Volume 53, Issue 1, 01 July 1970

Internal Rotation in Two‐Top Molecules. I. A General Theory
View Description Hide DescriptionThe dynamics is developed for internal rotation in two‐top molecules where both internal rotors may, or may not, be asymmetric. A framework fixed axis method (FFAM) is used for the formulation. The explicit and dependence of the moments of inertia is obtained for over‐all rotation, internal rotations, and coupling between over‐all and internal rotations. The Hamiltonian in proper Hermitian form is derived. Inertial parameters and rotational coefficients are calculated for two representative molecules.

Statistical Analysis of Transition Probability Matrices in the Strong Coupled Rotational Excitation Problem
View Description Hide DescriptionScattering matrices accurately computed via close‐coupling techniques are analyzed and discussed as a function of critical parameters of an atom–diatomic molecule scattering system. The usefulness of the test for delineating the region of strong coupling and ascertaining the range over which statistical approximations may be appropriate is demonstrated.

Electronic Wavefunctions for Atoms. III. Partition of Degenerate Spaces and Ground State of C
View Description Hide DescriptionThe atomic configuration‐interaction (CI) expansion is expressed in terms of constituents which are invariant under linear transformations of the radial one‐electron basis. For open‐shell states, the degenerate spaces are partitioned into maximal Hartree–Fock (HF) noninteracting spaces and minimal HF interacting spaces. This particular partition is shown to improve considerably the convergence of the atomic CI expansion, and it may be applied to molecular CI expansions in terms of symmetry orbitals. An exhaustive calculation of the ground state of C is carried out. A well‐defined linear transformation of the radial one‐electron basis is made in order to improve further the convergence of the CI series. The final 234‐term CI expansion (formed from a determinantal space of dimension 4836) obtained with an optimized basis, gives an energy (C), accounting for more than 93% of the correlation energy. The C wavefunction is believed to be expressed in its most rapidly convergent form. The advantages of the present approach to atomic CI calculations are discussed.

Polarization Dependence of the Two‐Photon Absorption of Tumbling Molecules with Application to Liquid 1‐Chloronaphthalene and Benzene
View Description Hide DescriptionThe two‐photon absorption cross section for photons of any polarization (linear, circular, or elliptical) is averaged over all orientations of the absorbing molecule. The result is given by , where and are molecular parameters and , and are simple functions of the polarization vectors. It is shown how the δ's may be calculated from theory and also how they may be measured by experiment. Experiments using only linearly polarized light are insufficient to determine all three δ's; hence, circularly polarized light will play an essential role in this spectroscopy. For absorption of two linearly polarized photons with angle θ between their polarization vectors, the angular dependence is , where and are simple combinations of the . We obtain two exact symmetry rules which permit allowed two‐photon transitions of different symmetries to be distinguished. For transitions from totally symmetric ground states the rules are: (1) If the excited state transforms like , or , then . (2) If the excited state transforms like , or , then . In cases of near resonance, when a single intermediate state dominates the formula for the cross section, we show that , and that linearly polarized light suffices for a complete investigation. These results are applied to liquid 1‐chloronaphthalene. We find two allowed two‐photon transitions which are assigned (perpendicular nodes) at 37 700 cm^{−1} and (total symmetry) at 42 600 cm^{−1}. This is in reasonable agreement with theoretical predictions of other authors. We have also examined the region of the second excited singlet of benzene, near 6.2 eV. We were not able to detect any two‐photon absorption, setting an upper limit of about 10^{−51} cm^{4}·sec/photon·molecule on its . This leads to an unequivocal assignment of for this state according to calculations of Jortner. In an Appendix we examine the effect of “hot spots” in the laser beam on the observed cross sections. We show that the elimination of the hot spots is of some importance, contrary to a statement of other authors.

Low‐Frequency Modes in Molecular Crystals. IX. Methyl Torsions and Barriers to Internal Rotation of Some Three‐Top Molecules
View Description Hide DescriptionThe low‐frequency vibrational spectra of (CH_{3})_{3}CCN, (CH_{3})_{3}CCCH, (CH_{3})_{3}CH, (CH_{3})_{3}SiH, (CH_{3})_{3}SiF, (CH_{3})_{3}P, and (CH_{3})_{3}N have been recorded for these molecules in both the gaseous and solid states. Both the degenerate and nondegenerate torsional modes were observed for the molecules in the solid state. The effects of condensation on the torsional modes have been obtained from the far‐infrared spectra of the molecules in the gaseous state. The importance of top–top interaction in the torsional potential energy has been demonstrated. The calculated harmonic barriers are 4.31, 4.10, 3.94, 2.49, 2.25, 3.58, and 4.35 kcal/mole for the (CH_{3})_{3}CCN, (CH_{3})_{3}CCCH, (CH_{3})_{3}CH, (CH_{3})_{3}SiH, (CH_{3})_{3}SiF, (CH_{3})_{3}P, and (CH_{3})_{3}N molecules, respectively, in the solid state. The top–top interaction values ranged from 0.8 kcal/mole for tertiary butylacetylene to 0.3 kcal/mole for isobutane, with an average value of 0.5 kcal/mole.

Calculation of the He–H Interaction Energy
View Description Hide DescriptionThe He–H interaction energy has been calculated by an SCF open‐shell procedure due to Roothaan. Results obtained are in good agreement with the interaction deduced from atomic‐beam measurements of Amdur and Mason. The present calculation has yielded lower values for the short‐range potential than other comparable theoretical calculations.

Polar Distortions in ReF_{7} and IF^{7}
View Description Hide DescriptionThe deflection of molecular beams of ReF_{7} and IF_{7} by inhomogeneous electric fields has been studied as a function of temperature. Polar components were readily observed in molecular beams of ReF_{7}, and their intensity increased as the temperature was lowered. A similar effect was just observable for IF_{7} at the lowest temperatures attainable. These observations show that the heptafluorides do not have rigid polar structures, but they are compatible with nonrigid distorted geometries for ReF_{7} and IF_{7}.

Focusing and Orienting Asymmetric‐Top Molecules in Molecular Beams
View Description Hide DescriptionAsymmetric‐top molecules can be deflected in an inhomogeneous electric field, and the deflected molecules can be oriented by allowing them to pass adiabatically into a uniform field. It is possible to account quantitatively for the transmission in a hexapole field if only first order and intermediate (or fast) Stark effects are considered. Rigid rotors with the dipole moment parallel to the a axis and internal rotors with low barriers to rotation have many levels which so interact and these types of molecules are easily deflected. Rigid rotors with the dipole parallel to the b axis have far fewer levels which interact; for these molecules the deflection is weak and may be undetectable. For rigid rotors and free internal rotors it is possible to obtain dipole moments by matching theoretical curves with experimental points.

Absolute Cross Section for and the Imprisonment Lifetimes for at Low Opacity
View Description Hide DescriptionSteady‐state hydrogen‐atom concentrations produced by the mercury‐photosensitized decomposition of molecular hydrogen are detected by Lyman‐αphotometry. On the basis of the natural lifetime of and the mechanism for the reaction, quenching plots are constructed, and the over‐all bimolecular rate constant for is calculated. The absolute cross section for is determined to be 10.8 ± 0.4 Å^{2} in the limit of low mercuryopacity. This result agrees with other recent experimental determinations. In addition, experimental values of imprisonment lifetimes for as a function of mercury concentration are estimated and are compared with other low‐opacity and high‐opacity results. The results are also compared to various theoretical predictions of imprisonment lifetimes.

Measured Lifetimes of Rotational and Vibrational Levels of Electronic States of N_{2}
View Description Hide DescriptionThe lifetimes of vibrational levels of the and electronic states of molecular nitrogen and of the electronic states of the positive molecular nitrogen ion were measured by photometrically monitoring the excited level number densities in a pulsed invertron. Heavy‐particle pressure damping cross sections were obtained from experimental studies of the pressure dependence of the reciprocal lifetimes. Lifetimes of individual rotational levels from to of the levels were measured. The lifetimes of all rotational levels were identical. However, our results suggest a dependence of the line strength on the rotational level different from that predicted by the Born–Oppenheimer approximation with zero rotational–vibrational interaction and zero electron spin–rotational interactions.

Ab Initio Study of the Geometries, Jahn–Teller Distortions, and Electronic Charge Distribution in the CH_{4} ^{+} Ion
View Description Hide DescriptionThe CH_{4} ^{+} ion is known to be involved in many ion–molecule reactions, presumably including those leading to the precursors of life, but little experimental information about it is available. In the present investigation, the energy of CH_{4} ^{+} in various geometries is calculated by the restricted SCF MO method using a Gaussian basis set. The ion is distorted from the regular tetrahedron because of the Jahn–Teller effect. Two stable geometries are found: tetragonal , dihedral angle = 53.3°, ; trigonal , H_{1}CH_{2} angle = 98.28°, hartree. Other geometries investigated are, in order of decreasing energy, regular tetrahedron, square plane, and CH_{3} ^{+} + H. The relations among these geometries are discussed in terms of orbital energies, energy components, and population analysis.

Surface Adsorption of Light Gas Atoms
View Description Hide DescriptionThe adsorption on solid surfaces of very light gas atoms is reconsidered. A variational wavefunction is constructed for the quantum‐mechanical ground state of the adsorbed atom, and improved values of adsorption energies are calculated for a few cases. The surface mobility at low temperatures is determined quantum mechanically, by use of the variational ground‐state wavefunction. Simple analytic approximations are derived for the sticking coefficient and the accommodation coefficient for gas atoms impinging on a surface. A few previous accurate calculations and some experiments are used to derive some general analytic semiempirical formulas for and as a function of the gas temperature. Surface recombination of diatomic molecules from two adsorbed atoms is considered briefly.

Theory of the Isotropic NMR Shifts in Trigonal Co(II) Complexes
View Description Hide DescriptionThe theory of both the contact and pseudocontact shift in Co(II) trigonal complexes is considered. The theory predicts a pseudocontact shift in Co(II)poly(1‐pyrazolyl)borate complexes, in good agreement with experimental results. The predicted contact shifts are found to be much different from that predicted by previously proposed theories. In the region of 200–400°K, the temperature dependence is found to deviate strongly from a dependence for the pseudocontact shift but not for the contact portion of the shift. The assumption made in earlier theories, that the contact interaction is the same for all six Kramer's doublets, is examined in detail.

Rotational Strength of Molecules: Application of the Exchange Theorem
View Description Hide DescriptionThe calculation of the rotational strength of molecules through the first order of the badness of the molecular wavefunction is investigated by applying double perturbation theory and the exchange theorem for off‐diagonal matrix elements. The method is applied to Eyring and co‐workers' one‐electron model of 3‐methylcyclopentanone, and exact and variational solutions for the model are obtained. The result leads one to hope that for more practically interesting problems the variational approach can be employed with some confidence.

Photoionization of Mercury Atoms between 10.5 and 72 eV
View Description Hide DescriptionThephotoionization cross sections to produce Hg^{+} and Hg^{2+} have been measured from their respective thresholds at 10.434 and 29.186 eV to a high‐energy limit of 72 eV. For single ionization the cross section rises to a maximum at more than 10 eV above the threshold associated with d‐electron removal. The cross section for double ionization is a nonnegligible fraction of the total cross section.

Classical Aspects of Energy Transfer in Molecular Systems
View Description Hide DescriptionThe decay time of the luminescence of a molecule S in front of a metal mirror depends markedly on its distance from the mirror. This phenomenon is quantitatively explained by considering the radiation field of this dipole, given by Hertz classical equation. This field arrives at the molecule, after being reflected at the mirror, with a retardation of the order of 10^{−15} sec. The decay time of the luminescence depends on the phase shift produced by this retardation, and thus on the ratio of the distance of the oscillator from the mirror, and the wavelength of the emitted light. By measuring the distance dependence of the decay time of the luminescence this retardation effect can be studied. In quantum‐mechanical terms the phenomenon can be described as being due to a stimulation or inhibition of the emission of the light quantum. In contrast to the known cases of stimulated emission, the stimulating field is the radiation field of the emitter quantum itself. The energy transfer from an excited molecule S to an acceptor A can be treated in a similar manner by considering the phenomenon as a retardation effect. In classical terms the field of S induces A to oscillate, and the induced field of A arriving at S slows down this oscillator. Simple equations are given for the energy transfer from an excited dipole or quadrupole, and for a row of many dipoles, oscillating in phase, to a weakly absorbing acceptor layer. The latter case is considered as a model for a J‐aggregating dye and by comparison with experimental data conclusions concerning the size of a aggregate are drawn.

Hall Effect in Lithium–Ammonia Solutions
View Description Hide DescriptionMeasurements of the Hall coefficient and electrical conductivity are reported for solutions of lithium in liquid ammonia. The concentration range is from 1.2 to 14 mol % metal (MPM) and the temperature range is from near 200 to 240°K, except in the miscibility gap. Hall coefficients equal to the values expected from the metal‐valence‐electron density are found above 9 MPM. Below 9 MPM the measured Hall coefficient R_{m} increases to about twice the free‐electron value . The latter result does not agree with that previously reported by Kyser and Thompson. is temperature independent at all concentrations. Data for the electrical conductivity show thermal activation of the mobility below 8 MPM. Changes in the concentration dependence of both and are observed near 3, 5, and 8 MPM. The solutions behave as liquid metals above 9 MPM. As the concentration is decreased from 9 to 3 MPM, departure from metallic behavior occurs and various criteria for metallic conduction are no longer satisfied. We believe deep traps are present below 9 MPM. At concentrations near 3 MPH the influence of free electrons is no longer seen.

Pressure Effects on the Vibrational Modes of K_{2}PtCl_{4}, K_{2}PdCl_{4}, K_{2}PtCl_{6}, and K_{2}PdCl_{6}
View Description Hide DescriptionPressure effects on the vibrational modes (internal and lattice) of tetragonal crystals of K_{2}PtCl_{4} and K_{2}PdCl_{4} were studied. The most pressure‐sensitive external mode for these compounds was the translational mode along the long axis , while the least sensitive was the translational mode along the short axis . Results with cubic crystals of K_{2}PtCl_{6} and K_{2}PdCl_{6} showed that the lattice mode demonstrated higher pressure dependency than the internal modes.

ESR Linewidth and Solution Stability Studies of Dilute Solutions of Cesium in Ethylamine–Ammonia Mixtures
View Description Hide DescriptionAn electron spin resonance(ESR) study of the m_{I} ‐dependent linewidth of the hyperfine pattern from cesium–amine solutions is reported. The ESR spectrum of the monomer in dilute solutions has Lorentzian‐shaped lines. A two‐state equilbrium model is sufficient to describe the linewidth dependence upon of an isothermal spectrum. Due to persistent problems with solution decomposition, however, data could not be obtained over a sufficient range of temperature and solvent composition to permit a distinction to be made among several possible models. A systematic study was made of the solution decomposition at room temperature. Solutions could be prepared which were stable for periods of weeks to months in the presence of excess metal and after some initial decomposition. However, for freshly prepared dilute solutions without excess metal the decomposition was much faster and depended on the surface‐to‐volume ratio of the container. Zero‐order decay of the optical absorption was observed for a solution in a 2‐mm‐diam tube.

Correlation Energy in Atomic Systems. VI. Comments on the Radial Correlation Energy
View Description Hide DescriptionA fraction of the radial correlation energy is computed for the first‐row atoms in the ground state as well as selected excited states. The same type of computation is reported for the ions of the isoelectronic series from Ne to A^{8+}. The wavefunction we have used is a linear combination of three determinants: One is the standard Hartree–Fock determinant, and the other two contain orbitals shrunken or expanded relative to those in the Hartree–Fock determinant. In the paper we discuss the technique needed to obtain the determinants and the physical interpretation of the results. The large fraction of correlation energy (over 20% for the Ne atom) obtained with such a small expansion (two determinants added to the Hartree–Fock determinant) is explained as a consequence of rejecting the orthogonality constraints among the orbitals. The results of this work seems to indicate that different techniques should be used in order to solve the different effects which are lumped together under the name of “correlation energy.”