In this paper effects of higher order Jahn-Teller coupling terms on the nonadiabatic dynamics are studied. Of particular interest is the case when the potential energy surfaces of the degenerate state show pronounced anharmonicity. In order to demonstrate the effects a two-dimensional E multiply sign in circle e Jahn-Teller model system is treated which is based on the e(') stretching vibration of the photoactive (2)E(') state of NO(3) as a realistic example. The sixth order E multiply sign in circle e Jahn-Teller Hamiltonian is derived in the diabatic representation which is valid for any system with a C(3) rotation axis. This diabatization scheme is compared to lower-order Jahn-Teller Hamiltonians and to symmetry adapted as well as ad hoc approximations. Lower-order potentials result in pronounced quantitative and qualitative differences in the dynamics, including differences in the evolution of mean values, the autocorrelation functions (and thus the corresponding spectra), and the electronic population evolution. In the particular example treated, the results of fourth and fifth order potentials are very similar to the sixth order reference system. In contrast, the approximate sixth order Hamiltonians, though the corresponding adiabatic surfaces seem to be nearly identical, results in pronounced differences. The possible consequences for the dynamics of realistic systems with higher dimensionality are briefly discussed.
A new diabatization method based on artificial neural networks (ANNs) is presented, which is capable of reproducing high-quality ab initio data with excellent accuracy for use in quantum dynamics studies. The diabatic potential matrix is expanded in terms of a set of basic coupling matrices and the expansion coefficients are made geometry-dependent by the output neurons of the ANN. The ANN is trained with respect to ab initio data using a modified Marquardt-Levenberg back-propagation algorithm. Due to its setup, this approach combines the stability and straightforwardness of a standard low-order vibronic coupling model with the accuracy by the ANN, making it particularly advantageous for problems with a complicated electronic structure. This approach combines the stability and straightforwardness of a standard low-order vibronic coupling model with the accuracy by the ANN, making it particularly advantageous for problems with a complicated electronic structure. This novel ANN diabatization approach has been applied to the low-lying electronic states of NO 3 as a prototypical and notoriously difficult Jahn-Teller system in which the accurate description of the very strong non-adiabatic coupling is of paramount importance. Thorough tests show that an ANN with a single hidden layer is sufficient to achieve excellent results and the use of a "deeper" layering shows no clear benefit. The newly developed diabatic ANN potential energy surface (PES) model accurately reproduces a set of more than 90 000 Multi-configuration Reference Singles and Doubles Configuration Interaction (MR-SDCI) energies for the five lowest PES sheets.
An analytical anharmonic six-dimensional three-sheeted potential energy surface for the ground and first excited states of the ammonia cation has been developed which is tailored to model the ultrafast photoinduced dynamics. Selected ab initio cuts, obtained by multireference configuration interaction calculations, have been used to determine the parameters of a diabatic representation for this Jahn-Teller and pseudo-Jahn-Teller system. The model includes higher-order coupling terms both for the Jahn-Teller and for the pseudo-Jahn-Teller matrix elements. The relaxation to the ground state is possible via dynamical pseudo-Jahn-Teller couplings involving the asymmetric bending and stretching coordinates. The photoelectron spectrum of NH3 and the internal conversion dynamics of NH3+ have been determined by wave packet propagation calculations employing the multiconfigurational time-dependent Hartree method. Three different time scales are found in the dynamics calculations for the second absorption band. The ultrafast Jahn-Teller dynamics of the two excited states occurs on a 5 fs time scale. The major part of the internal conversion to the ground state takes place within a short time scale of 20 fs. This fast internal conversion is, however, incomplete and the remaining excited state population does not decay completely even within 100 fs.
The tenacious symmetry breaking of the electronic wave function of the nitrate radical (NO3) and its effect on the ground-state potential energy surface is investigated in detail. The symmetry breaking of Hartree–Fock wave functions results from a dominance of the orbital localization effect over the resonance effect and leads to three different solutions, one symmetrical and two distorted ones, for the same electronic state. The respective equilibrium geometries of these solutions are points on different potential surfaces, making their comparison meaningless. The resonance effect is promoted by dynamic as well as static electron correlation. However, the dynamic correlation methods [e.g., many-body perturbation theory (MBPT) and coupled-cluster single double (CCSD)] cannot overcome the symmetry breaking of the reference function and the problem of multiple solutions persists. The symmetry breaking can be avoided by the complete active space self-consistent field (CASSCF) approach that yields unique, single-valued surfaces for all electronic states. However, a sufficiently large and appropriately selected active space has to be used to avoid unphysical distortion of the wave function. Still the orbital localization effect leads to equilibrium geometries of C2v symmetry which strongly depend on the state-averaging of the CASSCF wave function. Multireference single double configuration interaction (MR-SDCI) wave functions are also free of symmetry breaking, if the reference orbitals are and if the configuration space is invariant under the symmetry operations. MRCI geometry optimizations only result in D3h symmetric structures with bond lengths and harmonic frequencies in close agreement with experimental data.
A scheme to produce accurate full-dimensional coupled diabatic potential energy surfaces including dissociative regions and suitable for dynamical calculations is proposed. The scheme is successfully applied to model the two-sheeted surface of the (2)E″ state of the NO3 radical. An accurate potential energy surface for the NO₃⁻ anion ground state is developed as well. Both surfaces are based on high-level ab initio calculations. The model consists of a diabatic potential matrix, which is expanded to higher order in terms of symmetry polynomials of symmetry coordinates. The choice of coordinates is key for the accuracy of the obtained potential energy surfaces and is discussed in detail. A second central aspect is the generation of reference data to fit the expansion coefficients of the model for which a stochastic approach is proposed. A third ingredient is a new and simple scheme to handle problematic regions of the potential energy surfaces, resulting from the massive undersampling by the reference data unavoidable for high-dimensional problems. The final analytical diabatic surfaces are used to compute the lowest vibrational levels of NO₃⁻ and the photo-electron detachment spectrum of NO₃⁻ leading to the neutral radical in the (2)E″ state by full dimensional multi-surface wave-packet propagation for NO3 performed using the Multi-Configuration Time Dependent Hartree method. The achieved agreement of the simulations with available experimental data demonstrates the power of the proposed scheme and the high quality of the obtained potential energy surfaces.
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