Analytic derivative couplings for spin-flip configuration interaction singles and spin-flip time-dependent density functional theory

Abstract

We revisit the calculation of analytic derivative couplings for configuration interaction singles (CIS), and derive and implement these couplings for its spin-flip variant for the first time. Our algorithm is closely related to the CIS analytic energy gradient algorithm and should be straightforward to implement in any quantum chemistry code that has CIS analytic energy gradients. The additional cost of evaluating the derivative couplings is small in comparison to the cost of evaluating the gradients for the two electronic states in question. Incorporation of an exchange-correlation term provides an ad hoc extension of this formalism to time-dependent density functional theory within the Tamm-Dancoff approximation, without the need to invoke quadratic response theory or evaluate third derivatives of the exchange-correlation functional. Application to several different conical intersections in ethylene demonstrates that minimum-energy crossing points along conical seams can be located at substantially reduced cost when analytic derivative couplings are employed, as compared to use of a branching-plane updating algorithm that does not require these couplings. Application to H3 near its D(3h) geometry demonstrates that correct topology is obtained in the vicinity of a conical intersection involving a degenerate ground state.

Analytical Derivative Coupling for Multistate CASPT2 Theory

“…The XMS-CASPT2 calculations were performed using a vertical shift of 0.5 E h . All of the MECIs reported using unc-MRCI 18,56 were also found by XMS-CASPT2: the twisted-pyramid (Py), ethylidene (Et), C 3v ethylidene (C 3v -Et), H-migration (Hm) (S 0 /S 1 ), and twisted-orthogonal (To) (S 1 /S 2 ) MECIs.…”

“…First, to assess the accuracy of XMS-CASPT2 against unc-MRCI, 18,56 we optimized the MECIs of ethylene. We adopted the reference SA-CASSCF wave functions from Ref.…”

“…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.…”

First order nonadiabatic coupling matrix elements between excited states: Implementation and application at the TD-DFT and pp-TDA levels

“…The most prominent example is the formulation of fo-NACME within TD-DFT. Although many interesting developments [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] have been made for the TD-DFT formulation of the fo-NACME g ξ 0I between the ground and excited states, the corresponding TD-DFT formulation of the fo-NACME g ξ IJ between two excited states, which was once characterized as an open problem, [22][23][24][25] has only been achieved rather recently. 26 As a matter of fact, the particular formulation 26 is very general, in the sense that it encompasses all theoretical models that can be derived from either time-independent equation-of-motion (EOM) 27 or time-dependent response theory.…”