Lorenz S. Cederbaum

The multi-configurational time-dependent Hartree approach

Abstract A new multi-configurational approach to the time-dependent Schrodinger equation is proposed. This approach leads to working equations which are particularly simple and transparent. It can be used for n degrees of freedom and for any choice of the number of configurations. The new approach is tested on a model of coupled oscillators showing fast convergence towards the exact results as the number of configurations is increased.

Wave‐packet dynamics within the multiconfiguration Hartree framework: General aspects and application to NOCl

The multiconfigurational time‐dependent Hartree (MCTDH) approximation to the time‐dependent Schrodinger equation is tested for a realistic three‐dimensional example, the photodissociation of NOCl. The working equations of the MCTDH scheme introduced earlier are discussed in some detail. A computational scheme is presented which allows for efficient numerical MCTDH calculations. This scheme is applied to the photodissociation of NOCl after excitation to the S1 surface. The results are compared to the results of an exact wave‐packet dynamics calculation. Fast convergence of the MCTDH results toward the exact one is found as the number of configurations is increased. The computation times of the MCTDH calculations are found to be much shorter than those of the exact calculation. Even MCTDH calculations including sufficiently many configurations for a fully converged (quasiexact) description require over two orders of magnitude less CPU time than an exact calculation. The so‐called ‘‘natural populations’’ tha...

One-body Green's function for atoms and molecules: theory and application

The one-body Greens function is investigated by expanding the self-energy part up to third order. On this level some properties of the diagrams of the self-energy part are discussed. To estimate the contribution of higher orders of the self-energy part an effective time dependent interaction is introduced. It is found that the main contributions due to this interaction can be determined by considering the analytic properties of second and third order terms only. The numerical effort required can thus be strongly reduced. The theory is applied to calculate the vertical ionization potentials of B2H6. The calculation of the pole strengths shows that one may expect satellite lines in the photoelectron spectrum of B2H6 with about 10% of the intensity of the principal valence lines due to excitations accompanying ionization.

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.

Direct calculation of ionization potentials of closed-shell atoms and molecules

Vertical ionization potentials, electron affinities and information about quasi-particles can be obtained by using the technique of the single-particle propagator. The expansion of the self-energy part up to third order perturbation theory can be evaluated numerically, but does not lead, in most cases, to satisfying results. A theoretical and numerical analysis of the diagrammatic expansion of the self-energy part requires the introduction of a renormalized interaction and renormalized hole and particle lines.

Gas-Phase Multiply Charged Anions

Singly charged negative ions in the gas phase have attracted considerable experimental and theoretical attention over the past decades. However, the existence of free doubly or multiply charged negative ions, in particular those of small systems, has remained a curiosity and a matter of some controversy. Recent experimental and quantum mechanical studies show that multiply charged negative ions of small molecules and clusters can exist as isolated entities.

Approximately diabatic states from block diagonalization of the electronic Hamiltonian

In many cases of interest there is only a small number of electronic states which interact with each other through the nuclear motion and are well‐separated energetically from the other states. The aim of this work is to find a nearly diabatic (quasidiabatic) representation for the coupled states in which their coupling becomes small. Block diagonalization of the electronic Hamiltonian can accomplish this goal. It is achieved by a unitary transformation T which is uniquely determined by a ‘‘least action principle’’ which demands that T ‘‘does not do anything but block diagonalization.’’ By the help of the transformation we arrive at a decoupling of the relevant states from the rest and have to deal with a small matrix Hamiltonian. We have investigated in detail this block diagonalization procedure and succeeded in calculating the matrix elements of the total Hamiltonian in the new basis in closed form, in a nonperturbative way. Qualitative criteria are given to decide in which cases the method can success...

Correlation effects in the ionization of hydrocarbons

The spectral intensity for ionization as a function of binding energy for the valence electrons of ethylene, allene, butatriene, trans‐butadiene, acetylene, benzene, methane, ethane, and cyclopropane is computed by a many‐body Green’s function method. The results are used to interpret unidentified structures in experimental ionization spectra. For the ionization out of the inner valence orbitals of the unsaturated molecules the spectral intensity is found to be distributed over several lines, in sharp contrast to the ionization out of the inner valence orbitals of the saturated molecules where the greater part of the intensity appears in one main line. The reasons for this behavior are discussed. It is also found that there is a correspondence between the behavior of the spectral intensity in the inner valence region and the satellite structure in the outer valence region. For C6H6, C4H4, and C4H6 interesting satellite lines of considerable intensity are predicted to be situated in the outer valence regio...

On the accuracy of ionization potentials calculated by Green’s functions

A many‐body Green’s function method is used to calculate vertical valence ionization potentials to high accuracy for the atoms and molecules Ne, N2, F2, CO2, P2, H2O, and H2S. Large basis sets including several sets of polarization functions are used in the calculations to reach the limit of the presently achievable accuracy for molecular systems. The maximum errors in the computed ionization potentials are 0.1 to 0.25 eV depending on the molecule and the basis set. The results are extremely stable, when large basis sets are used. Comparison with other methods is made.

A many‐body approach to the vibrational structure in molecular electronic spectra. I. Theory

A general Hamiltonian which describes the coupled motion of electrons and nuclei in a molecule is derived. In the one‐particle approximation an exact solution for the vibrational intensity distribution of arbitrary electronic transitions (except those between linear and bent configurations) is given. Only the data of the initial electronic state are required and only linear equations have to be solved in the calculation. A formalism to include many‐body effects, in which also only properties of the initial electronic state are needed, is presented. To calculate the gross features of the spectral distribution, especially of importance for the interpretation of low resolution spectra, a moment expansion is derived. The influence of the coupling constants appearing in the Hamiltonian on the vibrational spectrum is briefly discussed.