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absorption alternant hydrocarbon amines aromatic atomic orbitals band benzene C. A. Coulson calculations carbanion carbon atoms Chem Christiansen effect closed-shell coefficients complex MO's computations conjugated conjugated systems coordinates copy corresponding coulomb integral defined Department of Physics discussed double bonds eigenvalues electron densities example excitation energies formulas frequencies given H. C. Longuet-Higgins Hartree-Fock hermitian hybrid hydrocarbon infra-red ionization energy isoaromatic LCAO approximation LCAO MO LCAO MO method many-center matrix Molecular Orbital Theory molecule MSO's Mulliken naphthalene non-neighbor normal notation obtained ortho orthogonal orthonormal overlap integrals paper Phys positions principal resonance structures Prof quantities R. S. Mulliken reactions refractive index resonance energy Roothaan Section secular equations Slater AO's spectra substitution symmetry Table tion transition complex two-center two-electron University of Chicago unpaired electrons unsaturation energy valence values vibrations wave function zero zero-energy MO