David Parker Craig

Molecular Orbital Calculations of the Lower Excited Electronic Levels of Benzene, Configuration Interaction Included

The lower excited π‐electron levels of benzene are calculated by the non‐empirical method of antisymmetrized products of molecular orbitals (in LCAO approximation) including configuration interaction. All configurations arising from excitation of one or two electrons from the most stable configuration are considered, and all many‐center integrals are retained. The results are in better agreement with experiment and valence‐bond calculations than those obtained previously by Craig in a calculation neglecting many‐center integrals. Configuration interaction is found to change the order of the 1B1u and 1E2g states but leave unchanged the order of the 3B1u and 3B2u states, in agreement with the assignments 1A1g—3B1u and 1A1g—1E2g for the experimental bands at 3.8 and 6.2 ev.

d Orbitals in Compounds of Second‐Row Elements. I. SF6

Optimum exponent values for 3s, 3p, and 3d orbitals of sulfur in SF6 have been calculated in an electrostatic approximation. The sulfur electrons are perturbed by fluorine potentials appropriate to self‐consistent field wave functions for the fluorine orbitals, and the energy minimized with respect to wave‐function exponents. The optimum values are k3s=2.0, k3p=1.6, and k3d=1.2, corresponding to expansion of 3s and 3p orbitals, and contraction of 3d, compared with free‐atom values. The values are remarkably stable to changes in valence‐orbital configurations as between SF6, S+F6−, S++F6=, and even S−F6+. They are also little affected by change in hybridization at fluorine, and should therefore be suitable for use in the construction of molecular wave functions.Although the calculated energies include no exchange terms they are still of some interest. They suggest for example that the promotion energy to the configuration sp3d2 of sulfur (estimated to be 25–31 eV) can be compensated by the energy of molecu...

Molecular packing in crystals of the aromatic hydrocarbons

The van der Waals energy, quadrupole-quadrupole coupling energy, and hydrogen-hydrogen repulsions have been calculated for the equilibrium structure of crystalline naphthalene and for several displaced structures. The displacements are small rotations of the molecules about their symmetry axes, phased so that the space-group symmetry and unit-cell dimensions are preserved. For structural variations of this type the hydrogen-hydrogen repulsions have a strong minimum within a few degrees angular variation from equilibrium, indicating that these repulsions are dominant and determine the crystal structure for this class of displacement. The attractive van der Waals and quadrupole interactions on the other hand are not minimized at the equilibrium structure; they vary slowly (by a few wavenumbers per degree rotation) and approximately linearly.

Configurational Interaction in Molecular Orbital Theory. A Higher Approximation in the Non-Empirical Method

The disagreements between calculations of the benzene energy states by the method of antisymmetric molecular orbitals (A. S. M. O.) and by the augmented valence-bond theory given in previous papers (Craig 1950a to c) are due, at least in part, to the neglect in the former of interaction between different ‘configurations’. Every scheme of assigning electrons to molecular orbitals is a configuration, and where states with different configurations have the same symmetry they interact with one another under the influence of electron repulsion and suffer energy changes. In this paper a study of these energy changes is made, using a limited set of configurations. The A. S. M. O. states are affected by amounts up to 5 eV, and this is enough to show that the A. S. M. O. theory cannot be used for the detailed understanding of molecular spectral bands. The inclusion of configurational interaction gives the next higher approximation and makes the method, in principle, as general as is compatible with the initial use of 2p atomic wave functions. The method ought to prove valuable for settling in a non-empirical way issues for which the correctness of the simple empirical methods is in doubt. Even in the improved theory, however, the numerical precision required to interpret spectral separations in the order of 1 eV will be difficult to attain without the use of three-centre integrals and some other refinements.

The Electronic States of Mixed Molecular Crystals. I. Theory for Shallow Traps

The energy states of mixed molecular crystals in the rigid lattice are treated with special reference to impurity molecules differing only by isotopic substitutions from the host molecules. The perturbation Hamiltonian is treated explicitly, and the calculation made by an elaboration on the Green function method used by Koster & Slater for electron traps. Formulae for the energy levels and transition moments are given for dilute crystals and for crystals with any concentration of guests arranged in a superlattice. Virtual coupling between different guest molecules (trap-to-trap coupling) is considered, and limiting formulae derived.

d Orbitals in Compounds of Second‐Row Elements. II. Comparison of H, C, F, and Cl as Ligands

Calculations have been made to contrast the effects of H, C, F, and Cl as ligands on loosely bound d orbitals of second‐row elements. Sets of one, two (at right angles), four (square), and six (octahedral) identical atoms are compared. The approximation is electrostatic, with the use of potentials derived from self‐consistent field wave functions. The order of effectiveness is F>Cl>C≫H. The first three are more nearly equal in their perturbing power than expected from their electronegativities, and hydrogen is surprisingly ineffective.The conclusions lend themselves to some generalization to the conditions of binding in second‐row elements. These are discussed, and some examples given.

The electronic states of mixed molecular crystals III*. The general trapping problem

A theory of energy levels is given for rigid lattice mixed crystals in which the impurity differs from the host in its intermolecular coupling properties as well as in excitation energy. The influence of secondary trapping sites, induced by the impurity in its neighbour host molecules, is considered. The effects of a vacancy, of an isotopically distinguished impurity, and of a deep trap are treated as special cases. While the band structure is sensitive in details to differences between host–guest and host–host resonance coupling its general features are unaffected except that for a range of values of coupling parameters and trap depths two levels may split away from the band instead of one. The secondary traps cause additional levels to split away from the band and are probably important in the process in which delocalized excitation in the host crystal becomes localized in the impurity, as in fluorescence quenching. Typical results of calculations based on the theory are given for mixed crystals with naphthalene as host.

Polar Structures in the Theory of Conjugated Molecules. III. The Energy Levels of Benzene

The energy levels of benzene are calculated from a basis consisting of the five non-polar structures and tw enty-four polar structures, using the method given in part II. The role of polar structures is discussed. The results include a suggested new assignment for the 2080 Å bands of A1g- E2g, instead of A1g-B1u as required by molecular orbital theory. An intense A1g- E1u transition is calculated at 7·9 eV instead of the observed 6·7 to 7·0 eV. The disagreement with molecular orbital theory, to be dealt with more fully in a later paper, is briefly discussed.

Electronic levels in simple conjugated systems I. Configuration interaction in cyclobutadiene

In the simplest cyclic system of π-electrons, cyclobutadiene, a non-empirical calculation has been made of the effects of configuration interaction within a complete basis of antisymmetric molecular orbital configurations. The molecular orbitals are made up from atomic wave functions and all the interelectron repulsion integrals which arise are included, although those of them which are three- and four-centre integrals are only known approximately. In this system configuration interaction is a large effect with a strongly differential action between states of different symmetry properties. Thus the 1A1g state is several electron-volts lower than the lowest configuration of that symmetry, whereas for 1B1g the comparable figure is about one-tenth of an electron-volt. The other two states examined, 1B2g and 3A2g are affected by intermediate amounts. The result is a drastic change in the energy-level scheme compared with that based on configuration wave functions. Neither the valence-bond theory nor the molecular orbital theory (in which the four states have the same energy) gives a satisfactory account of the energy levels according to these results. One conclusion from the valence-bond theory which is, however, confirmed, is the somewhat unexpected one that the non-totally symmetrical 1B2g state is more stable than the totally symmetrical 1A1g. On the other hand, it is clear that the valence-bond theory, with the usual value for its exchange integral, grossly exaggerates the resonance splitting of the states, giving separations between them several times too great. Thus the valence-bond theory leads to large values of the resonance energy (larger, per π-electron, than in benzene) and so associates with the molecule a considerable π-electron stabilization. This expectation has no support in the present more detailed and non-empirical calculations.

Polar structures in the theory of conjugated molecules I. Identification of the ethylene π-electron states

This and two of three parts to be published subsequently are concerned mainly with the so-called valence-bond theory of conjugated and aromatic molecules. An improvement to the method is described, which consists in adding to the usual set of structures some extra ones which are ‘polar’ in the sense that they show two of the π-electrons on one centre, and none on another centre, making these two centres carry respectively negative and positive charges. This adds a certain flexibility to the description of molecular states which is lacking when the electrons are supposed to be distributed one to each centre throughout. In this part a preliminary question is treated which bears on getting the new empirical parameters needed for including polar structures in the theory. This question is the assignment of the long wave-length bands in the spectrum of ethylene. The assignment is made with the help of a theoretical study of the ethylene energy levels in an approximation using antisymmetric molecular orbitals. Using this calculation as a guide, two transitions are assigned. A weak band, appearing at about 2000 Å, is taken to be 1Ag-1Ag9 and a strong one, having its maximum at about 1630 Å, is taken to be 1Ag–1Blu.