An integro-differential transform to analytically reduce H$_{2}$ molecular integrals

Molecular integrals that have a coordinate dependence akin to the bonding H$_{2}$ wave function are often carried out one-by-one, using hyper-spherical coordinates [1], Jacobi coordinates or bond-length coordinates [2], or confocal ellipsoidal coordinates [3]. An alternative strategy is to extend the general result developed by the author [4] for evaluating integrals of any number of products of multicenter ground-state or excited [5] atomic wave functions, Coulomb or Yukawa potentials, and Coulomb-waves [6] to include the H$_{2}$ molecular wave function. Modifications for semi-infinite integrals that terminate on a surface such as a Scanning Tunneling Microscope sample are also discussed. \\[4pt] [1] Y. Zhou, C. D. Lin and J. Shertzer, J. Phys. B: At. Mol. Opt. Phys. 26, 3937-3949 (1993).\\[0pt] [2] J. M. Hutson and P. Soldan, International Reviews in Physical Chemistry, 26(1) 1 - 28 (January 2007).\\[0pt] [3] J. P. Grivet, J. Chem. Educ., 79(1), 127 (2002).\\[0pt] [4] Jack C. Straton, \textit{Phys. Rev. A} \textbf{39}, 1676-84 (1989); Erratum \textit{Phys. Rev. A} \textbf{40}, 2819 (1989).\\[0pt] [5] Jack C. Straton, \textit{Phys. Rev. A}\textbf{ 41}, 71-7 (1990).\\[0pt] [6] Jack C. Straton, \textit{Phys. Rev. A} \textbf{42}, 307-10 (1990).