Volume 51, Issue 11, 01 December 1969

Upper and Lower Bounds to Long‐Range Intermolecular Potentials
View Description Hide DescriptionThe moment method developed by Gordon is used to calculate upper and lower bounds to the coefficient of in the expansion of the interatomic potentials of the systems, H–H, H–He, and He–He.

New Type of Triplet Species in the TCNQ Ion‐Radical Salts
View Description Hide DescriptionNew triplet states in the ion‐radical salt φ _{3}AsCH_{3} ^{+}(TCNQ)_{2} ^{−} over and above the regular triplet exciton state are reported. These states are characterized by the properties of their spectra. At least one of the triplet states is an excited state with a singlet–triplet splitting of 2.5 cm^{−1}. The maximum values of the zero‐field splittings and the limited angular dependence of the spectra appear to indicate that the triplets arise from two unpaired electrons delocalized over sites located on different adjacent TCNQ chains. The lack of hyperfine structure is interpreted to indicate that there may be some motion associated with one or all of the triplet entities, but that this motion, if it exists, is slower than that of the regular exciton.

Nuclear Resonance Determination of the Magnetic Space Group of CsMnCl_{3}·2H_{2}O
View Description Hide DescriptionThe Cl, Cs, and H nuclear magnetic resonance are used to examine the magnetic structure of antiferromagnetic Cs Mn Cl_{3}·2H_{2}O. The magnetic space group is , and the structure consists of eight sublattices with the sublattice magnetization along the axis. The linear chains invoked by other authors to explain the high‐temperature anomaly in the susceptibility and specific heat are shown to be antiferromagnetic. The large intrachain exchange postulated by these authors and the rather small observed Néel temperature are shown to be reconciled by the Green's‐function theory of the Néel temperature, provided the exchange between the chains is assumed to be relatively small.

Configuration Interaction in the Simple Nonionic Valence‐Bond Wavefunction for the H_{2}I_{2} Reaction Complex
View Description Hide DescriptionThe symmetry‐adapted MO configurations contained in the simple nonionic VB wavefunction for the H_{2}I_{2} system in the H_{2}+I_{2} and 2HI diatomic limits and in the complex at the semiempirically determined saddle point are identified and their relative weights obtained as a function of the iodine orbital parameters. Implications of the results with regard to attempts to estimate the potential barrier height at the saddle point and to the mechanism of the hydrogen–iodine exchange reaction are discussed.

Electron‐Impact Excitation Cross Sections of the Lowest‐Lying Triplet States of Benzene
View Description Hide DescriptionCalculations of electron‐impact excitation cross sections of the lowest‐lying triplet states of benzene are carried out, using the Ochkur and Ochkur–Rudge approximations. Electronic wavefunctions are constructed from the LCAO molecular orbitals for electrons in benzene, and nuclear motions are disregarded. It is found that the differential cross section has a peak at a large scattering angle in the low‐energy region. The angular distribution for the excitation of the states shows a broad subsidiary peak at a larger scattering angle. As the incident energy is lowered, the position of the peak in the angular distribution shifts towards larger scattering angles, and the subsidiary peak tends to vanish. The total excitation cross section for the lowest‐lying triplet states is about at low incident energy. Results of calculations are discussed and compared with experimental findings.

Electron Spin Resonance and Structure of the BF_{2} Radical
View Description Hide DescriptionThe BF_{2} radical has been detected and its structure determined from observation of the electron spin resonance of >γ‐irradiated molecules of BF_{3} trapped in the xenon matrix at 4.2°K. Hyperfine structure of both B and F was resolved and analyzed. The isotropic coupling constants are: for ^{10}B, 277.98 Mc/sec; for ^{11}B, 826.24 Mc/sec; and for ^{19}F, 532 Mc/sec. Analysis of the hyperfine structure shows that the unpaired electron is in the system, that 93% of the electron spin density is in a nonbonding hybrid on the B, and that the remaining 7% is in hybridized bonding orbitals of the two F atoms. The hybrid of the unpaired electron on the B has 44% character and 56% character. This orbital is in the molecular plane. The bond angle derived from the hybridization is 112°.

Symmetry Property of the Critical Point Responsible for Combination Bands in the OH Stretching Region of Ca(OH)_{2}
View Description Hide DescriptionThe complicated band structure of Ca(OH)_{2} in the OH stretching region can only be understood by assuming combinational transitions occuring in critical points at . According to a former paper, the bands closest to the center of the band pattern are due to combinations of an internal OH stretching mode with acoustical modes. Using symmetry considerations, it is shown in this paper which symmetry property the critical points responsible for such transitions must have. Points with little group symmetry were found as the most probable ones.

Low‐Temperature Infrared Spectra between 1200 and 20 cm^{−1} and Normal‐Coordinate Analysis of Silicates with Olivine Structure
View Description Hide DescriptionInfrared spectra of powdered samples of Mg_{2}SiO_{4} (olivine) and γ‐Ca_{2}SiO_{4} (space group ) were measured at liquid‐N_{2} and liquid‐He temperature between 1200 and 20 cm^{−1}. The low‐temperature spectra do not show noticeable band sharpening. Using a simple force field with five stretching‐type force constants and symmetry‐adapted coordinates, a normal‐coordinate analysis is carried out for both crystal compounds. It is shown that satisfactory agreement between observed band frequencies and normal frequencies may be obtained through few iteration cycles. A number of features of the conventionally used group‐vibration approach are confirmed by the normal‐coordinate result, which in turn leads to a complete and fairly detailed assignment of the olivine‐type infrared absorption spectra.

Excess Ultrasonic Attenuation and Volume Viscosity in Liquid Methane
View Description Hide DescriptionUltrasonic attenuation in liquid methane has been measured at temperatures between 94 and 146°K with pressures to 87 kg/cm^{2}. The measuredattenuation greatly exceeds that accounted for by the dissipation due to shear viscosity and thermal conductivity. This shows a considerable need for the volume viscosity in the attenuation equation of Navier–Stokes. The excess attenuation observed is attributed to the “intrinsic” volume viscosity in liquid methane. The measuredattenuation divided by the frequency squared varies from 0.605 × 10^{−16} cm^{−1} sec^{2} at a temperature of 94°K and pressure of 1.65 kg/cm^{2} to 1.90 × 10^{−16} cm^{−1} sec^{2} at a temperature of 145.6°K and pressure of 8.8 kg/cm^{2}. The intrinsic volume viscosity ranges from 2.26 × 10^{−3} g/cm·sec to 1.88 × 10^{−3} g/cm·sec over the same temperature and pressure variations stated above. It is not believed that the internal degrees of freedom in methane are contributing an extra term to the measuredattenuation as if by some relaxation mechanism.

Quantum Vibrational Transition Probabilities in Atom–Diatomic Molecule Collisions. II Linear and Multistep Intermolecular Potentials
View Description Hide DescriptionThree methods for the calculation of vibrational transition probabilities in colinear atom–diatomic molecule collisions are outlined. These are based on the approximation of the intermolecular potential by terms which permit the solution of the Schrödinger equation by separation of variables in each of several regions into which the configuration space of the system is divided. Boundary conditions between the regions lead to systems of linear equations the solutions to which yield quantities from which the transition probabilities are easily obtained. Plots of transition probabilities for various repulsive intermolecular potentials are shown and discussed.

Class of Potentials for the Description of the Interaction between Two Atoms
View Description Hide DescriptionKeeping in view the difficulty of a useful single convenient mathematical form of the interatomic potentials, we, in the present paper, have proposed a combination of potential forms to represent the potential between two atoms. These potential forms have the great advantage that, first, they have a fairly small number of parameters and, second, they are very convenient for further analysis. The potential forms are such that the corresponding Schrödinger equations can be solved exactly except in one case. The convenient mathematical form of the potential would enable us to interpret and analyze the energy and the angular momentum dependence of the scattering data with great ease. We have also attempted with a good degree of success to fit these potentials in the case of H_{2}, H^{2+}, and CO and have also studied the possible relationship between the various potential parameters and the spectroscopic constants.

Analysis of the Contribution of Internal Vibrations to the Statistical Weights of Equilibrium Conformations of Macromolecules
View Description Hide DescriptionThe statistical weights of equilibrium conformations of macromolecules contain contributions from internal vibrations. An analysis of such vibrations, in the absence and presence of solvent, is presented from a quantum‐statistical‐mechanical point of view. Several classical approximations to the quantum‐mechanically correct expression, with different degrees of accuracy, are derived. In all of these approximations, all internal degrees of freedom of the polymer are divided into two classes: hard (bond stretching and bond angle bending) and soft (torsional rotations around single bonds, i.e., variation of dihedral angles). Since the hardvariables oscillate many times before the softvariables change in value by an appreciable amount, the hardvariables can be treated effectively as parameters (i.e., not as independent variables), which are (i) functions of the instantaneous values of the soft variables, or (ii) simply constants, the latter treatment being less accurate. In treatment (i) the molecule is regarded as flexible, whereas in treatment (ii) bond lengths and bond angles are assumed to be rigidly fixed, while the dihedral angles can change. In both treatments, the sum of the zero‐point energies corresponding to the hard degrees of freedom must be added to the soft‐mode part of the energy unless the errors in the calculation of the latter are ≥0.1 kcal/unit, which is the usual magnitude for the change in zero‐point energies for various conformations. The soft degrees of freedom are treated classically, i.e., the statistical weight is given by integration of the Boltzmann factor over phase space. The integration over the momentum space of the soft variables yields a conformation‐dependent term, proportional to ln detG, which may be called the kinetic entropy (G being a coefficient matrix for the kinetic energy of a polymer in the canonical expression for the Hamiltonian). A practical method is given for the calculation of detG, and it is applied to a simple example. The result shows that the dependence of ln detG on the coordinates is usually not negligible. For states with small conformational fluctuations (helical polymer structures and globular proteins), the result of treatment (ii) can be used as a perturbational step to proceed to treatment (i). Further approximations, necessary for treating random‐coil states (ones with large conformational fluctuations), are discussed. The effect of solvent on the statistical weights is also discussed.

Lower Bounds for Expectation Values
View Description Hide DescriptionThe low‐bound formula for expectation values proposed recently by the author is applied to various powers of and in the normal helium atom, and the results are compared with those obtained previously by Jennings and Wilson and by Weinhold for the same problem.

Rapid Evaluation of Coulomb Integrals
View Description Hide DescriptionThe properties of Fourier transforms and single‐center expansions of Slater‐type orbitals are used to obtain formulas for general Coulomb integrals as finite linear combinations of overlap and nuclear attraction integrals, thereby permitting the explicit expression of Coulomb integrals in terms of the auxiliary functions normally used in one‐electron integral calculations. The formulas are relatively simple and have a form which indicates the avoidance of numerical difficulties found in other evaluation methods. Working formulas are given for all integrals arising from orbitals of principal quantum numbers 1 and 2.

Planar Vibrations of Carbon Skeleton of Polyenes
View Description Hide DescriptionPlanar vibrations of polyenes are described by a model of a zigzag chain with three force constants (two for alternating bonds, one for the angles); the principal features of experimental vibrational spectra are explained, and the contribution of angular deformations is emphasized.

LCAO–MO–SCF Studies of Carbon–Carbon Bond Cleavage in Ethylene Oxide
View Description Hide DescriptionNonempirical LCAO–MO–SCF studies of carbon–carbon bond cleavage in ethylene oxide indicate the presence of two open forms. In one form (the 90, 90 form) the terminal methylene groups are perpendicular to the C–O–C plane. In the other (the 0, 0 form), the terminal methylene groups are in the C–O–C plane. On the basis of molecular correlation diagrams such as those of Hoffmann and Woodward, one would expect that either of these open forms could add stereospecifically to olefins. Previously Huisgen had suggested that the 0, 0 open form was an intermediate in the 1, 2 cycloaddition of tetracyanoethylene oxide to olefins; however, a 90, 90 form is also consistent with the experimental data.

Modified Random‐Walk Problem and the Unwinding of DNA
View Description Hide DescriptionThe random‐walk problem is modified by letting the length and the duration of the walker's step change as a function of the distance from the origin. The theory is developed by taking into consideration the variation of both and with . This is accomplished by replacing and with their respective Gaussian averages over . A situation like this arises in the problem of the unwinding of DNA, when the problem is considered as one of rotational Brownian motion. In that case, the angular velocity increases as the DNA rod shortens because of unwinding. The effect of this variation is to reduce the unwinding time by a factor of 4/9 from that calculated previously on the basis of a constant angular velocity. Other improvements on previous calculations are made.

Paramagnetic Resonance Spectrum of O^{−} Trapped in KCl, RbCl, and KBr
View Description Hide DescriptionThe impurity ion O^{−} has been introduced into KCl, RbCl, and KBr and detected at 4°K by EPRspectroscopy. The center has orthorhombic symmetry. A quantitative understanding of the factor and of the O^{17}hyperfine structure was obtained with the aid of equations derived in a recent analysis of the an‐alogous S^{−} impurity. The hyperfine splitting was described by the atomic parameters , , and . The present results indicate that in an earlier investigation of O^{−} trapped in alkali iodide crystals erroneous values were obtained for these parameters.

Distribution of the Excess Energy in CN Produced in Photodissociation of Cyanogen Halides and Hydrogen Cyanide
View Description Hide DescriptionThe vibrational and rotational excitations of CN produced in photodissociation of cyanogen halides and hydrogen cyanide in the vacuum ultraviolet have been measured as a function of incident wavelengths. More than 70% of the total population is in levels up to . No population inversion was observed, indicating the photodissociation takes place without much change in the equilibrium C–N bond distance. The percent conversion of the excess energy to vibration is approximately 20% for cyanogen halides and about 12% for hydrogen cyanide, irrespective of the amount of excess energy, which is much less than that expected from the equipartition of energy in all vibrational degrees of freedom of the molecule. The rotational levels of CN are highly excited for all molecules. The extent of conversion of the excess energy to rotation is of the order of 10%–20% for ICN and ClCN, and only several percent for BrCN and HCN. The remaining energy must be distributed as kinetic energy between CN and atoms. The vibrational and rotational distributions are discussed in terms of the equilibrium geometries of the ground and excited molecules and of the final products. The CN state is also formed in photodissociation and apparently not directly but through the . The intensity of the CN red emission is much less than that of the violet. Various other photodissociation processes are discussed. In general, the extent of conversion of the excess energy to vibration is much less than that expected from the equipartition theory for most triatomic molecules. No vibrational population inversion has been observed.

Noniterative Solutions of Integral Equations for Scattering. I. Single Channels
View Description Hide DescriptionA new method (homogeneous integral solution) for solving collision problems utilizing an integral equation formalism is presented. The approach is noniterative and applies equally well to purely local interactions or problems with combined local and nonlocal interactions. The method involves transforming the integral equation of scattering into a Volterra integral equation of the second kind. It follows that even for nonlocal interactions, the wavefunction may be determined noniteratively from knowledge of its value at a single point (the origin). A simple numerical procedure is proposed for solution of the Volterra equation which allows one to avoid matrix inversions completely. At the end of the calculation, the scattering or matrix is obtained directly from the solutions. The method is illustrated by a calculation of the singlet and triplet s‐wave Hartree–Fock phase shifts for electron–H‐atom scattering.