Wavefunction polarity

The resulting eigenvalue ccPK is a good approximation of AE in the sense that it correctly represents an excitation energy obtained in the presence of a PCM reaction field kept frozen in its GS situation but still it cannot account for the wavefunction polarization. The consequence is that we cannot distinguish between equilibrium and nonequilibrium wavefunctions and thus in this approximation AEG°s neq = AEG°S = (o°K. By using this approximation, the equilibrium and nonequilibrium free energies for the excited state K become ... 

Kutzelnigg W 1992 Does the polarization approximation converge for large-rto a primitive or a symmetry-adapted wavefunction Chem. Phys. Lett. 195 77... 

A partial acknowledgment of the influence of higher discrete and continuum states, not included within the wavefunction expansion, is to add, to the tmncated set of basis states, functions of the fomi T p(r)<6p(r) where dip is not an eigenfiinction of the internal Flamiltonian but is chosen so as to represent some appropriate average of bound and continuum states. These pseudostates can provide fiill polarization distortion to die target by incident electrons and allows flux to be transferred from the the open channels included in the tmncated set. 

A set of polarized orbital pairs is described pictorially in figure B3.1.6. In each of the tln-ee equivalent temis in the above wavefunction, one of the valence electrons moves in a 2s+a2p orbital polarized in one direction while the other valence electron moves in the 2s - a2p orbital polarized in the opposite direction. For example, the first temi (2s - a2p )a(2s+a2p )P - (2s-a2p )P(2s+a2p )a describes one electron occupying a 2s-a2p polarized orbital while the other electron occupies the 2s+a2p orbital. The electrons thus reduce their... 

We often refer to Heitler and London s method as the valence bond (VB) model. A comparison between the experimental and the valence bond potential energy curves shows excellent agreement at large 7 ab but poor quantitative agreement in the valence region (Table 4.3). The cause of this lies in the method itself the VB model starts from atomic wavefunctions and adds as a perturbation the fact that the electron clouds of the atoms are polarized when the molecule is formed. 

In order to solve this problem of unboundedness, Argyres and Sfiat [17] decomposed the dipole moment operator into a periodic sawtooth function and its non periodic stair-case complement. The stair-case component is responsible of the localization of the electronic wavefunction whereas the sawtooth potential is associated with the periodic character of the polarization. Otto and Ladik [18-19] have proposed an alternative decomposition of the dipole moment operator. 

The second part of this paper concerns the choice of the atomic basis set and especially the polarization functions for the calculation of the polarizability, o , and the hyperpo-larizabiliy, 7. We propose field-induced polarization functions (6) constructed from the first- and second-order perturbed hydrogenic wavefunctions respectively for a and 7. In these polarization functions the exponent ( is determined by optimization with the maximum polarizability criterion. These functions have been successfully applied to the calculation of the polarizabilities, a and 7, for the He, Be and Ne atoms and the molecule. 

Now with the 2p valence polarization, it is possible to partly describe the polarizability since the first step of calculation with the unperturbed wavefunction, especially the parallel component which is generally easier to calculate in CPHF. The optimized... 

This calculation has shown the importance of the basis set and in particular the polarization functions necessary in such computations. We have studied this problem through the calculation of the static polarizability and even hyperpolarizability. The very good results of the hyperpolarizabilities obtained for various systems give proof of the ability of our approach based on suitable polarization functions derived from an hydrogenic model. Field—induced polarization functions have been constructed from the first- and second-order perturbed hydrogenic wavefunctions in which the exponent is determined by optimization with the maximum polarizability criterion. We have demonstrated the necessity of describing the wavefunction the best we can, so that the polarization functions participate solely in the calculation of polarizabilities or hyperpolarizabilities. 

Both objects are much less complicated than the total A -particle wavefunction itself, since they only depend on three spatial variables. The electron density is manifestly positive (or zero) everywhere in space while the spin-density can be positive or negative. If, by convention, there are more spin-up than spin-down electrons, the positive part of the spin-density will prevail and there will usually be only small regions of negative spin-density that arise from spin-polarization. This spin-polarization is physically important and is already included in the UHF method but not in the ROHF method that, by construction, can only describe the... 

A basic principle in quantum mechanics is the indistinguishability of particles. Thus, as indicated in Section 10.5, two particles of the same type in an ideal gas are characterized by a wavefunction, say f(r, 0j, tp 0%, spherical polar coordinates. If for simplicity this wave-function is written as (1,2), the permutation of the coordinates of the two identical particles can be represented by... 

In common with similar approaches that relate solvent accessible surface to cavity free energy90-93, the simple SMI model required careful parameterization, and assumed that atoms interacted with solvent in a manner independent of their immediate molecular environment and their hybridization76. In more recent implementations of the SMx approach, ak parameters are selected for particular atoms based on properties determined from the SCF wavefunction that is evaluated during calculation of the solute and solvent polarization energies27. On the other hand, the inclusion of more parameters in the solvation model requires access to substantial amounts of experimental data for the solvation free energies of molecules in the training set94 95. 

Finally, the use of DNP of shallow donors to enhance both 67Zn and surface ft nuclear polarizations has been demonstrated in ZnO nanoparticles by observation of EPR features rather than direct NMR observation [85, 87]. The electronic wavefunctions of these donors in ZnO have been probed by ENDOR experiments [36, 97], There is much potential for directly observing NMR with the sensitivity greatly enhanced by DNP not only in ZnO but in other nanoparticles as well. 

The impurity interacts with the band structure of the host crystal, modifying it, and often introducing new levels. An analysis of the band structure provides information about the electronic states of the system. Charge densities, and spin densities in the case of spin-polarized calculations, provide additional insight into the electronic structure of the defect, bonding mechansims, the degree of localization, etc. Spin densities also provide a direct link with quantities measured in EPR or pSR, which probe the interaction between electronic wavefunctions and nuclear spins. First-principles spin-density-functional calculations have recently been shown to yield reliable values for isotropic and anisotropic hyperfine parameters for hydrogen or muonium in Si (Van de Walle, 1990) results will be discussed in Section IV.2. 

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