Volume 34, Issue 4, 01 April 1961

Normal Coordinate Treatments and Calculated Thermodynamic Properties of Phosphoryl Chloride, Thiophosphoryl Chloride, and Phosphoryl Fluoride
View Description Hide DescriptionThe infrared and Raman spectra for phosphoryl chloride, thiophosphoryl chloride, and phosphoryl fluoride were collected and examined for the most probable values for the wave numbers, intensities, and depolarization factors. The data are as follows: The Raman displacements Δσ in cm^{—1}, the relative intensities I, and the depolarization factors ρ are for POCL_{3}: Δσ(1)ρ = 192.85 (8) 0.83, 267.39 (6) 0.64, 337.44 (7) 0.81, 486.24 (10) 0.05, 581.2 (3) 6/7, and 1289.9 (5) 0.04; for PSCl_{3}: 172 (5) 6/7, 247 (7) 6/7, 247 (calculated) 430 (10) 0.1, 538 (1) 6/7, and 753 (1) P; and for POF_{3}: 337 (w) 6/7, 476 (m) 6/7, 483 (from infrared) P, 875 (s) 0.05, 982 (vw) 6/7, and 1395 (m) 0.1. As for the infrared spectral data, those of G. Cilento et al., were used for PSCl_{3}, and those of Gutowsky and Liehr were used for POF_{3}. No published infrared spectral data were found for POCl_{3}. Also normal coordinate treatments were conducted for POCl_{3}, PSCl_{3}, POF_{3}, and PSF_{3} on the basis of a model having C _{3v } symmetry. The normal coordinate treatments gave the listed wave numbers as fundamentals and lend support for the 247 cm^{—1} band for PSCl_{3} and 483 cm^{—1} band (observed in the infrared and assigned as fundamental by Gutowsky and Liehr) for POF_{3} as the missing Raman bands. Moreover, the F matrix elements obtained for these molecules were determined in such a manner that those potential constants for the PCl_{3} group had nearly the same values in both POCl_{3} and PSCl_{3}, those for the PF_{3} group had nearly the same values in both POF_{3} and PSF_{3}, the one for the PO group had nearly the same value in both POCl_{3} and POF_{3}, and the one for the PS group had nearly the same value in both PSF_{3} and PSCl_{3}. The potential constants determined had the following values in md/A: For POCl_{3}, f _{PO}=9.890, f _{PCl}=2.466, f _{PClPCl}=0.399, for PSCl_{3}, f _{PS}=0.030, f _{PCl}=2.466, f _{PClPCl}=0.399; for POF_{3}, f _{PO}=9.890, f _{PF}=5.633, f _{PFPF}=0.483, and for PSF_{3}, f _{PS}=2.9694, f _{PF}=5.333, f _{PFPF}=0.183. Finally, the values of the thermodynamic properties for these substances were computed for the ideal gaseous state using the rigid rotor harmonic oscillator approximation at 1 atm from 200° to 1000°K.

NMR Spectra of Propyl Derivatives
View Description Hide DescriptionA perturbation treatment, carried to third order in the energies and first order in the intensities of the analysis of the propyl group spectra, is presented. Accurate values are given for the coupling constants and the chemical shifts of the common propyl derivatives, both for the pure compound and as extrapolated to infinite dilution in carbon tetrachloride.

Proton Chemical Shifts for the Alkyl Derivatives
View Description Hide DescriptionThe chemical shifts of a series of methyl, ethyl, propyl, and isopropyl derivatives have been studied in an effort to determine the distance and angular dependence of any contribution to the chemical shift arising from magnetically anisotropic substituent groups. It was found that electron withdrawal effects play a dominant role in determining the chemical shifts for methyl derivatives. The nearly exactly linear relation of the methyl shifts to electronegativity for the methyl halides seems to rule out any large influence due to magnetic anisotropy. The ethyl shifts were found to be determined by electron withdrawal effects plus a factor which acted equally at the α and β positions. It was found that this factor arises from the carbon‐carbon bond. By assigning a chemical shift due to the presence of the C–C bond, which is dependent in size on the substituent attached to the α carbon, the apparently anomalous frequencies observed for the alkyl derivatives can be accounted for. A possible explanation for the C–C bond shift may be regular changes in the paramagnetic term in the Ramsey equation due to changes in the excitation energy denominator when a C–C bond replaces a C–H bond.

Calculation of Complex Equilibrium with an Unknown Number of Phases
View Description Hide DescriptionAn extension of Brinkley's generalized procedure is proposed for calculating the equilibrium compositions of complex systems in which several phases are possible but their actual number and identities at equilibrium are not known a priori. In contrast to other methods, the present method eliminates the trial and error associated with presence or absence of phases. Thus, little computational effort is required beyond that expended when the number and identities of all phases are known. The essential equations are given together with a description of the computational procedure.

Changes in the Electronic Transitions of Aromatic Hydrocarbons on Chemical Substitution. I. Perturbation Theory for Substituted Cyclic Polyenes
View Description Hide DescriptionGeneral formulas are derived by first‐ and second‐order perturbation theory for the changes in the transition moment, transition probability, and frequency of aromatic cyclic‐polyene transitions produced by ideal chemical substitutions. The changes are described in terms of the interactions of three kinds of prototype electronic states: carbon‐ring states, substituent states, and charge‐transfer states. The interaction of the ring states with one another is regarded as an inductive effect of substitution; the interaction with the substituent and charge‐transfer states, as a conjugative effect. Using the symmetry properties of the prototype states and assuming that the interactions are caused by a sum of perturbation operators for the individual of substituents, it is shown how the changes depend on the nature, the number, and the positions of the substituents on the ring. Formulas pertaining to the singlet‐singlet pi‐electronic transitions in benzene are given.

Changes in the Electronic Transitions of Aromatic Hydrocarbons on Chemical Substitution. II. Application of Perturbation Theory to Substituted‐Benzene Spectra
View Description Hide DescriptionAn analysis is made of the changes that occur in the 2600, 2050, and 1850 A transitions of benzene on chemical substitution. Formulas derived by first‐ and second‐order perturbation theory, with coefficients evaluated by molecular orbital theory, are presented and applied to a large collection of intensity‐change and frequency‐shift data obtained from the literature. Most of these data pertain to the 2600 A transition. The first‐order intensity formula derived for the 2600 A transition (taking the excited state to be ^{1} B _{2u }) is found to hold quite well for substituents with monoshift (frequency shift on monosubstitution) less than 1500 cm^{‐1}; the first‐ and second‐order frequency‐shift formula, for substituents with monoshift less than 2000 cm^{‐1}. No attempt is made to analyze the intensity changes observed in the 2050 and 1850 A transitions as these changes are too small, relative to the initial intensity, to be reliably measured for weakly perturbing substituents from existing spectra. The frequency shifts, however, can be measured fairly reliably for these two transitions, and it is shown that the formulas derived on the basis of ^{1} B _{1u } and ^{1} E _{1u }excited states, respectively, hold for methyl substitution at least. Empirical values of the intensity and frequency perturbation parameters for the 2600 A transition are presented for over 30 substituents; values of the frequency perturbation parameters for the 2050 and 1850 A transitions for more than half of these are also presented. The meaning of the parametric values is discussed in the light of theoretical expectations.

Millimeter Wave Spectrum and Molecular Structure of Oxygen Difluoride
View Description Hide DescriptionThe molecular structure of oxygen difluoride (OF_{2}) has been studied by microwave spectroscopy techniques. A video microwave spectrometer was used to find 13 rotational absorption lines. Klystron‐driven crystal harmonic generators were used as energy sources for the spectrometer. The frequencies of the lines were measured with a precise frequency standard. Nine of the lines were assigned to rotational transitions of OF_{2} using a graphical method. The three average rotational constantsA, B, and C were determined from the exact energy solutions for the rotational transitions. The values for the rotational constants together with the effective moments of inertia calculated from them were A=61 567.71 Mc, I_{A} =8.21096 amu, A^{2}; B=11 066.54 Mc, I_{B} =45.6809; C=9 343.85 Mc; I_{C} =54.1088 amu, A^{2}. The effective values for the oxygen fluorine interatomic distance and the apex angle 2θ calculated from I_{A} and I_{B} were r=1.3896 A, 2θ=104.163. The rotational inertial defect was found to be +0.217 amu, A^{2}.

Influence of the Molecular Environment on the Carbonyl Frequency. Electronic Calculation
View Description Hide DescriptionThe K_{v}C=O force constants of formaldehyde, acetaldehyde, acetone, glyoxal, p‐benzoquinone, o‐benzoquinone, and of chloroacetaldehyde have been determined by Pariser‐Parr‐Pople's SCF‐MO procedure. The theoretical expression for the force constant corresponding to this theory is given. The K_{v}C=O force constant is found to decrease in the order formaldehyde, chloroacetaldehyde, acetaldehyde, acetone; this is due to the corresponding decrease of the effective electronegativity of the carbonyl carbon atom. The K_{v}C=O force constant decreases also in the series acetone, o‐benzoquinone, p‐benzoquinone, and in the series acetaldehyde, glyoxal; this is due to conjugation effects. The force constants calculated by this theory agree satisfactorily with the experimental values.

Thermoelectric Power of Silver Halides
View Description Hide DescriptionThermoelectric power measurements have been made on the systems AgCl+CdCl_{2}, AgBr+Ag_{2}S, and AgBr+CdS, as well as the pure silver halides, in the temperature range from 100° to 400°C. Silver metal electrodes were used. The behavior of AgCl and CdCl_{2} is similar to the previously investigated AgBr+CdBr_{2} system, except that the effect of the impurity is more pronounced in AgCl. The results of Cd‐doping of AgBr and AgCl are analyzed according to the theory of Howard and Lidiard to give the concentration of Frenkel defects, the ratio of mobilities, and the quantities q_{i} ^{*}+q_{v} ^{*}, q_{i} ^{*}+Ts_{i} ′, and q_{v} ^{*}+Ts_{v} ′, where q ^{*} and s′ are the heats of transport and entropies of formation for the interstitials and vacancies. The results are in agreement with conductivity data, but the heats of transport are surprisingly large and temperature dependent. It is concluded that association between Cd^{+ +} and Ag^{+}vacancies is negligible above 100°C, but that association between S^{— —} and Ag^{+}interstitials, and between Cd^{+ +} and S^{— —}, is significant even at 400°C.

Wave Functions and Correlation Energies for F, F^{—}, and Ne
View Description Hide DescriptionHartree‐Fock solutions have been obtained by the finite expansion technique and a comparison is made with other computational methods and results. Total energies, correlation energies, and one‐electron parameters are presented as well as a tabulation of the radial functions in analytic form. The correct sign and order of magnitude of the fluorine electron affinity is predicted.

Anisotropic Hyperfine Interactions in the ESR Spectra of Alkyl Radicals
View Description Hide DescriptionWe have studied the effect of anisotropic hyperfine interactions on the electron spin resonance(ESR) spectra of alkyl radicals trapped in polycrystalline matrices. The anisotropy broadens some or all of the hfs components, thus complicating the spectra. In alkyl radicals one has both isotropic and anisotropic hfs interactions with the α protons, but only an isotropic interaction with the β protons. Computed and experimental line shapes for the ethyl and propyl radicals are in qualitative agreement, provided that the hfs interaction is averaged over the various equilibrium orientations of the —CH_{2}· group. This implies a rapid reorientation of the —CH_{2}· group. It is noteworthy that when the two α protons are antiparallel the hyperfine anisotropy cancels and sharp intense hfs components result, while parallel orientations of the α protons give broad weak hfs lines. In particular, if the broad weak lines associated with the α proton hfs interactions are overlooked, the propyl radical spectrum appears to be a triplet, implying hfs interactions with the β protons only. In radicals where there is an odd number of α hydrogens (e.g. R′ — ĊH — R) there is no possibility of cancellation, and all the lines will be broad and weak. Our attempts to observe radicals of this type have been unsuccessful, most likely for this reason.

Microwave Spectrum, Structure, Dipole Moment, and Internal Barrier of Vinyl Silane
View Description Hide DescriptionThe structure of vinyl silane has been determined by studying the microwave spectra of each of its singly substituted isotopic species. Using Kraitchman's equations the following structural parameters were calculated:By studying the isotopic species containing an asymmetric silyl group the equilibrium conformation was found to be staggered, i.e., the silyl hydrogens are staggered with respect to the hydrogen on the central carbon. The symmetry axis of the silyl group was found to be tilted by an angle of 1°49′ from the Si–C bond axis towards the double bond. Comparison of the Si–C bond distance of vinyl silane with that of methyl silane indicates that recent estimates of the effect of changes in hybridization on the covalent radius of carbon are much too large. The barrier to internal rotation for vinyl silane has been calculated from splittings of groundstate rotational transitions of SiH_{3}CHCH_{2} and splittings of first‐excited state transitions of SiH_{3}CHCH_{2} and SiD_{3}CHCH_{2}, and also from Stark effectmeasurements on the K = 1, J = 2←1 transitions of SiH_{3}CHCH_{2}. The various calculations are all in good agreement, and the best value for the barrier is found to be 1500±30 cal/mole. Quadratic Stark effectmeasurements on the J = 2←1 transitions gave μ_{ a } = 0.648D, μ_{ b } = 0.133D, and μ = 0.66D. The resultant dipole moment makes an angle of 11±2° with the a axis of SiH_{3}CHCH_{2}.

Analysis of the Absorption Spectrum and Zeeman Effect of Thulium Ethylsulphate
View Description Hide DescriptionThe crystalline field interaction was calculated using first‐order perturbation theory on intermediate coupling wave functions of Tm^{3+} in a D _{3h } field. Good agreement with experimental data of Tm^{3+} diluted with La(C_{2}H_{5}SO_{4})_{3}·9H_{2}O was obtained. The following crystalline field parameters were chosen for best fit:

Tests for Chemisorption of Nitrogen on a Clean (100) Nickel Surface
View Description Hide DescriptionTests have been made for chemisorption of nitrogen on the (100) surface of a nickel crystal, using low‐energy electron diffraction and photoelectric work‐function determinations. No chemisorption was observed after exposures as high as 10^{‐3} mm Hg min at room temperature or at 350°C.

Three‐Dimensional FE‐MO Model. I. ΔH of Dissociation of Homonuclear Diatomic Molecules
View Description Hide DescriptionBy means of a three‐dimensional FE—MO model, the ΔH's of dissociation for homonuclear diatomic molecules can be estimated. The atoms are represented by cubes, and the molecules by rectangular parallepipeds. The parameters involved are the sizes of the boxes and the effective mass of the electrons. The spectroscopic terms for the ground states of both the atoms and the molecules are obtained from the model.

Proton Magnetic Resonance Studies of Structure, Diffusion, and Resonance Shifts in Titanium Hydride
View Description Hide DescriptionMeasurements of the protonmagnetic resonance at ∼26.9 Mc in titanium hydride samples, ranging in composition from TiH_{1.61} to TiH_{1.97}, have been made in the temperature range from —196° to about 200°C. The second moment of the protonresonance at the lower temperatures shows that the hydrogen atoms are randomly distributed among the lattice sites which are located tetrahedrally with respect to the titanium atoms. Self‐diffusion of the hydrogen atoms narrows the protonresonance above room temperature. The temperature dependence of the correlation frequency for the proton motions, obtained from the linewidths, leads to diffusionalactivation energies which increase with hydrogen content from 9.4 kcal/g atom for TiH_{1.607} to 10.2 for TiH_{1.923}. Moreover, the diffusion rate is directly proportional to the number of unfilled tetrahedral holes in the metallic lattice, which indicates that the self‐diffusion takes place via a vacancy mechanism.
Protonresonance shifts to higher applied magnetic fields were observed. They were measured at room temperature for all specimens and were found to increase from 0.01% for TiH_{1.607} to about 0.032% for TiH_{1.969}. For these two extreme compositions, the temperature dependence of the shift was measured between —95°C and 190°C and was found to be similar to the bulk susceptibility, the shifts for TiH_{1.969} exhibiting an anomaly at about 13°C as does the susceptibility. These results are interpreted semiquantitatively in terms of exchange interactions which pair spins of electrons in the conduction band with those of electrons localized on the hydrogen. The results suggest that the hydrogen is held in the lattice by a combination of covalent and ionic bonding, the latter involving a net positive charge on the hydrogen. The general importance of exchange interactions in intermetallic compounds is commented upon.

Approach to Thermodynamic Equilibrium
View Description Hide DescriptionThe properties of a macroscopic classical system consisting of some 10^{20} molecules are determined by a probability density functionW of the complete Γ space of moments and coordinates of all the molecules. This probability density function is that of the ensemble representing the totality of all experimental systems prepared according to the macroscopic specifications. The entropy is always to be defined as the negative of k times the integral over the distinguishable phase space of W lnWhΓ. However, the total probability density functionW, even for a thermodynamically isolated system, does not obey the Liouville equation, ∂W/∂t=LW, since small fluctuations due to its contact with the rest of the universe necessarily ``smoothes'' W, by smoothing the direct many‐body correlations in its logarithm. This smoothing is the cause of the entropy increase, and in systems near room temperature and above, in which there is heat conduction or chemical species diffusion, the smoothing keeps the true entropy numerically equal to that inferred from the local temperatures, pressures, and compositions. This, however, is by no means necessarily general. The criterion of thermodynamic isolation is not that the complete probability density functionW is unaffected by the surroundings, but that reduced probability density functionsw_{n} in the Γ space of n=2,3,... molecules evolve in time as if the system were unaffected by the surroundings. This criterion is sufficient to give a mathematically definable method of ``smoothing'' the complete probability density function. The smoothing consists of replacing the direct many‐body correlations in lnW by their average n‐body values, n=2,3,..., such that the smaller reduced probability density functionsw_{n} are unaffected.

Theoretical Molecular Transition Probabilities. I. The V–N Transition in H_{2}
View Description Hide DescriptionTheoretical investigation of the oscillator strength of the V–Ntransition in H_{2} has been carried out employing the alternative length, velocity, and acceleration operator methods in the calculations. By successive improvements in the approximate molecular wave functions assumed for the two states, convergence of the results obtained by the three methods toward a unique f value is demonstrated. The best wave functions employed yield an f value of 0.27 for the V–Ntransition in H_{2}. Because in general the three methods weight different spatial portions of the wave functions in the dipole strength integrals, comparison of the alternative numerical f values is shown to provide some insight into the goodness, over‐all and regional, of these wave functions. Agreement among the three values is also shown to be a more sensitive test of the goodness of the wave functions than are the usual energy criteria. All integrals necessary in these computations are shown to be expressible in terms of C _{αβ} ^{γδε} functions which are to be found in the literature. A systematic scheme for computing the oscillator strengths of any Σ—Σ transition involving one and two quantum‐number Slater orbitals in terms of these C functions is outlined.

The SPO (Split p‐Orbital) Method and Its Application to Ethylene
View Description Hide DescriptionDifficulties arise in the MO treatment of π‐electron systems due to electron correlation. Current methods allow, explicitly to some extent, for horizontal correlation (i.e., correlation of electron motions parallel to the carbon skeleton) but not for vertical correlation, (i.e., correlation of electron interchange between the two π lobes). A method for doing this, first suggested by M. J. S. Dewar and C. E. Wulfman [J. Chem. Phys. 29, 158, (1958)], is outlined and applied to ethylene with satisfactory results.

Relation of Perturbation Theory to Variation Method
View Description Hide DescriptionThe various order wave functions of the Rayleigh‐Schrödinger perturbation theory can be obtained directly by solving certain differential equations or by minimizing equivalent variational expressions. These expressions are related to the ordinary variation method. The perturbation series is shown to result in a unique way from the minimization of larger and larger portions of 〈ψ, Hψ〉/〈ψ, ψ〉. In addition to several orders of perturbation, each step gives the exact remainders and upper limits to the energy. The approach suggests several ``variation‐perturbation'' schemes.