Debye, the

In stead, the electrostatic con tribn tion conies from definin g a set of bond dipole moments associated woth polar bonds. These bond moments are defined in the m m psir.LxL(dbf) file along with the bond stretching parameters and are given in units of Debyes. The cen ter of th e dipole Is defined to be th e m Idpoint of the bond an d two dipoles p. and pj. separated by Rjj. as shown beltnv ... 

These heat capacity approximations take no account of the quantal nature of atomic vibrations as discussed by Einstein and Debye. The Debye equation proposed a relationship for the heat capacity, the temperature dependence of which is related to a characteristic temperature, Oy, by a universal expression by making a simplified approximation to the vibrational spectimii of die... 

Tunon et al.194 studied the water molecule in liquid water. The sample of conformations by the microscopic environment (water in this case) was obtained using Monte Carlo technique. The energy was calculated as in the approach of Stanton et al.189 i.e., using Eqs. 4.25 and 4.26. The solvent induced increase of the dipole moment amounted to 0.61 Debye in line with the results by Wei and Salahub and close to the experimental value of 0.75 Debye. The solvation enthalpy amounted —12.6 kcal/mol, while the value calculated by Salahub and Wei and the experimental ones were —10.4 kcal/mol and —9.9 kcal/mol, respectively. 

P. Debye, The Influence of Intramolecular Atomic Motion on Electron Diffraction Diagrams, J. Chem. Phys., 9 (1941) 55-60. 

P. Debye, The Collected Papers of Peter J. W. Debye, Interscience, New York, USA, 1913. 

The differences between ab initio and molecular mechanics generated dipole moments were discussed. The MM3(2000) force field is better able to reproduce experimental dipole moments for a set of forty-four molecules with a root mean squared deviation (rmsd) of 0.145 Debye compared with Hartree-Fock (rmsd 0.236 Debye), M0ller-Plesset 2 (rmsd 0.263 Debye) or MM3(96) force field (rmsd 0.164 Debye). The orientation of the dipole moment shows that all methods give comparable angle measurements with only small differences for the most part. This consistency within methods is important information and encouraging since the direction of the dipole moment cannot be measured experimentally. 

One classical example that apphes the electroneutrality principle is the electronic structure of carbon monoxide, a diatomic molecule with a very small dipole moment of 0.110 debye. The only electronic structure that satisfies the octet rule for CO is C=0 , a structure that corresponds to C and O, if the shared electron pairs are equally devided by the two atoms. Pauling showed that the electronegativity difference of 1.0 would correspond to about 22% partial ionic character for each bond, and to charges of and 0° +. A second possible electronic structure, C=O , does not complete the octet for carbon. The partial ionic character of the bonds corresponds to C0.44+ If these two structures contribute... 

The dipole moment of a molecule is the vectorial sum of the individual dipoles within it. Bond dipoles are usually represented using the symbol /x and are expressed in units of Debye. The dipoles result from charge separation. The carbon-carbon bond in ethane, H3C—CH3 is symmetrical and not expected to have a dipole moment. The carbon-oxygen bond of methanol (CH3OH), on the other hand, links two elements of differing electronegativity and is expected to have a significant molecular dipole. Methanol s molecular dipole is 1.7 whereas, for ethane, it is 0. 

Dipole moments are in Debyes the computational levels are arranged, from left to right, in what is conventionally considered lowest to highest. Calculations are by the author experimental values are taken from reference [lg], pp 326, 329, 332,335. For each level is given the number of positive and negative deviations and the arithmetic mean of the absolute values of the deviations. 

Fig. 9.12 Three-dimensional map of the calculated electrostatic potential at 0.25 nm above the symmetry plane in a hexagonally ordered network of dipoles with a dipole-dipole distance of 1.61 nm and a dipole moment of 10 Debye. The dipoles are positioned at the minima. Note that the potential is lowered at every position on the surface. Equipotential lines for —1.05, —0.84, —0.63,...

Fig. 6. The potential in the vicinity of a surface when ion-hydration interactions affect the anions (AWa) and the cations (AJTC) The other parameters are cE=0.1 M, iVA=lxi018 sites/m2, /VB=lxi018 sites/m2, H=iCr7 M, Oh=10"7 M, Kc=10 4 Ms ZA=10 4 M, e=80s Am=14.9 As m0=0, w=5 A, and (a) pH=4,pA/ v- =0 (b) pi 1=4, pAlv =—3 Debyes (c) pi 1=10,/ < / =0 (d) pH=10, pc v =3 Debyes. The values ofdo not affect the results plotted in (a) and (b), while the values ofptjz do not afFect the results plotted in (c) and (d). (e) The force between two identical surfaces for the same parameter values as in (a-d). Only the magnitude of the force is strongly dependent on the value of the surface dipoles and ion-hydration forces, but not its functional behaviour.

As shown by Debye, the potential energy, or intermolecular force (in this work, a+k) in one mole may be expressed by the following Eq. (12) in SI units... 

In all cases studied, the a-dipole moment component is increased beyond the value calculated from vector addition of the free monomer moments by 0.1-1 Debye. The large dipole moments and polarizabilities of the monomer substituents for the molecules in Table 4 suggest that these enhancements are electrostatically induced ... 

Borsenberger et al. (1995a) measured hole mobilities of TTA doped polymers with polymers with different dipole moments poly(styrene) (PS-1), poly(4-f-butylstyrene) (PS-2), poly(4-chlorostyrene) (PS-3), and bisphenol-A polycaibonate (PC). The dipole moments of PS-1 and PS-2 are near zero. For PC and PS-3, the values are 1.0 and 1.7 Debye. The dipole moment of TTA is 0.8 Debye. Figure 55 shows a series of photocurrent transients at different temperatures for 30% TTA doped PS-1 at 6.4 x 105 V/cm. W increases with decreasing temperature. For fields between 104 and a few multiples of 1CP v/cm, W increases with increasing field. Values of W were between 0.25 and 0.62. In all cases, W increases with decreasing TTA concentratioa Low-temperature transitions from nondispersive to dispersive transport, where the transients no longer show plateaus, were observed only at low concentrations. 

Hole mobilities of a series of pyrazoline, oxadiazole, and stilbene doped PC were described by Sugiuchi et al. (1991). The donor compounds were selected for differences in dipole moment and varied from 1.42 to 5.56 Debye. The results are shown in Fig. 96. The mobilities decrease with increasing dipole... 

Rommens et al. (1995) measured hole mobilities of l,3-di(dicyano-methylene)-2-allyl-2-methylindane (ADCMI) doped PC. The dipole moment of ADCMI is 3.9 Debye, the same as DCMI. Mobilities were determined from transit times derived by the method described by Scott et al. (1992). Over a wide range of fields, temperatures, and concentrations, the field dependencies... 

O. 3 Debye. The molecular moment is the vector sum of two group moments, each approximately 3.3 Debye. Figure 30 shows the field dependencies at different temperatures. The results were described as log/r < pE. Figure 31 shows the temperature dependence of the zero-field mobility. Figure 32 shows... 

---