Resonance integral coupling

To account for this behaviour these authors proposed an extension of the theory, given by Pople and Santry, which predicted that the coupling constant depends upon the energies of the s relative to those of the p, d, etc. electrons of the coupled nuclei and additionally upon the resonance integral between the outer-shell r electrons of the two atoms. It was considered that the first factor remained fairly constant for the P-P bonds and the observed variation was qualitatively explained by the dependence of the second factor upon the electronegativity and the bulkiness of the substituent. 

The interactions between localized spins on neighboring cations are treated by a perturbation theory in which the spin-dependent resonance integrals for parallel and antiparallel coupling of spins are... 

Pn is sometimes said to represent the coupling of q with term resonance integral has similar roots (Coulson C. A., Valence, Oxford University Press, Oxford, 2nd edn, p. 79). 

Linear response of hybridization to bond elongation. First the relation between hybridization and elongation of the C-H bond is considered. For this we need the mixed second order derivatives coupling the bond stretching with the hybridization ESVs. For every C-H bond in methane we can introduce diatomic coordinate frame with the t-axis directed along the bond and express the resonance integral related to this bond as ... 

V is the electronic coupling factor (the resonance integral), v is the velocity of nuclear motion, and Sj and Sf are the slopes of the initial and final terms in the Q,r region. If the exponent of the exponential function is small, then... 

The present section is a brief survey of experimental data on electron transfer rate and its theoretical treatment being focused on (a) the Franc-Condon (FC) factor and (b) electronic coupling (resonance integral) V. Role of the media molecular dynamics on ET is discussed in Sections 3.5.1 and 4.1.7... 

The description of imaging experiments in reciprocal space is not restricted to k space, the Fourier conjugate space of physical space. The modification of the spin density by other parameters like resonance frequencies, coupling constants, relaxation times, etc., can be treated in a similar fashion [Miil4]. For the frequency-dependent spin density, the Fourier transformation with respect to 2 is already explicitly included in (5.4.7). Introduction of a Ti-dependent density would require the inclusion of another integration over T2 in (5.4.7) and lead to a Laplace transformation (cf. Section 4.4.1). 

In the PPP case we have to deal with a three-dimensional parameter space, namely the resonance integral B0, the electron-phonon coupling constant a, and the on-site Coulomb repulsion integral y0. Thus we varied the values of B and a and calculated the energy of butadiene in the model at u,/u0 = 0 (p=l), 0.5 (p=2), 1.0 (p=3) and 1.5 (p=4). Note, that p is not a site index here. The values obtained (Eppp(up)) are compared with the corresponding Ecc Uj) energies. The energies are computed relative to Up=0. Then we calculated... 

In the weak coupling case, where the excitation energy is localized, a different treatment is needed. A generalized formula for the excitation energy transfer of weakly coupled systems was derived by Forster. He wrote equations describing the rate of a transition from a localized excited state, ipa M, to another localized excited state, VWi- When the distance between the two molecules, Rab, is not too short, the resonance integral can be approximated by the interaction energy between the transition dipole moments, Pa and Pb,... 

McWeeny, (ii) noniterative, coupled-Hartree—Fock (Hall—Hardisson ), (iii) noniterative, coupled Hartree—Fock (Coulson et al. ), (iv) London— McWeeny, based on an iterative ( 8a a " 27.245-247 Hiickel molecular orbital, (v) coupled-Hartree—Fock (Hall—Hardisson ) with variable resonance integrals, and (vi) coupled-Hartree—Fock (Coulson et al.253) with variable resonance integrals. When, in the preceding, we refer to variable resonance integrals, we mean that a wave function has been used that is... 

---