Dipole moment, calculation derivatives

DIPOLE MOMENTS CALCULATED FOR VARIOUS THIAZOLE DERIVATIVES... 

The deformed-chair conformation of ring A in a 4,4-dimethyl-3-oxo-5or-steroid has been confirmed by an X-ray study of a 17 -benzoyloxyandrostane derivative. The results agree with those of an earlier study of the 17-iodoacetate, and with the geometry indicated by force-field calculations. Dipole moments calculated by the application of molecular mechanics to 5a-androstane-3,17-dione and its distorted 4,4-dimethyl derivative are larger than those observed the reasons for these deviations are not yet clear. 

Dipole moments calculated by the method of Mazeika et al.252 for derivatives of 1 and 5 are summarized in Table II. The results compare with experimental values of 1.5 and 3.4 D for 1- and 2-methylindazole.253... 

The magnitude of the surface dipole. For the system hydrogen-nickel, formula (13) leads to a value of 0.66 D. The experimentally determined value 0.022 D. is therefore a factor of about 30 smaller. This is quite conceivable because (13) has been derived for a diatomic molecule. In our case one of the partners of the bond, the metal, has a very high polarizability, and hence the surface dipole will be quenched to a large extent. The value of the dipole moment calculated from (13), though larger than the experimental value, is still far smaller than that to be expected for a pure ionic bond (fora bond distance of 2 A. fj, = 10 D.). This is one of the reasons for us to think that the contribution of the ionic type M+X to the total bond... 

Few theoretical studies on the title compounds have been carried out. A CNDO/2 method for estimating dipole moments, which is successful for a variety of heterocyclic systems, produces calculated dipole moments for 2//-l,2,6-thiadiazine 1,1-dioxides (14) which are consistently higher (by 2-2.5 units) than experimentally determined values in dioxan solution <82JOC536>. In contrast, dipole moments calculated by classical vectorial methods are much more in agreement with experimental values. The error in the CNDO/2 derived values probably arises from lone pair repulsions between N-6 and the SO2 group, which are not described adequately by the CNDO/2 method. 

This is equivalent to the expression from first-order perturbation theory, (10.21). For non-variational wave functions the dipole moment calculated by the two approaches will be different, since the derivative of the wave function with respect to the field will not be zero. The second-order property, the dipole polarizability, is given by the derivative formula eq. (10.34) as shown in eq. (10.59). 

In the previous equation R is the density matrix derivative with respect to Qi. It can be calculated throu a coupled perturbed Hartree-Fock (CPHF) procedure. Notice that the presence of the term, that is, of the dipole moment matrix derivative in Eq. 7.14, is due... 

Computed dipole moments of proteins presented here refer to a particular point within the structures of the proteins named center of diffusion (CD). As is known, a calculated dipole moment depends on the choice of coordinate system origin when the total charge on the molecule is not zero. Experimental values of dipole moments are derived from the orientational behavior of molecules under electric field pulses, which obviously is independent of any coordinate system but can be biased by other factors. For example, Wegener " showed that rotational velocity > driven by the external electric field, E at low Reynold s number can be expressed as... 

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... 

The initial values, a, , are derived by correlations with dipole moments of a series of conjugated systems. The exchange integrals are taken from Abraham and Hudson [38] and are considered as being independent of charge. The r-charges are then calculated from the orbital coefficients, c,j, of the HMO theory according to Eq. (14). 

The function/( C) may have a very simple form, as is the case for the calculation of the molecular weight from the relative atomic masses. In most cases, however,/( Cj will be very complicated when it comes to describe the structure by quantum mechanical means and the property may be derived directly from the wavefunction for example, the dipole moment may be obtained by applying the dipole operator. 

The first empirical and qualitative approach to the electronic structure of thiazole appeared in 1931 in a paper entitled Aspects of the chemistry of the thiazole group (115). In this historical review. Hunter showed the technical importance of the group, especially of the benzothiazole derivatives, and correlated the observed reactivity with the mobility of the electronic system. In 1943, Jensen et al. (116) explained the low value observed for the dipole moment of thiazole (1.64D in benzene) by the small contribution of the polar-limiting structures and thus by an essentially dienic character of the v system of thiazole. The first theoretical calculation of the electronic structure of thiazole. benzothiazole, and their methyl derivatives was performed by Pullman and Metzger using the Huckel method (5, 6, 8). 

Dipole moments were calculated for a large number of thiazole derivatives the corresponding results are reported in Table 1-8. 

When you perform a single point semi-empirical or ab initio calculation, you obtain the energy and the first derivatives of the energy with respect to Cartesian displacement of the atoms. Since the wave function for the molecule is computed in the process, there are a number of other molecular properties that could be available to you. Molecular properties are basically an average over the wave function of certain operators describing the property. For example, the electronic dipole operator is basically just the operator for the position of an electron and the electronic contribution to the dipole moment is... 

A variety of methodologies have been implemented for the reaction field. The basic equation for the dielectric continuum model is the Poisson-Laplace equation, by which the electrostatic field in a cavity with an arbitrary shape and size is calculated, although some methods do not satisfy the equation. Because the solute s electronic strucmre and the reaction field depend on each other, a nonlinear equation (modified Schrddinger equation) has to be solved in an iterative manner. In practice this is achieved by modifying the electronic Hamiltonian or Fock operator, which is defined through the shape and size of the cavity and the description of the solute s electronic distribution. If one takes a dipole moment approximation for the solute s electronic distribution and a spherical cavity (Onsager s reaction field), the interaction can be derived rather easily and an analytical expression of theFock operator is obtained. However, such an expression is not feasible for an arbitrary electronic distribution in an arbitrary cavity fitted to the molecular shape. In this case the Fock operator is very complicated and has to be prepared by a numerical procedure. 

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. 

Cl density method, which uses analytic derivatives of the wavefunction to compute the dipole moments, resulting in much more accurate predictions, as is illustrated in this case. You can request the Cl density by including either DensityaCI or DensityaCurrenI in the route section of a Cl-Singles calculation, n... 

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... 

At this level of theory, the calculated equilibrium bond length is 110.47 pm, and the dipole moment changes sign around which may explain why one has to work so hard to achieve agreement with experiment. The dipole derivative can be found by numerical methods from the data points. 

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