The symmetric quasi-classical model using on-the-fly time-dependent density functional theory within the Tamm–Dancoff approximation

The primary computational challenge when simulating nonadiabatic ab initio molecular dynamics is the unfavorable compute costs of electronic structure calculations with molecular size. Simple electronic structure theories, like time-dependent density functional theory within the Tamm-Dancoﬀ approximation (TDDFT/TDA), alleviate this cost for moderately sized molecular systems simulated on realistic time scales. Although TDDFT/TDA does have some limitations in accuracy, an appealing feature is that, in addition to including electron correlation through the use of a density functional, the cost of calculating analytic nuclear gradients and nonadiabatic coupling vectors is often computationally feasible even for moderately-sized basis sets. In this work, some of the beneﬁts and limitations of TDDFT/TDA are discussed and analyzed with re-gard to its applicability as a “back-end” electronic structure method for the symmetric quasi-classical Meyer-Miller model (SQC/MM). In order to investigate the beneﬁts and limitations of TDDFT/TDA, SQC/MM is employed to predict and analyze a prototypical example of excited-state hydrogen transfer in gas-phase malonaldehyde. Then, the ring-opening dynamics of selenophene are simulated which highlight some of the deﬁ-ciencies of TDDFT/TDA. Additionally, some new algorithms are proposed that speed up the calculation of analytic nuclear gradients and nonadiabatic coupling vectors for a set of excited electronic states.