Spin-flip, tensor equation-of-motion configuration interaction with a density-functional correction: A spin-complete method for exploring excited-state potential energy surfaces

Abstract

We revisit the formalism of the spin-adapted, spin-flip (SA-SF) configuration-interaction singles (CIS) method based on a tensor equation-of-motion formalism that affords proper spin eigenstates without sacrificing single-reference simplicity. Matrix elements for SA-SF-CIS are then modified in a manner similar to collinear spin-flip time-dependent density functional theory (SF-TDDFT), to include a DFT exchange-correlation correction. The performance of this method, which we call SA-SF-DFT, is evaluated numerically and we find that it systematically improves the energies of electronic states that exhibit significant spin contamination within the conventional SF-TDDFT approach. The new method cures the state assignment problem that plagues geometry optimizations and ab initio molecular dynamics simulations using traditional SF-TDDFT, without sacrificing computational efficiency, and furthermore provides correct topology at conical intersections, including those that involve the ground state, unlike conventional TDDFT. As such, SA-SF-DFT appears to be a promising method for generating excited-state potential energy surfaces at DFT cost.

Analytical Derivative Coupling for Multistate CASPT2 Theory

“…20,[30][31][32][33] There have been attempts to resolve this problem. 31,32 In addition, spin-flip single-reference methods that treat the ground and excited states equally have been successfully applied to the computation of the electronic structure around conical intersections, 19,20,[34][35][36] yielding conical intersection structures that are in agreement with those obtained with CASSCF or MRCI. There have nevertheless been discrepancies in the energies of the conical intersections between SF-TDDFT and CASSCF computations.…”

“…11 More recently, the analytical evaluation of derivative couplings for single-reference theories has been extensively investigated, including those based on equation-of-motion coupled-cluster theory (EOM-CC), [12][13][14] configuration interactions singles (CIS), 15 time-dependent density functional theories (TDDFT), 16,17 and their spin-flip variants. [18][19][20] Standard single-reference methods are, however, known to incorrectly predict the dimensionality of the conical intersection spaces between the ground and excited states, because they do not compute the states on an equal footing. 20,[30][31][32][33] There have been attempts to resolve this problem.…”

“…These non-radiative transitions are induced by the derivative couplings [also often referred to as nonadiabatic coupling matrix elements (NACMEs)], [7][8][9][10][11][12][13][14][15][16][17][18][19][20] which are the couplings between the electronic and nuclear degrees of freedom. 21 We will mathematically define the derivative couplings in the following.…”

Effect of the diradical character on static polarizabilities and two-photon absorption cross sections: A closer look with spin-flip equation-of-motion coupled-cluster singles and doubles method

“…Several approaches have been developed in order to minimize or eliminate spin contamination in the SF methods. [67][68][69][70][71][72][73][74] Here we use the original, non-spin-adapted version 31,32 of EOM-SF-CC.…”

Hole-Hole Tamm-Dancoff-Approximated Density Functional Theory: A Highly Efficient Electronic Structure Method Incorporating Dynamic and Static Correlation

“…Spin contamination problems have plagued DFT-based spin-flip methods, [30][31] however, this has recently been addressed by combining SF-TDDFT with ad hoc corrections from DFT/MRCI. 32 Ensemble formulations of DFT include the spin-restricted ensemble-referenced Kohn-Sham (REKS) methods. 33 To date, REKS methods need to be formulated specifically for the chosen ensemble (defined by an active space, as in CASSCF), and a general formulation applicable to arbitrary active spaces is lacking.…”