Volume 41, Issue 9, 01 November 1964

Raman Spectrum of Anthracene
View Description Hide DescriptionRaman spectra of the anthracene solution are recorded using a Raman source of high luminosity. Twelve new frequencies are found and an assignment is proposed using earlier measurements on a single crystal.

Study of Two‐Center Integrals Useful in Calculations on Molecular Structure. V. General Methods for Diatomic Integrals Applicable to Digital Computers
View Description Hide DescriptionThe calculation of the electronic structure of atomic and molecular systems involves the determination of a number of integrals over the electronic coordinates. These calculations are feasible only by the use of high‐speed, large‐memory digital computers.
This discussion is based on a culmination of experience obtained in this laboratory with regard to methods useful in the evaluation of two‐center integrals by means of digital computers. The ground work for this paper, in terms of the analysis employed, is given in a series of papers by Roothaan, Ruedenberg, and Jaunzemis, but significant changes have evolved which offer considerable improvements and more economical calculations. The analysis presented here is especially the result of efforts to take full advantage of the capabilities of present digital computers. The methods advocated here are thought to be near optimal to a completely reliable and automatic computation of the electronic integrals in question with the desired accuracy. A not insignificant aspect of the methods given here is that an approach was sought which is unfailingly reliable and accurate regardless of the AO's involved in the integrals and at the same time as economical as possible.

Analytic Self‐Consistent Field Wavefunctions and Computed Properties for Homonuclear Diatomic Molecules
View Description Hide DescriptionThe analytic and computational framework for Hartree—Fock—Roothaan calculations on homonuclear diatomic molecules is presented. Several approaches to calculating the wavefunction are sketched as well as methods of computing molecular properties from the wavefunction. Emphasis is given to the efficient organization of these calculations for existing digital computers. Typical results obtained through the application of the programs and techniques developed are presented for the fluorine molecule.

Proton and Fluorine NMR Spectra of HBF_{2}
View Description Hide DescriptionProton and fluorine NMR spectra of HBF_{2} were recorded in the temperature range 140°K to 230°K. The values for the spin‐coupling constants J _{HF}, J ^{11} _{B—H} and J ^{11} _{B—F} are 108±1 Hz, 211±2 Hz, and 84±1 Hz, respectively. J _{HF} is temperature independent. The apparent values of J ^{11} _{B—H} and J ^{11} _{B—F} decrease below 165°K due to the interaction of rapidly fluctuating electric field gradients with the electric quadrupole moment of boron. The center of the proton multiplet is about 0.12 ppm downfield from the center of the terminal proton multiplet in diborane. The fluorine multiplet is about 60 ppm downfield from the fluorine resonance in BF_{3}, which in this case was a single structureless line. The dependence of ^{11}B–H coupling constants on the orbital hybridization of boron is discussed.

Generalization of the Activated Complex Theory of Reaction Rates. I. Quantum Mechanical Treatment
View Description Hide DescriptionIn its usual form activated complex theory assumes a quasiequilibrium between reactants and activated complex, a separable reaction coordinate, a Cartesian reaction coordinate, and an absence of interaction of rotation with internal motion in the complex. In the present paper a rate expression is derived without introducing the Cartesian assumption. The expression bears a formal resemblance to the usual one and reduces to it when the added assumptions of the latter are introduced. The new equation for the transmission coefficient contains internal centrifugal terms. The fourth assumption can also be weakened and a rotational interaction included in the formalism. In applications of the rate equation use can be made of the recent finding that in the immediate vicinity of a saddle point or a minimum, a potential energy surface can be imitated in some major topographical respects by a surface permitting separation of variables. The separated wave equation for the reaction coordinate is then curvilinear because of the usual curvature of the path of steepest ascent to the saddle point. Calculations of transmission coefficients and rates can be made and compared with those obtainable from the usual one‐dimensional Cartesian‐like calculations on the one hand and with some based on the numerical integration of the n‐dimensional Schrödinger equation on the other. An application to a common three‐center problem is discussed.

Generalization of the Activated Complex Theory of Reaction Rates. II. Classical Mechanical Treatment
View Description Hide DescriptionIn its usual classical form, activated‐complex theory assumes a particular expression for the kinetic energy of the reacting system, one being associated with a rectilinear motion along the reaction coordinate. The derivation of the rate expression given in the present paper is based on the general kinetic‐energy expression. A rate equation of the customary form is obtained: , where F‡ is the free energy of a system constrained to exist on a hypersurface in n‐dimensional space and F^{r} is the free energy of the reactants. The usual derivation is then reinterpreted, in terms of geodesic normal coordinates, to be somewhat more general than it appears.
Normally, rotation—vibration interaction is neglected, as in the above derivation, although not in treatments of some special reactions in the literature for which the centrifugal potential is important. A derivation is given which includes the influence of this centrifugal potential but which omits Coriolis effects.

Density Matrix Description of Coupled Spin Systems in the Presence of Two Strong Oscillatory Fields
View Description Hide DescriptionA density matrix description of coupled spin systems in the presence of two strong rf fields is given following a relaxation matrix formalism. The irradiating rf field, , has significant effects on the population distribution in a spin system even though the frequency of is not close to a resonance frequency of the system. Signal frequencies and intensities calculated in the limit of large amplitudes of the observing field with ω_{2} off resonance and ω_{1} saturating only a single line are compared with experimental proton—fluorine field‐sweep nuclear magnetic double resonance spectra of CHFCl_{2} and CH_{2}F_{2}. Apart from relaxation effects, the most important factor affecting the saturated intensities is the mixing of the pure states by .

Far‐Infrared Spectra of Cyanuric Acid, Uracil, and Diketopiperazine
View Description Hide DescriptionThe far‐infrared spectra of cyanuric acid, uracil, and diketopiperazine were measured in the region from 300 to 90 cm^{—1}. The GFmatrix method was applied to the analysis of lattice vibrations. The translational lattice vibrations were assigned to some of the observed bands. The force constants of hydrogen bonds were obtained.

Kerr Effect in Flexible Polymers
View Description Hide DescriptionA theory of the Kerr effect in flexible polymers is presented, which relates the electro‐optical birefringence to details of the polymer structure. Previous interpretations of the data are criticized. It is shown in particular that the Kerr effect should be quite sensitive to rotational hindering in the polymer molecule. The theory is applied to several model polymers and order‐of‐magnitude agreement with data for polyvinyl halides is obtained.

Relaxation of a Lorentz Gas with a Repulsive r^{—s} Force Law
View Description Hide DescriptionThe relaxation of a Lorentz gas (dilute light particle subsystem in a heavy particle heat bath) has been studied for a repulsive r^{—s} central force law interaction between the light and heavy particles. The Fokker—Planck equation for the velocity distribution functions of the light particle subsystem has been solved numerically for s=5, 9, 13, 21, and ∞ for various initial conditions. The dependence of the rate of relaxation and of the form of the time‐dependent velocity distribution function on the force law parameter s is discussed in light of the above results.

Effect of Pressure on the Viscosity and Dielectric Relaxation Time in Glycerol
View Description Hide DescriptionDielectric relaxation and viscosity data are presented for glycerol as a function of pressure and temperature.Viscosity data are given over a temperature range +10°C to —10°C and over a pressure range of atmospheric to 4000 kg/cm^{2}. Dielectric data are given at —6.7°C over the same pressure range. The form of the pressure dependence of the dielectric relaxation time appears to be Arrhenius and that of the viscosity is approximately Arrhenius. However, the pressure dependences of the dielectric time and the viscosity are significantly different, the ratio of η_{ s } to τ_{ D } varying by approximately two over the pressure range studied. The pressure dependence of η_{ s } and τ_{ D } were examined according to both the free volume theory of Williams, Landel, and Ferry (WLF) and the hole theory of Eyring. Both theories fail to give the proper pressure dependence of the data. When the WLF theory is applied to the data, the resulting form of the pressure dependence of η_{ s } is incorrect. Although the hole theory of Eyring predicts the correct form of the pressure dependence, a strongly temperature‐dependent hole volume, with a negative temperature coefficient of expansion, is needed to fit the experimental data.

Calculation of London Energies. II. An Iteration Procedure
View Description Hide DescriptionThe iteration of a previously discussed procedure for the approximate solution of the two‐particle partial differential equations of perturbation theory is presented. This iterative procedure is useful when the perturbation can be written as a finite sum of separable terms. The solution obtained is probably an asymptotic expansion of which the leading terms provide a good approximation to the exact solution. The two‐particle and nonadditive three‐particle London energies for interacting hydrogen atoms are calculated using the second and first iterations, respectively; the third and second iterations, respectively, of these energies diverge. The semiconvergence of the series is demonstrated and discussed, and further applications are mentioned.

Many‐Electron Theory of Atoms and Molecules. IV. Be Atom and Its Ions
View Description Hide DescriptionThe many‐electron theory is used and the correlation energy of Be is obtained as —2.567 eV, 99.87% of the experimental value. The theory gives each of the pair correlations as a separate minimum. The intershell correlations of 1s ^{2}2s Li‐like and 1s ^{2}2s ^{2} Be‐like ions are given for 3≤Z≤12 using the ``pair‐aufbau'' theory. The environmental effects of additional electrons on the correlation energy of a given subshell are obtained explicitly. The correlation energy ε(1s ^{2}) is reduced by 4.5×10^{—2} eV in going from Be^{2+} ion to the 1s ^{2} core of Be^{+} and by 4.7×10^{—2} eV from Be^{2+} to Be core. The corresponding changes in the 1s ^{2} parts of the Hartree—Fock energies are 5.7×10^{—4} eV and 17.5×10^{—4} eV. In this way the errors involved in the ``neglect of inner shells'' in calculating chemical or spectroscopicproperties from outer electrons alone can be examined in detail.

Many‐Electron Theory of Atoms and Molecules. V. First‐Row Atoms and Their Ions
View Description Hide DescriptionThe correlation energies of the 1s ^{2}2s ^{2} inner cores of the first‐row atoms B, C, ···, Ne are found to be very different from those of the corresponding four‐electron Be‐like ions, B^{+} to Ne^{6+}, due to the exclusion effects of the outer 2p electrons. Whereas the 2s ^{2}correlation, ε(2s ^{2}), in the 1s ^{2}2s ^{2} ions increases from —1.13 eV in Be to —3.2 eV in Ne^{6+}, the 2s ^{2}correlation in the neutral atoms decreases from —1.13 eV in Be to —0.27 eV in Ne. The many‐electron theory was used for the nonempirical 2s ^{2} calculations and included the use of the r _{12} coordinate. With these theoretical ε(2s ^{2}) values the correlation of a 2p electron with the 1s ^{2}2s ^{2} inner core is found to be large, ∼—1 eV. Also the 2p ^{2}correlation comes out about —1 eV. The results show that core energies will, in general, depend strongly on the state and number of the outer‐shell electrons and that intershell correlation interactions may be appreciable. Implications for π‐electron systems and the ligand‐field theory of inorganic complexes are discussed.

Scattering of High‐Velocity Neutral Particles. XIII. Ar–CH_{4}; A Test of the Peripheral‐Force Approximation
View Description Hide DescriptionCollision cross sections have been measured for argon atoms with energies between 700 and 2100 eV, scattered in room‐temperature methane. The results have been analyzed to obtain the average potential between an argon atom and a methane molecule,This result has been used as a test of combination‐rule approximations by comparing it with the average potential calculated from previous measurements on He–CH_{4}, He–He, and Ar–Ar. The peripheral‐force approximation gives consistent relations among the experimental results for these systems.

Infrared Study of the Crystalline Monohydrates of Nitric, Perchloric, and Sulfuric Acids
View Description Hide DescriptionThe infrared spectra of the solid monohydrates of three strong acids nitric, perchloric, and sulfuric were measured down to 50 cm^{—1}. The last two are completely ionic, viz., H_{3}O^{+}ClO_{4} ^{—} and H_{3}O^{+}HSO_{4} ^{—}, but the first one always seems to retain a trace of covalent structure, HNO_{3}·H_{2}O. In the three hydrogen‐bonded lattices the H_{3}O^{+} ions have libration frequencies of the order of 700 cm^{—1} and translation frequencies lying between 120 and 400 cm^{—1}. The frequencies of these lattice modes increase with the strengths of the hydrogen bonds. The deuterated hydrate of sulfuric acid gave only vitreous spectra because of supercooling. Likewise the room‐temperature phase of perchloric acid monohydrate showed broad, diffuse absorption bands due to the disordered orientation of the hydronium ions. The pyramidal configuration of the H_{3}O^{+} ion is confirmed definitely.

Cell Model for Quantum Fluids. II. Thermodynamic Properties of Liquid H_{2}
View Description Hide DescriptionThe thermodynamic properties of liquid hydrogen are computed on the basis of the cell model of Lennard‐Jones and Devonshire for those temperatures and volumes which are characteristic of its liquid state. The lowest energy levels are calculated exactly and the higher energy levels are calculated by the WKB method. The effects of the first three shells of neighbors are taken into account. The thermodynamic properties are in moderate agreement with experiment with the quantum corrections given accurately.

Ion Dissociation in the Drift Tube of a Time‐of‐Flight Mass Spectrometer: Spurious Fragments Arising from Charge‐Transfer and Dissociation Reactions of Retarded Ions
View Description Hide DescriptionSpurious fragment peaks that simulate fragment‐ion dissociation products formed in the drift‐tube reaction region have been observed in a time‐of‐flight mass spectrometer adapted for kinetic studies of ion dissociation processes. These peaks arise from processes occurring after the reactant ion has passed through the reaction region and entered the potential barrier that is normally used to separate reactants and products by selectively shifting their flight times. The flight‐time shifts characteristic of such spurious peaks depend on the distance from the ion source to the potential barrier, whereas the shifts characteristic of normal fragment peaks are independent of this distance. Comparisons of experimentally measured flight‐time shifts with analytically calculated values identify a fragment peak observed in association with the N_{2} ^{+} mass‐28 peak in N_{2}O as a spurious fragment peak, which represents not dissociation products of N_{2} ^{+} formed in the reaction zone, but neutrals formed inside the potential barrier. The absence of other fragment peaks then establishes that the neutrals are formed by the charge‐transfer processSince such spurious fragment peaks can, as in this case, be much larger than any real fragment peaks present, a cautious approach to peak identification is essential when using the TOF—potential barrier technique for ion dissociation studies. The recognition of such spurious fragment peaks is greatly facilitated by making flight‐time shift measurements at more than one value of the distance from the ion source to the potential barrier.

Structure in Ionization‐Efficiency Curves near Threshold from Alkanes and Alkyl Halides
View Description Hide DescriptionAppearance potentials have been measured by the retarding potential difference method on a time‐of‐flight mass spectrometer for: CH_{2} ^{+} from CH_{4}, CH_{3}Cl, CH_{3}Br, and CH_{3}I; CH_{2}X^{+} from CH_{3}F, CH_{3}Cl, CH_{3}Br and CH_{3}I; C_{2}H_{6} ^{+} and CH_{3} ^{+} from C_{2}H_{6}; C_{2}H_{5} ^{+} and C_{2}H_{5}X^{+} from C_{2}H_{5}X and C_{3}H_{7} ^{+}; and C_{3}H_{7}X^{+} from C_{3}H_{7}X where X is Cl, Br, or I. Substantially all of the structure in the ionization‐efficiency curves of fragment hydrocarbon ions can be accounted for by excitation potentials which are the same for all source molecules or by differences of appearance potentials between ion‐pair and ion—neutral processes which match known electron affinities. In all instances the appearance potential of a fragment ion at onset corresponded to an ion‐pairing process.

Amino Wagging and Inversion in Methylamines
View Description Hide DescriptionFine structures have been observed of the amino‐wagging bands at 780 cm^{—1} of CH_{3} ^{14}NH_{2}, at 776 cm^{—1} of CH_{3} ^{15}NH_{2}, at 625 cm^{—1} of CH_{3} ^{14}ND_{2}, and at 689 cm^{—1} of CH_{3} ^{14}NHD. For each vibration—rotation line an appreciable inversion splitting is observed. There is a marked coupling found between the inversion and the internal rotation; and the amount of the inversion splitting of each absorption line depends greatly upon the internal rotation quantum number σ (=0, +1, or —1) and the over‐all rotation quantum number K of the state in question. A hypothetical inversion splitting when the coupling were absent is estimated to be 31.6 cm^{—1} for the first excited state of the amino‐wagging vibration of CH_{3} ^{14}NH_{2}.