Electric dipole moment function

The vibrational intensities B(0 v) of fundamental and overtone modes may be related to the electric dipole moment function M(r) around the equilibrium internuclear distance of the diatomic molecule (Chackerian, 1976) via rotationless matrix elements... 

To determine an accurate electric dipole moment function (EDMF) for the X n state of OH requires a very high level of correlation treatment, since it is necessary to properly account for the O" character in the wave function. To calibrate approximate methods, an FCI dipole moment was computed at five representative r values using a [4s3p2d/2slp] Gaussian basis set. Of the variety of approximate methods compared with the FCI, the CASSCF/MRCI treatment reproduced the F( I results best, with an error of only 0.001 Aq in the position of the dipole moment maximum. The MRCI spectroscopic constants are also in excellent agreement with the FCI. At this level of correlation treatment, it did not make a substantial difference... 

An important property of molecules is the behavioiu of the electric dipole moment function near the equilibrium configuration, and the changes which oc cur on vibrational excitation. Electric resonance studies of the HCl molecule in its electronic ground state, carried out by Kaiser [90] are important in this respect, and also in showing, through the Cl quadrupole interaction, how the electric field gradient changes on vibrational excitation. 

Remark Electric dipole moment function determined from experimental data in [87Huf]. ... 

In a similar study Weis et al. [31] reported CEPA electric dipole moment functions of HCF (Z A and a A") represented by polynomials of the 4th order in the form of Eq. (19). Vibrational dipole moment matrix elements for a number of bands were calculated. 

This equation, with a = 0.25, was based on the observed electric dipole moments of HC1, HBr, and HI. Since then the value of the dipole moment of HF has been determined it is 1.98 D, which corresponds to 47% ionic character, whereas Equation 5 with a = 0.25 gives 59%. It seems justified to formulate an empirical function, based on the values 5, 11, 17, and 47% for the hydrogen halides HI, HBr, HC1, and HF, as calculated from their... 

Vibrational Properties. Figures 4 and 5 show the variation of the energy Eg and the electric dipole moment p as a function of the relevant geometrical variables for H2O and NHg respectively. For the Internal variables, the curves corresponding to the Isolated molecules are also shown (dashed lines) for comparison lhe20Sclllatlon frequencies v and dipole matrix elements <1, sre also... 

For any molecular vibration that leads to infrared absorption, there is a periodic change in electric dipole moment. In case the direction of this change is parallel to component of the electric vector of the infrared radiation, absorption takes place otherwise it does not. In oriented bulk polymers, the dipole-moment change can be confined to specified directions. The use of polarised infrared radiation in such a case leads to absorption which is a function of the orientation of the plane of polarisation. The... 

There are two rather different questions that arise when considering ionic structures in VB wave functions. The first of these we discuss is the contribution to electric dipole moments. LiH is considered as an example. In the next section we take up ionic structures and curve crossings, using LiF to illustrate the points. 

LiH is the simplest uncharged molecule that has a permanent electric dipole moment. We examine here some of the properties of the simplest VB functions for this molecule. The molecule is oriented along the z-axis with the Li atom in the positive direction. 

We also calculated the dipole moment functions for CO, BF, and BeNe with an ST03G basis, and it can be seen in Fig. 12.2 that there are real difficulties with the minimal basis. We have argued that the numerical value and sign of the electric... 

We can examine how induced polarization behaves as a function of an applied electric field, ( , by considering the induced electric dipole moment (cf. Section 6.1.2.2), as a Taylor series expansion in... 

An additional point that should be considered is that in the harmonic oscillator approximation, the selection mle for transitions between vibrational states is Ay = 1, where v is the vibrational quantum number and Ay > 1, that is, overtone transitions, which involve a larger vibrational quantum number change, are forbidden in this approximation. However, in real molecules, this rule is slightly relaxed due to the effect of anharmonicity of the oscillator wavefunction (mechanical anharmonicity) and/or the nonlinearity of the dipole moment function (electrical anharmonicity) [55], affording excitation of vibrational states with Ay > 1. However, the absorption cross sections for overtone transitions are considerably smaller than for Ay = 1 transitions and sharply decrease with increasing change in Av. 

If incident radiation with a frequency equal to one of the fundamental frequencies falls on a molecule, it may make a transition from the ground state to the appropriate fundamental level. These normal frequencies usually occur in the infra-red spectral region. The probability of such a transition occurring, however, depends on the relationship between the molecule s electric dipole moment (as a function of the nuclear coordinates) and the wavefunctions of the ground state and of the fundamental level. 

Like many other properties of the N-particle system, the electric dipole moment, p(p, q, t), is a function of the canonical variables and time. We define the classical dipole autocorrelation function, according to... 

The motion of the electrons is treated in the adiabatic approximation. For absorption in the infrared, the electrons remain in the ground state. The electric dipole moment of the complex of two molecules is the expectation value of the dipole moment operator over the ground electronic state, which is a function of the nuclear coordinates only. Specifically, the dipole moment of a complex of n molecules is dependent on the vibrational (r,) and orientational ( ,) coordinates, and on the position (J ,-) of the mass centers of the molecules i, for 1 < i < n,... 

Equation 3-15 leads to the amounts of ionic character for various values of the electronegativity difference given in Table 3-10. The function is shown as the curve in Figure 3-8, together with the experimental values of the ratio of the observed electric dipole moment to the product of the electronic charge and internuclear distance for a number of diatomic molecules composed of univalent elements. Points are... 

Fro. IX-1.—Values of the ratio of polarisation P to field strength E for hydrogen chloride gas, as a function of the reciprocal of the absolute temperature. The slope of the line is a measure of the permanent electric dipole moment of the molecules, and the intercept of the line is a measure of the temperature-independent polarizability of the molecules. 

To deduce whether a transition is allowed between two stationary states, we investigate the matrix element of the electric dipole-moment operator between those states (Section 3.2). We will use the Born-Oppenheimer approximation of writing the stationary-state molecular wave functions as products of electronic and nuclear wave functions ... 

The first term in the square bracket in this equation is the electric monopole moment, which is equal to the nuclear charge, Ze. The second term in the square bracket is the electric dipole moment while the third term in the square bracket is the electric quadmpole moment. For a quantum mechanical system in a well-defined quantum state, the charge density p is an even function, and because the dipole moment involves the product of an even and an odd function, the corresponding integral is identically zero. Therefore, there should be no electric dipole moment or any other odd electric moment for nuclei. For spherical nuclei, the charge density p does not depend on 0, and thus the quadmpole moment Q is given by... 

For slow collisions the transitions occur from the continuum state of the J — 0 (spherical) symmetry to the bound state of the J = 1 symmetry, and are induced by the electric dipole moment of the H — H system. This dipole moment is the expectation value of the dipole moment operator for all four particles with respect to the ground state leptonic wave function, D = where r, denote the positions of... 

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