Induced dipole moment, calculation

On the other hand, electric dipolar moments of the solute molecules can be obtained with standard methods in ab initio molecular orbital calculations, whereas the induced dipole moments in solution are determined from differences between the values obtained in solution and in the gas phase. 

However, the behavior of the local descriptors of reachvity is somewhat different. The local quantities are calculated using the Lowdin-based method of population analysis [47], It was observed that when the electric held is applied toward the more electronegative atom of the systems HF and HCN, the value of its nucleophilicity (CFF for electrophilic attack) decreases with increasing held strength (Figure 25.2c). The variation of FF can be well supported with the variation in the induced dipole moment, given in Table 25.1, of the species in... 

In order to relate the dressed state population dynamics to the more intuitive semiclassical picture of a laser-driven charge oscillation, we analyze the induced dipole moment n) t) and the interaction energy V)(0 of the dipole in the external field. To this end, we insert the solution of the TDSE (6.27) into the expansion of the wavefunction Eq. (6.24) and determine the time evolution of the charge density distribution p r, t) = -e r, f)P in space. Erom the density we calculate the expectation value of the dipole operator... 

As the centres of gravity of the positive and negative charges in a molecule of HC1 do not coincide, it must have a dipole moment which, in a symmetrical molecule, can only be produced by polarization by an external field. It is worth while to accentuate the difference of a permanent dipole in a molecule HC1, which exists independently of the field, and the induced dipole moment in an atom, which is proportional to the field = ccF. In this example there are two charges e at a distance r giving a dipole moment of er. For NaCl, where the charges and the distance are known, p can be calculated thus... 

H2-H2 dipole. Early attempts to calculate the induced dipole moments from first principles were described elsewhere [281]. Only in recent times could the substantial problems of such computations be controlled and precise data be generated by SCF and Cl calculations, so that that the basis set superposition errors were small enough and the Cl excitation level is adequate for the long-range effects. The details of the computations are given elsewhere [282, 281],... 

Other systems. Calculations of induced dipole moments have been made for a number of other systems, for example, for alkali-inert gas atomic pairs [24, 76, 218, 359],... 

W. Meyer. Ab initio calculations of collision-induced dipole moments. In G. Birnbaum, ed., Phenomena Induced by Intermolec. Interactions, p. 29, Plenum Press, New York, 1985. 

For classical line shape calculations one needs the induced dipole moment as function of time, p(R(t)), averaged over angular momenta and speeds of relative motion. In other words, one solves Newton s equation of motion, or one of its integrals, of the two-particle system. After suitable averaging, one obtains the spectral profile by Fourier transform. 

The nematic mean-field U, the molecule-field interaction potential, WE, and the induced dipole moment, ju d, are evaluated at different orientations using Equation (2.263), and then the coefficients of their expansion on a basis of Wigner rotation matrices can be calculated, according to Equation (2.268). The permittivity is obtained by a self-consistency procedure, because the energy WE and the induced dipole moment / md, as well as the reaction field contribution to the nematic distribution function p( l), themselves depend on the dielectric permittivity. 

Support to these assumptions has recently come from the analysis of the coupling between electrostatic and dispersion-repulsion contributions to the solvation of a series of neutral solutes in different solvents [31]. It has been found that the explicit inclusion of both electrostatic and dispersion-repulsion forces have little effect on both the electrostatic component of the solvation free energy and the induced dipole moment, as can be noted from inspection of the data reported in Table 3.1. These results therefore support the separate calculation of electrostatic and dispersion-repulsion components of the solvation free energy, as generally adopted in QM-SCRF continuum models. 

We have that all the polarization sites having the induced dipole moment, /jl"", are denoted by the index a and furthermore we calculate the induced dipole moment as... 

However, it would be a serious error to confuse electronegativity or ionization energy with hardness . The clearest counter-example is Tl(III) which is a rather soft central atom but which must have a rather high ionization energy. There are other physical properties which accentuate the opposite inequality signs of (1) even more, for instance the electric polarizability. Table 1 contains many values for this quantity a in the unit 10-24 cm3. Gaseous atoms and positive ions have polarizabilities which can be calculated from wavefunctions (9) by evaluating the sum of matrix elements of induced dipole moment ... 

One of the most of important applications of quadratic response theory, pertaining to spin-orbit properties, is the calculation of the spin-orbit induced dipole moment (phosphorescence, see section 7), which can be derived from the residue... 

The magnitude of the induced dipole moment that is produced when an indole molecule in its ground Sq and electronically excited Si states is polarized by the attachment of a hydrogen-bonded water molecule in the gas-phase complex indole-H20 have been determined as /i I(So) = 0.7 D atid /t I(Si) = 0.5 D <2005JCP1743011>. The permanent dipole moment values for the complex (/tlW(So) =4.4D and /tlW(Si) = 4.0 D) are substantially different from calculated values based on vector sums of the dipole moments of the component parts. The orientation of the induced moment is also significantly different in the two electronic states. 

The statistical average over the electronic degrees of freedom in Eq. [15] is equivalent, in the Drude model, to integration over the induced dipole moments pg and py. The Hamiltonian H, is quadratic in the induced dipoles, and the trace can be calculated exactly as a functional integral over the fluctuating fields pg and The resulting solute-solvent interaction energy... 

Since the intensity calculation can be reduced to calculating a and for deformed molecules, the availability of quantum chemical methods immediately led to attempts to employ them to determine vibrational intensities (Segal and Klein, 1967). The polarizability is the proportionality factor between the induced dipole moment and the inducing electric field. It is therefore necessary to use a perturbation treatment which takes the electric field into account. Two different approaches were explored the Finite... 

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