Volume 116, Issue 10, 08 March 2002
 ARTICLES

 Theoretical Methods and Algorithms

A new analytic form of ab initio potential energy function: An application to
View Description Hide DescriptionThe potential energy function (PEF) for has been generated by the modified Shepard interpolation method using the fourthorder Taylor expansion at the MP2/augccpVTZ level. The reference points for the interpolation have been set at only three points, i.e., the equilibrium structure plus two symmetrically equivalent points in the coupling region of OH symmetric and antisymmetric stretching modes. The vibrational selfconsistent field (VSCF) and virtual configuration interaction (VCI) methods have been applied to determine fundamentals, overtones, and combination bands of The mean absolute deviation over these energy levels from the corresponding ones determined by the direct VCI method is only 4.8 cm^{−1}.

Integration schemes for dissipative particle dynamics simulations: From softly interacting systems towards hybrid models
View Description Hide DescriptionWe examine the performance of various commonly used integration schemes in dissipative particle dynamics simulations. We consider this issue using three different model systems, which characterize a variety of different conditions often studied in simulations. Specifically, we clarify the performance of integration schemes in hybrid models, which combine microscopic and mesoscale descriptions of different particles using both soft and hard interactions. We find that in all three model systems many commonly used integrators may give rise to surprisingly pronounced artifacts in physical observables such as the radial distribution function, the compressibility, and the tracer diffusion coefficient. The artifacts are found to be strongest in systems, where interparticle interactions are soft and predominated by random and dissipative forces, while in systems governed by conservative interactions the artifacts are weaker. Our results suggest that the quality of any integration scheme employed is crucial in all cases where the role of random and dissipative forces is important, including hybrid models where the solvent is described in terms of soft potentials. Regarding the integration schemes, the best overall performance is found for integrators in which the velocity dependence of dissipative forces is taken into account, and particularly good performance is found for an approach in which velocities and dissipative forces are determined selfconsistently. Remaining temperature deviations from the desired limit can be corrected by carrying out the selfconsistent integration in conjunction with an auxiliary thermostat, in a manner that is similar in spirit to the wellknown Nosé–Hoover thermostat. Further, we show that conservative interactions can play a significant role in describing the transport properties of simple fluids, in contrast to approximations often made in deriving analytical theories. In general, our results illustrate the main problems associated with simulation methods in which dissipative forces are velocity dependent, and point to the need to develop new techniques to resolve these issues.

Functionals of quantities other than the electron density: Approximations to the exchange energy
View Description Hide DescriptionA new method is proposed for constructing approximations to the electron–electron interaction. In this approach tools of density functional theory, such as the gradient expansion, are employed. Traditional gradient expansions depend on the electron density ρ. Here, however, we propose an alternative route to ρ functionals, we derive functionals that depend solely on the noninteracting kinetic energy density τ(r) defined by where is a singleparticle orbital. We demonstrate the potential of our approach by constructing an approximation to the exchange energy of electrons that rivals the accuracy of generalized gradient approximations of density functional theory. The strategy presented here is quite general and suitable to construct a variety of nonelectrondensity functionals.

Analysis of the magnetic coupling in binuclear complexes. II. Derivation of valence effective Hamiltonians from ab initio CI and DFT calculations
View Description Hide DescriptionMost interpretations of the magnetic coupling J between two unpaired electrons rest upon simple valence models that involve essentially the ferromagnetic direct exchange contribution, and the antiferromagnetic effect of the delocalization resulting from the interaction between neutral and ionic determinants, whose energy difference is U. Ab initio valenceonly calculations give very poor estimates of J, whatever the definition of the magnetic orbitals, and large CI expansions are required to evaluate it properly. It is, however, possible to define valence effective Hamiltonians from the knowledge of the eigenenergies and the eigenvectors of these accurate CI calculations. When applied to four different complexes, this strategy shows that spin polarization may change the sign of the direct exchange interaction, and that dynamical correlation results in a dramatic reduction of the effective repulsion U. The present article also shows how and U effective parameters can be extracted from density functional theory(DFT) calculations and that the typical overestimation of J in DFT can be attributed to an excessive lowering of the effective onsite repulsion.

Polarizability of molecular clusters as calculated by a dipole interaction model
View Description Hide DescriptionWe have developed and investigated a dipole interaction model for calculating the polarizability of molecular clusters. The model has been parametrized from the frequencydependent molecular polarizability as obtained from quantum chemical calculations for a series of 184 aliphatic, aromatic, and heterocyclic compounds. A damping of the interatomic interaction at short distances is introduced in such a way as to retain a traceless interaction tensor and a good description of the damping over a wide range of interatomic distances. By adopting atomic polarizabilities in addition to atomtype parameters describing the damping and the frequency dependence, respectively, the model is found to reproduce the molecular frequencydependent polarizabilitytensor calculated with ab initio methods. A study of the polarizability of four dimers has been carried out: the hydrogen fluoride, methane, benzene, and urea dimers. We find in general good agreement between the model and the quantum chemical results over a wide range of intermolecular distances. To demonstrate the power of the model, the polarizability has been calculated for a linear chain of urea molecules with up to 300 molecules and one and twodimensional clusters of with up to 25 molecules. Substantial intermolecular contributions are found for the polarizabilityanisotropy, whereas the effects are small for the mean polarizability. For the mean polarizability of we find good agreement between the model and experiments both in the case of an isolated molecule and in a comparison of a planar cluster of 25 molecules with experimental results on thin films.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Photoelectron spectroscopy via the state of diacetylene
View Description Hide DescriptionPhotoelectron spectra are reported for onephoton resonant, twophotonionization of jetcooled diacetylene via a number of vibronic levels of the state. An improved value for the adiabatic ionization threshold is found to be 82 064±30 cm^{−1} (10.175±0.004 eV), in good agreement with the earlier result. The photoelectron spectra of different vibronic bands of the state nearly all show long progressions in what appear to be low frequency bending vibrations. At energies just above the ionization threshold, the observed progressions can be understood in terms of excitation of a single RennerTeller active mode in the ion, with RennerTeller parameters similar to those of the transbending mode in the ground state acetylene cation.

Single to triple ionization of propane due to electron impact: Cross sections for the different dissociation channels
View Description Hide DescriptionElectron impact single to triple ionization and subsequent dissociation of propane have been studied at an electron energy of 200 eV using a covariance mapping technique employing a focusing timeofflightmass spectrometer. The dissociation channels of up to triply ionized propane have been identified and the corresponding absolute cross sections for the different dissociation channels have been obtained. Results show that 88% of the singly ionized propane molecules are unstable and dissociate through more than 20 channels, among which 50% of the ions dissociate into or All the doubly ionized propane molecules are unstable and dissociate through more than 80 channels, among which 97% of the ions dissociate into ion pairs. The major dissociation channels for are and while the major ionic products from the dissociation of are and

Rotational level dependence of ground state recovery rates for OH in atmospheric pressure flames using the picosecond saturatingpump degenerate fourwave mixing probe technique
View Description Hide DescriptionWe report the first direct measurement of the rotational level dependency of the rate of recovery of initially depleted levels in the electronic ground state of OH produced in different flame environments at atmospheric pressure. The initial depopulation of a specific rotational level is accomplished by an intense picosecond pump pulse at 308 nm to partially saturate the electronic transition. The recovery of the depleted ground state population then is monitored by probing the same level via the (1,0) band at 283 nm using picosecond degenerate fourwave mixing(DFWM). Both laser wavelengths were derived from the pulseamplified and frequency doubled output of two independently tunable distributed feedback dye lasers operated with Rh101 and Rh6G in ethanol, respectively, and pumped with the second harmonic of a frequency doubled psNd:YAG laser. It is shown that the rate of repopulation of the depleted ground state levels decreases by 54% and 50% with increasing rotational quantum number, ranging from 2–16 and 2–13 for stoichiometric and flames, respectively. Within experimental error their absolute values in both flames are equal and are not noticeably sensitive to an unequal depletion of the Zeeman sublevels, as created for different polarization configurations of the saturating pump beam and the DFWM probe beams. The rate of averaged over all rotational transitions investigated is smaller by a factor of 3 than the corresponding average rate of the temporal DFWM signal intensity decay determined by us previously. The rate also is smaller than total depopulation rates obtained in the excited state of OH for similar flame conditions.

Structure and energetics of He_{2} ^{*} bubblestates in superfluid ^{4}He
View Description Hide DescriptionStructure and energetics of solvation of the triplet Rydberg states of the excimer in liquid (LHe) are analyzed using ab initio potentials and density functional methods. The results are used to interpret the known spectroscopy. Having established the reliability of the various semiempirical functionals, interfacial properties of the superfluid on molecular scales are discussed. Due to its spherical electron density, the state solvates in a spherical bubble of 7 Å radius in which the excimer freely rotates. This explains the observed rotationally resolved and absorption spectra. A deep potential minimum occurs at the equatorial node of the state, where a radially frozen belt of six He atoms can be sustained at inside an ellipsoidal cavity with major axis of 8 Å and a more diffuse minor axis of 6 Å. Despite the absence of a potential energy barrier, or a manybody interfacial tension preventing the wetting of the belt, the bare state is observed in emission. It is argued that in the superfluid,wetting is prevented by the hindered rotation of the excimer, hence the sensitivity of the emission to pressure induced quenching. The nodal plane in the state passes through the molecular axis, as such, rotation cannot provide protection against wetting and subsequent quenching of the state via the manifold; hence the absence of emission despite its large transition dipole. In its global minimum, the excimer sustains a shell of 16 He atoms, localized at the radial node of its Rydberg electron, at The shell, in turn, is contained in a nearly spherical bubble held at a radius of 13 Å by the extranodal electron density. The repulsion between extranodal electron density and LHe provides a barrier to filling of the deep nodal well, ensuring the stability of the bare excimer in a large spherical bubble. This explains the freerotor envelopes of the and emissions, and their negligible spectral shifts relative to the gas phase. The predicted minimum energy structures, the belted state and the crusted state, if formed, should be metastable.

Mean excitation energy, static polarizability, and hyperpolarizability of the spherically confined hydrogen atom
View Description Hide DescriptionCalculations of mean excitation energy, static polarizability, and hyperpolarizability, using the variation perturbation procedure are reported for the spherically confined hydrogen atom. The electric response properties and have been found to strongly depend upon the radius of confinement. The hyperpolarizabilty changes sign and becomes negative under strong confinement.

Controlling nucleation and growth of nanodroplets in supersonic nozzles
View Description Hide DescriptionWe present the first results for a new supersonic nozzle that decouples nucleation and droplet growth, and closely controls the supersaturation and temperature during nucleation. We characterize the expansions using pressure trace measurements, and the aerosolproperties using light scattering and small angle neutron scattering. We show that when nucleation and droplet growth are separated, the aerosolnumber density decreases, the average particle size increases, and the aerosol can be more monodisperse than that formed in a conventional nozzle. Under these conditions, we can estimate the nucleation rate J as a function of supersaturation S and temperature T directly from the experimental data. For we find that the nucleation rate is at and

Electronic spectroscopy of intermediates involved in the conversion of methane to methanol by
View Description Hide DescriptionSpecific ion–molecule reactions are used to prepare two intermediates of the reaction, and photodissociation of the jetcooled intermediates is examined in the visible and nearultraviolet using timeofflight mass spectrometry. The photodissociation spectrum of the aquo iron carbene complex shows transitions to at least four excited electronic states in the chromophore, with broad vibrational structure. Photoexcitation of the insertion intermediate leads to formation of and also triggers the reaction to produce The photodissociation spectrum of presents a vibrationally resolved band involving progressions in the excited state Fe–C stretch, Fe–O stretch, and O–Fe–C bend. The change in the Fe–C bond length in and upon photoexcitation is calculated from a Franck–Condon analysis of the vibronic features observed. The analysis of the experimental results is aided by hybrid Hartree–Fock/densityfunctional (B3LYP) calculations on and performed to determine molecular parameters, and timedependent density functional theory (TDDFT) calculations on to predict excited electronic states.

Vibrational motions and nuclear spin relaxation in paramagnetic complexes: Hexaaquonickel(II) as an example
View Description Hide DescriptionThe protonparamagneticrelaxation enhancement (PRE) in an aqueous solution of nickel(II) is described in terms of electron spin relaxation caused by damped vibrational motions of and symmetry. The damped vibrations generate a transient zerofield splitting (ZFS), of variable amplitude and variable principal direction in the molecular frame, and are modeled by the Smoluchowski equation. The parameters of the model are obtained from a combination of two approaches: first, quantumchemical calculations of the ZFS as a function of the geometry of the coordination shell of the nickel(II) ion and, second, moleculardynamic simulations generating a trajectory of water positions around the metal. The description of the electron spin dynamics is included in the calculations of the PRE in two ways: Using the traditional Solomon–Bloembergen–Morgan approach and also by means of the more general slowmotion theory. The calculated PRE as a function of the magnetic field, free of any adjustable parameters, is compared with the experimental data. The two methods of calculating the PRE agree with each other—and with the experimental data—at high magnetic field. At low field, the models predict very different PRE, and only the general model is in reasonable agreement with the experiments.

A theoretical determination of the methyl and aldehydic torsion farinfrared spectrum of propanal with the vibrational zero point correction
View Description Hide DescriptionThe methyl and aldehydic torsions farinfrared (FIR) spectrum of standard propanal is determined theoretically taking into account the vibrational zero point energy (ZPE) of the remaining small amplitude vibration modes in an anharmonic approach. For this purpose, the potential energy function obtained in a previous calculation at the restricted Hartree–Fock/secondorder Møller–Plesset level [J. Chem. Phys. 109, 2279 (1998)] is modified for the anharmonic ZPE corrections. With this corrected potential for the ZPE, the kinetic parameters, as well as the electric dipole moment variations, the FIR frequencies, and intensities for the methyl and aldehyde torsions of propanal were determined theoretically using a twodimensional approach. The calculated torsional band structures of propanal determined without and with the ZPE corrections were compared between themselves and with the available experimental data. It is found that the theoretical calculations permit one to reproduce and assign 24 of the 25 observed bands. In the same way, the introduction of the ZPE corrections is seen to yield more satisfactory frequency values for the aldehyde torsion, double quanta, and methyl–aldehyde combination bands.

Structures of small gold cluster cations Ion mobility measurements versus density functional calculations
View Description Hide DescriptionWe have performed ion mobilitymeasurements on gold cluster cations generated by pulsed laservaporization. For clusters with n<14, experimental cross sections are compared with theoretical results from density functional calculations. This comparison allows structural assignment. We find that room temperature gold cluster cations have planar structures for n=3–7. Starting at n=8 they form three dimensional structures with (slightly distorted) fragments of the bulk phase structure being observed for n=8–10.

The frequency detuning correction and the asymmetry of line shapes: The far wings of
View Description Hide DescriptionA farwing line shape theory that satisfies the detailed balance principle is applied to the system. Within this formalism, two line shapes are introduced, corresponding to band averages over the positive and negative resonance lines, respectively. Using the coordinate representation, the two line shapes can be obtained by evaluating 11dimensional integrations whose integrands are a product of two factors. One depends on the interaction between the two molecules and is easy to evaluate. The other contains the density matrix of the system and is expressed as a product of two threedimensional distributions associated with the density matrices of the absorber and the perturber molecule, respectively. If most of the populated states are included in the averaging process, to obtain these distributions requires extensive computer CPU time, but only have to be computed once for a given temperature. The 11dimensional integrations are evaluated using the Monte Carlo method, and in order to reduce the variance, the integration variables are chosen such that the sensitivity of the integrands on them is clearly distinguished. Numerical tests show that by taking into account about random selections, one is able to obtained converged results. We find that it is necessary to consider frequency detuning, because this makes significant and opposite contributions in the two bandaveraging processes and causes the lines to be asymmetric. Otherwise, the two line shapes become symmetric, are the same, and equal to the mean of the two shapes obtained including the frequency detuning effects. For the pure rotational band, we find that the magnitude of the line shape obtained from the positive line average is larger than that obtained from the negative line average for and vice versa for and their relative gap increases as the frequency displacement from the line center increases. By adopting a realistic potential model and optimizing its parameters, one is able to obtain these two line shapes and calculate the corresponding absorption coefficients that are in good agreement with laboratory data. Also, this same potential yields good theoretical values for other physical properties of the dilute gas.

The hydrogenbonded heterodimer between methylene cyclobutane and hydrogen chloride: Observation of an endo conformer
View Description Hide DescriptionThe formation of a hydrogen bond between methylene cyclobutane and hydrogen chloride has been investigated in the region 8–18 GHz using molecularbeam Fourier transformmicrowave spectroscopy. The rotational spectrum of an endo conformer in which methylene cyclobutane retains a puckered conformation and HCl is bonded in Tshape to the methylenic group has been observed. Searches for the exo form using Ar, Ne or He as carrier gases were unsuccessful. A symmetry like structure has been obtained for this conformer from the rotational data of three observed isotopomers and Ab initio calculations at level have been used to complement the analysis. These calculations predict the existence of both endo and exo conformers close in energy.

A globally smooth ab initio potential surface of the state for the reaction
View Description Hide DescriptionA procedure based on the reproducing kernel Hilbert space (RKHS) interpolation method has been implemented to produce a globally smooth potential energy surface (PES) for the state of the reaction from a set of accurate ab initio data, calculated at the multireference configuration interaction level with augmented polarized quadruplezeta basis sets and arranged on a threedimensional regular full grid in the Jacobi coordinates. The procedure includes removing a small number of questionable ab initio data points, implementing a recently developed technique for efficiently handling a partially filled grid, and adopting a sequence of regularizations for attaining additional smoothness. The resulting RKHS PES is analytic, firstorder differentiable, and fast to evaluate. Quasiclassical trajectory calculations have been performed and compared with the results based on a recent hybrid PES obtained from a combination of the RKHS interpolation in the entrance channel and Murrell–Carter (MC)type fitting in the exit channel from the same set of ab initio data. Comparisons with recent experimental measurements show improvement of the present RKHS PES over the existing hybrid RKHSMC PES. The results demonstrate that the entrance channel Jacobi coordinates can still be a good candidate in sampling the full configuration space for reactive systems involving three atoms.

Exploring the Bermuda triangle of homonuclear diatomic spectroscopy: The electronic spectrum and structure of
View Description Hide DescriptionThe optical spectrum of jetcooled has been observed for the first time. Laserinduced fluorescence(LIF) and wavelength resolved emission spectra were recorded using the pulsed discharge technique with a tetramethylgermane precursor. Analysis of the spectra yielded the vibrational constants and cm^{−1}. Highresolution rotationally resolved spectra of several bands of show two strong P and R branches and two very weak Q branches. We have assigned the band system as a Hund’s case (c) transition from the ground state to a excited state. The bond lengths derived from the rotational constants are Å and Å, an ∼0.16 Å increase on electronic excitation. Arguments are presented for assigning the transition to a electron promotion, although the observed increase in the bond length is much less than predicted by previous ab initio calculations. The absence of the component in the spectra has been attributed to an excited state predissociation.

A hierarchical family of global analytic Born–Oppenheimer potential energy surfaces for the reaction ranging in quality from doublezeta to the complete basis set limit
View Description Hide DescriptionA hierarchical family of analytical Born–Oppenheimer potential energy surfaces has been developed for the system. Ab initio calculations of near full configuration interaction (FCI) quality (converged to within were performed for a set of 4067 configurations with the augccpVDZ, augccpVTZ, and augccpVQZ basis sets. The complete basis set (CBS) limit energies were obtained using a highly accurate manybody basis set extrapolation scheme. Surfaces were fitted for the estimated CBS limit, as well as for the augccpVDZ, augccpVTZ, and augccpVQZ basis sets using a robust new functional form. The mean unsigned fitting error for the CBS surface is a mere 0.0023 kcal/mol, and deviations for data not included in the fitting process are of similarly small magnitudes. Highly accurate calculations of the saddle point and van der Waals minimum configurations were performed using basis sets as large as augmccpV7Z, and these data show excellent agreement with the results of the extrapolated potential surface. The remaining errors from fitting, correlation treatment, and basis set incompleteness for the new CBSlimit surface are lower by over an order of magnitude compared to any prior analytic surface, and are all now significantly smaller than nonBorn–Oppenheimer effects. We expect that this new family of potential surfaces will prove useful in studies elucidating the sensitivity of dynamical quantities to the quality of the potential surface.