Influence of internal degrees of freedom on the structure of one-dimensional systems

Summary The influence of internal degrees of freedom on the behaviour of one-dimensional systems is discussed. For systems with half-filled bands the coupling to internalviz. lattice coordinates decides whether Peierls distortion is caused by intramonomer coordinates or by a lattice coordinate. Thereby the various intramonomer degrees of freedom act cooperatively. We show that there is a small regime of parameters where both kinds of distortion exist simultaneously. For increasing temperature we find that distortions can also move from the lattice coordinate to the intramonomer coordinate.     

The electronic structure of molecules by a many-body approach: V. Ionization potentials and one-electron properties of cyclopentadiene and 1-sila-cyclopentadiene-(2,4)

The valence ionization potentials (IP's) of cyclopentadiene and 1-sila-cyclopentadiene-(2,4) are studied by an ab initio many-body approach which includes the effect of electron correlation and reorganization beyond the Hartree-Fock approximation. The Hartree-Fock approximation gives the correct ordering of the IP's for cyclopentadiene but this ordering does not agree with the results of the previous experimental and theoretical studies. The ordering is 1a₂(π), 2b₁(π), 4b₂, 6a₁, 5a₁, 3b₂, 1b₁ (π), 4a₁, 2b₂, 3a₁. For sila-cyclopentadiene the ordering of the IP's is: 1a₂(π), 4b₂, 2b₁(π), 6a₁, 1b₁(π), 5a₁, 3b₂, 4a₁, 3a₁, 2b₂. The Hartree-Fock approximation is found to be incorrect with respect to the ordering of the 4b₂ and 2b₁(π) IP's. A number of one-electron properties are calculated in the one-particle approximation and compared with the available experimental data.     

Competition between excitation and electronic decay of short-lived molecular states

The nuclear dynamics accompanying the excitation to and the subsequent decay of an electronic state is discussed. Particular attention is paid to cases, in which the whole process cannot be divided into two steps (excitation and decay) since the excitation and the decay times are of the same order of magnitude. The recently introduced time-dependent formulation of the theory describing the wave packets’ dynamics is extended to include the excitation process. The wave packets can be related to the intensity of the emitted particles. Most of the resulting integrals can actually be performed by employing eigenstates of the Hamiltonians corresponding to the involved potential energy surfaces. This leads to the so called “timeindependent” formulation of the theory. Computational details of the implementation of the corresponding “timedependent” and “time-independent” methods are presented. Illustrative applications are given to illuminate both the influence of the excitation process and the lifetime of the decaying state. It emerges that the intuitive interpretation of the spectra (within the above two step model) may fail. Insight into the process is gained by studying the evolution of the spectra as a function of time. The appearance of “atomic lines” due to dissociative decaying and final states is investigated in some detail.     

Charge transfer in the Cl-CO cluster induced by core ionization

Ab initio calculations of core-ionization spectra of the anion-molecule Cl-CO cluster are performed. Particular attention is paid to the investigation of charge-transfer screening processes accompanying core ionization of the CO molecule in the cluster. The charge-transfer processes are very efficient and favored by the presence of a low-lying unoccupied pi* orbital in CO capable of accepting an electron from Cl-. The O1s(-1) and C1s(-1) core-ionization spectra are calculated and compared. Both reveal a breakdown of the quasiparticle picture of core ionization caused by the charge-transfer processes. Remarkable differences between these two spectra are found which manifest themselves in distinct intensity distributions in the prominent low-energy spectral bands. The underlying reason for these differences is elucidated and linked with the preference of the pi* orbital to localize mainly on carbon. Core-ionization spectra of anion-molecule clusters are very sensitive to the type of the molecule involved as the comparative analysis of the O1s(-1) core-ionization spectra of the Cl-CO and Cl-H(2)O clusters show.     

Dilatation transformation and sum rules for general potentials including self-consistent field potentials

The eigenfunctions and energies of general dilated Hamiltonians are expanded in powers of the dilatation parameter. These expansions, augmented by stationarity and stability conditions, are used to derive exact sum rules for bound and resonance states. Particular attention is paid to Hamiltonians with potentials which depend on external parameters, such as the nuclear coordinates in molecules, and to self-consistent potentials. The sum rules can be employed in practical computations to improve the quality of the results and may also serve in analyzing the results from approximate calculations.     

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.     

The electronic structure of molecules by a many-body approach

The vertical valence ionization potentials of cyclopropane, ethylene oxide and ethylene imine are calculated by a many-body Green's function method. For C₃H₆ the ordering of the ionization potentials is 2e(), 1e(), 2a₁(), 1a₂(), 1e(). The assignment of the 2a₁ and the 1a₂ ionization potentials which has been controversial is thus clarified. The ordering is in agreement with the result obtained via Koopmans' theorem. For ethylene oxide and ethylene imine Koopmans' theorem fails in predicting the correct order of ionic states. For C₂H₄O the ordering of the ionization potentials is 2b ₁(), 4a ₁, 1a ₂(), 2b ₂,3a ₁, 1b ₁(), 1b ₂, 2a ₁ and for C₂H₅N 6a, 5a, 3a, 2a, 4a, 3a, 1a, 2a. The agreement of the computed ionization potentials with the experimental values is very satisfactory.     

On the existence of free doubly negative molecular ions

We present a theoretical analysis on the existence of doubly negative molecular ions in the gas phase. A thorough investigation involves the discussion of two main problems: the stability of the system with respect to dissociation and the stability to the loss of an electron. An adequate treatment of both problems requires the choice of proper basis sets as well as the application of higher levels of theory. As an example the BeF ₄ ^2? dianion is studied in detail. Here we use configuration interaction and many-body Green's function approaches. Strong basis set dependencies in the calculations are observed which have no analogy in neutral systems.