Wave functions vibronic

Figure 3, Wavepacket dynamics of the photodissociation of NOCl, shown as snapshots of the density (wavepacket amplitude squared) at various times, The coordinates, in au, are described in Figure b, and the wavepacket is initially the ground-state vibronic wave function vertically excited onto the 5i state. Increasing corresponds to chlorine dissociation. The density has been integrated over the angular coordinate. The 5i PES is ploted for the geometry, 9 = 127, the ground-state equilibrium value,...

Vo + V2 and = Vo — 2 (actually, effective operators acting onto functions of p and < )), conesponding to the zeroth-order vibronic functions of the form cos(0 —4>) and sin(0 —(()), respectively. PL-H computed the vibronic spectrum of NH2 by carrying out some additional transformations (they found it to be convenient to take the unperturbed situation to be one in which the bending potential coincided with that of the upper electi onic state, which was supposed to be linear) and simplifications (the potential curve for the lower adiabatic electi onic state was assumed to be of quartic order in p, the vibronic wave functions for the upper electronic state were assumed to be represented by sums and differences of pairs of the basis functions with the same quantum number u and / = A) to keep the problem tiactable by means of simple perturbation... 

The zeroth-order vibronic wave function is ut- Uy 0 0-I-). The zeroth-order energy is... 

IT. Total Molecular Wave Functdon TIT. Group Theoretical Considerations TV. Permutational Symmetry of Total Wave Function V. Permutational Symmetry of Nuclear Spin Function VT. Permutational Symmetry of Electronic Wave Function VIT. Permutational Symmetry of Rovibronic and Vibronic Wave Functions VIIT. Permutational Symmetry of Rotational Wave Function IX. Permutational Symmetry of Vibrational Wave Function X. Case Studies Lis and Other Systems... 

VII. PERMUTATIONAL SYMMETRY OF ROVIBRONIC AND VIBRONIC WAVE FUNCTIONS... 

Figure 10. Low-energy vibronic levels in the X2II state of HCCS computed in various approximations [152]. Hq zeroth-order approximation (both vibronic and spin-orbit couplings neglected). Hi. vibronic coupling taken into account, spin-orbit interaction neglected. Hi + Hs0 both vibronic and spin-orbit couplings taken into account. Solid horizontal lines K = 0 vibronic levels dashed line K — 1 dash-dotted lines K = 2 dotted lines K — 3. Values of the quantum numbers V4, N of the basis functions dominating the vibronic wave function of the level in question are indicated. Approximate correlation of vibronic states computed in various approximations is indicated by thin lines. In all cases the stretching quantum numbers are assumed to be zero.

VII. Permutational Symmetry of Rovibronic and Vibronic Wave Functions... 

Vibronic wave function, 283 Vinyl radical, 104,377-378 Virtual orbitals, 68,69... 

The complete wave function of a molecule is called the rovibronic wave function. In the simplest approximation, the rovibronic function is a product of rotational, vibrational, and electronic functions. For certain applications, the rotational motion is first neglected, and the vibrational and electronic motions are treated together. The rotational motion is then taken into account. The wave function for electronic and vibrational motion is called the vibronic wave function. Just as we separately classified the electronic and vibrational wave functions according to their symmetries, we can do the same for the vibronic functions. In the simplest approximation, the vibronic wave function is a product of electronic and vibrational wave functions, and we can thus readily determine its symmetry. For example, if the electronic state is an e2 state and the vibrational state is a state, then the vibronic wave function is... 

W. H. Miller In treating electronically nonadiabatic processes one often introduces (usually on physical grounds) a diabatic model, which has a nondiagonal electronic potential matrix, and then neglects any remaining derivative coupling. The total (vibronic) wave function is... 

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