17:7120-7133. [PMID: 34623139 DOI: 10.1021/acs.jctc.1c00478] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Abstract
Time-resolved near-edge X-ray absorption fine structure (TR-NEXAFS) spectroscopy is a powerful technique for studying photochemical reaction dynamics with femtosecond time resolution. In order to avoid ambiguity in TR-NEXAFS spectra from nonadiabatic dynamics simulations, core- and valence-excited states must be evaluated on equal footing and those valence states must also define the potential energy surfaces used in the nonadiabatic dynamics simulation. In this work, we demonstrate that hole-hole Tamm-Dancoff-approximated density functional theory (hh-TDA) is capable of directly simulating TR-NEXAFS spectroscopies. We apply hh-TDA to the excited-state dynamics of acrolein. We identify two pre-edge features in the oxygen K-edge TR-NEXAFS spectrum associated with the S2 (ππ*) and S1 (nπ*) excited states. We show that these features can be used to follow the internal conversion dynamics between the lowest three electronic states of acrolein. Due to the low, O(N2) apparent computational complexity of hh-TDA and our GPU-accelerated implementation, this method is promising for the simulation of pre-edge features in TR-NEXAFS spectra of large molecules and molecules in the condensed phase.
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Affiliation(s)
- Edward G Hohenstein
- Department of Chemistry and The PULSE Institute, Stanford University, Stanford, California 94305, United States.,SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California 94025, United States
| | - Jimmy K Yu
- Department of Chemistry and The PULSE Institute, Stanford University, Stanford, California 94305, United States.,SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California 94025, United States.,Biophysics Program, Stanford University, Stanford, California 94305, United States
| | - Christoph Bannwarth
- Department of Chemistry and The PULSE Institute, Stanford University, Stanford, California 94305, United States.,SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California 94025, United States
| | - Nanna Holmgaard List
- Department of Chemistry and The PULSE Institute, Stanford University, Stanford, California 94305, United States.,SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California 94025, United States
| | - Alexander C Paul
- Department of Chemistry, Norwegian University of Science and Technology, NTNU, 7491 Trondheim, Norway
| | - Sarai D Folkestad
- Department of Chemistry, Norwegian University of Science and Technology, NTNU, 7491 Trondheim, Norway
| | - Henrik Koch
- Department of Chemistry, Norwegian University of Science and Technology, NTNU, 7491 Trondheim, Norway.,Scuola Normale Superiore, Piazza dei Cavaleri 7, 56126 Pisa, Italy
| | - Todd J Martínez
- Department of Chemistry and The PULSE Institute, Stanford University, Stanford, California 94305, United States.,SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California 94025, United States
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8
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Liu J, Cheng L. Unitary coupled-cluster based self-consistent polarization propagator theory: A quadratic unitary coupled-cluster singles and doubles scheme. J Chem Phys 2021; 155:174102. [PMID: 34742195 DOI: 10.1063/5.0062090] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The development of a quadratic unitary coupled-cluster singles and doubles (qUCCSD) based self-consistent polarization propagator method is reported. We present a simple strategy for truncating the commutator expansion of the unitary version of coupled-cluster transformed Hamiltonian H̄. The qUCCSD method for the electronic ground state includes up to double commutators for the amplitude equations and up to cubic commutators for the energy expression. The qUCCSD excited-state eigenvalue equations include up to double commutators for the singles-singles block of H̄, single commutators for the singles-doubles and doubles-singles blocks, and the bare Hamiltonian for the doubles-doubles block. Benchmark qUCCSD calculations of the ground-state properties and excitation energies for representative molecules demonstrate significant improvement of the accuracy and robustness over the previous UCC3 scheme derived using Møller-Plesset perturbation theory.
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Affiliation(s)
- Junzi Liu
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Lan Cheng
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, USA
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9
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Thomas S, Hampe F, Stopkowicz S, Gauss J. Complex ground-state and excitation energies in coupled-cluster theory. Mol Phys 2021. [DOI: 10.1080/00268976.2021.1968056] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Affiliation(s)
- Simon Thomas
- Department Chemie, Johannes Gutenberg-Universität Mainz, Mainz, Germany
| | - Florian Hampe
- Department Chemie, Johannes Gutenberg-Universität Mainz, Mainz, Germany
| | - Stella Stopkowicz
- Department Chemie, Johannes Gutenberg-Universität Mainz, Mainz, Germany
| | - Jürgen Gauss
- Department Chemie, Johannes Gutenberg-Universität Mainz, Mainz, Germany
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10
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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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11
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Gulania S, Kjønstad EF, Stanton JF, Koch H, Krylov AI. Equation-of-motion coupled-cluster method with double electron-attaching operators: Theory, implementation, and benchmarks. J Chem Phys 2021; 154:114115. [PMID: 33752380 DOI: 10.1063/5.0041822] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We report a production-level implementation of the equation-of-motion (EOM) coupled-cluster (CC) method with double electron-attaching (DEA) EOM operators of 2p and 3p1h types, EOM-DEA-CCSD. This ansatz, suitable for treating electronic structure patterns that can be described as two-electrons-in-many orbitals, represents a useful addition to the EOM-CC family of methods. We analyze the performance of EOM-DEA-CCSD for energy differences and molecular properties. By considering reduced quantities, such as state and transition one-particle density matrices, we compare EOM-DEA-CCSD wave functions with wave functions computed by other EOM-CCSD methods. The benchmarks illustrate that EOM-DEA-CCSD is capable of treating diradicals, bond-breaking, and some types of conical intersections.
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Affiliation(s)
- Sahil Gulania
- Department of Chemistry, University of Southern California, Los Angeles, California 90089, USA
| | - Eirik F Kjønstad
- Department of Chemistry, Norwegian University of Science and Technology, 7491 Trondheim, Norway
| | - John F Stanton
- Quantum Theory Project, Departments of Chemistry and Physics, University of Florida, Gainesville, Florida 32611, USA
| | - Henrik Koch
- Scuola Normale Superiore, Piazza dei Cavaleri 7, 56126 Pisa, Italy
| | - Anna I Krylov
- Department of Chemistry, University of Southern California, Los Angeles, California 90089, USA
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12
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Abstract
![]()
In
coupled cluster theory, the electronic states are biorthonormal
in the sense that the left states are orthonormal to the right states.
Here, we present an extension of this formalism to a left and right
total molecular wave function. Starting from left and right Born–Huang
expansions, we derive projected Schrödinger equations for the
left and right nuclear wave functions. Observables may be extracted
from the resulting wave function pair using standard expressions.
The formalism is shown to be invariant under electronic basis transformations,
such as normalization of the electronic states. Consequently, the
nonadiabatic coupling elements can be expressed with biorthonormal
electronic wave functions. Calculating normalization factors that
scale as full configuration interaction is not necessary, contrary
to claims in the literature. For nonadiabatic nuclear dynamics, we
need expressions for the derivative couplings in the biorthonormal
formalism. These are derived in a Lagrangian framework.
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Affiliation(s)
- Eirik F Kjønstad
- Department of Chemistry, Norwegian University of Science and Technology, Trondheim 7491, Norway
| | - Henrik Koch
- Department of Chemistry, Norwegian University of Science and Technology, Trondheim 7491, Norway.,Scuola Normale Superiore, Piazza dei Cavalieri, 7, Pisa PI 56126, Italy
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13
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Mai S, González L. Molecular Photochemistry: Recent Developments in Theory. Angew Chem Int Ed Engl 2020; 59:16832-16846. [PMID: 32052547 PMCID: PMC7540682 DOI: 10.1002/anie.201916381] [Citation(s) in RCA: 77] [Impact Index Per Article: 19.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2019] [Revised: 02/12/2020] [Indexed: 12/16/2022]
Abstract
Photochemistry is a fascinating branch of chemistry that is concerned with molecules and light. However, the importance of simulating light-induced processes is reflected also in fields as diverse as biology, material science, and medicine. This Minireview highlights recent progress achieved in theoretical chemistry to calculate electronically excited states of molecules and simulate their photoinduced dynamics, with the aim of reaching experimental accuracy. We focus on emergent methods and give selected examples that illustrate the progress in recent years towards predicting complex electronic structures with strong correlation, calculations on large molecules, describing multichromophoric systems, and simulating non-adiabatic molecular dynamics over long time scales, for molecules in the gas phase or in complex biological environments.
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Affiliation(s)
- Sebastian Mai
- Photonics InstituteVienna University of TechnologyGusshausstrasse 27–291040ViennaAustria
| | - Leticia González
- Institute of Theoretical ChemistryFaculty of ChemistryUniversity of ViennaWähringer Strasse 171090ViennaAustria
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14
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Song C, Martínez TJ. Reduced scaling extended multi-state CASPT2 (XMS-CASPT2) using supporting subspaces and tensor hyper-contraction. J Chem Phys 2020; 152:234113. [PMID: 32571032 DOI: 10.1063/5.0007417] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023] Open
Abstract
We present a reduced scaling formulation of the extended multi-state CASPT2 (XMS-CASPT2) method, which is based on our recently developed state-specific CASPT2 (SS-CASPT2) formulation using supporting subspaces and tensor hyper-contraction. By using these two techniques, the off-diagonal elements of the effective Hamiltonian can be computed with only O(N3) operations and O(N2) memory, where N is the number of basis functions. This limits the overall computational scaling to O(N4) operations and O(N2) memory. Thus, excited states can now be obtained at the same reduced (relative to previous algorithms) scaling we achieved for SS-CASPT2. In addition, we also investigate how the energy denominators can be factorized with the Laplace quadrature when some of the denominators are negative, which is critical for excited state calculations. An efficient implementation of the method has been developed using graphical processing units while also exploiting spatial sparsity in tensor operations. We benchmark the accuracy of the new method by comparison to non-THC formulated XMS-CASPT2 for the excited states of various molecules. In our tests, the THC approximation introduces negligible errors (≈0.01 eV) compared to the non-THC reference method. Scaling behavior and computational timings are presented to demonstrate performance. The new method is also interfaced with quantum mechanics/molecular mechanics (QM/MM). In an example study of green fluorescent protein, we show how the XMS-CASPT2 potential energy surfaces and excitation energies are affected by increasing the size of the QM region up to 278 QM atoms with more than 2300 basis functions.
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Affiliation(s)
- Chenchen Song
- Department of Chemistry and the PULSE Institute, Stanford University, Stanford, California 94305, USA
| | - Todd J Martínez
- Department of Chemistry and the PULSE Institute, Stanford University, Stanford, California 94305, USA
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15
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Mai S, González L. Molekulare Photochemie: Moderne Entwicklungen in der theoretischen Chemie. Angew Chem Int Ed Engl 2020. [DOI: 10.1002/ange.201916381] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022]
Affiliation(s)
- Sebastian Mai
- Institut für Photonik Technische Universität Wien Gußhausstraße 27–29 1040 Wien Österreich
| | - Leticia González
- Institut für theoretische Chemie Fakultät für Chemie Universität Wien Währinger Straße 17 1090 Wien Österreich
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16
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Sorbelli D, Belanzoni P, Saue T, Belpassi L. Ground and excited electronic states of AuH 2via detachment energies on AuH 2− using state-of-the-art relativistic calculations. Phys Chem Chem Phys 2020; 22:26742-26752. [DOI: 10.1039/d0cp05204c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
AuH2 is not as simple as it may seem at first glance!
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Affiliation(s)
- Diego Sorbelli
- Department of Chemistry
- Biology and Biotechnology
- University of Perugia
- 06123 Perugia
- Italy
| | - Paola Belanzoni
- Department of Chemistry
- Biology and Biotechnology
- University of Perugia
- 06123 Perugia
- Italy
| | - Trond Saue
- Laboratoire de Chimie et Physique Quantiques
- UMR 5626 CNRS – Université Toulouse III-Paul Sabatier
- F-31062 Toulouse
- France
| | - Leonardo Belpassi
- Institute of Chemical Science and Technologies “Giulio Natta” (CNR-SCITEC) c/o Department of Chemistry
- Biology and Biotechnology
- University of Perugia
- 06123 Perugia
- Italy
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17
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Faber R, Kjønstad EF, Koch H, Coriani S. Spin adapted implementation of EOM-CCSD for triplet excited states: Probing intersystem crossings of acetylacetone at the carbon and oxygen K-edges. J Chem Phys 2019; 151:144107. [PMID: 31615219 DOI: 10.1063/1.5112164] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We present an equation of motion coupled cluster singles and doubles approach for computing transient absorption spectra from a triplet excited state. The implementation determines the left and right excitation vectors by explicitly spin-adapting the triplet excitation space. As an illustrative application, we compute transient state X-ray absorption spectra at the carbon and oxygen K-edges for the acetylacetone molecule.
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Affiliation(s)
- Rasmus Faber
- DTU Chemistry, Technical University of Denmark, Kemitorvet Build. 207, DK-2800 Kongens Lyngby, Denmark
| | - Eirik F Kjønstad
- Department of Chemistry, Norwegian University of Science and Technology, N-7491 Trondheim, Norway
| | - Henrik Koch
- Department of Chemistry, Norwegian University of Science and Technology, N-7491 Trondheim, Norway
| | - Sonia Coriani
- DTU Chemistry, Technical University of Denmark, Kemitorvet Build. 207, DK-2800 Kongens Lyngby, Denmark
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18
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Kjønstad EF, Koch H. An Orbital Invariant Similarity Constrained Coupled Cluster Model. J Chem Theory Comput 2019; 15:5386-5397. [PMID: 31487174 DOI: 10.1021/acs.jctc.9b00702] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
We present a similarity constrained coupled cluster method able to describe conical intersections between two excited electronic states of the same symmetry. For a given pair of states, this singles and doubles method (SCCSD) is unique and orbital invariant. The computational cost scales as the sixth power with respect to the number of orbitals, and preliminary calculations indicate that the excitation energy difference relative to CCSD is within the error range of CCSD (approximately 0.10 eV). We also analyze the size-scaling properties of the orthogonality condition. For a projected orthogonality condition we show, and demonstrate numerically, that the method is rigorously size-intensive.
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Affiliation(s)
- Eirik F Kjønstad
- Department of Chemistry , Norwegian University of Science and Technology , 7491 Trondheim , Norway.,Scuola Normale Superiore , Piazza dei Cavalieri, 7 , 56126 Pisa , Province of Pisa , Italy
| | - Henrik Koch
- Department of Chemistry , Norwegian University of Science and Technology , 7491 Trondheim , Norway.,Scuola Normale Superiore , Piazza dei Cavalieri, 7 , 56126 Pisa , Province of Pisa , Italy
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19
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Ibele LM, Nicolson A, Curchod BFE. Excited-state dynamics of molecules with classically driven trajectories and Gaussians. Mol Phys 2019. [DOI: 10.1080/00268976.2019.1665199] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
Affiliation(s)
- Lea M. Ibele
- Department of Chemistry, Durham University, Durham, UK
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20
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Pokhilko P, Epifanovsky E, Krylov AI. General framework for calculating spin-orbit couplings using spinless one-particle density matrices: Theory and application to the equation-of-motion coupled-cluster wave functions. J Chem Phys 2019; 151:034106. [PMID: 31325926 DOI: 10.1063/1.5108762] [Citation(s) in RCA: 31] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023] Open
Abstract
Standard implementations of nonrelativistic excited-state calculations compute only one component of spin multiplets (i.e., Ms = 0 triplets); however, matrix elements for all components are necessary for deriving spin-dependent experimental observables. Wigner-Eckart's theorem allows one to circumvent explicit calculations of all multiplet components. We generate all other spin-orbit matrix elements by applying Wigner-Eckart's theorem to a reduced one-particle transition density matrix computed for a single multiplet component. In addition to computational efficiency, this approach also resolves the phase issue arising within Born-Oppenheimer's separation of nuclear and electronic degrees of freedom. A general formalism and its application to the calculation of spin-orbit couplings using equation-of-motion coupled-cluster wave functions are presented. The two-electron contributions are included via the mean-field spin-orbit treatment. Intrinsic issues of constructing spin-orbit mean-field operators for open-shell references are discussed, and a resolution is proposed. The method is benchmarked by using several radicals and diradicals. The merits of the approach are illustrated by a calculation of the barrier for spin inversion in a high-spin tris(pyrrolylmethyl)amine Fe(II) complex.
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Affiliation(s)
- Pavel Pokhilko
- Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482, USA
| | - Evgeny Epifanovsky
- Q-Chem, Inc., 6601 Owens Drive, Suite 105, Pleasanton, California 94588, USA
| | - Anna I Krylov
- Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482, USA and Institut für Physikalische Chemie, Johannes Gutenberg-Universität Mainz, Duesbergweg 10-14, D-55128 Mainz, Germany
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21
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Maradzike E, DePrince AE. Modeling core-level excitations with variationally optimized reduced-density matrices and the extended random phase approximation. J Chem Phys 2018; 149:234101. [PMID: 30579305 DOI: 10.1063/1.5048924] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The information contained within ground-state one- and two-electron reduced-density matrices (RDMs) can be used to compute wave functions and energies for electronically excited states through the extended random phase approximation (ERPA). The ERPA is an appealing framework for describing excitations out of states obtained via the variational optimization of the two-electron RDM (2-RDM), as the variational 2-RDM (v2RDM) approach itself can only be used to describe the lowest-energy state of a given spin symmetry. The utility of the ERPA for predicting near-edge features relevant to x-ray absorption spectroscopy is assessed for the case that the 2-RDM is obtained from a ground-state v2RDM-driven complete active space self-consistent field (CASSCF) computation. A class of killer conditions for the CASSCF-specific ERPA excitation operator is derived, and it is demonstrated that a reliable description of core-level excitations requires an excitation operator that fulfills these conditions; the core-valence separation (CVS) scheme yields such an operator. Absolute excitation energies evaluated within the CASSCF/CVS-ERPA framework are slightly more accurate than those obtained from the usual random phase approximation (RPA), but the CVS-ERPA is not more accurate than RPA for predicting the relative positions of near-edge features. Nonetheless, CVS-ERPA is established as a reasonable starting point for the treatment of core-level excitations using variationally optimized 2-RDMs.
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Affiliation(s)
- Elvis Maradzike
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, USA
| | - A Eugene DePrince
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, USA
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22
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Benda Z, Jagau TC. Understanding Processes Following Resonant Electron Attachment: Minimum-Energy Crossing Points between Anionic and Neutral Potential Energy Surfaces. J Chem Theory Comput 2018; 14:4216-4223. [DOI: 10.1021/acs.jctc.8b00444] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Zsuzsanna Benda
- Department of Chemistry, University of Munich (LMU), D-81377 Munich, Germany
| | - Thomas-C. Jagau
- Department of Chemistry, University of Munich (LMU), D-81377 Munich, Germany
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23
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Liu J, Asthana A, Cheng L, Mukherjee D. Unitary coupled-cluster based self-consistent polarization propagator theory: A third-order formulation and pilot applications. J Chem Phys 2018; 148:244110. [DOI: 10.1063/1.5030344] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Junzi Liu
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Ayush Asthana
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Lan Cheng
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Debashis Mukherjee
- Raman Center for Atomic, Molecular and Optical Sciences, Indian Association for the Cultivation of Science, Kolkata 700-032, India
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24
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Copan AV, Sokolov AY. Linear-Response Density Cumulant Theory for Excited Electronic States. J Chem Theory Comput 2018; 14:4097-4108. [DOI: 10.1021/acs.jctc.8b00326] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Andreas V. Copan
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, United States
| | - Alexander Yu. Sokolov
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, United States
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25
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Shamasundar KR. Diagonal Born–Oppenheimer correction for coupled-cluster wave-functions. Mol Phys 2018. [DOI: 10.1080/00268976.2018.1448946] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
Affiliation(s)
- K. R. Shamasundar
- Department of Chemical Sciences, Indian Institute of Science Education and Research (IISER) Mohali, Mohali, India
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26
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Faraji S, Matsika S, Krylov AI. Calculations of non-adiabatic couplings within equation-of-motion coupled-cluster framework: Theory, implementation, and validation against multi-reference methods. J Chem Phys 2018; 148:044103. [DOI: 10.1063/1.5009433] [Citation(s) in RCA: 31] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022] Open
Affiliation(s)
- Shirin Faraji
- Department of Chemistry, University of Southern California, Los Angeles, California 90089, USA
- Zernike Institute for Advanced Materials, Groningen, The Netherlands
| | - Spiridoula Matsika
- Department of Chemistry, Temple University, Philadelphia, Pennsylvania 19122, USA
| | - Anna I. Krylov
- Department of Chemistry, University of Southern California, Los Angeles, California 90089, USA
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27
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Kjønstad EF, Myhre RH, Martínez TJ, Koch H. Crossing conditions in coupled cluster theory. J Chem Phys 2017; 147:164105. [DOI: 10.1063/1.4998724] [Citation(s) in RCA: 32] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Eirik F. Kjønstad
- Department of Chemistry, Norwegian University of Science and Technology, 7491 Trondheim, Norway
- Department of Chemistry and the PULSE Institute, Stanford University, Stanford, California 94305, USA
| | - Rolf H. Myhre
- Department of Chemistry, Norwegian University of Science and Technology, 7491 Trondheim, Norway
- Department of Chemistry and the PULSE Institute, Stanford University, Stanford, California 94305, USA
| | - Todd J. Martínez
- Department of Chemistry and the PULSE Institute, Stanford University, Stanford, California 94305, USA
| | - Henrik Koch
- Department of Chemistry, Norwegian University of Science and Technology, 7491 Trondheim, Norway
- Department of Chemistry and the PULSE Institute, Stanford University, Stanford, California 94305, USA
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