Volume 115, Issue 19, 15 November 2001
 ARTICLES

 Theoretical Methods and Algorithms

Description of a highdensity homogeneous electron gas with the Yasuda density matrix functional
View Description Hide DescriptionDescription of a spinunpolarized homogeneous electron gas with the Yasuda functional applied to the exact 1matrix gives rise to a formalism that correctly accounts for the logarithmic divergence of the correlation energy per volume at the highdensity limit. The linear dependence of the ontop pair distribution function for antiparallel spins on the parameter is also correctly reproduced. A comparison of the relevant proportionality constant with its exact counterpart fixes the value of the adjustable parameter that enters the Yasuda functional.

Computing phase equilibria by parallel excluded volume tempering
View Description Hide DescriptionWe present a Monte Carlo scheme for the computation of phase equilibria at high densities. At these high densities, all conventional simulation techniques that rely on insertions and deletions of particles, e.g., the Gibbs ensemble technique, will have problems because the acceptance probability for these moves is very low. Furthermore, the efficiency of these methods strongly depends on the complexity of the system, e.g., degree of polymerization and branching of the components. Our new method is based upon simulating a path of independent systems in the grandcanonical ensemble. Each system has a slightly different interaction potential, ranging from a full excluded volume potential to an ideal gas, as well as different imposed chemical potentials of each component. This path is constructed in such a way that the average number of molecules of a specific component per system is constant along the path. To sample all systems of the path efficiently, we apply a parallel tempering procedure to exchange configurations of two adjacent systems. The advantage of these exchanges is that, for the full excluded volume system, one does not have to rely on particle insertions and deletions in this system to sample the full phase space, but rather on particle insertions and deletions in systems with soft interactions. Without excluded volume interactions, the acceptance of insertions is independent of molecular size and shape; hence our method does not suffer from the problems of the conventional methods. We have tested our method for very simple systems (LennardJones particles) and found exact agreement with Gibbs ensemble simulations. For these simple systems the conventional techniques to compute phase equilibria are much more efficient. However, we expect that for long chain molecules this situation will be reversed.

The Step and Slide method for finding saddle points on multidimensional potential surfaces
View Description Hide DescriptionWe present the Step and Slide method for finding saddle points between two potentialenergy minima. The method is applicable when both initial and final states are known. The potentialenergysurface is probed by two replicas of the system that converge to the saddle point by following isoenergetic surfaces. The value of the transitionstate potential is bracketed in the process, such that a convergence criterion based on the potential can be used. We applied the method to study diffusion mechanisms of a small Ag cluster on a Ag(111) surface using an embeddedatom method potential. Our approach is comparable in efficiency to other commonly used methods.

Towards extending the applicability of density functional theory to weakly bound systems
View Description Hide DescriptionWhile the attempts currently in progress in several groups for the rigorous inclusion of dispersion interactions in density functional theory(DFT) calculations mature and evolve into practical methodology, we contribute to the debate on the applicability of current functionals to the calculation of weak interaction with a systematic investigation of a few, typical, weakly bound systems. We have used both pure DFT and a hybrid approach in which the total interaction energy is partitioned into two parts: (a) the dispersion energy which, in a first approximation is the contribution due to intermonomer correlations and (b) all other interactions. The first component is accurately obtained at all distances of interest by means of a wellknown damped multipolar expansion of the dispersion energy while for the second component different approximations will be evaluated. The need to avoid double counting a fraction of the correlation energy when using the hybrid approach and the choice of the appropriate functional are also discussed. We consider four systems of increasing binding strength, namely the and dimers, the benzene dimer, the water dimer, and a few metal carbonyls. For pure DFT calculations we confirm the conclusion reached by others concerning (a) the strong dependence of the results on the choice of the GGA functional for dispersiondominated interaction (noble gases and benzene) with the overall tendency to yield underbinding and (b) the relatively accurate, functionalindependent, description for that DFT gives of water, which we attribute to the fact that this system is dominated by electrostatic interactions. For the carbonyls we find that DFT yields results which area again strongly dependent on the choice of the functional and show a tendency to give overbinding. Our hybrid method shows instead shortcomings only for the noble gases. The problem in this case is traceable to the wellknown difficulties that all current functionals experience at medium–large intermonomer separations. The quality of the hybrid results improves markedly for benzene due to the large value of both dispersion and repulsive interactions at the equilibrium distance for this dimer, which makes the balance between the two, less delicate. Excellent results are also obtained for water (for the same reason as indicated above) and more significantly for the carbonyls where we find that dispersion contributes to the binding more than it could be guessed a priori. We do not claim to have found a general solution to this difficult problem, but we aim at providing a quantitative assessment to where the problems are pointing at directions from which a general solution may, eventually, emerge.

Towards multireference equivalents of the G2 and G3 methods
View Description Hide DescriptionThe effect of replacing the standard singledeterminant reference wave functions in variants of G2 and G3 theory by multireference (MR) wave functions based on a fullvalence complete active space has been investigated. Twelve methods of this type have been introduced and comparisons, based on a slightly reduced G21 test set, are made both internally and with the equivalent singlereference methods. We use CASPT2 as the standard MRMP2 method and as the higher correlation procedure in these calculations. We find that MRG2(MP2,SVP), MRG2(MP2), and MRG3(MP2) perform comparably with their singlereference analogs, G2(MP2,SVP), G2(MP2), and G3(MP2), with mean absolute deviations (MADs) from the experimental data of 1.41, 1.54, and 1.23 kcal mol^{−1}, compared with 1.60, 1.59, and 1.19 kcal mol^{−1}, respectively. The additivity assumptions in the methods have been tested by carrying out and calculations, which correspond to largebasisset calculations. These give MADs of 1.84 and 1.58 kcal mol^{−1}, respectively, i.e., the agreement with experiment is somewhat worse than that obtained with the MRG2(MP2) and MRG3(MP2) methods. In a third series of calculations, we have examined pure MP2 and MRMP2 analogs of the G2 and G3 procedures by carrying out largebasisset MP2 and calculations. The resultant methods, which we denote G2/MP2, G3/MP2, MRG2/MP2, and MRG3/MP2, give MADs of 4.19, 3.36, 2.01, and 1.66 kcal mol^{−1}, respectively. Finally, we have examined the effect of using MCQDPT2 in place of CASPT2 in five of our procedures, and find that there is a small but consistent deterioration in performance. Our calculations suggest that the MRG3(MP2) and MRG3/MP2 procedures may be useful in situations where a multireference approach is desirable.

Realspace computation of dynamic hyperpolarizabilities
View Description Hide DescriptionA realspace method is developed to calculate molecular hyperpolarizabilities in the timedependent density functional theory. The method is based on the response function formalism which was developed by Senatore and Subbaswamy for the third harmonic generation of raregas atoms [Phys. Rev. A 35, 2440 (1987)]. The response equations are discretized in real space employing a uniform grid representation in the threedimensional Cartesian coordinate, and are solved with iterative methods such as conjugategradient and conjugateresidual methods. The method works efficiently for both small and large molecules, and for any nonlinear optical processes up to third order. The spatial convergence of the calculation can be examined with two intuitive parameters, the grid spacing and the spatial box size. Applications of our method are presented for raregas atoms and molecules, and Our results agree well with other calculations employing basis functions except for a slight deviation in a large molecule,

Comparison of inherent, instantaneous, and saddle configurations of the bulk LennardJones system
View Description Hide DescriptionThe configurational energies, order parameters and normal mode spectra associated with inherent structure, inherent saddle, and instantaneous configurations of the bulk LennardJones system are compared. Instantaneous structures are generated by sampling configurations from an isothermalisobaric ensemble Monte Carlo simulation. Local minimization of the potential, starting from a given instantaneous configuration is used to determine the corresponding inherent structure. The inherent saddles are obtained by local minimization on a pseudopotential surface defined in terms of the square magnitude of the potential gradient. In the solid phase, no stationary points of order greater than zero are sampled and minimizations of both the potential, as well as of the pseudopotential, always lead to the same global minimum energy crystalline configuration. The energies of instantaneous configurations of the solid show a clear negative correlation with the secondorder bond orientational parameters. The instantaneous normal mode spectrum of the solid close to melting has a fairly prominent imaginary branch and is sufficiently smoothed out by local disorder that it qualitatively resembles the liquid phase INM spectrum. In the liquid phase, the inherent, saddle, and instantaneous structures form distinct sets of configurations. The thermal averages of the saddle energies and force constants lie between that of the instantaneous and inherent structures. The temperature dependence of the mean saddle energy and force constant is essentially parallel to that of the corresponding instantaneous quantities. The fraction of imaginary modes for the saddle configurations is approximately half that of the instantaneous configurations. The most striking similarity between the instantaneous and saddle configurations is the linear relationship between the index density and the configurational energy. The most notable difference between the two sets of configurations is the reduction to zero of the fraction of imaginary modes of the saddle configurations on freezing, making the saddle normal mode spectra qualitatively different in the liquid and solid phases.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Spectroscopic properties of lead trimer and Potential energy surfaces, spin–orbit and Jahn–Teller effects
View Description Hide DescriptionSpectroscopicproperties of the lowlying electronic states of neutral, cationic, and anionic lead trimer are investigated. We have obtained the bending potential energy surfaces of several electronic states of and both with and without spin–orbit coupling. These computations were carried out using high level techniques that included electron correlationeffects and spin–orbit coupling simultaneously using a multireference relativistic configuration interaction (RCI) scheme in the double group, subsequent to complete activespace–multiconfiguration selfconsistentfield (CAS–MCSCF) computations. We have computed the equilibrium geometries, vibrational frequencies, excitation energies, atomization energies, ionization potentials, and adiabatic electron affinities. Our computations facilitated the assignment of the anion photodetachment spectra of and explained the “closedshell singlet like” structures in the observed photodetachment spectra. Our computations show that spin–orbit coupling has a substantial impact on the geometries (bond angles changing up to 20°) and the potential energy surfaces, which exhibit multiple minima separated by barriers due to avoided crossings and substantial spin–orbit mixings. The interplay between the Jahn–Teller effect and spin–orbit coupling was considered, and it was shown that the Jahn–Teller coupling is quenched by spin–orbit effect for but for the neutral trimer the bending potential energy surface of the ground state exhibits multiple minima due to a combination of these effects. The spin–orbit effect was also shown to reduce the strength of the Pb–Pb bonding and the atomization energy of Our computed atomization energy of including spin–orbit coupling is 224 KJ/mole in full agreement with the experimental value of 224 KJ/mole. We have shown that the spin–orbit coupling enhances the stability of while it weakens dramatically compared to lighter analogs such as

Femtosecond photoelectron imaging on pyrazine: Spectroscopy of and Rydberg states
View Description Hide DescriptionTwocolor and onecolor resonance enhanced multiphoton ionizationphotoelectron spectroscopies (REMPI–PES) have been applied to Rydberg states of jetcooled pyrazine. The and members of Rydberg series converging to the ground state of the cation and the member of a Rydberg series converging to an excited state of the cation were observed. The photoelectron angular distributions (PADs) measured via the state drastically differed for the twocolor and onecolor REMPI experiments. This behavior is ascribed to different molecular axis alignments created by the twophoton excitation schemes. The PADs were also used to discriminate between the different Rydberg series.

Intramolecular isotope effects in the reactions of and with HD
View Description Hide DescriptionIntramolecular isotope effects in the bond formingreactions following collisions of both and with HD have been investigated experimentally. For the system the bondforming pathway forming exhibits a strong intramolecular isotope effect favoring the formation of at low collision energies. For the system the bondforming pathway forming also exhibits a strong intramolecular isotope effect favoring the formation of at low collision energies. However, in the system a weak, and previously unobserved, channel, forming exhibits no intramolecular isotope effect over the collision energy regime (0.2–0.5 eV) investigated. The absence of an intramolecular isotope effect in the formation of casts doubt on the previous explanation of such isotope effects as resulting from orientation effects in the approach of the dication to the HD molecule. Using a recently proposed mechanism for the reaction of with an analysis of the statistical and zeropoint factors affecting the competition between the bondforming channels is presented. This analysis shows that such factors can readily explain the intramolecular isotope effects observed in these reactive systems.

Ab initio CASPT2//CASSCF study of the reaction
View Description Hide DescriptionThe ground potential energy surface (PES) of the system was studied with the CASPT2//CASSCF ab initio method. We analyzed the degree of validity of an earlier ab initio study by us that used the Møller–Plesset (MP) method. Both the present CASPT2//CASSCF calculations and the highest level MP calculations (PUMP4//UMP2) showed that the main reaction channel (OH+OH) has no energy barrier along the minimum energy path. This result is consistent with the absence of experimental activation energy. The CASPT2//CASSCF and PUMP4//UMP2 results, however, show important differences, mainly concerning the energy, due to the dominant openshell singlet character of the ground PES. To make an accurate general description of this system, ab initio calculations using multireference methods like the one discussed here are required. Nevertheless, the earlier PUMP4//UMP2 calculations can be taken as a reasonable starting point for characterizing the ground PES of this system. Moreover, the pseudotriatomic analytical potential energy surface derived in the previous work to interpret the experimental results is a reasonable model for describing the reaction.

Ab initio, VTST, and QCT study of the potential energy surface of the reaction
View Description Hide DescriptionAn ab initio study based on the CASSCF (Complete Active Space SelfConsistent Field) and CASPT2 (SecondOrder Perturbation Theory on a CASSCF wave function) methods has been carried out on the ground potential energy surface (PES) involved in the relevant atmospheric reaction between and to produce and NO. Also, some intersections between PES have been studied. The stationary points have been characterized and a grid of more than 800 points have been fitted to an analytical function. This analytical representation of the PES has been used to obtain kinetic and dynamic properties of the reaction. The rate constant of this reaction has been calculated at different levels of theory [variational transition state theory (VTST) and quasiclassical trajectory(QCT) methods] and has been compared with the experimental values (overall rate constant including physical electronic quenching) obtaining a good agreement. The QCT method has also been employed to study the properties of products from both the abstraction and insertion microscopic mechanisms. The vibrational distribution of NO arising from the reaction at 100 K has also been calculated and compared with the experimental ones. In this case, the agreement between the theoretical and the experimental results is not so good, the experimental vibrational distribution being less excited. Future work is necessary to determine the origin of this difference.

Collisioninduced absorption in the fundamental band of I. Determination of the quadrupole transition moment
View Description Hide DescriptionAn experimental value for the quadrupole transition moment of the fundamental band of has been determined by fitting the collisioninduced enhancement spectrum of with Ar as the perturber. The observed quadrupoleinduced absorption increases linearly with the Ar density, and is comparable to the allowed dipole intensity due to Coriolis interaction with the band at approximately 125 amagats. Ignoring vibrationrotation interaction and Coriolis interaction,, we equate the measured slope of the integrated intensity versus to the theoretical expression for the quadrupoleinduced absorption, and obtain the value for the quadrupole transition matrix element. A theoretical value has been determined by largescale ab initio calculations and, considering both the theoretical approximations and experimental uncertainties, we regard the agreement as good, thus confirming our interpretation of the enhancement as due to the quadrupole collisioninduced mechanism.

Spectroscopic properties of mixed gallium arsenide tetramers: and
View Description Hide DescriptionSpectroscopicproperties of the lowlying electronic states of and their anions and cations are computed by the complete activespace selfconsistent field (CASSCF) followed by multireference configuration interaction (MRSDCI) calculations that included up to 4.4 million configurations. Whereas the ground state of is found to be a symmetric triangular pyramidal structure, the ground state of is predicted to undergo JahnTeller distortion to a state with a folded geometry. The ground state of the ion is found to be surprisingly a planar structure but the ground state of the ion exhibits a nonplanar JahnTeller distorted geometry. The energy separations of a number of excited electronic states have been computed to predict the spectra of these species. The equilibrium geometries, vibrational frequencies, atomization energies, adiabatic ionization potentials,electron affinities, and other properties for the electronic states of and are computed and discussed. Large differences in the equilibrium geometries of the anion and the neutral are predicted to result in considerable vibrational progression the anion photoelectron spectra.

On the energy dependence of the hyperfine interaction in excited states of
View Description Hide DescriptionWe report on the hyperfine structure of levels of 62 vibronic states in the 16 850–21 500 cm^{−1} region, as determined via quantum beatspectroscopy. The hyperfine structure of these levels of mixed electronic character is dominated by the Fermicontact interaction, and a decrease in the hyperfine splittings with increasing energy is revealed when our results are compared with previous studies in the 11 200–13 700 cm^{−1} region. This comparison also reveals the loss of a correlation between band intensity and Fermicontact constant. A detailed comparison of our results with theoretical predictions for the 16 600–18 700 cm^{−1} region is presented. We find that vibrational averaging of the Fermicontact interaction is reflected in the hyperfineinteraction of bands in this region, and should also be a factor in producing the small hyperfine splittings observed at energies near dissociation threshold.

The unimolecular dissociation of HCO. V. Mixings between resonance states
View Description Hide DescriptionThe unimolecular dissociation of HCO in its ground electronic state is considered. By performing calculations (filter diagonalization, absorbing potential) for nonzero angular momentum quantum numbers, it is demonstrated how mixings with nearby “background” states affect the linewidths of the narrower resonance states. This explains qualitatively the theoretically as well as experimentally observed behavior of the linewidth as a function of the vibrational quantum numbers.

The unimolecular dissociation of the OH stretching states of HOCl: Comparison with experimental data
View Description Hide DescriptionThe unimolecular dissociation of the pure OH stretching states of hypochlorous acid (HOCl) in the ground electronic state is investigated for The dynamics calculations are performed on an accurate potential energy surface and employ filter diagonalization in connection with an imaginary absorbing potential. The dependence of the linewidth (or dissociation rate) on the total angular momentum is emphasized. Resonance enhancements due to mixings with other vibrational states, which have substantially larger rates, are clearly observed—in qualitative agreement with recent measurements. The average width increases, in quantitative agreement with experiments, by four orders of magnitude, from for to about for

Structure and charge transfer dynamics of the molecular cluster
View Description Hide DescriptionIn this paper we have investigated the interaction potential and the charge transfer processes at low collision energies in the system. The angular dependence of the lowest doublet potential energy surfaces (PES), correlating with and has been given in terms of spherical harmonics, while the dependence on the intermolecular distance has been represented by proper radial coefficients. Such coefficients, which account for van der Waals, induction, charge transfer, and electrostatic contributions, have been predicted by empirical correlation formulas. The PES so obtained have been employed to calculate cross sections for the charge transfer process at low collision energy A good agreement between calculated and experimental cross sections is obtained by assuming that the duration of the nonadiabatic transition has to match the time required for the molecular rearrangement into the final vibrational state. As a consequence the efficient formation of product ions into specific vibrational states is limited to well defined ranges of impact parameters. This treatment leads to a unified description of the major experimental findings.

The Ar–HCl potential energy surface from a global mapfacilitated inversion of statetostate rotationally resolved differential scattering cross sections and rovibrational spectral data
View Description Hide DescriptionA recently developed global, nonlinear mapfacilitated quantum inversion procedure is used to obtain the interaction potential for based on the rotationally resolved statetostate inelastic cross sections of Lorenz, Westley, and Chandler [Phys. Chem. Chem. Phys. 2, 481 (2000)] as well as rovibrational spectral data. The algorithm adopted here makes use of nonlinear maps to reveal the complete family of surfaces that reproduce the observed scattering and spectral data to within its experimental error. A nonlinear analysis is performed on the error propagation from the measured data to the recovered family of potentials. The family of potentials extracted from the inversion data is compared to the Hutson H6(4,3,0) surface [Phys. Chem. 96, 4237 (1992)], which was unable to fully account for the inelastic scattering data [Phys. Chem. Chem. Phys. 2, 481 (2000)]. There is excellent agreement with H6(4,3,0) in the attractive well, where Hutson’s surface is considered most reliable. There is also good longrange agreement. However, it is shown that H6(4,3,0) predicts too soft a wall for the linear Ar–HCl configuration and significantly too steep a wall for linear Ar–ClH. These differences account for the systematically backscattered inelastic cross sections computed using the H6(4,3,0) surface. The new, nonlinear inversion results provide a global Ar–HCl interaction potential with reliable error bars that are consistent with all of the experimental data.
 Condensed Phase Dynamics, Structure, and Thermodynamics: Spectroscopy, Reactions, and Relaxation

Moleculardynamics simulation of homogeneous nucleation in the vapor phase
View Description Hide DescriptionTen independent quenches of a gas of 40 000 LennardJones particles are followed until the systems exhibit droplet growth. The cluster distributions and the kinetics are determined for the quenched quasiequilibrium state, at the onset of nucleation and at droplet growth. All the distributions are isomorphic with the particle distribution in the equilibrium gas state and asymptotically given by simple exponentials. The kinetics show detailed balance of particles and clusters which join and which leave the successful critical nuclei. The systems exhibit chaoticlike behavior with respect to the onset of nucleation, so that only marginal changes in a system will change the onset of nucleation.