Application of the pople-santry-segal CNDO method to the cyclopropylcarbinyl and cyclobutyl cation and to bicyclobutane

A general discussion of approximate methods for obtaining self‐consistent molecular orbitals for all valence electrons of large molecules is presented. It is shown that the procedure of neglecting differential overlap in electron‐interaction integrals (familiar in π‐electron theory) without further adjustment may lead to results which are not invariant to simple transformations of the atomic orbital basis set such as rotation of axes or replacement of s, p orbitals by hybrids. The behavior of approximate methods in this context is examined in detail and two schemes are found which are invariant to transformations among atomic orbitals on a given atom. One of these (the simpler but more approximate) involves the complete neglect of differential overlap (CNDO) in all basis sets connected by such transformations. The other involves the neglect of diatomic differential overlap (NDDO) only, that is only products of orbitals on different atoms being neglected in the electron‐repulsion integrals.

Approximate Self-Consistent Molecular Orbital Theory. I. Invariant Procedures

In a number of recent publications, [1] – [5], we have discussed the asymptotic form of the dynamics of a general type of random one-dimensional chains. The equations we discuss are of the form 

$${{\rm{C}}_n}\left( {\frac{{{\rm{d}}{{\rm{V}}_n}}}{{{\rm{dt}}}}} \right) = {{\rm{W}}_{n + 1}}\left( {{{\rm{V}}_{n,n + 1}} - {{\rm{V}}_n}} \right) + {{\rm{W}}_{n - 1}}\left( {{{\rm{V}}_{n,n - 1}} - {{\rm{V}}_n}} \right),\,\,\,\,{{\rm{W}}_{n,n + 1}} = {{\rm{W}}_{n,n + 1}},$$

(1)

are independent positive random variables. Equations of this type arise in a variety of physical contexts. They can represent a master equation for hopping-type transport over random barriers (the Cn=1, the Wn,n+1 random hopping rates); a master equation for excitation transfer along a one-dimensional array of traps of random depth (the Cn random Boltzmann factors, the Wn,n+1=1); an electric transmission line (the Cn random capacitors or the Wn,n+1 random conductances); a random Heisenberg ferromagnetic chain at low temperatures (the Cn=1, Vn representing spin wave destruction operators, and the Wn,n+1 random near-neighbor exchange integrals). Replacing dVn/dt in (1) by d2Vn/dt2, they represent a harmonic chain with random masses (the Cn) or random force constants (the Wn,n+1).

Excitation Dynamics in Random One-Dimensional Systems

The interest in studying electrical conduction and polarization phenomena in polymers has increased since last year. Besides the classical problems of conduction, polarization and breakdown in polymeric insulators, interesting for the electric and electronic industry, new aspects are being considered by more and more research groups in the field. One of these is the application of the dielectric method, especially the depolarization technique, for studying molecular mobilities, i.e., multiple phase transitions in polymeric systems. Combined with mechanical relaxation, thermal analysis, magnetic resonance and with some additional techniques dielectric spectroscopy is becoming a powerful tool for studying the phase-structure of such complex polymer systems as blends, filled, and reinforced materials. This way the dielectric technique is helpful in quality control even of such systems which are not used in the electrical or electronic industry.

http://ieeexplore.ieee.org/iel7/7731603/7731604/07731995.pdf

Electrical properties of polymers

Self-consistent charge and configuration (SCCC) molecular orbital calculations are reported for 32 selected octahedral and tetrahedral first-row transition-metal complexes containing halide and chalcogenide ligands. It is found that for the range of metal oxidation states II through IV, Fsigma, chosen to fit the experimental Delta, is a function of only the metal atomic number for constant Fpi. In the range of formal metal oxidation numbers V through VII, Fsigma is also a function of oxidation number.Calculated and observed trends in covalency, Delta values, and first L-->M charge-transfer energies are compared. The conclusion is drawn that the molecular orbital method, in its present formulation, gives a reasonable account of the ground states and low excited states in simple metal complexes.

/pdf/molecular-orbital-theory-for-octahedral-and-tetrahedral-2e628w8vry.pdf

Molecular Orbital Theory for Octahedral and Tetrahedral Metal Complexes

The association and polar character of various carboxylic acids have been studied in the solvents benzene and heptane by means of measurements of the electric polarization in very dilute solutions. The data have been analyzed by assuming an equilibrium between dimers and monomers of the acid molecules. A rather large anomalous contribution to the polarization of the dimer has been found. Possible origins of this polarization have been briefly considered.

Electric Polarization of Carboxylic Acids in Dilute Solutions of Nonpolar Solvents I. The Relation of Electric Polarization to the Association of Carboxylic Acids in Hydrocarbon Solvents

Approximate SCF LCAO—MO calculations have been carried out for the ground‐state properties of four hydrogen halides; six internuclear distances were considered. In the model only the bonding electrons are considered explicitly. The effect of the inner electrons were taken account of by semiempirical methods. The electron pair is described by a single configurational wavefunction and the MO's are built from 1s and np AO's. The matrix elements are obtained utilizing the Mayer—Sklar, Mulliken, Pariser, and Pople approximations. As a secondary study the effect of the Wolfsberg—Helmholtz parameter K, in the resonance terms is studied.The calculated binding energies, equilibrium bond distances, dipole moments, vibrational force constants, and breaking forces obey the same trends as in experimental data. Moreover the magnitudes for these calculated quantities are in substantial agreement with experiment. This agreement can be improved for a given physical property of the series by introducing the arbitrary param...

Simplified SCF Method for σ‐Bonded Systems. I. Physical Properties of Hydrogen Halides

The electrical polarization is examined which arises from the motion of mobile charges roving in quasi‐one‐dimensional domains which are long compared to lattice spacings or to interatomic bonds. Such polarizations can be quite large. Relative dielectric constants of up to 1 000 000 can result. The discussed polarization is marked by its ready saturation at low field strengths. Using a polaron model, the nomadic dielectric polarization magnitude and its ready saturation at moderate field strengths is calculated and the results of the model are found to be in reasonable agreement with experiment. Experimental precautions to be taken in ascribing and identifying nomadic polarization as the cause of high polarizability in a given solid are described.

Nomadic polarization in quasi-one-dimensional solids

The effective use of dielectric polarization measurements in investigating the association of polar molecules in non-polar solvents has been largely confined to a study of the association of alcohols. These show significant changes in their state of aggregation in a range of concentrations sufEiciently high so that the equipment and methods hitherto available for dielectric constant measurements in solutions can be successfully applied to the investigation of their extent of association. The case of the carboxylic acids in non-polar solvents is quite different. Freezing point determinations show that extremely low concentrations must be attained before significant changes in the state of aggregation occur. This range of concentrations in the case of many of the acids lies below 2 X mole fraction. As a consequence it has been difficult to make sufficiently accurate measurements by most of the methods for molecular weight determination in solution to yield quantitative information about the molecular state of these acids in dilute solution in non-polar solvents. While it has been possible to use the freezing point method, this is applicable only a t a single temperature and so gives information about temperature coefficients and energies of association only through the use of estimates made at other temperatures by other methods. In this paper a description will be given of some of the improvements which were made in apparatus and methods in order to carry out dielectric polarization measurements in very low concentrations in non-polar solvents under anhydrous conditions. In view of the low concentrations involved it is necessary to include a comprehensive statement of the errors of the method. A detailed discussion of the methods employed for interpreting and analyzing the results from the standpoint of the association of the solutes is aIso incIuded.

Herbert A. Pohl

Papers

Electric Polarization of Carboxylic Acids in Dilute Solutions of Nonpolar Solvents I. The Relation of Electric Polarization to the Association of Carboxylic Acids in Hydrocarbon Solvents

Simplified SCF Method for σ‐Bonded Systems. I. Physical Properties of Hydrogen Halides

Nomadic polarization in quasi-one-dimensional solids

Polarization measurements on carboxylic acids in dilute solution in non‐polar solvents