Electric dipolar moment

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. 

Dunham s consideration of available spectra of HCl in 1930 [1,2] resulted in production of a radial function for electric dipolar moment that we express in a contemporary form, similar to that in formula 56 but in terms of variable x, defined in formula 15, instead of z, defined in formula 21 ... 

At that time the permanent electric dipolar moment po of HCl had already been estimated to be 3.59 X10 C m [128], but Dunham made no use of this value hence we leave po in symbolic form. One or other value of coefficient p2 depends on a ratio (l/p(x) 0)/(2 p(x) 0) of pure vibrational matrix elements of electric dipolar moment between the vibrational ground state and vibrationaUy excited state V = 1 or 2. We compare these data with an extended radial function derived from 33 expectation values and matrix elements in a comprehensive statistical treatment [129],... 

On the basis of these formulae one can convert measurements of area, which equals the integral in the latter formula, under spectral lines into values of coefficients in a selected radial function for electric dipolar moment for a polar diatomic molecular species. Just such an exercise resulted in the formula for that radial function [129] of HCl in formula 82, combining in this case other data for expectation values (0,7 p(v) 0,7) from measurements of the Stark effect as mentioned above. For applications involving these vibration-rotational matrix elements in emission spectra, the Einstein coefficients for spontaneous emission conform to this relation. 

As an alternative procedure to predict coefficients of a radial function p(x) for electric dipolar moment, one might attempt to convert the latter function from polynomial form, as in formula 91, which has unreliable properties beyond its range of validity from experimental data, into a rational function [13] that conforms to properties of electric dipolar moment as a function of intemuclear distance R towards limits of united and separate atoms. When such a rational function is constrained to yield the values of its derivatives the same as coefficients pj in a polynomial representation, that rational function becomes a Fade approximant. For CO an appropriate formula that conforms to properties described above would be... 

Quantum-Chemical Calculations of Radial Functions for Rotational and Vibrational g Factors, Electric Dipolar Moment and Adiabatic Corrections to the Potential Energy for Analysis of Spectra... 

Computational spectrometry, which implies an interaction between quantum chemistry and analysis of molecular spectra to derive accurate information about molecular properties, is needed for the analysis of the pure rotational and vibration-rotational spectra of HeH in four isotopic variants to obtain precise values of equilibrium intemuclear distance and force coefficient. For this purpose, we have calculated the electronic energy, rotational and vibrational g factors, the electric dipolar moment, and adiabatic corrections for both He and H atomic centres for intemuclear distances over a large range 10 °m [0.3, 10]. Based on these results we have generated radial functions for atomic contributions for g g,... 

According to convention we suppose that the g factors of a neutral diatomic molecule can be partitioned into a term depending on the electric dipolar moment d or its derivative AdJAR and an irreducible non-adiabatic contribution g, [19,28]... 

For a molecular ion with charge number Q a transformation between isotopic variants becomes complicated in that the g factors are related directly to the electric dipolar moment and irreducible quantities for only one particular isotopic variant taken as standard for this species these factors become partitioned into contributions for atomic centres A and B separately. For another isotopic variant the same parameters independent of mass are still applicable, but an extra term must be taken into account to obtain the g factor and electric dipolar moment of that variant [19]. The effective atomic mass of each isotopic variant other than that taken as standard includes another term [19]. In this way the relations between rotational and vibrational g factors and and its derivative, equations (9) and (10), are maintained as for neutral molecules. Apart from the qualification mentioned below, each of these formulae applies individually to each particular isotopic variant, but, because the electric dipolar moment, referred to the centre of molecular mass of each variant, varies from one cationic variant to another because the dipolar moment depends upon the origin of coordinates, the coefficients in the radial function apply rigorously to only the standard isotopic species for any isotopic variant the extra term is required to yield the correct value of either g factor from the value for that standard species [19]. 

Although the relation between the vibrational g factor and the derivative of electric dipolar moment, equation (10), is formally equivalent to the relation between the rotational g factor and this dipolar moment, equation (9), there arises an important distinction. The derivative of the electrical dipolar moment involves the linear response of the ground-state wave function and thus a non-adiabatic expression for a sum over excited states similar to electronic contributions to the g factors. The vibrational g factor can hence not be partitioned in the same as was the rotational g factor into a contribution that depends only on the ground-state wave function and irreducible non-adiabatic contribution. Nevertheless g "(R) is treated as such. A detailed expression for ( ) in terms of quantum-mechanical operators and a sum over excited states, similar to equations (11) and (12), is not yet reported. 

Table 2. Calculated electric dipolar moment and derivative of dipolar moment ddJdR, both in atomic units, of in electronic ground state as a function of...

Of rows in the next group for electric properties, the fourth shows the total electric dipolar moment. The next five rows present an analysis of net electronic populations associated with each atomic centre, according to an atomic polar tensor [13] each value listed represents the net alteration of electronic population associated with a particular atomic centre through its participation as a constituent of the particular molecule in a specific isomeric form. To distinguish the two hydrogenic atomic centres if they lie in chemically inequivalent positions, is nearer a carbon atom than H likewise if the two nitrogens have inequivalent positions N, is nearer a carbon atom than Ni,. The next six rows present elements of a symmetric... 

Table 16-1. Energies, electric dipolar moments, net atomic populations, vibrational polarizabilities and mean vibrational molecular polarization, magnetizability and contributions thereto, isotropic g tensor and nuclear and electronic paramagnetic and diamagnetic contributions thereto, principal moments of inertia and rotational parameters calculated for H2 C N2 in seven structural isomers... 

Like electric dipolar moment, the magnetic and other electric, properties of molecules deduced from spectral experiments pertain inevitably to expectation... 

For cyanamide, the components of electric dipolar moment/10 C m parallel to inertial axes are = 14.14 and = 3.03 [33], slightly larger than our calculated values = 13.33 and p = 2.878 the total moment from experiment is 14.46 X 10 C m, correspondingly larger than our calculated value in Table 16-3. We compare our calculated rotational parameters with the effective rotational parameters/m for the vibrational ground state — A = 1041.19325, B = 33.78923475 and C = 32.90918052 [34], which are all a little larger than the calculated values. Our calculations indicate that both these isomers have a nonlinear spine, consistent with experiment for both structural isomers those calculated internuclear distances, in Table 16-3, agree satisfactorily with the values deduced from experiment for cyanamide. 

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