1
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Majee K, Chakraborty S, Mukhopadhyay T, Nayak MK, Dutta AK. A reduced cost four-component relativistic unitary coupled cluster method for atoms and molecules. J Chem Phys 2024; 161:034101. [PMID: 39007370 DOI: 10.1063/5.0207091] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/06/2024] [Accepted: 06/12/2024] [Indexed: 07/16/2024] Open
Abstract
We present a four-component relativistic unitary coupled cluster method for atoms and molecules. We have used commutator-based non-perturbative approximation using the "Bernoulli expansion" to derive an approximation to the relativistic unitary coupled cluster method. The performance of the full quadratic unitary coupled-cluster singles and doubles method (qUCCSD), as well as a perturbative approximation variant (UCC3), has been reported for both energies and properties. It can be seen that both methods give results comparable to those of the standard relativistic coupled cluster method. The qUCCSD method shows better agreement with experimental results due to the better inclusion of relaxation effects. The relativistic UCC3 and qUCCSD methods can simulate the spin-forbidden transition with easy access to transition properties. A natural spinor-based scheme to reduce the computational cost of relativistic UCC3 and qUCCSD methods has been discussed.
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Affiliation(s)
- Kamal Majee
- Department of Chemistry, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
| | - Sudipta Chakraborty
- Department of Chemistry, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
| | - Tamoghna Mukhopadhyay
- Department of Chemistry, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
| | - Malaya K Nayak
- Theoretical Chemistry Section, Bhabha Atomic Research Centre, Trombay, Mumbai 400085, India
- Homi Bhabha National Institute, BARC Training School Complex, Anushakti Nagar, Mumbai 400094, India
| | - Achintya Kumar Dutta
- Department of Chemistry, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
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2
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Kumar A, Asthana A, Abraham V, Crawford TD, Mayhall NJ, Zhang Y, Cincio L, Tretiak S, Dub PA. Quantum Simulation of Molecular Response Properties in the NISQ Era. J Chem Theory Comput 2023; 19:9136-9150. [PMID: 38054645 DOI: 10.1021/acs.jctc.3c00731] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/07/2023]
Abstract
Accurate modeling of the response of molecular systems to an external electromagnetic field is challenging on classical computers, especially in the regime of strong electronic correlation. In this article, we develop a quantum linear response (qLR) theory to calculate molecular response properties on near-term quantum computers. Inspired by the recently developed variants of the quantum counterpart of equation of motion (qEOM) theory, the qLR formalism employs "killer condition" satisfying excitation operator manifolds that offer a number of theoretical advantages along with reduced quantum resource requirements. We also used the qEOM framework in this work to calculate the state-specific response properties. Further, through noiseless quantum simulations, we show that response properties calculated using the qLR approach are more accurate than the ones obtained from the classical coupled-cluster-based linear response models due to the improved quality of the ground-state wave function obtained using the ADAPT-VQE algorithm.
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Affiliation(s)
- Ashutosh Kumar
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Ayush Asthana
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Vibin Abraham
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - T Daniel Crawford
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Nicholas J Mayhall
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Yu Zhang
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Lukasz Cincio
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Sergei Tretiak
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
- Center for Integrated Nanotechnologies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Pavel A Dub
- Chemistry Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
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3
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Dreuw A, Papapostolou A, Dempwolff AL. Algebraic Diagrammatic Construction Schemes Employing the Intermediate State Formalism: Theory, Capabilities, and Interpretation. J Phys Chem A 2023; 127:6635-6646. [PMID: 37498297 DOI: 10.1021/acs.jpca.3c02761] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/28/2023]
Abstract
Algebraic diagrammatic construction (ADC) schemes represent a family of ab initio methods for the calculation of excited electronic states and electron-detached and -attached states. All ADC methods have been demonstrated to possess great potential for molecular applications, e.g., for the calculation of absorption or photoelectron spectra or electron attachment processes. ADC originates from Green's function or propagator theory; however, most recent ADC developments heavily rely on the intermediate state representation or effective Liouvillian formalisms, which comprise new ADC methods and computational schemes for high-order properties. The different approaches for the calculation of excitation energies, ionization potentials, and electron affinities are intimately related, and they provide a coherent description of these quantities at equivalent levels of theory and with comparable errors. Most quantum chemical program packages contain ADC methods; however, the most complete ADC suite of methods can be found in the recent release of Q-Chem.
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Affiliation(s)
- Andreas Dreuw
- Interdisciplinary Center for Scientific Computing, Ruprecht-Karls University, 69120 Heidelberg, Germany
| | - Antonia Papapostolou
- Interdisciplinary Center for Scientific Computing, Ruprecht-Karls University, 69120 Heidelberg, Germany
| | - Adrian L Dempwolff
- Interdisciplinary Center for Scientific Computing, Ruprecht-Karls University, 69120 Heidelberg, Germany
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Kim Y, Krylov AI. Two Algorithms for Excited-State Quantum Solvers: Theory and Application to EOM-UCCSD. J Phys Chem A 2023; 127:6552-6566. [PMID: 37505075 DOI: 10.1021/acs.jpca.3c02480] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/29/2023]
Abstract
Near-term quantum devices promise to revolutionize quantum chemistry, but simulations using the current noisy intermediate-scale quantum (NISQ) devices are not practical due to their high susceptibility to errors. This motivated the design of NISQ algorithms leveraging classical and quantum resources. While several developments have shown promising results for ground-state simulations, extending the algorithms to excited states remains challenging. This paper presents two cost-efficient excited-state algorithms inspired by the classical Davidson algorithm. We implemented the Davidson method into the quantum self-consistent equation-of-motion unitary coupled-cluster (q-sc-EOM-UCC) excited-state method adapted for quantum hardware. The circuit strategies for generating desired excited states are discussed, implemented, and tested. We demonstrate the performance and accuracy of the proposed algorithms (q-sc-EOM-UCC/Davidson and its variational variant) by simulations of H2, H4, LiH, and H2O molecules. Similar to the classical Davidson scheme, q-sc-EOM-UCC/Davidson algorithms are capable of targeting a small number of excited states of the desired character.
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Affiliation(s)
- Yongbin Kim
- Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482, United States
| | - Anna I Krylov
- Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482, United States
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Asthana A, Kumar A, Abraham V, Grimsley H, Zhang Y, Cincio L, Tretiak S, Dub PA, Economou SE, Barnes E, Mayhall NJ. Quantum self-consistent equation-of-motion method for computing molecular excitation energies, ionization potentials, and electron affinities on a quantum computer. Chem Sci 2023; 14:2405-2418. [PMID: 36873839 PMCID: PMC9977410 DOI: 10.1039/d2sc05371c] [Citation(s) in RCA: 14] [Impact Index Per Article: 14.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/26/2022] [Accepted: 01/26/2023] [Indexed: 01/30/2023] Open
Abstract
Near-term quantum computers are expected to facilitate material and chemical research through accurate molecular simulations. Several developments have already shown that accurate ground-state energies for small molecules can be evaluated on present-day quantum devices. Although electronically excited states play a vital role in chemical processes and applications, the search for a reliable and practical approach for routine excited-state calculations on near-term quantum devices is ongoing. Inspired by excited-state methods developed for the unitary coupled-cluster theory in quantum chemistry, we present an equation-of-motion-based method to compute excitation energies following the variational quantum eigensolver algorithm for ground-state calculations on a quantum computer. We perform numerical simulations on H2, H4, H2O, and LiH molecules to test our quantum self-consistent equation-of-motion (q-sc-EOM) method and compare it to other current state-of-the-art methods. q-sc-EOM makes use of self-consistent operators to satisfy the vacuum annihilation condition, a critical property for accurate calculations. It provides real and size-intensive energy differences corresponding to vertical excitation energies, ionization potentials and electron affinities. We also find that q-sc-EOM is more suitable for implementation on NISQ devices as it is expected to be more resilient to noise compared with the currently available methods.
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Affiliation(s)
- Ayush Asthana
- Department of Chemistry, Virginia Tech Blacksburg 24061 VA USA
- Virginia Tech Center for Quantum Information Science and Engineering Blacksburg 24061 VA USA
| | - Ashutosh Kumar
- Theoretical Division, Los Alamos National Laboratory Los Alamos 87545 NM USA
| | - Vibin Abraham
- Department of Chemistry, University of Michigan Ann Arbor 48109 MI USA
| | - Harper Grimsley
- Department of Chemistry, Virginia Tech Blacksburg 24061 VA USA
- Virginia Tech Center for Quantum Information Science and Engineering Blacksburg 24061 VA USA
| | - Yu Zhang
- Theoretical Division, Los Alamos National Laboratory Los Alamos 87545 NM USA
| | - Lukasz Cincio
- Theoretical Division, Los Alamos National Laboratory Los Alamos 87545 NM USA
| | - Sergei Tretiak
- Theoretical Division, Los Alamos National Laboratory Los Alamos 87545 NM USA
- Center for Integrated Nanotechnologies, Los Alamos National Laboratory Los Alamos 87545 NM USA
| | - Pavel A Dub
- Chemistry Division, Los Alamos National Laboratory Los Alamos 87545 NM USA
| | - Sophia E Economou
- Department of Physics, Virginia Tech Blacksburg 24061 VA USA
- Virginia Tech Center for Quantum Information Science and Engineering Blacksburg 24061 VA USA
| | - Edwin Barnes
- Department of Physics, Virginia Tech Blacksburg 24061 VA USA
- Virginia Tech Center for Quantum Information Science and Engineering Blacksburg 24061 VA USA
| | - Nicholas J Mayhall
- Department of Chemistry, Virginia Tech Blacksburg 24061 VA USA
- Virginia Tech Center for Quantum Information Science and Engineering Blacksburg 24061 VA USA
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Wang M, Fang WH, Li C. Assessment of State-Averaged Driven Similarity Renormalization Group on Vertical Excitation Energies: Optimal Flow Parameters and Applications to Nucleobases. J Chem Theory Comput 2023; 19:122-136. [PMID: 36534617 DOI: 10.1021/acs.jctc.2c00966] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Abstract
We present a comprehensive excited-state benchmark for the state-averaged (SA) driven similarity renormalization group (DSRG) [Li, C.; Evangelista, F. A. J. Chem. Phys. 2018, 148, 124106]. Following the QUEST database [Véril, M.; Scemama, A.; Caffarel, M.; Lipparini, F.; Boggio-Pasqua, M.; Jacquemin, D.; Loos, P.-F. Wiley Interdiscip. Rev. Comput. Mol. Sci. 2021, 11, e1517], 280 vertical transition energies of 35 medium-sized molecules are computed using the SA-DSRG derived second- and third-order perturbation theories (PT2/PT3) along with a nonperturbative approach [sq-LDSRG(2)]. Comparing to the theoretical best estimates, the optimal flow parameter is found to be 0.35 and 2.0 Eh-2 for SA-DSRG-PT2 and SA-DSRG-PT3, respectively. For SA-sq-LDSRG(2), a flow parameter of 1.5 Eh-2 provides converged equations without compromising the accuracy. We then assess the accuracy of the SA-DSRG hierarchy using these parameters. The SA-DSRG-PT2 scheme outperforms the level-shifted CASPT2 by 0.10 eV in mean absolute error (MAE), yet this accuracy is slightly inferior than that of CASPT2 with the ionization-potential-electron-affinity shift. Both SA-DSRG-PT3 and SA-sq-LDSRG(2) yield a MAE of 0.10 eV, which is comparable to that of CASPT3 (0.09 eV). Finally, we compute vertical excitation energies of several low-lying singlet states of nucleobases. The SA-sq-LDSRG(2) approach provides highly accurate results for π → π* excitations, while n → π* transitions are better described by SA-DSRG-PT3.
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Affiliation(s)
- Meng Wang
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China
| | - Wei-Hai Fang
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China
| | - Chenyang Li
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China
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7
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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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8
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Hodecker M, Dempwolff AL, Schirmer J, Dreuw A. Theoretical analysis and comparison of unitary coupled-cluster and algebraic-diagrammatic construction methods for ionization. J Chem Phys 2022; 156:074104. [DOI: 10.1063/5.0070967] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023] Open
Affiliation(s)
- Manuel Hodecker
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
| | - Adrian L. Dempwolff
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
| | - Jochen Schirmer
- Theoretical Chemistry, Heidelberg University, Im Neuenheimer Feld 229, 69120 Heidelberg, Germany
| | - Andreas Dreuw
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
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9
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Dempwolff AL, Hodecker M, Dreuw A. Vertical ionization potential benchmark for unitary coupled-cluster and algebraic-diagrammatic construction methods. J Chem Phys 2022; 156:054114. [DOI: 10.1063/5.0079047] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Adrian L. Dempwolff
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
| | - Manuel Hodecker
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
- Department of Theoretical Chemistry and Biology, KTH Royal Institute of Technology, Malvinas Väg 10, 114 28 Stockholm, Sweden
| | - Andreas Dreuw
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
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10
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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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11
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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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12
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Thielen SM, Hodecker M, Piazolo J, Rehn DR, Dreuw A. Unitary coupled-cluster approach for the calculation of core-excited states and x-ray absorption spectra. J Chem Phys 2021; 154:154108. [PMID: 33887935 DOI: 10.1063/5.0047134] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In this work, we present the core-valence separation (CVS) approximation applied to unitary coupled-cluster (UCC) theory for the calculation of core-excited states and the simulation of x-ray absorption spectroscopy (XAS). Excitation energies and oscillator strengths of small- to medium-sized organic molecules have been computed using the second-order and extended second-order UCC schemes (CVS-UCC2 and CVS-UCC2-x) as well as the third-order scheme (CVS-UCC3). All results are compared to the corresponding algebraic-diagrammatic construction methods and experimental data. The agreement between CVS-UCC and experimental data demonstrates its potential as a new approach for the calculation of XAS.
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Affiliation(s)
- Sebastian M Thielen
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, D-69120 Heidelberg, Germany
| | - Manuel Hodecker
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, D-69120 Heidelberg, Germany
| | - Julia Piazolo
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, D-69120 Heidelberg, Germany
| | - Dirk R Rehn
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, D-69120 Heidelberg, Germany
| | - Andreas Dreuw
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, D-69120 Heidelberg, Germany
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13
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Misiewicz JP, Turney JM, Schaefer HF, Sokolov AY. Assessing the orbital-optimized unitary Ansatz for density cumulant theory. J Chem Phys 2020; 153:244102. [PMID: 33380073 DOI: 10.1063/5.0036512] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022] Open
Abstract
The previously proposed Ansatz for density cumulant theory that combines orbital-optimization and a parameterization of the 2-electron reduced density matrix cumulant in terms of unitary coupled cluster amplitudes (OUDCT) is carefully examined. Formally, we elucidate the relationship between OUDCT and orbital-optimized unitary coupled cluster theory and show the existence of near-zero denominators in the stationarity conditions for both the exact and some approximate OUDCT methods. We implement methods of the OUDCT Ansatz restricted to double excitations for numerical study, up to the fifth commutator in the Baker-Campbell-Hausdorff expansion. We find that methods derived from the Ansatz beyond the previously known ODC-12 method tend to be less accurate for equilibrium properties and less reliable when attempting to describe H2 dissociation. New developments are needed to formulate more accurate density cumulant theory variants.
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Affiliation(s)
- Jonathon P Misiewicz
- Center for Computational Quantum Chemistry, University of Georgia, Athens, Georgia 30602, USA
| | - Justin M Turney
- Center for Computational Quantum Chemistry, University of Georgia, Athens, Georgia 30602, USA
| | - Henry F Schaefer
- Center for Computational Quantum Chemistry, University of Georgia, Athens, Georgia 30602, USA
| | - Alexander Yu Sokolov
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, USA
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14
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Hodecker M, Dreuw A. Unitary coupled cluster ground- and excited-state molecular properties. J Chem Phys 2020; 153:084112. [PMID: 32872855 DOI: 10.1063/5.0019055] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
A scheme for the calculation of molecular properties within the framework of unitary coupled-cluster (UCC) theory in both the electronic ground and excited states is presented. The scheme is based on an expectation-value ansatz, similar to the equation-of-motion coupled-cluster method or the intermediate state representation (ISR) approach of the algebraic-diagrammatic construction (ADC) scheme. Due to the UCC ansatz, the resulting equations cannot be given by closed-form expressions but need to be approximated. Explicit expressions for the expectation value of a general one-particle operator correct through second order in perturbation theory have been derived and coded for the electronic ground state as well as for excited states of predominant single-excitation character. The resulting equations are shown to be equivalent to those of the second-order ADC/ISR procedure. As first computational tests, the second-order UCC method (UCC2) and the one employing third-order amplitudes (also eigenvectors) together with the second-order density matrix, denoted as UCC3(2), are applied to the calculation of dipole moments for a series of small closed- and open-shell systems as well as 4-cyanoindole and 2,3-benzofuran and compared to full configuration interaction or experimental results. For the aromatic organic molecules, the UCC2 method is shown to be sufficient for the ground-state dipole moment, whereas the UCC3(2) scheme is superior for excited-state dipole moments.
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Affiliation(s)
- Manuel Hodecker
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, D-69120 Heidelberg, Germany
| | - Andreas Dreuw
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, D-69120 Heidelberg, Germany
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15
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Hodecker M, Thielen SM, Liu J, Rehn DR, Dreuw A. Third-Order Unitary Coupled Cluster (UCC3) for Excited Electronic States: Efficient Implementation and Benchmarking. J Chem Theory Comput 2020; 16:3654-3663. [PMID: 32396348 DOI: 10.1021/acs.jctc.0c00335] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
The efficient implementation of the third-order unitary coupled-cluster scheme (UCC3) for the calculation of excited electronic states is reported. The UCC3 scheme and its second-order UCC2 variant have been benchmarked and compared to Jacquemin's recently introduced, as well as Thiel's well-established, benchmark sets for excitation energies and oscillator strengths. For the latter, the calculation of 134 excited singlet and 71 excited triplet states of 28 small- to medium-sized organic molecules has revealed that UCC2 exhibits a mean error and standard deviation of 0.36 ± 0.41 eV for singlet states and 0.22 ± 0.21 eV for triplet states, whereas UCC3 revealed an accuracy of 0.06 ± 0.27 eV for singlet and -0.22 ± 0.15 eV for triplet states. In addition, the oscillator strengths obtained with effective transition moments correct through second order in perturbation theory are in very good agreement with literature data.
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Affiliation(s)
- Manuel Hodecker
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, D-69120 Heidelberg, Germany
| | - Sebastian M Thielen
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, D-69120 Heidelberg, Germany
| | - Junzi Liu
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, United States
| | - Dirk R Rehn
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, D-69120 Heidelberg, Germany
| | - Andreas Dreuw
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, D-69120 Heidelberg, Germany
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16
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Hodecker M, Rehn DR, Dreuw A. Hermitian second-order methods for excited electronic states: Unitary coupled cluster in comparison with algebraic-diagrammatic construction schemes. J Chem Phys 2020; 152:094106. [PMID: 33480727 DOI: 10.1063/1.5142354] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Employing an intermediate state representation (ISR) approach, Hermitian second-order methods for the calculation of electronic excitation energies are presented and compared in detail. These comprise the algebraic-diagrammatic construction scheme for the polarization propagator, a hybrid second-order ISR scheme based on traditional coupled-cluster theory as well as two similar approaches based on a unitary coupled-cluster (UCC) ansatz. Although in a strict perturbation-theoretical framework all prove to be identical, differences emerge when the corresponding converged cluster amplitudes are used and depending on how the similarity-transformed UCC Hamiltonian is evaluated. The resulting excitation energies, however, do not significantly differ for systems well described by means of perturbation theory.
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Affiliation(s)
- Manuel Hodecker
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, D-69120 Heidelberg, Germany
| | - Dirk R Rehn
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, D-69120 Heidelberg, Germany
| | - Andreas Dreuw
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, D-69120 Heidelberg, Germany
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17
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Banerjee S, Sokolov AY. Third-order algebraic diagrammatic construction theory for electron attachment and ionization energies: Conventional and Green’s function implementation. J Chem Phys 2019; 151:224112. [DOI: 10.1063/1.5131771] [Citation(s) in RCA: 23] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Samragni Banerjee
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, USA
| | - Alexander Yu. Sokolov
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, USA
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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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Chatterjee K, Sokolov AY. Second-Order Multireference Algebraic Diagrammatic Construction Theory for Photoelectron Spectra of Strongly Correlated Systems. J Chem Theory Comput 2019; 15:5908-5924. [DOI: 10.1021/acs.jctc.9b00528] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Koushik Chatterjee
- 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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Tikhonov SA, Fedorenko EV, Mirochnik AG, Osmushko IS, Skitnevskaya AD, Trofimov AB, Vovna VI. Spectroscopic and quantum chemical study of difluoroboron β-diketonate luminophores: Isomeric acetylnaphtholate chelates. SPECTROCHIMICA ACTA. PART A, MOLECULAR AND BIOMOLECULAR SPECTROSCOPY 2019; 214:67-78. [PMID: 30769153 DOI: 10.1016/j.saa.2019.02.002] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/14/2018] [Revised: 01/23/2019] [Accepted: 02/02/2019] [Indexed: 06/09/2023]
Abstract
The electronic structure and optical properties of the isomeric difluoroboron β-diketonates, 2,2-difluoro-4-methylnaphtho-[2,1-e]-1,3,2-dioxaborin (I) and 2,2-difluoro-4-methylnaphtho-[1,2-e]-1,3,2-dioxaborin (II), were studied by means of X-ray photoelectron, absorption and luminescence spectroscopies. The experimental results were interpreted using high-level ab initio quantum chemical computations, including the algebraic-diagrammatic construction method for the polarization propagator of the second and third orders (ADC(2) and ADC(3)), the outer-valence Green's function (OVGF) method, and the time-dependent density functional (TDDFT) approach. The X-ray photoelectron measurements were assigned in the entire energy range using the results of the Kohn-Sham orbital calculations which employed the B3LYP functional. Pronounced hypsochromic shift of crystal-state fluorescence was observed in I upon the lowering of temperature, which can be explained by the deterioration of the conditions for excimers formation. According to our results, remarkable feature of II, absent in I, is its phosphorescence at room temperature. Basing on our calculations, a decay mechanism for the S1 state was proposed, explaining the observed differences in the phosphorescence of I and II.
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Affiliation(s)
- Sergey A Tikhonov
- Far Eastern Federal University, School of Natural Sciences, Vladivostok 690950, Russian Federation.
| | - Elena V Fedorenko
- Institute of Chemistry, Far Eastern Branch of the Russian Academy of Sciences, Vladivostok 690022, Russian Federation
| | - Anatolii G Mirochnik
- Institute of Chemistry, Far Eastern Branch of the Russian Academy of Sciences, Vladivostok 690022, Russian Federation
| | - Ivan S Osmushko
- Far Eastern Federal University, School of Natural Sciences, Vladivostok 690950, Russian Federation
| | - Anna D Skitnevskaya
- Irkutsk State University, Laboratory of Quantum Chemistry, Irkutsk 664003, Russian Federation
| | - Alexander B Trofimov
- Irkutsk State University, Laboratory of Quantum Chemistry, Irkutsk 664003, Russian Federation; Favorsky Irkutsk Institute of Chemistry, Siberian Branch of the Russian Academy of Sciences, Irkutsk 664033, Russian Federation
| | - Vitaliy I Vovna
- Far Eastern Federal University, School of Natural Sciences, Vladivostok 690950, Russian Federation
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Sokolov AY. Multi-reference algebraic diagrammatic construction theory for excited states: General formulation and first-order implementation. J Chem Phys 2018; 149:204113. [DOI: 10.1063/1.5055380] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Alexander Yu. Sokolov
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, USA
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