Propagators in Quantum Chemistry, 2nd Edition

Chapter 7

Temperature-Dependent Perturbation Theory

Consider the partition function

with β = 1/kT, N₀ the number operator for electrons, and the hamiltonian H = H₀ + V split into an unperturbed part H₀ and a perturbation V. The factorization

is introduced, where the relation S(β) = exp[β(H₀ – μN₀)] exp[– β(H – μN₀)] is used. Correspondingly, the unperturbed partition function

is defined permitting the expression Z(β) = Z₀(β)S(β)₀, where the average …₀ is formed with the density operator ρ = Z₀^–1(β) exp[–β(H₀ – μN₀)].

Since S(0) = 1, it follows that Explicit differentiation yields

and the notation ...