Volume 123, Issue 11, 15 September 2005
 COMMUNICATIONS


Reaction barrier heights from an exactexchangebased densityfunctional correlation model
View Description Hide DescriptionA recent exactexchangebased densityfunctional model of nondynamical and dynamical correlation [A.D. Becke, J. Chem. Phys.122, 064101 (2005)] is tested on 70 barrier heights for a variety of reaction types: hydrogen transfer reactions, heavyatom transfer reactions, nucleophilic substitutions, association reactions, and unimolecular rearrangements, including both even and oddelectron systems. The mean absolute error with respect to accurate reference data is . This is achieved without any refitting of the parameters of the model to the barrier height data.

Direct computation of characteristic temperatures and relaxation times for glassforming polymer liquids
View Description Hide DescriptionCharacteristic temperatures and structuralrelaxation times for different classes of glassforming polymer liquids are computed using a revised entropytheory of glass formation that permits the chain backbone and the side groups to have different rigidities. The theory is applied to glass formation at constant pressure or constant temperature. Our calculations provide new insights into physical factors influencing the breadth of the glass transition and the associated growth of relaxation times.

HyperRayleigh scattering spectrum of liquid nitromethane
View Description Hide DescriptionThe vertical vertical (VV), horizontal vertical (HV), and vertical horizontal (VH) hyperRayleigh scattering (HRS) spectra were measured for liquid at . The main HRS spectral component has a width , which gives an orientation relaxation time in good agreement with other experiments. However, the VH spectrum also contains a previously unobserved strong narrow peak at zerofrequency shift, absent from the VV and HV spectra, which is due to a slowly relaxing longitudinal orientation mode. The upper bound on the width of this peak is 5 MHz, which corresponds to a relaxation time.
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 ARTICLES

 Theoretical Methods and Algorithms

Modeling solvent effects on electronspinresonance hyperfine couplings by frozendensity embedding
View Description Hide DescriptionIn this study, we investigate the performance of the frozendensity embedding scheme within densityfunctional theory [J. Phys. Chem.97, 8050 (1993)] to model the solvent effects on the electronspinresonance hyperfine coupling constants (hfcc’s) of the molecule. The hfcc’s for this molecule depend critically on the outofplane bending angle of the NO bond from the molecular plane. Therefore, solvent effects can have an influence on both the electronic structure for a given configuration of solute and solvent molecules and on the probability for different solute (plus solvent) structures compared to the gas phase. For an accurate modeling of dynamic effects in solution, we employ the CarParrinello moleculardynamics (CPMD) approach. A firstprinciplesbased Monte Carlo scheme is used for the gasphase simulation, in order to avoid problems in the thermal equilibration for this small molecule. Calculations of small water clusters show that microsolvation effects of water molecules due to hydrogen bonding can be reproduced by frozendensity embedding calculations. Even simple sumofmoleculardensities approaches for the frozen density lead to good results. This allows us to include also bulk solvent effects by performing frozendensity calculations with many explicit water molecules for snapshots from the CPMD simulation. The electronic effect of the solvent at a given structure is reproduced by the frozendensity embedding. Dynamic structural effects in solution are found to be similar to the gas phase. But the small differences in the average structures still induce significant changes in the computed shifts due to the strong dependence of the hyperfine coupling constants on the outofplane bending angle.

Calculation of nuclear magnetic shieldings using an analytically differentiated relativistic shielding formula
View Description Hide DescriptionTwo expressions for nuclearmagneticshielding tensor components based on analytically differentiating the electronic energy of a system are presented. The first is based on a secondorder DouglasKrollHess approach, in which the offdiagonal block terms of the transformed Dirac Hamiltonian are diminished to second order with respect to both the electrostatic nuclear attraction potential and the magnetic vector potential . The second expression is based on the method of BaryszSadlejSnijders, in which the offdiagonal block terms in the transformed Dirac Hamiltonian are completely eliminated with respect to purely terms, while they are diminished to second order with respect to terms including . The two approaches are applied to the calculation of nuclear magnetic shieldings of , , and noble gas systems with common gauge origins. The results show that relativistic corrections of higher than second order are negligibly small, except for the paramagnetic parts of I, Te, and Xe shieldings. The present calculations yield very large positive values for the anisotropy of proton shielding, , of HI compared to previous reports. Unfortunately, no experimental values for the anisotropy of proton shielding in HI are available for verification.

Calculation of optical rotation with timeperiodic magneticfielddependent basis functions in approximate timedependent densityfunctional theory
View Description Hide DescriptionWe report the implementation of a method for the calculation of optical rotation. This method is based on the timedependent densityfunctional theory and utilizes timeperiodic magneticfielddependent basis functions. The calculations are based on a density fit. It is demonstrated that additional terms in the analytical expression appearing from derivatives of the approximated Coulomb potential are necessary to provide the gaugeorigin independence of the results within a given numerical accuracy. Contributions from these terms also restore the symmetry between the electric and magnetic perturbations in the optical rotationtensor.

Genetic mapping of the distribution of minima on the potential energy surface of disordered systems
View Description Hide DescriptionWe show that genetic algorithms and energy minimizations in combination provide a highly efficient tool for mapping lowenergy minima on the erratic and complex potentialenergysurfaces of grossly disordered materials. The distribution of energy minima mimics with sufficient accuracy the lowenergy portion of the parent distribution of minima and allows accurate calculation of configurational Boltzmann averaged structural and thermodynamic properties in cases where a small fraction of the minima is thermally accessible. The distribution of energy minima obtained using genetic algorithms is biased, and consequently the properties converge slowly at high temperatures. In contrast, an optimized set of a few randomly chosen configurations provides a statistical representable selection for the accurate calculation of configurationalaveraged properties at high temperatures, but gives a poor description of the lowenergy portion of minima. Thus the properties calculated using the random algorithm are hampered by the presence of systematic errors in cases where a small fraction of the minima is thermally accessible. The inherently slow convergence of both the genetic algorithm and the random selection at intermediate temperatures is tackled by combining the lower fraction of the distribution of minima obtained using genetic algorithms with the intermediate and upper fraction from the random (nonbiased) selection of configurations. For this purpose we introduce a cutandscaletype scheme. The resulting combined distribution allows accurate calculation of properties at all temperatures.

Molecular photoionization cross sections in electron propagator theory: Angular distributions beyond the dipole approximation
View Description Hide DescriptionCorrections to dipole approximation results for angular distributions in photoionization of firstrow hydrides have determined by using Dyson orbitals calculated with ab initio electron propagator theory and by considering the full multipole expansion for the incident photon representation. The relative importance of firstorder corrections which consist of electric quadrupole and magnetic dipole terms and of higherorder terms has been estimated as a function of photon energy. Multipole corrections to the dipole approximation depend on photon energy and on the characteristics of the Dyson orbitals.

An examination of the validity of nonequilibrium moleculardynamics simulation algorithms for arbitrary steadystate flows
View Description Hide DescriptionNonlinearresponse theory of nonequilibrium moleculardynamics simulation algorithms is considered under the imposition of an arbitrary steadystate flow field. It is demonstrated that the SLLOD and DOLLS algorithms cannot be used for general flows, although the SLLOD algorithm is rigorous for planar Couette flow. Following the same procedure used to establish SLLOD as the valid algorithm for planar Couette flow [D. J. Evans and E. P. Morriss, Phys. Rev. A30, 1528 (1984)], it is demonstrated that the pSLLOD algorithm is valid for arbitrary flows and produces the correct nonlinear response of the viscous pressure tensor.

Condensedtoatoms electronic Fukui functions within the framework of spinpolarized densityfunctional theory
View Description Hide DescriptionA simple formalism devised to calculate the condensedtoatoms Fukui function [R. R. Contreras, P. Fuentealba, M. Galván, and P. Pérez, Chem. Phys. Lett.304, 405 (1999)] has been further analyzed within a spinpolarized densityfunctional theory framework. The model is based on a frozencore approximation to these local reactivity indices [M. Galván, A. Vela, and J. L. Gázquez, J. Phys. Chem.92, 6470 (1988)], giving us an extended local reactivity description of systems based on the frontier spinup and spindown molecular orbitals. Degenerate molecular spin orbitals have been explicitly included in our modelequations. Computational results for the nitric oxide (NO) and some simple carbene systems are presented in order to test the model. These quantities have been discussed in the context of changes both in charge density and spin density within the context of electron charge transfer or spinpolarization processes.

Fast localized orthonormal virtual orbitals which depend smoothly on nuclear coordinates
View Description Hide DescriptionWe present here an algorithm for computing stable, welldefined localized orthonormal virtual orbitals which depend smoothly on nuclear coordinates. The algorithm is very fast, limited only by diagonalization of two matrices with dimension the size of the number of virtual orbitals. Furthermore, we require no more than quadratic (in the number of electrons) storage. The basic premise behind our algorithm is that one can decompose any given atomicorbital (AO) vector space as a minimal basis space (which includes the occupied and valence virtual spaces) and a hardvirtual (HV) space (which includes everything else). The valence virtual space localizes easily with standard methods, while the hardvirtual space is constructed to be atom centered and automatically local. The orbitals presented here may be computed almost as quickly as projecting the AO basis onto the virtual space and are almost as local (according to orbital variance), while our orbitals are orthonormal (rather than redundant and nonorthogonal). We expect this algorithm to find use in localcorrelation methods.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Path integral methods for rotating molecules in superfluids
View Description Hide DescriptionWe present a path integral Monte Carlo (PIMC) methodology for quantum simulation of molecular rotations in superfluid environments such as helium and parahydrogen that combines the sampling of rotational degrees of freedom for a molecular impurity with multilevel Metropolis sampling of Bose permutation exchanges for the solvating species. We show how the present methodology can be applied to the evaluation of imaginary time rotational correlation functions of the molecular impurity, from which the effective rotational constants can be extracted. The combined rotation/permutation sampling approach allows for the first time explicit assessment of the effect of Bose permutations on molecular rotation dynamics, and the converse, i.e., the effect of molecular rotations on permutation exchanges and local superfluidity. We present detailed studies showing that the effect of Bose permutations in the solvating environment is more significant for the dynamics of heavy than light molecules in helium, and that Bose permutation exchanges are slightly enhanced locally by molecular rotation. Finally, the examples studied here reveal a size dependence of rotational excitations for molecules possessing a strongly anisotropic interaction with helium in clusters between and .

The molecular symmetry and electronic spectroscopy of 7azaindole dimer: Its protontransfer channels
View Description Hide DescriptionThe potentialenergy surfaces for the proton transfer in the doubly hydrogenbonded dimer of 7azaindole in its lowest excited electronic states were examined. The dimer with symmetry in its lowest excited electronic states, and , undergoes concerted doubleproton transfer via transition states of the same symmetry placed at energies 4.55 and higher, respectively. This suggests that the activation barriers for the doubleproton transfer, if any, are lower than . Emission from the dimers resulting from the doubleproton transfer involves a Stokes shift of , as theoretically estimated from the 00 components of the absortion and emission transitions of the dimer. Surprisingly, however, the calculations suggest that the green emission cannot arise from the state generated by a doubleproton transfer, because this structure possesses an imaginary frequency. In the 7azaindole dimer of symmetry, the first excited electronic state,, lies below . This excited state can be the starting point for singleproton transfers giving a zwitterionic form that can dissociate into the protonated and deprotonated forms of 7azaindole, the former being electronically excited. This situation of lower symmetry is consistent with the mutational scheme proposed by Goodman [Nature (London)378, 237 (1995)].

Electron attachment and detachment, and the electron affinities of and
View Description Hide DescriptionRate constants have been measured for electron attachment to and to using a flowingafterglow Langmuirprobe apparatus (at a He gas pressure of ). In both cases only the parent anion was formed in the attachment process. The attachment rate constantsmeasured at room temperature are and , respectively. Rate constants were also measured for thermal electron detachment from the parent anions of these molecules. For detachment is negligible at room temperature, but increases to at . For , the detachment rate at was . The attachment/detachment equilibrium yielded experimental electron affinities and . Electronic structure calculations were carried out for these molecules and related using densityfunctional theory and the compound method. The EAs are found to decrease by , on average, with each F substitution by H. The calculated EAs are in good agreement with the present experimental results.

Laser cooling of vibrational degrees of freedom of a molecular system
View Description Hide DescriptionWe consider the cooling of vibrational degrees of freedom in a photoinduced excited electronic state of a model molecular system. For the various parameters of the potential surfaces of the ground and excited electronic states and depending on the excitation frequency of a singlemode laser light, the average energy or average vibrational temperature of the excited state passes through a minimum. The amount of cooling is quantified in terms of the overlap integral between the ground and excited electronic states of the molecule. We have given an approach to calculate the FranckCondon factor for a multimode displaceddistortedrotated oscillatorsurface of the molecular system. This is subsequently used to study the effect of displacement, distortion, and Duschinsky rotation on the vibrational cooling in the excited state. The absorption spectra and also the average energy or the effective temperature of the excited electronic state are studied for the above model molecular system. Considering the nonCondon effect for the symmetryforbidden transitions, we have discussed the absorption spectra and average temperature in the excitedstate vibrational manifold.

Rotational lineintegrated photoabsorption cross sections corresponding to the band of NO:A molecular quantumdefect orbital procedure
View Description Hide DescriptionThe rotational lineintegrated photoabsorption cross sections corresponding to the band of the nitric oxide (NO) molecule at 295 K, calculated with the molecular quantumdefect orbital methodology, are in rather good accord with the experimental measurements available in the literature. The achieved results are of straightforward use in atmospheric chemistry, such as in the assessment of the NO photodissociation rate constant, which is of great relevance for atmospheric modeling.

Computational spectroscopy of heliumsolvated molecules: Effective inertia, from small He clusters toward the nanodroplet regime
View Description Hide DescriptionAccurate computer simulations of the rotational dynamics of linear molecules solvated in He clusters indicate that the largesize (nanodroplet) regime is attained quickly for light rotors (HCN) and slowly for heavy ones (OCS, , and ), thus challenging previously reported results. Those results spurred the view that the different behavior of light rotors with respect to heavy ones—including a smaller reduction of inertia upon solvation of the former—would result from the lack of adiabatic following of the He density upon molecular rotation. We have performed computer experiments in which the rotational dynamics of OCS and HCN molecules was simulated using a fictitious inertia appropriate to the other molecule. These experiments indicate that the approach to the nanodroplet regime, as well as the reduction of the molecular inertia upon solvation, is determined by the anistropy of the potential, more than by the molecular weight. Our findings are in agreement with recent infrared and/or microwave experimental data which, however, are not yet totally conclusive by themselves.

A computational study of some electric and magnetic properties of gaseous and
View Description Hide DescriptionWe present the results of an extended computational study of the electric and magnetic properties connected to CottonMouton birefringences, on the trifluoro and trichloroborides in the gas phase. The electric dipole polarizabilities, magnetizabilities, quadrupole moments, and higherorder hypersusceptibilities—expressed as quadratic and cubic frequencydependent response functions—are computed within HartreeFock, densityfunctional, and coupledcluster response theories employing singly and doubly augmented correlationconsistent basis sets and London orbitals in the magnetic property calculations. The results, which illustrate the capability of timedependent densityfunctional theory for electronrich systems, are compared with available experimental data. Revised values of both experimentally derived quadrupole moment of , , and magnetizability anisotropy of , , both obtained in birefringence experiments that neglect the effects of higherorder hypersusceptibilities, are presented. In the theoretical limit the traceless quadrupole moments of and are determined to be and , respectively.

Exploring the JahnTeller and pseudoJahnTeller conical intersections in the ethane radical cation
View Description Hide DescriptionWe report a theoretical account on the static and dynamic aspects of the JahnTeller(JT) and pseudoJahnTeller (PJT) interactions in the ground and first excited electronic states of the ethane radical cation. The findings are compared with the experimental photoionization spectrum of ethane. The present theoretical approach is based on a model diabatic Hamiltonian and with the parameters derived from ab initio calculations. The optimized geometry of ethane in its electronic ground state revealed an equilibrium staggered conformation belonging to the symmetry point group. At the vertical configuration, the ethane radical cation belongs to this symmetry point group. The ground and lowlying electronic states of this radical cation are of , , , and symmetries. Elementary symmetry selection rule suggests that the degenerate electronic states of the radical cation are prone to the JT distortion when perturbed along the degenerate vibrational modes of symmetry. The state is estimated to be above the state and below the state at the vertical configuration. The symmetry selection rule also suggests PJT crossings of the and the electronic states of the radical cation along the vibrational modes of symmetry and such crossings appear to be energetically favorable also. The irregular vibrational progressions, with numerous shoulders and small peaks, observed below 12.55 eV in the experimental recording are manifestations of the dynamic JT effect. Our findings revealed that the PJT activity of the degenerate vibrational modes is particularly strong in the electronic manifold which leads to a broad and diffuse structure of the observed photoelectron band.

Theoretical studies of , and complexes in aqueous solution and gas phase
View Description Hide DescriptionExtensive ab initio calculations both in gas phase and solution have been carried out to study the equilibrium structure, vibrational frequencies, and bonding characteristics of various actinyl (, and ) and their hydrated forms, (, 5, and 6). Bulk solvent effects were studied using a continuum method. The geometries were fully optimized at the coupledcluster singles doubles (CCSD), densityfunctional theory(DFT), and MøllerPlesset (MP2) level of theories. In addition vibrational frequencies have been obtained at the CCSD as well as MP2/DFT levels. The results show that both the shortrange and longrange solvent effects are important. The combined discretecontinuum model, in which the ionic solute and the solvent molecules in the first and second solvation shells are treated quantum mechanically while the solvent is simulated by a continuum model, can predict accurately the bonding characteristics. Moreover, our values of solvation free energies suggest that five and sixcoordinations are equally preferred for , and fivecoordinated species are preferred for and . On the basis of combined quantumchemical and continuum treatments of the hydrated complexes, we are able to determine the optimal cavity radii for the solvation models. The coupledcluster computations with large basis sets were employed for the vibrational spectra and equilibrium geometries both of which compare quite favorably with experiment. Our most accurate computations reveal that both five and sixcoordination complexes are important for these species.