We present a current, up-to-date review of the surface hopping methodology for solving nonadiabatic problems, 25 years after Tully published the fewest switches surface hopping algorithm. After reviewing the original motivation for and failures of the algorithm, we give a detailed examination of modern advances, focusing on both theoretical and practical issues. We highlight how one can partially derive surface hopping from the Schrödinger equation in the adiabatic basis, how one can change basis within the surface hopping algorithm, and how one should understand and apply the notions of decoherence and wavepacket bifurcation. The question of time reversibility and detailed balance is also examined at length. Recent applications to photoexcited conjugated polymers are discussed briefly.

Ozonolysis of alkenes, an important nonphotolytic source of hydroxyl (OH) radicals in the troposphere, proceeds through energized Criegee intermediates that undergo unimolecular decay to produce OH radicals. Here, we used infrared (IR) activation of cold CH3CHOO Criegee intermediates to drive hydrogen transfer from the methyl group to the terminal oxygen, followed by dissociation to OH radicals. State-selective excitation of CH3CHOO in the CH stretch overtone region combined with sensitive OH detection revealed the IR spectrum of CH3CHOO, effective barrier height for the critical hydrogen transfer step, and rapid decay dynamics to OH products. Complementary theory provides insights on the IR overtone spectrum, as well as vibrational excitations, structural changes, and energy required to move from the minimum-energy configuration of CH3CHOO to the transition state for the hydrogen transfer reaction.

In this paper, we develop a surface hopping approach for calculating linear absorption spectra using ensembles of classical trajectories propagated on both the ground and excited potential energy surfaces. We demonstrate that our method allows the dipole-dipole correlation function to be determined exactly for the model problem of two shifted, uncoupled harmonic potentials with the same harmonic frequency. For systems where nonadiabatic dynamics and electronic relaxation are present, preliminary results show that our method produces spectra in better agreement with the results of exact quantum dynamics calculations than spectra obtained using the standard ground-state Kubo formalism. As such, our proposed surface hopping approach should find immediate use for modeling condensed phase spectra, especially for expensive calculations using ab initio potential energy surfaces.

Intermolecular interactions, stereodynamics, and coupled potential energy surfaces (PESs) all play a significant role in determining the outcomes of molecular collisions. A detailed knowledge of such processes is often essential for a proper interpretation of spectroscopic observations. For example, nitric oxide (NO), an important radical in combustion and atmospheric chemistry, is commonly quantified using laser-induced fluorescence on the A 2 Σ + ← X 2 Π transition band. However, the electronic quenching of NO (A 2 Σ + ) with other molecular species provides alternative nonradiative pathways that compete with fluorescence. While the cross sections and rate constants of NO (A 2 Σ + ) electronic quenching have been experimentally measured for a number of important molecular collision partners, the underlying photochemical mechanisms responsible for the electronic quenching are not well understood. In this paper, we describe the development of high-quality PESs that provide new physical insights into the intermolecular interactions and conical intersections that facilitate the branching between the electronic quenching and scattering of NO (A 2 Σ + ) with H 2 , N 2 , and CO. The PESs are calculated at the EOM-EA-CCSD/d-aug-cc-pVTZ//EOM-EA-CCSD/aug-cc-pVDZ level of theory, an approach that ensures a balanced treatment of the valence and Rydberg electronic states and an accurate description of the open-shell character of NO. Our PESs show that H 2 is incapable of electronically quenching NO (A 2 Σ + ) at low collision energies; instead, the two molecules will likely undergo scattering. The PESs of NO (A 2 Σ + ) with N 2 and CO are highly anisotropic and demonstrate evidence of electron transfer from NO (A 2 Σ + ) into the lowest unoccupied molecular orbital of the collision partner, that is, the harpoon mechanism. In the case of ON + CO, the PES becomes strongly attractive at longer intermolecular distances and funnels population to a conical intersection between NO (A 2 Σ + ) + CO and NO (X 2 Π) + CO. In contrast, for ON + N 2 , the conical intersection is preceded by an ∼0.40 eV barrier. Overall, our work shines new light into the impact of coupled PESs on the nonadiabatic dynamics of open-shell systems.

We report a surface hopping approach for modeling the full time- and frequency-resolved differential absorbance spectra (beyond the inhomogenous limit) obtained in ultrafast pump-probe experiments. In our approach, we combine dynamical information obtained from ensembles of classical trajectories propagated on the ground and on the excited potential energy surfaces to directly calculate optical response functions and hence spectral lineshapes. We demonstrate that our method is exact for the model problem of two shifted harmonic potentials with identical harmonic frequencies in the absence of electronic relaxation. We then consider a model three state system with electronic relaxation and show that our method is able to capture the effects of nonadiabatic excited state dynamics on the time-dependent differential absorbance spectra. Furthermore, by comparing our spectra against those spectra calculated with either an (1) inhomogenous expression, (2) ground-state Kubo theory, or (3) excited-state Kubo theory, we show that including dynamical information from both the ground and excited potential energy surfaces significantly improves the reliability of the semiclassical approximations. As such, our surface hopping method should find immediate use in modeling the time-dependent differential abosrbance spectra of ultrafast pump-probe experiments.