Single vibronic level fluorescence spectra from Hagedorn wavepacket dynamics.

In single vibronic level (SVL) fluorescence experiments, the electronically excited initial state is also excited in one or several vibrational modes. Because computing such spectra by evaluating all contributing Franck-Condon factors becomes impractical (and unnecessary) in large systems, here we propose a time-dependent approach based on Hagedorn wavepacket dynamics. We use Hagedorn functions-products of a Gaussian and carefully generated polynomials-to represent SVL initial states because in systems whose potential is at most quadratic, Hagedorn functions are exact solutions to the time-dependent Schrödinger equation and can be propagated with the same equations of motion as a simple Gaussian wavepacket.

Finite-temperature vibronic spectra from the split-operator coherence thermofield dynamics.

We present a numerically exact approach for evaluating vibrationally resolved electronic spectra at finite temperatures using the coherence thermofield dynamics. In this method, which avoids implementing an algorithm for solving the von Neumann equation for coherence, the thermal vibrational ensemble is first mapped to a pure-state wavepacket in an augmented space, and this wavepacket is then propagated by solving the standard, zero-temperature Schrödinger equation with the split-operator Fourier method. We show that the finite-temperature spectra obtained with the coherence thermofield dynamics in a Morse potential agree exactly with those computed by Boltzmann-averaging the spectra of individual vibrational levels.

High-order geometric integrators for the local cubic variational Gaussian wavepacket dynamics.

Gaussian wavepacket dynamics has proven to be a useful semiclassical approximation for quantum simulations of high-dimensional systems with low anharmonicity. Compared to Heller's original local harmonic method, the variational Gaussian wavepacket dynamics is more accurate, but much more difficult to apply in practice because it requires evaluating the expectation values of the potential energy, gradient, and Hessian. If the variational approach is applied to the local cubic approximation of the potential, these expectation values can be evaluated analytically, but they still require the costly third derivative of the potential.

Isotope Effects on the Electronic Spectra of Ammonia from Ab Initio Semiclassical Dynamics.

Despite its simplicity, the single-trajectory thawed Gaussian approximation has proven useful for calculating the vibrationally resolved electronic spectra of molecules with weakly anharmonic potential energy surfaces. Here, we show that the thawed Gaussian approximation can capture surprisingly well even more subtle observables, such as the isotope effects in the absorption spectra, and we demonstrate it on the four isotopologues of ammonia (NH, NDH, NDH, and ND). The differences in their computed spectra are due to the differences in the semiclassical trajectories followed by the four isotopologues, and the isotope effects─narrowing of the transition band and reduction of the peak spacing─are accurately described by this semiclassical method.

High-order geometric integrators for the variational Gaussian approximation.

Among the single-trajectory Gaussian-based methods for solving the time-dependent Schrödinger equation, the variational Gaussian approximation is the most accurate one. In contrast to Heller's original thawed Gaussian approximation, it is symplectic, conserves energy exactly, and may partially account for tunneling. However, the variational method is also much more expensive.

Family of Gaussian wavepacket dynamics methods from the perspective of a nonlinear Schrödinger equation.

Many approximate solutions of the time-dependent Schrödinger equation can be formulated as exact solutions of a nonlinear Schrödinger equation with an effective Hamiltonian operator depending on the state of the system. We show that Heller's thawed Gaussian approximation, Coalson and Karplus's variational Gaussian approximation, and other Gaussian wavepacket dynamics methods fit into this framework if the effective potential is a quadratic polynomial with state-dependent coefficients. We study such a nonlinear Schrödinger equation in full generality: we derive general equations of motion for the Gaussian's parameters, demonstrate time reversibility and norm conservation, and analyze conservation of energy, effective energy, and symplectic structure.