Reaction coordinate analysis of the S1-S0 internal conversion of azulene

NAC-TDDFT: Time-Dependent Density Functional Theory for Nonadiabatic Couplings

First-order nonadiabatic coupling (NAC) matrix elements (fo-NACMEs) are the basic quantities in theoretical descriptions of electronically nonadiabatic processes that are ubiquitous in molecular physics and chemistry. Given the large size of systems of chemical interests, time-dependent density functional theory (TDDFT) is usually the first choice of methods. However, the lack of many-electron wave functions in TDDFT renders the formulation of NAC-TDDFT for fo-NACMEs conceptually difficult. Because of this, various variants of NAC-TDDFT have been proposed in the literature from different standing points, including the Hellmann-Feynman-like expression and auxiliary/pseudo-wave function (AWF)-, equation-of-motion (EOM)-, and time-dependent perturbation theory (TDPT)-based formulations. Based on critical analyses, the following conclusions are made here: (1) The Hellmann-Feynman-like expression, which is rooted in exact wave function theory, is hardly useful due to huge demand on basis sets. (2) Although most popular, the AWF variants of NAC-TDDFT are not theoretically founded and become ambiguous particularly for the fo-NACMEs between two excited states, although they do agree with the EOM and TDPT variants under the Tamm-Dancoff approximation. (3) The TDPT variant of NAC-TDDFT is theoretically most rigorous but suffers from numerical instabilities on the one hand and does not differ to a significant extent from the EOM variant on the other hand. (4) As such, the EOM variant of NAC-TDDFT for the fo-NACMEs between the ground and excited states and between two excited states is solely the right choice in practice. These formal analyses are fully supported by numerical experimentations, taking azulene as a showcase. The proper implementation of the EOM variant of NAC-TDDFT is also highlighted, showing that the fo-NACMEs between the ground and excited states and between two excited states are computationally very much the same as the analytic energy gradients of DFT and TDDFT, respectively. Possible future developments of the EOM variant of NAC-TDDFT are also highlighted. Its extensions to spin-adapted open-shell TDDFT and proper treatment of spin-orbit couplings (which are another source of force for electronically nonadiabatic processes) are particularly warranted in the near future.

A systematic model study quantifying how conical intersection topography modulates photochemical reactions

Despite their important role in photochemistry and expected presence in most polyatomic molecules, conical intersections have been thoroughly characterized in a comparatively small number of systems. Conical intersections can confer molecular photoreactivity or photostability, often with remarkable efficacy, due to their unique structure: at a conical intersection, the adiabatic potential energy surfaces of two or more electronic states are degenerate, enabling ultrafast decay from an excited state without radiative emission, known as nonadiabatic transfer. Furthermore, the precise conical intersection topography determines fundamental properties of photochemical processes, including excited-state decay rate, efficacy, and molecular products that are formed. However, these relationships have yet to be defined comprehensively. In this article, we use an adaptable computational model to investigate a variety of conical intersection topographies, simulate resulting nonadiabatic dynamics, and calculate key photochemical observables. We varied the vibrational mode frequencies to modify conical intersection topography systematically in four primary classes of conical intersections and quantified the resulting rate, total yield, and product yield of nonadiabatic decay. The results reveal that higher vibrational mode frequencies reduce nonadiabatic transfer, but increase the transfer rate and resulting photoproduct formation. These trends can inform progress toward experimental control of photochemical reactions or tuning of molecules' photochemical properties based on conical intersections and their topography.

Semiclassical Approach to Photophysics Beyond Kasha's Rule and Vibronic Spectroscopy Beyond the Condon Approximation. The Case of Azulene

Azulene is a prototypical molecule with an anomalous fluorescence from the second excited electronic state, thus violating Kasha's rule, and with an emission spectrum that cannot be understood within the Condon approximation. To better understand the photophysics and spectroscopy of azulene and other nonconventional molecules, we developed a systematic, general, and efficient computational approach combining the semiclassical dynamics of nuclei with ab initio electronic structure. First, to analyze the nonadiabatic effects, we complement the standard population dynamics by a rigorous measure of adiabaticity, estimated with the multiple-surface dephasing representation. Second, we propose a new semiclassical method for simulating non-Condon spectra, which combines the extended thawed Gaussian approximation with the efficient single-Hessian approach. S₁ ← S₀ and S₂ ← S₀ absorption and S₂ → S₀ emission spectra of azulene, recorded in a new set of experiments, agree very well with our calculations. We find that accuracy of the evaluated spectra requires the treatment of anharmonicity, Herzberg-Teller, and mode-mixing effects.

Metal-organic charge transfer can produce biradical states and is mediated by conical intersections

The present paper illustrates key features of charge transfer between calcium atoms and prototype conjugated hydrocarbons (ethylene, benzene, and coronene) as elucidated by electronic structure calculations. One- and two-electron charge transfer is controlled by two sequential conical intersections. The two lowest electronic states that undergo a conical intersection have closed-shell and open-shell dominant configurations correlating with the 4s(2) and 4s(1)3d(1) states of Ca, respectively. Unlike the neutral-ionic state crossing in, for example, hydrogen halides or alkali halides, the path from separated reactants to the conical intersection region is uphill and the charge-transferred state is a biradical. The lowest-energy adiabatic singlet state shows at least two minima along a single approach path of Ca to the π system: (i) a van der Waals complex with a doubly occupied highest molecular orbital, denoted Φ(2)(1), and a small negative charge on Ca and (ii) an open-shell singlet (biradical) at intermediate approach (Ca...C ≈2.5-2.7 Å) with molecular orbital structure (1)(2), where (2) is an orbital showing significant charge transfer form Ca to the π-system, leading to a one-electron multicentered bond. A third minimum (iii) at shorter distances along the same path corresponding to a closed-shell state with molecular orbital structure has also been found; however, it does not necessarily represent the ground state at a given CaC distance in all three systems. The topography of the lowest adiabatic singlet potential energy surface is due to the one- and two-electron bonding patterns in Ca-π complexes.

Energy transfer of highly vibrationally excited naphthalene. I. Translational collision energy dependence

Energy transfer between highly vibrationally excited naphthalene and Kr atom in a series of translational collision energies (108-847 cm(-1)) was studied separately using a crossed-beam apparatus along with time-sliced velocity map ion imaging techniques. Highly vibrationally excited naphthalene in the triplet state (vibrational energy: 16,194 cm(-1); electronic energy: 21,400 cm(-1)) was formed via the rapid intersystem crossing of naphthalene initially excited to the S(2) state by 266 nm photons. The collisional energy transfer probability density functions were measured directly from the scattering results of highly vibrationally excited naphthalene. At low collision energies a short-lived naphthalene-Kr complex was observed, resulting in small amounts of translational to vibrational-rotational (T-->VR) energy transfer. The complex formation probability decreases as the collision energy increases. T-->VR energy transfer was found to be quite efficient at all collision energies. In some instances, nearly all of the translational energy is transferred to vibrational-rotational energy. On the other hand, only a small fraction of vibrational energy is converted to translational energy. The translational energy gained from vibrational energy extend to large energy transfer (up to 3000 cm(-1)) as the collision energy increases to 847 cm(-1). Substantial amounts of large V-->T energy transfer were observed in the forward and backward directions at large collision energies.

Theoretical Prediction of the S1−S0 Internal Conversion of 6-Cyanoazulene

Ab initio complete active-space self-consistent field (CASSCF) and second-order Multireference Möller-Plesset perturbation (MRMP2) calculations were performed to examine the S1-S0 internal conversion of 6-cyanoazulene (6CNAZ). The azulene skeletons of 6CNAZ in S0 and S1 have features that resemble those of azulene. The stable geometry in S0 is characterized by (i) a C2v structure, (ii) an aromatic bond-equalized structure in which all the peripheral skeletal bond distances resemble an aromatic CC bond distance, and (iii) a single bond character of the transannular bond. The stable geometry in S1 is characterized by a nonaromatic C2v structure. Contrary to similarities of the stable geometries in S0 and S1 between 6CNAZ and azulene, the conical intersection (S1/S0-CIX) of 6CNAZ is different from that of azulene. The S1/S0-CIX of 6CNAZ takes a planar structure, whereas that of azulene takes a nonplanar structure in the seven-membered ring (Amatatsu, Y.; Komura, K. J. Chem. Phys. 2006, 125, 174311/1-8). On the basis of those computational findings, we predict the photochemical behavior of 6CNAZ in the S1-S0 internal conversion.