The laser induced fluorescence ( LIF ) spectrum of the à ²∆ - X̃ ²Π transition was obtained for SiCN generated by laser ablation under supersonic free jet expansion. The vibrational structure, particularly that associated with the bending mode, of the dispersed fluorescence ( DF ) spectra from single vibronic levels ( SVL's ) is too complicated to analyze by the usual formulation derived from perturbational approach. Successful analysis requires us to numerically diagonalize the vibronic Hamiltonian, in which Renner-Teller ( R-T ), anharmonicity, spin-orbit ( SO ), Herzberg-Teller ( H-T ), Fermi, and Sears interactions have been considered, where the Sears resonance is a second-order interaction combined from SO and H-T interactions with ∆K = ±1, ∆Σ = ±1, and ∆P = 0. Accurate results were obtained from this procedure reproducing experimental observations within the deviations of our instrumental resolution,  ∼ 5 cm⁻¹. The mixing coefficients of the two vibronic levels are comparable to those obtained from computational studiesV. Brites, A. O. Mitrushchenkov, and C. Léonard, J. Chem. Phys. 138, 104311 (2013); C. Léonard, Private communication.

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V. Brites, A. O. Mitrushchenkov, and C. Léonard, J. Chem. Phys. 138, 104311 (2013); C. Léonard, Private communication..

In spectroscopic parlance, a linear triatomic molecule is one whose potential energy minimum occurs at a linear geometry. We have recently discussedT. Hirano, U. Nagashima, J. Mol. Spectrosc., 314, 35-47 (2015)^,T. Hirano, U. Nagashima, P. Jensen, J. Mol. Spectrosc. 343, 54-61 (2018).^,T. Hirano, U. Nagashima, P. Jensen, J. Mol. Spectrosc. (2018), https://doi.org/10.1016/j.jms.2017.12.011; and references therein.hat any linear triatomic molecule will be observed as being "bent" on ro-vibronic average in any ro-vibronic state. As quantum mechanics asserts, we have to characterize Nature through "observation." Theoretically we make observations of molecular structures by calculating the expectation values of the structural parameters over the relevant ro-vibronic wavefunctions. In computational molecular spectroscopy studies, we have shown that for many linear triatomic molecules such as ⁶∆ FeNC, ⁶∆ FeCN, ²Π BrCN⁺, ³Φ CoCN, ²∆ NiCN, ¹Σ⁺ CsOH, ³Σ⁻ FeCO, and ²Π NCS, the ro-vibrationally averaged structure (zero-point structure, for example) is slightly bent with a bond angle supplement 180^° − ∠(A-B-C) [where ∠(A-B-C) is the bond angle] in the range from 7.5^° (NCS) to 22.5^° (C₃). We have also described the theoretical background^b for this fact using a Laguerre-Gauss type wavefunction for the doubly degenerate bending oscillator; the average "bentness" is basically caused by the inseparability of the bending motion from the free rotation about the molecular axis. Our finding is in contradiction to the well-established paradigm in spectroscopy that the ro-vibrationally averaged structure of a linear molecule is linear. In particular, it throws doubt on the so-called r₀ structures routinely determined for linear triatomic molecules under the a priori assumption that ro-vibrationally averaged bond-angle of a linear molecule should be 180^°. In the following talk, we discuss how experimentally derived rotational-constant values are to be interpreted.

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T. Hirano, U. Nagashima, J. Mol. Spectrosc., 314, 35-47 (2015)\end T. Hirano, U. Nagashima, P. Jensen, J. Mol. Spectrosc. 343, 54-61 (2018). T. Hirano, U. Nagashima, P. Jensen, J. Mol. Spectrosc. (2018), https://doi.org/10.1016/j.jms.2017.12.011; and references therein.t

As discussed in the preceding talk, any linear triatomic molecule will be observed as being "bent" on ro-vibronic average in any ro-vibronic state.T. Hirano, U. Nagashima, J. Mol. Spectrosc., 314, 35-47 (2015)^,T. Hirano, U. Nagashima, P. Jensen, J. Mol. Spectrosc. 343, 54-61 (2018).^,T. Hirano, U. Nagashima, P. Jensen, J. Mol. Spectrosc. (2018), https://doi.org/10.1016/j.jms.2017.12.011; and references therein.xperimentally derived B₀ constants are the results of the "observation" of Nature. This suggests that the observed B₀ values are in fact those for the ro-vibrationally averaged bent structures. The easiest way to check this proposition is to interpret the set of B₀ values of isotopologues taking the bond-angle as a "variable," discarding the preconceived, conventional notion that the ro-vibrationally averaged bond angle of a linear molecule is 180^°. We have shown in previous publications^a that bond length values derived from a set of experimental B₀ values under the assumption of a linear r₀ structure, is not the ro-vibrationally averaged bond lengths, but their projections onto the molecular axis. Therefore, when the projection angle is not accounted for, the bond length values obtained from the B₀ values may differ significantly from the averaged bond lengths. We will show how we can derive physically sound ro-vibrational structures from the experimentally reported B₀ values, taking the FeCO, NCS, HCO⁺, HCN, and C₃ molecules as examples. The averaged bond-angle deviations from the linearity, derived from experimentally reported B₀ values of multiple isotopologues, are 7.8^°, 9.5^°, 12.5^°, 14.3^°, and 23.4^°, respectively, for NCS, FeCO, HCO⁺, HCN, and C₃ in their respective vibrational ground states. Thus, we can conclude that both theoretically (as described in the preceding talk) and experimentally (as shown here), the ro-vibrationally averaged structure of a linear molecule is observed as being bent.

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T. Hirano, U. Nagashima, J. Mol. Spectrosc., 314, 35-47 (2015)\end T. Hirano, U. Nagashima, P. Jensen, J. Mol. Spectrosc. 343, 54-61 (2018). T. Hirano, U. Nagashima, P. Jensen, J. Mol. Spectrosc. (2018), https://doi.org/10.1016/j.jms.2017.12.011; and references therein.E

Computation of the dipole moment in a ro-vibrationally averaged molecular state of a triatomic molecule requires the 3D potential energy surface and the associated ro-vibrational wavefunctions. Consequently, in most cases, the experimentally derived value of the dipole moment in the ro-vibronic ground state is compared with the theoretical dipole moment value for the "equilibrium geometry." We have proposed in recent publicationsT. Hirano, U. Nagashima, J. Mol. Spectrosc., 314, 35-47 (2015)^,T. Hirano, U. Nagashima, P. Jensen, J. Mol. Spectrosc. 343, 54-61 (2018).^,T. Hirano, U. Nagashima, P. Jensen, J. Mol. Spectrosc. (2018), https://doi.org/10.1016/j.jms.2017.12.011.hat any linear molecule, whose potential energy minimum occurs at a linear configuration, is observed as being bent on ro-vibrational average. That gives rise to the question recently asked by a reviewer of our paper:^c Why does the averaged dipole moment vanish for a symmetrical triatomic molecule of type ABA, such as CO₂? In the present talk we show that there is no contradiction, for linear triatomic molecules, between our proposition of a bent averaged geometry and the experimentally derived, vibrationally averaged dipole moment value. We must consider two facts: 1) for a linear molecule, the rotation about the a axis, which approximately coincides with the molecular axis, cannot be separated from the bending motion described by variation of the bond angle in the instantaneous molecular plane, and 2) the dipole moment function is an odd function of the angle describing this rotation. Therefore, only the a axis component of the dipole moment can be observed (and it, too, vanishes by symmetry for an ABA molecule). Taking CO₂ and HCO⁺ as examples, we show, from the theoretical view point, how the dipole moment is observed in the experimental study, typically in Stark spectroscopy. Our theoretically predicted dipole moment value for the ro-vibronic ground state of HCO⁺, 3.933 D, is in good agreement with that determined from Stark experiments,B. J. Mount, M. Redshaw, E. G. Myers, Phys. Rev. A, 85, 012519 (2012)..921(31) D (quoted uncertainty in parentheses, in units of the last digit).

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T. Hirano, U. Nagashima, J. Mol. Spectrosc., 314, 35-47 (2015)\end T. Hirano, U. Nagashima, P. Jensen, J. Mol. Spectrosc. 343, 54-61 (2018). T. Hirano, U. Nagashima, P. Jensen, J. Mol. Spectrosc. (2018), https://doi.org/10.1016/j.jms.2017.12.011.t B. J. Mount, M. Redshaw, E. G. Myers, Phys. Rev. A, 85, 012519 (2012).3

r0pt Figure An important aspect of vibrational anharmonicity results from the substantial changes in molecular geometry and bonding that occur in the coordinate space of large-amplitude nuclear motion. Examples of such large-amplitude motion include torsional motion, inversion, the intermolecular motions within clusters, and reaction coordinates. Here we show that the Jahn-Teller formalism, when suitably extended, provides a precise description of the variation of the small-amplitude vibrational frequencies in a large-amplitude coordinate space. The locations where the small-amplitude frequencies cross are vibrational conical intersections (CIs) and multiple CIs may occur in one molecular system. In this work, we expand the motion of one molecular fragment relative to the other in spherical harmonics to allow an even-handed treatment of large-amplitude motion in 4π steradians. The molecular systems treated include CH₃OH, CH₃SH, and the complexes of CH₄ with F⁻ and Na⁺ ions. The Jahn-Teller formalism provides a general treatment of near-resonant interactions including their explicit dependence on large-amplitude nuclear coordinates. It also includes a crude adiabatic basis, which allows for convenient computation of the fully coupled quantum nuclear dynamics. The opportunities and limitations of this approach will be discussed.

Great advances in quantum chemistry calculations for molecules over the last decade has left a cogent need to make theory testable by experiments. One area of fundamental interest is the computation of both spectroscopic and dynamical properties of molecules near conical intersections between different electronic states. Experiments on naturally occurring and spectroscopically accessible conical intersections in Jahn-Teller molecules provide excellent benchmarks for computations. This talk discusses an approach which allows direct computation of experimental parameters determined from rotationally resolved experiments. An Effective Rotational Hamiltonian (ERH) for Jahn-Teller active system with a C₃ or C₅ symmetry axis is presented. Methods for calculating the parameters of the ERH using electronic structure and vibrational mode data from coupled cluster calculations are reported. Furthermore theory is advanced to develop a prescription for obtaining observable rovibronic parameters like the rotational distortion parameter, h₁, and transition intensities for systems with a C₃ and C₅ symmetry axis. An important goal of these calculations is to compare experimentally observable parameters to those from highly developed theoretical tools presently available.

In Part I, the theoretical motivations for studying spectroscopic and dynamic properties of molecules near conical intersections were outlined. Jahn-Teller active molecules were identified as excellent candidates for these studies, as vibronic eigenfunctions are calculatable utilizing either electronic structure methods or by fitting experimental results from vibronic spectra. Here, we discuss the utility of these eigenfunctions in the calculation of matrix elements necesary toward understanding rovibronic experimental spectra of Jahn-Teller molecules. As an example, the determination of the Watson distortion term, h₁, of the Jahn-Teller rotational Hamiltonian will be presented. In the cyclopentadienyl radical, h₁ in the vibrationless level of the ground electronic state, X̃²E^′′₁, is well determined experimentally and reproducable via our theoretical methods. Tabulated h₁ values for vibrationally excited states provide insights toward rotational structure, and thus identification and assignment, of observable vibrational transitions. For the nitrate radical, comparison of computational and experimental results for h₁ in the òE^′′ state provide a background for evaluating the potential energy surface of NO₃.

In recent years, organic optoelectronic materials have attracted considerable attention due to their ease of production and fabrication and great potentials in industrial applications. However, their efficiencies can be strongly limited by non-radiative decay pathways in which the excited energies are lost in the form of thermal energy. In the present study, we focused on two families of organic optoelectronic materials, the derivatives of naphthalene and those of boron-dipyrromethene (BODIPY), and characterized their efficiencies using the fluorescence quantum yield (ϕ_fl) - the probability that a photoexcited molecule fluoresces a photon rather than undergoing a non-radiative decay. To predict these ϕ_fl's, we developed inexpensive, accurate and transferable semi-empirical methods based on time-dependent density functional theory (TDDFT) and its multiple variants, and examined two non-radiative decay mechanisms - internal conversion (IC) and intersystem crossing (ISC). We managed to predict radiative rates (k_fl), IC rates (k_IC), and ISC rates (k_ISC), and controlled the mean absolute error (MAE) within 0.4 orders of magnitude. These results, in combination, allowed us to reproduce ϕ_fl's with an MAE of 0.2 for organic optoelectronic materials in question. During this process, we discovered two novel IC pathways through low-energy distorted transition states and intermediates, and indicated that the energy gap law is inadequate to estimate the activation energy (E_a) and account for k_IC and k_ISC. The present study paves the way for the rational design of organic optoelectronic devices by high-throughput computations.