Relativistic effects frequency

Predict the structure and frequencies for this compound using two or more different DFT functionals and the LANL2DZ basis set augmented by diffuse functions (this basis set also includes effective core potentials used to include some relativistic effects for K and Cs). How well does each functional reproduce the observed spectral data ... 

Hay, P. J., Martin, R. L., 1998, Theoretical Studies of the Structures and Vibrational Frequencies of Actinide Compounds Using Relativistic Effective Core Potentials With Hartree-Fock and Density Functional Methods ... 

In Table 5.3 we list MRCI+Q spectroscopic constants for N2 obtained with one of our largest basis sets. Of the remaining errors compared to experiment, we can estimate that about 0.001 A of the error in the bond length arises from relativistic effects [71]. These would also increase the frequency slightly. Explicit calculations... 

To explain the advantages of our proposals let us start from simple analytical estimates of the relativistic effects in transition frequencies. The contribution of the relativistic correction to the energy can be obtained as an expectation value (V) of the relativistic perturbation V, which is large in the vicinity of the nucleus only. The wave function of an external electron near the nucleus is presented in, for example, [22]. A simple calculation of the relativistic correction to the energy of external electron gives the following result ... 

The IS — 2S transition obeys the selection rule AF = 0, Am = 0 and is almost field-independent However, the g-factor for the bound electron is slightly less than for free space due to relativistic effects, and this gives the transition a small first-order field dependence. In the IS state the g-factor is g(lS) = g0 (1 - a2/3) [10]. The relativistic term is proportional to the binding energy so that g(2S) = ge (1 - a2/12). Thus, the field-dependence of the transition IS- 2S, (F=l,m=l AF=0,Am=0) leads to a frequency shift... 

It follows from Tables I and II that relativistic effects have a sizable influence on bond energies,bond distances,as well as vibrational frequencies for the compounds containing the heavier 5d-member (Au or Hg) within the triad. 

Relativistic effects are finally seen to increase vibrational frequencies of the third row compounds by up to 100%.The relativistic frequencies are further in better accord with experiment than the non-relativistic values.Results similar to ours have been found in studies based on other methods (12). 

Tab. 1 a) Spectroscopic parameters (bond length), (bond depth) and o) (vibrational frequency) for Cu2, Ag2 and Auj from relativistic and non-relativistic calulations compared to experimental values, b) Relativistic effects for the spectroscopic parameters for the same diatomic molecules. 

The example of neon, where relativistic contributions account for as much as a0.5% of 711, shows that relativistic effects can turn out to be larger for high-order NLO properties and need to be included if aiming at high accuracy. Some efforts to implement linear and nonlinear response functions for two- and four-component methods and to account for relativity in response calculations using relativistic direct perturbation theory or the Douglas-Kroll-Hess Hamiltonian have started recently [131, 205, 206]. But presently, only few numerical investigations are available and it is unclear when it will become important to include relativistic effects for the frequency dispersion. 

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