Types Of Potential Functions Research Articles

The Dimensions and Dipole Moments of Poly(propylene glycol) Chains

Conformational energies of poly(propylene glycol) chains were calculated using classical torsional and nonbonded interaction potentials. It was shown that distinct energy minima occurred at rotational angles about the skeletal C—O bond including an asymmetric carbon, which were displaced by about −25, 0, and 20° (or 25, 0, and −20°) from the conventional symmetric positions of trans (T), gauche (G), and another gauche (G′), respectively. Two types of potential functions were used for the van der Waals interaction energy; from the comparison of experimental data for dimension and dipole moment with the theoretical values calculated in the rotational isomeric approximation, the one recommended by Scott and Scheraga and by Abe et al., was found to be appropriate for PPG chains. Calculations also showed that the mean-square moments increase with increasing syndiotacticity, although their extent was smaller than those predicted for asymmetric vinyl chains. Theory and experiment for the mean-square moments were in fair agreement in terms of their magnitude and dependence on tacticity and on molecular weight without introducing any adjustable parameter.

Trapping States Formed by Structural Defects in Molecular Crystals

Abstract Results of calculations of the energetic distributions of trapping states in simple molecular crystals are given in the paper. A crystal with primitive regular unit cells has been taken into account, and three kinds of simple isolated linear defects have been considered: an edge dislocation, a linear array of vacancies, and a defect formed by a linear array of molecules larger than the host ones. Equilibrium positions of molecules in the vicinity of the defects have been calculated describing the intermolecular interactions by the Lennard-Jones type potential function. Local values of the polarization energy and hence depths and distributions of traps formed by molecules neighbouring to the defects have been calculated in the ion-dipole approximation. It has been shown that the formation of trapping states by thermal vibrations can be neglected as being a small effect.

A new approach in atomic configuration interaction calculations

A new type of potential function is derived from the atomic Hartree-Fock self- consistent potential which has almost identical occupied orbitals, but an adjustable set of unoccupied bound orbitals. Comparisons are made between the properties of this potential and the Hartree-Fock potential for trivalent praesodymium. It is shown that the use of the new potential introduces considerable simplifications into atomic configuration interaction calculations.

The microwave spectra of cyanamide: Conclusions from [formula omitted]a transitions

Microwave spectra have been observed for the species NH 2CN, NHDCN, ND 2CN, 15NH 2CN, NH 2C 15N, 15ND 2CN and ND 2C 15N. The nonplanar nature of the molecule is confirmed and the following structural parameters obtained N 1N 2 = 2.506 ± 0.002 Å, N 1C = 1.346 ± 0.005 Å, CN 2 = 1.160 ± 0.005 Å, N 1H = 1.001 ± 0.015 Å, HN̂ 1H = 113°31′ ± 2°, out of plane angle (see text) = 37°58′ ± 1°. (N 1 is the amino nitrogen atom and N 2 that the cyanide group.) From an analysis of perturbations occurring in the spectra the lowest inversion splittings in NH 2CN, NHDCN and ND 2CN have been estimated as 50, 33 and 15 cm −1, respectively. Calculations concerning the barrier to inversion are presented assuming a Manning type potential function. The μ a component of the dipole moment is measured as 4.32 ± 0.08 D for the vibrational ground state, and 4.27 ± 0.08 D for the first excited inversion state.

Periodic potential functions for pseudorotation and internal rotation

A computer program which uses matrix diagonalization techniques has been developed for determining the energy levels and wave-functions for periodic potential functions of the form V = 1 2 ∑ V n(1-cos nφ), where terms with n ranging from 1 to 6 can be used. The mass related internal rotation constant B is also allowed to vary as a function of the phase φ. The energy level patterns of eight different types of potential functions, which are typical for internal rotation and pseudorotation, have been determined. Several applications of such calculations for the interpretation of vibrational data are discussed.

Normal coordinate treatment and assignment of fundamental vibrations of vinyl fluoride and the seven deuterovinyl fluorides

The results of a unified normal coordinate treatment for vinyl fluoride and the seven deuterated species are presented. Our calculation confirms the out-of-plane assignment of Scherer and Potts. For the in-plane vibrations, we have used a modified valence-force type of potential function and, on the basis of the results, we are presenting a satisfactory assignment for most of the fundamentals. Investigation of the liquid spectra is recommended to resolve the ambiguity of the remaining few undecided in-plane fundamentals.

Statistical Thermodynamics of Binary Liquid Mixtures

Abstract By means of the cell method and using the Sutherland type potential function for pair interactions between molecules, a statistical theory was formulated for binary liquid mixtures consisting of rigid spherical molecules differing in size. A formula was derived for cohesive energy as a function of the volume of liquid, and studied in combination with the radial distribution function. The applicability of the square-well type potential function within a cell was also examined. Formulas for excess thermodynamic functions were derived and their applicability investigated. For 22 binary systems consisting of nearly spherical molecules, excess thermodynamic functions were calculated and compared with data in literature. The results show that the theory is applicable to the mixtures.

Influence of anharmonicity on the parameters of an exponential potential for heavy rare gas solids

Anharmonic parameters of the Buckingham type potential function have been computed at 0 °K for solid argon, krypton and xenon. The contribution of cubic and quartic terms of potential energy expansion to Helmholtz free energy has been taken into account by an iteration method. The results are compared with quasiharmonic parameters of the same potential. The effect of anharmonicity is found to be negligible in the case of krypton and xenon.

Normal coordinate treatment and assignment of fundamental vibrations of vinyl chloride and the seven deuterovinyl chlorides

The assignments of the fundamental wave numbers of vinyl chloride and the seven deuterovinyl chlorides have been reinvestigated on the basis of a normal coordinate treatment with a valence force type potential function. A six-constant out-of-plane and a 25-constant in-plane potential function reproduced the observed fundamental wave numbers very satisfactorily. The present calculations remove the violations to Rayleigh's rule in the hitherto adopted fundamental assignments and give reliable estimates of the uncertain or unobserved fundamental wave numbers.

The grain boundary energy and configuration of inert gas crystals—II

The expression derived in the previous paper (1) (hereafter referred to as (1)) for the average inverse power potential energy of interaction between a particle at a fixed distance above a half-crystal face and the half-crystal is applied to a calculation of the minimum energy spacing and interfacial energy between two perfect half-crystals placed together to form a “completely misfitting” grain boundary. The grain boundary energies and spacings of various juxtiposed surfaces of face-centered cubic argon at 0°K are calculated as examples with the following results in ergs cm 2 : (100)–(110), 41.7; (100)–(111), 22.8; (111)–(111), 16.0. This method would seem to be applicable to any system obeying the specified type of potential function when there is a continuous spontaneous generation of dislocations in two dimensions at the boundary as appears to be the case for large angle twist or tilt boundaries.

Effective Carrier Mobility in Surface-Space Charge Layers

Carriers held to a region near the surface by the potential well of a space charge layer may have their mobility reduced by surface scattering, if the width of the well is of the order of a mean free path. An effective mobility, which may differ from the bulk mobility by as much as a factor of ten, has been obtained from a solution of the Boltzmann equation. Solutions have been carried out for two types of potential functions: (a) a linear potential corresponding to a constant space-charge field, and (b) a solution of Poisson's equation including an external bias applied normal to the surface. The results have been used to calculate changes in surface conductance of germanium with changes in surface potential and predict the "field effect" and "channel effect" mobilities.

Scattering of High-Velocity Neutral Particles. IV. He–A; A–He

Total collision cross sections have been measured for helium atoms with energies between 500 and 2100 ev, scattered in room temperature argon, and for argon atoms with energies between 600 and 2100 ev, scattered in room temperature helium. In each case, two detectors of different geometric aperature have been used, and potential energy functions have been obtained by procedures previously applied to helium scattered in helium. The average function for the potential energy between a helium atom and an argon atom derived from the measured cross sections may be represented by V(r)=9.95×10−11/r7.25ergs,for values of r between 1.64A and 2.27A. Since this potential is in good agreement with the geometric mean of the potential between two helium atoms and that between two argon atoms in the range represented by the arithmetic average of the individual interaction distances, it is suggested that the parameters of a point repelling type potential function may, in general, be combined in this manner.

Infra-Red and Raman Spectra of Polyatomic Molecules. VII. C2D6

The infra-red spectrum of gaseous C2D6 has been investigated from 2 to 22μ, and the Raman spectrum of the liquid has been photographed. These data have been analyzed for both the symmetries D3d and D3h. It is concluded that the equilibrium configuration of ethane cannot be reliably determined from the analysis of the data now available on the vibrational spectra of C2H6 and C2D6. However, the ``uncertain frequency'' of C2H6 is determined by application of the product rule if the symmetry is D3d. A modified valence force type potential function containing interaction terms between the two methyl groups is found to fit the fundamental frequencies of the light and heavy ethanes quite well.

The Isotope Effect in the Vibration Spectrum of CCl4

The fine structure in certain of the Raman lines of CCl4 observed by Langseth and interpreted by him as being due to a lack of symmetry in the four carbon valencies has been shown to be accountable for as a purely isotopic effect. Rosenthal's general theory of the isotope effect in molecules of this type has been applied to the case of CCl4 in an attempt to differentiate between two types of potential function which have been proposed for this molecule. The fine structure patterns predicted on the different theories have been worked out. Unfortunately the existing experimental data are not sufficiently good to allow a decision to be made as to which is the better function.

The Normal Frequencies of Vibration of Symmetrical Pyramidal Molecules AB3 with Application to the Raman Spectra of Trihalides

The symmetrical pyramidal molecule AB3 is treated by a general normal-coordinate method, six force constants being required. The convenience of the use of ``symmetry coordinates'' is illustrated in obtaining the formulas for the normal frequencies for several types of potential functions. It is found that with two constants the central force treatment and valence force treatments fit the data equally well. The four constants K, H, K′ and H′ of the potential function 2V=KΣiΔRi2+12HR02Σij′Δαij2+K′Σij′ΔRiΔRj +2H′R02(Δα12Δα23+Δα23Δα31+Δα31Δα12)for certain trihalides are obtained from Raman data. The interatomic distances calculated using these values of K in the empirical relation found by Badger for diatomic molecules agree with the distances obtained by other methods to within about 0.1A.