Frank E. Harris

Molecular Orbital Theory

Publisher Summary This chapter deals with the formal problem of reducing molecular orbital calculations to expressions involving one- and two-electron integrals over the spatial coordinates, with coefficients determined by the group theoretical properties of the spin functions and the electronic permutations. This problem is encountered, for example, when one undertakes to write the expectation value of the Hamiltonian for a given anti-symmetrized spin-orbital product, and in that particular case, the answer is well-known. The focus is on wave functions, which are constructed to be eigenfunctions of the spin, and shall consider the reduction of expressions not only for the energy and other spin-free one- and two-electron operators, but also for general one- and two-electron spin-dependent operators, such as the spin density or the Fermi contact interaction. It has been shown as how a spin-projected single-determinantal wave function based on different spatial orbitals for different spins can be related to the matrix representation method, and it is shown, how to calculate expectation values of both spin-free and spin-dependent operators.

Ab Initio Calculations on 62 Low‐Lying States of the O2 Molecule

Ab initio calculations have been made on the 62 low‐lying states of molecular O2 which result from the combination of O atoms in 3P, 1D, and 1S atomic states. The calculations are done at nine different internuclear separations, and potential‐energy curves are presented for all states. Twelve bound states were found: the lowest seven have been observed; two others have been predicted before; three are new. The state ordering agrees with experiment except for the c 1Σu− state. Possible reasons for this discrepancy are discussed. The remaining errors in the bound‐state energy separations are rationalized. Data possibly bearing on the unobserved bound states are cited. Repulsive‐state curves are used to discuss predissociation in the Schumann–Runge bands and to illustrate avoided‐crossing phenomena.

Studies of Hydrogen‐Bonded Systems. I. The Electronic Structure and the Double Well Potential of the N–H···N Hydrogen Bond of the Guanine—Cytosine Base Pair

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Molecular Orbital Studies of Diatomic Molecules. I. Method of Computation for Single Configurations of Heteronuclear Systems

R. Hoffmann, J. Chem. Phys. 39, 1307 (1963).

More Special Functions

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Open‐Shell Orthogonal Molecular Orbital Theory

L. C. Cusachs, J. Chem. Phys. 43, 8157 (1965).

Multicenter Integrals in Quantum Mechanics. I. Expansion of Slater‐Type Orbitals about a New Origin

For hydrogen‐bonded complexes we outline an LCAO—MO—SCF method which considers explicitly the σ electrons of the hydrogen‐bond region and the π electrons of the surrounding ligands. The protonic potential function is obtained by solution of these SCF equations for a series of proton positions. The electronic structure and the potential function of the middle N–H···N hydrogen bond of the guanine—cytosine base pair have been calculated by this method. The integrals appearing in the problem have been approximated semiempirically and several alternative approximations have been tested. The calculated π electronic structure and orbital energies conform with the result of a previous SCF calculation treating the H bond parametrically. The calculated charge distribution in the H‐bond region is in agreement with the mainly covalent character of the N–H bond and mainly electrostatic character of the H···N bond for equilibrium configuration. The empirical and electrostatic models agree well with our model with respe...

Dielectric Polarization in Polar Substances

This paper describes a method of molecular orbital calculation for heteronuclear diatomic molecules, in the approximation of a single spatial configuration which is a product of one‐electron functions. The method is applicable to systems in which the one‐electron orbitals are not required to be either orthogonal or filled in pairs. A practical procedure is presented for treating permutational symmetry and spin for an arbitrary spatial wave function, and using this procedure we consider simultaneously all the spin configurations associated with the chosen spatial wave function. The wave functions used are parametric expressions in spheroidal coordinates, and include the usual Slater orbitals as special cases. All necessary integrals are evaluated in a manner suitable for machine computation. A computer program to implement this method of calculation has been prepared, and with it an approximate energy level for a 6‐electron molecule can be obtained in about 8 min. Provision was made to program the computer...

Molecular Orbital Studies of Excited States of HeH

This chapter surveys a number of sets of special functions of importance in physics. Where appropriate, the survey includes generating functions, Rodrigues formulas, the relevant differential equation, orthogonality conditions, and applications. The discussion covers Hermite functions (with applications to the quantum harmonic oscillator and to molecular vibrations), Laguerre functions (with application to the hydrogen atom), Chebyshev polynomials (with application to numerical analysis), hypergeometric and confluent hypergeometric functions, the dilogarithm (with application to electronic structure computations), and elliptic integrals.