The dispersed fluorescence spectrum from the S₁ origin of PhCCCN is reported. This molecule, which consists of a cyanoacetylene chain fused to an aromatic phenyl ring, is a potential candidate for astronomical detection. The high resolution spectrum was obtained under jet-cooled, gas-phase conditions with a rotational temperature of roughly 2 K, and appears to encode rich information about the vibronic coupling in this species. The experimentally observed peaks are assigned to emissions from the S₁ (Ã\text ¹B₂) origin to a₁ vibrational levels of the ground state, which are dipole allowed and governed by FC factors, and to b₂ vibrational levels of the ground state, made possible by vibronic interactions between S₁ and S₂ (B̃\text ¹A₁) states. The S₀ vibrational structure features a combined Fermi and Darling-Denison resonance near 950 cm⁻¹, which is accurately reproduced by diagonalization of an effective Hamiltonian containing the three a₁ states involved. A KDC Hamiltonian is employed to treat the vibronic b₂ features.

Water clusters provide an opportunity to explore the effects of hydrogen bonding on short and long-range structures. Clusters also provide the opportunity to make detailed comparisons between experiment and calculation due to the small number of atoms involved. An area of long-standing interest is the relative energies of the different structures of water clusters. While identifying the minimum energy structure of a particular sized cluster is straight forward, once zero-point energy (ZPE) and thermal effects are accounted for, the relative energies of various structures change. In this talk, we will focus on (H₂O)₆ for which the lowest energy structure is the prism. When the ZPE is taken into account for (H₂O)₆, the cage becomes lower in energy than the prism. However, when the hexamer is fully deuterated, the ground state structure has been assigned as the prism by Pate and coworkers. Previous Diffusion Monte Carlo (DMC) calculations of the ZPE of the cage and prism structures showed that (H₂O)₆ is localized in the cage, while the cage and prism structures of (D₂O)₆ have nearly identical ground state energies. These calculations also indicated that there is a high computational cost to obtain reliable results, which is due to the large ensemble sizes needed for the convergence of the ZPE. Mallory, J. D. and Mandelshtam, V. A., J. Phys. Chem. A (2015), 119, 6504-6515.he expense of these calculations is traced to the nature of the couplings between the high and low frequency vibrations of these clusters. In this talk, we will present a modified DMC approach in which we introduce a guiding function that provides a good description of the intramolecular vibrations of the water clusters.Lee, V. G. M. and McCoy, A. B., J. Phys. Chem. A (2019), 123, 37, 8063-8070.pecifically, the local energy, E_L = ∧HΨ_T/Ψ_T, is used in place of the potential energy surface for the purpose of sampling. Using this method allows us to reduce the computational cost in the evaluation of the ZPE and the ground state wave function by roughly an order of magnitude. Based on these studies, we confirm that the ground state for (H₂O)₆ is a cage, but we find that for (D₂O)₆, the ZPEs calculated for the cage and prism structures are nearly identical, and the identification of the lowest energy structure is highly sensitive to the subtle details of the potential energy surface that is used for these calculations. Mallory, J. D. and Mandelshtam, V. A., J. Phys. Chem. A (2015), 119, 6504-6515.T Lee, V. G. M. and McCoy, A. B., J. Phys. Chem. A (2019), 123, 37, 8063-8070.S

Diffusion Monte Carlo (DMC) is a technique that can be used to obtain the ground state energy and ground state wave function given a potential energy surface (PES) that fully describes the system of interest. However, one complication with this technique is that in order to obtain accurate results for molecular systems that have couplings between the high and low frequency vibrations, large ensemble sizes are needed. Mallory, J. D. and Mandelshtam, V. A., J. Phys. Chem. A (2015), 119, 6504-6515.ne approach to combat these large ensemble sizes is to use partial importance sampling to describe the high-frequency vibrations. This approach has been applied to studies of neutral water clusters, where a significant reduction in the ensemble sizes that were needed in the simulations was achieved. Lee, V. G. M. and McCoy, A.B., J. Phys. Chem. A (2019), 123, 37, 8063-8070. In this talk, I will describe the applications of this approach through the study of two systems, where the high-frequency vibrations are highly sensitive to the value of the coordinates associated with the low-frequency vibrations. The first system is CH₅⁺, where the equilibrium CH bond lengths vary from 1.09 to 1.20 Å in the low energy stationary points on the PES. In the ground state, each CH oscillator samples all these positions leading to a dependence of the CH frequency on the coordinates that are associated with the large amplitude vibrations that connect these minima. The second system of interest is protonated water clusters where the high-frequency shared proton stretch frequency varies between 1000 to 3000 cm⁻¹depending on its environment. By using correlations between the bond lengths and frequencies of the CH and OH oscillators and the structure of the ion, a flexible function can be constructed to approximate the effect that the environment has on these vibrations. By describing the CH and OH wavefunctions through importance sampling based on these flexible functions and allowing the other coordinates to be sampled using standard DMC techniques we can reduce the ensemble size needed to obtain converged zero-point energies and ground state wave functions. Extensions of these studies to larger systems, where these couplings between high and low frequency vibrations are prevalent, will also be discussed.

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Footnotes:

Mallory, J. D. and Mandelshtam, V. A., J. Phys. Chem. A (2015), 119, 6504-6515.O Lee, V. G. M. and McCoy, A.B., J. Phys. Chem. A (2019), 123, 37, 8063-8070.

The fitting and assignment of the rotational spectra of Coriolis-coupled distorted rotors is considerably more difficult than for isolated distorted rotors due to the sensitivity of a non-linear least-squares fit to the initial parameters and the lack of a priori predictions of the Coriolis coupling coefficients for all but the simplest couplings. Herein, we present our efforts to automatically generate computational predictions of Coriolis coupling coefficients (G_α, F_βγ, and their corresponding centrifugal distortion terms) using the outputs of Gaussian or CFOUR programs. The theory for deriving vibration-rotation couplings (through Van Vleck-style perturbation of the vibration-rotation Hamiltonian) and the formulas necessary for calculating a variety of coupling coefficients (G_α, F_βγ for ∑_i|∆v_i| ≤ 3 and G_α^J, G_α^K, F_βγ^J, F_βγ^K for ∑_i|∆v_i| = 2) have been known for some time, yet only predictions of G_α for ∑_i|∆v_i| = 2 have been used. Our implementation for predicting coupling coefficients of low order in rotation (G_α and F_βγ) is straightforward. We found for terms of higher order (G_α^J, G_α^K, F_βγ^J, F_βγ^K), however, that it is necessary to carry out reductions of the respective formulas. We therefore adapted the methodology used for reducing the centrifugal distortion to obtain predictions of the coupling coefficients that can be used for a priori prediction and for post-fitting comparison directly to those determined experimentally.

Linear response (LR) protocols like time dependent density functional theory (TDDFT) or equation of motion coupled cluster (EOM-CC) are often used to compute energies of electronic excited states. While effective for valence excitations, LR methods are susceptible to catastrophic failure for problems like core excitations or charge-transfer states, where the optimal excited state orbitals differ considerably from the ground state reference. Orbital optimized (OO) methods are more effective for such problems, as they permit relaxation of excited state orbitals beyond linear response. Widespread usage of OO methods has however been hindered by their propensity to collapse to the ground state instead of the desired excited state. This is a direct consequence of excited states typically being unstable saddle points in orbital space. We present a orbital optimization protocol that reliably converges to the closest stationary point to the initial guess, by minimizing the square of the energy gradient instead of explicitly attempting to extremize the energy. The computational cost of this square gradient minimization (SGM) method is only between 2-3 times the cost of ground state orbital optimization (per iteration). SGM+DFT therefore can be readily applied to large systems. We subsequently demonstrate the utility of SGM by application to doubly excited states, core excitations and charge-transfer states. Specifically, we show that cheap DFT based OO approaches can predict energies of doubly excited states to significantly greater accuracy than expensive, LR coupled cluster approaches (that often have > 1 eV error). Similarly, we demonstrate that a DFT based protocol employing SGM predicts core excitation energies (at both the K and L edges) to < 0.5 eV RMS error (while TDDFT often has > 10 eV error). Finally, we demonstrate prediction of charge transfer excitation energies to low error with DFT/SGM - in stark contrast to standard TDDFT. Time permitting, we would also discuss use of SGM with methods like complete active space self-consistent field (CASSCF) to tackle strongly correlated excited states and model conical intersections. References: Hait, D. and Head-Gordon M. J. Chem. Theory Comput., ASAP (2020); Hait, D. and Head-Gordon M. J. Phys. Chem. Lett. 11, 3, 775-786 (2020).

The importance of the breakdown of the Born-Oppenheimer (BO) approximation in the vicinity of a conical intersection has spurred the recent development of computational approches that involve vibronic coupling between electronic states. Computational chemistry has mainly focused on conical intersections along reaction paths. Jahn-Teller type conical intersections offer a spectroscopically accessible alternative that can be used for benchmarking these calculations. The presence of Jahn-Teller and pseudo-Jahn-Teller couplings not only leads to additional terms in the rotational Hamiltonian but also modify how well known terms like Coriolis coupling and spin-rotation coupling are computed. In this talk we build upon the general quantum chemical method pioneered by Köppel, Domcke and Cederbaum H. KöPPEL AND W. DOMCKE AND L. S. CEDERBAUM  Multimode Molecular Dynamics Beyond the Born-Oppenheimer Approximation. Adv. Chem. Phys. 57, (1984), 59-246o tackle molecules with vibronic coupling wherein ab initio electronic structure calculations in the adiabatic limit are used as the starting point for calculating properties of molecules in the regime where the BO approximation breaks down. A model vibronic Hamiltonian is parameterized using derivatives of adiabatic potential energy surfaces. Vibronic eigenvectors are obtained from this model Hamiltonian that allow the calculation of parameters in the rotation-spin Hamiltonian that can be determined experimentally from high resolution spectroscopy. H. KöPPEL AND W. DOMCKE AND L. S. CEDERBAUM  Multimode Molecular Dynamics Beyond the Born-Oppenheimer Approximation. Adv. Chem. Phys. 57, (1984), 59-246t

Effects due to vibronic and spin angular momentum have long been observed in rotationally resolved spectra of Jahn-Teller active molecules. The breakdown of the Born-Oppenheimer approximation in these molecules leads to complications in their vibronic spectra. The molecular picture is further complicated due to the coupling of spin angular momenta with rotational and vibronic angular momentum. Values of these coupling constants have been determined by many high resolution rotationally resolved spectroscopic experiments. However, the presence of a conical intersection in the adiabatic potential energy surfaces has made getting a reliable quantum chemistry calculation of these terms challenging. In this talk we present methods that have been developed to make first principles calculations of vibronic angular momenta and Coriolis coupling constants from quantum chemistry. Further methods have been developed to calculated spin related terms (spin-orbit quenching and spin rotation coupling), using ab initio methods and model vibronic hamiltonian. We report a comparision of calculations of these parameters with corresponding results determined from high resolution spectroscopy for molecules like methoxy radical and cyclopentadienyl radical.

Benchmark scalar-relativistic delta-coupled-cluster calculations of hetero-site double core ionization energies of small molecules containing second-row elements are presented. Comparing with equation-of-motion coupled-cluster method, the delta-CC method with core-valence separation shows high accuracy for calculating single core ionization energies with relative low computational cost^[1,2]. This study has focused on high-spin triplet components of two-site double core-ionized states, which are single reference in character and consistent with the use of standard coupled-cluster methods. Contributions to computed double core ionization energies from electron-correlation and basis-set effects as well as corrections to the core-valence separation approximation have been analyzed. Based on systematic convergence of computational results with respect to these effects, delta-coupled-cluster calculations have been shown to be capable of providing accurate double core ionization energies with remaining errors estimated to be below 0.3 eV. The predictions for the double core ionization energies of CF₄, CH₃F, CH₃CF₃, and CH₂FCF₃ are reported. The perspective of these molecules to be used in the experimental studies of two-site double core-ionized states that are involved in x-ray pump/x-ray probe studies of electronic and molecular dynamics following inner shell ionization or excitation is discussed.

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X. Zheng and L. Cheng, J. Chem. Theory Comput. 15, 4945(2019).

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J. Liu, D. Matthews, S. Coriani and L. Cheng, J. Chem. Theory Comput. 15, 1642(2019).

A three dimensional discrete variable representation (DVR) is developed for the general case of a rare gas atom interacting with an asymmetric top molecule and applied to the case of argon-haloethylene heterodimers. The position of the rare gas is specified relative to the principal inertial axis system (in a I^r representation) by the spherical polar coordinates (r, θ, ϕ). While the DVR for r is straightforward, those for θ and ϕ presented particular challenges, which are discussed. In common with all DVR approaches, the present DVR is well suited for systems where the intermolecular potential is calculated on a grid of discrete points and provides easy access to the wave functions in the DVR coordinates. The method is applied to the well-characterized argon-cis-1,2-difluoroethylene system and used to predict the tunneling splitting and argon-molecule vibrational wave functions in argon-vinyl chloride for which the molecular structure and rotational spectrum remain a puzzle.

An algebraic approach based on unitary algebras to calculate Franck-Condon factors (FCF's) is presented. The method is based on the unitary group approach, which consists in adding a scalar boson to the ν-D harmonic oscillator space, taking advantage of the transformation brackets connecting the energy, coordinate and momentum representations. In this scheme the solutions are given in terms of an expansion of harmonic oscillator functions. In this way the overlaps are expressed in terms of simple scalar product of the eigenvectors. As a benchmark to illustrate our approach the case of two 1D-Morse potentials is presented. Discussions concerned with both non-Condon contributions and the harmonic limit are included. FCF's involving the 1D-Morse and asymmetric double Morse potentials are also considered. As an application, the FCF's involving the S-S stretching in the S₂O molecule are described in terms of two Morse potentials.