Index of content:
Volume 105, Issue 12, 22 September 1996

The influence of morphology on the vibrational spectra of crystalline aerosols: SF_{6} and CO_{2}
View Description Hide DescriptionIntense infrared absorptions of small particles suspended in a dissimilar medium show effects that allow one to deduce, at least in principle, the morphology of the particles. These effects have their origins in the discontinuity in optical constants at the surface of the particle, and may be described analytically when the particles are spherical or ellipsoidal. This paper addresses the problems that arise when the particles under consideration are crystalline and have sharp edges and corners. Analytical descriptions are not available for such cases and it is shown that a numerical implementation the current standard electrostatic approach does not converge for cubes. However, convergence can be obtained by chamfering the edges and corners of the simulated particle. Experimental spectra are reported for suspended microcrystallites of sulfur hexafluoride and of carbon dioxide. The spectra were simulated using a variety of morphologies and it is concluded that the sulphur hexafluoride particles were cubes while the carbon dioxide particles were cuboctahedra.

Spectroscopy and electron detachment dynamics of C^{−} _{4}, C^{−} _{6}, and C^{−} _{8}
View Description Hide DescriptionResonantmultiphoton detachment spectroscopy has been used to obtain vibrationally resolved spectra of the C ^{2}Π←X ^{2}Π electronic transitions in C^{−} _{4}, C^{−} _{6}, and C^{−} _{8}. Transitions due to vibrational excitations in the totally symmetric stretching modes as well as the bending modes are observed. The electron detachment dynamics subsequent to multiphoton absorption are studied by measuring the electron emission time profiles and electron kinetic energy distributions. The observation of delayed electron emission combined with the form of the electron kinetic energy distributions indicates that these species undergo the cluster equivalent of thermionic emission. This interpretation is supported by comparing the experimental results to a microcanonical model for cluster thermionic emission.

Long‐range potential of B1(^{3}Σ^{+}) state based on a near‐dissociation expansion of the mercury–argon molecules
View Description Hide DescriptionA long‐range potential of B1(^{3}∑^{+}) state of the mercury–argon molecules was derived using a LeRoy–Bernstein procedure. The procedure was applied to B1(^{3}∑^{+})←X0(^{1}∑^{+}) excitation spectrum that was recorded previously. A dissociation energy, an effective vibrational index at the dissociation limit, and an asymptotic behavior of the B1(^{3}∑^{+}) state potential energy curve were determined. The result was compared with others available in the literature showing versatility of the method.

Microwave spectrum of silylidene H_{2}CSi
View Description Hide DescriptionRotational spectral lines of the H_{2}CSi molecule are observed in the millimeter‐wave and submillimeter‐wave regions. The molecule is produced in a glow‐discharge plasma of a gaseous mixture of SiH_{4} and CO. Rotational constants and centrifugal distortion constants have precisely been determined from observed frequencies of 32 a‐type transitions with J=5–4 to J=12–11 and K _{ a }=0 to K _{ a }=4. From the observed inertial defect, the vibrational frequency of the CH_{2} rocking mode is estimated to be as low as 331 cm^{−1}, which is consistent with the large quartic centrifugal distortion constants, D _{ JK } and d _{2}. Higher‐order centrifugal distortion constants up to the octic terms are necessary to obtain a good fit between the observed and calculated frequencies within experimental uncertainties. The low vibrational frequency and the necessity of the higher‐order centrifugal distortion terms indicate a floppy nature of the CH_{2} rocking mode. A preliminary radioastronomical search for H_{2}CSi in space has been carried out toward a few astronomical sources without success.

Reliable anisotropic dipole properties, and dispersion energy coefficients, for O_{2} evaluated using constrained dipole oscillator strength techniques
View Description Hide DescriptionConstrained anisotropic dipole oscillator strength techniques are used to obtain reliable values for a wide range of anisotropic and isotropic dipole properties of O_{2}, including the dipole–dipole dispersion energy coefficients for the interaction of O_{2} with O_{2}, H_{2}, N_{2}, CO, He, Ne, Ar, Kr, and Xe. Some of the anisotropic constraints required for our calculations are obtained via dipole sum rules from ab initio, multireference configuration interaction (CI) wave functions for the ground state of O_{2}. The individual dipole properties of O_{2} considered include the dipole oscillator strength sums S _{ k }, k=2,1,0(−1/2)−2,−3,−4,..., the logarithmic dipole sums L _{ k } and mean excitation energiesI _{ k }, k=2(−1)−2, and, as a function of wavelength, the dynamic polarizability and its anisotropy, the total depolarization ratio, the Rayleigh scattering cross section, and the Verdet constant. Our constrained dipole oscillator strength results are often the only reliable, and sometimes the only available, ones for many of the properties and dispersion energies considered.

Molecular rotations in vibronically coupled systems
View Description Hide DescriptionA new general method to compute rovibronic energy levels and eigenstates in molecules with possibly strong vibronic coupling is presented. The method can be applied to arbitrary coupling mechanisms of electronic potential energy surfaces and is not limited to a special type of molecule. Explicit criteria for the applicability of the method are derived. To investigate different types of rovibronic interactions, parameter studies for linear and bilinear E×ε Jahn–Teller systems are performed. As an application to a real molecule we investigate the rotational structure of the Li_{3} electronic A state. A variety of possible nontrivial effects is found which cannot be explained by rotational–vibrational coupling on a single electronic potential energy surface. Attention is paid to construct explicit effective Hamiltonians describing the findings. The rovibronic motion on potential surfaces with equivalent minima is also discussed in this context.

Product rotational polarization in photon‐initiated bimolecular reactions
View Description Hide DescriptionThis paper concerns the semiclassical description, calculation and measurement of angular momentumpolarization in the products of elementary gas‐phase bimolecular reactions. A unified, semiclassical treatment of the centre‐of‐mass correlated (k,k′,j′) angular distribution involving the reagent and product relative velocity and the product angular momentum vectors is described, and is related to other methodologies already existing in the literature. Explicit expressions are provided enabling experimentalists to extract rotational polarization information from crossed‐molecular beam and photon‐initiated reaction studies, under a variety of experimental conditions. Furthermore, the strategy developed is well suited to the theoretical calculation of reaction product polarization, in particular, using classical trajectory methods. An illustrative example of such a calculation is presented, and the centre‐of‐mass polarization data provided is used to simulate the laboratory frame rotational moments that can be determined experimentally using 1+1 Doppler‐resolved polarized Laser product probing techniques.

The unimolecular dissociation of HCO. II. Comparison of calculated resonance energies and widths with high‐resolution spectroscopic data
View Description Hide DescriptionWe present a theoretical study of the unimolecular dissociation resonances of HCO in the electronic ground state,X̃^{1} A′, using a new ab initiopotential energy surface and a modification of the log‐derivative version of the Kohn variational principle for the dynamics calculations. Altogether we have analyzed about 120 resonances up to an energy of ≊2 eV above the H+CO threshold, corresponding to the eleventh overtone in the CO stretching mode (v _{2}=11). The agreement of the resonance energies and widths with recent stimulated emission pumping measurements of Tobiason et al. [J. Chem. Phys. 103, 1448 (1995)] is pleasing. The root‐mean‐square deviation from the experimental energies is only 17 cm^{−1} over a range of about 20 000 cm^{−1} and all trends of the resonance widths observed in the experiment are satisfactorily reproduced by the calculations. The assignment of the states is discussed in terms of the resonance wave functions. In addition, we compare the quantum mechanical state‐resolved dissociation rates with the results of classical trajectory calculations and with the predictions of the statistical model.

Photochemistry of adsorbed molecules. XV. Localized atomic scattering in the photolysis of HI/LiF(001) and HI/NaF(001)
View Description Hide DescriptionWe have compared the ‘‘elastic’’ H atom angular‐scattering, P _{el}(θ′), of HI(ad) photolyzed at 248 nm for LiF and NaF substrates, both experimentally and theoretically. The observed P _{el}(θ′) for elastic scattering were similar for LiF and NaF, with a peak in the range 43°–48°. The P _{el}(θ′) for H from HI/NaF was broader than that for H from HI/LiF. Energy distributions, P(E _{ T′}), for H recoiling from HI/LiF and HI/NaF are also reported. A semiempirical potential‐energy surface (pes) is given for HI adsorbed on NaF, based on an earlier one for LiF [J. Chem. Phys. 94, 978 (1991)]. Ab initio ‘‘density function theory’’ (DFT) calculations were performed to verify the suitability of this pes; the DFT points were in satisfactory agreement with the semiempirical pes. For HI/LiF the DFT calculation gave a heat of adsorption of about 9 kcal/mol, the semiempiricalmodel gave 5 kcal/mol, and experiment gave 7 kcal/mol. We have computed H atom scattering by the classical trajectory method for two different models one involving dense and the other perforated arrangements of the HI adsorbate molecules. Comparison with the experimental results showed that the second model gave a better description of both P _{el}(θ′) and P(E _{ T′}) for HI/LiF and HI/NaF. The calculations showed that the angular and energy distributions of the scattered H were sensitive to the size of the vacancies between adjacent adsorbate molecules. The study also indicates the importance of unit‐cell size in relation to the size of the adsorbate molecule in determining adsorbate geometry and hence the energy and angular distributions of the scattered photofragments.

Conservation of the Kr^{+}(^{2} P _{1/2}) state in the reactive quenching of Kr(5s′[1/2]_{0}) atoms by halogen‐containing molecules
View Description Hide DescriptionThe second metastable state of Kr, 5s′[1/2]_{0}, was generated from the first metastable state, 5s[3/2]_{2}, by optical pumping in a flow reactor. Under optimum conditions, the entire Kr(5s[3/2]_{2}) concentration could be removed with more than 40% conversion to the Kr(5s′[1/2]_{0}) state, which is stable in He carrier gas. The Kr(5s′[1/2]_{0}) and Kr(5s[3/2]_{2}) states have the Kr^{+}(^{2} P _{1/2}) and Kr^{+}(^{2} P _{3/2}) ion cores, respectively, as do the Kr^{+}X^{−}(D) and Kr^{+}X^{−}(B,C) states. The reactions of a series of fluorine‐, chlorine‐, and bromine‐containing molecules, RX, with the Kr(5s′[1/2]_{0}) and Kr(5s[3/2]_{2}) atoms were studied by measuring the total quenching rate constants and by observing the KrX(B,C,D) product emission spectra. In contrast to the Kr(5s[3/2]_{2}) atoms, which give KrX(B and C) products, the Kr(5s′[1/2]_{0}) atoms have a high propensity to give KrX(D) plus a lesser amount of KrX(B), depending on the reagent, as products. Discrimination against KrX(C) formation by reactions of Kr(5s′[1/2]_{0}) atoms is severe. The reactions with F_{2}, NF_{3}, and N_{2}F_{4} exhibit the highest conservation of the Kr^{+}(^{2} P _{1/2}) core, and these Kr(5s′[1/3]_{0}) reactions give ≳70% KrF(D). The total quenching constants of Kr(5s′[1/2]_{0}) atoms generally are equal to those for Kr(5s[3/2]_{2}), but the branching fractions for KrX* formation from Kr(5s′[1/2]_{0}) atoms generally are smaller than for Kr(5s[3/2]_{2}) atoms. A correlation diagram based on conservation of Kr^{+} ion‐core state and Ω=0^{−} is developed to discuss these trends and the reactions of the Xe(6s′[1/2]_{0} and 6s[3/2]_{2}) atoms. Due to the absence of KrX(C–A) emission from the Kr(5s′[1/2]_{0}) atom reactions, the KrX(B–A) and Kr(D–A) transitions could be observed and the radiative branching ratios to the X and A states were assigned.

Wave packet dynamics and photofragmentation in time‐dependent quadratic potentials
View Description Hide DescriptionWe study the dynamics of generalized harmonic oscillator states in time‐dependent quadratic potentials and derive analytical expressions for the momentum space and the Wigner phase space representation of these wave packets. Using these results we consider a model for the rotational excitation of a diatomic fragment produced in the photofragmentation of a triatomic molecule and we highlight the signatures of classical mechanics in the final product distribution of this process.

Structure and bonding in mixed silicon–carbon clusters and their anions
View Description Hide DescriptionDensity functional calculations with simulated annealing have been performed for singly charged mixed silicon‐carbon cluster anions Si_{ n }C_{ m } ^{−} and for neutral Si_{ n }C_{ m } clusters with up to eight atoms. The calculations predict the existence of a number of previously unknown isomers and identify two classes of anion structure: carbon‐rich (chainlike) and silicon‐rich (three‐dimensional), with pronounced differences in the vertical detachment energies (VDE, transitions to states of the neutral clusters). The results provide insight into recent photoelectron detachment measurements on the anions.

Rotating around the quartic angular momentum barrier in fast multipole method calculations
View Description Hide DescriptionThe fast multipole method (FMM) evaluates the potential interactions of point charges (or masses) in time scaling linearly with their number. The FMM requires the ability to manipulate multipole and Taylor expansions. These manipulations are conventionally performed using a set of O(L ^{4}) translation operators, where L is the degree of the expansion. We introduce a method which achieves O(L ^{3}) scaling by rotating the expansions such that translation is always along the quantization or Z axis. It retains the FMM error bound. An overall speedup approaching a factor of 3 for relatively high orders of multipoles (L=21) is demonstrated. This procedure makes high accuracy potential evaluations substantially more efficient.

Saddle‐node bifurcations in the LiNC/LiCN molecular system: Classical aspects and quantum manifestations
View Description Hide DescriptionA classical‐quantum correspondence study of a saddle‐node bifurcation in a realistic molecular system is presented. The relevant classical structures (periodic orbits and manifolds) and its origin are examined in detail. The most important conclusion of this study is that, below the bifurcation point, there exists an infinite sequence of precursor orbits, which mimic for a significant period of time the (future) saddle‐node orbits. These structures have a profound influence in the quantum mechanics of the molecule and several vibrational wave functions of the system present a strong localization along the saddle‐node periodic orbits. A striking result is that this scarring effect also takes place well below the bifurcation energy, which constitutes a manifestation of the so‐called ‘‘ghost’’ orbits in configuration and phase space. This localization effect has been further investigated using wave packet dynamics.

Surprising cases of divergent behavior in Mo/ller–Plesset perturbation theory
View Description Hide DescriptionHigh‐order Mo/ller–Plesset perturbation calculations have been carried out for several small molecules and compared to full configuration interaction (FCI) results. The convergence of the Mo/ller–Plesset series is found to depend crucially on the one‐electron basis sets. Addition of diffuse basis functions leads in some cases to divergent behavior of the Mo/ller–Plesset series, even for highly single reference dominated systems as Ne and HF. The results thus questions the usefulness of higher‐order perturbation calculations as a vehicle for obtaining arbitrary accuracy of quantum chemical calculations and raises the fundamental theoretical question: When does Mo/ller–Plesset perturbation theory converge for many‐electron systems in extended basis sets?

Extensive ab initio study of the OH+HCN reaction: Low lying electronic states of the stationary points on the ^{2} A′ surface
View Description Hide DescriptionWe found many stationary points (minima and transition states) for the title reaction on the ^{2} A′ surface at unrestricted Hartree–Fock self‐consistent field (UHF‐SCF) level with two different basis sets. Stable adducts, as suggested by previous experimental works, have been ascertained and several reaction paths are obtained through intrinsic reaction coordinate (IRC) calculations. A link to the HNC+OH reaction is possible. Multiconfiguration SCF (MC‐SCF) calculations have been carried out for the addition reaction with the lowest energy barrier in order to eliminate the spin contamination error on these geometries. Correlation energy at the stationary points was estimated via a perturbative scheme, Mo/ller–Plesset at fourth order (MP4) which does not seem adequate for such a system, and via multireference double configuration interaction (MR‐DCI) with extrapolation to full CI values for ground and first excited states. Electronic excitations may open some reaction channels.

Phase behaviors of supercooled water: Reconciling a critical point of amorphous ices with spinodal instability
View Description Hide DescriptionThe anomalies of supercooled water in thermodynamic response functions at atmospheric pressure, the phase transition between low and high density amorphousices(LDA and HDA), and a predicted fragile–strong transition are accounted for in a unified manner by reconciling an idea due to Stanley and co‐workers introducing a second critical point separating LDA and HDA ices with a conjecture proposed by Speedy that LDA is a different phase from a normal water, called water II. The reconciliation is made on the basis of results from extensive molecular dynamics simulations at constant pressure and temperature. It is found that there exist large gaps around temperature 213 K in thermodynamic, structural, and dynamic properties at atmospheric pressure, suggesting liquid–liquid phase transition. This transition is identified with an extension of the experimentally observed LDA–HDA transition in high pressure to atmospheric pressure. Thus, we propose a new phase diagram where the locus of the second critical point is moved into negative pressure region. With this simple modification, it becomes possible to account for the divergence of the thermodynamic response functions at atmospheric pressure in terms of the critical point and the spinodal‐like instability of HDA. The unstable HDA undergoes a transition to LDA phase in lower temperature. The transition is also observed in high pressure region such as 200 MPa while it disappears at negative pressure, −200 MPa. This reinforces our proposed phase diagram in which there is no continuous path from a supercooled state to LDA at atmospheric pressure. It is argued that the HDA–LDA transition is accompanied by a fragile–strong transition. A possible mechanism of avoiding crystallization of aqueous solutions is also discussed in terms of a difference in hydrogen bond number distribution between LDA and HDA.

Spinodal decomposition of colloids in the initial and intermediate stages
View Description Hide DescriptionSpinodal decomposition of colloids in the initial and intermediate stages is described on the basis of the Smoluchowski equation. Hydrodynamic interaction is treated in an approximate way. In the intermediate stage, where a dominant length scale exists, the static structure factor is found to exhibit universal scaling behavior. The corresponding dynamic scaling function is derived from the nonlinear equation of motion for the static structure factor. This scaling function is a much more sharply peaked function of the wave vector than the well‐known empirical Furukawa scaling function, which applies to the transition stage where sharp interfaces contribute considerably, giving rise to a Porod tail at larger wave vectors. The wave vector where the static structure factor exhibits a maximum is found to vary with time—in the intermediate stage—like ∼t ^{−α}, where the exponent α varies between 0.2 and 1.1, depending on the relative importance of hydrodynamic interaction. Experiments on a microemulsion and binary polymer melt confirm the predicted scaling behavior.

Molecular dynamics simulation for the cluster formation process of Lennard‐Jones particles: Magic numbers and characteristic features
View Description Hide DescriptionCluster formation of Lennard‐Jones particles (65 536 atoms in a unit cell with an overall number density equal to 0.0149) was simulated by molecular dynamics. The temperature was set to decrease linearly with time by various thermostats, starting from a gas state temperature and ending at zero temperature. With the Nosé–Hoover thermostat, it was found that the translational temperature of the clusters suddenly decreased almost to zero when the cluster formation drastically increased around a reduced temperature (T*) of 0.5, while the internal temperature decreased linearly. Using the Andersen thermostat, which could simulate the aggregation of particles in an inert gas, both the internal and translational temperatures decreased almost linearly with time. When these thermostats were used, cluster–cluster and cluster–atom collisions did not give any magic number peaks in the size distribution up to 250 atoms/cluster at any temperature. Careful tracing of the cluster growth of 13‐atom clusters showed no difference in reactivity between icosahedral and nonicosahedral clusters. To simulate cooling in a supersonic jet, a thermostat which controlled only the translational temperature was introduced. After the clusters were formed by cooling the system with this thermostat, their internal temperature stayed at T*≊0.5, while the translational temperature decreased linearly to zero with time as it was controlled. A long‐time evaporation from these high‐temperature clusters gave peaks at 13 and 19 (and less significantly at 23 and 26) which are magic number sizes corresponding to single, double, triple, and quadruple icosahedra, respectively. The internal temperatures of 13‐ and 19‐atom clusters were higher than those of other size clusters. Higher evaporation energy was observed for the clusters of 13, 19, 23, and 26 atoms than for other size clusters after the long‐time evaporation, but only the 13‐atom clusters had the higher evaporation energy after cooling by the Andersen thermostat. These results suggest that magic number clusters were formed by evaporation to be trapped at the magic number sizes, and not by either cluster–atom or cluster–cluster collisions. Analyses of the radial distribution functions and the overall shapes of the generated solidlike clusters consisting of many isomers revealed the following characteristic features: The clusters around 13 and 26 atoms were close to being spherical, and the clusters around 19 atoms were oblate. Clusters around 13 atoms had an icosahedron‐based structure. The clusters around 55 atoms formed by the Nosé–Hoover and the Andersen thermostats were close to spherical and had an ordered structure. Clusters from 30 to 50 atoms had a disordered structure or a mixture of the different series of structures.

Transformation kinetics in one‐dimensional processes with continuous nucleation: The effect of shielding
View Description Hide DescriptionA derivation is presented for the fraction of material transformed as a function of time, X(t), for one‐dimensional phase transformations which occur via continuous nucleation and growth and which produce anisotropic particles. This derivation, which accounts for shielding effects and does not assume site saturation, is the first such derivation given for this type of problem. The analytical formulas which are found are evaluated in an approximate fashion for two different values of growth rate anisotropy. The results are compared with numerical simulations, and it is shown that the expressions derived are highly accurate.