Self-Consistent Constricted Variational Theory RSCF-CV(∞)-DFT and Its Restrictions To Obtain a Numerically Stable ΔSCF-DFT-like Method: Theory and Calculations for Triplet States.

Abstract

In this paper, the relaxed self-consistent field infinite order constricted variational density functional theory (RSCF-CV(∞)-DFT) for triplet calculations is presented. Here, we focus on two main features of our implementation. First, as an extension of our previous work by Krykunov and Ziegler ( J. Chem. Theory Comput. 2013 , 9 , 2761 ), the optimization of the transition matrix representing the orbital transition is implemented and applied for vertical triplet excitations. Second, restricting the transition matrix, we introduce RSCF-CV(∞)-DFT-based numerically stable ΔSCF-DFT-like methods, the most general of them being SVD-RSCF-CV(∞)-DFT. The reliability of the different methods, RSCF-CV(∞)-DFT and its restricted versions, is examined using the benchmark test set of Silva-Junior et al. ( J. Chem. Phys. 2008 , 129 , 104103 ). The obtained excitation energies validate our approach and implementation for RSCF-CV(∞)-DFT and also show that SVD-RSCF-CV(∞)-DFT mimics very well ΔSCF-DFT, as the root-mean-square deviations between these methods are less than 0.1 eV for all functionals examined.