Geometrical relaxation

Table III displays VEDEs obtained with the Brueckner-reference methods discussed in Section 5.2 and augmented, correlation-consistent, triple- basis sets [41]. AEDEs include zero-point energy differences and relaxation energies pertaining to geometrical relaxation on the neutral s potential energy surface. The average absolute error with respect to experiment is 0.05 eV [26].

It should be noted that no geometrical relaxation of the excited state geometry was considered in our calculations. Such relaxations may well occur to some degree and would then enhance the localization of the electronic excitation. However the relatively narrow spectral bandwidth suggests that the geometrical changes associated with excitation into the first excited singlet state are only minor. 

Let us now turn to the mixed, partly inverted (N, F)-representation describing the geometrically relaxed, but externally closed molecular system. The relevant thermodynamic potential is now defined by the partial Legendre transformation of W(N, Q) which replaces Q by F in the list of the system parameters of state ... 

It should also be realized that the generalized softness matrix of Equations 30.12 and 30.16 represents the compliant description of the electronic coordinate N coupled to the system geometric relaxations (see Section 30.3). Indeed, the relaxed geometry global softness of the geometrical representation,... 

It would be most desirable to have a direct link between the geometrical relaxations and the force constant changes. From molecular vibrational spectroscopy it is well known that the intramolecular force constants show a scaling behavior, Badger s rule ... 

Due to the complexity of MgP-P dimer systems, ah initio quantum mechanical studies designed to ascertain the importance of geometric relaxations must be delayed for future investigations. In this regard Warshel (36, rf. ) has applied a variety of semi-empirical and semi-... 

The geometric relaxation described in Section 12.3.1 occurs by redistributing the bond valence between the bonds until GII and BSI both have acceptable values, but in some cases this relaxation is restricted by symmetry. In the case of per-ovskite, the cubic symmetry of the archetypal ABO3 structure (Fig. 10.4) does not allow any of the bonds to relax unless the symmetry is lowered. Thus true cubic perovskites are rare since they can only exist if the A and B ions are exactly the right size. Most perovskites have a reduced symmetry that allows the bonds to relax. For compounds in which the A-O bonds are stretched, the relaxation takes the form of a rotation of the BOg octahedra and results in a reduction of the coordination number of A. The various relaxed structures based on different expected coordination numbers were modelled in Section 11.2.2.4. 

Therefore, the interpretation of such structures should be performed carefully and preferably in combination with other experimental or theoretical techniques. Nevertheless, the large database of STM results, which in combination with other experimental and theoretical surface science investigations have solved many problems correctly, often rely on the Tersoff Hamann interpretation (62-65). In this sense, the Tersoff-Hamann theory has proved itself very successful, but when applying it to STM characterizations of more complicated samples, one has to be aware of the limitations of the model. The sample wave functions may be distorted by the close proximity of the tip to the surface, and the forces between the tip and sample may lead to geometric relaxations of the atoms in the surface layer beneath the tip (66). Moreover, the tip is in this model represented by a simple x-wave, so that the chemical composition of the tip is neglected. In reality the nature of the tip may, however, differ significantly from this situation because of adsorbates or other contaminants present on the tip apex (53). 

In the present calculation both e-e and e-v interactions are included for the HOMO shell of C6o- E-e exchange terms are treated essentially exactly, in the assumptions that (i) inter-band couplings can be neglected, and only act as a renormalization of the Coulomb parameters and that (ii) the latter are independent of the charge n in the HOMO. In principle, due to both orbital and geometrical relaxation, the effective... 

A similar system to that discussed in ref. [44] (tetrazine, tetrazole and pyrrole) has been studied by Manalo et al. [47] by means of the CSGT/ASC method at the B3LYP/6-311++G(2d,2p) level. The cavity was defined by using the Pauling radius for each solute atom. In this paper the effects of geometric relaxation (indirect effects) are found to be small, and the direct influence of the intensity of the solvent reaction field on the shielding constants dominates. However, the indirect effect has been found to be important for N, A-dimethylacetamidine in IEF-PCM calculations [48],... 

Peak I (parallel polarized) originates from 7T-7T transitions between delocalized (d) levels. Its transition energy is blueshifted with respect to the experimental data due to solid state effects and geometric relaxation, neglected in the theoretical calculations discussed here [32,69]. Peak III originates from l —> d /d —> l (l localized) transitions and has a dominant polarization perpendicular to the chain axis, while peak IV results from l —> l excitations and is polarized parallel to the chain axis. 

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