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Bao S, Raymond N, Zeng T, Nooijen M. Vibrational Electronic-Thermofield Coupled Cluster (VE-TFCC) Theory for Quantum Simulations of Vibronic Coupling Systems at Thermal Equilibrium. J Chem Theory Comput 2024; 20:5882-5900. [PMID: 38950345 DOI: 10.1021/acs.jctc.4c00338] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/03/2024]
Abstract
A vibrational electronic-thermofield coupled cluster (VE-TFCC) approach is developed to calculate thermal properties of non-adiabatic vibronic coupling systems. The thermofield (TF) theory and a mixed linear exponential ansatz based on second-quantized Bosonic construction operators are introduced to propagate the thermal density operator as a "pure state" in the Bogoliubov representation. Through this compact representation of the thermal density operator, the approach is basis-set-free and scales classically (polynomial) as the number of degrees of freedoms (DoF) in the system increases. The VE-TFCC approach is benchmarked with small test models and a real molecular compound (CoF4- anion) against the conventional sum over states (SOS) method and applied to calculate thermochemistry properties of a gas-phase reaction: CoF3 + F- → CoF4-. Results shows that the VE-TFCC approach, in conjunction with vibronic models, provides an effective protocol for calculating thermodynamic properties of vibronic coupling systems.
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Affiliation(s)
- Songhao Bao
- Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - Neil Raymond
- Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - Tao Zeng
- Department of Chemistry, York University, Toronto, Ontario M3J 1P3, Canada
| | - Marcel Nooijen
- Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
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Zhai H, Larsson HR, Lee S, Cui ZH, Zhu T, Sun C, Peng L, Peng R, Liao K, Tölle J, Yang J, Li S, Chan GKL. Block2: A comprehensive open source framework to develop and apply state-of-the-art DMRG algorithms in electronic structure and beyond. J Chem Phys 2023; 159:234801. [PMID: 38108484 DOI: 10.1063/5.0180424] [Citation(s) in RCA: 13] [Impact Index Per Article: 13.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/09/2023] [Accepted: 11/16/2023] [Indexed: 12/19/2023] Open
Abstract
block2 is an open source framework to implement and perform density matrix renormalization group and matrix product state algorithms. Out-of-the-box it supports the eigenstate, time-dependent, response, and finite-temperature algorithms. In addition, it carries special optimizations for ab initio electronic structure Hamiltonians and implements many quantum chemistry extensions to the density matrix renormalization group, such as dynamical correlation theories. The code is designed with an emphasis on flexibility, extensibility, and efficiency and to support integration with external numerical packages. Here, we explain the design principles and currently supported features and present numerical examples in a range of applications.
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Affiliation(s)
- Huanchen Zhai
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Henrik R Larsson
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Seunghoon Lee
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Zhi-Hao Cui
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Tianyu Zhu
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Chong Sun
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Linqing Peng
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Ruojing Peng
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Ke Liao
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Johannes Tölle
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Junjie Yang
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Shuoxue Li
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Garnet Kin-Lic Chan
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
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Van Benschoten W, Petras HR, Shepherd JJ. Electronic Free Energy Surface of the Nitrogen Dimer Using First-Principles Finite Temperature Electronic Structure Methods. J Phys Chem A 2023; 127:6842-6856. [PMID: 37535315 PMCID: PMC10440793 DOI: 10.1021/acs.jpca.3c01741] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/14/2023] [Revised: 07/20/2023] [Indexed: 08/04/2023]
Abstract
We use full configuration interaction and density matrix quantum Monte Carlo methods to calculate the electronic free energy surface of the nitrogen dimer within the free-energy Born-Oppenheimer approximation. As the temperature is raised from T = 0, we find a temperature regime in which the internal energy causes bond strengthening. At these temperatures, adding in the entropy contributions is required to cause the bond to gradually weaken with increasing temperature. We predict a thermally driven dissociation for the nitrogen dimer between 22,000 to 63,200 K depending on symmetries and basis set. Inclusion of more spatial and spin symmetries reduces the temperature required. The origin of these observations is explored using the structure of the density matrix at various temperatures and bond lengths.
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Affiliation(s)
| | - Hayley R. Petras
- Department
of Chemistry, University of Iowa, Iowa City, Iowa 52242, United States
| | - James J. Shepherd
- Department
of Chemistry, University of Iowa, Iowa City, Iowa 52242, United States
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Van Benschoten WZ, Shepherd JJ. Piecewise Interaction Picture Density Matrix Quantum Monte Carlo. J Chem Phys 2022; 156:184107. [DOI: 10.1063/5.0094290] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The density matrix quantum Monte Carlo (DMQMC) set of methods stochastically samples the exact $N$-body density matrix for interacting electrons at finite temperature. We introduce a simple modification to the interaction picture DMQMC method (IP-DMQMC) which overcomes the limitation of only sampling one inverse temperature point at a time, instead allowing for the sampling of a temperature range within a single calculation thereby reducing the computational cost. At the target inverse temperature, instead of ending the simulation, we incorporate a change of picture away from the interaction picture. The resulting equations of motion have piecewise functions and use the interaction picture in the first phase of a simulation, followed by the application of the Bloch equation once the target inverse temperature is reached. We find that the performance of this method is similar to or better than the DMQMC and IP-DMQMC algorithms in a variety of molecular test systems.
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Dan X, Xu M, Yan Y, Shi Q. Generalized master equation for charge transport in a molecular junction: Exact memory kernels and their high order expansion. J Chem Phys 2022; 156:134114. [PMID: 35395901 DOI: 10.1063/5.0086663] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We derive a set of generalized master equations (GMEs) to study charge transport dynamics in molecular junctions using the Nakajima-Zwanzig-Mori projection operator approach. In the new GME, time derivatives of population on each quantum state of the molecule, as well as the tunneling current, are calculated as the convolution of time non-local memory kernels with populations on all system states. The non-Markovian memory kernels are obtained by combining the hierarchical equations of motion (HEOM) method and a previous derived Dyson relation for the exact kernel. A perturbative expansion of these memory kernels is then calculated using the extended HEOM developed in our previous work [M. Xu et al., J. Chem. Phys. 146, 064102 (2017)]. By using the resonant level model and the Anderson impurity model, we study properties of the exact memory kernels and analyze convergence properties of their perturbative expansions with respect to the system-bath coupling strength and the electron-electron repulsive energy. It is found that exact memory kernels calculated from HEOM exhibit short memory times and decay faster than the population and current dynamics. The high order perturbation expansion of the memory kernels can give converged results in certain parameter regimes. The Padé and Landau-Zener resummation schemes are also found to give improved results over low order perturbation theory.
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Affiliation(s)
- Xiaohan Dan
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China and University of Chinese Academy of Sciences, Beijing 100049, China
| | - Meng Xu
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China and University of Chinese Academy of Sciences, Beijing 100049, China
| | - Yaming Yan
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China and University of Chinese Academy of Sciences, Beijing 100049, China
| | - Qiang Shi
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China and University of Chinese Academy of Sciences, Beijing 100049, China
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