Finite-temperature many-body perturbation theory for anharmonic vibrations: Recursions, algebraic reduction,...

Area of Science:

• Theoretical Chemistry
• Statistical Mechanics
• Quantum Many-Body Theory

Background:

• Accurate calculation of thermodynamic properties requires accounting for anharmonic vibrational effects.
• Existing methods often struggle with size consistency and basis set dependence.
• Finite-temperature many-body perturbation theory provides a framework but needs unified treatment.

Purpose of the Study:

• To develop a unified, diagrammatically size-consistent theory for finite-temperature perturbation expansions of anharmonic vibrational contributions.
• To establish a basis-set-free formalism capable of analytically summing anharmonic effects over infinite states.
• To provide efficient computational strategies for applying the theory to molecular gases and solids.

Main Methods:

• Formulation via Rayleigh-Schrödinger-style recursions to generate sum-over-states formulas.
• Development of two strategies for reducing formulas: algebraic factorization and finite-temperature normal-ordered second quantization.
• Proof of linked-diagram theorem for size consistency and thermal Wick's theorem.

Main Results:

• A diagrammatically size-consistent and basis-set-free theory for anharmonic vibrational thermodynamics.
• Analytical summation of anharmonic effects over infinite states with guaranteed convergence.
• Demonstration of computational algorithms up to eighth order without nonconvergence issues.

Conclusions:

• The presented unified theory provides a robust and accurate method for calculating thermodynamic properties.
• The developed strategies significantly expedite the reduction of complex sum-over-states formulas.
• The formalism is applicable to both molecular gases and solids, offering broad utility.