The linear relation between the magnetic circular dichroism (benzene 'Aig -'B2-transition) of monosubstituted and 1,4-disubstituted benzenes and the substituent constants a and OfR are compared. In all cases, better linear correlations were found between the magnetic circular dichroism and aR. (benzene 'Aig --lB2, transition) data of monosubstituted and 1,4-disubstituted benzenes with both ar and aR. The experimental procedure and equipment are exactly the same as those described in the previous paper (2) and will not be described here. We have measured the MCD of X-C6H4-I (X=H, CH3, Cl, Br, I, OH, NH2, NO2, or CO2H), X-C6H4-NO2 (X=H, CH3, F, Cl, Br, I, NH2, NO2, or CO2H), and X-C6H4-CO2H (X=H, CH3, F, Cl, Br, I, OH, NH2, CN, or NO2) in methanol solutions. Data of the MCD of monosubstituted benzenes are taken from the previous paper (2).In Table 1
In a self-consistent field calculation, a formula for the off-diagonal matrix elements of the core Hamiltonian is derived for a nonorthogonal basis set by a polyatomic approach. A set ofparameters is then introduced for the repulsion integral formula of Mataga-Nishimoto to fit the experimental data. The matrix elements computed for the nonorthogonal basis set in the aielectron approximation are transformed to those for an orthogonal basis set by the I~wdin symmetrical orthogonalization.Semiempirical calculations using the Hartree-Fock equation (1) with a zero differential overlap (2-7) neglect the overlap integrals and assume orthogonality of a set of atomic orbitals. These approaches have been rationalized through the use ofthe Lowdin orthogonalized atomic orbital (8). Explanations of the earlier Pariser-Parr method (2-4) have been given by Gladney (9), Fischer-Hjalmars (10), Berthier et al. (11), and several other authors (12-14); a systematic treatment of the zero differential overlap assumption using the nonorthogonal atomic orbitals has been compared with the procedure using the nonorthogonal Lowdin atomic orbitals by Fischer-Hjalmars (15-18); and further application of the orthogonal transformation has been carried out by Adams and Miller (19,20). Linderberg (21,22) has shown that the equivalence of the dipole length and velocity form of oscillator strength places a condition on the parameters used in the Pariser-Parr model. For the case of two orbitals centered at positions A and B and having a vanishing gradient perpendicular to the axis connecting them, Linderberg has derived Eq. 1. h2 L aS4 mRv OR' [a1] where 4A and 1k are the atomic orbitals on atoms A and B, SAV = (4+,j4,), R AV = (R, -Rv), and f3A is a resonance integral between the orbitals ',, and 4p. This procedure is a diatomic approach and neglects the higher order corrections that would occur in polyatomic molecules. There is not, however, a proper limit when B approaches A in this formula. To compute a, for the diagonal matrix elements of the core Hamiltonian, one needs to know / values for the nonorthogonal basis set, but we now only have /8 values for the orthogonal basis set, as given by Eq. 1. The /8 values for the nonorthogonal basis set can be obtained by the procedure described below. Derivation of the off-diagonal matrix element of the core Hamiltonian The fundamental equations for the self-consistent field method are FC = ESC, IF -ESI = 0, Ci s Cj = 8ij, [2] where F is the Fock matrix, E is the eigenvalue matrix of F, C is the eigenmatrix of F, Bij is the Kronecker delta, and S is the overlap matrix. The zero differential overlap approximation leads to the familiar contradiction of neglecting the overlap integral on the one hand and taking a nonzero value of the resonance integral on the other hand.The L6wdin orthogonalized atomic orbitals and the Mulliken approximation (23) can be combined into a computational method in a self-consistent field calculation. The nonorthogonal orbitals, 4i,, are transformed into the orthogo...
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.