Dipole moment derivative

Pulay P, FogarasI G, Pang F and Boggs J E 1979 Systematic ab initio gradient calculation of molecular geometries, force constants and dipole moment derivatives J. Am. Chem. Soc. 101 2550... 

Force Constants and Dipole-Moment Derivatives of Molecules from Perturbed Hartree-Fock Calculations I J. Gerratt and I. M. Mills Journal of Physical Chemistry 49 (1968) 1719... 

Cheam, T. C., and S. Krimm. 1985. Infrared Intensities of Amide Modes in N-methyl-acetamide and Poly(Glycine I) From Ab Initio Calculations of Dipole Moment Derivatives of N-methylacetamide. J. Chem. Phys. 82, 1631-1641. 

Pulay, P., G. Fogarasi, F. Pang, and J. E. Boggs. 1979b. Systematic Ab Initio Gradient Calculation of Molecular Geometries, Force Constants, and Dipole Moment Derivatives. J. Am. Chem. Soc. 101, 2550-2560. 

During recent years DFT methods have been used to reproduce vibrational frequencies and IR intensities (dipole moment derivatives) with high accuracy (scaling factors are close to unity).29,60,61 We therefore used the B3LYP and BLYP functionals to calculate the spectra of la and its isotopomers, and indeed the calculated frequencies, isotopic shifts, and intensities are now in excellent agreement with the experimental values (Fig. 3).62 A careful reexamination... 

It is well established that the average lengths of CH bonds are consistently 0.003 to 0.004 A longer than the corresponding CD bonds in the ground vibrational state (see Fig. 12.1, its caption, and Section 12.2.3). It remains only to establish the dipole moment derivative, (9p/9r), at the equilibrium bond length. That is available from theoretical calculation or spectroscopic measurement (via precise measurements of IR intensities of vibration-rotation bands). Calculations based on Equation 12.7 yield predicted dipole moment IE s in reasonable agreement with experiment. 

An alternative approach is to apply stronger fields and only use energies calculated for positive field strengths in generating the polynomial fit. In this case the energy is a function of both odd and even powers in the polynomial fit. We will show that the dipole moments derived from our non-BO calculations with the procedure that uses only positive fields and polynomial fits with both even and odd powers match very well the experimental results. Thus in the present work we will show results obtained using interpolations with even- and odd-power polynomials. Methods other than the finite field method exist where the noise level in the numerical derivatives is smaller (such as the Romberg method), but such methods still do not allow calculation of odd-ordered properties in the non-BO model. 

The fixed partial charge (FPC) model (35) assumes that the electrons follow the nuclear motion perfectly and serve merely to screen the nuclear charge. The dipole moment derivative contribution from each nucleus is (5R /9Ga)o where... 

In these models, the local dipole moment derivative contribution becomes... 

Several other molecular orbital models have been applied to the analysis of VCD spectra, primarily using CNDO wave functions. The nonlocalized molecular orbital model (NMO) is the MO analog of the charge flow models, based on atomic contributions to the dipole moment derivative (38). Currents are restricted to lie along bonds. An additional electronic term is introduced in the MO model that corresponds to s-p rehybridization effects during vibrational motion. 

As discussed earlier, VCD depends on both the electric and magnetic dipole moment derivatives in a molecule. The simpler descriptions of VCD focus only on local electric dipole moment derivatives that have an overall chiral disposition. More advanced descriptions of VCD allow for induced electronic currents or charge flows in molecules, which give rise to additional magnetic dipole moment intensity. Such additional contributions are likely whenever delocaliz-able electron density is present in a molecule. 

The electrostatic properties of the molecule may be used as a criterion for judging the MEM enhancement. Using the uniform prior density, the MEM molecular dipole moment derived by the discrete boundary partitioning of space (chapter 6) is only 1.3 D, compared with 9.1 D based on the experimental density,... 

Under such conditions, of course, an essentia] change occurs in the effective dipole moment derivative value along the nuclear coordinate depending upon the entire chain bonding. 

With the development of analytical energy derivative methods135 l67, the calculation of vibrational frequencies (second derivatives of the energy with regard to atomic coordinates) and infrared absorption intensities (derivatives of the energy with regard to components of electronic field and atomic coordinates, i.e. dipole moment derivatives) both at the HF and correlation corrected levels has become routine168. There are six (two a " + four e)... 

Ha et al.272 used an essentially DZ basis to calculate the force constants and dipole moment derivatives. 

The polarities of AH bonds increase upon hydrogen bond formation, usually leading to larger dipole moments of the complexes than expected from vectorial addition of the components. Furthermore, also the significantly enhanced IR intensities indicate an increase in the dipole moment derivatives on hydrogen bond formation. 

Amos RD (1984) Dipole-moment derivatives of H2O and H2S. Chem Phys Lett 108 185-190... 

Most ab initio analyses of vibrational spectra invoke a double-harmonic assumption wherein the potential energy surface in the vicinity of the minimum is fit to a function that involves only quadratic dependence of the energy with respect to the nuclear motions. The intensities of the normal vibrational modes are extracted from the derivatives of the dipole moment, taken as linear with respect to nuclear coordinates. Within this approximation, the intensities of the fundamentals are proportional to the square of the dipole moment derivatives with respect to normal coordinates ". ... 

Both electrical and mechanical anharmonicity can be considered in the calculations. This was done using higher energy and dipole moment derivatives. Despite the use of relatively small basis sets, the anharmonieity constants were in surprisingly good eoineidence with experiment. 

Swanton, D. J., Bacskay, G. B., and Hush, N. S., An ab initio SCF calculation of the dipole-moment derivatives and infrared-absorption intensities of the water-dimer molecule, Chem. Phys. 82,303-315(1983). 

Table 8 Dipole moments derived from static permittivities of aqueous solutions...

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