F. A. Matsen

High‐spin hydrocarbons

The existence of a class of (very) high‐spin hydrocarbons is predicted on the basis of (a) new theorems for valence‐bond models, (b) classical structure theory, (c) standard theorems for molecular orbital theory, (d) several small‐system calculations with Hubbard and PPP Hamiltonians, and (e) a large‐system cluster expansion calculation applied to the polyallyl high‐spin candidates. Some properties, especially the magnetic ones, for these conjugated alternants are briefly discussed.

Electron Affinities, Methyl Affinities, and Ionization Energies of Condensed Ring Aromatic Hydrocarbons

The electron affinities of condensed ring aromatic molecules are calculated from half‐wave‐reduction potentials and the absolute potential of the normal calomel electrode. The results correlate with molecular orbital theory and frequency of absorption and extrapolate to the work function of graphite. A parallel correlation is made for the ionization energies. A correlation is also shown to exist between the electron affinity and the methyl affinity defined by Szwarc. Finally the results are discussed in terms of the approximate self‐consistent field theory of Pople, from which it is possible to make an a priori estimate of the work function of graphite.

Spin-Free Quantum Chemistry

A picture of reality drawn with a few sharp lines cannot be expected to be adequate to the variety of all its shades. Yet even so the drafsman must have courage lo draw the lines firm. H. Weyl in Philosophy of Mathematics and Natural Science

Antisymmetrized Hückel Orbital Calculations of Ionization Potentials and Electron Affinities of Some Aromatic Hydrocarbons

Antisymmetrized Huckel orbital calculations of the ionization energy and the electron affinity have been made for twenty‐three condensed‐ring aromatic molecules. In these calculations differential overlap has been neglected. The calculated ionization energies together with the polariographic reduction potentials permit the estimation of solvation energies of molecular ions.

The Near Ultraviolet Absorption Spectrum of Toluene Vapor

The experimental work of Savard and the theoretical work of Sponer on the absorption spectrum of toluene vapor is extended. A spectrum of 209 bands was observed with partial resolution of the fine structure. A tentative analysis is given based on ground state frequencies 514, 620, 785, 1003, 1012, 1176, and 1209, which correlate completely with Raman data; on excited state frequencies, 456, 528, 751, 932, 964, and 1186; and on difference frequencies 59 and 178 cm−1. Assuming C2v symmetry, all frequencies below 1300 cm−1 of symmetry class A1 appeared in 1–0 transitions and with one exception in 0–1 transitions. In addition, a vibrational frequency of symmetry class B1, deriving from an eg+ vibration in benzene, appeared strongly both in the ground and excited state.

Simple Configuration‐Interaction Wave Functions. I. Two‐Electron Ions: A Numerical Study

The ground state energies of the two‐electron ions from H— to Ne8+ are calculated for the simple wave function (1s1s′)+λ(2p)2 with optimized orbital exponents. The use of the difference between the calculated energy and the experimental energy as a function of the atomic number for accurate extrapolation is explored. The expectation values of the operators rn(n≥—2), δ(3)(r1), and δ(3)(r12) are compared with those obtained from more accurate wave functions.The ground state energies of the two‐electron ions from H— to Ne8+ are calculated for the simple wave function (1s1s′)+λ(2p)2 with optimized orbital exponents. The use of the difference between the calculated energy and the experimental energy as a function of the atomic number for accurate extrapolation is explored. The expectation values of the operators rn(n≥—2), δ(3)(r1), and δ(3)(r12) are compared with those obtained from more accurate wave functions.

One‐Center Wavefunction for the Ground State of the HeH+ Molecular Ion

The HeH+ molecular ion is a member of that class of diatomic hydride molecular ions which are one‐center systems at R=0 and at R=∞. The total electronic energy of the ground state of HeH+ has been calculated over a wide range of R with a 30‐term orbital product wavefunction centered on the helium nucleus. The results are compared with a James and Coolidge‐type calculation and with a two‐center orbital product calculation. The results in the order Evett, Anex, and present calculation are Re=1.432, 1.446, 1.464 a.u.; ωe=3600, 3378, 3184 cm—1; and E(R=1.4 a.u.)=—2.9730, —2.9742, —2.9691 a.u. The energy of the present calculation is the lowest for R greater than about 2 a.u. and is lower than the classical polarization energy for 2 4 a.u. the one‐center interaction energies [E(R)—E(∞)] lie quite close to the classical polarization energies.

Open shell calculations for the two- and three-electron ions

Open shell calculations are made for all the three-electron atomic systems of the second period of the periodic table. These results are compared with corresponding two-electron and experimental energies. It is noted that the improvement of open shell over closed shell calculations becomes less with increasing atomic number. In parallel trend the disparity of both from the experimental results increases with Z. An electron affinity of zero is found for the helium atom.

The Unitary Group and the Many-Body Problem*

Publisher Summary The unitary group formulation of many-body theory is an alternative to the conventional second-quantized formulation for particle-conserving problems. It differs from the latter by its replacement of products of creation and annihilation operators with infinitesimal generators of the unitary group that generate orbital transformations and by imposing statistics with a selection of invariant subspaces rather than by selection of Lie algebras. This chapter discusses only a small fraction of the many-body theory but is representative enough to show how the unitary group formulation is applied. Some of the features are (1) the employment of finite Hilbert subspaces, (2) the use of generators as operators that are bounded on these subspaces, and (3) time-independent matrix evaluation and derivation of the (– 1) H+L rule. The chapter also employs the superoperator formulation, which is particularly well suited to the unitary group, permitting a straightforward development of the random-phase approximation and hence a time-independent development of the time-independent Greens function.

Computation of vibrational-rotational energy levels of diatomic potential curves

Abstract The radial portion of the nuclear motion wave function is obtained by expanding its eigenfunctions in a truncated harmonic oscillator basis set. The method was tested giving results as good as or better than numerical integration or Dunham analysis. In addition, the method yields explicit wave functions in a useful form. The accuracy of solutions and the rate of convergence with increasing basis set size has been investigated for several methods of determining the parameters which specify a particular basis set.