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

Abstract

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.

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

“…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.…”

Selective reactivity of glycosyl cation stereoisomers: the role of intramolecular hydrogen bonding

“…Comparison of spectra calculated from both methods allows for some consideration of both temperature and quantum nuclear effects, where a comprehensive quantum mechanical method for finite-temperature anharmonic spectra calculation is still unfeasible for systems of this size. 49 Calculated spectra of the conformers of the galactopyranoside cation anomers and oxocarbenium ion epimers were compared, respectively, with the IRMPD spectra from the undissociated cations of methyl-α- and β- d -galactopyranoside and their fragments with the loss of methanol. A comparison is made between the calculated spectra of the talosyl oxocarbenium ion and the IRMPD spectra of the likely 21 galactosyl oxocarbenium ion.…”