Finite field techniques

We have have now paved the way for computational strategies to take form. Immediately Eq. (94) invites to the basic and straightforward idea of numerical differentiation, which is known in the literature as the finite-field technique. For atomic calculations, this idea is easily implemented in an existing code for any electronic structure method, as it only involves the response of the electronic density to the external static field in accordance with Fig. 6. In the absence of the perturbation, the dipole moment is zero due to the spherical symmetry of the atom, but in the presence of the external field the Coulomb force acts on the electrons as well as the atomic nucleus thereby displacing them in opposite directions the nucleus tends to move along with and tire electrons opposed to the electric field E with an induced dipole moment pc as a result. 

There is a distinction between two groups of methods. The first is the finite field technique.35 In this case finite perturbations representing the external fields are added to the molecular hamiltonian and the calculation of the ground state wavefunction and energy is carried out as for the unperturbed molecule. The finite field method can be applied in conjunction with any quantum mechanical method that is available for molecular calculations. There are two principal subdivisions of the finite field method. In one of these terms of the form tff-Fi... 

Maroulis et al.122 have applied their static polarizability, finite field technique to a study of the 22 electron diatomics CP , BC1, CC1+ and PO+. The vibrational contribution to the ground state polarizability has also been calculated. The dipole polarizability and other properties of YbF have been investigate in the unrestricted Dirac-Fock approximation by Parpia123 and the static second hyperpolarizability of the Cu2 dimer has been calculated in a correlation corrected UHF study by Shigemoto et al.124... 

Calculations on Complexes, Dimers, Clusters, Excited States. - Mar-oulis has used his finite-field technique to explore the hyperpolarizabilities of the rare gas diatoms Hc2, Nc2, At2 and Kt2 and the interaction hyperpolarizability of hydrogen fluoride with a neon atom. 

The polarizability of rare gas Ceo endohedral complexes, Rg Ceo, has been investigated using the finite field technique at the DFT level using the B3LYP, PBE, and SVWN exchange-correlation functionals. The polarizabilities of these complexes are found to be distinctly smaller than the sum of the polarizabilities of their constituents. In particular, for Rg going from He to Kr, the polarizability of the complex increases much more slowly than... 

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