Dipole moment, electric calculation

Figure 3. Absorption curve defining the maximum molar extinction coefficient as sf and the half band width at 8°/e as A,-. The dipole strength, Dg, which is the square of the magnitude of the electric transition dipole moment is calculated by the equation shown, as is the oscillator strength,. Reproduced, with permission, from [3].

At any level, a calculation of first-order properties simply reduces to a determination of an expectation value using the wave function P. For example, the electric dipole moment is calculated as... 

The perturbation operator in the calculation of electric dipole moments, electric dipole polarizabilities and hyperpolarizabilities, i.e. the electric dipole moment operator Eq. (4.30), contains the position vector r of the electrons, which implies that the tail of the wavefunction becomes important. However, this is not well described in GTOs as discussed before and it is therefore essential to include additional valence functions with very small exponents C - so-called diffuse basis functions. In the Pople-style basis sets this is done in the 6-31G-I- and 6-31G- -- - basis sets, where in the -h basis set one diffuse function is added only for second- and third-row atoms, while in the - -+ basis set one diffuse function is also added for hydrogen (Clark et al., 1983). In the series of correlation consistent and polarization consistent basis sets one set of diffuse functions of each type present in the basis set is added in the aug-cc-pVXZ (Kendall et at, 1992 Woon and Dunning Jr., 1993, 1994 Balabanov and Peterson, 2005) and aug-pc-n (Jensen, 2002c) version of these basis sets. In the series of correlation consistent basis sets it is also possible to add two or more sets of diffuse functions in the d-aug , t-aug and so forth versions. 

Essentially all experimentally measured properties can be thought of as arising through the response of the system to some externally applied perturbation or disturbance. In turn, the calculation of such properties can be formulated in terms of the response of the energy E or wavefunction P to a perturbation. For example, molecular dipole moments p are measured, via electric-field deflection, in terms of the change in energy... 

Now, the quadrupole moment can next be calculated by differentiating the potential to get the electric field due to the dipole moment. The reader can now see that an infinite series can be thus generated. The total electric field is simply the sum of all the individual multipole contributions, given by... 

Gaussian also predicts dipole moments and higher multipole moments (through hexadecapole). The dipole moment is the first derivative of the energy with respect to an applied electric field. It is a measure of the asymmetry in the molecular charge distribution, and is given as a vector in three dimensions. For Hartree-Fock calculations, this is equivalent to the expectation value of X, Y, and Z, which are the quantities reported in the output. 

Theoreticians did little to improve their case by proposing yet more complicated and obviously unreUable parameter schemes. For example, it is usual to call the C2 axis of the water molecule the z-axis. The molecule doesn t care, it must have the same energy, electric dipole moment and enthalpy of formation no matter how we label the axes. I have to tell you that some of the more esoteric versions of extended Hiickel theory did not satisfy this simple criterion. It proved possible to calculate different physical properties depending on the arbitrary choice of coordinate system. 

Basis-set sensitivity is important, as it was for the calculation of electric dipole moments. Several experimental values in the literamre refer to measurements corrected neither for zero-point vibrations nor for centrifugal effects. 

This is not an SCRF model, as the dipole moment and stabilization are not calculated in a self-consistent way. When the back-polarization of the medium is taken into account, the dipole moment changes, depending on how polarizable the molecule is. Taking only the first-order effect into account, the stabilization becomes (a is the molecular polarizability, the first-order change in the dipole moment with respect to an electric field, Section 10.1.1). 

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... 

Nevertheless, Murrell, Kettle, and Tedder conclude in their book on valence theory57 that there is no correlation between the electric dipole moment of a bond and the electronegativity difference. They have plotted the values of the electric dipole moments of eight bonds against the difference in the values of the Mulliken electronegativity (see Figure 1-2). (The bond moments for OH, NH, PH, NF, and PF are calculated from the... 

A sequence of calculations can be performed with various applied electric fields in which the dipole moment of the molecule is evaluated, as described above. The 3x3 polarisability tensor, can therefore be constructed. 

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