Volume 60, Issue 7, 01 April 1974

Effective pair potentials for liquid Na and liquid K
View Description Hide DescriptionRecent x‐ray structure data has been used to generate effective pair potentials for liquid sodium and liquid potassium. This is done on the basis of three current theories (Percus‐Yevick, hypernetted chain, and Born‐Green) which relate the effective pair potential to the radial distribution function. Qualitatively, all the three pair potentials have similar features. Contrary to the recent suggestion of Howells and Enderby, the Born‐Green theory seems to be equally applicable to liquid metals.

Theoretical studies of heavy‐atom magnetic shielding in some small polyatomic molecules
View Description Hide DescriptionPerturbed Hartree‐Fock calculations are performed on the molecules CH_{4}, C_{2}H_{2}, C_{2}H_{4}, C_{2}H_{6}, CH_{3}F, CH_{3}OH, H_{2}O, NH_{3}, and C_{6}H_{6} to obtain the heavy‐atom NMR shielding constants and magnetic susceptibilities. Slater‐type atomic orbitals (STO's) are used as the basis set. Various aspects of this model, including the dependence on basis‐set size and on the origin of the vector potential, are examined. The results are compared with the available experimental data and with other ab initio and semiempirical treatments.

Polarization study of electronic transitions in molecules in a stretched PVA matrix using their projected three‐dimensional vibrational space
View Description Hide DescriptionA method is described for determining the direction of an optical transition in the chain molecules or guest molecules in a stretched polymer matrix with a quantitative elegance comparable to that of polarized single crystal spectroscpy (PSCS). The method consists in using the three‐dimensional vector (ray) space formed by the vibrational and electronic transition moments of the molecules. It determines the polarization ratios for four of these transitions: Three of them are linearly independent and constitute a monoclinic system of axes; the remaining one is the transition whose direction in the vibrational vector space of the molecules is to be determined. The method leads to the determination of an orientation parameter K that is described in terms of the molecular orientation distribution function of the relevant molecules in the stretched polymer matrix, without assuming any explicit form of that function. It has been applied to three aromatic molecules incorporated as guests in the PVA matrix and gives directions of electronic transitions in them that differ in most cases from those determined previously on the basis of assumptions regarding their molecular orientation distribution function in the stretched PVA matrix and the identity of their molecular orientation axis. These directions compare well with those obtained in mixed crystals using PSCS. Better agreement with SCF‐calculated theoretical results is also obtained.

ESR spectra of BrO_{3} and
View Description Hide DescriptionESR spectra of x‐irradiated single crystals of KBrO_{3} show that the paramagnetic species previously identified as BrO_{3} has a large, nonaxial quadrupole interaction and nonparallel principal axes for the g, A, and Qtensors. These findings suggest that the ESR signal should be assigned to a ion having C_{s} symmetry rather than to BrO_{3}. ESR spectra of x‐irradiated crystals of KNO_{3}doped with bromate ions exhibit a signal from a bromine‐containing species having a cylindrical spin Hamiltonian analogous to that of ClO_{3}. We assign this signal to the species BrO_{3}. Both assignments are supported by a modified extended Hückel calculation of field gradients and spin densities at the bromine nuclei of BrO_{3} and .

Magnetic circular dichroism of the ^{4} A _{1}, ^{4} E region in the antiferromagnetics MnF_{2} and K_{2}MnF_{4}
View Description Hide DescriptionLiquid helium temperature magnetic circular dichroism(MCD) data are presented and analyzed in some detail for the ^{4} A _{1}, ^{4} E region of MnF_{2} and K_{2}MnF_{4} with attention focused on the magnetic dipole origins. The MCD technique is ideal in this regard since it shows very prominent pseudo‐A terms for the π‐polarized origins while effectively ``filtering out'' almost all of the much more intense electric dipole absorption. In this experiment, the ^{4} A _{1} origin of MnF_{2} has been directly observed for the first time about 143 cm^{−1} to the blue of the ^{4} Eθ origin, as predicted. The signs of the A terms provide an independent confirmation of the accepted order of the two states. The observed magnitudes of the MCD and absorption parameters can be rationalized on the basis of a simple octahedral model if substantial mixing (85%/15%) of the ^{4} E θ and ^{4} A _{1} states is assumed. In K_{2}MnF_{4} two very sharp ([inverted lazy s]1 cm^{−1}) magnetic dipole origins are observed in the π and axial spectrum separated by 25.1 cm^{−1} which show very prominent A terms of opposite sign. Theoretical analysis of the MCD shows that the higher energy of these must correspond to the ^{4} E ε origin. The lower energy origin is assigned to ^{4} E θ, and a prominent A term about 350 cm^{−1} to the blue can be assigned with reasonable confidence to the ^{4} A _{1} origin, which is not evident in the absorptionspectrum. The A terms that have been assigned to the three origins vanish above the spin‐flop field as expected. The absorption and MCD parameters for ^{4} E ε are substantially smaller relative to ^{4} E θ and ^{4} A _{1} than is predicted on the basis of a simple octahedral model.

Rotational energy for spherical tops. I. Vibronic ground state
View Description Hide DescriptionThe rotational energy for spherical top molecules in their vibronic ground state is given in a general form to all orders. The sixth‐order result is developed explicitly.

Rotational energy for spherical tops. II. Triply‐degenerate fundamental
View Description Hide DescriptionThe Hamiltonian for a triply‐degenerate fundamental of spherical top molecules is extended to sixth order of approximation. Formulas for the energy levels are given.

Energy levels and potential energy curves for H_{2}, N_{2}, and O_{2} with an independent particle model
View Description Hide DescriptionEnergy levels for valence and Rydberg states are calculated for H_{2}, N_{2}, and O_{2}. An independent particle model (IPM) with an effective one‐electron potential whose nuclear charge depends on the electron position is utilized to approximate the Coulomb and exchange interactions. An analytical generalization of the potential parameters to reflect a change in internuclear separation yields accurate average molecular potential energy curves E(R) when experimental ion energies E ^{+}(R) are added to IPM molecular orbital energies ε(R), viz., E(R)=E ^{+}(R)+ε(R). A convergence formula for incrementing the energy in the numerical integration procedure is presented.

Numerical results on the radius of gyration of surface interacting self‐avoiding walks
View Description Hide DescriptionInformation on , the radius of gyration of surface interacting self‐avoiding walks, has been obtained by the method of exact enumeration. In particular, it was found that in the limit where γ ≃1.23. The configurational ratio , where is the mean square end‐to‐end distance, was found to reach a limiting value of 0.1355 in the presence of a barrier as opposed to the known value of 0.157 obtained in the absence of a barrier.

Disappearances of COOH infrared bands of benzoic acid
View Description Hide DescriptionInfrared spectra of benzoic acid and benzoic acid‐d were obtained in the range of temperatures from liquid nitrogen to liquid helium. The C=O stretching band at 1688 cm^{−1}, the strongest absorption band of this compound in the over‐all infrared region at room temperature, decreases in intensity with decreasing temperature and disappears near liquid‐helium temperatures. Near this temperature, also lost was the band at 959 cm^{−1} which has been assigned to the OH out‐of‐plane vibration. For the deuterated species both bands at 1689 and 1679 cm^{−1}, which have been interpreted as splitting due to Fermi resonance of the C=O stretching vibration, were lost. Close to the positions of these lost bands, alternative bands, which are assignable to the same modes and increase in intensity with decreasing temperature, are found. The results support the postulate proposed in our earlier work that two distinct equilibrium configurations of benzoic acid dimer coexist in the crystal.

On the theory of Brownian motion. VII. A hot particle in a dense medium
View Description Hide DescriptionStarting from the Liouville equation and using projection operator techniques, we derive a Fokker‐Planck equation for a Brownian particle that has a temperature T _{0} different from the temperature of the ambient medium. The medium is assumed to be dense. The resulting equation has the form of a Fokker‐Planck equation for a nonspherical particle in a medium at T _{0}, with two additional terms and two new friction coefficients. These new coefficients have the structure of the autocorrelation function of the intermolecular force (respectively, torque) with a microscopic analog of the rate of entropy production due to heat flow.

Frequency dependent transport coefficients in binary mixtures
View Description Hide DescriptionThe results of the modified Kubo technique are applied to the transport coefficients characterizing a binary mixture of fluids in order to provide a coherent treatment of systems that relax through their vibrational degrees of freedom. The transport coefficients are used in equations for the sound velocity and attenuation and the generalized structure factor in scattered light intensity. The results are consistent with those of previous investigators, and the technique may be generalized to multicomponent systems and to systems exhibiting other relaxing modes.

Raman spectrophotometric study of zinc thiocyanate solutions
View Description Hide DescriptionThe well‐known ambidentate nature of the thiocyanate ion is exemplified by its complexes with the Group IIb metal cations, in which zinc tends to be N bonded, mercury to be S bonded, and cadmium, a borderline case, has been shown to be bridged in aqueous solution (Cd–NCS–Cd). An investigation was initiated in order to more closely study the aqueous zinc/thiocyanate system, in particular to see if zinc can be induced to show either a change in bonding preference or bridging. Raman spectroscopy combined with the method of continuous variations was used to study a series of aqueous zinc thiocyanate solutions in which the ratio (R) of thiocynate to zinc was varied from 0.25 to 9. Under these conditions, there is no spectroscopic evidence for bridging thiocyanate ions or for a change in the bonding preferences of zinc. However, the results obtained were consistent with the existence of four distinct complex species corresponding to the mono‐, di‐, tri‐, and tetra‐substituted zinc ion. Furthermore, there is strong evidence that the two lower species are octahedrally coordinated with water as the other ligand while the higher species are tetrahedral. Comparison of spectra from the C–N stretching region of aqueous solutions with high R values [where the species is predominant] with similar spectra of in organic solvents reveals that the A _{1} mode in aqueous solutions is more intense than the F _{2} stretching mode while the converse is true in the organic systems. If the additivity of bond polarizabilities were rigorously obeyed, this reversal of intensities would not be expected. In certain cases this type of behavior has been explained by means of the resonance Raman effect. However, this does not seem to be the explanation in the present case.

Electron paramagnetic resonance studies of transitionmetal oxalates and their photochemistry in single crystals. I. K_{3}[Cr(C_{2}O_{4})_{3}] · 3H_{2}O in K_{3}[Al(C_{2}O_{4})_{3}] · 3H_{2}O
View Description Hide DescriptionThe spin‐Hamiltonian parameters and axis directions of two inequivalent complexes in single K_{3}Al(C_{2}O_{4})_{3} · 3H_{2}O crystals have been determined by EPR, and a search for EPR evidence of photochemical reactions in the crystals has been made. The complexes and their environments are asymmetric. The orientations in the crystal have been obtained from the axis directions. The substitutions, structure, and orientations are compared with the available crystallographic information. The existence of two inequivalent complexes is related to the degree of hydration of the crystal. No photochemical reactions in the crystals are observed, and the maximum quantum yields consistent with these observations are very small.

Comment on determination of the interaction potential between Ar and HCl
View Description Hide DescriptionTo test the accuracy of the Gordon‐Kim theory of intermolecular forces, predicted and experimental values are compared for Ar–HCl. The method appears to accurately predict the short‐range repulsive forces and also the position (but possibly not the depth) of the potential well.

Stoichiometry, Mössbauer spectrum, and magnetic susceptibility of the one‐dimensional conductor iridium carbonyl chloride
View Description Hide DescriptionCarbon and chlorine analyses of the linear chain compound Ir(CO)_{3}Cl confirm the report by Krogmann et al. that it is partially oxidized. The results are consistent with the formulation Ir(CO)_{3−x }Cl_{1+x }(x = 0.08 ± 0.02) or Ir(CO)_{3}Cl_{1+x }(x = 0.10 ± 0.03). The latter formulation is preferred because recoilless absorption measurements of the 73 keV ^{193}Ir γ‐ray show no indication of a line attributable to a species other than partially oxidized Ir(CO)_{3}Cl units. Presumably the ``extra'' chloride occurs in disordered interchain positions. The Mössbauer absorption is a temperature independent (1.8 – 35 °K) doublet with isomer shift − 0.03 ± 0.01 mm/sec relative to iridiummetal and quadrupole splitting 2.11 ± 0.02 mm/sec. For 4.3 ≤ T < 25 °K, the molar magnetic susceptibility corrected for ligand and metal core diamagnetism,, follows the Curie law for 25 < T ≤ 280 °K, the susceptibility is given by . The susceptibility and Mössbauer results indicate that in the range 1.8–280 °K the charges arising from partial oxidation of Ir(CO)_{3}Cl chains are not localized on individual atoms. The results are therefore inconsistent with a model requiring transition from a metallic state to a smallbandgap magnetic Mott insulator, but can be accounted for in terms of the interrupted metal strand model or the one‐dimensional disorder model. For the latter, the Curie contribution to the susceptibility leads to an estimate that the disorder ``localized'' states are spread over ∼ 25 Ir atoms. If the Curie component of the susceptibility is assigned to paramagnetic structure defects, the results are also consistent with the model in which a high‐temperature metallic state undergoes a continuous transition to a low temperature Peierls band insulator. The origin of the discontinuity at T ≈ 25 °K in the slope of the T ^{−1} dependence of is at present unknown.

Magnetic susceptibility of the one‐dimensional electron gas; application to BDP(TCNQ)_{2}
View Description Hide DescriptionThe magnetic susceptibility of the noninteracting electron gas has been studied on the basis of free electrons and the tight‐binding model, with application to the properties of organic conducting materials. Theoretical curves of susceptibility versus temperature are presented. The gradual transition from low temperature Pauli paramagnetism to the high temperature Curie law region is shown. In the transition region, the one‐dimensional systems show a peak in the susceptibility of the order of 110% of the low temperature limit. The magnetic susceptibility of the compound BDP(TCNQ)_{2} is interpreted in terms of a one‐dimensional tight‐binding model with an energy bandwidth of 0.07 eV.

Angular momentum adapted wavefunctions and their reduced transition density matrices
View Description Hide DescriptionThe construction of angular momentum adapted kets is discussed first. The reduced transition density matrices of two arbitrary angular momentum adapted states are then expressed in terms of rotationally invariant components and in terms of ``standard state'' matrix elements. The latter results reduce to formulas obtained by McWeeny and Mizuno for spin angular momentum density matrices.

Photoionization of atomic nitrogen
View Description Hide DescriptionRelative photoionization cross sections were measured for atomic nitrogen from 870 to 600 Å at a wavelength resolution (FWHM) of 0.83 Å. Five members of the autoionizing Rydberg series 2s 2p ^{3}(^{5} S ^{0})np ^{4} P were observed, and values of the line shape parameters q, Γ, and ρ^{2} were determined for the two lowest energy transitions (n = 3 and 4). Oscillator strengths were estimated for both transitions after normalizing the present data to absolute photoionization cross section measurements. The results are q = −1.7±0.1, Γ=0.027_{5}±0.003 eV ρ^{2}=0.51±0.04, and f =0.0058_{0}±0.0010_{9} for the n = 3 transition and q = − 1.7 ± 0.1, Γ = 0.010 ± 0.003 eV, ρ^{2} = 0.58 ± 0.15, and f =0.0024_{0}±0.0010_{0} for the n =4 transition. The photoionization cross section showed no other structure in the wavelength region from the NI ionization threshold to 600 Å.

Quantum correction factors for classical small angle scattering by inverse power potentials
View Description Hide DescriptionAn integral expression is derived for a quantum correction factor that gives the semiclassical differential elasticscattering cross section as a multiple of the Kennard small angle classical scattering cross section. The correction factor is evaluated numerically using the Landau‐Lifshitz approximation for inverse power potentials with s =4, 5, 6, and 8. The quantum correction is compared at very small angles with existing semiclassical small angle formulas. The relevance of this theory to the small angle elasticscattering found in reactive systems where the reaction cross section is determined by the collisions which surmount the centrifugal barrier is considered.