Frequency-dependent hyperpolarizabilities in the Mo/ller–Plesset perturbation theory

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Abstract
A formulation for calculating frequency‐dependent hyperpolarizabilities in the Mo/ller–Plesset perturbation theory is presented as the correlation correction to the TDHF approximation. Our quasienergy derivative (QED) method is applied, and the difference between the QED method and the pseudoenergy derivative (PED) method by Rice and Handy is discussed. The Lagrangian technique is utilized to obtain simple and practical expressions for response properties in which the TDHF orbital rotation parameters satisfy the 2n+1 rule and the Lagrange multipliers satisfy the 2n+2 rule. Explicit expressions for response properties up to third order [μ, α(−ω1;ω1), β(−ωσ;ω1,ω2)] are derived in the second‐order Mo/ller‐Plesset perturbation theory.