H. Köppel

Interplay of Jahn–Teller and pseudo‐Jahn–Teller vibronic dynamics in the benzene cation

The static and dynamic aspects of the vibronic interaction of the B 2E2g and C 2A2u electronic states of C6H+6 are analyzed. In the approximation of linear vibrational and vibronic coupling, the model Hamiltonian for this system comprises eight nonseparable vibrational modes, six of which are degenerate (two of A1g symmetry, four of E2g symmetry, and two of E2u symmetry). The coupling constants are estimated from existing ab initio SCF and semiempirical (CNDO/S) calculations. The topology of the adiabatic potential‐energy surfaces of this class of model Hamiltonians is investigated. It is shown that the model exhibits a variety of conical intersections which dominate the vibronic dynamics. The dynamical problem is solved with simultanteous inclusion of six vibrational modes, four of which are degenerate (the Jahn–Teller coupling of two of the E2g modes is negligible). Hamiltonian matrices with dimensions up to 6×106 are diagonalized using the Lanczos algorithm. After some adjustments of coupling constan...

New method for calculating wave packet dynamics: Strongly coupled surfaces and the adiabatic basis

The nuclear dynamics on potential energy surfaces with a conical intersection is investigated on the basis of exact (numerical) integration of the time‐dependent Schrodinger equation. The ethylene cation is chosen as a typical realistic model system. Complementing earlier work we study the dynamics also in the adiabatic basis, which will be seen to allow for a more profound understanding of the decay and dephasing processes occurring in the system. The computational effort exceeds considerably that of propagation in the diabatic basis, to which previous related studies have been confined. To solve the resulting computational problems we develop and present a special multidimensional adaptation of the finite basis set method utilizing the product structure of the basis. It allows us to calculate propagation in a general potential including three vibrational modes. For the time integration a fourth order differencing scheme is introduced which is faster than the second order differencing‐scheme and predicto...

Dynamics on potential energy surfaces with a conical intersection: Adiabatic, intermediate, and diabatic behavior

The nuclear dynamics on potential energy surfaces which are strongly vibronically coupled through a conical intersection is investigated by exact (numerical) integration of the time‐dependent Schrodinger equation. Results for realistic model systems including three nuclear degrees of freedom are presented: C2H+4, pyrazine and NO2. It was found previously for C2H+4 that the wave packet moves after an initial decay mainly on the lower adiabatic surface. This observation could be confirmed also for pyrazine and NO2. By varying the coupling strength λ also other types of behavior could be identified. A transition from adiabatic via intermediate to a diabatic nature of the system dynamics is found upon decreasing λ. Population of diabatic and adiabatic states in the long time limit are calculated by classical phase‐space statistics. Analytic relations between the population of the diabatic states and the dynamical observables, coordinates and momenta, are derived. They allow for a deeper understanding of their...

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.

On the statistical behaviour of molecular vibronic energy levels

Abstract Electronic spectra of polyatomic molecules often exhibit a high density of complicated energy levels, making a detailed analysis of the individual levels unfavourable. In these cases, statistical tests provide an appropriate means for analysing the spectra. Fluctuation measures are presented and evaluated for calculated and experimental molecular spectra as examples. The results are compared with the predictions of random matrix theory.

Spectroscopic effects of conical intersections of molecular potential energy surfaces

A simple vibronic coupling model involving two electronic states and two vibrational modes is considered. The model is based on harmonic diabatic potentials and linear coupling of the diabatic electronic states. It is shown that the adiabatic electronic potential energy surfaces exhibit, in general, a conical intersection. The well known E × E and E × B Jahn-Teller problems are contained as special cases. Using numerical methods the optical absorption spectrum is calculated exactly. Extremely complex vibronic spectra are obtained when the conical intersection occurs within the Franck-Condon (FC) zone. The exact vibronic spectra are compared with spectra calculated in the adiabatic and FC approximation. The genuine spectroscopic effects of conical intersections are revealed by a comparison with the results of standard one-dimensional vibronic coupling calculations. The presence of a conical intersection limits the applicability of the adiabatic and FC approximations much more strongly than in the one-dimen...

Multistate vibronic interactions in the benzene radical cation. II. Quantum dynamical simulations

The multistate vibronic dynamics in the X 2E1g-Ẽ 2B2u electronic states of the benzene radical cation is investigated theoretically by an ab initio quantum-dynamical approach. The vibronic coupling scheme and the ab initio values of the system parameters are adopted from the previous Paper I. Vibronic line spectra are obtained with the Lanczos procedure. Extensive calculations on wave-packet propagation have been performed with the aid of the multiconfiguration time-dependent Hartree method. Up to five coupled electronic potential energy surfaces and 13 vibrational degrees of freedom have been included in these calculations. As a result, the impact of a third electronic state (X or B) on a strongly coupled manifold (B-C or D-Ẽ states) is quantitatively assessed. It leads to a restructuring of the spectral envelope which is stronger for the B-D-Ẽ than for the X-B-C system. The internal conversion dynamics is characterized by a stepwise transfer of electronic population to the lowest electronic s...

The visible absorption spectrum of NO2: A three-mode nuclear dynamics investigation

Abstract The vibronic band origins of the visible absorption spectrum of NO2 are calculated theoretically with the aid of a simple model Hamiltonian for the coupled electronic and vibrational motions. Including all three vibrational modes in the calculation and using ab initio values of the relevant parameters, we obtain satisfactory qualitative agreement with experiment. In particular, the observed high density and irregular intensity distribution of the band origins is reproduced correctly by the calculation. The present results confirm unambiguosly that the anomalous vibronic structure of the 2 B 2 ← 2 A 1 transition is caused by strong nonadiabatic interactions between the 2B2 and 2A1 electronic states of NO2. They also show that simple deconvolution procedures, which are often used to deperturb irregular spectra, are not applicable to the 2 B 2 ← 2 A 1 transition of NO2. To further explore the strength of the nonadiabatic effects in NO2, we calculate the mixing of the different electronic species in the vibronic eigenstates and compare it to several relevant experimental quantities.

Ultrafast non-radiative decay via conical intersections of molecular potential-energy surfaces: C2H4+

Abstract Conical intersections of molecular potential-energy surfaces are shown to lead to ultrashort (decay time ⪡ 1 ps) non-radiative decay of electronically excited molecules. In this work we calculate the ultrashort decay time for the Ā-X conical intersection in the ethylene radical cation with the aid of ab initio derived parameters and obtain a value of 0.7 × 10 −14 s. We perform the calculations by exact (within the model hamiltonian adopted) numerical integration of the time-dependent Schrodinger equation. The results are compared to those obtained within a Greens function approach. They show a pronounced mutual influence of the vibrational levels of the upper potential-energy surface on the non-radiative decay time. By analyzing the time evolution of the molecular wavefunction on a microsecond time scale we give arguments for a strong quenching of the radiative rate. This rationalizes the absence of detectable emission in C 2 H 4 − and other radical cations. The importance of conical intersections and their impact on molecular dynamics in open-shell systems is pointed out.

Dissociation and predissociation on coupled electronic potential energy surfaces : a three-dimensional wave packet dynamical study

The dissociation process of a triatomic molecule with strongly coupled electronic states is investigated by wave packet dynamics. Rotational and vibronic motion are separated for vanishing total angular momentum (J=0) in a linear molecule with conically intersecting Σ and Π electronic potential energy surfaces. All three remaining nuclear degrees of freedom are treated exactly. The time evolution of a wave packet prepared initially by photoionization of the neutral molecule is studied for different values of the nonadiabatic couplings and for different values of other relevant parameters. The potential surfaces studied include those modeling important aspects of the HCN+ system. Time dependent populations of diabatic and adiabatic electronic states are presented. The results can be interpreted by adapting ideas developed for vibronic coupling in bound systems to the dissociative situation.