Generalization of analytic energy third derivatives for the RHF closed-shell wave function: Derivative energy and integral formalisms and the prediction of vibration–rotation interaction constants

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Abstract
The general restricted Hartree–Fock (RHF) closed-shell energy analytic third derivative method is presented together with details concerning its implementation and that of the derivative integral algorithm. The viability of the energy equation and the integral techniques are illustrated by calculations on water, hydrogen cyanide, and formaldehyde with double zeta (DZ), double zeta plus polarization (DZP), triple zeta (TZ), triple zeta plus polarization (TZP), and triple zeta plus two sets of polarization (TZ2P) basis sets. Cubic force constants in reduced normal coordinates are reported for these basis sets. The cubic force constants are then applied in the prediction of the vibration–rotation interaction constants αBr (B=A, B, C) for these molecules.