Resolution-of-the-identity approximation for complex-scaled basis functions.

A resolution-of-the-identity (RI) approximation for two-electron integrals over Gaussian basis functions with a complex-scaled exponent is presented. Such functions are used in non-Hermitian quantum mechanics to represent electronic resonances by L2 integrable wave functions with complex energies. We have implemented this new RI approximation for second-order Møller-Plesset perturbation (MP2) theory as well as for the Coulomb and exchange contributions in Hartree-Fock (HF) theory. We discuss the differences to the standard RI approximation of Hermitian quantum mechanics and demonstrate the utility of the non-Hermitian RI-MP2 and RI-HF methods by computations of the orientation-dependent ionization rates of CO, C6H6, and C10H8 in static electric fields. Our results illustrate that RI-MP2 correctly describes correlation effects in molecular electronic resonances while the computational cost is low enough to allow for investigations of medium-sized molecules.