Showing papers by "Henry Eyring published in 1954"

Equilibrium Theory of Unimolecular Reactions

Abstract: This paper develops an equilibrium theory of unimolecular reactions, and shows how this theory is related to other theories, such as the Rice‐Ramsperger‐Kassel treatment. Unimolecular decomposition reactions and isomerization reactions are described in terms of statistical mechanics and quantum mechanics (potential energy surfaces). The nature of the transmission coefficient is discussed in detail.

Use of Nuclear Attraction Integral Approximations in Molecular Quantum Mechanics

Abstract: Most molecular quantum‐mechanical studies of today make use of eigenfunctions composed of atomic orbitals. Such eigenfunctions give rise to difficult multicenter integrals which are usually evaluated by approximate methods. A study of the accuracy of such methods and of their derived results has long been desirable. Certain approximations for three‐center nuclear attraction integrals are here examined.Complete sample calculations are made with the approximate integral values for the triatomic activated complex molecule, H3. The use of the Mulliken approximate evaluation of integrals in the Heitler‐London treatment for H3 gives a binding energy 7.6 kcal/mole less than does the use of exact integrals. On modifying the Heitler‐London treatment by inclusion of screening constants for the outer and central atomic orbitals the Mulliken type approximate integrals gave for a trial calculation a binding energy 5.3 kcal/mole better than the best previous determination. This trial calculation (using the parametric v...

Use of Electron Repulsion Integral Approximations in Molecular Quantum Mechanics

Abstract: Straightforward theoretical calculation for molecular systems using eigenfunctions built up from atomic orbitals and employing actual and approximate methods for the evaluation of certain integrals have recently been widely applied with considerable success. Most of these calculations have evaluated the difficult multicentered electron repulsion integrals by use of an approximate formula suggested by Mulliken, in terms of Coulombic and overlap integrals. Previous work has indicated the general utility of this relationship. Here, direct numerical comparison is made of actual and approximate values of the multicenter 1s orbital integrals. The comparisons indicate that this approximation of integrals is moderately accurate over a wide range of internuclear configurations. Direct calculations of the energy of the linear triatomic hydrogen complex molecule with this approximate integral formula disclose that the total binding energy obtained by the two procedures is different by several kcal/mole. However the energy variation with internuclear separations obtained from the approximate calculations has its minimum very near that obtained using actual integrals. This indicates that energy minimization by variation of the parameters included in the trial eigenfunction may be accomplished using these approximate integrals. Single calculations may then be made using these ``best'' parametric values.

Approximate Integral Evaluations Used in the Molecular Quantum Mechanics of Nonlinear Molecules

Abstract: Molecular energy calculations employing actual and approximate multicenter angular dependent integral evaluations are compared. Individual integral values for three‐center integrals used in calculations for the triangular H3+ ion as computed by exact methods and by the approximate formulas of Mulliken and of Rudenberg are given. The results indicate that angular and distance relations of the nuclear skeleton of this polyatomic ion are determinable at almost the identical ``best'' value found using the much more laborious exact integral calculations. The energies of the approximate evaluations, however, indicate that once these ``best'' parametric values are determined the more exact calculations must be used. The approximate evaluations of second angular derivatives of integrals that are dependent on the angular and distance relations of component molecular nuclei are also computed and compared. Use of such derivatives in determination of approximate zero point energies, vibrational frequencies, and force...

Evaluation of Some Electron Repulsion Integrals Needed in Molecular Quantum Mechanics. II. Use of the Neumann Expansion in Evaluation of Two Electron Three‐Center Repulsion Integrals

Abstract: Formulation of two types of three‐center electron interaction integrals in convergent series is explicitly considered. These expressions place no restrictions on the effective nuclear charges of the composite atomic orbitals. The basic expansions are made in elliptical coordinates. The auxiliary functions used are discussed in detail and when of known form, references to the original literature are cited. Examples arising in the triatomic hydrogen molecular complex are given. Possibilities of extension of the method to complex molecules are pointed out.

Evaluation of Some Electron Repulsion Integrals Needed in Molecular Quantum Mechanics. A Method of Calculation of Two Electron Multi‐Center Repulsion Integrals without the Use of the Neumann Expansion

Abstract: Consideration has been given to two of the electronic repulsion integrals arising in the quantum‐mechanical energy calculation of the triatomic hydrogen molecular complex when no restrictions are placed on the effective nuclear charges of the composite atomic orbitals. The formulation of the integrals is first developed on a general basis and then restricted to the H3 molecule. The possibility of extension of the mathematical processes to similar electron interaction integrals in more complex molecules is pointed out. The integration formulas are given as rapidly converging series.

Federal support of basic research at a state university

Abstract: Examines federal support of basic research, with comparisons to similar systems in other countries.