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Volume 104, Issue 20, 22 May 1996

Calculation of vibrational (J=0) excitation energies and band intensities of formaldehyde using the recursive residue generation method
View Description Hide DescriptionWe use the recursive residue generation method (RRGM) with an exact kinetic energy operator to calculate vibrational excitation energies and band intensities for formaldehyde. The basis is a product of one‐dimensional potential optimized discrete variable representation (PO‐DVR) functions for each coordinate. We exploit the symmetry by using symmetry adapted basis functions obtained by taking linear combinations of PO‐DVR functions. Our largest basis set consists of 798 600 functions (per symmetry block). The Lanczos tridiagonal representation of the Hamiltonian is generated iteratively (without constructing matrix elements explicitly) by sequential transformations. We determine a six‐dimensional dipole moment function from the ab initiodipole moment values computed at the QCISD level with a 6‐311++G(d,p) basis set. We converged all A _{1}, B _{2} and B _{1}vibrational states up to the combination band with two quanta in the C–O stretch and one quantum in a C–H stretch at about 6 350 cm^{−1} above zero point energy. We present a simulated (J=0) infrared spectrum of CH_{2}O for transitions from the ground state.

Determination of first hyperpolarizability of nonlinear optical chromophores by second harmonic scattering using an external reference
View Description Hide DescriptionFirst hyperpolarizabilities (β) of two tricyanovinylthiophene nonlinear optical chromophores were determined using second harmonic, hyper‐Rayleigh, scattering. The use of an external standard in the determinations is compared with the previous use of an internal standard. The first hyperpolarizability of the well‐known chromophore 4 dimethylamino 4′ nitrostilbene (DANS) was also determined using the external standard method and its value is compared to those in the literature. A new method of analyzing the hyper‐Rayleigh scattering signal by recording a histogram of the scattered energy is reported. This method is shown to give more reliable results in a shorter period of time than the usual static gate method. The histogram function provides additional information in the form of the histogram width which is shown to be an indication of the mean‐square concentration fluctuations of the chromophores in solution. The effects of molecular interactions on the concentration dependence of the hyper‐Rayleigh scattering signal is discussed. It is shown that depending on the concentration range, the β value of para‐nitroaniline, used as the external standard, can agree with two different values reported in the literature. Results on the depolarization ratio of the hyper‐Rayleigh scattered light from one of the tricyanovinylthiophene chromophores are presented. At low concentration the depolarization ratio agrees with the theoretically predicted value based on C _{2v } symmetry. However, at higher concentration the measured depolarization ratio increases indicating molecular interactions.

A phenomenological model for the vibrational dependence of hydrogen interchange tunneling in HF dimer
View Description Hide DescriptionWe present a phenomenological model to account for the observations of the hydrogen interchange tunneling at N=v _{1}+v _{2}=1–3 of the free (v _{1}) and the bound (v _{2}) HF stretches of (HF)_{2}. Good agreement is obtained between calculations and observations at the levels (v _{1},v _{2}) of v _{1}−v _{2}=±1 for both N=1 and 3, suggesting that the observed hydrogen tunneling splittings in these levels are direct rather than the results of many extraneous perturbations. The model also predicts well the ratios of the rates of vibrational predissociation at these states, in addition to the splittings. We attribute the unusually large vibrational dependence of the splittings upon valence bond excitation to the result of interbond coupling between the two HF local oscillators. Significant differences in the vibrational energy of the level (1,2) as well as the tunneling splitting at (2,0) between observation and prediction are, however, noted.

Infrared spectrum and theoretical study of the dinitrogen pentoxide molecule (N_{2}O_{5}) in solid argon
View Description Hide DescriptionFourier Transform Infrared (FTIR)spectra of the covalent dinitrogen pentoxide molecule isolated in a solid argon matrix at 10 K are reported. The measured frequencies in the 200–4000 cm^{−1} region are in close agreement with gas phase values previously reported. An accurate and sophisticated ab initio study showed that the stable equilibrium structure, C _{2} symmetry, was in agreement with the structure previously determined by electron diffraction data.

Structure and vibrational dynamics of sodium sulfate/sodium chromate solid solutions
View Description Hide DescriptionSolid solutions of Na_{2}SO_{4}/Na_{2}CrO_{4} are studied using laser Raman spectroscopy,infrared spectroscopy and differential scanning calorimetry. When the chromate ion concentration increases, the lattice expands continuously and a higher temperature sulfate phase, phase III, is stabilized to room temperature. The site group and correlation field splitting are also studied as a function of the relative sulfate\chromate ion concentration. The transition enthalpy from phase III to a higher temperature sulfate phase, phase I, has been measured. The calculated transition entropy is perfectly explained by a mixing entropy model.

Elastic constants of ice VI by Brillouin spectroscopy
View Description Hide DescriptionThe elastic constants of ice VI have been determined at −2 °C and 7.2 kbar by single crystalBrillouin spectroscopy. The adiabatic elastic moduli were found to be C _{11}=26.8, C _{12}=14.5, C _{13}=12.8, C _{33}=26.2, C _{44}=6.3, and C _{66}=10.4×10^{4} bar, within approximately 1.5%. Large (125 mm^{3}) single crystals were grown in a high pressure cell and in situBrillouin spectra were collected at various crystal orientations about the laboratory z‐axis. Ice VI crystals were oriented, while under pressure, by using the birefringent properties and Brillouin spectral behavior. Several polycrystalline elastic properties are derived using the bulk adiabatic moduli and a comparison with previous results is made.

Ultraviolet spectroscopy of HgAr in a supersonic jet: A new determination of the A ^{3}0^{+} state potential
View Description Hide DescriptionWe report high‐resolution fluorescence studies of the rotational structure of the HgAr A ^{3}0^{+}–X ^{1}0^{+} (1≤v′≤6, v″=0) vibrational bands which occur near to the Hg 6s ^{2} ^{1} S _{0}–6s6p ^{3} P _{1} (254 nm) atomic resonance. The molecules were formed in a supersonic jet expansion and were excited by UV radiation produced by intracavity second‐harmonic generation in a cw dye laser. The intensity profile of each band was reproduced by a theoreticalmodel. Least‐squares fits to the experimental spectra yielded accurate values for the band origins, rotational constants, and isotope shifts. This information was used in a Rydberg–Klein–Rees evaluation of the A ^{3}0^{+} potential, which was found to differ slightly, but significantly, from a Morse function in the region probed by this experiment.

On the role of conical intersections in photodissociation. V. Conical intersections and the geometric phase in the photodissociation of methyl mercaptan
View Description Hide DescriptionThe geometric, or Berry, phase effect is particularly diabolical when it is associated with a conical intersection of two states of the same symmetry. A recently developed algorithm for determining a conical intersection of two states of the same symmetry provides the basis for a general approach for characterizing paths that give rise to the geometric phase effect in this instance. This approach is used, with wave functions in excess of 1.5 million configuration state functions, to determine a conical intersection and associated paths in the Franck–Condon region of the photodissociation process CH_{3}SH(X ^{1} A′)+hν→CH_{3}SH(1,2 ^{1} A″)→CH_{3}S+H or CH_{3}+SH. Derivative couplings along these paths are also determined. The implications for photodissociation dynamics are discussed.

Semiempirical MNDO, AM1, and PM3 direct dynamics trajectory studies of formaldehyde unimolecular dissociation
View Description Hide DescriptionDirect dynamics calculations are performed, using the semiempirical neglect of diatomic differential overlap (NDDO) molecular orbitaltheory, to explore the level of electronic structuretheory required to accurately describe the product energy partitioning when formaldehyde dissociates into hydrogen and carbon monoxide. Trajectories are initiated at the saddlepoint and are propagated for the short time needed to form products, by obtaining the energy and gradient directly from the NDDO theory. The resulting product energy partitioning is compared to available experimental data and the findings of two previous trajectory studies, including one ab initio trajectory study at the HF/6‐31G** level of theory [Chem. Phys. Lett. 228, 436 (1994)]. The MNDO, AM1, and PM3 semiempirical Hamiltonians are studied, as well as Hamiltonians based on specific reaction parameters (SRP). For the latter, the original PM3 and AM1 parameters are adjusted to reproduce some ab initiopotential energy surface properties, such as stationary points and part of the reaction path. A series of NDDO‐SRP Hamiltonians are chosen by fitting different features of a HF/6‐31G** potential energy surface. Only qualitative agreement is found between the product energy distributions of the NDDO‐SRP Hamiltonians and that of the HF/6‐31G** Hamiltonian. This result is consistent with the well known difficulty of reproducing a HF/6‐31G** Hamiltonian with a NDDO‐SRP model, since dynamic correlation is not treated in ab initio SCF, but is incorporated into semiempirical methods. Trajectory results with NDDO‐SRP Hamiltonians, which reproduce a few experimental and/or high‐level ab initio stationary points, are in poor agreement with the experimental product energy partitioning. Reparameterizing the NDDO Hamiltonian is laborious, and only a few properties of the potential energy surface can be reproduced at the same time. This indicates the limitations of the NDDO‐SRP approach, which might be well suited for locally interpolating ab initio data, but not for quantitatively describing global potential energy surfaces.

Photochemistry of phosgene in the solid phase: Dissociation, ejection, and thermal desorption
View Description Hide DescriptionUnderstanding photochemistry and energy transfer mechanisms in molecular solid films is of interest to many scientific issues, ranging from matrix‐assisted laser desorption ionization mass spectrometry to photochemical processes on polar stratospheric cloud particles. We present a study of a model system: the photochemistry (hν=1.2–6.4 eV) of a molecular Cl_{2}CO solid film at low laser power density, 10 μJ–1 mJ/cm^{2} for ∼10 ns pulses. At hν≥3.5 eV, photon absorption by Cl_{2}CO leads to a major photodissociation channel resulting in CO (g) and Cl (g) and a minor molecular Cl_{2}CO ejection channel. Both photodissociation and molecular ejection are observed at the lowest laser power density and their yields depend linearly on pulse energy. This result establishes a single photon photoexcitation mechanism. The electronically excited Cl_{2}CO in the surface region of the solid film can either dissociate or convert its electronic energy to translational motion in Cl_{2}CO. The translational energy distribution of CO (g) from the photodissociation channel is bimodal: the flux‐weighted mean translational energy of the fast channel is photonenergy dependent (〈E _{trans}〉=210, 135, and ∼90 meV at hν=6.4, 5.0, and 3.5 eV, respectively), while the slow channel is independent of photonenergy and corresponds to completely thermalized CO molecules (〈E _{trans}/2k〉=84±3 K). The mean translational energy of photoejected Cl_{2}CO is 〈E _{trans}〉=220±20 meV. In addition to photoejection, there is also a distinctively different thermal desorption channel due to transient laser heating.

Photochemistry of phosgene in the solid phase: State‐resolved dissociation dynamics
View Description Hide DescriptionThe translational, rotational, and vibrational state distributions of CO (g) resulting from the single photonphotodissociation of Cl_{2}CO in the condensed phase at ∼90 K have been determined by time‐of‐flight (TOF) distribution measurement and resonance‐enhanced multiphoton ionization (REMPI) spectroscopy. The TOF distribution of CO (g) is bimodal. Internal state characterization of the slow channel reveals a completely thermalized origin, with a rotational temperature of T _{rot}=88±5 K, which is equal to the translational temperature as well as the substrate temperature. We believe these slow CO molecules originate from photodissociation below the topmost surface of the molecular film and achieve thermal equilibrium with the substrate before escaping into the gas phase. Internal state characterization of the fast channel shows, on the other hand, an energetic origin: at hν=5.0 eV, the rotational distribution, with an overall flux‐weighted mean rotational energy of 〈E _{rot}〉=0.12±0.01 eV, is non‐Boltzmann and can be approximated by a bimodal distribution with rotational temperatures of 210±40 K at low J″(s) and 2200±300 K at high J″(s); the relative vibrational population is N _{ν=1}/N _{ν=0}=0.33±0.05. Both rotational and translational distributions of fast CO show positive correlation with photonenergy. These CO molecules must be promptly ejected into the gas phase, carrying nascent energetic information from the photodissociation reaction on the surface of the molecular film. For electronic excitation events that result in photodissociation, 74% of the excess excitation energy is distributed in the translational and internal motions of products (CO and Cl); only 26% of the available energy is converted to motions of surrounding molecules.

Effects of the interactions between dissociative states and control of the product branching ratios in predissociation
View Description Hide DescriptionThe influence of the interactions between the dissociative states on the product branching ratios in predissociation is theoretically analyzed. We adopt the OH molecule as a model system and treat indirect dissociation processes with quantum interferences from the direct dissociation pathways eliminated. Various hypothetical coupling schemes between the bound electronic state and the dissociative states, and those among the dissociative states are employed. When a single dissociative state is involved in the dissociation with no interactions among the asymptotically degenerate states, recoil limit branching ratios of the triplet oxygen fine structure components O(^{3} P _{ j }, j=0,1,2) are attained at all energies. When a dissociative state, coupled with the bound state, is allowed to interact with other dissociative states correlating to the same atomic term, the product branching ratios approach recoil limit values only at a high energy limit. Predissociation through more than one dissociative state, interacting with each other, results in branching ratios that highly depend on the vibrational and angular momentum quantum numbers of the bound electronic state at energies below the dissociation limit to O(^{1} D). Above the threshold to O(^{1} D), the interactions between the dissociation channels give rise to highly oscillating branching ratios as a function of excitation energy. These findings are discussed in connection with the recent experiment of Gordon and co‐workers [J. Chem. Phys. 103, 6811 (1995)] on the spin–orbit control in the predissociation of HCl.

Angular distribution of molecular Auger electrons
View Description Hide DescriptionA general theory is developed for the angular distribution of Auger electrons emitted in the decay of molecular vacancies created by electron impact. The molecules are assumed as freely rotating. General expressions are derived where the angular distribution of the emitted Auger electrons is related to the anisotropy of the molecular axis distribution and to the shape and spatial orientation of the electronic orbitals prior to the Auger emission. Particular emphasis is placed on the correct formulation of the coherences produced during the ionization which requires an extension of previously derived formulas. The obtained equations are a necessary first step for future numerical calculations.

Quantum mechanical three‐dimensional wavepacket study of the Li+HF→LiF+H reaction
View Description Hide DescriptionA three‐dimensional time‐dependent quantum mechanical wavepacket method is used to calculate the state‐to‐state reaction probabilities at zero total angular momentum for the Li + HF → LiF +H reaction.Reaction probabilities starting from several different initial HF vibrational–rotational states (v=0,j=0,1,2) and going to all possible open channels are computed over a wide range of energies. A single computation of the wavepacket dynamics yields reaction probabilities from a specific initial quantum state of the reactants to all possible final states over a wide range of energies. The energy dependence of the reaction probabilities shows a broad background structure on which resonances of varying widths are superimposed. Sharp resonance features seem to dominate particularly at low product translational energies. There are marked changes in the energy dependence of the reaction probabilities for different initial or final diatom rotational quantum numbers, but it is noticeable that, for both reactants and products, odd and even rotational quantum numbers give rise to similar features. Our results clearly identify some resonance features which are present in the reaction probability plots for all product and initial states, though they appear in the form of sharp peaks in some plots and sharp dips in others. We speculate that these features arise from reactive scattering resonances which serve to redistribute the flux preferentially to particular product quantum states. The present calculations extend to higher energies than previously published time‐independent reactive scattering calculations for this system.

Reactions of benzene with rhodium cluster cations: Competition between chemisorption and physisorption
View Description Hide DescriptionThe reactions of Rh^{+} _{ n } cations, n=1–40, with C_{6}H_{6} and C_{6}D_{6} were investigated under single collision conditions in a Fourier‐transform‐ion‐cyclotron‐resonance mass spectrometer. For clusters with up to 18 rhodium atoms, dissociativechemisorption, accompanied by total or partial dehydrogenation in competition with nondissociative adsorption of an intact benzene molecule (physisorption) was observed. For clusters with n≳18 only the nondissociative adsorption was observed in the primary reaction step. Besides some enhancement of the nondissociative adsorption channel for cluster sizes n=9, 11, 12, and 13, deuteration has little effect upon the observed reactions. The atomic rhodium cation reacts after a few seconds induction time to an arene complex, which then forms a bis‐arene complex in a secondary reaction step. Rhodium dimer alone exhibits some cleavage of the Rh–Rh bond, resulting also in the Rh–C_{6}H^{+} _{6} complex.

Energy and angular momentum control of the specific opacity functions in the Ba+HI→BaI+H reaction
View Description Hide DescriptionCrossed‐beam and beam‐gas experiments on the reaction Ba+HI→BaI+H have been performed, in which the most probable collision energy ranges from 3 to 17 kcal/mol. The results, combined with previous experimental studies on this reaction system, show a remarkable collision energy dependence. Between low and high collision energies, a transition occurs in the intensity, width, and peak location of the product vibrational and rotational population distributions. The onset of this transition is estimated to occur at approximately 5 kcal/mol. For collision energies smaller than 5 kcal/mol, the product vibrational distribution is bell shaped and peaks at v=12. For collision energies larger than 5 kcal/mol, a second maximum appears at v=0 in the vibrational distribution. The rotational distributions of the crossed‐beam experiments are extremely narrow but broaden at lower collision energies. As the collision energy is increased above 5 kcal/mol, the BaI rotational excitation is very near the energetic limit, and the maximum for the BaI(v=0) rotational population distribution moves from J=415.5 to J=538.5. In contrast, below the transition onset, the maximum remains unchanged around J=420.5. Moreover, the peaks of the BaI(v=1) and BaI(v=2) rotational distributions appear at successively lower J values, as expected from energy conservation arguments. The nature of the kinematic constraints for this reaction allows the determination of the opacity functions for the production of the BaI product in a specific vibrational level v. Detailed analysis of the collision energy dependence of the specific opacity functions offers insight into the role of conservation of energy and angular momentum in influencing this reaction. At low collision energies, the maximum reactive impact parameter, b _{max}, is determined by an angular momentum (centrifugal) barrier. At collision energies larger than 5 kcal/mol, conservation of energy dictates the value of b _{max}. These two processes are identified as the mechanisms that control the Ba+HI reaction cross section. The transition between the two mechanisms provides an interpretation for the bimodal character of the BaI product internal‐state distribution.

Termolecular proton transfer reactions assisted by ionic hydrogen bond formation: Reactions of aromatic cations with polar molecules
View Description Hide DescriptionWe present a new method that applies resonant‐two‐photon ionization to generate reactant ions selectively in the source of a high‐pressure mass spectrometer (R2PI‐HPMS) for kinetic and equilibrium studies. Applications to reactions that would be obscured otherwise in a complex system are illustrated in mixtures of benzene with polar solvent molecules (S). We observe a novel type of proton transferreactions from C_{6}H_{6} ^{+•} to two S molecules where S=CH_{3}CN, CH_{3}OH, C_{2}H_{5}OH and CH_{3}COOC_{2}H_{5}, and from C_{6}H_{5}CH_{3} ^{+•} to two S molecules where S=CH_{3}OH and C_{2}H_{5}OH to form protonated solvent S_{2}H^{+} dimers. The reactions are driven by the strong hydrogen bonds in the S_{2}H^{+} dimers and therefore require the formation of the hydrogen bond concertedly with proton transfer, to make the process energetically feasible. The adducts (C_{6}H_{6} ^{+•})S are observed with blocked solvent molecules where the subsequent switching reaction to yield S_{2}H^{+} is slow, but not with alcohol reactants that can form hydrogen‐bonded chains that facilitate fast subsequent proton extraction. Correspondingly, kinetic simulations suggest that the mechanism proceeds through (C_{6}H_{6} ^{+•})S+S→S_{2}H^{+}+C_{6}H_{5} ^{•} and C_{6}H_{6} ^{+•}+2S→S_{2}H^{+}+C_{6}H_{5} ^{•}reactions, respectively. The rate coefficients of these reactions are in the range 10^{−13}−10^{−12} cm^{3} s^{−1} for the reaction through a bimolecular switching channel and in the range 10^{−26}−10^{−28} cm^{6} s^{−1} for reaction through a direct termolecular proton extraction mechanism. The relation to energetics and reactant structure is examined.

Product representation of potential energy surfaces
View Description Hide DescriptionThe recently proposed scheme for representing multidimensional potential energy surfaces as a linear combination of products of one‐dimensional functions is extended. The extensions prove to be important if one proceeds to higher dimensions. An iteration procedure is introduced which can further improve the representation. The product representation of potential energy surfaces is especially well suited to be employed within the framework of the multiconfiguration time‐dependent Hartree (MCTDH) approximation. The potential representation scheme cannot only be used to represent given analytical potential energy surfaces, but also to interpolate multidimensional surfaces on given, e.g. ab initio, product grid points. The product representation method is applied to the three‐dimensional S1 electronic surface of NOCl and to a six‐dimensional model Coulomb potential. To check the quality of the NOCl surface representation, the photoabsorption spectrum for an excitation from the S0 to the S1 surface is computed. Weight functions are shown to be easily implemented and, in the case of the NOCl surface, allow a substantial reduction of the number of required expansion coefficients. Exploiting the underlying symmetries of the potential under consideration can further reduce the computational effort, as is shown in the example of the Coulomb potential. Finally, the NOCl S1 potential surface defined on 616 ab initio points is interpolated, as an example for the product interpolation scheme.

The interaction representation and nonadiabatic corrections to adiabatic evolution operators. II. Nonlinear quantum systems
View Description Hide DescriptionThis paper reports further applications of the recently developed interaction representation form of infinite order operator corrections to adiabatic evolution operators. Previous work derived the form of the correction, and applied the methodology to a bilinearly coupled system bath model. In this paper we present results on coupled quantum systems in which the coupling is highly nonlinear. The method is both easy to implement and numerically accurate.

Relativistic potential energy surfaces of XH_{2} (X=C, Si, Ge, Sn, and Pb) molecules: Coupling of ^{1} A _{1} and ^{3} B _{1} states
View Description Hide DescriptionPotential energy surfaces of the ^{1} A _{1} and ^{3} B _{1} states for XH_{2} molecules (X=C, Si, Ge, Sn, Pb) are investigated with ab initio full valence multiconfigurational self‐consistent field wave functions, using effective core potentials. Spin–orbit coupling is also calculated to construct relativistic potential energy surfaces. The relativistic potential energy surfaces are compared with the adiabatic nonrelativistic potentials. Simple one dimensional Landau–Zener transition probabilities are calculated at the minimum energy crossing points of XH_{2} molecules to estimate the intersystem crossing probability.