Wave function parameters, nuclear magnetic

Molecular theory of the VCD by Stephens involves the determination of wave-function parameters perturbed with respect to the nuclear displacements and the magnetic perturbation. It means, it requires solution of 3V-I-3 response equations N is the number of atoms in the system). Theory of the VCD spectra is constructed within the following assumptions of (a) Born-Oppenheimer approximation (BO) (15.1), in which total wavefunction is a product of electronic and nuclear wave functions for an electronic reference state gO and vibrational state gl ... 

Almost all the parameters yielded by the various types of radiofrequency spectroscopy arise from the interaction of nuclear magnetic or electrostatic moments with the magnetic or electrostatic fields produced by the surrounding electrons. A consideration of the way these interactions arise shows that they fall into two groups one of the groups contains terms proportional to the electron density at the nucleus, N, itself, Vn(0), and consequently reflects only the s-character of the wave-function centered on N, v>n while the other is proportional to the value for all or some of the electrons surroimding the nucleus N (Table 1). This latter term vanishes for s-type orbitals and for p, d, f orbitals of the same principal quantum number has values in the order p > > d > > f. In practice this means that in a first approximation, only p-electrons contribute to and that the direct effect of the d-orbitals is only... 

Linear response theory expression Alternatively, the spin-spin coupling constant can be expressed using the linear response theory formalism. Let us write the electronic energy of the system perturbed by the nuclear magnetic dipole moments M/f in the form E = E(Mjf, A), where A are the variational parameters of the wave function. A may represent orbital rotation parameters for the SCF wave function, or orbital rotation parameters and coefficients of the configuration interaction expansion for the MCSCF... 

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