Electronic Structure. Potential Energy Functions

1 Electronic Structure. Potential Energy Functions Valence States 

NH2 is one of the first and one of the best examples of the Renner-Teller effect. The very detailed analysis of the NH2 absorption spectrum by Dressier and Ramsay [3] showed that the spectrum is based on a transition between the two electronic states and 

Potential curves for the symmetric and antisymmetric stretching were calculated by ab initio SCF and Cl methods [20]. Potential curves for NH2 as a function of one NH bond length (second bond length and bond angle are fixed) were obtained by ab initio SCF calculations up to the dissociation limit [21, 25]. The shape of the potential energy curve 

Total energies of twelve core-hole states were calculated by using ab initio Cl methods. These Rydberg states belong to the vertical excitations from a 1ai electron in the ground state X Bi into four quartet (two one Ai, and one A2 and eight doublet (four Bi, two Ai, and two As) states [28]. 

Ionization potentials of NH2 were measured by photoelectron spectroscopy (PES), by photoionization (PI) and electron impact (El) mass spectrometry, and were calculated by ab initio methods (MCSTEP, MP4, MCSCF). The first two adiabatic ionization potentials of NH2 are listed in the following table. 

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One of the important electrochemical interfaces is that between water and liquid mercury. The potential energy functions for modeling liquid metals are, in general, more complex than those suitable for modeling sohds or simple molecular liquids, because the electronic structure of the metal plays an important role in the determination of its structure." However, based on the X-ray structure of liquid mercury, which shows a similarity with the solid a-mercury structure, Heinzinger and co-workers presented a water/Hg potential that is similar in form to the water/Pt potential described earlier. This potential was based on quantum mechanical calculations of the adsorption of a water molecule on a cluster of mercury atoms. ... 

The characteristic structure of the actinide spectra is mainly determined by the special properties of the 5 f wave functions these, in turn, arise from the special nature of the 5 f effective potential-energy function Ueff (5f). Uetf describes the effect on the 5 f electrons of the attraction by the nucleus as well as of all the interactions with other electrons. It contains also a centrifugal term, 1(1 -I- l)/2 r, of particular importance for the properties of 5f wave functions, the effect of which will be illustrated later in more detail. 

We have shown the molecular orbital theory origin of structure - function relationships for electronic hyperpolarizability. Yet, much of the common language of nonlinear optics is phrased in terms of anharmonic oscillators. How are the molecular orbital and oscillator models reconciled with one another The potential energy function of a spring maps the distortion energy as a function of its displacement. A connection can indeed be drawn between the molecular orbitals of a molecule and its corresponding effective oscillator . 

In order to explain the band structure for the small confinement regime the nature of the potential energy function in the Hamiltonian has been examined in the internal space. Since, for quasi-one-dimensional quantum dots, the electrons can only move along the z coordinate, their x and y dependence is neglected in the analysis. The internal space is defined by a unitary transformation from the independent electron coordinates (z, Z2, , zn) into the correlated electron coordinates (za, zp,...). The coordinate za represents the totally symmetric center-of-mass coordinate za = 7=(zi + Z2 + + zn), and the remaining correlated electron coordinates zp,..., zn represent the internal degrees of freedom of the N electrons [20,21]. In the case of two electrons the correlated coordinates are defined by... 

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