The question of how to describe the crossing of molecular electronic states is one of the most challenging issues in contemporary chemical dynamics. In recent years, the fundamental concept of conical intersections (CIs) of electronic potential energy surfaces (PESs) has emerged, which allows extremely fast and efficient switching of a molecule between its excited and ground electronic states. CIs are ubiquitous in polyatomic molecules. Because they generically allow the crossings of the Born-Oppenheimer (BO) adiabatic PESs, they have become the crucial mechanistic elements of the rapidly growing area of nonadiabatic chemistry. The most critical consequence of CIs is a complete breakdown of the adiabatic BO approximation. That means that the reorganization of fast-moving electrons and nuclear vibrations must be treated concurrently. Ideally, the theoretical description should be quantum mechanical in this situation. However, because of the complexity, the necessary approximations often make it difficult to conclusively predict dynamic behavior of large polyatomic molecules. In addition, a nonunique diabatic electronic representation (describing coupling between states in the electronic Hamiltonian) is essential to avoid the singular nature of the nuclear kinetic coupling terms of the unique adiabatic electronic representation. This Account describes both the challenges and some recent advances in quantum mechanical studies of nonadiabatic molecular processes, highlighting results from our recent work examining the static aspects of CIs and their dynamical consequences. The spectroscopic implications of the Jahn-Teller (JT) and pseudo-Jahn-Teller (PJT) intersections in complex molecular systems are discussed. Our work probes the underlying details of complex vibronic spectra of systems of growing sizes in terms of both electronic and nuclear degrees of freedom. The necessity of extension of the theoretical treatment beyond a linear vibronic coupling approach is addressed. Our results establish highly overlapping band structures due to JT and PJT CIs, a bimodal distribution of spectral intensity that originates from strong JT coupling, and the role of intermode bilinear coupling in the progressions of vibronic bands. Investigations of the quantum dynamics of the prototypical naphthalene radical cation were aimed at understanding its photostability, lack of fluorescence emissions, and diffuse interstellar bands. This work established extremely fast relaxation of this radical cation through CIs. Simulations of the interplay of electronic and relativistic spin-orbit coupling in the photodetachment spectroscopy of ClH(2)(-), in conjunction with experimental data, support the existence of a shallow van der Waals well in the reactive Cl + H(2) PES. These results also reveal a quenching of electronic coupling by the relatively strong spin-orbit coupling. In addition, we studied the dynamics of the prototypical H + H(2) reaction from a new perspective by explicitly including the coupling between the two energy surfaces of its JT split degenerate ground electronic state. Although individual reaction probabilities show partial sensitivity to nonadiabatic effects, the theoretical results reveal that they are not important for the dynamical outputs such as integral reaction cross sections and thermal rate constants.
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