Volume 116, Issue 8, 22 February 2002
 COMMUNICATIONS


(Meta)stability domain of ice XII revealed between ≈158–212 K and ≈0.7–1.5 GPa on isobaric heating of highdensity amorphous ice
View Description Hide DescriptionHighdensity amorphousice was heated at constant pressures of between 0.52 to 1.9 GPa from 77 K up to 240 K. The formed phases were characterized by xray diffractograms of samples recovered under liquid at 1 bar. The (meta)stability domain of ice XII thus revealed extends between ≈158–212 K from ≈0.7 to ≈1.5 GPa. We further discuss whether ice XII has a lowtemperature region of stability within the ice VI domain. Our (meta)stability domain of ice XII is in a different region of water’s phase diagram than that shown by Koza et al. [Phys. Rev. Lett. 84, 4112 (2000)].
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 ARTICLES

 Theoretical Methods and Algorithms

Efficient use of the correlation consistent basis sets in resolution of the identity MP2 calculations
View Description Hide DescriptionThe convergence of the secondorder Møller–Plesset perturbation theory (MP2) correlation energy with the cardinal numberX is investigated for the correlation consistent basisset series ccpVXZ and For the augccpVXZ and series the convergence of the MP2 correlation contribution to the dipole moment is studied. It is found that, when dshell electrons cannot be frozen, the ccpVXZ and basis sets converge much slower for thirdrow elements then they do for first and secondrow elements. Based on the results of these studies criteria are deduced for the accuracy of auxiliary basis sets used in the resolution of the identity (RI) approximation for electron repulsion integrals. Optimized auxiliary basis sets for RIMP2 calculations fulfilling these criteria are reported for the sets ccpVXZ, augccpVXZ, and with T, and Q. For all basis sets the RI error in the MP2 correlation energy is more than two orders of magnitude smaller than the usual basisset error. For the auxiliary augccpVXZ and sets the RI error in the MP2 correlation contribution to the dipole moment is one order of magnitude smaller than the usual basis set error. Therefore extrapolations towards the basisset limit are possible within the RI approximation for both energies and properties. The reduction in CPU time obtained with the RI approximation increases rapidly with basis set size. For the ccpVQZ basis an acceleration by a factor of up to 170 is observed.

Two functions of the density matrix and their relation to the chemical bond
View Description Hide DescriptionWe examine and compare two previously introduced functions of the oneparticle density matrix that are suitable to represent its offdiagonal structure in a condensed form and that have illustrative connections to the nature of the chemical bond. One of them, the LocalizedOrbital Locator (LOL) [J. Molec. Struct. (THEOCHEM) 527, 51 (2000)], is based only on the noninteracting kineticenergy density τ and the charge density ρ at a point, and gives an intuitive measure of the relative speed of electrons in its vicinity. Alternatively, LOL focuses on regions that are dominated by single localized orbitals. The other one, the Parity Function P [J. Chem. Phys. 105, 11134 (1996)], is a section through the Wigner phasespace function at zero momentum, and contains information about the phase of the interference of atomiclike orbital contributions from bound centers. In this paper, we discuss the way in which these functions condense information in the density matrix, and illustrate on a variety of examples of unusual chemical bonds how they can help to understand the nature of “covalence.”

Perturbative corrections to the equationofmotion spin–flip selfconsistent field model: Application to bondbreaking and equilibrium properties of diradicals
View Description Hide DescriptionWe present perturbative corrections to a recently introduced spin–flip selfconsistent field (SFSCF) wave function. The spin–flip model describes both closed and open shell singlet states within a single reference formalism as spin–flipping, e.g., excitations from a triplet reference state for which both dynamical and nondynamical correlation effects are much smaller than for the corresponding singlet state. The simplest spin–flip model employs a SCF wave function for the reference state, and the resulting equations for target states are therefore identical to configuration interaction singles (in spin–orbital form). While being a qualitatively correct zeroorder wave function, SFSCF should be augmented by dynamical correlation corrections to achieve a quantitative accuracy. The results demonstrate that the secondorder approximation to the more theoretically complete spin–flip coupledclustermodel (truncated at double substitutions) represents a systematic improvement over the SFSCF model.

Logarithmic moments of relaxation time distributions
View Description Hide DescriptionIn this paper a novel way to quantify “nonexponential” relaxations is described. So far, this has been done in two ways: (1) by fitting empirical functions with a small number of parameters, (2) by calculation of the underlying distribution function of (exponential) relaxations using regularization methods. The method described here is intermediate, it does not assume a specific functional form but also does not aim at the complete distribution but only its logarithmic moments It is shown that these exist (in contrast to the linear moments) and can be calculated analytically for all currently used empirical descriptions of nonexponential relaxations. Therefore, the logarithmic moments represent a common basis for comparing literature data from authors which prefer different empirical formulas (e.g., those of Kohlrausch and HavriliakNegami). The logarithmic moments are also shown to be related in a simple way to the (linear) moments of an underlying distribution of activation energies giving them a physical significance.

Two Krylov space algorithms for repeated large scale sparse matrix diagonalization
View Description Hide DescriptionTwo simple algorithms for the diagonalization of a set of sparse symmetric matrices of the form for large values of are proposed and investigated. The numerical strategies economize computer resources by requiring the reconstruction of the Lanczos basis for a small number of times compared to Each member of the set is assumed to have a smaller number of nonzero elements compared to A. Both numerical procedures are derived from the Lanczos algorithm and use periodically a recursion to obtain the Lanczos vectors. Tests are conducted with both random symmetric matrices and with DVR Hamiltonians containing parametric potentials. The performance of the algorithms in terms of numerical accuracy, stability, and CPU time is studied as a function of two properties of the matrix set

Centroidbased methods for calculating quantum reaction rate constants: Centroid sampling versus centroid dynamics
View Description Hide DescriptionA new method was recently introduced for calculating quantum mechanical rate constants from centroid molecular dynamics (CMD) simulations [E. Geva, Q. Shi, and G. A. Voth, J. Chem. Phys. 115, 9209 (2001)]. This new method is based on a formulation of the reaction rate constant in terms of the positionflux correlation function, which can be approximated in a well defined way via CMD. In the present paper, we consider two different approximated versions of this new method, which enhance its computational feasibility. The first approximation is based on propagating initial states which are sampled from the initial centroid distribution, on the classical potential surface. The second approximation is equivalent to a classicallike calculation of the reaction rate constant on the centroid potential, and has two distinct advantages: (1) it bypasses the problem of inefficient sampling which limits the applicability of the full CMD method at very low temperatures; (2) it has a well defined TST limit which is directly related to pathintegral quantum transition state theory (PIQTST). The approximations are tested on a model consisting of a symmetric doublewell bilinearly coupled to a harmonic bath. Both approximations are quite successful in reproducing the results obtained via full CMD, and the second approximation is shown to provide a good estimate to the exact highfriction rate constants at very low temperatures.

New implementation of the trajectory surface hopping method with use of the Zhu–Nakamura theory. II. Application to the charge transfer processes in the 3D system
View Description Hide DescriptionThe newly implemented trajectory surface hopping (TSH) method for the collinear system with use of the Zhu–Nakamura semiclassical theory of nonadiabatic transition [C. Zhu, K. Nobusada, and H. Nakamura, J. Chem. Phys. 115, 3031 (2001)] is extended to treat 3D nonadiabatic reactions. Since the avoided crossing seam becomes a twodimensional surface in the 3D system, the nonadiabatic transition region and the possibility of classically forbidden hops are enlarged very much in comparison with those in the collinear case. As a result, the contribution of the classically forbidden hops is quite a bit enhanced in the 3D system. Conservation of total angular momentumJ is taken into account by slightly rotating the direction of momentum during the hop in the classically forbidden case. The method is tested by applying to the charge transfer processes in the 3D system for Numerical results clearly demonstrate that the new TSH method works very well at all energies and for all initial vibrational states considered compared to the old TSH method based on the Landau–Zener formula. The significant discrepancy between the two TSH methods survives even at high collision energy and high vibrational states in contrast to the collinear case, indicating the importance of the classically forbidden hops in 3D systems. The new TSH method is considered to be a very promising method to deal with high dimensional nonadiabatic dynamics. It should also be noted that the new TSH method does not require any knowledge of nonadiabatic coupling and is based only on adiabatic potentials.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

A combined crossedbeam, ab initio, and Rice–Ramsperger–Kassel– Marcus investigation of the reaction of carbon atoms with benzene, and benzene,
View Description Hide DescriptionThe reactions of atomic carbon, with benzene, and with benzene, were investigated at twelve collision energies between 8.8 and 52.5 kJ mol^{−1} using the crossed molecular beams technique. Forwardconvolution fitting of the data, highlevel electronic structure calculations, and Rice–Ramsperger–Kassel–Marcus (RRKM) investigations on the singlet and triplet potential energy hyperface suggest that at low collision energies the chemical reactiondynamics are indirect and dominated by large impact parameters. As the collision energy increases, smaller impact parameters become more important, and the chemical dynamics is increasingly direct. At all collision energies, the reaction proceeds on the triplet surface via a barrierless addition of the carbon atom to form a bicyclic intermediate followed by ring opening of the initial collision complex to a sevenmembered ring intermediate (cycloheptatrienylidene). The latter decomposes without exit barrier to the thermodynamically less stable 1,2didehydrocycloheptatrienyl radical, and its deuterated counterpart. The formation of a adduct is observed as a second channel. The barrierless route for the destruction of benzene can help to model important pathways for the synthesis of higher polycyclic aromatic hydrocarbon derivatives in the interstellar medium, in outflows of dying carbon stars, in hydrocarbonrich planetary atmospheres, as well as in oxygenpoor combustion flames.

Spectroscopy on rare gas–doped silver clusters in helium droplets
View Description Hide DescriptionThe optical spectrum of in a helium droplet, first measured by Federmann et al. [Eur. Phys. J. D 9, 11 (1999)], is studied over a broad wavelength range (237–450 nm) by resonant two photonionization. A strong resonance is found in accordance to recent ab initio calculations.Doping the droplet additionally with rare gas atoms leads to a shift of the mean resonance position, which depends on the type and the number of attached atoms. In contrast to the redshift obtained for argon, krypton, and xenon, for neon a net shift of the resonance to shorter wavelengths is observed. The dosagedependence of the displacements will qualitatively be explained.

Sensitivityenhanced nuclear quadrupole correlation spectroscopy: Application of single transition operators in nuclear quadrupole resonance of halfinteger nucleus
View Description Hide DescriptionSingle transition operators are adapted to simplify the density matrix theory for the spin dynamics calculation of quadrupole nuclei with more than one spin transition in zero field. We employ the formalism on the spin system with axial symmetry to obtain the responses of multiple pulses for nuclear quadrupole resonance regardless the spin relaxation. The theoretical calculation for pulse response is illustrated from onepulse to multipulse and onedimension to multidimension explicitly. Subsequently sensitivityenhanced nuclear quadrupolecorrelation spectroscopy (SENQCOSY) is proposed and demonstrated. Experimental results are compared with conventional nuclear quadrupolecorrelation spectroscopy (NQCOSY) for in system. The maximum sensitivity is enhanced by a factor of 2.66, which are in good agreement with theoretical prediction.

Collision effects in the nonlinear Raman response of liquid carbon disulfide
View Description Hide DescriptionA model of the polarizability of carbon disulfide dimers was constructed, using polarizabilities from accurate timedependent density functional theory calculations as reference. This direct reaction field model takes dipoleinduced dipole effects, induced multipole effects and effects due to the overlap of the electronic clouds into account in an approximate way. The importance of the induced multipole and the overlap effects is investigated. This polarizabilitymodel is subsequently used to calculate the thirdorder timedomain Raman response of liquid carbon disulfide. These results are compared to experimental data and earlier calculated response in which only dipoleinduced dipole effects on the polarizability were included. The multipole effects are found to give a significant contribution to the subpico second part of the thirdorder Raman response.

Anomalous isotopic predissociation in the state of
View Description Hide DescriptionUsing a tunable, narrowbandwidth vacuumultraviolet source based on thirdharmonic generation from excimerpumped dyelaser radiation, the photoabsorption cross sections of and have been recorded in high resolution. Rotational analyses have been performed and the resultant term values fitted to the Hamiltonian of Brown and Merer [J. Mol. Spectrosc. 74, 488 (1979)]. A large rotationless isotope effect is observed in the predissociation, wherein the Lorentzian linewidth component for is a factor of ∼50 smaller than the corresponding linewidth. This effect, a consequence of the nonadiabatic rotationless predissociation mechanism, is described using a coupledchannel treatment of the strongly Rydbergvalencemixed states. Significant J, parity, and sublevel dependencies observed in the isotopic rotational widths are found to derive from an indirect predissociation mechanism involving an accidental degeneracy with the level, itself strongly predissociated by Rydbergvalence interactions, together with Luncoupling (rotational) interactions between the Rydberg components of the F and E states. Transitions into the level are observed directly for the first time, specifically in the spectrum.

Electron binding energies of dipolebound anions at the coupled cluster level with single, double, and triple excitations: and
View Description Hide DescriptionThe electron binding energies for the weak dipolebound anions and were found to be 13.2 and 35.7 cm^{−1}, respectively, at the coupled cluster level of theory with single, double, and triple excitations [CCSDT]. A more approximate approach, in which the triples contribution is treated perturbatively [CCSD(T)], provides an electron binding energy which is underestimated for by 25% and overestimated for by 19%. The new results provide benchmarks for model potentials aiming to reproduce dynamical correlation effects in electron–molecule interactions.

Generation of semiclassical and delocalized vibrational wave packet motion of HF molecules oriented in an external static electric field
View Description Hide DescriptionThe quantum dynamics of the HF molecule is investigated in the presence of a static electric field and coherent infrared radiation. The time dependent dynamics is induced by infrared multiphoton excitation and the time evolution of the rovibrational wave packet is calculated in configuration space. Results are given for static field strengths needed to orient molecules such that their internal dynamics can be described by simplified, purely vibrational models. For highly oriented HF molecules, time intervals of approximate duration of 70 fs occur repeatedly during and after the excitation in which the reduced vibrational wave packet motion is nearly semiclassical (“semiclassical windows”). The occurrence of these time intervals can be made more regular after the excitation, if the pulse duration is chosen adequately.

Magnitude and orientation dependence of intermolecular interaction between perfluoroalkanes: High level ab initio calculations of and dimers
View Description Hide DescriptionIntermolecular interaction energies of eight orientation dimers and seven orientation dimers were calculated with electron correlation correction by the secondorder Møller–Plesset perturbation (MP2) method. The dimer and dimer have the largest binding energies. Electron correlation correction increases the attraction considerably, while the effects of electron correlation beyond MP2 are small. Electrostatic and induction energies are not large in all cases. This indicates that dispersion interaction is mainly responsible for the attraction. The calculated binding energy of the dimer (0.69 kcal/mol) is about 60% larger than that of the dimer (0.44 kcal/mol), while the binding energy of the dimer (1.02 kcal/mol) is close to that of the dimer (0.90 kcal/mol). The intermolecular separations (C⋯C distance) in the and dimers at the potential minima are close (4.0 and 3.8 Å, respectively), while the separation in the dimer (4.8 Å) is appreciably larger than that in the dimer (4.0 Å). The larger intermolecular separation in the dimer reduces dispersion energy. Therefore the binding energies of the and dimers are not largely different. The molar volume of is substantially larger than that of due to bulky fluorine atoms. The small difference of the binding energies suggests that the large molecular volume of perfluoroalkanes is the cause of their small heats of vaporization per volume.

Sulfur excitation of and Core–valence and valence–valence–exchange interaction and geometryspecific transitions
View Description Hide DescriptionSulfur excitation of and is reported. The experiments made use of monochromatic synchrotron radiation from the BW1 beam line at the HASYLAB (Hamburg, Germany), where total cation yields and photoionizationmass spectra were investigated as a function of the source temperature that was used for evaporation of αsulfur. The nearedge structure undergoes characteristic changes as a function of the source temperature, reflecting significant size and geometrydependent changes in electronic structure of the sulfur clusters. The detailed analysis of the nearedge features is obtained from ab initio (MRSDCI) calculations that focus on and The present results are discussed in comparison to previous work on innershell excited sulfur clusters as well as condensed sulfur. The nearedge structure of is compared to that of and yielding characteristic differences in core–valence and valence–valence–exchange interaction.

Raman spectroscopic studies on matrixisolated phosphorus molecules and
View Description Hide DescriptionThe Raman spectra of and molecules have been studied in nitrogen, argon, krypton, and xenon matrices at 15 K. The vibrational frequencies of the molecule are up to 14 higher than the experimental gas phase data. This apparent blueshift is not caused by matrix effects but rather due to an underestimation of the fundamentals in the gas phase as a course of the elevated temperatures. The observed frequencies confirm a recent theoretical prediction on the basis of highlevel calculations. From the observed frequencies of the molecule a general valence force field was calculated.
 Condensed Phase Dynamics, Structure, and Thermodynamics: Spectroscopy, Reactions, and Relaxation

Kinetics of phase transformations in a model with metastable fluid–fluid separation: A molecular dynamics study
View Description Hide DescriptionBy molecular dynamics (MD) simulations we study the crystallization process in a model system whose particles interact by a spherical pair potential with a narrow and deep attractive well adjacent to a hard repulsive core. The phase diagram of the model displays a solid–fluid equilibrium, with a metastable fluid–fluid separation. Our computations are restricted to fairly small systems (from 2592 to 10368 particles) and cover long simulation times, with constant energy trajectories extending up to MD steps. By progressively reducing the system temperature below the solid–fluid line, we first observe the metastable fluid–fluid separation, occurring readily and almost reversibly upon crossing the corresponding line in the phase diagram. The nucleation of the crystal phase takes place when the system is in the twofluid metastable region. Analysis of the temperature dependence of the nucleation time allows us to estimate directly the nucleationfree energy barrier. The results are compared with the predictions of classical nucleation theory. The critical nucleus is identified, and its structure is found to be predominantly fcc. Following nucleation, the solid phase grows steadily across the system, incorporating a large number of localized and extended defects. We discuss the relaxation processes taking place both during and after the crystallization stage. The relevance of our simulation for the kinetics of proteincrystallization under normal experimental conditions is discussed.

Predicting the Newtonian viscosity of complex fluids from high strain rate molecular simulations
View Description Hide DescriptionThe prediction of viscosity by molecular simulation has been a goal of molecular modeling essentially since its inception. With today’s computing power, the Newtonian or zero shear viscosity of a low molecular weight fluid can easily be determined using equilibrium and nonequilibrium molecular dynamics simulation methods. However, both methods are constrained to systems with relatively short relaxation times that are accessible on the timescale of a molecular dynamics simulation. Here we demonstrate that using a simple scaling relation enables us to predict the Newtonian viscosity of a molecule at any state point for a small fraction of the time that it takes to obtain the same result through nonequilibrium or equilibrium molecular dynamics simulation.