Dipole function, spectroscopic

Spectroscopic measurement. Specifically, if the induced dipole moment and interaction potential are known as functions of the intermolecular separation, molecular orientations, vibrational excitations, etc., an absorption spectrum can in principle be computed potential and dipole surface determine the spectra. With some caution, one may also turn this argument around and argue that the knowledge of the spectra and the interaction potential defines an induced dipole function. While direct inversion procedures for the purpose may be possible, none are presently known and the empirical induced dipole models usually assume an analytical function like Eqs. 4.1 and 4.3, or combinations of Eqs. 4.1 through 4.3, with parameters po, J o, <32, etc., to be chosen such that certain measured spectral moments or profiles are reproduced computationally. 

In recent years, a dependable dipole function for He-Ar, last column of Table 4.3, has been obtained [278] which we compare with the universal dipole function mentioned [23], Fig. 4.5. The He-Ar interaction potential is one of the better known functions [13] and suggests Rmj = 6.518 bohr. Both functions were normalized to unity at the separation R = 5 bohr in the figure. The comparison shows that at small separations the logarithmic slope of the most dependable dipole function is roughly one half that of the universal p, and p diverges rapidly from p(R) for R — o. Similar discrepancies have been noted for other rare gas systems (Ne-Ar, Ne-Kr, and Ar-Kr [152]). Even if for these other systems the dipole function is not as well known as it is for He-Ar, it seems safe to say that for the rare gas mixtures mentioned the induced dipole function is definitely not identical with the universal function at the distances characteristic of the spectroscopic interactions the universal dipole function is not consistent with some well established facts and data. We note that the ratio of // (/ ) and the He-Ar potential is indeed reasonably constant over the range of separations considered (not shown in the figure). 

The same procedure is, in principle, employed in the case of water. Only the degree of complexity is far larger than in the case of simple fluids. Again, essentially two sources of information can be used. One is to compute the interaction energy of a pair of water molecules at some few hundreds of configurations and then fit these results to an analytical function. The second is to guess an analytical form and then determine the parameters of this function (often referred to as a model function) that best fit to some experimental quantities, e.g., second virial coefficient, dipole moment, spectroscopic data, etc. 

Another related issue is the computation of the intensities of the peaks in the spectrum. Peak intensities depend on the probability that a particular wavelength photon will be absorbed or Raman-scattered. These probabilities can be computed from the wave function by computing the transition dipole moments. This gives relative peak intensities since the calculation does not include the density of the substance. Some types of transitions turn out to have a zero probability due to the molecules symmetry or the spin of the electrons. This is where spectroscopic selection rules come from. Ah initio methods are the preferred way of computing intensities. Although intensities can be computed using semiempirical methods, they tend to give rather poor accuracy results for many chemical systems. 

Results. Figure 5.6 compares the classical and quantum profiles of the spectral function, VG (o), of He-Ar pairs at 295 K (light and heavy solid curves, respectively), over a wide frequency band. Whereas at the lowest frequencies the profiles are quite similar, at the higher frequencies we observe increasing differences which amount up to an order of magnitude. The induced dipole [278] and the potential function [12] are the same for both computations. Bound state contributions have been suppressed we have seen above that for He-Ar at 295 K, the spectroscopic effects involving van der Waals molecules amount to only 2% at the lowest frequencies, and to much less than that at higher frequencies. 

Solvatochromic data, specifically absorption or transition energies (E s), have been obtained for the dye phenol blue in supercritical fluids as a function of both temperature and pressure. These data will be used to compare the "solvent strength" of these fluids with liquid solvents. He will use the terms "solvent strength" and "Et" synonymously in this paper such that they include the magnitude of the polarizability/volume as well as the dipole moment. The "solvent strength" has been characterized by the spectroscopic solvatochromic parameter, E, for numerous liquid solvents (9 JU, J7,JJ3). 

Ground State of CO. The CO molecule has been extensively studied, both experimentally and theoretically. Table 14 compares ground-state 02+) spectroscopic constants calculated by the Hartree-Fock method109 and by the density functional approach99 with experiment.104 In addition to these spectroscopic constants, the polar nature of the molecule provides a further measurable quantity, the dipole moment. Since the intensities of infrared vibration-rotation bands allow the dipole moment to be determined as a function of C-O separation this provides a useful comparison with the results of ab initio calculations. For example, the positive sign obtained from the equilibrium dipole moment by Hartree-Fock calculations was viewed as a reason to question the negative value found experimentally, whereas the current view is that the positive sign is a defect of the Hartree-Fock method. 

In the following paragraphs we give selected examples of the use of our wavefunctions and potential curves to predict or confirm various spectroscopic features of the alkalis. We know of plans to observe Li2 spectra in at least two laboratories (23, 24) so some predictions regarding the spectra appear to be in order. Julienne (25) has used our wavefunctions for LI2 to calculate the electronic transition dipole moment function corres-... 

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