A variant of the MP2-R12 class of theories is introduced using an arbitrary geminal function in the place of r(12). Integrals are derived for the case where the geminal is expanded in a basis of Gaussian functions in the interelectronic distance. Recurrence relations are derived that do not depend on the exponents of the Gaussian geminals, allowing much of the integration work to be performed after summations over the geminal expansion. Sample calculations at various levels of explicitly correlated MP2 theory are presented for He, Ne, and water. (C) 2004 American Institute of Physics.