Surface-dipole moment

Ha T-K, Lewerenz M, Marquardt R and Quack M 1990 Overtone Intensities and dipole moment surfaces for the Isolated CH chromophore In CHD3 and CHF3 experiment and ab initio theory J. Chem. Phys. 93 7097-109... 

Absorption and Resonance Emission Spectra of S02(X1A2/C1B2) Calculated from Ab Initio Potential Energy and Transition Dipole Moment Surfaces. 

The electrical double layer has been dealt with in countless papers and in a number of reviews, including those published in previous volumes of the Modem Aspects of Electrochemistry series/ The experimental double layer data have been reported and commented on in several important works in which various theories of the structure of the double layer have been postulated. Nevertheless, many double layer-related problems have not been solved yet, mainly because certain important parameters describing the interface cannot be measured. This applies to the electric permittivity, dipole moments, surface density, and other physical quantities that are influenced by the electric field at the interface. It is also often difficult to separate the electrostatic and specific interactions of the solvent and the adsorbate with the electrode. To acquire necessary knowledge about the metal/solution interface, different metals, solvents, and adsorbates have been studied. 

H. Lin, J. Zheng, and W. Thiel, Mol. Phys., 2005, 103, 359], and it makes use of dipole moment surfaces calculated ab initio. We apply the theory to NH3 and demonstrate that the theoretical results show good agreement with experimental findings. 

We have also checked the effect on the rms deviation of including higher order terms in equation (46). Extending the expansion in equation (46) to sixth order, we obtain an rms deviation of 0.00006 D in the fitting to the 3X14,440 ab initio dipole moment values. However, the number of parameters required is about 400, substantially more than with the fourth-order expansion. These results demonstrate the very high internal consistency (i.e., smoothness) of the ab initio dipole moment surface. 

Having derived the symmetry relations between the expansion parameters in equation (55), we can proceed to fit the expansions through the ab initio dipole moment values. The expansion parameters in the expressions for and fiy are connected by symmetry relations since these two quantities have E symmetry in and so and fiy must be fitted together. The component ji, with A" symmetry, can be fitted separately. The variables p in equation (55) are chosen to reflect the properties of the potential surface, rather than those of the dipole moment surfaces. Therefore, the fittings of fi, fiy, fifi require more parameters than the fittings of the MB dipole moment representations. We fitted the 14,400 ab initio data points using 77 parameters for the component and 141 parameters for fi, fiy. The rms deviations attained were 0.00016 and 0.0003 D, respectively. 

The transition moments are calculated from the ab initio dipole moment surface, represented in the xyz axis system as described above. They are defined as... 

The accuracy of the dipole moment surfaces is documented by the calculated transition moments in Table 3. 

In Fig. 5, the agreement of the calculated absolute intensity values with the corresponding experimental values is an indication of the high quality of the ab initio dipole moment surfaces employed in the calculation. The qualitatively correct appearance of the bands indicates that our solution of the rotation-vibration Schrodinger equation and the potential energy surface employed are satisfactory. It should be emphasized that the ab initio potential energy and dipole moment surfaces have not been adjusted to fit experiment. 

VISCOSITY, DIELECTRIC CONSTANT, DIPOLE MOMENT, SURFACE TENSION, AND REFRACTIVE INDEX... 

As already mentioned, one of the main weaknesses of the simple reflection method is the fact that the electronic transition dipole moment, (or the transition dipole moment surface, TDMS for polyatomic molecules in Section 4) is assumed to be constant. This weakness will remain in the Formulae (12), (27) and (29) derived below. The average value of the square of the TDM (or TDMS) is then included in amplitude A and A = A /V. In Formulae (3), (3 ) and (3") the mass (or isotopologue) dependent parameters are p and the ZPE. In contrast, W and V., which define the upper potential, are mass independent. This Formula (3) is already known even if different notations have been used by various authors. As an example, Schinke has derived the same formula in his book [6], pages 81, 102 and 111. Now, the model will be improved by including the contribution of the second derivative of the upper potential at Re- The polynomial expansion of the upper potential up to second order in R - Re) can be expressed as ... 

Here E,j, is the energy of the initial state and R is the nuclear geometry. The division by 3 in (14) comes from orientational averaging. In this form, calculation of the absorption cross section requires the initial vibrational wave function, the transition dipole moment surface and the excited state potential. The reflection principle can be employed for direct or near direct photodissociation. It is again an approximation where the ground state wave function is reflected off the upper potential curve or surface. Prakash et al and Blake et al. [84-86] have used this theory to calculate isotope effects in N2O photolysis. 

W. Hiickel. The American FIAT Re--view 35, 1-34 (1950). Review association, dipole moments, surface tension, IR, dielectric constants. 

Buenker, R. J., Bonacic Koutecky, V., Pogliani, L., Potential energy and Dipole moment Surfaces for Simultaneous Torsion and Pyramidalization of Ethylene in Its Lowest lying Singlet Excited States A Cl Study of the Sudden Polarization Effect, J. Chem. Phys. 1980,73, 1836 1849. 

Lodi, L., Tolchenov, R.N., Tennyson, J., Lynas-Gray, A.-E., Shirin, S.V., Zobov, N.F., Polyansky, O.L., Csaszar, A.G., van Stralen, J.N.R, Visscher, L. A new ab initio ground state dipole moment surface for the water molecule, J. Chem. Phys. 2007, submitted. 

Here we describe the essential features of the application of the lOSA to reactive photodissociation. More details of the approach will be published elsewhere [ 53]. We wish to calculate the photodissociation cross sections I discussed in Section 1. For most problems, the transition dipole moment surface i will not be known. It is unlikely that will have a significant effect as it is not a highly oscillatory function like the scattering wavefunction, nor a highly localized function like the bound state. Thus, it should be a reasonable approximation to compute... 

G. S. Kedziora and I. Shavitt, Calculation and Fitting of Potential Energy and Dipole Moment Surfaces for the Water Molecule FuUy ab initio Determination of Vibrational Transition Energies... 

Beside spectroscopic and thermodynamic isotope effects treated in the preceding sections, isotope effects related to the structure of the molecules manifest themselves in a variety of physical and physicochemical properties, such as density, permittivity, compressibility, dipole moment, surface tension, etc. It is not possible to give a comprehensive treatment of the subject here useful reviews have been given among others by Rabinovich (1970) and Jancso and Van Hook (1974). For illustration of the magnitude of the isotope effects, differences in various physical properties between water and heavy water are collected in Tahh 15.1. 

Note that the alignment axis Z and the direction Z of propagation of the electromagnetic field do not coincide. The electric field is then rotated in the M molecular frame, in which we know the three dipole moment surfaces, via theL and M frames through the series of transformations... 

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