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A unified theory is presented for finite-temperature many-body perturbationexpansions of the anharmonic vibrational contributions to thermodynamicfunctions: the free energy, internal energy, and entropy. The theory isdiagrammatically size-consistent at any order, as ensured by the linked-diagramtheorem proved here, and thus applicable to molecular gases and solids on anequal footing. It is also a basis-set-free formalism, just like its underlyingBose-Einstein theory, capable of summing anharmonic effects over an infinitenumber of states analytically. It is formulated by theRayleigh-Schrodinger-style recursions, generating sum-over-states formulas forthe perturbation series, which unambiguously converges at thefinite-temperature vibrational full-configuration-interaction limits. Twostrategies are introduced to reducing these sum-over-states formulas intocompact sum-over-modes analytical formulas. One is a purely algebraic methodthat factorizes each many-mode thermal average into a product of one-modethermal averages, which are then evaluated by the thermal Born-Huang rules.Canonical forms of these rules are proposed, dramatically expediting thereduction process. The other is finite-temperature normal-ordered secondquantization, which is fully developed in this study, including a proof ofthermal Wick's theorem and the derivation of a normal-ordered vibrationalHamiltonian at finite temperature. The latter naturally defines afinite-temperature extension of size-extensive vibrational self-consistentfield theory. These reduced formulas can be represented graphically as Feynmandiagrams with resolvent lines, which include anomalous and renormalizationdiagrams. Two order-by-order and one general-order algorithms of computingthese perturbation corrections are implemented and applied up to the eighthorder. The results show no signs of Kohn-Luttinger-type nonconvergence.

journal of chemical physics online/the journal of chemical physics/journal of chemical physics

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