Hybridization effects second derivatives

This can be thought about either in terms of hybrid orbitals , e.g., pd and sp hybrids as shown above, or alternatively in terms of a Taylor series expansion of a function (d functions are the first derivatives of p functions, p functions are the first derivatives of s functions). While the first way of thinking is quite familiar to chemists (Pauling hybrids), the second offers the advantage of knowing what steps might be taken next to effect further improvement, i.e., adding second, third,.. . derivatives. 

The main purpose of this section is consideration of the FIR spectra due to the second dipole-moment component, p(f). However, for comparison with the experimental spectra [17, 42, 51] we should also calculate the effect of a total dipole moment ptot. In Refs. 6 and 8 the modified hybrid model44 was used, where reorientation of the dipoles in the rectangular potential well was considered. In this section the effect of the p(f) electric moment will be found for the hat-curved, potential, which is more adequate than the rectangular potential pertinent to the hybrid model. In Section VI.B we present the formula for the spectral function of the hat-curved model modified by taking into account the p(f) term (derivation of the relevant formula is given in Section VI.E). The results of the calculations and discussion are presented, respectively, in Sections VI.C and VI.D. 

It is possible to derive instructive information concerning the general features of the electronic structure of a bond systems by making drastic assumptions on the value of the parameters a and fi. First, one obtains a bond orbital scheme if all resonance integrals between hybrids not involved in a chemical bond jure set equal to zero consequently, the delocalization effects can be treated by the standard perturbation theory of the molecular-orbital method second, if all the Coulomb integrals are... 

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