H.-D. Meyer

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.

Calculation of resonance energies and widths using the complex absorbing potential method

The spectral properties of Hamilton operators perturbed by a complex absorbing potential (CAP) are studied. For a wide class of CAPS proper eigenvalues of the perturbed Hamilton operator converge to Siegert resonance eigenvalues of the unperturbed Hamiltonian with decreasing CAP strength. The errors in the calculation of complex resonance energies caused by the additional CAP and by finite basis set representation are examined. In order to minimize these errors a scheme of approximations is provided. The application of this method allows for the use of real L2 basis sets. The feasibility and accuracy of the proposed method is demonstrated by calculations of resonance energies of a model potential and of the 2 Pi g shape resonance of N2.

Approaches to the approximate treatment of complex molecular systems by the multiconfiguration time-dependent Hartree method

A consistent treatment of environmental effects is proposed in the framework of the multiconfiguration time-dependent Hartree (MCTDH) method. The method is extended in view of treating complex molecular systems which require an exact quantum dynamics for a certain number of “primary” modes while an approximate dynamics is adequate for a class of “secondary” modes. The latter may correspond to the weakly coupled modes in a polyatomic molecule, or the first solvent shell in a solute-solvent complex. For these modes, a description in terms of parameterized functions is introduced. The MCTDH working equations are generalized to allow for the nonorthogonality of these functions, which may take, e.g., a multidimensional Gaussian form. The formalism is developed on the level of both the wave function description and the density matrix description. Dissipative effects are accounted for in terms of a stochastic Hamiltonian approach versus master equation approach in the respective descriptions.

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.

Multiconfigurational time‐dependent Hartree study of complex dynamics: Photodissociation of NO2

The multiconfigurational time‐dependent Hartree (MCTDH) approach is applied to an example showing very complex dynamics: the wave‐packet dynamics on the three‐dimensional B2 potential‐energy surface of NO2. The ability of the MCTDH scheme to describe accurately the severe splitting of the wave packet on a saddle‐shaped surface is demonstrated. Internal checks of the MCTDH calculation enable us to assess the degree of convergence without the need to resort to a numerically exact wave‐packet calculation. As a representative observable the photodissociation spectrum is calculated and discussed. The A1/B2 vibronic coupling is neglected in our study, but the dynamics on the diabatic B2 surface is treated in its full three dimensionality.

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.

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...

Block Lanczos and many-body theory: Application to the one-particle Green's function

The importance of the block or band Lanczos method for many-body Green’s function calculations of atomic and molecular systems is discussed. The usual computation schemes for determining the Green’s function involve the diagonalization of Hermitian secular matrices. Considerable numerical difficulties arise, on the one hand, from the size of these matrices and, on the other hand, from the large number of eigenvalues and eigenvectors which often need to be computed in practice. In the case of the one-particle Green’s function it is shown how the computational effort of the diagonalization process can be substantially reduced using block Lanczos. The proposed procedure which consists of a block Lanczos ‘‘prediagonalization’’ and a subsequent diagonalization of the resulting smaller secular matrices quite naturally exploits the specific structure of the secular problems encountered. Its computational performance is demonstrated in a model application to the benzene molecule. The calculation of the complete valence-shell ionization spectra of the systems BeF42 , BeF3 , and BeF2 is devised as a further application of the method in the particular case where the treatment of the full secular problem is computationally prohibitively expensive.

Temporary anions - calculation of energy and lifetime by absorbing potentials: the resonance

The calculation of energies and lifetimes of metastable molecules requires the treatment of both the continuum and correlation effects. We describe the complex absorbing potential approach incorporated within a configuration-interaction framework. The absorbing potential method allows a very efficient solution of the continuum problem, making possible a detailed study of the correlation effects that turn out to be surprisingly strong. The famous resonance is studied as a test case and much attention is paid to an internally balanced treatment of the metastable state. Our findings are rationalized within a simple model that is then used to understand the results of various previous studies.