Dipole moments, relativistic effects

Relativistic effects on the structure and energy of the heavier group 14 dihydrides have been studied216. For I+Si, inclusion of relativistic effects caused little change in the predicted values <0.05° in L H—Si—H, <0.0005 A in r(Si—H), <0.02 D in the dipole moment and <0.6 kcalmol-1 in energy. 

If W were known exactly, the value of a first-order property calculated from equation (12) would be exact. In practice, only an approximation to W is known, and it is important to know how the expectation value differs from the exact value. Since errors in calculated dipole moments due to the breakdown of the Bom-Oppenheimer approximation are likely to be small8 (typically 0.002 a.u.), and for most molecules relativistic effects can be ignored,6 there are two separate remaining problems in practice. The first concerns the likely accuracy when the wavefunction is at the Hartree-Fock limit, the second the effect of using a truncated basis set to obtain a wavefunction away from the Hartree-Fock limit. 

The Mulliken analysis data of Table 9 show Bh03Cl to be more covalent (a larger OP) than Tc03Cl and Re03Cl. Such an increase in covalence is typical of halides and oxyhalides of the elements at the beginning of the transactinide series (Rf, Db and Sg) and this is a relativistic effect as discussed earlier. The dipole moments increase from the Tc to the Bh compound... 

First-principles quantum chemical calculations including relativistic effects have been carried out for dipole moments, polarizabilities, and first- and second-order hyperpolarizabilities for tellurophene. The estimated values were compared with the observed ones measured by the optical Kerr effects <2000SM185, 2003JMT207>. 

Ramos, Pyper and Malli (21) have recently discussed (using the RIP) the relativistic effects in bonding and dipole moments for these... 

RELATIVISTIC EFFECTS FOR DIPOLE MOMENTS OF DIATOMICS OF HEAVY ELEMENTS... 

Furthermore, relativistic effects have been shown to be fairly significant in non-energetic properties, e.g., dipole moment, and it is hoped that the accurate prediction of non-energetic properties would supplement the criterion for the quality of a relativistic wavefunction in future. Thus, the knotty bottlenecks of ab initio fully relativistic DF SCF calculations have been broken, and it is... 

The Stark effect on the magnetic fine structure occurs as a result of disturbance of atomic levels under the influence of the relativistic and correlation effects as well as the interaction with external electric field F. If the fields are weak enough the centre of multiplet is shifted and there occurs the splitting of sublevels of atomic multiplet n, L, J. The dipole moment induced in an atom by a uniform electric field F is for most purposes expressed as a linear function of F, but higher... 

During the last 10-20 years, a large number of efficient theoretical methods for the calculation of linear and nonlinear optical properties have been developed— this development includes semi-empirical, highly correlated ab initio, and density functional theory methods. Many of these approaches will be reviewed in later chapters of this book, and applications will be given that illustrate the merits and limitations of theoretical studies of linear and nonlinear optical processes. It will become clear that theoretical studies today can provide valuable information in Are search for materials with specific nonlinear optical properties. First, there is the possibility to screen classes of materials based on cost and time effective calculations rather then labor intensive synthesis and characterization work. Second, there is Are possibility to obtain a microscopic understanding for the performance of the material—one can investigate the role of individual transition channels, dipole moments, etc., and perform systematic model Improvements by inclusion of the environment, relativistic effects, etc. 

A description of the theory of parity nonconserving transitions in heavy atoms is presented. Issues of the accurate solution of the many-body problem and the correct incorporation of relativistic and radiative effects are addressed, and the related field of electric dipole moments of atoms is briefly described. 

An increase in dipole moments, He, of the low symmetry molecules (group-6 MOCI4, MO2CI2 and group-7 MO3CI) in the transition element groups was predicted by DFT calculations [144,145,153,154]. The polarizabilities of the group-8 MO4 show a saw-tooth behaviour (Table 7). [le and a, as well as the molecular size, are decreased by relativistic effects. 

The numerical examples of the role of relativistic effects in the calculations of dipole moments of Cm//, AgH and AuH diatomic species and dipole polarizabilities of GeO, SnO and PbO molecules are shown in Tables 4.3 and4.4. 

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