Volume 61, Issue 8, 15 October 1974

EPR of Tb^{3+}, Pr^{3+}, Gd^{3+}, and Eu^{3+} ions in single crystal La_{2}O_{2}S
View Description Hide DescriptionElectron paramagnetic resonance measurements of some trivalent rare earth ions in single crystal La_{2}O_{2}S have been performed at low temperatures. At approximately 1.5 K, two sets of four [I=(3/2)] Tb^{+3} lines have been observed. Site I has a minimum resonance position when the magnetic field is parallel to the c axis and has the following parameters: g _{∥}=4.404±0.008, , Δ=0.234±0.004 cm^{−1}, A=0.05±0.002 cm^{−1}. Site II has a minimum resonance position in the a‐c plane at an orientation 45° from the c axis and has parameters g _{∥}=17.8, g _{⊥}≈0, Δ=0.18 cm^{−1}, A=0.216 cm^{−1}. In the Tb^{+3}doped sample, there appears another set of six lines which can be attributed to the hyperfine structure of Pr^{+3} [I=(5/2)]. The parameters for these lines are g _{∥}=4.1, , Δ=0.122 cm^{−1}, A=0.189 cm^{−1}. Studies were also made on the seven‐line fine structure spectrum for Gd^{+3}, an S‐state ion, for which g _{∥}=1.992 and . No signals from Eu^{3+} have been observed.

Interpretation of Raman spectra of van der Waals dimers in argon
View Description Hide DescriptionThe rotational and vibrational eigenenergies of all bound and predissociating states of the dimer are computed, together with certain averages of the nuclear wavefunctions needed for the computation of the Raman intensities for each transition. The MSV III potential of Parson, Siska, and Lee is used. With this information the complete rotational and vibration‐rotation Raman spectra of the argon van‐der‐Waals molecule is obtained and found to consist of truncated and superimposed line sequences. They are thus characteristically different from such spectra of ordinary molecules. A theoretical ``low‐resolution'' spectrum is obtained by superposition of approximated instrumental profiles for each line in the spectrum. At the lowest temperature (103°K) of the experiment nearly all of the observed intensity distribution is due to the dimer Ar_{2}. At high temperatures (300°K) the experimental spectrum is due largely to the scattering of light by pairs of atoms in fly‐by collisions, not to molecules. The Raman intensity maxima at ±8.3 cm^{−1} shift, therefore, must be explained in terms of the former. The apparent insignificance of the rotation‐vibration Raman bands in comparison to the pure rotational bands can be explained by adoption of a simple model for the anisotropy of the polarizability tensor.

Intramolecular excimer formation in carbazole double molecules
View Description Hide DescriptionThe emission properties of various carbazole ``double'' molecules in solution have been investigated. One compound in particular, namely 1,3‐bis(N‐carbazolyl) propane, a useful model coumpound for poly(N‐vinylcarbazole), has been studied in detail. Both steady state and transient measurements are utilized to determine rate and thermodynamic parameters for the formation of intramolecular excimers. Results on other model coumpounds in which the carbazole groups are symmetrically or unsymmetrically attached to the 1,3 positions of a propane chain are used to offer qualitative insight regarding the geometry of the intramolecular excimer state.

Vibrational reduced partition function of the Morse oscillator
View Description Hide DescriptionThe anharmonicity correction factor for the vibrational reduced partition function of the Morse oscillator has been numerically evaluated. The effect of anharmonicity on the reduced excitation factor u/(1−e^{−u} ) opposes the effect of e^{ux}/4, the usual anharmonicity correction. At all levels of anharmonicity, the former correction exhibits its maximum effects near u=4, where its magnitudes are not negligible compared to that of the correction for the zero‐point energy factor.

Measurement of the rate of excitation and deactivation of OCS(001), N_{2}O(001), CS_{2}(001), and C_{2}N_{2}(00100) using laser excited CO as a pumping source
View Description Hide DescriptionThe laser fluorescence method has been used to measure CO(ν=1) collisional transfer rates in several binary and ternary gas mixtures at 296°K. Excitation of the CO(ν=1) level was achieved using pulsed 4.6 μm radiation from a frequency doubled CO_{2} laser. The relative inertness of CO molecules towards V→T deactivation greatly facilitates the study of vibrational relaxation rates of the additive species in selected cases. In this paper, intermolecular V→V transfer rates at 296°K are reported for CO(ν=1) with N_{2}O, OCS, SO_{2}, CS_{2}, C_{2}N_{2}, and for CO(ν=2) with CO. In addition, the additive deactivation rates were determined for the following collisional processes: N_{2}O(001) with N_{2}O, CO, Ar; OCS(001) with OCS, CO, Ar; CS_{2}(001) with CS_{2}, CO; and C_{2}N_{2}(00100) with C_{2}N_{2} and CO.

Spline representation. I. Linear spline bases for atomic calculations
View Description Hide DescriptionThe use of a basis of cardinal splines for atomic calculations with the expansion method is proposed. The basis has the property that the coefficients C_{p} in the orbital expansion are given by C _{−1}=φ′(r _{0}), C_{p} =φ(r_{p} ), p=0,1, ···, N, and C_{N}+1=φ′(r_{N} ), where r _{0}, r _{1}, ···,r_{N} is the mesh of knots on which the spline is defined. The basis functions χ_{ p }(r) are continuous with continuous first and second derivatives, and may readily be calculated from the expansion , where d_{k} (r)=1 if r_{k}−1 ≤ r<r_{k} and 0 otherwise and S_{ksp} is a matrix of coefficients which are uniquely determined by the mesh alone and may be constructed by simple algebraic operations, the most complex being the inversion of a single (N+1)×(N+1) matrix. Atomic Hartree‐Fock matrix elements are given by simple polynomial expressions. The number of two‐electron integrals increases only as the square of the number of basis functions and can be stored in factored form, so that the storage requirements for the two‐electron integrals are trivial. The largest two arrays (equal in size) are the density matrix and the matrix elements of the exchange operator. The results of numerical tests for the hydrogen atom using several different distributions of mesh points are presented. It is found that the number of mesh points required is smaller than for standard numerical methods by a factor of about 4. The accuracy of a linear spline representation with N + 1 knots is comparable to that of a Gaussian expansion with N basis functions.

Reorientation of poly‐γ‐benzyl glutamate liquid crystals in a magnetic field
View Description Hide DescriptionNMR was used to investigate the magnetic reorientation of a nematic mesophase composed of a racemic mixture of poly‐γ‐benzyl glutamate in dichloromethane. The results are explained quantitatively utilizing the theory of micropolar continuum mechanics as introduced by Eringen.

Molecular properties of excited electronic states: The ã ^{3}A″ and Ã ^{1}A″ states of formaldehyde
View Description Hide DescriptionAb initio self‐consistent‐field wavefunctions and molecular properties have been calculated for the three lowest electronic states of H_{2}CO. For the ground state, a variety of basis sets were used, the largest being an uncontracted Gaussian basis: C(11s 7p 2d), O(11s 7p 2d), H(6s 1p). For the excited states, the above basis was contracted to C(7s 5p 2d), O(7s 5p 2d), H(4s 1p). Ground state molecular properties agree well with the earlier theoretical study of Neumann and Moskowitz, and with available experimental data. The z components (along the CO bond axis) of the excited statedipole moments have been measured, and the present a priori predictions reproduce experiment rather closely. Other properties reported include quadrupole moments, octupole moments, and electric field gradients.

Proton and deuterium magnetic resonance study of the aqueous nickelous complex
View Description Hide DescriptionThe absorption signals of protons and deuterons in bound and nonbound water molecules in the aqueous nickelous system were observed. From the PMR and DMR measurements, the hyperfine coupling constants were calculated and found to be (1.3±0.1)×10^{5} and (2.0±0.2)×10^{4} Hz, respectively. The spin density at the proton (and deuteron) nuclei was calculated to be (2.9±0.3)×10^{−5} electrons/a.u.^{3}, in accordance with theoretical expectations. The rate constant at 298°K for the exchange of water was found to be 3×10^{4} sec^{−1}, and the activation energy 12 kcal/mole. The relaxation time of the electron at 243°K, assuming T _{1e } =T _{2e } was found to be 1.9×10^{−12} sec and the activation ernergy 0.8 kcal/mole. The temperature dependence of the proton transverse relaxation rate was studied. It is suggested that in the absence of chemical exchange the transverse relaxation rate is governed both by the relaxation of the nickelous unpaired electrons and by the diffusional motion of the water molecules. Methods of estimating the diffusionalcorrelation time are discussed.

Covalent bonding of Mn^{2+} ions in octahedral and tetrahedral coordination
View Description Hide DescriptionThis paper is divided into four parts: The first part (Sec. I) contains a brief review of different assumptions made by several authors for the numerical values of the free Mn^{2+} ion parameters. It is shown that if only the Racah parameters B and C are taken into account, then the Orgel‐Griffith choice B=960 cm^{−1}, C=3325 cm^{−1} seems to be the best one. Tanabe and Sugano's figures lead to errors as high as 3800 cm^{−1}. Adding only the Racah‐Trees correction α does not seriously improve the fitting of levels ^{4} G, ^{4} D, and ^{4} F because a singular set of equations is then obtained. An exact experimental agreement can be obtained for all quartet levels by simultaneously using the Racah‐Trees correction α and the seniority correction β. The best fit values of the adjustable parameters relevant to the Mn^{2+} ion are given; it is found that α and β do not differ very much from Shadni's values. Section II deals with the well‐known use of the two normalization parameters N_{t}, N_{e} for describing covalent bonding. A routine method is developed for performing these calculations by using the three traces of the ^{4} E, ^{4} T _{1}, and ^{4} T _{2} matrices (if experimentally available). The interest of using these traces, rather than the energies of individual levels, lies in the fact that the energy sum of ^{4} E(^{4} G) and ^{4} E(^{4} D) levels deviates only slightly from a linear function of the Koide and Pryce covalency parameter, while the energy sum of ^{4} T _{1} and ^{4} T _{2} levels does not depend on any assumption upon Dq. This method is extensively applied in Sec. IV. In Sec. III is an attempt to obtain condensed analytical expressions by means of Lohr's INDO approximation for covalent bonding. These expressions allow some discussion about the validity of the method described above: It is shown that the use of the conventional Dq formalism can still be justified (with a suitable modified value of Dq) when only the metal‐ligand interaction is taken into account, but it is no longer correct if the ligand‐ligand terms are introduced in the calculation. In Sec. IV, we have used the ``method of traces'' described in Sec. II for deriving tables of covalency and normalization parameters for several manganese‐containing crystals: MnF_{2}, MnCl_{2}, MnBr_{2}, NaCl:Mn, ⋯ . We found that the accuracy of the experimental results presently available is in some cases very poor and new measurements by means of more modern techniques are needed. Specifically, an error as high as 6000 cm^{−1} has been found on the ^{4} T _{1}(^{4} P) level in Pappalardo's classical paper on MnCl_{2}. Nevertheless, the Dq values we obtain are in the right order Dq(MNBr_{2})<Dq(MnCl_{2})<Dq(MnF_{2}), while the reverse order was presented in the pioneer paper by Stout. In addition, other materials of interest for luminescence studies are discussed. In ZnF_{2}:Mn, covalency parameters are about the same as in MnF_{2}, but Dq is stronger in zinc fluoride. In ZnS:Mn, it is shown that the first excited level above those issuing from ^{4} G is ^{4} T _{2}(^{4} D) and not ^{4} T _{1}(^{4} P), except for unreasonably low values of Dq. Finally, we turned to Zn_{2}SiO_{4}:Mn and we have used recent data by Palumbo and Brown on the excitation spectra for computing the ligand field parameters.

Calculation of the total energy in the multiple scattering‐Xα method. I. General theory
View Description Hide DescriptionThe multiple scattering‐Xα method has been shown in previous work to be an accurate model for many properties of molecules and solids. However, in certain cases it has been found to be unreliable in determining total energies. This difficulty has been attributed mostly to the implementation of the multiple scattering part of the model rather than to the Xα approximation itself, since the multiple scattering equations are usually solved in the simplified ``muffin‐tin'' form. In this paper, it is shown, in general, how one can calculate the error involved in this approximation by means of a procedure which is analogous to first‐order perturbation theory and which establishes an upper bound to the exact Xα total energy. Expressions for the corresponding corrections to the one‐electron eigenvalues are also derived.

Calculation of the total energy in the multiple scattering‐Xα method. II. Numerical technique and results
View Description Hide DescriptionIn the previous paper (I) it was shown how in general the error caused by the muffin‐tin approximation in the calculation of the Xα total energy could be estimated and could thereby establish an upper bound to the exact Xα energy of a molecular or solid state system. In the present paper (II) we describe the numerical techniques used to evaluate the non‐muffin‐tin correction to the muffin‐tin Xα energy and give the results for two pilot calculations on the C_{2} and Ne_{2} molecules. It is found that the NMT correction results in a dramatic qualitative and quantitative improvement in the potential curves of these two molecules.

Interatomic potentials for krypton and xenon
View Description Hide DescriptionAccurate potentials for ground state krypton‐krypton and xenon‐xenon interactions are derived using a wide range of experimental evidence including second virial coefficients, gas transport properties, solid state data, known long‐range interactions, spectroscopic information on dimers, and new measurements of differential scattering cross sections. In calculating solid‐state properties account is taken of long‐range many‐body interactions. The use of the potentials permits a critical intercomparison of various kinds of experimental data. A ``corresponding states'' comparison of the shapes of the potentials for different inert gas pairs is given. It is concluded that contributions of overlap‐dependent many‐body interactions to condensed‐phase properties of argon, krypton, and xenon are very small.

On the phase transition in a gas of rodlike particles: A modified square‐well model
View Description Hide DescriptionA recent calculation by Brenner, McQuarrie, and Olivares on the effect of attractive forces on the order‐disorder phase transition in a gas of long hard rods is extended to include a more realistic attractive interaction potential. Rather than use the conventional square‐well potential, we modify the attractive part of the potential such that the attractive interaction energy is proportional to area of overlap of the attractive regions. This is meant to reflect the fact that the more two rods are in register, the stronger is their attraction. The effects of well depth and well width on the thermodynamic parameters characterizing the phase transition are re‐examined. This modified model yields significantly different results than the previous one for several of the transition parameters.

Interaction potential and reaction dynamics of He(2^{1} S, 2^{3} S)+Ne, Ar by the crossed molecular beam method
View Description Hide DescriptionDifferential elasticscattering cross sections of metastable He(2^{1} S) and He(2^{3} S) with Ne and Ar were measured at thermal collision energies by the crossed molecular beam method. The interaction potentials of these systems are found to be similar to those of alkali‐rare gas systems. The excitation transfer from He(2^{1} S) to Ne and the Penning and associative ionization processes in He(2^{1} S,2^{3} S) and Ar collisions only occur when interatomic distances are shorter than given critical values and interaction potentials are repulsive. The ratios of associative to Penning ionization cross sections were also measured for collisions of metastable He(2^{1} S,2^{3} S) and Ar as a function of collision energies. These results combined with the opacity function derived from differential elasticscattering cross sections of He(2^{1} S,2^{3} S) and Ar provide some information on the long range interaction of He+Ar^{+}.

Rotation and vibration spectra for the H_{2}O dimer: Theory and comparison with experimental data
View Description Hide DescriptionThe ground state binding energy (BE), rotational and vibrational energy levels, and line strengths for radiative transitions between some of these energy levels are calculated for the [H_{2}O]_{2} molecule. These quantities are computed for three intermolecular potentials published for the [H_{2}O]_{2} molecule, two of which were calculated by MO SCF techniques and one which was derived from an empirical point charge model for the water molecule. The value of BE calculated for two of the potentials is approximately 6 kcal/mole, and for the third is approximately 3 kcal/mole. The total concentration of [H_{2}O]_{2} in equilibrium with H_{2}O vapor is calculated for the sets of energy levels determined for these potentials. Results are compared with available experimental data. Using calculated values of line strengths and experimental data for the integrated absorptions for two rotational transitions, an independent value is deduced for the equilibrium concentration of [H_{2}O]_{2} in fair agreement with values calculated from two of the intermolecular potentials. The theoretical calculations for BE and the equilibrium concentration of [H_{2}O]_{2} are also compared with those obtained from analysis of experimental data for the second virial coefficient B _{2}(T) of H_{2}O vapor. The theoretical values for BE bracket the value of 3–4 kcal/mole obtained from analysis of the data for B _{2}(T). A discussion of our results is presented, along with suggestions for experimental work to search for the spectrum of [H_{2}O]_{2} in the absorptionspectrum of H_{2}O vapor.

Chloroethylene photochemical lasers: Vibrational energy content of the HCl molecular elimination products
View Description Hide DescriptionChemical laser techniques have been used to determine relative photochemical product yields and HCl^{†} (v′ ≤4) photoelimination product vibronic state distributions resulting from chloroethylene (CH_{2}=CHCl, CH_{2}=CDCl, CH_{2}=CCl_{2}, cis‐ and trans‐CHCl=CHCl, and CHCl=CCl_{2}) photolyses at λ ≥ 1550 Å. The observed highly nonstatistical product vibronic state distributions are successfully matched by a bootstrap reaction dynamics model which considers sudden structural distortion and intramolecular relaxation of HCl as it separates from acetylene or haloacetylene products. Chloroethylene vacuum ultraviolet absorption spectra (λ≥ 1400 Å) are also reported. All available spectroscopic, photochemical, and product energy partitioning data are used to formulate a state‐to‐state photochemical reaction mechanism for HCl photoelimination from the chloroethylenes.

Characteristic energy losses, luminescence spectra, and their lifetimes for RbI and KI under low energy electron impact
View Description Hide DescriptionEvaporated thin films of RbI and KI have been examined at 25–300°K under low energy electron impact. The emission of RbI at 470 nm was excited at 3.8 to 5.4 eV electron energy as well as at the first optical exciton (5.7 eV) and above. The 395 nm band was excited at ≥5.1 eV and possibly below this energy. The lifetimes τ_{470} and τ_{395} at 40°K are both 10^{−5} sec at ≥5.4 eV electron energy while τ_{395} decreases to 3.5 × 10^{−7} sec in the range 4.0 to 4.7 eV. τ_{470} decreases below 5.4 eV to 10^{−7} sec at 4.4 dV, and is too weak to measure at <4.4 eV. The 400 nm band of KI was excited at 30°K in the range 4.2–5.4 eV as well as at and above the first optical exciton, 5.8 eV. The 294 nm band of KI and the 315 nm band of RbI were excited principally at and above the region of the step, 6.2 and 6.0 eV, respectively. The lifetimes of the 376 nm band of KI in the range 25–80°K were the same for 4.7 and 6.2 eV electron energy, below and above the first optical exciton energy. For each system the evidence indicates that the low energy emitters can be excited directly. The small Stokes shifts approximate those expected for cubic relaxation. Population of lower energy emitting states from other states lying below the first optical exciton may be responsible for lifetimes anomalies.

Formation of by the reaction of metastable ions with O_{2}
View Description Hide DescriptionThe production of by the ion‐molecule reaction was investigated using a photoionizationmass spectrometer. The photoionization efficiency for production of by this reaction was measured from threshold at 742±2 Å (16.71±0.05 eV) to 650 Å (19.07 eV). The appearance potential of the ion corresponds to reaction of ions initially formed in the v′=5 vibrational level of the a ^{4}Π_{ u } state.

Semiclassical treatment of atom‐asymmetric rotor collisions; rotational excitation of formaldehyde at low energies
View Description Hide DescriptionThe formalism necessary for the application of ``classical S‐matrix'' theory to collisions of an atom with a rigid asymmetric rotor is derived. This is applied to rotational excitation of formaldehyde by H_{2} (taken to be spherically symmetric) at energies from 10 to 15°K. Classical Monte Carlo trajectory calculations were also carried out for the same system in the energy range 10–40°K. The results support the proposal of Townes and Cheung that a collisional mechanism is responsible for the 1_{11} →1_{10} anomalous absorption of formaldehyde in cool interstellar dustclouds.