Leon L. Combs

Exact Finite Method of Lattice Statistics. I. Square and Triangular Lattice Gases of Hard Molecules

A general, feasible approach is presented for the evaluation of the statistical thermodynamics of interacting lattice gases. Exact solutions are obtained for lattice systems of infinite length and increasing finite width, using the matrix method which treats all densities on an equivalent basis. Through the application of symmetry reduction and the use of an electronic computer to perform logical as well as arithmetical operations, widths of up to 24 sites for two‐dimensional lattices can be handled. For examples studied, rapid convergence is obtained away from transition regions and in the vicinity of phase transitions the behavior appears to be a sufficiently regular function of the width to allow meaningful extrapolation to systems of infinite width. Two problems of two‐dimensional lattice gases are solved as illustrations of the technique: the square and triangular lattice gases with infinite repulsive interactions preventing the simultaneous occupancy of adjacent lattice sites (excluded‐volume effect...

Exact Finite Method of Lattice Statistics. II. Honeycomb‐Lattice Gas of Hard Molecules

Thermodynamic properties have been obtained using the matrix method for a two‐dimensional honeycomb‐lattice gas of hard molecules which prevent simultaneous occupancy of nearest‐neighbor sites. Exact results have been obtained for cylinders of infinite length and finite circumference from 6 to 18 sites. Uniform trends with increasing circumference lend confidence to extrapolations used to infer the behavior of systems of infinite width. We find a great similarity with the corresponding square‐lattice gas and a second‐order phase transition at activity z=7.92±0.08, reduced pressure p/kT=1.12±0.05, and relative density ρ/ρ0=0.845±0.02. The compressibility appears to be infinite at the transition.

Low resolution microwave spectra and indo calculations of phenylisothiocyanate and phenylisocyanate

Abstract The low resolution spectra of φNCS and φNCO have been studied in the microwave R-band region. The spectroscopic constant ( B + C ) has been evaluated for both molecules. These data have been used to obtain information on the orientation of the linear NCS and NCO group relative to the bond from the phenyl ring. The results indicate an opening of the φ-N-C angle over that found in the hydrogen counterparts HNCS and HNCO. A modified INDO calculation yields structural parameters which are consistent with the trends observed, and indicate that the opening of the angle in going from HNCS (HNCO) to φNCS (φNCO) can be attributed to delocalization with the phenyl ring.

Anomalous Energy Minima by Semiempirical Calculations

Abstract During our investigations of potential barriers to various types of internal rotation we have observed several apparently false energy minima. Our first contact with these suspicious barriers arose from a set of calculations on FNO2 using the techniques INDO1 and CNDO/22. Total energy calculated by INDO as a function of the O-N-O angle is presented in Fig.

One‐Center Molecular Orbitals for HeH++ and HeH+ with Variable Origin

The feasibility of using a variable expansion point in one‐center calculations is investigated for the ground states of HeH++ and HeH+ with very limited basis sets of Slater‐type atomic orbitals. The energy improvement resulting from variation of the expansion point appears to be economical only if the wavefunction is of the simplest possible form, 1s or (1s1s). For these functions the maximum effect of varying the origin occurs in the vicinity of 0.4 a.u., where the improvement in the electronic energy is somewhat less than 2%.

A semiempirical study of the sugar radicals in irradiated cytidylic acid b and deoxyadenosine.

The possible radical species resulting from irradiation of the sugar groups in deoxyadenosine and cytidylic acid b are studied by the semiempirical technique INDO. The calculated unpaired spin density and hyperfine coupling constants are compared with experimental data. These comparisons and calculated relative energeis of each species indicate that both molecules yield the same radical species upon irradiation.

Anomalous Energy Minima Studies by Mindo/3

Abstract A previous publication1 utilizing the INDO2 and CND0/23 semi-empirical SCF-MO techniques has shown that these methods predict anomalous minima in the potential surfaces of small molecules and molecular ions, particularly those of type 0-X-0. Two studies have bcmen published concerning the removal of such anomalous pre-dictiors. The first approach4 involved reparameterization of the INDO method – specifically involving the Slater exponents α, and the bonding parameters B° of carbon and oxygen – to remove the anomalous iinimum from the potential surface of C02. It was de-monstrated that reparameterization could be used to remove the Salse minimum in this case; but only at the expense of the other predictive qualities of INDO, or with the prediction of an unreal-istically broad energy minimum – neither of which could b e con-sidered an acceptable solution.

Semiempirical calculations of internal barriers to rotation and ring puckering: III. A reparameterization study1

Abstract A previous study of semiempirical techniques demonstrated that the present methods are not satisfactory for studying rotational barriers. In this report the parameters for possible reoptimization are studied, and the variables that are determined to be barrier related are the orbital exponents, ζ, and the bonding parameters,β o i . Optimum values of these parameters for hydrogen, carbon and oxygen are determined for ethane, cyclobutane, acetone, cyclobutanone, isobutylene and methylenecyclobutane to predict good barrier heights, good bond angles and good bond distances. Such values are seen to be obtainable, but carbon atoms in these molecules do not have the same parameter values. The ζ and β o values so obtained are applied to a few other molecules and it is observed that these parameters do yield improved barrier heights, bond angles, and bond distances for molecules other than the ones involved in the reparameterization. Several other approaches to a reparameterization scheme are also suggested.

Reparameterization of Semiempirical Techniques to Remove Anomalous Energy Minima

Abstract Semiempirical molecular orbital calculations have been shown to predict double minima potential surfaces which are not confirmed by further experimental or theoretical evidence.1 These same techniques predict barriers to internal rotation which are not only in large error but may not even follow the experimental trends.2 These discrepancies offer a large decrease in self confidence for the application of these techniques to molecular systems where direct experimental evidence is not available, and these are often the circumstances where one wants a theory to be used. Therefore, our research group is in the process of reparameterizing the procedure INDO3 to yield barriers to internal rotation, bond angles, and bond lengths within reliable confidence limits. During this process of determining new parameters we have observed that some sets of parameters will also remove the anomalous energy minima predicted by the original INDO parameters. To illustrate this we consider in this paper the molecule CO2.

Anomalous Energy Minima Surfaces

The phenomenon of level crossings as predicted by the semiempirical techniques for certain molecules when the total energy is viewed as a function of some conformational property is examined using the extended Hueckel method, the iterated Hueckel method, the iterated extended Hueckel method, and an ab-initio procedure with a minimal basis set. The molecule chosen is CO/sub 2/. Potential energy curves calculated by the various methods, dipole moments, and net charges all as a function of bond angle are plotted. It is noted that great care must be taken especially when the molecules of interest contain atoms of high electronegativity. 12 references. (JFP)