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In this review, we summarize the computationally efficient time-dependent approaches to calculating the vibronic spectra including one-photon/two-photon absorption (OPA/TPA), emission, circular dichroism (CD), and resonance Raman/hyper-Raman scattering (RRS/RHRS) spectra with inclusion of the mode-mixing, Frank-Condon (FC) and Herzberg-Teller (HT) effects. At first, a unified dependency of spectral differential cross sections (SDCSs) on a generalized linear polarizability is derived in view of the relationship between SDCSs and the linear or nonlinear polarizabilities. Then, the Green's function technique is adopted to calculate the polarizability to avoid the tedious summation over the large number of vibrational states. To demonstrate the computational accuracy and efficiency, we apply the generalized time-dependent approaches to calculate the OPA(E)/TPA, RRS, and RHRS spectra of a series of radicals and organic molecules. The computational accuracy is demonstrated by a close comparison between the simulated spectra and the available experimental data. In the spectral calculations, we apply our recently developed analytical energy-derivative approaches for the excited states within the framework of time-dependent density functional theory (TDDFT) to calculate the electronic-structure parameters which enter the expressions of SDCSs, such as the excited-state geometries, energy gradient, harmonic vibrational frequencies, the geometrical derivatives of transition dipole moments, and so forth. It is found that the integrated approach which combines the time-dependent approach to SDCSs with the analytical energy-derivative approaches for TDDFT excited-state structure parameters breaks the bottlenecks of vibronic spectroscopy calculation down. © 2014 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

In the modeling of spin‐crossing reactions, it has become popular to directly explore the spin‐adiabatic surfaces. Specifically, through constructing spin‐adiabatic states from a two‐state Hamiltonian (with spin‐orbit coupling matrix elements) at each geometry, one can readily employ advanced geometry optimization algorithms to acquire a "transition state" structure, where the spin crossing occurs. In this work, we report the implementation of a fully‐variational spin‐adiabatic approach based on Kohn‐Sham density functional theory spin states (sharing the same set of molecular orbitals) and the Breit‐Pauli one‐electron spin‐orbit operator. For three model spin‐crossing reactions (predissociation of N2O, singlet‐triplet conversion in CH2, and CO addition to Fe(CO)4), the spin‐crossing points were obtained. Our results also indicated the Breit‐Pauli one‐electron spin‐orbit coupling can vary significantly along the reaction pathway on the spin‐adiabatic energy surface. On the other hand, due to the restriction that low‐spin and high‐spin states share the same set of molecular orbitals, the acquired spin‐adiabatic energy surface shows a cusp (ie, a first‐order discontinuity) at the crossing point, which prevents the use of standard geometry optimization algorithms to pinpoint the crossing point. An extension with this restriction removed is being developed to achieve the smoothness of spin‐adiabatic surfaces. [ABSTRACT FROM AUTHOR]