Wavefunction dimer

In the following section, step by step a qualitative picture is formed describing the impact of intcrmolecular interactions oil the absorption and luminescence of organic conjugated chains. The present calculations do not distinguish between dimers and aggregates (for which the wavefunctions of adjacent chains interact in the ground state, due to, for instance, solid-state effects) and excimers (where overlap occurs only upon photoexcitation) [29]. 

Regarding the emission properties, AM I/Cl calculations, performed on a cluster containing three stilbene molecules separated by 4 A, show that the main lattice deformations take place on the central unit in the lowest excited state. It is therefore reasonable to assume that the wavefunction of the relaxed electron-hole pair extends at most over three interacting chains. The results further demonstrate that the weak coupling calculated between the ground state and the lowest excited state evolves in a way veiy similar to that reported for cofacial dimers. 

A fruitful approach to the problem of intermolecular interaction is perturbation theory. The wavefunctions of the two separate interacting molecules are perturbed when the overlap is nonzero, and standard treatment [49] yields separate contributions to the interaction energy, namely the Coulombic, polarization, dispersion, and repulsion terms. Basis-set superposition is no longer a problem because these energies are calculated directly from the perturbed wavefunction and not by difference between dimers and monomers. The separation into intuitive contributions is a special bonus, because these terms can be correlated with intuitive molecular... 

The y>Ee(R) are the radial free-state wavefunctions (see Chapter 5 for details). The free state energies E are positive and the bound state energies E(v,S) are negative v and ( are vibrational and rotational dimer quantum numbers t is also the angular momentum quantum number of the fth partial wave. The g( are nuclear weights. We will occasionally refer to a third partition sum, that of pre-dissociating (sometimes called metastable ) dimer states,... 

Bound states are readily included in the line shape formalism either as initial or final state, or both. In Eq. 6.61 the plane wave expression(s) are then replaced by the dimer bound state wavefunction(s) and the integration(s) over ky and/or kjj2 are replaced by a summation over the n bound state levels with total angular momentum J n or J . The kinetic energy is then also replaced by the appropriate eigen energy. In this way the bound-free spectral component is expressed as [358]... 

Atoms at solid surfaces have missing neighbors on one side. Driven by this asymmetry the topmost atoms often assume a structure different from the bulk. They might form dimers or more complex structures to saturate dangling bonds. In the case of a surface relaxation the lateral or in-plane spacing of the surface atoms remains unchanged but the distance between the topmost atomic layers is altered. In metals for example, we often find a reduced distance for the first layer (Table 8.1). The reason is the presence of a dipole layer at the metal surface that results from the distortion of the electron wavefunctions at the surface. 

One can dissociate the NO dimer simply by increasing the N-N bond distance to infinity. One can also require that during that process the molecule remain on the singlet surface, which by definition has a wavefunction and thus density that has equal spin-up and spin-down components everywhere in space. We are not interested in spin-restricted dynamics. We are interested in the much more balanced chemical dynamics that treats each half of the dissociated dimer correctly in DFT via a spin-polarized calculation. This decision must be made independent of whether or not one wants to use spatial symmetry to reduce the cost of the calculation. Spin-unrestricted DFT chemical dynamics will be called balanced in the following. 

The accuracy of the MO-VB wavefunction is expected to be close to that of a full SD-CI wavefunction involving excitations to the full virtual spaces of each monomer (vertical excitations). Very recently, a new version of the MO-VB optimization scheme has been developed that is apt to guarantee that the wavefunction approaches as close as possible the full SD-CI limit, via saturation of the optimal virtual space. Explorative calculations on the very challenging helium dimer system are encouraging. 

BH3 is an important small molecule for which experimental data are lacking, since it readily dimerizes to BsHe. Several earlier papers were devoted to this question, particularly studies by Kutzelnigg and co-workers, who562 estimated from IEPA calculations that the dimerization energy is 151 +21 kJ mol-1. BHa was also studied in SCF calculations some years ago by Schwartz and Allen,583 who considered the inner-shell and valence-shell ionization energies. More recently, Goddard and Blint have discussed GVB wavefunctions for BH3.155... 

In Eqn. (5), the angular brackets impley averages over the asymmetric rotor wave-function as well as the vibrational wavefunction. Rz is the component of R along the space-fixed z-axis. The final step is to relate the coupling constants in Eqn. (5) to those of the monomer. In general, the expressions depend on the complexity of the monomers and on the dimer rotational state observed. For a large number of cases, a linear type dimer in a K=0 rotational state may be assumed, and Eqn. (5) may be expressed as... 

In the work described here, we have dedicated special emphasis not only to the characterization of fhe low lying energetic levels, but also to the associated wavefunctions exploiting the availability of realistic potential energy surfaces. This study completes the faithful picture of the internal dynamics of the system involving levels pertaining to the lowest energy states for the dimers. 

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