Volume 125, Issue 14, 14 October 2006
 COMMUNICATIONS


Intramolecular vibrational energy redistribution as state space diffusion: Classicalquantum correspondence
View Description Hide DescriptionWe study the intramolecular vibrational energy redistribution (IVR) dynamics of an effective spectroscopic Hamiltonian describing the four coupled high frequency modes of CDBrClF. The IVR dynamics ensuing from nearly isoenergetic zerothorder states, an edge (overtone) and an interior (combination) state, is studied from a state space diffusion perspective. A wavelet based timefrequency analysis reveals an inhomogeneous phase space due to the trapping of classical trajectories. Consequently the interior state has a smaller effective IVR dimension as compared to the edge state.

A quantitative account of quantum effects in liquid water
View Description Hide DescriptionWe report converged quantum statistical mechanical simulations of liquid water with the Tholetype Model (version 2.1), Flexible, polarizable (TTM2.1F) interaction potential for water. Simulations of total length of with a time step for a periodic unit cell of 256 molecules with up to 32 replicas per atom suggest that the quantum effects contribute to the liquid enthalpy of formation at . They furthermore demonstrate for the first time a quantitative agreement with experiment for the heights and broadening of the intramolecular OH and HH peaks in the radial distribution functions.

Photo ejection of water molecules from amorphous ice films
View Description Hide DescriptionWater molecules are photoejected upon laser irradiation from the surface of icefilmsgrown on graphite (0001) and . The films are deposited at temperatures between 40 and and irradiated with nanosecond laser pulses. The process is investigated in the wavelength range between 275 and . The wavelength and photon flux dependence suggest a multiphoton process with energy threshold of around . The photodetachment is less effective or negligible from films annealed at temperatures above the amorphous–crystalline transition temperature of icefilms. Coverage dependence of the phenomena relates the photo yield to surface roughness. Electronic excitation mechanism related to the defects in ice is proposed to explain the observations.
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 ARTICLES

 Theoretical Methods and Algorithms

Multireference correlation in long molecules with the quadratic scaling density matrix renormalization group
View Description Hide DescriptionWe have devised a local ab initio density matrix renormalization group algorithm to describe multireference correlations in large systems. For long molecules that are extended in one of their spatial dimensions, we can obtain an exact characterization of correlation, in the given basis, with a cost that scales only quadratically with the size of the system. The reduced scaling is achieved solely through integral screening and without the construction of correlation domains. We demonstrate the scaling, convergence, and robustness of the algorithm in polyenes and hydrogen chains. We converge to exact correlationenergies (in the sense of full configuration interaction, with precision) in all cases and correlate up to 100 electrons in 100 active orbitals. We further use our algorithm to obtain exact energies for the metalinsulator transition in hydrogen chains and compare and contrast our results with those from conventional quantum chemical methods.

Computation of dipole, quadrupole, and octupole surfaces from the variational twoelectron reduced density matrix method
View Description Hide DescriptionRecent advances in the direct determination of the twoelectron reduced density matrix (2RDM) by imposing known representability conditions have mostly focused on the accuracy of molecular potential energy surfaces where multireference effects are significant. While the norm of the 2RDM’s deviation from full configuration interaction has been computed, few properties have been carefully investigated as a function of molecular geometry. Here the dipole, quadrupole, and octupole moments are computed for a range of molecular geometries. The addition of Erdahl’s condition [Int. J. Quantum Chem.13, 697 (1978)] to the , , and conditions produces dipole and multipole moments that agree with full configuration interaction in a doublezeta basis set at all internuclear distances.

Electronelectron and electronnucleus correlation effects on exponent values of Gaussiantype functions for quantum protons and deuterons
View Description Hide DescriptionElectronelectron and electronnucleus correlationeffects on exponent values of Gaussiantype functions (GTFs) for quantum protons and deuterons in , , , , and HF molecular systems and their deuterated counterparts were analyzed using the secondorder MøllerPlesset (MP2) level of theory of the multicomponent molecular orbital (MCMOMP2) method. This method can simultaneously determine both nuclear and electronic wave functions. Results showed that the average value of the optimized in single type GTF for a proton and a deuteron is similar to that determined using the HartreeFock level of the MCMO (MCMOHF) method. In contrast, due to the electronnucleus correlationeffect, the  and type GTFs are delocalized compared with those determined using the MCMOHF method. For the Hbonded complexes, differences in the interaction energy induced by the H/D isotope effect were clearly evident because the bond distance for D complex is longer than the for H complex. Also, the basis set superposition error for the interaction energy in every H complex was similar to that in every D complex. The results here clearly demonstrate that the protonic and deuteronic basis functions based on values for correlationeffects can be applied to the detailed analysis of the quantum effects of protons and the H/D isotope effect in widespread fields that involve H bonds and weak interactions, such as the function of biological molecules, chemical reaction processes, and the design of new materials.

Condensed phase ionic polarizabilities from plane wave density functional theory calculations
View Description Hide DescriptionA method is presented to allow the calculation of the dipole polarizabilities of ions and molecules in a condensedphase coordination environment. These values will be useful for understanding the optical properties of materials and for developing simulation potentials which incorporate polarization effects. The reported values are derived from plane wave density functional theory calculations, though the method itself will apply to firstprinciples calculations on periodic systems more generally. After reporting results of test calculations on atoms to validate the procedure, values for the polarizabilities of the oxide ion and various cations in a range of materials are reported and compared with experimental information as well as previous theoretical results.

Cumulative reaction probabilities: A comparison between quasiclassical and quantum mechanical results
View Description Hide DescriptionThis article presents a quasiclassical trajectory(QCT) method for determining the cumulative reaction probability (CRP) as a function of the total energy. The method proposed is based on a discrete sampling using integer values of the total and orbital angular momentum quantum numbers for each trajectory and on the development of equations that have a clear counterpart in the quantum mechanical (QM) case. The calculations comprise cumulative reaction probabilities at a given total angular momentum, as well as those summed over . The latter are used to compute QCTrate constants. The method is illustrated by comparing QCT and exact QM results for the , , , and reactions. The agreement between QCT and QM results is very good, with small discrepancies between the two data sets indicating some genuine quantum effects. The most important of these involves the value of the CRP at low energies which, due to the absence of tunneling, is lower in the QCT calculations, causing the corresponding rate constants to be smaller. The second is the steplike structure that is clearly displayed in the QM CRP for , which is much smoother in the corresponding QCT results. However, when the QCT density of reactive states, i.e., the derivatives of the QCT CRP with respect to the energy, is calculated, a succession of maxima and minima is obtained which roughly resembles those found in the QM calculations, although the latter are considerably sharper. The analysis of the broad peaks in the QCT density of reactive states indicates that the distributions of collision times associated with the maxima are somewhat broader, with a tail extending to larger collision times, than those associated with the minima. In addition, the QM and QCT dynamics of the isotopic variants mentioned above are compared in the light of their CRPs. Issues such as the compliance of the QCT CRP with the law of microscopic reversibility, as well as the similarity between the CRPs for ortho and para species in the QM and QCT cases, are also addressed.

Extracting effective normal modes from equilibrium dynamics at finite temperature
View Description Hide DescriptionA general method for obtaining effective normal modes of a molecular system from molecular dynamics simulations is presented. The method is based on a localization criterion for the Fourier transformed velocity timecorrelation functions of the effective modes. For a given choice of the localization function used, the method becomes equivalent to the principal mode analysis (PMA) based on covariance matrix diagonalization. On the other hand, a proper choice of the localization function leads to a novel method with a strong analogy with the usual normal modeanalysis of equilibrium structures, where the Hessian system at the minimum energy structure is replaced by the thermal averaged Hessian, although the Hessian itself is never actually calculated. This method does not introduce any extra numerical cost during the simulation and bears the same simplicity as PMA itself. It can thus be readily applied to ab initiomolecular dynamics simulations. Three such examples are provided here. First we recover effective normal modes of an isolated formaldehyde molecule computed at in very good agreement with the results of a normal modeanalysis performed at its equilibrium structure. We then illustrate the applicability of the method for liquid phase studies. The effective normal modes of a water molecule in liquid water and of a uracil molecule in aqueous solution can be extracted from ab initiomolecular dynamics simulations of these two systems at .

A “partitioned leaping” approach for multiscale modeling of chemical reaction dynamics
View Description Hide DescriptionWe present a novel multiscale simulation approach for modeling stochasticity in chemical reaction networks. The approach seamlessly integrates exactstochastic and “leaping” methodologies into a single partitioned leaping algorithmic framework. The technique correctly accounts for stochastic noise at significantly reduced computational cost, requires the definition of only three modelindependent parameters, and is particularly well suited for simulating systems containing widely disparate species populations. We present the theoretical foundations of partitioned leaping, discuss various options for its practical implementation, and demonstrate the utility of the method via illustrative examples.

W4 theory for computational thermochemistry: In pursuit of confident subkJ/mol predictions
View Description Hide DescriptionIn an attempt to improve on our earlier W3 theory [A. D. Boese et al., J. Chem. Phys.120, 4129 (2004)] we consider such refinements as more accurate estimates for the contribution of connected quadruple excitations , inclusion of connected quintuple excitations , diagonal BornOppenheimer corrections (DBOC), and improved basis set extrapolation procedures. Revised experimental data for validation purposes were obtained from the latest version of the Active Thermochemical Tables thermochemicalnetwork. The recent CCSDT(Q) method offers a costeffective way of estimating , but is insufficient by itself if the molecule exhibits some nondynamical correlation. The latter considerably slows down basis set convergence for , and anomalous basis set convergence in highly polar systems makes twopoint extrapolation procedures unusable. However, we found that the difference converges quite rapidly with the basis set, and that the formula offers a very reliable as well as fairly costeffective estimate of the basis set limit contribution. The contribution converges very rapidly with the basis set, and even a simple doublezeta basis set appears to be adequate. The largest contribution found in the present work is on the order of (for ozone). DBOCs are significant at the level in hydride systems. PostCCSD(T) contributions to the corevalence correlationenergy are only significant at that level in systems with severe nondynamical correlation effects. Based on the accumulated experience, a new computational thermochemistry protocol for first and secondrow maingroup systems, to be known as W4 theory, is proposed. Its computational cost is not insurmountably higher than that of the earlier W3 theory, while performance is markedly superior. Our W4 atomization energies for a number of key species are in excellent agreement (better than on average, 95% confidence intervals narrower than ) with the latest experimental data obtained from Active Thermochemical Tables. Lowercost variants are proposed: the sequence is proposed as a converging hierarchy of computational thermochemistry methods. A simple a priori estimate for the importance of postCCSD(T) correlation contributions (and hence a pessimistic estimate for the error in a W2type calculation) is proposed.

The Jarzynski identity derived from general Hamiltonian or nonHamiltonian dynamics reproducing or ensembles
View Description Hide DescriptionThe Jarzynski identity (JI) relates nonequilibrium work averages to thermodynamic free energy differences. It was shown in a recent contribution [M. A. Cuendet, Phys. Rev. Lett.96, 120602 (2006)] that the JI can, in particular, be derived directly from the NoséHoover thermostated dynamics. This statistical mechanical derivation is particularly relevant in the framework of molecular dynamics simulation, because it is based solely on the equations of motion considered and is free of any additional assumptions on system size or bath coupling. Here, this result is generalized to a variety of dynamics, along two directions. On the one hand, specific improved thermostating schemes used in practical applications are treated. These include NoséHoover chains, higher moment thermostats, as well as an isothermalisobaric scheme yielding the JI in the ensemble. On the other hand, the theoretical generality of the new derivation is explored. Generic dynamics with arbitrary coupling terms and an arbitrary number of thermostating variables, both nonHamiltonian and Hamiltonian, are shown to imply the JI. In particular, a nonautonomous formulation of the generalized NoséPoincaré thermostat is proposed. Finally, general conditions required for the JI derivation are briefly discussed.

Effective multipoles and Yukawa electrostatics in dressed molecule theory
View Description Hide DescriptionIn this paper we derive the multipolar expansion of the screened Coulomb potential in electrolyte solutions with molecular solvent. The solute and solvent molecules can have arbitrary sizes, shapes, and internal charge distributions. We use the exact statistical mechanical definition of renormalized charge distributions coming from “dressed molecule theory” to determine the effective multipoles of a molecule immersed in an electrolyte. The effects of manybody correlations are fully included in our formally exact theory. We restrict ourselves to sufficiently dilute solutions so the screened Coulomb potential decays for large distances like a Yukawa function, , where is the distance and is the decay length (it is normally different from the Debye length). The resulting “Yukawa electrostatics” differ in many respects from ordinary, unscreened electrostatics. The “Yukawa charge” of a molecule (the lowest order moment in the multipolar expansion) is in general not equal to its Coulombic charge and it is not the integral of the renormalized charge distribution of the molecule. Moreover, as shown in this paper, the multipolar expansion of the Yukawa potential does not correspond, contrary to the case of the Coulomb potential, to its asymptotic expansion for large . As a consequence, the charge term in the multipolar expansion is not the leading term in the asymptotic expansion. Instead, for large values, multipoles of all orders contribute to the leading asymptotic term. Thus, the electrostatic potential from, for example, an electroneutral solvent molecule in an electrolyte solution has generally the same range as that from an ion. The proper asymptotic expansion for electrostatic interactions in electrolytes is derived. It is briefly shown how the multipole expansion formalism can also be applied in the PoissonBoltzmann approximation for primitive modelelectrolytes.

Analytic calculation of the diagonal BornOppenheimer correction within configurationinteraction and coupledcluster theory
View Description Hide DescriptionSchemes for the analytic calculation of the diagonal BornOppenheimer correction (DBOC) are formulated and implemented for use with general singlereference configurationinteraction and coupledclusterwave function models. Calculations are reported to demonstrate the convergence of the DBOC with respect to electroncorrelation treatment and basis set as well as to investigate the sizeconsistency error in configurationinteraction calculations of the DBOC. The importance of electroncorrelation contributions to the DBOC is illustrated in the computation of the corresponding corrections for the reactionenergy and activation barrier of the reaction as well as of the atomization energy for transbutadiene.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Photodissociation dynamics of fluorobenzene at 157 and : Branching ratios and distributions of kinetic energy
View Description Hide DescriptionFollowing photodissociation of fluorobenzene at 193 and , we detected the products with fragmentationtranslational spectroscopy by utilizing a tunable vacuum ultraviolet beam from a synchrotron for ionization. Between two primary dissociation channels observed upon irradiation at 193 , the HFelimination channel dominates, with a branching ratio of and an average release of kinetic energy of 103 ; the Helimination channel has a branching ratio of and an average release of kinetic energy of 18.6 . Photofragments H, HF, , and produced via the onephoton process have nearly isotropic angular distributions. Both the HFelimination and the Helimination channels likely proceed via the groundstate electronic surface following internal conversion of ; these channels exhibit small fractions of kinetic energy release from the available energy, indicating that the molecular fragments are highly internally excited. We also determined the ionization energy of to be .

The stability of allyl radicals following the photodissociation of allyl iodide at
View Description Hide DescriptionThe photodissociation of allyl iodide at was investigated by using a combination of vacuumultraviolet photoionization of the allyl radical, resonant multiphoton ionization of the iodine atoms, and velocity map imaging. The data provide insight into the primary C–I bond fission process and into the dissociativeionization of the allyl radical to produce . The experimental results are consistent with the earlier results of Szpunar et al. [J. Chem. Phys.119, 5078 (2003)], in that some allyl radicals with internal energies higher than the secondary dissociation barrier are found to be stable. This stability results from the partitioning of available energy between the rotational and vibrational degrees of freedom of the radical, the effects of a centrifugal barrier along the reaction coordinate, and the effects of the kinetic shift in the secondary dissociation of the allyl radical. The present results suggest that the primary dissociation of allyl iodide to allyl radicals plus is more important than previously suspected.

Low frequency backbone vibrations of individual conformational isomers: Tryptamine
View Description Hide DescriptionThe low frequency vibrations of the ethylamino backbone of six conformers of tryptamine have been studied in the ground and excited states using dispersed fluorescence spectroscopy, rotationally resolved laser induced fluorescence, and ab initio calculations. Four low frequency vibrational modes of the backbone, which involve torsional and librational motions of the ethylamino group, have been identified. The three anti conformers show a substantially different vibrational pattern than the four conformers in which the amino group is in gauche position with respect to the pyrrole and the phenyl ring, respectively.

Linear and nonlinear circular dichroism of methylcyclopentanone
View Description Hide DescriptionLinear and nonlinear circular dichroism of methylcyclopentanone is reported in the gas and liquid phases. Measurements of resonanceenhanced multiphoton ionization circular dichroism (REMPICD) for nozzlejet expanded molecular beams of the equatorial conformer of are presented. Monitoring either massselected cations or photoelectrons produced via REMPI through the Rydberg transition yielded a REMPICD of , where refers to the ion/electron signal for left/right circularly polarized light. A racemic mixture of 3methylcyclopentanone showed no significant CD; however, the signal fluctuations were much larger than that observed for the resolved methylcyclopentanone as might be expected for the small number of ions produced from slightly unequal numbers of enantiomers in each laser shot. Gas phase, vibrationally resolved, onephoton CD for vapor phase methylcyclopentanone (i.e., admixture of five axial and equatorial forms) was measured to be and at photon energies corresponding to the one (nonresonant) and two( resonance) photon energy levels. The onephoton CD (of the room temperature population of conformers) at an energy corresponding to the ionization step was measured previously to be which is of the same sign as the REMPICD. The first step is also near a positive CD region. This suggests that the REMPICD is determined primarily by both the initial and continuum steps. The onephoton CDs for the equatorial and axial forms of 3MCP are calculated, using GAUSSIAN03, to be approximately equal but having opposite sign for the transitions of interest. The CD for 3MCP in cyclohexane is found to be strongly temperature dependent as a result of the presence of both the axial and equatorial conformers. The energy difference between the two conformers is determined from a van’t Hoff plot of these data to be in cyclohexane and is smaller than measurements employing other methods.

Effects of microsolvation on uracil and its radical anion:
View Description Hide DescriptionMicrosolvation effects on the stabilities of uracil and its anion have been investigated by explicitly considering the structures of complexes of uracil with up to five water molecules at the level of theory. For all five systems, the global minimum of the neutral cluster has a different equilibrium geometry from that of the radical anion. Both the vertical detachment energy (VDE) and adiabatic electron affinity (AEA) of uracil are predicted to increase gradually with the number of hydrating molecules, qualitatively consistent with experimental results from a photodetachmentphotoelectron spectroscopy study [J. Schiedt et al., Chem. Phys.239, 511 (1998)]. The trend in the AEAs implies that while the conventional valence radical anion of uracil is only marginally bound in the gas phase, it will form a stable anion in aqueous solution. The gasphase AEA of uracil was higher than that of thymine by and this gap was not significantly affected by microsolvation. The largest AEA is that predicted for , namely, . The VDEs range from .

Isotope effects in the infrared spectra of OCS–He complexes and clusters
View Description Hide DescriptionInfrared spectra of the OCS–He van der Waals complex and of clusters have been studied in the region of the OCS fundamental band using a tunable diode laser to probe a pulsed supersonic slit jet. For the complex, the spectrum of the normal isotope,, has been considerably extended and the  and substituted forms have been recorded for the first time. The data could be analyzed satisfactorily using a conventional asymmetric rotor Hamiltonian with sextic centrifugal distortion terms. For the clusters, the  and substituted forms have been observed and assigned for , including some transitions with higher values than previously reported for the normal isotope, e.g., . The observed vibrational shifts, relative to the free OCS molecule, were very similar to those of the normal isotope, and most of the difference could be explained by simple scaling. These results constitute a subtle and precise probe of intermolecular forces and dynamical effects in a system which is of current interest for cluster studies.