Transition internuclear separation

The reason why one chose to follow the main liquid-crystalline to gel phase transition in DPPC by monitoring the linewidth of the various or natural abundance resonance is evident when we consider the expressions for the spin-lattice relaxation time (Ti) and the spin-spin relaxation time T2). The first one is given by 1/Ti oc [/i(ft>o) + 72(2ft>o)] where Ji coq) is the Fourier transform of the correlation function at the resonance frequency o>o and is a constant related to internuclear separation. The relaxation rate l/Ti thus reflects motions at coq and 2coq. In contrast, the expression for T2 shows that 1/T2 monitors slow motions IjTi oc. B[/o(0) -I- /i(ft>o) + /2(2u>o)], where /o(0) is the Fourier component of the correlation function at zero frequency. Since the linewidth vi/2 (full-width at half-maximum intensity) is proportional to 1 / T2, the changes of linewidth will reflect changes in the mobility of various carbon atoms in the DPPC bilayer. 

The oscillatory structure just mentioned has been clearly demonstrated to result from quantum-mechanical phase-interference phenomena. The necessary condition264,265 for the occurrence of oscillatory structure in the total cross section is the existence in the internuclear potentials of an inner pseudocrossing, at short internuclear distance, as well as an outer pseudo-crossing, at long internuclear distance. A schematic illustration of this dual-interaction model, proposed by Rosenthal and Foley,264 is shown in Fig. 37. The interaction can be considered to involve three separate phases, as discussed by Tolk and et al. 279 (1) the primary excitation mechanism, in which, as the collision partners approach, a transition is made from the ground UQ state to at least two inelastic channels U, and U2 (the transition occurs at the internuclear separation 7 , the inner pseudocrossing, in Fig. 37), (2) development of a phase difference between the inelastic channels,... 

A linear approximation of the potential is certainly too sweeping a simplification. In reality, Vr varies with the internuclear separation and usually rises considerably at short distances. This disturbs the perfect (mirror) reflection in such a way that the blue side of the spectrum (E > Ve) is amplified at the expense of the red side (E < 14).t For a general, nonlinear potential one should use Equations (6.3) and (6.4) instead of (6.6) for an accurate calculation of the spectrum. The reflection principle is well known in spectroscopy (Herzberg 1950 ch.VII Tellinghuisen 1987) the review article of Tellinghuisen (1985) provides a comprehensive list of references. For a semiclassical analysis of bound-free transition matrix elements see Child (1980, 1991 ch.5), for example. 

These dynamical parameters are integrals over the internuclear separations R, as well as the electronic coordinates r through the electronic transition dipole matrix elements, R). These electronic transition dipole matrix elements... 

Figure I. Schematic representation of the multiphoton process for studying the selective photolysis of Oj. Typical molecular potentials are plotted as functions of internuclear separation with radiative transitions shown by arrows. The first transition causing photolysis is designated la for predissociation or lb for direct dissociation. The second transition used to excite the dissociation products, Cs, to the readily ionized state, Cs is 2 and 2 shows a possible transition for fluorescent...

A demonstration of the efficacy of MBER spectroscopy is the recent experiments on HF carried out by Bass, DeLeon, and Muenter [14]. In an effort to obtain Stark, Zeeman, and hyperfine properties, measurements were made that gave accurate values for both the ground and first excited vibrational levels of HF. Conventional resonance experiments can be done if the D = 1 state can be sufficiently populated. Using a color center IR laser to excite HF to u = 1, J = 1 levels, all the properties measured for the u = 0 and V = 1 states had essentially identical precision. The results included dipole moments, magnetic shielding anisotropies, rotational magnetic moments, magnetic susceptibilities, transition moments, and first and second derivatives with respect to internuclear separation of the properties. 

The electronic transition from the ground state to an electronically excited state will often entail changes in vibrational as well as electronic energy. This results from excitation of the molecule to one of the various vibronic levels of the excited electronic state. This process can be illustrated by a diagram of potential energy versus internuclear separation. Such a diagram is very difficult to represent for a polyatomic molecule, but it can be instructive for a diatomic molecule (Fig. 5). 

Fig. 5 The influence of the Franck-Condon principle on the appearance of the absorption band in a diatomic molecule where the equilibrium internuclear separations are (a) identical in the ground and excited states, (b) smaller in the excited state, and (c) greater in the excited state. The spectra representations (d), (e), and (f) correspond to the situations depicted in (a), (b), and (c), respectively. The numbers in (a) represent the vibrational quantum numbers in the ground and excited states and in (d), (e), and (f) the transitions between these sublevels.

Hefferlin, R., Davis, W.B., and Ileto, J. 2003. An Atlas of Forecasted Molecular Data I Internuclear Separations of Main-Group and Transition-Metal Neutral Gas-Phase Diatomic Molecules in the Ground State. Journal of Chemical Information Computer Science 43 622-628. 

Consider two electronic states between which a transition is permitted the two curves in Fig. 25.9 show the variation in the electronic energy with internuclear separation in the two states. The vibrational energy levels are shown as the horizontal lines and are labeled with the vibrational quantum numbers. In addition, very closely spaced rotational levels are associated with every vibrational level these are only shown next to the lowest level in each state. 

Table 5. Calculated energy differences between isoelectronic pairs of neutral and positively-charged diatomic hydrides. An internuclear separation of 1.0 A was used for all systems. All values are in hartrees. Percentage differences from Exn-Evi/ are given in parentheses. The transition state nuclear charge for the nonhydrogen atom is given by Z ...

In the limit R —0, each spheroidal eigenfunction n m > reduces to a particular spherical function n/m >, specified by a —> —1(1 -h 1). Likewise, in the limit R —> oo, each nam > becomes a particular parabolic function nrm >, which in turn can be obteuned from Equation (8) as a linear combination of spherical functions with the gi given by the Clebsch-Gordan coefficients.[9] Regardless of the internuclear separation, and, consequently, of the coordinate system chosen, the total number of nodes of the eigenfunctions is conserved at n — m — 1. Other aspects of the transition to these limits have been examined and illustrated by Coulson and Robinson. [6]... 

The molecular transition has a dipole transition moment iJi(R) that depends on the internuclear separation R(A B) and that approaches zero fovR oo [1094]. It is caused by the induced dipole-dipole interaction from the polarizability of the collision partners. 

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