Volume 44, Issue 1, 01 January 1966

Analysis of Carr—Purcell Spin‐Echo NMR Experiments on Multiple‐Spin Systems. I. The Effect of Homonuclear Coupling
View Description Hide DescriptionThe effect of homonuclear coupling in a molecule on Carr—Purcell spin‐echo (CPSE) nuclear magnetic resonance experiments is investigated. A density‐matrix approach is used to derive a general equation for the CPSE train of multiple‐spin molecules in the liquid state. This general equation predicts a CPSE train modulated with one or more frequencies, whose relative amplitudes are, in general, not equal. Unmodulated contributions may also arise. It is shown that the modulation frequencies and their relative amplitudes are functions not only of the relative chemical shifts and coupling constants, but are strongly dependent on the separation between the 180° pulses, t_{cp}. In addition, the modulation can always be eliminated by making the pulse repetition rate, 1/t_{cp}, large with respect to all the relative chemical shifts and coupling constants. It is also shown that, for weak coupling, it is possible to derive simplified equations by neglecting the nonsecular part of the coupling Hamiltonian, but this approximation is valid only when 1/t_{cp} is of the order of, or smaller than the relative chemical shifts.
Procedures for solving the general equation to obtain closed formulas for the CPSE train of a specific system are discussed. Solutions for spin‐½ nuclei are treated in detail. Closed equations are derived for the AB, A_{2}B, and A_{3}B systems, and they are used in some numerical calculations. Simplified weak‐coupling formulas are also derived for these systems, and their range of validity is discussed.
A very brief discussion of heteronuclear coupling is presented.

Molecular Orbital Theory for Octahedral and Tetrahedral Metal Complexes
View Description Hide DescriptionSelf‐consistent charge and configuration (SCCC) molecular orbital calculations are reported for 32 selected octahedral and tetrahedral first‐row transition‐metal complexes containing halide and chalcogenide ligands. It is found that for the range of metaloxidation states II through IV, F _{σ}, chosen to fit the experimental Δ, is a function of only the metal atomic number for constant F _{π}. In the range of formal metaloxidation numbers V through VII, F _{σ} is also a function of oxidation number.
Calculated and observed trends in covalency, Δ values, and first L→M charge‐transfer energies are compared. The conclusion is drawn that the molecular orbital method, in its present formulation, gives a reasonable account of the ground states and low excited states in simple metal complexes.

Electronic Spectrum of (2, 2)Paracyclophane. II
View Description Hide DescriptionThe studies of the absorption and fluorescence spectra of single crystals of (2, 2)paracyclophane in the region 3300–3100 Å reported in a previous paper have been extended. Well‐characterized samples with the (hk0) developed crystal plane were used. In absorption two distinct spectra were obtained in the two polarization components. The fluorescence was strongly polarized in one direction (parallel to the fourfold c axis) and represents the mirror image of the equally polarized absorption component. It was concluded that the observations prove conclusively that the differently polarized spectral components represent transitions to two different electronic states, with an energy difference of 369 cm^{−1}. The lowest‐energy transition certainly contains the 0–0 line and all available evidence supports the conclusion that also the second transition has allowed character. The only interpretation consistent with all observed features of the spectra is as follows. The two observed states are the gerade dimer states (B _{2g } and B _{3g } in D _{2h }) being the out‐of‐phase combinations of the B _{2u } and B _{1u } benzene moiety states. The transitions have allowed character due to a torsional distortion of the molecule in the excited state. The interpretation is fully consistent with theoretical energy calculations.

Theoretical Studies of Transannular Interactions. I. Benzene Excimer Fluorescence and the Singlet States of the Paracyclophanes
View Description Hide DescriptionThe changes in the electronic transition energies of benzene which occur on dimerization have been calculated. It is shown that the energy‐level splittings due to the interactions between neutral‐excitation states are too small to explain the observed anomalous emission from concentrated benzene solutions and the absorption spectra of the paracyclophanes. To extend the theory, the eight‐electron problem is treated for configurationally interacting neutral‐excitation and charge‐resonance states. Intermolecular overlap is included in a way consistent with the use of a core potential in the Goeppert‐Mayer—Sklar representation. Use is also made of Hückel LCAO molecular orbital wavefunctions and a linear combination of four Slater carbon‐atom 2pπ wavefunctions fit to an SCF function. The anomalous emission from benzene solutions can now be understood to arise from transitions from the lowest excimer state of α‐level parentage for benzene molecules ∼3 or ∼3.3 Å apart when ground‐state repulsion is taken into account. The solution absorption spectra of the paracyclophanes are interpreted within this framework of neutral‐excitation—charge‐resonance configuration interaction. Finally, dimer symmetries different from D _{6h }, have been invesigated in an attempt to understand the absorption spectra of single crystals of [2.2] paracyclophane.

First Differential Ionization Efficiency Curves for Fragment Ions by Electron Impact
View Description Hide DescriptionElectron‐impact dissociations which yield an ion pair have been studied, by examination of first‐differential ionization efficiency curves. No evidence has been found for the occurrence of recently postulated reactions RH→R^{+}+H^{−} in hydrocarbons.

Crystal Structure and Optical Properties of (CH_{3})_{2}NH_{2}CuCl_{3}
View Description Hide DescriptionThe crystal structure of (CH_{3})_{2}NH_{2}CuCl_{3} has been determined by x‐ray diffraction techniques. The compound contains approximately planar Cu_{2}Cl_{6} ^{=} dimers which contain two bridging chlorine atoms. All Cu–Cl bond distances in the dimer are approximately 2.3 Å and all bond angles approximately 90°. The crystals are pleochroic with maximum visible absorption when the electric vector is parallel to the [301] direction.

Infrared Spectra of Crystalline and Matrix‐Isolated Carbonyl Sulfide
View Description Hide DescriptionThe infrared spectrum of carbonyl sulfide has been examined as a polycrystalline film at 80°K and also in matrix‐isolated form, using argon, nitrogen, and CS_{2} as the matrix materials. Particular attention has been given to the ν_{3} vibration, which appears as an abnormally broad and asymmetric band in solid OCS. The asymmetry of ν_{3} does not appear to be the result of any significant reflection effects nor is it due to disorder in the crystal. A study of the concentration dependence of the ν_{3} frequency in isotopic mixtures shows that a good part of the asymmetry can be attributed to the ν_{3} absorption of molecules containing ^{33}S and ^{34}S. Spectra of dilute mixtures of OCS in argon matrices display absorption by both isolated molecules and molecular pairs. The features of the spectrum are qualitatively accounted for in terms of a simple model of pairs interacting through transition‐dipole coupling. In both N_{2} and CS_{2} matrices, the evidence suggests two different sites for the OCS molecule in the host lattice.

Absolute Gross Ionization Cross Sections for Electrons (0.6–12 keV) in Hydrocarbons
View Description Hide DescriptionMeasurements have been made of absolute gross ionization cross sections for 0.6–12 keV electrons in the following hydrocarbons: the series of alkanes from methane to hexane, a number of alkenes, butadiene, and benzene. A description of the experimental technique is given, the results are compared with those of other authors and the additivity of the cross sections is discussed.
In all cases the energy dependence of the cross sections is in agreement with the theoretical relation: the cross section σ is proportional to M_{I} ^{2} E _{e1} ^{−1} lnE _{e1}, which gives a possibility of comparing with photoionization cross sections.

Symmetry Rules for Optical Rotation
View Description Hide DescriptionIt is shown that to produce optical rotation in a chromophore, a potential function must have the symmetry properties of a pseudoscalar in the symmetry group of the unperturbed chromophore. It is thus possible to establish regional rules of optical rotation without recourse to particular models and assumptions of the electronic states of the chromophore. Formulas and geometric representations of the resulting regional rules are given for a number of symmetries which are encountered in molecular problems. The results are not applicable to coupled oscillator models of optical rotation.

Sign of J _{HF} in CHFCl_{2}
View Description Hide DescriptionIf a nuclear spin is relaxed by two relaxation mechanisms with the same correlation time, the NMR lines may have differing relaxation rates. The fluorine nuclear spin in CHFCl_{2} at low temperature is relaxed by dipole—dipole interaction and by an anisotropy in the chemical shift. The sign of the coupling constant between fluorine and hydrogen (J _{HF}) has been determined from the relaxation pattern. J _{HF} turns out to be positive.

Thermal Relaxation Absorption of Sound in the Deuterated Methanes at 26°C
View Description Hide DescriptionThe thermal relaxation absorption in the deuterated methanes has been obtained by the tube method for frequencies between 20 and 640 kc/sec·atm. The relaxation time, transition probability, and collision efficiency were determined for each gas. The collision efficiency as a function of molecular weight has been found to follow a simple relation of the form: P _{10}∝[M]^{−½}.

Electron Paramagnetic Resonance of Divalent Manganese in Ammonium Chloride
View Description Hide DescriptionThe electron paramagnetic resonance of divalent manganese in NH_{4}Cl has been studied at X‐band frequencies. Several unexpected features of the spectrum are observed because the microwave quantum used is very close to the smaller of the two electronic zero‐field splittings. The entire spectrum can be explained by assuming there is a vacancy in the nearest‐neighbor NH_{4} ^{+} position to each manganese ion.

Non‐Gaussian Corrections to Van Hove's G_{s} (r, t) for a Monatomic Gas
View Description Hide DescriptionNon‐Gaussian corrections to Van Hove's self‐correlation function,G_{s} (r, t), are studied for real monatomic gases. G_{s} (r, t) is identified with the motion of a tagged atom in a dilute gas, where the motion is determined entirely by free streaming and random binary collisions with the untagged atoms. In this description, G_{s} (r, t) is the velocity integral of a distribution functionf(r, v, t) which is initially Maxwellian, localized at the origin, and which satisfies a linearized Boltzmann equation. Spatial moments of G_{s} (r, t) are calculated using the Lennard‐Jones (12–6) potential and the modified Buckingham exp (14–6) potential as interatomic potentials. Results are compared with those using a rigid‐sphere potential and with those of Rahman from a high‐density molecular‐dynamics calculation. It is found that (i) the behavior of non‐Gaussian corrections is qualitatively similar in all the cases, (ii) the corrections are larger for higher densities, and (iii) at low densities, the corrections increase almost by a factor of 2 when attractive forces are included.
It is also shown that the moments approach (through space‐dependent BE) and the velocity correlation‐function approach (through velocity—space BE) in calculating the non‐Gaussian corrections are equivalent.

Extended Hartree—Fock Wavefunctions: Optimized Valence Configurations for H_{2} and Li_{2}, Optimized Double Configurations for F_{2}
View Description Hide DescriptionAs a step beyond the Hartree—Fock technique in the search for better energies,wavefunctions, and the general description of molecular formation and dissociation, a configuration‐mixing method of the following nature is developed and illustrated for H_{2}, Li_{2}, and F_{2}. The wavefunctionconsists of several optimized configurations obtained by replacing one of the σ‐orbitals of the primary configuration (in our case the Hartree—Fock) by orbitals of different kinds. All the orbitals involved are orthonormalized, insuring orthonormalization of the configurations themselves. The present method determines energetically the optimum combination of both the mixing coefficients A_{k} and the linear orbital parameters by the solution of SCF‐type equations and insures dissociation of the molecule to two Hartree—Fock atoms. A program based upon this formalism has been constructed by the authors for the IBM 7094 computer and is capable of handling homonuclear diatomic molecules using as many as ten configurations with up to 33 two‐center symmetry basis functions. Results obtained are energetically better than conventional multiconfiguration studies and since our method is designed to account for added correlationenergy associated with molecular formation, calculated potential curves much more realistic than the Hartree—Fock ones can be realized. Sample calculations which represent a partial‐optimization procedure within the framework of the analysis are given for the molecules H_{2}, Li_{2}, and F_{2}. We feel, however, that these results are quite close to the truesolution. The binding energies obtained with these optimized configuration functions are 4.63, 0.93, and 0.54 eV for H_{2}, Li_{2}, and F_{2}, respectively, as contrasted with the Hartree—Fock dissociation energies of 3.64, 0.17, and −1.37 eV.

Vibrational Analysis of Acetone, Acetaldehyde, and Formaldehyde
View Description Hide DescriptionNormal‐coordinate calculations have been carried out for the molecules acetone, acetone‐d _{6}, acetaldehyde, acetaldehyde‐d _{4}, acetaldehyde‐d _{1}, formaldehyde, and formaldehyde‐d _{2}. Infrared and Raman spectra for acetone, acetone‐d _{6}, and acetaldehyde‐d _{4} were measured and assigned. Together with experimental data and assignments taken from the literature for the other molecules, these yield an almost complete set of fundamental frequencies.
These frequencies were used to derive approximate force fields for these molecules and to investigate the transferability of the force constants. Calculations were carried out with both the Urey—Bradley force field (UBFF) and the valence‐force field (VFF) with selected interaction constants. The Urey—Bradley force field is not satisfactory unless it is augmented with some valence‐force interaction constants. In the valence‐force approximation it is not possible to make an unambiguous choice of the nondiagonal constants. However, a most probable force field is indicated, which on the one hand reproduces the experimental frequencies and on the other hand shows reasonable values for diagonal and nondiagonal force constant.
The CO stretching constant, K _{CO}, and the force constants around the CO group appear to be nontransferable among these molecules. The most probable force field indicates a decrease in the value of K _{CO} in going from formaldehyde to acetaldehyde, to acetone. It is noted that the choice of interaction constants has a great influence on the values of the diagonal force constants and on the normal coordinates. Anharmonicity effects are also found to influence the values of the force constants and may affect the resulting conclusions.

Hyperfine Coupling Constants of 2,2‐Bis‐p‐nitrophenyl−1‐picrylhydrazyl
View Description Hide DescriptionPolycrystalline samples of 2,2‐bis‐p‐nitrophenyl−1‐picrylhydrazine, which are doped with 2,2‐bis‐p‐nitrophenyl−1‐picrylhydrazyl (free radical), have been prepared. The EPR absorption of the samples has exhibited seven partially resolved hyperfine lines. The observed hyperfine spectrum has been computer fitted by adjusting the nuclear hyperfine coupling constants of the free radical. The results have indicated that the difference between densities of the unpaired electron at the two nitrogen nuclei of the free‐radical molecule is larger in the case of the polycrystalline samples than in the case of liquid‐solution samples.

ESR Absorption of Cesium and Rubidium Solutions in Ethylamine
View Description Hide DescriptionElectron spin resonanceabsorption spectra of cesium and rubidium solutions in ethylamine have been observed at temperatures between −29° and +23°C. These spectra are characterized by a sharp single‐line resonance near the center of a hyperfine pattern. The lines of a hyperfine pattern vary in amplitude and breadth. The larger amplitude, narrower lines lie near the center of the spectrum. The hyperfine patterns are attributed to ^{85}Rb and ^{133}Cs nuclei interacting with an unpaired electron. The spin density at the ^{85}Rb nucleus varies from 1.05±0.1×10^{24} cm^{3} at −25°C to 1.90±0.05×10^{24} cm^{3} at 23°C and at the ^{133}Cs nucleus from 2.29±0.03×10^{24} cm^{3} at −29°C to 2.80±0.03×10^{24} cm^{3} at −10°C. The variations in line breadths are interpreted in terms of the structure of the metal monomer. The difference in g values between the single‐line resonance and the hyperfine pattern is attributed to spin—orbit coupling in the monomer and structural implications are discussed. The single‐line resonance is assigned to the solvent anion, i.e., the solvated electron.

Diatomic Forces and Force Constants. I. Errors in the Hellmann—Feynman Method
View Description Hide DescriptionDiatomic forces and force constants can be calculated from the Hellmann—Feynman (H—F) theorem and its derivatives but this theorem omits terms which do not vanish, in general, unless the wavefunction is exact. Using common approximate valence bond and molecular orbital wavefunctions for H_{2}, of both the scaled and unscaled type, we have evaluated the terms which are omitted in this manner. In each case the total theoretical force and the force constants were determined as well. We note that the H—F theorem, when used with approximate wavefunctions, can assume a variety of inequivalent forms depending upon the set of electronic coordinates held constant during differentiation. Two such forms are studied in detail, namely the virial and electrostatictheorems. Various equivalent expressions for the quadratic and cubic force constants (k _{2} and k _{3}) are developed by taking the first two derivatives of these theorems. Some of our expressions are new and one, in particular, has immediate computational advantages. A new approximation for k _{3} is tested and the implications of our study for the perturbation treatment of force constants is noted.

Diatomic Forces and Force Constants. II. Variation—Perturbation Method
View Description Hide DescriptionAccording to Rayleigh—Schrödinger perturbation theory the quadratic (k _{2}) and cubic (k _{3}) force constants of a diatomic molecule are completely determined by the unperturbed and first‐order wavefunctions, ψ_{0} and ψ_{1}. We approximate ψ_{1} using the Hylleraas variation technique which optimizes a trial function, , by minimizing an expression for k _{2}. Calculations were carried out on H_{2} with the virial form of the Hellmann—Feynman theorem. Several approximate ψ_{0}'s, all of the scaled variety, were tested along with two 's containing one and two variation parameters, respectively. Although it is not required by the theory the best results for both k _{2} and k _{3} were obtained with the more flexible trial function. Furthermore, with this we found that improving ψ_{0} (in the sense of lower E _{0}) had a salutary effect in all but one case. The major error in the better calculations arises not from the ψ_{1} terms but from evaluating and . But the latter are readily available experimental quantities since they depend only on the total electronic energy and equilibrium internuclear distance. A semiempirical method for determining force constants is thus suggested. The results are excellent. For example, with the Weinbaum function as ψ_{0}, k _{2}=0.362 and k _{3}=−1.43 (in atomic units) as compared to the experimental values of 0.368 and −1.30.

Multicomponent Polyelectrolyte Solutions. Part III. Determination of Activity of KCl in Potassium Polyvinylsulfonate Solutions by Use of a Cation‐Sensitive Glass Electrode
View Description Hide DescriptionThe activities of KCl in potassium polyvinylsulfonate solutions have been investigated in cells without liquid junction as a function of temperature, electrolyte, and polyelectrolyte concentrations. Potassium‐sensitive glass electrodes in conjunction with Ag–AgCl electrodes were used. Results are expressed in terms of the ratio of the derivative of the emf with respect to polymer molality, at constant KCl molality, and the derivative of the emf with respect to KCl molality, at constant polymer molality. The relation of this quantity to membrane‐distribution coefficients is established and the results are compared with polyelectrolyte theory.