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Vera, Mario Hernandez; Jagau, Thomas-C (2019): Resolution-of-the-identity approximation for complex-scaled basis functions. In: Journal of Chemical Physics, Vol. 151, No. 11, 111101
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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 L-2 integrable wave functions with complex energies. We have implemented this new RI approximation for second-order Moller-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.