Normal ordered exponential approach to thermal properties and time-correlation functions: general theory and simple examples

Nooijen, Marcel; Bao, Songhao

doi:10.1080/00268976.2021.1980832

Cited by 3 publications

(7 citation statements)

References 37 publications

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“…The VE-TFCC approach can be regarded as a specific application of the more general TNOE approach developed by Nooijen and Bao. 37 In the latter approach, a normal-ordered exponential ansatz is introduced to parametrize the thermal density operator for a general quantum many-body Hamiltonian (either Bosonic or Fermionic). The thermal properties can be approximated through cumulant expansion of density matrices of low ranking cluster operators by applying unique contraction rules and the generalized Wick's theorem.…”

Section: Discussionmentioning

confidence: 99%

“…However, in our formulation, the physical properties are directly mapped through the cumulant expression of the thermal density matrices, i which is based on our previous work of the TNOE approach. 37 To verify the soundness of this formulation, we use eq 62 to calculate i j † of a two modes uncoupled vibrational model, whose Hamiltonian reads…”

Section: = =mentioning

confidence: 99%

“…Note that our TFCC formulation is slightly different from the original work on TF dynamics by Harsha et al In the original formulation, response theory and Λ-equations are applied to calculate the physical properties in the same way as the canonical coupled cluster theory. However, in our formulation, the physical properties are directly mapped through the cumulant expression of the thermal density matrices, which is based on our previous work of the TNOE approach …”

Section: Theorymentioning

confidence: 99%

“…Recently, there has been a resurgence of interest in this topic. Many attempts have been made to obtain a time-dependent coupled cluster (TDCC) or many-body perturbation theory (MBPT) formulation for directly calculating thermal properties of quantum many-body systems. − However, most of these works focus on either pure electronic systems or single-surface pure vibrational systems. In this work, we develop an approach for multi-surface vibronic coupling systems.…”

Section: Introductionmentioning

confidence: 99%

“…This work can be viewed as a statistical mechanics formulation of our previous work on the vibrational electronic coupled cluster (VECC) method for real time non-adiabatic dynamics . It is a specific application of the thermal normal-ordered exponential (TNOE) approach developed by Nooijen and Bao for vibronic models. To simplify the TNOE formulation, we introduced thermofield (TF) dynamics and a thermal density operator in the Bogoliubov representation, inspired by the works by Harsha et al − For a thermal density operator in the Bogoliubov representation, the TNOE ansatz reduces to the simple exponential ansatz and the approach becomes single-reference-like.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Vibrational Electronic-Thermofield Coupled Cluster (VE-TFCC) Theory for Quantum Simulations of Vibronic Coupling Systems at Thermal Equilibrium

Bao,

Raymond,

Zeng

et al. 2024

J. Chem. Theory Comput.

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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 (CoF 4 − anion) against the conventional sum over states (SOS) method and applied to calculate thermochemistry properties of a gas-phase reaction: CoF 3 + F − → CoF 4 − . 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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Section: Discussionmentioning

confidence: 99%

Section: = =mentioning

confidence: 99%

Section: Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Vibrational Electronic-Thermofield Coupled Cluster (VE-TFCC) Theory for Quantum Simulations of Vibronic Coupling Systems at Thermal Equilibrium

Bao,

Raymond,

Zeng

et al. 2024

J. Chem. Theory Comput.

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Finite-temperature many-body perturbation theory for anharmonic vibrations: Recursions, algebraic reduction, second-quantized reduction, diagrammatic rules, linked-diagram theorem, finite-temperature self-consistent field, and general-order algorithm

Qin,

Hirata

2023

The Journal of Chemical Physics

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A unified theory is presented for finite-temperature many-body perturbation expansions of the anharmonic vibrational contributions to thermodynamic functions, i.e., the free energy, internal energy, and entropy. The theory is diagrammatically size-consistent at any order, as ensured by the linked-diagram theorem proved in this study, and, thus, applicable to molecular gases and solids on an equal footing. It is also a basis-set-free formalism, just like its underlying Bose–Einstein theory, capable of summing anharmonic effects over an infinite number of states analytically. It is formulated by the Rayleigh–Schrödinger-style recursions, generating sum-over-states formulas for the perturbation series, which unambiguously converges at the finite-temperature vibrational full-configuration-interaction limits. Two strategies are introduced to reduce these sum-over-states formulas into compact sum-over-modes analytical formulas. One is a purely algebraic method that factorizes each many-mode thermal average into a product of one-mode thermal averages, which are then evaluated by the thermal Born–Huang rules. Canonical forms of these rules are proposed, dramatically expediting the reduction process. The other is finite-temperature normal-ordered second quantization, which is fully developed in this study, including a proof of thermal Wick’s theorem and the derivation of a normal-ordered vibrational Hamiltonian at finite temperature. The latter naturally defines a finite-temperature extension of size-extensive vibrational self-consistent field theory. These reduced formulas can be represented graphically as Feynman diagrams with resolvent lines, which include anomalous and renormalization diagrams. Two order-by-order and one general-order algorithms of computing these perturbation corrections are implemented and applied up to the eighth order. The results show no signs of Kohn–Luttinger-type nonconvergence.

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Time dependent vibrational electronic coupled cluster (VECC) theory for non-adiabatic nuclear dynamics

Bao,

Raymond,

Nooijen

2024

The Journal of Chemical Physics

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A time-dependent vibrational electronic coupled-cluster (VECC) approach is proposed to simulate photo-electron/UV-VIS absorption spectra as well as time-dependent properties for non-adiabatic vibronic models, going beyond the Born–Oppenheimer approximation. A detailed derivation of the equations of motion and a motivation for the ansatz are presented. The VECC method employs second-quantized bosonic construction operators and a mixed linear and exponential ansatz to form a compact representation of the time-dependent wave-function. Importantly, the method does not require a basis set, has only a few user-defined inputs, and has a classical (polynomial) scaling with respect to the number of degrees of freedom (of the vibronic model), resulting in a favorable computational cost. In benchmark applications to small models and molecules, the VECC method provides accurate results compared to multi-configurational time-dependent Hartree calculations when predicting short-time dynamical properties (i.e., photo-electron/UV–VIS absorption spectra) for non-adiabatic vibronic models. To illustrate the capabilities, the VECC method is also successfully applied to a large vibronic model for hexahelicene with 14 electronic states and 63 normal modes, developed in the group by Aranda and Santoro [J. Chem. Theory Comput. 17, 1691, (2021)].

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Normal ordered exponential approach to thermal properties and time-correlation functions: general theory and simple examples

Cited by 3 publications

References 37 publications

Vibrational Electronic-Thermofield Coupled Cluster (VE-TFCC) Theory for Quantum Simulations of Vibronic Coupling Systems at Thermal Equilibrium

Vibrational Electronic-Thermofield Coupled Cluster (VE-TFCC) Theory for Quantum Simulations of Vibronic Coupling Systems at Thermal Equilibrium

Finite-temperature many-body perturbation theory for anharmonic vibrations: Recursions, algebraic reduction, second-quantized reduction, diagrammatic rules, linked-diagram theorem, finite-temperature self-consistent field, and general-order algorithm

Time dependent vibrational electronic coupled cluster (VECC) theory for non-adiabatic nuclear dynamics

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