Volume 62, Issue 4, 15 February 1975
Index of content:

Studies by electron paramagnetic resonance of K‐ and Na‐ bromides doped with Eu^{2+}
View Description Hide DescriptionThe electron paramagnetic resonance of Eu^{2+} in orthorhombic sites of NaBr and KBr has been observed at 1.2 and 300 K using an X−band spectrometer. The spin−Hamiltonian parameters for Eu^{2+} ions in NaBr have been determined for the first time. Some disagreement between the results obtained at room temperature and those reported recently by other workers for the KBr host is noted. Absolute signs of the spin−Hamiltonian parameters were determined from the relative intensities of the resonance lines at liquid helium temperatures. In both studies the sign of the b ^{0} _{2} term was found to be positive, and is therefore in agreement with the sign reported by Nair e t a l. for Eu^{2+} in KCl and by Aguilar e t a l. for Eu^{2+} in NaCl. The behavior of the second−order spin−Hamiltonian paramerer b ^{0} _{2} as a function of the lattice size is discussed.

Absolute infrared intensities and band shapes in pure solid CO and CO in some solid matrices
View Description Hide DescriptionThe infrared absorption spectra of carbon monoxide in argon matrices have been studied over a wide range of CO concentrations. The absolute infrared intensities of pure crystalline CO and of CO in argon matrices have been measured. The technique of using the second moment to determine the baseline of the absorption band has been tested and found to improve the data. The absolute integrated molar absorption coefficient of pure solid CO was found to be A=58.1±5.50 km mol^{−1} (1 km/mole=100 cm/mmole) and that for CO in the argon matrices is 66.5±2.4 km mol^{−1}. The two values are believed to be the same within experimental error. Studies were also made of CO trapped in different matrices, including SF_{6}, C_{6}H_{6}, and CCl_{4}. The absolute intensity of CO increases from the gas phase (A=58.0 km mole^{−1}) to the pure solid phase (A=58.1) or to the solid matrices (66.5−114 km mol^{−1}, depending on the matrix) apparently due for the most part to the electric field effect. The band shapes have been analyzed to obtain the second and fourth moments and hence the intermolecular torques and dipole time−correlation functions. The large values for the torques and slow decay of the correlation function with time from one system to another suggest that the CO molecules have either greatly hindered rotation or no rotation at all in the pure solid and in the solid matrices.

Vibration–vibration energy transfer in laser excited SO_{2}: Further evidence for a slow V–V step
View Description Hide DescriptionThe rate of fluorescence rise and fall has been measured for the ν_{3} state of SO_{2} as a function of pressure in pure SO_{2} and SO_{2}−rare gas mixtures pumped by a Q−switched CO_{2} laser. The results of these experiments are consistent with rapid equilibration of ν_{1} and ν_{3} stretching modes (∼135 collisions) followed by a very slow equilibration of the ν_{1}, ν_{3} stretches with the ν_{2} bend (∼2600 collisions) in pure SO_{2}. The presence of metastable, vibrationally hot stretching modes with vibrationally cold bending modes suggests the possibility of achieving a population inversion in SO_{2} by infrared laserpumping. The parameters and possibilities for obtaining vibrationally selective chemical reactions in SO_{2} are considered.

Many‐body calculation of the atomic hyperfine coupling constant: The lithium atom
View Description Hide DescriptionThe atomic hyperfine coupling constant of the lithium atom in the ^{2} Sground state is calculated by taking into account a correlation based on the wavefunctions of Clementi, Roothaan, and Yoshimine, including higher−order Exclusion−Principle−Violating (EPV) diagrams of first and second kind. The result is 2.91±0.02 a. u., compared with the experimental value 2.9096. Detailed comparison is made with the work by Chang, Pu, and Das who have calculated the coupling constant as 2.89±0.02 a. u. According to the comparison with the work of Chang e t a l., there is good agreement between individual diagrams, considering the difference in potentials used and the total result, the small difference in the latter being due to the higher order EPV diagrams effect considered by the present calculation.

PNO–CI (pair natural orbital configuration interaction) and CEPA–PNO (coupled electron pair approximation with pair natural orbitals) calculations of molecular systems. I. Outline of the method for closed‐shell states
View Description Hide DescriptionThe methods of configuration interaction with double substitutions to pair natural orbitals (PNO−CI) and of the coupled electron pair approximation (CEPA) proposed by W. Meyer are improved by combination with a new scheme of the calculation of the pair natural orbitals (PNO) and an efficient iterative scheme for the diagonalization of the CI matrix. The relevant matrix elements for the closed shell case are tabulated, the quantities that are pertinent for an analysis of the correlation energy are defined, and the organization of the computer programs is described.

PNO–CI (pair natural orbital configuration interaction) and CEPA–PNO (coupled electron pair approximation with pair natural orbitals) calculations of molecular systems. II. The molecules BeH_{2}, BH, BH_{3}, CH_{4}, CH^{−} _{3}, NH_{3} (planar and pyramidal), H_{2}O, OH^{+} _{3}, HF and the Ne atom
View Description Hide DescriptionPNO−CI and CEPA−PNO calculations are performed in a systematic way for the molecules BeH_{2}, BH, BH_{3}, CH_{4}, CH^{−} _{3}, NH_{3}, H_{2}O, H_{3}O^{+}, HF, and the neon atom. Two types of Gaussian basis sets are used: the ’’small basis,’’ which contains one set of polarization functions on the heavy atom and one on the hydrogen atoms, and the ’’standard basis,’’ which contains two d and one f set on the heavy atom and two p sets on the hydrogen atoms. For neon, in addition, a ’’large’’ basis is used. The improvement of the energy due to the different polarization functions is discussed in detail. The computed correlation energies are analyzed in terms of quantities defined in Paper I, in particular, in terms of the IEPA (independent electron pair) correlation energies E^{IEPA} _{μ} and the error ΔE _{IEPA} of the IEPA approximation. The pair interaction contributions ΔE_{μν} to E _{IEPA} are usually smaller in absolute value in the localized than in the canonical representation. In the canonical description ΔE_{μν} values of either sign occur so that because of a partial cancellation, ΔE _{IEPA} is usually smaller in absolute value than for localized pairs where almost all ΔE_{μν} are positive. Nevertheless the localized representation turns out to be generally preferable, mainly because it is more economical. The correlation energies accounted for in calculations that give rigorous upper bonds are in the order of ?85% of the exact correlation energies for the standard basis sets and ?70% as obtained with the small basis sets. The force constants and equilibrium geometries of BH, BeH_{2}, and NH_{3} are calculated using the small basis sets. The role of the correlation energy for the inversion barrier of NH_{3} (and the isoelectronic species CH_{3} ^{−} and OH_{3} ^{+}) is discussed in detail.

An acoustical method for determining the thermal and momentum accommodation of gases on solids
View Description Hide DescriptionThe velocity and absorption of sound in He, Ne, and Ar have been measured at room temperature and pressures ranging from 6.0−0.3 torr. The gases were contained in a tungsten tube 0.953 cm i.d. Flashing this tube at approximately 1900°C in a high vacuum before the measurements produced a marked increase in the soundvelocity and a marked decrease in the sound absorption. The effect has been attributed to a decrease in the thermal and momentum accommodation coefficients produced by removing the adsorbed gases from the tungstensurface. In the presence of mischmetal getter, the accommodation coefficients for the surface after flashing remained constant for a period of two weeks. When oxygen was admitted to the system momentarily to a pressure of a few torr and then pumped out, the soundvelocity and absorption in the noble gases returned to values corresponding to higher accommodation coefficients. The effect was repeatable. Comparison of the measuredabsorption and velocity with theoretical curves places reasonable limits on the permissible values for the energy and tangential−momentum accommodation coefficients.

Dynamics of molecular reorientational motion and vibrational relaxation in liquids. Chloroform
View Description Hide DescriptionVibrational and rotational (dipole and second−order tensor)correlation functions were obtained by Fourier inversion of infrared and Raman vibrational band contours of the three ∥ and one ⊥ fundamental of liquid CHCl_{3}, CDCl_{3}, and isotopically pure CH^{35}Cl_{3}. All correlation functions are nonexponential at short times and approximately exponential for long times. The symmetry axis of the molecule reorients by ’’free’’ jumps of about 1/3 rad, turning through a root−mean−square angle of 1 radian within 2psec by about 13 orientational jumps. Computer simulations show that Jdiffusion is too fast beyond 1 psec and that Mdiffusion fits the data up to 4 psec (τ_{ J } = 0.12 psec); thereafter, Mdiffusion is too slow. The Raman rotational correlation time is approximately equal to the NMR quadrupolar correlation time; the infrared rotational correlation time is only 0.75 of a corresponding dielectric relaxation time. Vibrational relaxation in the symmetric near−infrared carbon−hydrogen stretch is of the same order of importance as rotational relaxation; however, the dynamics of the vibrational relaxation of this mode do not support the presence of ’’hydrogen bonding’’ in the neat liquid. In the symmetric far−infrared carbon−chlorine deformation mode, vibrational relaxation is of considerably lesser significance than rotational relaxation throughout the whole time domain, whereas the rate of vibrational relaxation of the symmetric midinfrared carbon−chlorine stretch is intermediate to those of the other two symmetric fundamentals. None of these modes obeys vibrational energy dissipation or resonance vibrational energy transfer mechanism induced by dipole−dipole interaction. The ratios of the derived polarizabilitytensor elements, which are required to evaluate the rotational correlation function of the degenerate mode (carbon−hydrogen deformation), were computed from formulations relating them to the bond polarizabilities: It appears that its Raman and infrared correlation function does not contain the same vibrational correlation function and that the respective contour is determined essentially by nonorientational relaxation processes. An extensive analysis of the experimental errors inherent in our Raman band contour determinations is presented, as well as a critical comparison of our conclusions with previous results in the literature.

Theoretical description of the diimide molecule
View Description Hide DescriptionThe N_{2}H_{2} molecule is only metastable and as a consequence is not well characterized experimentally. Therefore, we have carried out extensive Hartree−Fock calculations in order to determine equilibrium geometries, one−electron properties, and the relative energies of the c i s and t r a n s isomers. In addition, Hartree−Fock and multiconfiguration calculations were carried out to determine the mechanism for isomerization. The t r a n s isomer was found to be 6.6 kcal/mole more stable than the c i s form using a basis set which included polarization functions. The lowest energy path found for isomerization occurred by inversion about one nitrogen (rather than rotation about the NN bond) with an activation energy of 47 kcal/mole. Excitation energies for the lowest singlet and triplet excited states are also presented.

Augmented random phase approximation
View Description Hide DescriptionAn infinite set of ladder diagrams are summed to yield an augmented random phase approximation (ARPA) to the Bethe−Salpeter amplitude equation. The final equation is of the easily solved form of the RPA amplitude eigenvalueequation but with a more complete (augmented) vertex which is the product of a matrix and an inverse matrix. The diagonal ARPA vertex is obtained by taking only the diagonal terms of the inverse matrix, making inversion necessary. The diagonal ARPA should include the most important hole−hole and particle−particle terms which are left out of the RPA. The final ARPA equation is derived two ways, by direct diagram summation and from the integral equation for the ladder vertex.

A limited basis molecular orbital calculation on H_{2}O and H_{2}O^{+}
View Description Hide DescriptionAn MO−SCF calculation on five states of H_{2}O^{+} and on the ground state of H_{2}O is shown to yield molecular geometries, force constants, ionization energies, and for the neutral ground state, relative infrared intensities in good agreement with experimental results, and, where available, with more sophisticated calculations.

The spline representation: II. Shell orbitals and exponential spline bases
View Description Hide DescriptionThe cardinal spline expansion method for atomic calculations, introduced in a preceding article, is extended from linear to exponential splines. These are obtained by replacing the spline basis functions χ_{ p }(r) by χ_{ p }(u), where u = e−ζr. An orbital multiplying factor r n−1e ^{−ζ} n l ^{ r } is introduced for each shell in order to improve convergence. The Hartree−Fock equations for closed−shell atoms are transformed to equations for nodeless orbitals localized in atomic shells (shell orbitals), and the construction of shell orbitals for atoms embedded in molecules is discussed briefly. Explicit expressions for the one−center matrix elements are derived. A major advantage of the linear spline representation, viz., that the number of two−electron integrals increases only as the square of the basis size and the off−diagonal integrals can be factored, is retained. A comparison is made of the relative advantages and disadvantages of linear and exponential spline representations with regard to probable storage requirements, computing time, and program complexity. No numerical results are given, for the purpose of this work is to assess the optimum strategy for subsequent numerical studies. The linear spline representation, which can also be used for calculating shell orbitals, appears to be the most promising approach for further work.

Delta‐function model for short‐range interatomic forces: Correlation scheme for closed‐shell atoms and ions
View Description Hide DescriptionA correlation scheme is developed for the short−range interaction energies between rare−gas atoms and positive and negative ions with rare−gas configurations. The exponential form of the correlation and the relation between the exponental and pre−exponential constants are predicted by a delta−function model. The exponential constants are found to correlate with the softness parameters obtained from Hartree−Fock−Slater calculations on single atoms and ions. Comparisons are made with experimental beam scattering data, a b i n i t i o quantum−mechanical calculations, and the electron−gas model of Gordon and Kim. The over−all agreement is good.

Improved upper bounds on Knudsen permeabilities through a bed of spheres
View Description Hide DescriptionIn a previous publication, a variational upper bound on the permeability of a porous medium to Knudsen flow was presented. The bounds were calculated for a model pore structure generated from randomly placed, freely overlapping solid spheres. In this paper, the improvement of these bounds is discussed.

Predicted ionization potentials for 70 alkali metal triatomic molecules containing Li, Na, K, Rb, and Cs
View Description Hide DescriptionPredictions are made of ionization potentials for 70 alkali metal triatomic molecules containing Li, Na, K, Rb, and Cs using a perturbation method based upon the use of Simons type model pseudopotentials. The usefulness of the results to experimentalists is pointed out.

Microwave spectra of 1,3‐difluoroallene and fluoroallene
View Description Hide DescriptionThe microwave spectra of 1,3−difluoroallene and fluoroallene have been recorded from 12.4 to 40.0 GHz. For the 1,3−difluoroallene molecule, both R−branch and Q−branch assignments have been made for the ground vibrational state for the b−type transitions. The rotational constants were found to be: A = 25101.15±0.12, B = 2170.02±0.07, and C = 2117.40±0.04 MHz. The value of the dipole moment was obtained from Stark splittings to be 1.77±0.01 D. For the fluoroallene molecule, only R−branch a−type transitions were assigned from which the B and Crotational constants were determined to be 4300.11±0.05 and 4039.34±0.05 MHz, respectively. The dipole moment components for fluoroallene were found to be: μ_{a} = 1.44, μ_{ b } = 1.34, and μ_{ t } = 1.97 D from the Stark splittings. The dipole moments are compared to those of similar molecules.

Molecular orbital theory of the hydrogen bond. X. Monosubstituted carbonyls as proton acceptors
View Description Hide DescriptionA b i n i t i o SCF calculations with a minimal STO−3G basis set have been performed to determine equilibrium structures and energies for a series of mixed dimers formed from water and substituted carbonyl compounds. These dimers may be represented by the general formula HOH⋅⋅⋅OCHR, where R may be CH_{3}, NH_{2}, OH, F, CHO, and C_{2}H_{3}. For each dimer in this series except water−formic acid, two equilibrium structures have been found, in which the substituent R is ’’c i s’’ or ’’t r a n s’’ to the proton donor water molecule with respect to the carbonyl CO bond. Except for a cyclic equilibrium water−formamide dimer, all equilibrium dimers have open−chain t r a n s structures consistent with the General Hybridization Model. There is only a small variation in the hydrogen bondenergies of equilibrium dimers HOH⋅⋅⋅OCHR, except for the water−formamide dimers which are significantly more stable than all others in this series. The structures and energies of the equilibrium dimers HOH⋅⋅⋅OCHR have been analyzed in terms of the effect of the substituent R on the proton accepting ability of the substituted carbonyl compound RCHO.

Hydrodynamic analysis of non‐hard‐core interactions in the rotational relaxation of molecules; ESR data
View Description Hide DescriptionMolecular reorientation for symmetric tops is analyzed in terms of a stickiness factor (s) which measures, in terms of a hydrodynamic model, the lag of the fluid motion relative to that of the particle surface. For s = 1 and s = 0, the hydrodynamic problem is that of ’’stick’’ and ’’slip’’ boundary conditions for symmetric tops. For truly hydrodynamic situations, 0 ? s ⩽ 1, but since molecular reorientation is nonhydrodynamic, negative values of s are possible. Reorientational data obtained from ESR spectra, for vanadyl acetylacetonate in a number of solvents, including a series of alcohols, are analyzed in terms of the s factor.

Theory of unsymmetric polymer–polymer interfaces
View Description Hide DescriptionSolutions have been obtained to equations which described the interface between two immiscible polymers and are more general than the equations first introduced by Helfand and Tagami. Gaussian random−walk statistics are assumed for the macromolecules. As a consequence of the present work, limitations of the earlier theory are removed, particularly the assumption that the properties of the two polymers when pure are identical. Calculations are performed for a variety of polymers and comparison with experiment is made.

Interfacial tensions of three fluid phases in equilibrium
View Description Hide DescriptionIt is suggested that it may be a general thermodynamic law that when three mutually saturated fluid phases are in equilibrium, the three interfacial tensions σ satisfy the triangle inequality σ_{max} < σ_{med} + σ_{min}, where σ_{max} is the largest of the three, σ_{med} the median, and σ_{min} the smallest. An argument for the inequality is given, and systems in which to test it experimentally are suggested. The quantitative law by which the interfacial tensions vanish as the three fluid phases become identical at a tricritical point is derived by an adaptation of an earlier argument on the vanishing of the interfacial tension on approach to the tricritical point in phase−separated ^{3}He−^{4}He mixtures.