Volume 106, Issue 5, 01 February 1997
Index of content:

Hydration and Raman scattering studies of levitated microparticles: Ba(NO_{3})_{2}, Sr(NO_{3})_{2}, and Ca(NO_{3})_{2}
View Description Hide DescriptionThe phase transformation and hydration of inorganic salt particles composed of alkaline earth metal nitrates, Ba(NO_{3})_{2}, Sr(NO_{3})_{2}, and Ca(NO_{3})_{2}, are investigated in a quadrupole cell, in which a levitated single microparticle is in dynamic equilibrium with water vapor under controlled humidity conditions. Laser Raman and Mie scattering techniques are used to probe the chemical and physical states of the microparticle before and after phase transformation. Because of the high degree of supersaturation that only a suspended solutiondroplet can attain before solidifying, metastable states not predicted from bulk solution thermodynamics often result. Thus it is found that, except for Ba(NO_{3})_{2} particles which form the stable anhydrous crystalline state upon efflorescence, Sr(NO_{3})_{2} and Ca(NO_{3})_{2}dropletssolidify to a metastable amorphous state that contains residual water persisting even in high vacuum. Raman spectra of the amorphous particles reveal that the nitrate ions form contaction pairs with the bivalent cations and that the residual water molecules possess very little, if any, hydrogen bond characteristics. The deliquescence properties of the amorphous particles, which are found to be different from those expected of the bulk crystalline states, are also reported.

The vibrationally resolved C 1s core photoelectron spectra of methane and ethane
View Description Hide DescriptionRecent progress in the development of highresolution electron spectrometers in combination with highly monochromatized undulator radiation has allowed observation of the vibrationally resolved gasphase C 1sphotoelectron spectra of methane and ethane. For both molecules, the C–H stretching modes are well resolved and for ethane the active C–C stretching mode has been observed for the first time. The spectra have been measured at low kinetic energies and detailed fittings using postcollision interaction line profiles have been made both, using a free parameter fit and a fit adhering to a linear coupling model. The free parameter fit allows for any anharmonicity in the vibrational energies. The linear coupling model, on the other hand, assumes that the initial and final state potential curves are harmonic and differ only in the normal coordinates. This simple model is used to reduce the number of free parameters in the fit, which greatly simplifies the analysis. An intensity model based on the linear coupling predicts that the intensities of the C–H stretching modes are directly related to the number of C–H bonds around the core ionized atom. The result is verified for ethane and shows a potential for further reduction of free parameters for large molecules and polymers.Ab initio calculations of molecular geometry and vibrational frequencies have also been carried out using the equivalent core (Z+1) approximation. The values predicted for the decrease in bond length have then been compared to those determined empirically by the linear coupling approach. The calculation of ethane indicates that symmetric C–H and C–C stretching modes are important upon core ionization. The corresponding vibrational frequencies have been calculated and agree well with observed values.

Paramagnetism of caesium titanium alum
View Description Hide DescriptionCaesiumtitanium alum, CsTi(SO_{4})_{2}⋅12H_{2}O, is a β alum and exhibits a large trigonal field and a dynamic Jahn–Teller effect. Exact calculations of the linear ^{2}T_{2}⊗e Jahn–Teller coupling show that in the strict S _{6} site symmetry the ground multiplet consists of a Kramers doublet 2Γ_{6} with magnetic splitting factors g _{∥}=1.1 and g _{⊥}=0, a Γ_{4}Γ_{5} doublet at ∼60 cm^{−1} with g _{∥}=2.51 and g _{⊥}=0.06 and another Γ_{4}Γ_{5} doublet at ∼270 cm^{−1} with g _{∥}=1.67 and g _{⊥}=1.83. The controversial g values observed below 4.2 K, g _{∥}=1.25 and g _{⊥}=1.14, are shown to arise from low symmetry distortions. These distortions couple the vibronic levels and induce into the ground state the offdiagonal axial Zeemaninteraction that exists between the first excited and the ground vibronic levels.

New assignments in the UV spectroscopy of the small benzene–argon clusters: The effects of a structureselective vibrational predissociation
View Description Hide DescriptionIn this paper, new experimental results using UV spectroscopy of the small benzene–Ar _{n} clusters are presented. We have found evidence for the vibrational predissociation of the state of some of these species on a nanosecond time scale and we propose a new assignment for the UVspectral features of this system. This assignment is consistent with other experimental data and it accounts additionally for the previously reported spectral anomalies, in particular the ionization potential measurements of these species. The twocolor R2PI spectra performed can thus be considered as nanosecond pump–probe experiments that allow us to estimate the relaxation rate of the state of these clusters. The vibrational relaxation is found to be strongly size and structure dependent: The two isomers [(1/1) and (2/0)] of the n=2 species exhibit different lifetimes differing by at least one order of magnitude. The size dependence of the relaxation process within the onesided isomer series appears also paradoxical since the relaxation rates of the (3/0) and (4/0) species are found to be smaller than that of the (2/0). These properties are discussed in relationship with the symmetry of these species.

The (2n+1)thorder offresonant spectroscopy from the (n+1)thorder anharmonicities of molecular vibrational modes in the condensed phase
View Description Hide DescriptionAssuming that the polarizability is a linear function of the nuclear coordinate, i.e., α(q)=α_{0}+α_{1}q, we obtain analytical expressions of the (2n+1)thorder signals and show that the leading order of the signals (n>1) is proportional to g_{n+1} , where g_{n+1} is the coefficient of the anharmonic potential V(q)=g_{3} q^{3}/3!+g_{4}q^{4}/4!+⋅⋅⋅. In other words, detection of the (2n+1)thorder signal implies the direct observation of the (n+1)thorder anharmonicity within the approximation. Based on this fact we discuss a possibility to detect the (n+1)thorder anharmonicity directly from the (2n+1)thorder experiment. Calculations are made by using novel Feynman rules for the nonequilibrium multitime correlation functions relevant to the higherorder offresonant spectroscopy. The rules have been developed by the authors and are presented compactly in this paper. With the help of a conventional doublesided Feynman diagram, we draw physical pictures of higherorder offresonant optical processes. Representative calculations for CHCl_{3} of the fifth, seventh, and ninthorder optical processes are presented and discussed.

Intensity perturbations from vibrational resonance coupling in isotropic Raman spectra of neat liquids and solutions
View Description Hide DescriptionThe influence of vibrational resonance coupling (VRC) on the intensity of isotropic Raman spectra is investigated theoretically for neat liquids and binary mixtures. Experimental studies of the effect are presented for overlapping Raman bands in binary liquid solutions (DMSO/CHCl_{3} and DMSO/CDCl_{3}) perturbed by hydrogen bonding between the two components. The vibrational resonance coupling perturbation leads to a nonlinear density dependence of the intensity, and is strongly dependent on the presence of short range order. An estimate of the typical magnitude of the intensity perturbation due to VRC is made by assuming that the coupling derives from the interaction of vibrational transition dipoles. It is concluded that the intensity perturbations are ordinarily quite small except in the case of low frequency vibrations having large transition dipoles, or in the case of very strong orientational correlations. For VRC between vibrations localized on molecules of different species, the role of the frequency matching is explored theoretically and experimentally, and it is found that the frequency mismatch must to be small compared to thermal energy kT for appreciable intensity perturbations to be observed.

Ab initio theoretical study of the methyl and phosphine torsion modes in ethylphosphine
View Description Hide DescriptionIn this paper, the far infrared (FIR) methyl and phosphine torsional frequencies and intensities are determined theoretically in ethylphosphine from ab initio calculations. For this purpose, the potential energy function for the double rotation of the methyl and phosphine groups in the electronic ground state is determined in a standard calculation by using the MP2/RHF and a631 basis set, with full optimization of the geometry. The numerical results are fitted to a symmetry adapted analytical form and introduced together with the kinetic parameters into the Hamiltonian operator. The Schrödinger equation for these two motions is solved by developing the solutions on the basis of products of trigonometric functions. From the energy levels, the torsional functions and the dipole moment variations the FIR spectrum is synthesized. A new assignment is proposed for some transtrans and the gauchegauche transitions between the phosphine levels. Additional transitions between the methyl levels are also proposed. It is concluded that a two dimensional calculation is indispensable for reproducing the FIR torsional spectrum in the region from 200 to .

Mode excitation dynamics in the fragmentation of : An helicity decoupling study
View Description Hide DescriptionA full quantum study of the fragmentation dynamics for argon trimer ions is carried out using a previously computed potential energy surface (PES). The initial and final internal states which are being considered are the bending–stretching states of the trimer and the rotovibrational states of the residual dimer ion. The treatment employs the helicity decoupling approximation over a broad range of total angular momentum values (J) and analyses the final distribution of rotational–vibrational states as a function of the metastable states of the J values and of the “tumbling” (helicity) quantum number Ω. It is found that at least two different effects, one mainly dynamically related to the centrifugal barrier and another to the orientational nature of the coupling potential field, can be discerned to explain the fragmentation results.

Crossedbeam reaction of carbon atoms with hydrocarbon molecules. III: Chemical dynamics of propynylidyne and cyclopropynylidyne formation from reaction of with acetylene,
View Description Hide DescriptionThe reaction between ground statecarbon atoms, C(^{3} P_{j} ), and acetylene, C_{2}H_{2} (X ^{1}Σ), is studied at three collision energies between 8.8 and 45.0 kJ mol^{−1} using the crossed molecular beams technique. Product angular distributions and timeofflight spectra of C_{3}H at m/e=37 are recorded. Forwardconvolution fitting of the data yields weakly polarized centerofmass angular flux distributions decreasingly forward scattered with respect to the carbonbeam as the collision energy rises from 8.8 to 28.0 kJ mol^{−1}, and isotropic at 45.0 kJ mol^{−1}. Reaction dynamics inferred from the experimental data and ab initio calculations on the triplet C_{3}H_{2} and doublet C_{3}H potential energy surface suggest two microchannels initiated by addition of C(^{3} P_{j} ) either to one acetylenic carbon to form strans propenediylidene or to two carbon atoms to yield triplet cyclopropenylidene via loose transition states located at their centrifugal barriers. Propenediylidene rotates around its B/C axis and undergoes [2,3]Hmigration to propargylene, followed by C–H bond cleavage via a symmetric exit transition state to lC_{3}H(X ^{2}Π_{j}) and H. Direct stripping dynamics contribute to the forwardscattered second microchannel to form cC_{3}H(X ^{2}B_{2}) and H. This contribution is quenched with rising collision energy. The explicit identification of lC_{3}H(X ^{2}Π_{j}) and cC_{3}H(X ^{2}B_{2}) under single collision conditions represents a oneencounter mechanism to build up hydrocarbon radicals in the interstellar medium and resembles a more realistic synthetic route to interstellar C_{3}H isomers than hitherto postulated ion–molecule reactions. Relative reaction cross sections to the linear versus cyclic isomer correlate with actual astronomical observations and explain a higher [cC_{3}H]/[lC_{3}H] ratio in the molecular cloud TMC1 (≈1) as compared to the circumstellar envelope surrounding the carbon star IRC+10216 (≈0.2) via the atomneutral reaction C(^{3}P_{j})+C_{2}H_{2} (X ^{1}Σ).

Reactantproduct decoupling method for statetostate reactive scattering: A case study for 3D H+H exchange reaction
View Description Hide DescriptionIn this paper, we present theoretical and computational details of implementing the recently developed reactantproduct decoupling (RPD) method (J. Chem. Phys. 105, 6072 (1996)) for statetostate quantum reactive scattering calculations of the prototypical H + Hreaction in three dimensions. The main purpose of this paper is to explore important features of the RPD scheme for use as a general and efficient computational approach to study statetostate quantum dynamics for polyatomic reactions by using 3D H + H as an example. Specific computational techniques and numerical details are explicitly provided for efficient application of this method in the timedependent (TD) implementation. Using the RPD method, the calculated statetostate reaction probabilities for the 3D H + Hreaction are in excellent agreement with those from the timeindependent variational calculations, and the computational cost of the RPD method is significantly lower than other existing TD methods for statetostate dynamics calculations.

Relaxation dynamics of multilevel tunneling systems
View Description Hide DescriptionA quantum mechanical treatment of an asymmetric doublewell potential (DWP) interacting with a heat bath is presented for circumstances where the contribution of higher vibrational levels to the relaxation dynamics cannot be excluded from consideration. The deep quantum limit characterized by a discrete energy spectrum near the barrier top is considered. The investigation is motivated by simulations on a computer glass which show that the considered parameter regime is “typical” for DWPs responsible for the relaxation peak of sound absorption in glasses. Relaxation dynamics resembling the spatial and energydiffusioncontrolled limit of the classical Kramers’ problem, and Arrheniustype behavior is found under specific conditions.

Anomalous diffusion of small particles in dense liquids
View Description Hide DescriptionWe present here a microscopic and selfconsistent calculation of the selfdiffusion coefficient of a small tagged particle in a dense liquid of much larger particles. In this calculation the solute motion is coupled to both the collective density fluctuation and the transverse current mode of the liquid. The theoretical results are found to be in good agreement with the known computer simulation studies for a wide range of solute–solvent size ratio. In addition, the theory can explain the anomalous enhancement of the selfdiffusion over the Stokes–Einstein value for small solutes, for the first time. Further, we find that for large solutes the crossover to Stokes–Einstein behavior occurs only when the solute is 2–3 times bigger than the solvent molecules. The applicability of the present approach to the study of selfdiffusion in supercooled liquids is discussed.

Branching ratio for the production of and by controlled electron impact on HOD
View Description Hide DescriptionThe and emission spectra have been measured by 17 eV electron impact on the mixtures of and with several mixing ratios. The intensity ratio of the emission to that of , , in the spectra of the mixture has been estimated using the and spectra obtained from pure and pure . As a result, is proportional to the ratio of the Hatom quantity to the D atom in the mixture, indicating that is independent of the fraction of HOD in the mixture. The following emission intensity ratios are obtained. where means the total emission cross section of by electron impact on pure HOD, and the others are similar.

A unified framework for quantum activated rate processes. II. The nonadiabatic limit
View Description Hide DescriptionA recently proposed unified theoretical framework for quantum activated rate constants is further developed and explored. The case of electronically nonadiabatic rate processes is considered, and the weak coupling limit explicitly investigated by an expansion of the rate constant expression. By virtue of this approach, a semiclassical Golden Rule expression is derived after a series of steepest descent approximations. The semiclassical analysis in turn reveals a closed form path integral expression for the quantum activated rate constant in the nonadiabatic (Golden Rule) limit which is free of harmonic and/or classical approximations for the manydimensional nuclear (vibronic) modes. The latter expression is amenable to direct calculation in realistic systems through computer simulation.

Dielectric and pressure virial coefficients of imperfect gases: CO_{2}–SF_{6} mixtures
View Description Hide DescriptionDielectric and pressure virial coefficients of five mixtures of CO_{2}–SF_{6} have been determined at 322.85 K. The quadrupole moment of CO_{2} calculated from the dielectric second virial coefficient of the CO_{2}–SF_{6} mixture is (4.48±0.30)×10^{−26} esu cm^{2}. This value is in excellent agreement with the most recent value determined by the direct method of induced birefringence by Battaglia et al. The hexadecapole moment of SF_{6} calculated from the second dielectric virial coefficient of the pure gas is (10.75±0.75)×10^{−42} esu cm^{4}.

Association and isotopic exchange reactions of CH(CD)[X ^{2}Π]+CO
View Description Hide DescriptionThe reaction rates for and with normal isotopic abundance CO and have been studied at 293 K for pressures between 12.5 and 500 Torr and at 100 Torr for temperatures between 293 and 650 K. The pressure and temperature dependence of the addition reaction of CH with CO have been measured. The addition rate coefficient can be fit to the expression 7.2±0.3×10^{−12} (T/293)^{−2.4±0.2} cm^{3} molecule^{−1} s^{−1} at 100 Torr total pressure (He buffer). A fit of the pressure dependence to a Troe expression with F_{c}=0.6 yields a lowpressure rate constant(k_{0}) of 2.4±0.3×10^{−30} cm^{6} molecule^{−2} s^{−1}. The rate for carbon atom exchange has been measured by comparison of the labeled and unlabeled reaction rates. The isotopic exchange reaction is 1.0±0.2×10^{−12} cm^{3} molecule^{−1} s^{−1} at 20 Torr. The deuterium isotope effect on the exchange rate is large, with an inverse kinetic isotope effect (k _{H}/k _{D})=0.28±0.08 at 20 Torr. This inverse isotope effect reflects the competition between collisional stabilization and isomerization, and is a convolution of isotope effects for the isomerization, unimolecular dissociation, and stabilization rates. The experimental results are consistent with a mechanism for exchange that involves isomerization of an HCCO adduct via an oxiryl intermediate, and indicate that insertion into the C–O bond is not important in this reaction.

Equilibrium yield for helium incorporation into buckminsterfullerene: Quantumchemical evaluation
View Description Hide DescriptionThe binding energy and equilibrium constant for the endohedral He@C_{60} compound have been determined from ab initio and density functional(DFT) calculations. Very large grids for the numerical integration are necessary to converge the DFT results to within 0.1 kcal/mol. Gradientcorrected DFT methods incorrectly predict He@C_{60} to be less stable than He+C_{60}. At the highest ab initio level employed, i.e., secondorder Mo/ller–Plesset perturbation theory (MP2) with extended basis sets and counterpoise corrections, He@C_{60} is bound by 2.0 kcal/mol. The equilibrium constant for He incorporation into C_{60} has been evaluated from Hartree–Fock and DFT interaction potentials adjusted to reproduce the MP2 binding energy. Computed equilibrium yields at 3000 atm and 900 K exceed 10%, compared with 0.1% observed in the experiment, which indicates that suitable catalysts could increase the observed yield significantly.

Avoiding long propagation times in wave packet calculations on scattering with resonances: A new algorithm involving filter diagonalization
View Description Hide DescriptionWe present a new and more efficient implementation of a hybrid approach to computing the solution of scattering problems affected by resonances. In the computationally expensive part of the calculation, wave packet propagation is used to obtain the timedependent wave function Ψ(t) up to some time τ at which direct scattering is over. This part is made efficient by using a recently introduced modification for the absorbing boundary conditions evolution operator which allows the use of real operator algebra if the initial wave function is chosen real. In the second part of the calculation, filter diagonalization is used to efficiently obtain the energies, widths, and expansion coefficients of resonances needed to describe the long time behavior of the scattering wave function. This part is made efficient by using a recently introduced algorithm which avoids the storage of energydependent basis functions. We demonstrate the application of the method to a twodimensional reactive scattering problem.

The CC3 model: An iterative coupled cluster approach including connected triples
View Description Hide DescriptionAn alternative derivation of manybody perturbationtheory (MBPT) has been given, where a coupled cluster parametrization is used for the wave function and the method of undetermined Lagrange multipliers is applied to set up a variational coupled clusterenergy expression. In this variational formulation, the nthorder amplitudes determine the energy to order 2n+1 and the nthorder multipliers determine the energy to order 2n+2. We have developed an iterative approximate coupled cluster singles, doubles, and triples model CC3, where the triples amplitudes are correct through second order and the singles amplitudes are treated without approximations due to the unique role of singles as approximate orbital relaxation parameters. The compact energy expressions obtained from the variational formulation exhibit in a simple way the relationship between CC3, CCSDT1a [Lee et al., J. Chem. Phys. 81, 5906 (1984)] CCSDT1b models [Urban et al., J. Chem. Phys. 83, 4041 (1985)], and the CCSD(T) model [Raghavachari et al., Chem. Phys. Lett. 157, 479 (1989)]. Sample calculations of total energies are presented for the molecules H_{2}O, C_{2}, CO, and C_{2}H_{4}. Comparisons are made with full CCSDT, CCSDT1a, CCSDT1b, CCSD(T), and full configuration interaction (FCI) results. These calculations demonstrate that CC3 and CCSD(T) give total energies of a similar quality. If results obtained by CC3 and CCSD(T) differ significantly, neither method can be trusted. In contrast to CCSD(T), timedependent response functions can be obtained for CC3.

The ^{3} A _{2}, ^{1} A _{2}, ^{3} B _{2}, and ^{1} B _{2} electronic states of CH_{2}: Small bond angle states
View Description Hide DescriptionMolecular structures with very small bond angles are a curiosity in chemistry. The two triplet (^{3} A _{2} and ^{3} B _{2}) and two singlet (^{1} A _{2} and ^{1} B _{2}) excited states of CH_{2} have been investigated systematically using ab initioelectronic structure theory. For these four states total energies and physical properties including geometries, dipole moments, harmonic vibrational frequencies, and associated infrared intensities were determined with the single and double excitation configuration interaction (CISD) method using four different basis sets. It is confirmed in this study that the four states of CH_{2} all have bent structures with longer CH bond lengths and smaller bond angles than the four lowerlying (X̃, ã, b̃, and c̃) states of CH_{2}. At the CISD optimized geometries single point energies were determined with complete active space selfconsistentfield (CASSCF) and CASSCF secondorder configuration interaction (SOCI) levels of theory. For the triplet excited states single point energies were also determined employing coupled cluster with single and double excitations (CCSD) and CCSD with perturbative triple excitations methods. At the CISD level with the largest basis set, the triple zeta plus triple polarizations with two sets of higher angular momentum and two sets of diffuse functions basis set [TZ3P(2 f,2d)+2diff], the bond angles were predicted to be 40.6° (^{3} A _{2}), 46.1° (^{1} A _{2}), 76.3° (^{3} B _{2}), and 81.3° (^{1} B _{2}), while the dipole moments were determined to be 2.35 (^{3} A _{2}), 2.26 (^{1} A _{2}), 1.69 (^{3} B _{2}), and 1.60 debye (^{1} B _{2}), respectively. With the most accurate method in this study, the CASSCFSOCI level with the TZ3P(2 f,2d)+2diff basis set, the energy separations (T_{e} value) between the ground state (X̃ ^{3}B_{1}) and the four excited states were predicted to be 73.7 kcal/mol (3.20 eV, 25 800 cm^{−1}) for the ^{3} A _{2} state, 96.8 kcal/mol (4.20 eV, 33 800 cm^{−1}) for the ^{1} A _{2} state, 151.0 kcal/mol (6.55 eV, 52 800 cm^{−1}) for the ^{3} B _{2} state, and 182.5 kcal/mol (7.91 eV, 63 800 cm^{−1}) for the ^{1} B _{2} state, respectively.