Resolution-of-the-identity second-order Møller–Plesset perturbation theory with complex basis functions: Benchmark calculations and applications to strong-field ionization of polyacenes

Abstract

We study the performance of the resolution-of-the-identity (RI) approximation for complex basis functions that we recently introduced [M. Hernández Vera and T.-C. Jagau, J. Chem. Phys. 151, 111101 (2019)] for second-order Møller-Plesset (MP2) perturbation theory as well as for the Coulomb and exchange contributions in Hartree-Fock theory. The sensitivity of this new RI-MP2 method toward the basis set and the auxiliary basis set is investigated, and computation times are analyzed. We show that the auxiliary basis set can be chosen purely real, that is, no complex-scaled functions need to be included. This approximation enables a further speedup of the method without compromising accuracy. We illustrate the application range of our implementation by computing static-field ionization rates of several polyacenes up to pentacene (C 22 H 18 ) at the RI-MP2 level of theory. Pronounced anisotropies are observed for the ionization rates of these molecules.

Theory of electronic resonances: fundamental aspects and recent advances

“…Only recently, however, steps were taken to extend these techniques to complex-variable methods. 105,106 Specifically, the resolution-of-the-identity (RI) approximation has been applied to ERIs over complex-scaled basis functions. The RI approximation exploits that, for a basis set of atom-centered Gaussian functions, the pair space of orbital products is often markedly redundant.…”

“…This is caused by the exponential dependence of the ionization rate on the binding energy; in a polyatomic molecule the contribution of individual channels to the overall ionization rate varies greatly depending on orientation. 104–106…”

“…The choice of electronic-structure model is of central importance for the accurate description of molecular resonances. Complex scaling, complex basis functions, and complex absorbing potentials have been combined with a variety of methods; implementations of Hartree–Fock (HF), 150,151,156 density functional theory (DFT), 181–183 multireference configuration interaction (MRCI), 153,154,165,168 resolution-of-the-identity second-order Møller–Plesset perturbation theory (RI-MP2), 105,106 extended multiconfigurational quasidegenerate perturbation theory (XMCQDPT2), 184 algebraic diagrammatic construction (ADC), 185–188 symmetry-adapted-cluster configuration interaction (SAC-CI), 189 multireference coupled-cluster (MRCC), 190 and equation-of-motion (EOM)-CC methods 67,157,162,166 have been reported. Since there exist different ways to set up a complex-variable calculation, the comparison of results obtained using different implementations is not straightforward.…”

Variational Solutions for Resonances by a Finite-Difference Grid Method

“…Recently, there is increasing interest among chemists concerning the use of non-Hermitian QM for the calculations of molecular resonances. For example, the most recent developments of the QCHEM quantum chemistry package enable calculations of shape type and Feshbach molecular resonances [ 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 ]. In addition, such methods have been employed in the study of RNA bases [ 19 , 20 ].…”

Ab Initio Complex Transition Dipoles between Autoionizing Resonance States from Real Stabilization Graphs

“…For example, see the ab initio calculation of high-order harmonic generation for helium atoms. , Evaluation of transition dipole moments involving resonance states has been reported for atoms using complex scaling , and for molecular anions using complex absorbing potentials (CAPs) . In addition, it is worth mentioning the calculations of Stark shifts and ionization rates of field-induced resonances using complex scaled coupled cluster singles and doubles (CCSD) for atoms and via complex basis functions for molecules − in which the electronic ground state in the presence of static electric fields becomes metastable. However, within these methods, the calculations are performed directly in the complex plane, which typically require more computational effort as compared to methods that work predominantly in the real space and then dilate into the complex plane (e.g., stabilization method − ).…”