Volume 130, Issue 6, 14 February 2009
 ARTICLES

 Theoretical Methods and Algorithms

CCSD(T) study of the farinfrared spectrum of ethyl methyl ether
View Description Hide DescriptionBand positions and intensities for the farinfrared bands of ethyl methyl ether are variationally determined from a threedimensional (3D) potential energy surface calculated with CCSD(T)/ccpVTZ theory. For this purpose, the energies of 181 selected geometries computed optimizing parameters are fitted to a 3D Fourier series depending on three torsional coordinates. The zero point vibrational energy correction and the search of a correct definition of the methyl torsional coordinate are taken into consideration for obtaining very accurate frequencies. In addition, second order perturbation theory is applied on the two molecular conformers, trans and cisgauche, in order to test the validity of the 3D model. Consequently, a new assignment of previous experimental bands, congruent with the new ab initio results, is proposed. For the most stable transconformer, the , , and fundamental transitions, computed at 115.3, 206.5, and , are correlated with the observed bands at 115.4, 202, and . For the cisgauche the three band positions are computed at 91.0, 192.5, and . Calculations on the isotopomer confirm our assignment. Intensities are determined at room temperature and at 10 K. Structural parameters, potential energy barriers, anharmonic frequencies for the neglected modes, and rotational parameters (rotational and centrifugal distortion constants), are also provided.

Molecular orientation studies by pulsed electronelectron double resonance experiments
View Description Hide DescriptionPulsed electronelectron double resonance (PELDOR) has proven to be a valuable tool to measure the distribution of long range distances in noncrystalline macromolecules. These experiments commonly use nitroxide spin labels as paramagnetic markers that are covalently attached to the macromolecule at specific positions. Unless these spin labels are flexible in such a manner that they exhibit an almost random orientation, the PELDOR signals will—apart from the interspin distance—also depend on the orientation of the spin labels. This effect needs to be considered in the analysis of PELDOR signals and can, moreover, be used to obtain additional information on the structure of the molecule under investigation. In this work, we demonstrate that the PELDOR signal can be represented as a convolution of a kernel function containing the distance distribution function and an orientation intensity function. The following strategy is proposed to obtain both functions from the experimental data. In a first step, the distance distribution function is estimated by the Tikhonov regularization, using the average over all PELDOR time traces with different frequency offsets and neglecting angular correlations of the spin labels. Second, the convolution relation is employed to determine the orientation intensity function, using again the Tikhonov regularization. Adopting small nitroxide biradical molecules as simple examples, it is shown that the approach works well and is internally consistent. Furthermore, independent molecular dynamics simulations are performed and used to calculate PELDOR signals, distance distributions, and orientational intensity functions. The calculated and experimental results are found to be in excellent overall agreement.

The subtle business of model reduction for stochastic chemical kinetics
View Description Hide DescriptionThis paper addresses the problem of simplifying chemical reaction networks by adroitly reducing the number of reaction channels and chemical species. The analysis adopts a discretestochastic point of view and focuses on the model reaction set , whose simplicity allows all the mathematics to be done exactly. The advantages and disadvantages of replacing this reaction set with a single producing reaction are analyzed quantitatively using novel criteria for measuring simulation accuracy and simulation efficiency. It is shown that in all cases in which such a model reduction can be accomplished accurately and with a significant gain in simulation efficiency, a procedure called the slowscale stochastic simulation algorithm provides a robust and theoretically transparent way of implementing the reduction.

Molecular photoionization cross sections by Stieltjes–Chebyshev moment theory applied to Lanczos pseudospectra
View Description Hide DescriptionStieltjes imaging technique is widely used for the ab initio computation of photoionization cross sections and decay widths. The main problem hampering the application of the standard Stieltjes imaging algorithms in conjunction with highlevel ab initio methods to polyatomic molecules is the requirement of full diagonalization of excessively large Hamiltonian matrices. Here we show that the full diagonalization bottleneck can be overcome by applying the Stieltjes imaging procedure to Lanczos pseudospectrum of the atomic or molecular Hamiltonian. Using the helium and neon atoms as examples, we demonstrate that the Lanczos pseudospectrum obtained after only a relatively small number of iterations can be used for Stieltjestype calculations of photoionization cross sections essentially without loss of accuracy. The new technique is applied to the calculation of the total photoionization cross section of benzene within an ab initio approach explicitly taking into account single and double electronic excitations. Good agreement with experimental results is obtained.

Intensity tracking for theoretical infrared spectroscopy of large molecules
View Description Hide DescriptionWe present an approach for the direct calculation of vibrational normal modes with high infrared intensities based on a modetrackinglike algorithm [M. Reiher and J. Neugebauer, J. Chem. Phys.118, 1634 (2003)] but with distinct features: no collective guess vibration is utilized but highintensity distortions are constructed. Only the modes of interest with the highest infrared intensities are then targeted irrespective of a predefinition of the underlying collective normal coordinates. This leads to a fast access to the most important features in infrared spectra. The different implementations of the mode selection procedure are validated on a set of small organic molecules as well as on the metal complex tris(ethylenediaminato)cobalt(III) and the peptide alldecaalanine. As a critical test case, approximate infrared spectra of Schrock’s dinitrogen molybdenum complex are calculated via intensity tracking.

Dominant reaction pathways in highdimensional systems
View Description Hide DescriptionThis paper is devoted to the development of a theoretical and computational framework denominated dominant reaction pathways (DRPs) to efficiently sample the statistically significant thermally activated reaction pathways, in multidimensional systems. The DRP approach is consistently derived from the Langevin equation through a systematic expansion in the thermal energy, . Its main advantage with respect to existing simulation techniques is that it provides a natural and rigorous framework to perform the path sampling using constant displacement steps, rather than constant time steps. In our previous work, we have shown how to obtain the set of most probable reaction pathways, i.e., the lowest order in the expansion. In this work, we show how to compute the corrections to the leading order due to stochastic fluctuations around the most probable trajectories. We also discuss how to obtain predictions for the evolution of arbitrary observables and how to generate conformations, which are representative of the transition state ensemble. We illustrate how our method works in practice by studying the diffusion of a point particle in a twodimensional funneled external potential.

Linearscaling atomic orbitalbased secondorder Møller–Plesset perturbation theory by rigorous integral screening criteria
View Description Hide DescriptionA Laplacetransformed secondorder Møller–Plesset perturbation theory (MP2) method is presented, which allows to achieve linear scaling of the computational effort with molecular size for electronically local structures. Also for systems with a delocalized electronic structure, a cubic or even quadratic scaling behavior is achieved. Numerically significant contributions to the atomic orbital (AO)MP2 energy are preselected using the socalled multipolebased integral estimates (MBIE) introduced earlier by us [J. Chem. Phys.123, 184102 (2005)]. Since MBIE provides rigorous upper bounds, numerical accuracy is fully controlled and the exact MP2 result is attained. While the choice of thresholds for a specific accuracy is only weakly dependent upon the molecular system, our AOMP2 scheme offers the possibility for incremental thresholding: for only little additional computational expense, the numerical accuracy can be systematically converged. We illustrate this dependence upon numerical thresholds for the calculation of intermolecular interaction energies for the S22 test set. The efficiency and accuracy of our AOMP2 method is demonstrated for linear alkanes, stacked DNA base pairs, and carbon nanotubes: e.g., for DNA systems the crossover toward conventional MP2 schemes occurs between one and two base pairs. In this way, it is for the first time possible to compute wave functionbased correlation energies for systems containing more than 1000 atoms with 10 000 basis functions as illustrated for a 16 base pair DNA system on a singlecore computer, where no empirical restrictions are introduced and numerical accuracy is fully preserved.

Contracted Gaussian basis sets for Douglas–Kroll–Hess calculations: Estimating scalar relativistic effects of some atomic and molecular properties
View Description Hide DescriptionDouglas–Kroll–Hess (DKH) contracted Gaussian basis sets of double, triple, and quadruple zeta valence qualities plus polarization functions (, , T, and Q, respectively) for the atoms H–Ar and DZP and TZP for K–Kr are presented. They have been determined from the corresponding nonrelativistic basis sets generated previously by Jorge et al. We have recontracted the original basis sets, i.e., the values of the contraction coefficients were reoptimized using the relativistic DKH Hamiltonian. The effect of DKH at the coupledcluster level of theory on the ionizationenergy of some atoms and dissociation energy and geometric parameters for a sample of molecules is discussed. Our results were compared with theoretical and experimental values reported in the literature.

A functional of the onebodyreduced density matrix derived from the homogeneous electron gas: Performance for finite systems
View Description Hide DescriptionAn approximation for the exchangecorrelation energy of reduceddensitymatrixfunctional theory was recently derived from a study of the homogeneous electron gas [N. N. Lathiotakis, N. Helbig, and E. K. U. Gross, Phys. Rev. B75, 195120 (2007)]. In the present work, we show how this approximation can be extended appropriately to finite systems, where the Wigner Seitz radius , the parameter characterizing the constant density of the electron gas, needs to be replaced. We apply the functional to a variety of molecules at their equilibrium geometry and also discuss its performance at the dissociation limit. We demonstrate that, although originally derived from the uniform gas, the approximation performs remarkably well for finite systems.

Inertial effects in the orientational relaxation of rodlike molecules in a uniaxial potential
View Description Hide DescriptionThe inertial rotational Brownian motion and dielectric relaxation of an assembly of noninteracting rodlike polar molecules in a uniaxial potential are studied. The infinite hierarchy of differentialrecurrence relations for the equilibrium correlation functions is generated by averaging the governing inertial Langevin equation over its realizations in phase space. The solution of this hierarchy for the onesided Fourier transforms of the relevant correlation functions is obtained using matrix continued fractions yielding the longitudinal dipole correlation function, the correlation time, and the complex polarizability, which are calculated for typical values of the model parameters. Pronounced inertial effects appear in these characteristics in the highfrequency region for low damping. The exact longitudinal correlation time is compared with the predictions of the Kramers theory of the escape rate of a Brownian particle from a potential well as extended by Mel’nikov and Meshkov [J. Chem. Phys.85, 1018 (1986)]. In the low temperature limit, the universal Mel’nikov and Meshkov formula for the inverse of the escape rate provides a good estimate of the longitudinal correlation time for all values of the dissipation including the very low damping, very high damping, and Kramers turnover regimes. Moreover, the lowfrequency part of the spectra of the longitudinal correlation function may be approximated by a single Lorentzian with a halfwidth determined by this universal escape rate formula.

A highly parallelizable integral equation theory for three dimensional solvent distribution function: Application to biomolecules
View Description Hide DescriptionThree dimensional (3D) hydration structure is informative to clarify the functions of hydrated waters around a protein. We develop a new approach to calculate 3D solvation structure with reasonable computational cost. In the present method, the total solvation structure is obtained using conventional one dimensional reference interaction site model (RISM) followed by integrating the 3D fragment data, which are evaluated around each atom (site) of solute. Thanks to this strategy, timeconsuming 3D fast Fourier transformation, which is required in 3DRISM theory, can be avoided and highparallel performance is achieved. The method is applied to small molecular systems for comparison with 3DRISM. The obtained results by the present method and by 3DRISM show good agreement. The hydration structures for a large protein computed by the present method are also consistent with those obtained by xray crystallography.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Electronic structure of coordinatively unsaturated molybdenum and molybdenum oxide carbonyls
View Description Hide DescriptionResults of density functional theory calculations on coordinatively unsaturated molybdenum carbonyl and molybdenum oxide carbonyl anion and neutral complexes observed in previous experimental studies [Wyrwas, Robertson, and Jarrold, J. Chem. Phys.126, 214309 (2007)] and extended to related complexes are reported. The ground and lowlying electronic states were calculated for the most stable structures predicted for (, 5 and 6), , and . Interesting trends are predicted with CO addition, electron addition, and oxidation of the Mo center. In all cases, anions have stronger Mo–CO bond energies, which is attributed to enhanced backdonation. This enhancement is more dramatic for the molybdenum oxo complexes because the highest occupied molecular orbitals shift from Mo to the backbonds with the addition of oxygen to the Mo center. Sequential addition of CO for all species results in a sequential stabilization of low spin states and a destabilization of higher spin states. Further, average Mo–CO bond lengths increase as carbonyls are sequentially added. This effect is attributed to fewer electrons per Mo–CO backbond. Finally, addition of O to appears to weaken the Mo–CO bonds, and addition of CO to appears to weaken Mo–O bonds. The calculations are validated by favorable agreement between the available measured anion photoelectron spectra and simulated spectra based only on calculated spectroscopic parameters (vibrational frequencies and normal coordinate displacements).

Entropy behavior in cluster melting
View Description Hide DescriptionWe analyze the configurational excitation of a cluster for both a microcanonical and a canonical ensemble of atoms and apply this analysis to the LennardJones cluster of 13 atoms. Dividing the cluster excitations into configurational and thermal classes, we evaluate the anharmonicity coefficient of atomic vibrations and the entropy jump as a function of temperature on the basis of computer simulations of the LennardJones 13atom cluster as a canonical and a microcanonical ensemble of atoms. This analysis shows the role of anharmonicity of atomic vibrations and exhibits the importance of the temperature dependence of the entropy jump in the range of phase coexistence for cluster thermodynamics.

Success and pitfalls of the isolobal analogy: Depth and breadth of the boron connection
View Description Hide DescriptionThe extent and depth of the socalled boron connection suggested recently by the present author [J. Chem. Phys.128, 184305 (2008)] for the isovalent species [following similar connection of dianions] are further investigated by considering larger species up to and additional isovalent moieties. Here we consider, using density functional and coupled clusters theory, isovalent and clusters, in comparison to the corresponding carboranes and to each other for , 12. Special attention is given to the species, where the corresponding carborane is highly fluxional, and to , where the “parent structures” of the corresponding and dianions have drastically different symmetries. The structures generated by substitutions on , as well as , are compared and interrelated for both and . The carborane generated from the dianion provides an illustrative example of carborane rearrangements, reverting after geometry optimization to the second lowest meta isomer of symmetry, 0.12 eV above the lowest energy para isomer. This demonstrates the amphidirectional character of the boron connection. It is found that is the upper limit of the range in which the isolobal analogy is fully operative not only for the lowest but also for the second and third lowest energy states. For all three pairs of structures are isovalent, isostructural, and isolobal. For large values of the boron connection, although not fully isolobal, is still valid in a broader and more general sense, still providing deeper and broader fundamental understanding and insight for both species. It was also found that the clusters are not fully homologous (isolobal) neither to the isovalent clusters nor to the corresponding carboranes, preferring structures in which the two carbon atoms are always in adjacent positions. This is attributed to the relative weakness of the Ge–Ge and Ge–C bonds relative to Si–Si and Si–C bonds and the “inert pair effect.”

Slow photoelectron velocitymap imaging spectroscopy of , , and
View Description Hide DescriptionHigh resolution photoelectron spectra of , , and anions are reported, obtained using slow electron velocitymap imaging. The spectra show well resolved transitions to the neutral ground state of all three species and to the excited state of and . This study yields the adiabatic electron affinity of , , and , the spinorbit splitting in the state of each radical, and the term energy of the state in and . Relatively little vibrational activity is observed, indicating small geometry changes upon photodetachment. This result, plus the observation of transitions to neutral quartet states, indicates that the anions all have linear ground states.

The chemistry of nitrogen oxides on small sizeselected cobalt clusters,
View Description Hide DescriptionFourier transform ion cyclotron resonance mass spectrometry has been employed to study the reactions of gasphase cationic cobaltclusters, , with nitric oxide, NO, and nitrous oxide, , under single collision conditions. Isolation of the initial cluster permits detailed investigation of fragmentation channels which characterize the reactions of all but the largest clusters studied. In reaction with , most clusters generate the monoxides without fragmentation, cobalt atom loss accompanying only subsequent reactions. By contrast, chemisorption of even a single NO molecule is accompanied by fragmentation of the cluster. The measured rate coefficients for the reaction as a function of cluster size are significantly smaller than those calculated using the surface charge capture model, while for NO the rates are comparable. The reactions have been studied under high coverage conditions by storing clusters for extended periods to permit multiple reactions to occur. This leads to interesting chemistry on the surface of the cluster resulting in the formation of stable oxide clusters and/or the decomposition of nitric oxide on the cluster with the resulting loss of molecular nitrogen.

The simulated photoelectron spectrum of 1propynide
View Description Hide DescriptionThe negative ion photoelectron spectrum of 1propynide is computed by employing the multimode vibronic coupling approach. A threestate quasidiabatic Hamiltonian, , is reported, which accurately represents the ab initio determined equilibrium geometries and harmonic frequencies of the ground state as well as the lowlying Jahn–Teller distorted components of the excited state. It also reproduces both the minimum energy crossing point (MECP) on the symmetryrequired conical intersection seam and the MECP on the same symmetry conical intersection seam. includes all terms through second order in internal coordinates for both the diagonal and offdiagonal blocks. It is centered at the MECP and is determined using ab initio gradients and derivative couplings near both the MECP and the equilibrium geometry. This construction is enabled by a recently reported normal equation based algorithm. The symmetry of the system is used to significantly reduce the computational cost of the ab initio treatment. This is then expressed in a vibronic basis that is chosen for its ability to reduce the dimension of the vibronic expansion. The vibronic Hamiltonian matrix is diagonalized to obtain a negative ion photoelectron spectrum for 1propynide. The determined spectrum compares favorably with previous spectroscopic results. In particular, the lines attributable to the state are found to be much weaker than those corresponding to the state of 1propynyl. This diminution of the state is attributable principally to the conical intersection rather than an intrinsically small electronic transition moment for the production of the state.
 Condensed Phase Dynamics, Structure, and Thermodynamics: Spectroscopy, Reactions, and Relaxation

High frequency dynamics in liquids and supercritical fluids: A comparative inelastic xray scattering study
View Description Hide DescriptionThe microscopic dynamics of four prototype systems (water, ammonia, nitrogen, and neon) across the critical temperature has been investigated by means of highresolution inelastic xray scattering. The experimental line shape has been described using a model based on the memory function formalism. Two main relaxations, the thermal and the structural one, were observed in all the investigated systems. We found that the microscopic mechanism driving the structural relaxation clearly changes, being mainly governed by intermolecular bond rearrangements below the critical temperature and by binary collisions above it. Moreover, we observed that the relative weight of the thermal relaxation systematically increases on approaching the critical temperature, thus allowing for the observation of a transition from an adiabatic to an isothermal regime of sound propagation. Finally, we found the presence of an additional instantaneous relaxation, likely related to the coupling between collective vibrational modes and intramolecular degrees of freedom.

A direct test of the correlation between elastic parameters and fragility of ten glass formers and their relationship to elastic models of the glass transition
View Description Hide DescriptionWe present an impulsive stimulated scattering test of the “shoving model” of the glass transition and of the correlation between the fragility index and the ratio of instantaneous elastic moduli of eight supercooled liquids. Samples of triphenyl phosphite, DC704 (tetramethyl tetraphenyl trisiloxane), fluoroaniline, , diethyl phthalate, propylene carbonate, toluidine, phenyl salicylate (salol), 2benzylphenol, and Santovac 5 (5phenyl 4ether), were cooled to their respective glass transition temperatures and the elastic moduli directly measured at the highest accessible shear frequencies. The shear modulus was then measured every 2 K as deeply as permitted into the liquid state for all liquids except propylene carbonate. Our results, in conjunction with dynamical relaxation data for these liquids obtained from the literature, lend credence to the notion that the dynamics of the glass transition are governed by the evolution of the shear modulus but do not suggest a strong correlation between the fragility index and the ratio of the elastic moduli.

Nanometer range correlations between molecular orientations in liquids of molecules with perfect tetrahedral shape: , , , and
View Description Hide DescriptionNeutron and xray weighted total scattering structure factors of liquidcarbon, silicon, germanium, and tin tetrachlorides, , , , and , have been interpreted by means of reverse Monte Carlo modeling. For each material the two sets of diffraction data were modeled simultaneously, thus providing sets of particle coordinates that were consistent with two experimental structure factors within errors. From these particle configurations, partial radial distribution functions, as well as correlation functions characterizing mutual orientations of molecules as a function of distance between molecular centers were calculated. Via comparison with reference systems, obtained by hard sphere Monte Carlo simulations, we demonstrate that orientational correlations characterizing these liquids are much longer ranged than expected, particularly in carbon tetrachloride.