Finite perturbation

The MNDO method [17] coupled with the finite perturbation (FP) technique [18], as implemented in the MOPAC5 [19] program has been used throughout this work. 

These compounds have been the subject of several theoretical [7,11,13,20)] and experimental[21] studies. Ward and Elliott [20] measured the dynamic y hyperpolarizability of butadiene and hexatriene in the vapour phase by means of the dc-SHG technique. Waite and Papadopoulos[7,ll] computed static y values, using a Mac Weeny type Coupled Hartree-Fock Perturbation Theory (CHFPT) in the CNDO approximation, and an extended basis set. Kurtz [15] evaluated by means of a finite perturbation technique at the MNDO level [17] and using the AMI [22] and PM3[23] parametrizations, the mean y values of a series of polyenes containing from 2 to 11 unit cells. At the ab initio level, Hurst et al. [13] and Chopra et al. [20] studied basis sets effects on and y. It appeared that diffuse orbitals must be included in the basis set in order to describe correctly the external part of the molecules which is the most sensitive to the electrical perturbation and to ensure the obtention of accurate values of the calculated properties. 

From our experimental results and different models used in theoretical calculations using either CND0/2 (23-25, 37>38) and PCIL0 methods (26,27), or the electric field effect by IND0 finite perturbation theory (28), the following models can be supposed ... 

The experimental 3J(HH) spin-spin coupling constants for Ha, Hp, and Hp for the -isomer 22 were quite satisfactorily reproduced (A = 0.1 - 1 Hz) by calculations, using a finite perturbation method (FPT level (26), Perdew/IGLO-III at a MP2/6-31G(d)) geometry for the model structure (E)-1 -cyclopropyl-2-(trimethylsilyl)ethyl cation. The calculations confirm the /rexperimentally observed carbocation 22 (20, 27, 28). The (E)- 1-cyclopropy 1-2-... 

To confirm equation (4), we used the FPT (Finite Perturbation Theory) INDO (Intermediate Neglect of Differential Overlap) method (39) to calculate the Jqjj for various values of torsion angles. A comparison of the experimental and calculated values is plotted in Figure 5. 

Fibrillin, calcium binding, 46 473, 474, 477 Fibulin-I, calcium binding, 46 473 Field desorption mass spectroscopy, 28 6, 21 Field effects, of astatophenols, 31 66 Fine structure, 13 193-204 Fingerprinting of polymetalates, 19 246-248 Finite perturbation theory, 22 211, 212 First transition series, substitution, transferrins, 41 423 26... 

In most DFT coupling calculations the FC contribution is calculated using the finite perturbation theory, FPT, using either a single36 or a... 

A DFT-based third order perturbation theory approach includes the FC term by FPT. Based on the perturbed nonrelativistic Kohn-Sham orbitals spin polarized by the FC operator, a sum over states treatment (SOS-DFPT) calculates the spin orbit corrections (35-37). This approach, in contrast to that of Nakatsuji et al., includes both electron correlation and local origins in the calculations of spin orbit effects on chemical shifts. In contrast to these approaches that employed the finite perturbation method the SO corrections to NMR properties can be calculated analytically from... 

The y-gauche effect involving only C-H bonds has been recently investigated by means of a modified version of the INDO finite perturbation theory of 13C chemical shifts, using butane as a model. (41) While the expected geometrical dependence on the methyl chemical... 

The experimentally measured coupling constant J(HaHy)exp. = 5.5 Hz is reproduced by calculations for the endo-si y substituted model structure 44 using a finite perturbation level (FPT) 26) (Perdew/IGLO-III) approach J(HaHy)caic. = 5.9 Hz, whereas only 1.2 Hz is calculated for the HaHy-coupling constant in the exo-si y substituted model structure 45. Finally the bonding orbital of the bridging C-C-bond between Cq and Cy in these type of bicyclobutonium ions can be visualized by calculations of the natural bond orbitals (NBO s) (Figure 13). 

Calculations in terms of the self-consistent finite perturbation theory (SCPT) and analysis of contributions of localized molecular orbitals in terms of the polarization propagator theory (CLOPPA), conducted by Krivdin and Kuznetsova, indicate additivity of coupling constants in saturated, sterically strained heterocycles. Their... 

Beer and Grinter (143) using the finite perturbation theory at the INDO level of approximation indicate that the combined orbital and spin-dipolar contributions are less than 1 % of the observed coupling. 

Beer and Grinter used finite perturbation theory to calculate J(Si-H), J(Si-H), (161) and J(Si-C) (143) as well as the analogous phosphorus couplings. The best results are obtained for J(Si-Q (Table XXI) for which the correlation coefficient of the best fit of calculated to observed values is 0-985. The various calculated contributions to J(Si-C) are in Table XXI. Clearly, the orbital and spin-dipolar terms, which are small and also of opposite sign, have little effect on the calculated value of J. It is concluded that the Fermi contact term is probably sufficient for the calculation of J(Si-Q and that inclusion of silicon d orbitals is not required. 

---