Potential energy curves wave functions

Each unsealed 0 at a specific R, in the case of diatomic molecules, gives rise to a scaled energy curve the envelope of a family of such curves can be taken to be the optimal intemuclear potential energy. Exact wave functions, minimal STO-SCF wave functions optmized with respect to coefficients and orbital exponents, and Hartree-Fock wave functions yield the optimal intemuclear potential-energy curves which satisfy the virial. At the minimum in the optimal PE-curve (—V /2 R ) will be unity. McLean uses the Dunham analysis (3b) to determine the spectroscopic constants through the potential curve... 

However, because of the avoided crossing of the potential energy curves the wave functions of Vq and Fi are mixed, very strongly at r = 6.93 A and less strongly on either side. Consequently, when the wave packet reaches the high r limit of the vibrational level there is a chance that the wave function will take on sufficient of the character of Na + 1 that neutral sodium (or iodine) atoms may be detected. 

The wave function of Eqs. (14) and (15) was widely used to obtain BO potential energy curves and adiabatic corrections for the ground state (Kolos et al., 1986 Kotos and Rychlewski 1993, Wolniewicz 1993, 1995a) and electronically excited... 

Figure 22 Schematic drawing of nuclear wave functions with 30 (to the left) and 3 (to the right) vibrational quanta. The little dots indicate the vibrational wave function amplitude at the classical turning points of the potentials. Portions of the potential energy curves are shown as thick lines. The horizontal lines indicate the energy of the vibronic (vibrational plus electronic) states.

Fig. 2. Potential energy curves of F2 from all-electron (A.E.) and effective potential (E.P.) calculations using two-configuration MCSCF wave functions. 

Fig. 6. Average relativistic effective core potential and relativistic effective core potential energy curves for two states of Bi2. HF, Hartree-Fock GVB(pp), eight-configuration perfect-pairing generalized valence bond FVCI, full-valence Cl based on the GVB(pp) wave functions FV7R, full-valence Cl plus single and double promotions to virtual MOs relative to seven-dominant configurations. (The FVCI and FV7R calculations include the REP-based spin-orbit operator.)...

In the simple reflection principle model the vibrational wave function is determined for the lower (ground) electronic state. It is then reflected using the upper electronic potential onto the energy axis as sketched in Figure 7.2. The width of the spectrum is related to the width of the vibrational wave function in the ground state and to the slope of the dissociative potential energy curve. The differences between the model spectrum and the experimental spectrum in Figure 7.2 will be discussed in Section 6.1. 

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