Analytic evaluation of nonadiabatic coupling terms at the MR-CI level. I. Formalism

Abstract

An efficient and general method for the analytic computation of the nonandiabatic coupling vector at the multireference configuration interaction (MR-CI) level is presented. This method is based on a previously developed formalism for analytic MR-CI gradients adapted to the use for the computation of nonadiabatic coupling terms. As was the case for the analytic energy gradients, very general, separate choices of invariant orbital subspaces at the multiconfiguration self-consistent field and MR-CI levels are possible, allowing flexible selections of MR-CI wave functions. The computational cost for the calculation of the nonadiabatic coupling vector at the MR-CI level is far below the cost for the energy calculation. In this paper the formalism of the method is presented and in the following paper [Dallos et al., J. Chem. Phys. 120, 7330 (2004)] applications concerning the optimization of minima on the crossing seam are described.

Dynamics of dissociative electron attachment to ammonia

“…2) for the resonance and virtual states, both extrapolated to equilibrium geometry. A wavepacket (initial vibrational wave function multiplied by √ Γ [33][34][35] ) was placed on the resonance curve at R e and propagated using the calculated Euclidean norm of the full nonadiabatic (derivative) coupling matrix, ||h|| [36][37][38], to connect the resonance and virtual states. The results shown in Fig.…”

Analytical Derivative Coupling for Multistate CASPT2 Theory

“…The other approach is to use the following equivalent expression 9,10 that is written in terms of σ X rs alone,…”

“…Historically, analytical derivative couplings for multi-configurational methods were first studied [such as the state-averaged complete active space self-consistent field (SA-CASSCF) [7][8][9] and uncontracted multireference configuration interaction (unc-MRCI) methods. 7,10 ] These two models nevertheless have disadvantages: SA-CASSCF is essentially a mean-field model with static correlation treatment, and does not describe dynamical correlation; unc-MRCI is computational very demanding and is often used without double excitations (i.e., MRCIS that does not describe dynamical correlation). 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.…”

“…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.…”

On the construction of quasidiabatic state representations of bound adiabatic state potential energy surfaces coupled by accidental conical intersections: Incorporation of higher order terms

“…All electronic structure calculations reported in this work employed the COLUMBUS suite of electronic structure codes. 19,26 Figure 1 depicts the triazolyl radical and indicates the atom labeling used in this section. …”