Quartic scaling analytical gradients of scaled opposite-spin CC2

Abstract

An implementation of analytical gradients, transition moments and excited state properties for scaled opposite-spin (SOS) CC2 and a SOS variant of the algebraic diagrammatic construction through second order ADC(2) is presented. The time-determining fifth order scaling steps in the algorithms are replaced by schemes with only fourth order scaling computational costs using a “resolution of the identity” approximation for the electron repulsion integrals and a numerical Laplace transformation of the orbital energy denominators. This leads to a significant reduction of the computational costs for geometry optimizations of large systems.This work is an extension to the recently presented quartic scaling algorithm for SOS–CC2 energies for ground and excited states. The Laplace error for adiabatic electronic excitation energies and excited state structures is found to be very small. SOS–ADC(2) provides for adiabatic electronic excitation energies, excited state structure parameters, harmonic vibrational frequencies as well as dipole moments and transition strengths an accuracy similar to SOS–CC2. Timings for ground and excited state calculations are reported and applications to a chlorophyll molecule and a ditopic 2,2′:6′,2″-bis(terpyridine) with 160 atoms demonstrate how the new implementation extends the applicability of these methods for large systems.