Electronic state potentials

Fourier transform of a time dependent function that involves dynamical motions on the initial and final electronic states potential energy surfaces. 

Fig. 12.2 Left The ground (X, solid line), excited (6, dashed line) and dissociative [a1g(3II), dotted line] electronic state potentials of the iodine molecule. The arrow indicates the electronic excitation. The initial excited wave packet is located in the Franck-Condon region near to the inner classical turning point of the B state. The transition from the B to the a state is forbidden by symmetry in the isolated molecule but becomes allowed when the molecule is placed in a solvent.

Raman Spectroscopy The time-dependent picture of Raman spectroscopy is similar to that of electronic spectroscopy (6). Again the initial wavepacket propagates on the upper excited electronic state potential surface. However, the quantity of interest is the overlap of the time-dependent wavepacket with the final Raman state 4>f, i.e. < f (t)>. Here iff corresponds to the vibrational wavefunction with one quantum of excitation. The Raman scattering amplitude in the frequency domain is the half Fourier transform of the overlap in the frequency domain,... 

The remainder of this paper is organized as follows In Sect. 5.2, we present the basic theory of the present control scheme. The validity of the theoretical method and the choice of optimal pulse parameters are discussed in Sect. 5.3. In Sect. 5.4 we provide several numerical examples i) complete electronic excitation of the wavepacket from a nonequilibrium displaced position, taking LiH and NaK as examples ii) pump-dump and creation of localized target wavepackets on the ground electronic state potential, using NaK as an example, and iii) bond-selective photodissociation in the two-dimensional model of H2O. A localized wavepacket is made to jump to the excited-state potential in a desirable force-selective region so that it can be dissociated into the desirable channel. Future perspectives from the author s point of view are summarized in Sect. 5.5. 

Csaszar AG, Allen WD, Yamaguchi Y, Schaefer III HF (2000) Ab initio determination of accurate ground electronic state potential energy hypersurfaces for small molecules. In Jensen P, Bunker PR (eds) Computational molecular spectroscopy, Wiley, United Kingdom, ppl5-69... 

Within the separable harmonic approximation, the < f i(t) > and < i i(t) > overlaps are dependent on the semi-classical force the molecule experiences along this vibrational normal mode coordinate in the excited electronic state, i.e. the slope of the excited electronic state potential energy surface along this vibrational normal mode coordinate. Thus, the resonance Raman and absorption cross-sections depend directly on the excited-state structural dynamics, but in different ways mathematically. It is this complementarity that allows us to extract the structural dynamics from a quantitative measure of the absorption spectrum and resonance Raman cross-sections. 

The case of a very weakly re-hydrogen bonded fluorobenzene-methanol complex. A gradient-corrected density functional and MP2 study of the ground electronic state potential energy surface118... 

We consider a system for which there can be a reaction on the ground-electronic-state potential energy surface, and ask how that reaction can be mediated by excitation to, evolution on, and stimulated deexcitation from, an excited electronic state. The excitation and stimulation pulse shapes, durations, and separations required to achieve selectivity of product formation depend on the properties of the excited-state potential energy surface. In the relevant time domain, which is defined by the shape of the excited-state potential energy surface, we shall show that it is possible to take advantage of the localization in phase space of the time-dependent quantum mechanical amplitude and thereby carry our selective chemistry. 

Studies of this system show a broad range of control over the I to I product ratio. For example, a superposition of ,> and 3> (the first and third vibrational states of the ground-electronic-state potential energy surface) allows an increase of the yield of I from 30%, the value attained by excitation with one frequency, to more than 70%. Furthermore, using a diatomic model for CH3I, BS were able to define conditions which reduce the I yield to zero or increase it fully to one. 

Ballhausen s latest book [30], Molecular Electronic Structures of Transition Metal Complexes appeared in 1979, 25 years after his first article. It can be seen as his answer to the question What is a molecule - in particular a transition metal complex He starts with his conclusion from a series of articles on the chemical bond [31], Chemistry is one huge manifestation of quantum mechanics . He then introduces the Bom-Oppenheimer approximation as the basis for applying electronic and nuclear coordinates, and lets the picture of a molecule unfold itself with the concepts of electronic states, potential surfaces, transitions, vibronic couplings, etc. The presentation is traditional, but contains many refinings in the discussion of a molecule s ground state as well as its excited states. The world of transition metal complexes is favoured through the choice of examples. 

Figure 19 The Raman spectrum and time cross correlation function when the motion on the excited electronic state potential is anharmonic, compare to Figs. 17 and 18, which are for a harmonic approximation. (Top, a) Computed time correlation function using a wide window function (b) The maximal entropy representation of this function, determined from the spectrum. Note the clear separation of time scales due to the anharmonicity (cf. Fig. 20). (Bottom) The Raman excitation spectrum obtained from the computed time correlation function (a). The arrows are the sequence of computations (a) is determined from the dynamics. The spectrum is determined from (a). The maximum entropy cross-correlation function (b) uses only the spectrum as input.

Csaszar, A.G., Allen, W.D., Yamaguchi, Y, Schaeter III, H.F. Ab initio determination of accurate ground electronic state potential energy hypersurtaces for small molecules, in Jensen, P., Bunker, P.R., editors. Computational Molecular Spectroscopy. New York Wiley 2000, p. 15-68. 

That is, transitions are normally between states of the same spin. Other selection rules may relate to the geometrical symmetry of the molecule. The molecular transitions seen in the visible and ultraviolet regions of the spectrum must be transitions from one rotational-vibrational-electronic state to another. We shall consider this in detail for a hypothetical diatomic molecule for which the ground state and excited state potential curves are those shown in Figure 10.8. For both electronic state potential energy curves there are sets of vibrational states and rotational sublevels. Notice that the equilibrium distance is not the same for both curves and that the curvature (i.e., the force constant) is not the same either. Thus, there are a different vibrational frequency and a different rotational constant for each electronic state. This has to be taken into account in working out the transition frequencies. 

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