Volume 109, Issue 7, 15 August 1998
 COMMUNICATIONS


Second molecular hyperpolarizability of diaminodinitro spirobifluorene: An experimental study on thirdorder nonlinear optical properties of a spiroconjugated dimer
View Description Hide DescriptionNonlinear optical properties of a fixed molecular dimer, 2,2^{′}diamino7,7^{′}dinitro9,9^{′}spirobifluorene (ANSF), have been investigated in solution by the degenerate fourwave mixing technique. It has been observed that the orientationally averaged second molecular hyperpolarizability of ANSF in THF is enhanced ten times in comparison with its monomer unit, 2amino7nitrofluorene. Since electronic coupling between monomer units in ANSF is negligible owing to symmetry, we attribute the large enhancement to the orientational effect of the two constituting dipoles with possible involvement of vibronic coupling and spiroconjugation.

Geminate recombination and vibrational relaxation dynamics of aqueous chlorine dioxide: A timeresolved resonance Raman study
View Description Hide DescriptionThe photochemical dynamics of aqueous chlorine dioxide (OClO) are investigated using timeresolvedresonanceRaman spectroscopy. Stokes and antiStokes spectra are measured as a function of time following photoexcitation of OClO using degenerate pump and probe wavelengths at 390 nm. The temporal evolution of OClO Stokes intensity is found to be consistent with the reformation of groundstate OClO by subpicosecond geminate recombination of the primary ClO and O photofragments. AntiStokes intensity is observed for transitions corresponding to the symmetric stretch of OClO demonstrating that upon geminate recombination, excess vibrational energy is deposited along this coordinate. Dissipation of this energy to the surrounding solvent occurs with a time constant of ∼9 ps. Finally, a delay in the appearance of OClO antiStokes intensity relative to geminate recombination is observed demonstrating that the excess vibrational energy available to OClO is initially deposited along the resonance Raman inactive asymmetric stretch coordinate with the exchange of energy between this coordinate and the symmetric stretch occurring with a timeconstant of ∼5 ps.

Molecular model for the simultaneous orientational and translational ordering in a twodimensional liquid
View Description Hide DescriptionWe present a molecular–statistical theory of the phase transition from the twodimensional isotropic liquid to the phase which has the elements of the orientational and translational order combined in a single order parameter. This phase possesses the glide symmetry, similar to the herringbone order in crystals, and is related to the mesophases observed in Langmuirmonolayers. The microscopic definition of the herringbone order parameter is presented and the transition temperatures from the isotropic to the nematic, smectic, and the herringbone phases are expressed in terms of the direct correlation function of the twodimensional isotropic fluid. The relative stability of these phases is discussed. The transition temperature into the herringbone phase is estimated using the simple model of hard discs interacting via the quadrupole–quadrupole potential that promotes the herringbone order.
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 THEORETICAL METHODS AND ALGORITHMS


A challenge for density functionals: Selfinteraction error increases for systems with a noninteger number of electrons
View Description Hide DescriptionThe difficulty of widely used density functionals in describing the dissociation behavior of some homonuclear and heteronuclear diatomic radicals is analyzed. It is shown that the selfinteraction error of these functionals accounts for the problem—it is much larger for a system with a noninteger number of electrons than a system with an integer number of electrons. We find the condition for the erroneous dissociation behavior described by approximate density functionals: when the ionization energy of one dissociation partner differs from the electron affinity of the other partner by a small amount, the selfinteraction error will lead to wrong dissociation limit. Systems with a noninteger number of electrons and hence the large amount of selfinteraction error in approximate density functionals arise also in the transition states of some chemical reactions and in some chargetransfer complexes. In the course of analysis, we derive a scaling relation necessary for an exchangecorrelation functional to be selfinteraction free.

The exchange energy functional in a weak magnetic field
View Description Hide DescriptionA density functional theory for the Kohn–Sham exchange energy of a bounded, closed shell system in a weak, uniform, magnetic field is presented. The form obtained vanishes when the electron density is radial and, unlike the unscreened exchange energy of a locally uniform electron gas, does not diverge due to the Coulomb interaction. The role of the exchangecorrelation functional in the context of magnetic response theory is also examined.

Calculation of and reaction probabilities within the multiconfiguration timedependent Hartree approach employing an adiabatic correction scheme
View Description Hide DescriptionThe multiconfiguration timedependent Hartree (MCTDH) method is employed to calculate initialstate selected reaction probabilities for the two isotopic reactions with initial states =0–3 and total angular momentum To compute the reaction probabilities, an initial wave packet is prepared and propagated in time employing the recently developed constant meanfield integrator, thus reducing the computational effort by an order of magnitude. An adiabatic correction scheme is introduced which allows the initial wave packet to be moved from the asymptotic region of the educt channel close to the interaction region. The calculations are performed on the LiuSiegbahnTruhlarHorowitz (LSTH) potential surface which is expanded in products of onedimensional functions of the Jacobian coordinates. Initialstate selected reaction probabilities are computed for total energies up to 2.5 eV utilizing a combined flux operator/complex absorbing potential approach.

A new algorithm for Reverse Monte Carlo simulations
View Description Hide DescriptionWe present a new algorithm for Reverse Monte Carlo (RMC) simulations of liquids. During the simulations, we calculate energy, excess chemical potentials, bondangle distributions and threebody correlations. This allows us to test the quality and physical meaning of RMCgenerated results and its limitations. It also indicates the possibility to explore orientational correlations from simple scattering experiments. The new technique has been applied to bulk hardsphere and LennardJones systems and compared to standard Metropolis Monte Carlo results.

An accelerated Metropolis method
View Description Hide DescriptionWe propose a stochastic method to reduce the autocorrelation time of a general Monte Carlo(MC) method and apply it to the variational quantum Monte Carlo (VMC) simulation of fullcore atoms. We achieve a reduction in autocorrelation time of at least a factor of four compared with the standard method. Further, we find an approximate analytic fit to our results which gives a comparable reduction in autocorrelation time at essentially no cost. Our analytic form is independent of the geometry of the system being modeled and, therefore, can be easily applied to the VMC simulation of solids; it may also prove useful in any MC simulation where there are widely varying length scales. Results are presented for C, F, and Si.

Dissipative tunneling control by elliptically polarized fields
View Description Hide DescriptionThe tunneling dynamics of a dissipative twolevel system that is strongly driven by elliptically polarized electric fields is investigated. The dissipative dynamics is governed within the noninteractingblipapproximation for the stochastic forces by a generalized master equation (GME). With the focus being on viscousfriction, we compare exact numerical solutions of the GME with analytical approximations to both the transient and the asymptotic, longtime periodic dynamics. Novel phenomena are identified: These are a selective control on localization (or, as well, on delocalization) of the tunneling dynamics, or the inversion of an initially induced localization by a static bias via multiphotonassisted tunneling. These effects can be selectively tuned as a function of the eccentricity parameter of corresponding field amplitudes. In particular, the case of a circularly polarized driving field with yields a dramatic enhancement of the relaxation rate at resonances, when an integer multiple of the angular driving frequency matches the asymmetry energy induced by a static bias.

Globally uniform semiclassical wave functions for multidimensional systems
View Description Hide DescriptionThe globally uniform semiclassical approximation for energy eigenstates developed by D. Zor and K. G. Kay [Phys. Rev. Lett. 76, 1990 (1996)] is derived explicitly for the case of multidimensional systems and is applied to two test cases. The adiabatic switching approximation is used to obtain various quantities that enter the semiclassical expression. Two formulations of the method are examined: one requiring several trajectories for each desired state and another requiring only a single trajectory per state. The multitrajectory version yields accurate results for all states investigated (overlap between semiclassical and quantum eigenstates >0.98), including some influenced by classical chaos. The singletrajectory treatment, however, is more efficient, gives accurate results for regular states, and is even applicable for certain chaotic states, although the multipletrajectory method is preferred in such cases. Despite the substantial resemblance of the present theory to the frozen Gaussian approximation (FGA), it is a true semiclassical approximation and is found to produce wave functions that are significantly more accurate than those obtained from the FGA for all states examined.
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 GAS PHASE DYNAMICS AND STRUCTURE: SPECTROSCOPY, MOLECULAR INTERACTIONS, SCATTERING, AND PHOTOCHEMISTRY


Spectroscopy of buffergas cooled vanadium monoxide in a magnetic trapping field
View Description Hide DescriptionSpectroscopy of buffergas cooled vanadium monoxide (VO) is performed in the presence of a magnetic trapping field and at low field. VO is created via laser ablation. A helium buffer gas, chilled by a dilution refrigerator, cools molecules to 1.8±0.2 K within 10 ms. The measured rotational temperature is 1.5±0.8 K. Spatially resolved Zeeman spectra allow the magnetic broadening terms of several optical transitions to be determined. The density of VO decays with a characteristic time of 60 ms, thus precluding the observation of trapping.

An accurate ab initio HOCl potential energy surface, vibrational and rotational calculations, and comparison with experiment
View Description Hide DescriptionAccurate ab initio multireference configuration interaction (CI) calculations with large correlationconsistentbasis sets are performed for HOCl. After extrapolation to the complete basis set limit, the ab initio data are precisely fit to give a semiglobal threedimensional potential energy surface to describe HOCl→Cl+OH from high overtone excitation of the OHstretch. The average absolute deviation between the ab initio and fitted energies is for energies up to 60 kcal/mol relative to the HOCl minimum. Vibrational energies of HOCl including the six overtones of the OHstretch are computed using a vibrationalCl method on the fitted potential and also on a slightly adjusted potential. Nearspectroscopic accuracy is obtained using the adjusted potential; the average absolute deviation between theory and experiment for 19 experimentally reported states is Very good agreement with experiment is also obtained for numerous rotational energies for the ground vibrational state, the ClOstretch fundamental, and the fifth overtone of the OHstretch.

Predictions of rate constants and estimates for tunneling splittings of concerted proton transfer in small cyclic water clusters
View Description Hide DescriptionWe present transfer rates for the concerted hydrogen exchange in cyclic water clusters based on ab initio hypersurfaces. The studied hydrogen exchange involves bond breaking and forming and is in contrast to flipping motions of “free” hydrogen atoms in a “chemical” reaction. The rates are calculated for gasphase systems using canonical, variational transition state theory. Multidimensional tunneling corrections are included assuming both a small and a large reaction path curvature. Hybrid density functional theory was used to evaluate the potential energy hypersurface with interpolated corrections of second order perturbation theory at the three stationary points for both systems. Large curvature tunneling corrections are included in duallevel direct ab initio dynamics for the cyclic tri and tetramer of water. The ridge of the reaction swath serves as an estimate for the tunneling probability of various straightline corner cutting paths. Our results suggest that the investigated species interconvert on a time scale of seconds. The groundstate tunneling splitting is proportional to the square root of the transition probability at the energy of the minima, which is available from the calculation of tunneling corrections. The associated tunneling splittings are estimated to be between and which is close to the experimental resolution limit.

Photodissociation of ozone in the Chappuis band. III. Product state distributions
View Description Hide DescriptionWe discuss the vibrational and rotational state distributions of groundstate following the photodissociation of in the Chappuis band. They are obtained from timedependent wave packet calculations employing ab initiopotential energy surfaces for the and electronic states and the nonadiabatic elements, which couple these states. The satisfying agreement with experimental results underlines that the essential mechanisms of this twostate process are well described.

Very strong hydrogen bonds in neutral molecules: The phosphinic acid dimers
View Description Hide DescriptionAb initio molecular orbital and density functional theories have been used to study the structures and binding energies of the dimers of phosphinic acid (PA) and its dimethyl derivative (DMPA). For the first compound we have located all possible minima of the potential energy surface, while for the second only the most stable dimer was considered. The geometries were fully optimized at the and levels of theory. The harmonic vibrational frequencies were evaluated at the same levels, while the final energies were obtained using a approach. Both phosphinic acid and its dimethyl derivative form cyclic dimers in the gas phase, where the two monomers are held together by hydrogen bonds (HBs) which are significantly stronger than those found for their carboxylic analogs. The estimated dimerization enthalpies for PA (23.2) and DMPA (23.2 kcal/mol) are the highest reported so far for neutral homodimers in the gas phase and almost twice those measured for formic and acetic acid dimers. For the particular case of DMPA this estimated value is in very good agreement with the experimental one As a consequence of the large strength of the HBs, the activation barriers associated with the concerted double proton transfer are also sizably smaller than those predicted for their carboxylic analogs. These barriers become negligibly small when zero point energy (ZPE) corrections are taken into account and therefore tunneling must be very efficient. The calculated harmonic vibrational frequencies for the most stable DMPA dimer are consistent with its experimental infrared (IR) spectrum in the gas phase, which shows a characteristic structure of the ν(OH) band, typically associated with strongly hydrogen bonded complexes. Internal cooperative effects are not negligible in the case of phosphinic acid dimers, and the hydrogen bonds in the global minimum are about 1.0 kcal/mol stronger than those found in other stable dimers where only one of these linkages exists.

Definitive ab initio structure for the radical and resolution of the P–O stretching mode assignment
View Description Hide DescriptionPrevious ab initio studies of the radical have reported dramatically differing P–O bond distances when using spinrestricted wave functions predicting two artifactual isomers of a singly bonded oxygencentered radical and a doubly bonded phosphoruscentered radical. We show that large basis sets coupled with high levels of dynamical electron correlation are required to correctly describe the P–O bond in as well as the unpaired electron density as evidenced by the Fermi contact terms and anisotropic components of the and hyperfine splitting (hfs) constants. The optimized geometry, harmonic vibrational frequencies, and hfs constants of were determined at several coupledcluster levels of theory using both spinrestricted (ROHF) and spinunrestricted (UHF) Hartree–Fock reference wave functions. The geometrical parameters at the coupledcluster level with single, double, and perturbatively applied triple substitutions [CCSD(T)] using Dunning’s correlation consistent polarized valence quadrupleζ basis set (ccpVQZ) are These are in excellent agreement with those derived from recent gas phase microwave data, with the surprising exception of the P–H distance which deviates 0.02 Å from experiment. The value of the P–O harmonic stretching frequency at the CCSD(T) level within the ccpVQZ basis set is in good agreement with the experimental fundamental frequency of obtained by Withnall and Andrews and in constrast to previous speculation that this experimental band may have been misassigned. Hyperfine splitting constants determined at the level are in very good agreement with experimental values with an average deviation of 23 MHz.

Microwave spectrum and molecular structure of the radical
View Description Hide DescriptionThe rotational spectral lines of the and radicals in the electronic ground state are observed with a sourcemodulation microwave spectrometer and a Fouriertransform microwave spectrometer. Molecular constants including hyperfine interaction constants are determined for and by a leastsquares method. By using the obtained centrifugal distortion constants and inertial defects, the harmonic force field is evaluated, and the frequency of the vibrational mode (out of plane) is calculated to be This value is much smaller than that of the related molecule indicating a floppy motion along the outofplane mode. The zeropoint vibrational average structure was determined as follows; and where the numbers in parentheses represent three times the standard deviation.

Effects of reagent rotation on the dynamics of the reaction: A full dimension quantum study
View Description Hide DescriptionWe have extended the timedependent wave packet method to calculate cross sections and rate constants for rotationally excited initial states by using the centrifugal sudden (CS) approximation. A detailed study of the effects of rotational excitation of reagents on the title reaction on the WDSE PES has been carried out. It is found that (a) OH rotational excitation very mildly enhances the total cross section, (b) rotational excitation quite substantially reduce the cross section, and (c) simultaneous OH and rotational excitation has a largely uncorrelated effect. As a result, we found that the thermal rate constant can be obtained fairly accurately by only taking into account the effect of rotation. A model calculation by changing the mass of an O atom reveals that the weak dependence of the cross section on OH rotation is not because the O atom is left relatively stationary by OH rotation. We speculate that it may be a general feature for the diatomdiatom reaction that the nonreactive diatom acts as a spectator not only vibrationally but also rotationally. It was also found that the “shifting” approximation works quite well for the reaction. On the other hand, the effect of on the dynamics is found to be much stronger and more complicated than the effect, making the approximation not good for the reaction.

The state of revisited
View Description Hide DescriptionVibrational levels up to of the state of which dissociates to have been observed in highresolution Fourier transform records of fluorescence. From a revised analysis of this system, we have constructed a rotationless Rydberg–Klein–Rees (RKR) potential curve which extends to Vibrational and rotational constants have been calculated from this curve. The parameters describing the Coulombic interactions between atoms are given in a Hund’s case (c) basis. From this work, the dissociation energy for the state is found to be leading to a new value of for this state.

Mixed silicon–carbon dianions and their stability in the gas phase
View Description Hide DescriptionFree dianionic mixed silicon–carbon clusters have been studied by standard ab initio methods. Branched, chainlike, and cyclic isomers have been investigated in detail. The smallest system that has been found to be clearly stable with respect to electron autodetachment and fragmentation is a triangular seven atomic dianion, better referred to as Chainlike isomers are less stable than the corresponding branched isomers. The onset of electronic stability within the chainlike structural class is predicted to occur at the eight atomic cluster dianion Small stable cyclic isomers have not been found. The bonding mechanisms of the excess electrons in the different isomers are discussed and the systems are compared with other small gasphase dianions. Furthermore, the essentially different principles of building up dianionic, monoanionic, and neutral mixed silicon–carbon clusters are explained and discussed.
