Volume 117, Issue 2, 08 July 2002
 ARTICLES

 Theoretical Methods and Algorithms

Kinetics of reversible diffusion influenced reactions: The selfconsistent relaxation time approximation
View Description Hide DescriptionThe simplest general theory of the kinetics of reversible diffusioninfluenced reactions that is exact both at short and long times for and is presented. The formalism is based on an approximate set of reactiondiffusion equations for the pair distribution functions which incorporate the influence of the chemical reaction by using effective rate constants that are determined selfconsistently. For small deviations from equilibrium and contact reactivity, the relaxation function is given explicitly in the Laplace domain in terms of the Smoluchowski rate coefficient that describes the corresponding diffusion controlled irreversible reaction. Consequently, the kinetics can be easily obtained for arbitrary diffusion coefficients and equilibrium concentrations.

Theoretical investigations of quadrupolar spin dynamics in the suddenpassage regime
View Description Hide DescriptionThe theoretical approach utilizing bimodal Floquet theory in the quadrupolar/centraltransition interaction frame, presented in an earlier article [J. D. Walls, K. H. Lim, and A. Pines, J. Chem. Phys. 116, 79 (2002)], is extended to describe the more complicated spin dynamics of spin systems. Rotary resonance effects occur when the strength of the radiofrequency irradiation, matches the sample spinning speed, at the conditions integral). At these conditions, conversions of both triplequantum and fivequantum coherences to centralquantum coherence are observed. Between rotary resonance conditions fivequantum as well as triplequantum coherences can be created from equilibrium magnetization via a nutation mechanism. In addition, effective transfer between fivequantum and triplequantum coherences also is observed in between rotary resonance conditions. These effects have been investigated theoretically and verified by both numerical calculations and experimental results.

Analysis of the molecular density: STO densities
View Description Hide DescriptionA partition of the molecular density for Slater basis sets (STO), which parallels one previously developed for Gaussian basis sets (GTO), is reported. The atomic fragments are expanded in spherical harmonics times radial factors. Each fragment contains all the onecenter charge distributions centered in the atom plus the part of every twocenter distribution assigned to the atom by the partition criterion. The performance of the procedure is analyzed, concluding that the analysis gives highly accurate representations of the molecular density at a very low cost. Moreover, the results of the analysis are illustrated with the study of the densities in CO and and the comparison of the atomic densities obtained from STO and GTO molecular calculations.

Electrostatics on particles: Phenomenological and orientational density functional theory approach
View Description Hide DescriptionIn order to describe efficiently the solvation of complex solutes in computer simulations, we introduce several simple particlebased models with the requirement that they yield, on average, either an exact or approximate representation of the macroscopic laws of electrostatics. First, in a phenomenological approach, electrostatics of continuous media is formulated in terms of a polarization density free energy functional, which is projected on randomly distributed discrete LennardJones pseudoparticles. The resulting model is that a polarizable fluid, in which the induced dipoles describe both orientational and electronic polarization. The problem of the connection between the macroscopic dielectric constant and the pseudoparticles polarizability is examined and important deviations with respect to the commonly accepted Clausius–Mossotti relation are found. Dipolar saturation effects can also be added to the model to yield a “nonlocal Langevin solvent model” and an approximate, numerically very efficient, “local Langevin solvent model.” The two models are implemented in molecular dynamics simulations and their solvation properties are compared to continuous electrostatics for simple solutes such as spherical ions or ion pairs. Their computational efficiency is also discussed and compared to explicit microscopic solventmodels. Then a statistical mechanics approach based on orientational density functional theory ideas is presented. Starting from a microscopic Hamiltonian describing a polar solvent, and for a given position of all the solvent molecules, a preliminary thermodynamic average over all the possible orientations of the molecules is performed. This can done by defining an orientational freeenergy functional which, at a formal stage, is perfectly welldefined and exact. Minimization of the functional with respect the angular degrees of freedom yields an effective Hamiltonian acting on the translational degrees of freedom only which can be explored via molecular dynamics simulations. The simplest approximation for the orientational functional yields a version of the nonlocal Langevin solventmodel mentioned above. More general approximations are suggested.

On a debate over the simulation and mapping of physical clusters in small cells
View Description Hide DescriptionThis paper attempts to resolve some issues in a published debate concerning the types of approximations involved, either implicitly or explicitly, in an innovative method for the simulation of small physical clusters. The method consists of first simulating the probability that a cluster will be found in a small subvolume of a macrovolume, followed by the use of this probability in the evaluation of the equilibrium number of clusters in the macrosystem. Under certain conditions the quantitative accuracy of the method remains high, regardless of the approximations. However, some of the approximations are subtle and impact the fundamental basis of statistical mechanics. Therefore, it is important to understand them as thoroughly as possible.

Calculating electron current in a tightbinding model of a fielddriven molecular wire: Application to xylyldithiol
View Description Hide DescriptionA recently developed Floquet theorybased formalism for computing electron transport through a molecular bridge coupled to two metalelectrodes in the presence of a monochromatic ac radiation field is applied to an experimentally relevant system, namely a xylyl–dithiol molecule in contact at either end with goldelectrodes. In this treatment, a nondissipative tightbinding model is assumed to describe the conduction of electric current. Net current through the wire is calculated for two configurations of the electrode–wire–electrode system. In one, symmetric, configuration, the electrodes are close and equidistant from the bridge molecule. In the other, asymmetric configuration, one electrode is farther away representing the tip of a scanning tunneling microscope located at this distance from the bridge molecule (the other end being chemisorbed to a gold substrate). For both configurations, electron current is calculated for a range of experimental inputs, including dc bias and the intensity and frequency of the laser. Via absorption/emission of photons, resonant conditions may be achieved under which electron transport is significantly enhanced compared to the unilluminated analog. Calculations show that this can be accomplished with experimentally accessible laser field strengths.

Chiroptical properties from timedependent density functional theory. II. Optical rotations of small to medium sized organic molecules
View Description Hide DescriptionWe report an implementation for the computation of optical rotations within the Amsterdam Density Functional program package. The code is based on timedependent density functional response theory.Optical rotations have been calculated for a test set of 36 organic molecules with various density functionals, and employing basis sets of different quality. The results obtained in this work with nonhybrid functionals are comparable in quality to those recently reported by other authors for the B3LYP hybrid functional, but show a somewhat larger tendency to produce outlyers. The median error is approximately for specific rotations as compared to experimental data (approximately 30% median deviation from experimental values). Thereby it is demonstrated that density functional computations can be employed to assist with the solution of stereochemical problems in case the specific rotations of the species involved are not small and their structures are rigid. Recent newly developed functionals are investigated with respect to their applicability in computations of optical rotations.

Flexible transition state theory for a variable reaction coordinate: Derivation of canonical and microcanonical forms with angular momentum conservation
View Description Hide DescriptionThis paper extends work previously presented [J. Chem. Phys. 113, 2648 (2000)] to establish a rigorous expression for the angular momentum resolved microcanonical reactive flux. A kinetic energy expression in terms of the angular momentum, based on the coordinate system described in the above reference, is derived. Analytic integration over momenta conjugate to the coordinates that describe the relative orientation of the fragments is effected at the canonical level. The Laplace transform relation between canonical and microcanonical coefficients is then exploited to yield the angular momentum dependent microcanonical reactive flux. Evaluation of the resulting rate expression involves a numerical integral whose dimension, in most cases, is the same as the integrals in corresponding canonical and standard microcanonical forms.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Structural and electronic properties of and Zintl anions from density functional theory
View Description Hide DescriptionStructural optimizations and frequency analyses have been performed on free and Zintl anions and ionization potentials and electron affinities calculated for using the density functional theory(DFT) of Becke’s threeparameter hybrid functional with the Perdew/Wang 91 expression. The DFT results obtained for small clusters are further checked with both the secondorder Møller–Plesset perturbation theory (MP2) and the configuration interaction calculations with all single and double substitutions from the Hartree–Fock reference determinant (CISD). Free anions are found to share the same geometries as naked Zintl anions observed in solids with a systematical expansion in bond lengths within about 5%. Intensive searches indicate that two isomers, a tricapped trigonal prism and a slightly distorted tricapped trigonal prism exist for and while nido clearly favors the monocapped antisquare prism structure. HOMOLUMO energy gaps >2.23 eV are obtained for series at the DFT level, except which has a much narrower energy gap of 1.16 eV. The calculated Gibbs free energy change of conversion reaction involving nonagermanides has the value of providing the first quantum chemistry evidence that the geometrically deduced mixed valent couple of and in a previous study is thermodynamically unstable compared to two anions. The calculated stabilization energies of and exhibit similar variation trends, clearly indicating a maximum at a minimum at and an obvious recovery at and 10. The calculated normal vibrational frequencies reproduce the six observed Raman peaks of naked with an averaged discrepancy of 11 cm^{−1}. Facecapped or edgecapped deltahedral structures are predicted for binary anions and and neutrals. The magic numbers at 9, and 10 obtained in both stabilization energies and ionization potentials well reproduce the abundance distributions of observed in timeofflight mass spectra. The validity of the Zintl–Klemm–Busmann principle in and neutrals is supported by the finding that sizable electron transfers from K atoms to nuclei occur in these clusters and the nuclei approach corresponding structures of free closo anions.

The system: An experimental potential energy surface and calculated rotovibrational levels of the molecular nitrogen dimer
View Description Hide DescriptionAn accurate new representation for the potential energy surface for the dimer has been obtained from the analysis of scatteringexperiments from our laboratory, and of available second virial coefficient data. A harmonic expansion functional form describes the salient geometries of the dimer and accounts for the relative contributions to the intermolecular interaction from components of different nature. The equilibrium geometry is a T conformation with well depth 13.3 meV (107.14 cm^{−1}) and at a distance of 4.03 Å. In order to assist in the analysis of spectra, we calculated the bound rotovibrational states for the system for by solving a secular problem over the exact Hamiltonian, considering the monomers as rigid rotors, and where the Coriolis coupling is included.

The lowest and ionpair states of ClF: Nonadiabatic effects and emission spectra
View Description Hide DescriptionThe structure of the states correlating with the ionic products and their emission are studied. Ab initio potential energy curves of ClF published recently and computed electronic dipole moments for parallel transitions between the ion pair and valence states, as reported in the present work, are used to calculate vibrational energies and emission spectra in the adiabatic and nonadiabatic approximations. It is shown that spectroscopic and emission properties of the state can be quite accurately described in the adiabatic approximation. On the contrary, the and states are nonadiabatically mixed due to the strong radial coupling caused by significant variation of the and contributions, similar to that observed for the and states. Nonadiabatic calculations carried out for the and ionpair states clearly demonstrate the influence of the radial coupling on the emission spectra, although do not reproduce quantitatively the entire range of experimental vibrational energies.

Femtosecond laser pulse control of electron transfer processes
View Description Hide DescriptionLaserpulse guided ultrafast electron transfer(ET) is studied theoretically for different types of donor–acceptor systems. The pulse initiates an optical transition from the electronic ground state into an excited state and controls the ET. The computations concentrate on systems where (a) the excited state (donor) is coupled to an acceptor level and where (b) the ET proceeds as an internal conversion from the excited state to the ground state. For both examples the manifold of vibrational coordinates is mapped on a single reaction coordinate coupled to a dissipative reservoir of further coordinates. Utilizing the methods of dissipative quantum dynamics combined with the optimal control (OC) scheme, it is demonstrated that control fields really exist which drive the ET in the required manner. Various properties of the OC algorithm are discussed when applied to dissipative dynamics and a scheme is proposed to avoid pinning in a local extremum.

Free radicals in superfluid liquid helium nanodroplets: A pyrolysis source for the production of propargyl radical
View Description Hide DescriptionAn effusive pyrolysis source is described for generating a continuous beam of radicals under conditions appropriate for the heliumdroplet pickup method. Rotationally resolved spectra are reported for the vibrational mode of the propargyl radical in heliumdroplets at 3322.15 cm^{−1}. Stark spectra are also recorded that allow for the first experimental determination of the permanent electric dipole moment of propargyl, namely, −0.150 and −0.148 D for ground and excited states, respectively, in good agreement with previously reported ab initio results of −0.14 D. The infrared spectrum of the mode of propargylbromide is also reported. The future application of these methods for the production of novel radical clusters is discussed.

Velocity map imaging of ionmolecule reaction products:
View Description Hide DescriptionThe velocity map imaging technique is applied to massselected and elimination products from the reaction studied under crossedbeam conditions at 0.21 eV collision energy. For both reactions we obtain the joint scattering probability distribution where E and Θ are the product translational energy and scattering angle. The fraction of available energy deposited into product translation is 0.4 for compared with 0.1 for For the product, the angular distribution is forwardbackwards symmetric and sharply peaked at Θ=0 and 180°. is not separable into the product of an energy and an angular function; rather, the angular distribution peaks more sharply at higher translational energy. Evidently, incipient products equilibrate in the exitchannel well, from which they decay statistically. The product translational energy distribution is consistent with orbitingtransition state phasespace theory with no exitchannel barrier. In addition, the energyintegrated angular distributionT(Θ) is consistent with the predictions of the early statistical complex decay model of Miller and Herschbach for fragmentation from a transition state that is a prolate top. In sharp contrast, for the products exhibits a substantial hot, nonstatistical tail towards high energy. Perhaps the channel has a late potential energy barrier some 0.5 eV above products, but we view this explanation as highly unlikely. Instead, we suggest that the potential energy from an earlier multicenter transition state is funneled efficiently, and highly nonstatistically, into product translation. This surprising conclusion may apply to products for the entire family of reactions of the late3D series transition metal cations and with alkanes.

Vibrational energy levels of methyl cation
View Description Hide DescriptionThe potential energy surface for methyl cation is calculated using an extrapolated full coupledcluster/complete basis set (FCC/CBS) theory. The equilibrium C–H bond length is obtained as 1.0884 Å. The vibrational energy levels of both and cations are computed using a variational method, based on the accurate potential energy surface. The fundamental frequencies in cm^{−1} are predicted to be 2942.27 1377.82 3108.29 and 1387.01 for and 2082.99 1070.31 2339.99 and 1015.70 for respectively.

New analytical surfaces and theoretical rate constants for the reaction
View Description Hide DescriptionWe report two new analytical fits of the ground potential energy surface (PES) and the first excited PES involved into the title reaction and its reverse, using ab initio electronic structure calculations from Papers I and II along with new grids of ab initio points by means of the secondorder perturbation theory on CASSCF wave function [CASPT2 (17,12) G2/augccpVTZ] reported here (1250 points for the PES and 910 points for the PES). Some experimental data were also introduced to better account for the exoergicity and the experimental rate constant at 300 K. The final rootmeansquare deviations of the fits were 1.06 and 1.67 kcal/mol for and the PESs, respectively, for the NOO abstraction and insertion regions of the PESs. Thermal rate constants were calculated (300–5000 K) for both the direct and reverse reactions by means of the variational transition state theory with the inclusion of a microcanonical optimized multidimensional tunneling correction, obtaining a very good agreement with the experimental data within all the temperature range. The new analytical PES presents several stationary points not introduced in previous analytical surfaces, and describes accurately the minimum, which seems to be very accessible according to the trajectories run in a preliminary quasiclassical trajectory study. The new analytical PES has a lower energy barrier than the previous one, which increases significantly the contribution of this PES to the total rate constant at high temperatures. Moreover, the new analytical PESs not only describe accurately the regions of the NOO system but also the ONO or near regions.

The lowest doublet and quartet potential energy surfaces involved in the reaction. II. Ab initio study of the symmetry insertion mechanism
View Description Hide DescriptionIn the present work we have carried out ab initio complete active space selfconsistent field (CASSCF) and secondorder perturbation theory on CASSCF wave function (CASPT2) calculations and also some density functional theory calculations with the augccpVTZ Dunning’s basis set on the lowest and doublet and quartet potential energy surfaces (PES) that could be involved in the title reaction. Thus, several minima, transition states, and surface crossings have been found for the insertion reaction mechanism. The results agree very well with available experimental data [i.e., for and with other previous ab initio calculations. Six  and four type surface crossings were located and classified for these PES’, whose only one (i.e., has been previously reported in theoretical and experimental studies. Highenergy barriers were found for the direct insertion mechanism (3.11 and 2.54 eV for the lowest doublet and quartet PES’ at the CASPT2/augccpVTZ level, respectively), clearly showing that this competitive mechanism is much less favorable than the direct abstraction or the indirect insertion reaction mechanisms reported in Paper I.

Observation and analysis of the infrared spectra of near 3950 and near 2900
View Description Hide DescriptionSpectra were recorded in the H–F stretching fundamental region for and in the D–F region for using a laser differencefrequency spectrometer coupled to a slitnozzle expansion. By varying the ratio of oxygen to carrier gas, beam temperatures ranging from 5 to 16 K were obtained. One standard uncertainty for the relative frequency position of unblended lines is 0.0001 cm^{−1}. Each spectrum was visually subdivided into a stronger (cold) spectrum and a weaker (hot) spectrum. Lines in the cold spectrum were fit to nearly experimental error, using a rotational Hamiltonian for openshell complexes taken from the literature. For 21 rotational and spin–rotational parameters (10 each for the upper and lower state plus the band origin) were used to fit 86 transitions to a standard deviation of 0.0002 cm^{−1}. For 23 rotational and spin–rotational parameters were used to fit 83 transitions to a standard deviation of 0.0003 cm^{−1}. The slightly poorer quality of the fit for than for is probably related to the somewhat larger vibrational amplitudes expected for the van der Waals motions in the protonated species. In spite of strenuous efforts, a simultaneous global fit to measurement error of the eight coldspectrum branches and fourteen hotspectrum branches could not be achieved, suggesting some improvement in the model used to derive the fitting Hamiltonian may be necessary.

Structure, electronic properties, and vibrational spectra of the water octamer with an extra electron: Ab initio study
View Description Hide DescriptionThe structure of the electron–water octamer has been investigated for the first time, using ab initio calculations. The lowestenergy conformer and the next lowest energy conformer are predicted to be the major and minor isomers with small and large vertical electron detachment energies. The binding energies and vibrational spectra are investigated.

Cluster nucleation effects in CO(Ar)_{n}: A stochastic analysis
View Description Hide DescriptionA previously discussed potential energy surface for the CO molecule interacting with one Ar atom is extended to evaluate its dependence on molecular vibrations. The and the adiabatic potential energy surfaces are employed within a stochastic treatment to obtain the vibrational transition energy changes as the number of rare gas atoms around the CO molecule is increased. The present calculations yield shifts of the excitation energy for the transition in Ar cluster of variable size which are in fair agreement with experimental expectations for the limiting case of solid argon. The details of the preferential structuring and clustering of the adatoms around the dopant molecule are obtained from diffusion Monte Carlo calculations and are extensively analyzed. The specifics of the system behavior are discussed and a driving microscopic mechanism is suggested on the basis of the energy balance between the interaction potentials that are present in the title system.