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Volume 105, Issue 3, 15 July 1996

On the energetics of the lower excited states of N‐methylpyrrole
View Description Hide DescriptionAn absorption,fluorescence excitation, and (2+1) resonantly enhanced multiphoton ionizationspectroscopic investigation was carried out on the lowest excited state of N‐methylpyrrole (NMP). Transitions to and from this state were shown to give rise to the structured bands observed around 240 nm. An energy‐dissipative channel was found that was only slightly higher in energy. Possible assignments of this channel in NMP and its relation to the states of pyrrole are discussed.

Quantum treatment of the effects of dipole–dipole interactions in liquid nuclear magnetic resonance
View Description Hide DescriptionExperimental observation of anomalous intermolecular cross‐peaks in two‐dimensional solutionNMR spectra have attracted significant recent attention. Extremely simple pulse sequences on extremely simple samples with large equilibrium magnetization give resonances in the indirectly detected dimension which are simply impossible in the conventional density matrix framework of NMR. Here we extend a recently proposed density matrix treatment [Science 262, 2005 (1993)] to calculate the exact time evolution for a variety of pulse sequences. This density matrix treatment explicitly removes two fundamental assumptions of the standard theory—it includes the dipolar interaction between spins in solution (which is only partially averaged away by diffusion) and completely removes the high temperature approximation to the equilibrium density matrix [exp(−βH)≊1−βH]. We compare this quantum mechanical treatment to a corrected classical model, which modifies the dipolar demagnetizing field formulation to account for the effects of residual magnetization, and show that the quantum picture can be reduced to this corrected classical model when certain assumptions about the retained dipolar couplings are valid. The combination of quantum and classical pictures provides enormously better predictive power and computational convenience than either technique alone.

Time and temperature dependence of optical linewidths in glasses at low temperature: Spectral diffusion
View Description Hide DescriptionThe standard theoretical model of two‐level systems in low‐temperature glasses is modified so that the temperature dependence of the effective homogeneous optical linewidth is in agreement with experiment. This alters the time dependence of the width due to spectral diffusion. The new results fit recent experiments without the need for gaps in the distribution function of flip rates of the two‐level‐systems or the addition of extra distribution functions.

Bound states of He atoms on Ag(110)
View Description Hide DescriptionThe spectrum of bound states of He atoms adsorbed on Ag(110) is calculated, using an interaction potential based on effective medium theory EMT for the repulsive term A exp(−bz) and the Zaremba–Kohn form for the attractive van der Waals dispersion term. The electronic charge density of the host in the selvedge region is modeled by superimposing atomic‐charge densities using the Herman–Skillman tables and the prefactor A of the repulsive term is fitted to the exact ground state energy obtained from elastic He scattering data. Comparisons are made with the bound‐state spectrum extracted from the measured resonances in the He scattering data and with the results of several other models used in the current literature. An assessment of the role played by higher‐order dispersion contributions to the attractive potential is also included.

Experimental and theoretical studies of the decomposition of N_{2}O catalyzed by chlorine
View Description Hide DescriptionKinetic isotope effects (KIEs) for the thermal decomposition of N_{2}O catalyzed by chlorine were experimentally determined in the temperature range 773–923 K, and may be expressed as follows: KIE_{ t }(^{15}N)=(4100/T−1.90)±0.15, KIE_{ p }(^{15}N)=(3940/T−2.35)±0.10 and KIE(^{18}O)=(6990/T−3.60)±0.25. An Arrhenius fit to the measured rate constants resulted in an activation energy of 136±8 kJ mol^{−1} and a preexponential factor of 7.7×10^{7±0.1} m^{3} mol^{−1} s^{−1}. The KIEs were interpreted according to the Bigeleisen formalism. Furthermore, we calculated the activation energy following the Sanderson bond‐energy–bond‐order relationship, and the preexponential factor from transition state theory and compared them to experimental values. Additionally, ab initiomolecular theory was employed to study parts of the potential energy surface of the elementary bimolecular reaction between a N_{2}O molecule with a Cl atom. Equilibrium geometries, energies and harmonic vibrational frequencies were calculated at the HF/6‐31G* and MP2/6‐31G* level for some distinct stationary points on the potential energy surface, with energy refinements at the MP2/6‐311G* level. In our study the transition state was located by the eigenvalue‐following method. The ab initio properties of the transition state and reactants were also used for an evaluation of the kinetic isotope effects.

Further analysis of solutions to the time‐independent wave packet equations of quantum dynamics. II. Scattering as a continuous function of energy using finite, discrete approximate Hamiltonians
View Description Hide DescriptionWe consider further how scattering information (the S‐matrix) can be obtained, as a continuous function of energy, by studying wave packet dynamics on a finite grid of restricted size. Solutions are expanded using recursively generated basis functions for calculating Green’s functions and the spectral density operator. These basis functions allow one to construct a general solution to both the standard homogeneous Schrödinger’s equation and the time‐independent wave packet, inhomogeneous Schrödinger equation, in the non‐interacting region (away from the boundaries and the interaction region) from which the scattering solution obeying the desired boundary conditions can be constructed. In addition, we derive new expressions for a ‘‘remainder or error term,’’ which can hopefully be used to optimize the choice of grid points at which the scattering information is evaluated. Problems with reflections at finite boundaries are dealt with using a Hamiltonian which is damped in the boundary region as was done by Mandelshtam and Taylor [J. Chem. Phys. 103, 2903 (1995)]. This enables smaller Hamiltonian matrices to be used. The analysis and numerical methods are illustrated by application to collinear H+H_{2} reactive scattering.

Computational study of many‐dimensional quantum vibrational energy redistribution. I. Statistics of the survival probability
View Description Hide DescriptionWe statistically analyze the dynamics of vibrational energy flow in a model system of anharmonic oscillators which are nonlinearly coupled, with a local topology. The spectra of many basis states of similar energy are computed, for different values of the magnitude of the coupling in the Hamiltonian between these states. From individual spectra of zero order basis states at each coupling strength the individual survival probabilities are determined, which are then used in computing statistical averages. When the average fluctuation of the survival probability is small, in the strongly coupled limit, the average survival probability closely follows a semiclassical diffusion prediction and reflects a predicted linear dependence of the rate of energy flow on coupling strength. When the average fluctuation is large, in the weakly coupled limit, the average survival probability closely follows a power law decay of t ^{−1}, in agreement with a quantum extension of the diffusion picture. In this regime, individual survival probabilities show strong quantum beats. We conclude that these large variations reflect a strong influence of quantum interference in the weakly coupled limit.

On the effects of an internal barrier on fast four‐atom ion–molecule reactions
View Description Hide DescriptionWe investigate the influence of an internal barrier on an exothermic adiabatic reactionmodel between diatomic ions and molecules. Reaction cross‐sections are calculated from quasi‐classical trajectories for different initial vibrational and rotational states of the reactants and for relative collision energies in the range from 0.01 to 3 eV. It is shown that the height of a late internal barrier strongly influences both the characteristics of the state‐selected cross‐sections and the energy distributions of the products. In contrast to complex formation in the entrance region according to the Langevin model our analysis emphasizes the role of the full potential energy surface for an understanding of the dynamics of ion–molecule reactions.

Picosecond dynamics of cresyl violet H‐aggregates adsorbed on SiO_{2} and SnO_{2} nanocrystallites
View Description Hide DescriptionThe H‐aggregates of cresyl violet dye which are formed on the negatively charged SiO_{2} and SnO_{2}nanocrystallites, exhibit relatively short‐lived excitonic singlet state with a lifetime of about 35 ps. The difference absorption maximum (λ_{max}=470 nm) is blue shifted compared to the corresponding singlet excited state of monomer (λ_{max}=515 nm). Time‐resolved transient absorption measurements show that these dye aggregates are capable of injecting electrons from the triplet excited state into SnO_{2}nanocrystallites. The rate constant for heterogeneous electron transfer as measured from the formation of cation radical and electron trapping in SnO_{2}nanocrystallites was 2.0×10^{8} s^{−1}.

Pulse length control of Na^{+} _{2} photodissociation by intense femtosecond lasers
View Description Hide DescriptionFragmentation dynamics of the molecular ion Na^{+} _{2}irradiated by an intense femtosecond pulse laser is studied using quantum wave packet propagations. It is demonstrated that the pulse duration (20–250 fs) can be used as a control parameter for both the total dissociation probability and the branching ratio between different dissociation channels. This pulse length effect is important when the duration of the pulse is shorter than the vibrational period of the molecular ion in the ground state. The effects of laser intensity (10^{11}–3×10^{12} W/cm^{2}), wavelength (680–780 nm) and initial vibrational level on the dissociationdynamics are also studied.

The correlation between hydrogen bond tunneling dynamics and the structure of benzoic acid dimers
View Description Hide DescriptionWe report a correlation between the rate of incoherent tunneling associated with proton transfer in hydrogen bonds and the structure of aromatic carboxylic acid dimers. The compressibility of the hydrogen bond in benzoic acid, specifically the oxygen–oxygen distance r(O⋅⋅O), has been measured as a function of hydrostatic pressure up to 3.2 kbar using neutronpowderdiffraction. All data were recorded at a temperature of 5 K. Using previously published pressure dependence NMRmeasurements, we have investigated the relationship between the dynamics in the quantum regime and r(O⋅⋅O) in the hydrogen bonds of benzoic acid. The incoherent tunneling rate increases exponentially with decreasing r(O⋅⋅O). This behavior is attributed to the increase in the tunneling matrix element as the potential wells and the localized eigenfunctions of the double minimum potential which characterize the system are brought into closer proximity. There is a quantitative agreement between this study, in which the hydrogen bonds are compressed by the application of pressure, and the behavior exhibited by two benzoic acid derivatives with different oxygen–oxygen distances at ambient pressure.

High pressure range of addition reactions of HO. II. Temperature and pressure dependence of the reaction HO+CO⇔HOCO→H+CO_{2}
View Description Hide DescriptionThermal rate constants of the complex‐forming bimolecular reaction HO+CO■HOCO→H+CO_{2} were measured between 90 and 830 K in the bath gas He over the pressure range 1–700 bar. In addition, the vibrational relaxation of HO in collisions with CO was studied between 300 and 800 K. HO was generated by laser photolysis and monitored by saturated laser‐induced fluorescence. The derived second‐order rate coefficients showed a pronounced pressure and complicated non‐Arrhenius temperature dependence. Above 650 K, the disappearance of HO followed a biexponential time law, indicating thermal instability of collisionally stabilized HOCO. By analyzing the corresponding results, an enthalpy of formation of HOCO of ΔH ^{ o } _{ f,0}=−(205±10) kJ mol^{−1} was derived. On the basis of energy‐ and angular‐momentum‐dependent rates of HOCO formation, activated complex properties for the addition reaction HO+CO→HOCO were derived from the limiting high‐pressure rate constants; with the limiting low‐pressure rate constants, activated complex properties for the dissociation HOCO→H+CO_{2} could be fitted as well. The observed transitions between low‐ and high‐pressure limiting rate constants were well reproduced with these molecular parameters and collisional contributions; some evidence for rotational effects in collisional energy transfer was found. The surprisingly successful theoretical modeling of all available experimental data (80–2800 K, 0.0001–700 bar) allows for a satisfactory data representation of the rate coefficients over very wide ranges of conditions.

High‐pressure range of the addition of HO to HO. III. Saturated laser‐induced fluorescence measurements between 200 and 700 K
View Description Hide DescriptionThe addition of HO to HO was studied by saturated laser induced fluorescence at temperatures between 200 and 700 K and at pressures of the bath gas helium up to 100 bar. In combination with earlier measurements at 298 K, a set of falloff curves is constructed for the given temperature range. The limiting high‐pressure rate constant for the reaction HO+HO(+He)→H_{2}O_{2}(+He) follows as k _{1,∞}=(2.6±0.8)×10^{−11} (T/300 K)^{0±0.5} cm^{3} molecule^{−1} s^{−1}, practically independent of the temperature between 200 and 400 K. At higher temperatures, k _{1,∞} decreases. These results serve as a reference for statistical adiabatic channel model calculations of the recombination rate.

Photofragment imaging by sections for measuring state‐resolved angle‐velocity differential cross sections
View Description Hide DescriptionWe describe a two‐dimensional (2D) imaging technique for recording state‐specific photofragment angle‐velocity (θ,v) distributions. In these experiments the photofragment images are recorded as 2D sections of the 3D angular distributions using state‐specific ionization in a time‐of‐flight mass spectrometer. We compare this method to previous methods that record 2D projections of the 3D distribution. The 2D sections represent cartesian flux‐velocity maps in the center of mass and are related to angle‐velocity differential cross sections by a simple geometric factor. Two studies are highlighted. In the first, new results are presented for the A state photodissociation of CH_{3}I to CH_{3}+I. (θ,v) images are presented for I atom in the ^{2} P _{3/2} and ^{2} P _{1/2} spin–orbit states following photodissociation at 266 and 304 nm. The principal result is detection of the weak perpendicular transitions to the ^{3} Q _{1} state (at 304 nm) and the ^{1} Q state (at 266 nm) that underlie the strong parallel transition to the ^{3} Q _{0} state. We also report the ratio of cross sections σ_{⊥}/σ_{∥}, the anisotropy and branching ratio for I(^{2} P _{3/2}) and I(^{2} P _{1/2}), and the ^{3} Q _{0}–^{1} Qsurface crossing probability. In a second study the photodissociation of O_{3} to O_{2}(v)+O(^{3} P _{ j=2,1,0}) was measured. A bimodal anisotropicvelocity distribution was measured for O(^{3} P) corresponding to maximum in the O_{2}(v) vibrational distribution of v=15 and 27, in general agreement with a previous measurement. The anisotropies of the high‐ and low‐velocity components were measured to be β≊1.1 and 0.4, respectively.

Electron transfer of betaine‐30 in the inverted region
View Description Hide DescriptionWe use a density matrix theory to describe the photoinduced electron transfer dynamics of betaine‐30 in solution, including environmental effects which may lead to relaxation and dephasing. We restrict ourselves to only one reaction coordinate. The remaining degrees of freedom of the molecule and the solvent form the environment which is bilinearly coupled to the relevant system. We investigate the S _{1}→S _{0} reverse electron transfer of betaine‐30 in solution, which occurs in the Marcus inverted region. We compare the temperature dependence of our theoretical results with experimental data and other theoretical predictions.

Cross sections for collisions of low‐energy electrons with the hydrides PH_{3}, AsH_{3}, SbH_{3}, SnH_{4}, TeH_{2}, and HI
View Description Hide DescriptionWe calculated integral and differential cross sections for scattering of low‐energy electrons by two groups of hydrides from 10 to 30 eV. The first group is composed by the hydrides of elements in the same column of the Periodic Table and includes PH_{3}, AsH_{3}, and SbH_{3}. The second group is formed by hydrides in the same row and includes SnH_{4}, SbH_{3}, TeH_{2}, and HI. The calculations employed the Schwinger multichannel method with norm‐conserving pseudopotentials [M.H.F. Bettega, L.G. Ferreira, and M.A.P. Lima, Phys. Rev. A 47, 1111 (1993)]. Our goal is to find similarities and differences in the cross sections in these two groups.

Electronic states of ketene
View Description Hide DescriptionState of the art ab initio techniques of molecular electronic structure theory have been employed to investigate different structural aspects of the electronic states of ketene. Vertical excitation energies of more than 40 singlet and triplet states have been determined from equation‐of‐motion coupled cluster singles and doubles (EOM‐CCSD) and configuration interaction singles (CIS) calculations employing extended basis sets. Most importantly, all singlet and triplet electronic states below 70 000 cm^{−1}, close to the first ionization potential of ketene, 77 500 cm^{−1} have been determined. Only four pure excited valence states have been identified: the 1 ^{3} A _{1}, 2 ^{3} A _{1}, 1 ^{3} A _{2}, and 1 ^{1} A _{2} states. Vertical ionization energies have also been determined at the EOM‐CCSD level. They are found to be in nice accord with the available experimental results. All lower‐lying members of the Rydberg series of ketene terminating at 77 500 cm^{−1} are assigned based on theoretical data, symmetry considerations, and use of the Rydberg formula and the available experimental results. High‐quality estimates are given for the possible occurrence of fluorescence emission from the first singlet state of ketene.

Theoretical study of conjugation, hyperconjugation, and steric effect in B_{2}D_{4} (D=H, F, OH, NH_{2}, and CH_{3})
View Description Hide DescriptionThe rotational barriers of BD_{2} in B_{2}D_{4} (D=H, F, OH, NH_{2}, and CH_{3}) are examined in terms of conjugation, hyperconjugation, and steric effect at the level of HF/6‐31G*. By deleting or keeping the π orbitals on the boron atoms in the HFSCF calculations, for the first time we are able to analyze the hyperconjugation effect on molecular structures and stabilities quantitatively. In the perpendicular structure of B_{2}H_{4}, hyperconjugation results in the shortening of B–B bond from 1.705 to 1.679 Å and stabilizes the system by 3.1 kcal/mol. For B_{2}D_{4} systems in which D are π donors, there is a competition between the steric effect and π electronic delocalization. The former prefers a perpendicular conformation while the latter prefers a planar one. For B_{2}F_{4} and B_{2}(NH_{2})_{4}, these two factors are comparable and therefore, the rotational barrier is close to zero. For B_{2}(OH)_{4}, the intramolecular hydrogen bonds stabilize the planar structure significantly. For B_{2}(CH_{3})_{4}, however, steric effect dominates and consequently perpendicular structures are overwhelmingly preferred.

The accuracy of the pseudopotential approximation. II. A comparison of various core sizes for indium pseudopotentials in calculations for spectroscopic constants of InH, InF, and InCl
View Description Hide DescriptionSmall‐ and medium‐core pseudopotentials representing [Ar]3d ^{10}‐ and [Kr]‐like cores, respectively, have been adjusted for the In atom, supplementing the energy‐consistent three‐valence‐electron large‐core ([Kr]4d ^{10} core) pseudopotential of the Stuttgart group. The performance of these potentials is tested against those of other groups and against experiment, in calculations for the ground‐state potential curves of InH, InF, and InCl, both at the self‐consistent‐field and correlated levels. The role of the core size is discussed, and systematic errors of large‐ and medium‐core pseudopotentials are analyzed.

On the energy invariance of open‐shell perturbation theory with respect to unitary transformations of molecular orbitals
View Description Hide DescriptionA number of recently proposed single‐reference open‐shell perturbation theories based on a spin‐restricted open‐shell Hartree‐Fock reference function are examined, with an emphasis on a consistent formalism within which the theories may be compared. In particular, the effect of unitary transformations among the molecular orbitals on the energy is discussed. Of the seven different perturbation theories examined here, the restricted Mo/ller–Plesset theory, open‐shell perturbation theory method 1, the method of Hubač and Čársky, Z‐averaged perturbation theory, and invariant open‐shell perturbation theory methods are found to be invariant to all types of rotations for which the reference wave function is unaffected, though all are invariant to transformations of a more limited nature. Explicit equations for the generalized invariant forms of each perturbation theory are presented, in order to provide working equations for extension of the theories to local correlation schemes or coupled‐cluster perturbational corrections, among others.