Molecular integrals over partially generalised Hermite-Gaussian functions

Hermite-Gaussian functions (HG) are generalised in four different ways. By keeping the Gaussian part unchanged and by allowing different scaling in the Hermite polynomials special generalised Hermite-Gaussian functions (SGHG) are introduced. Composed Hermite-Gaussian functions (CHG) are defined as prescribed linear combinations of SGHG. Off-centre shift either in the Hermite part or in the Gaussian part of SGHG defines Hermite off-centre (HOCHG) and Gaussian off-centre (GOCHG) Hermite-Gaussian functions, respectively. The above four types of functions are called partially generalised Hermite-Gaussian functions (PGHG). A relationship between PGHG and HG functions functions is established in the paper. The molecular integrals over PGHG functions can be given directly in terms of molecular integrals over HG functions.