Graham A. Worth

Molecular dynamics of pyrazine after excitation to the S2 electronic state using a realistic 24-mode model Hamiltonian

The molecular dynamics of pyrazine after excitation to the S2 electronic state is investigated using the S2 absorption spectrum as a benchmark. We first present a realistic model Hamiltonian including all 24 vibrational modes of the pyrazine molecule. Using this model, we determined the potential energy surfaces of the lowest two excited states, S1 and S2, which are strongly coupled to each other. We then treated the nuclear motion of all 24 vibrational modes using the multiconfiguration time-dependent Hartree (MCTDH) wave packet propagation method. This method obtains results of good accuracy with acceptable computational effort for such a large system. The calculated spectrum is in good agreement with the experimental one. Furthermore, our results shed light on the role of the 20 modes which are only weakly coupled to the system, and demonstrate that essential physical features, such as symmetries, have to be considered when one wants to treat the molecular dynamics of pyrazine realistically.

Relaxation of a system with a conical intersection coupled to a bath: A benchmark 24-dimensional wave packet study treating the environment explicitly

In this paper the phenomenon of the ultrafast relaxation of a system coupled to a small bath is treated. The system, representing the pyrazine molecule, contains 4 vibrational modes and 2 electronic states coupled via a conical intersection, and the bath is a set of up to 20 harmonic oscillators. The dynamics of the complete system are described by wave packet propagation using the multiconfiguration time-dependent Hartree method. By the use of multidimensional single-particle functions it was possible to obtain results of a high quality, even for the complete system with 24 degrees of freedom. The full wave function for the system and bath are analyzed to reveal the characteristics of the system-bath interaction, such as energy transfer to the bath, or the effect of the bath on the state populations. The results show that the damping due to the bath model adopted is not only nonhomogeneous but also selective: certain high frequencies are found to remain at long times.

Using the MCTDH wavepacket propagation method to describe multimode non-adiabatic dynamics

The MCTDH method has been used successfully to treat the non-adiabatic dynamics of a number of systems. These are hard problems due to the number of modes that need to be included in a calculation, and the strong coupling between the nuclear and electronic motion at conical intersections connecting electronic states in these systems. In this review, an overview of the basic theory of the method is given highlighting how it is able to treat larger systems than other quantum dynamics methods. The vibronic coupling model Hamiltonian is also described, which provides a good starting point for the description of these systems. Examples of calculations made and systems treated are given. Finally, a development of the basic MCTDH method in which some of the usual time-dependent basis functions are replaced by Gaussian wavepackets is outlined. This method promises not only to treat larger systems, but to provide a consistent quantum–semiclassical framework.

Solving the time-dependent Schrödinger equation for nuclear motion in one step: direct dynamics of non-adiabatic systems

A review of direct dynamics methods is given, focusing on their application to non-adiabatic photochemistry–i.e. systems in which a conical intersection plays an important role. Direct dynamics simulations use electronic structure calculations to obtain the potential energy surface only as it is required ‘on-the-fly’. This is in contrast to traditional methods that require the surface to be globally known as an analytic function before a simulation can be performed. The properties and abilities, with descriptions of calculations made, of the three main methods are compared: trajectory surface hopping (TSH), ab initio multiple spawning (AIMS), and variational multi-configuration Gaussian wavepackets (vMCG). TSH is the closest to classical dynamics, is the simplest to implement, but is hard to converge, and even then not always accurate. AIMS solves the time-dependent Schrödinger more rigorously, but as its basis functions follow classical trajectories again suffers from poor convergence. vMCG is harder to implement, but its basis functions do not follow classical trajectories and it converges much faster.

The effect of a model environment on the S2 absorption spectrum of pyrazine: A wave packet study treating all 24 vibrational modes

The absorption spectrum of pyrazine to the S2 electronic state can be usefully described by a 4‐mode system interacting with a 20‐mode bath. In this paper wave packet propagation techniques, using the multiconfiguration time‐dependent Hartree approach, are used to study this problem. The investigation was made in stages so as to study the nature of the wave function needed to correctly describe various properties of this multimode problem: the absorption spectrum; the energy exchange between the system and the bath; and the rate of inter‐state crossing. It was found that, despite the relatively weak system–bath coupling, a multiconfigurational wave function was necessary to describe the interaction between the two parts of the problem. While it was not possible to treat the full 24‐mode problem with such a wave function, the spectrum for a 14‐mode system, which includes all the important bath modes, has been calculated in this way. The results, in agreement with the path integral calculations of Krempl et...

All mode dynamics at the conical intersection of an octa-atomic molecule: Multi-configuration time-dependent Hartree (MCTDH) investigation on the butatriene cation

The ground state and the first excited electronic states of the octa-atomic butatriene cation (C4H4+) exhibit a multidimensional conical intersection. This intersection is energetically low lying and is located in the vicinity of the Franck–Condon region of the neutral molecule’s ground state. The conical intersection thus dominates the nuclear dynamics in ionization processes of this molecule. This is a particularly interesting example of vibronic coupling, introducing what appears to be a new, structured band into the energy spectrum. In this work, the potential energy surfaces and their intersection are investigated by ab initio methods. A diabatic model Hamiltonian including all possible linear, quadratic and bilinear vibronic coupling terms is introduced, with coupling constants determined by a fit to the ab initio data. The nuclear dynamics of all 18 vibrational modes is then evaluated by propagating the wave packet using the multi-configuration time-dependent Hartree method. Finally, the photoelect...

Full quantum mechanical molecular dynamics using Gaussian wavepackets

Abstract We present the first application of a promising new method for quantum dynamics calculations. Based on the efficient multiconfiguration time-dependent Hartree wavepacket propagation algorithm, it can treat part, or all, of the wavepacket using Gaussian functions. The Gaussian parameters evolve using variational, coupled equations of motion. In this way the Gaussian basis functions evolve so as to optimally describe the wavepacket. Here, a four-dimensional Henon–Heiles potential surface is used to demonstrate that only a few Gaussian functions are required, and convergence on the full quantum mechanical result is rapid.

Multimode quantum dynamics using Gaussian wavepackets: The Gaussian-based multiconfiguration time-dependent Hartree (G-MCTDH) method applied to the absorption spectrum of pyrazine

The Gaussian-based multiconfiguration time-dependent Hartree (G-MCTDH) method is applied to calculate the S(2)(pipi( *)) absorption spectrum of the pyrazine molecule, whose diffuse structure results from the ultrafast nonadiabatic dynamics at the S(2)-S(1) conical intersection. The 24-mode second-order vibronic-coupling model of Raab et al. [J. Chem. Phys. 110, 936 (1999)] is employed, along with 4-mode and 10-mode reduced-dimensional variants of this model. G-MCTDH can be used either as an all-Gaussian approach or else as a hybrid method using a partitioning into primary modes, treated by conventional MCTDH basis functions, and secondary modes described by Gaussian particles. Comparison with standard MCTDH calculations shows that the method converges to the exact result. The variational, nonclassical evolution of the moving Gaussian basis is a key element in obtaining convergence. For high-dimensional systems, convergence is significantly accelerated if the method is employed as a hybrid scheme.

Multiconfigurational system-bath dynamics using Gaussian wave packets: Energy relaxation and decoherence induced by a finite-dimensional bath

The quantum dynamics of an anharmonic oscillator coupled to a bath of up to 60 harmonic oscillators is investigated by a new multiconfigurational hybrid method for wave packet propagation. The method, originally proposed in [Burghardt, Meyer, and Cederbaum, J. Chem. Phys. 111, 2927 (1999)], represents a variant of the multiconfiguration time-dependent Hartree method including a moving basis of Gaussian functions. Energy relaxation and quantum decoherence induced by the zero-temperature oscillator bath are shown to be accurately described by the new method. Decoherence rates for a bath with a discretized ohmic spectral density are found to be consistent with golden-rule predictions for T=0.

Exploring the sloped-to-peaked S2/S1 seam of intersection of thymine with electronic structure and direct quantum dynamics calculations

The role of the seam of intersection between the lowest (pi,pi*) and (n,pi*) excited states in the decay of electronically excited singlet thymine has been investigated with ab initio complete active space self-consistent field (CASSCF) calculations and direct dynamics variational multiconfiguration Gaussian (DD-vMCG) quantum dynamics on the full-dimensional CASSCF surface, with 39 degrees of freedom. The seam has a sloped-to-peaked topography, and the dynamics at the different segments of the seam have been studied by varying the initial conditions of the propagation. When the wave packet is directed to the peaked segments, part of it traverses the seam, stays on the (pi,pi*) state and heads towards decay to the ground state. In contrast to this, when the wave packet is driven to sloped seam segments it bounces back to the minimum of the (pi,pi*) state. Significant population transfer to the (n,pi*) state is observed in both cases. The results suggest that a sloped-to-peaked topography can be used to control photochemical reactivity, by driving the wave packet to different regions of the seam where a different outcome of the propagation can be expected.