Volume 128, Issue 24, 28 June 2008
 ANNOUNCEMENTS


Announcement: Online manuscript submission and peer review via Peer XPress
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 COMMUNICATIONS


A generalized Poisson equation and shortrange selfinteraction energies
View Description Hide DescriptionWe generalize the Poisson equation to attenuated Newtonian potentials. If the attenuation is at least exponential, the equation provides a local mapping between the density and its potential. We use this to derive several density functionals for the shortrange selfinteraction energy.

A prepolarizer for dissolution dynamic nuclear polarization
View Description Hide DescriptionApart from their very classical use to build polarized targets for particle physics, the methods of dynamic nuclear polarization (DNP) have more recently found application for sensitivity enhancement in highresolution NMR, both in the solid and in the liquid state. It is often thought that the possible signal enhancement in such applications deteriorates when the DNP is performed at higher fields. We show that for a dissolutionDNP method that uses conventional (2,2,6,6tetramethylpiperidine 1oxyl) radicals as the paramagnetic agent, this is not the case for fields up to .

Absolute levelresolved reactive and inelastic rate constants in
View Description Hide DescriptionWe have used nuclear paritychanging collisions to obtain absolute leveltolevel rate constants for reactive scattering in a triatomic system with identical nuclei. We have determined rate constants for the system, from laserinduced fluorescence spectra of lithium vapor in a heat pipe oven. Paritypreserving collisions yielded measurements of absolute rotationally and vibrationally inelastic rate constants as well. We compare the reactive rate constants with statistical prior distributions and the inelastic results with previously measured results on the system.
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 ARTICLES

 Theoretical Methods and Algorithms

Timedependent densityfunctional theory in the projector augmentedwave method
View Description Hide DescriptionWe present the implementation of the timedependent densityfunctional theory both in linearresponse and in timepropagation formalisms using the projector augmentedwave method in realspace grids. The two technically very different methods are compared in the linearresponse regime where we found perfect agreement in the calculated photoabsorption spectra. We discuss the strengths and weaknesses of the two methods as well as their convergence properties. We demonstrate different applications of the methods by calculating excitation energies and excited state Born–Oppenheimer potential surfaces for a set of atoms and molecules with the linearresponse method and by calculating nonlinear emission spectra using the timepropagation method.

Atomic approximation to the projection on electronic states in the DouglasKrollHess approach to the relativistic KohnSham method
View Description Hide DescriptionWe suggest an approximate relativistic model for economical allelectron calculations on molecular systems that exploits an atomic ansatz for the relativistic projection transformation. With such a choice, the projection transformation matrix is by definition both transferable and independent of the geometry. The formulation is flexible with regard to the level at which the projection transformation is approximated; we employ the freeparticle Foldy–Wouthuysen and the secondorder DouglasKrollHess variants. The (atomic) infiniteorder decoupling scheme shows little effect on structural parameters in scalarrelativistic calculations; also, the use of a screened nuclear potential in the definition of the projection transformation shows hardly any effect in the context of the present work. Applications to structural and energetic parameters of various systems (diatomics AuH, AuCl, and , two structural isomers of , and uranyl dication solvated by 36 water ligands) show that the atomic approximation to the conventional secondorder DouglasKrollHess projection (ADKH) transformation yields highly accurate results at substantial computational savings, in particular, when calculating energy derivatives of larger systems. The sizedependence of the intrinsic error of the ADKH method in extended systems of heavy elements is analyzed for the atomization energies of clusters .

Probability distributions of molecular observables computed from Markov models
View Description Hide DescriptionMolecular dynamics (MD) simulations can be used to estimate transition rates between conformational substates of the simulated molecule. Such an estimation is associated with statistical uncertainty, which depends on the number of observed transitions. In turn, it induces uncertainties in any property computed from the simulation, such as free energy differences or the time scales involved in the system’s kinetics. Assessing these uncertainties is essential for testing the reliability of a given observation and also to plan further simulations in such a way that the most serious uncertainties will be reduced with minimal effort. Here, a rigorous statistical method is proposed to approximate the complete statistical distribution of any observable of an MD simulation provided that one can identify conformational substates such that the transition process between them may be modeled with a memoryless jump process, i.e., Markov or Master equation dynamics. The method is based on sampling the statistical distribution of Markov transition matrices that is induced by the observed transition events. It allows physically meaningful constraints to be included, such as sampling only matrices that fulfill detailed balance, or matrices that produce a predefined equilibrium distribution of states. The method is illustrated on MD simulations of a hexapeptide for which the distributions and uncertainties of the free energy differences between conformations, the transition matrix elements, and the transition matrix eigenvalues are estimated. It is found that both constraints, detailed balance and predefined equilibrium distribution, can significantly reduce the uncertainty of some observables.

Comparative ab initio studies on the molecular structure and spectroscopic properties of : Single reference versus multireference methods
View Description Hide DescriptionThe electronic excitation energies, molecular geometry, quadratic force fields, and vibrational frequencies in the ground and lowlying excited and electronic states of iron difluoride are studied at sophisticated levels of theory. Two families of basis sets, nonrelativistic and Douglas–Kroll–Hess relativistic, are used that range in quality from triple to quintuple. These are augmented by additional diffuse functions (on fluorine atoms) and tight functions (on all atoms) for the description of corevalence correlation and utilized to determine complete basis set molecular properties. The quality of electron correlation treatment using conventional single reference coupled cluster methods CCSD and CCSD(T) is compared to that attained at the multiconfigurational quasidegenerate secondorder perturbation theory and the electron attachment equationofmotion coupled cluster (EOMEACCSD) levels. Spinorbit coupling effects are studied by the SOMCQDPT2 method using the full Breit–Pauli spinorbit operator. Effects of spin contamination in the coupled cluster molecular calculations are carefully analyzed. Results of the single reference CCSD(T) and multireference calculations are found to be in a remarkable agreement. The calculations indicate that the EOMEACC approach provides a suitable tool for an accurate treatment of and other systems where delicate electron correlationeffects have to be carefully dealt with. The inclusion of relativistic effects is shown to be necessary for an accurate description of the molecular geometry and excitation energies of . The results of calculations are in good agreement with the experimental data available. The predicted molecular properties are compared to those of the related .

Integrated computational approach to vibrationally resolved electronic spectra: Anisole as a test case
View Description Hide DescriptionA new general and effective procedure to compute Franck–Condon spectra from first principles is exploited to elucidate the subtle features of the vibrationally resolved optical spectra of anisole. Methods based on the density functional theory and its timedependent extension for electronic excited states [ and ] have been applied to geometry optimizations and harmonic frequency calculations. Perturbative anharmonic frequencies [J. Chem. Phys.122, 014108 (2005)] have been calculated for the ground state, and the Duschinsky matrix elements have been used to evaluate the corresponding anharmonic corrections for the first excited electronic state. The relative energetics of both electronic states has been refined by single point calculations at the coupled clusters (CC) level with the augccpVDZ basis set. Theoreticalspectra have been evaluated using a new optimized implementation for the effective computation of Franck–Condon factors. The remarkable agreement between theoretical and experimental spectra allowed for revision of some assignments of fundamental vibrations in the state of anisole.

Dynamic correlations with timedependent quantum Monte Carlo
View Description Hide DescriptionIn this paper, we solve quantum manybody problem by propagating ensembles of trajectories and guiding waves in physical space. We introduce the “effective potential” correction within the recently proposed timedependent quantum Monte Carlo methodology to incorporate the nonlocal quantum correlationeffects between the electrons. The associated correlation length is calculated by adaptive kernel density estimation over the walker distribution. The general formalism is developed and tested on onedimensional helium atom in laser field of different intensities and carrier frequencies. Good agreement with exact results for the atomic ionization is obtained.

Rototranslational sum rules for electromagnetic hypershielding at the nuclei and related atomic Cartesian derivatives of the optical rotatory power
View Description Hide DescriptionTwo molecular properties, the nuclear electromagnetic hypershielding and the gradient of the electric dipole–magnetic dipole polarizability, have been calculated using the timedependent Hartree–Fock method. Provided the Hellmann–Feynman theorem is satisfied, these quantities are equivalent and are related through the relation, where is the atomic number of atom and the magnitude of the electron charge. In such a case, the determination of the nuclear electromagnetic hypershielding presents the computational advantage over the evaluation of the gradient of of requiring only the knowledge of nine mixed secondorder derivatives of the density matrix with respect to both electric and magnetic fields instead of the ( is the number of atoms) derivatives of the density matrix with respect to the Cartesian coordinates . It is shown here for the molecule that very large basis sets such as the augccpVQZ or the R12 basis are required to satisfy the Hellmann–Feynman theorem. These basis set requirements have been substantiated by considering the corresponding rototranslational sum rules. The origin dependence of the rototranslational sum rules for the gradient of has then been theoretically described and verified for the molecule.

Quantum initial condition sampling for linearized density matrix dynamics: Vibrational pure dephasing of iodine in krypton matrices
View Description Hide DescriptionThis paper reviews the linearized path integral approach for computing time dependent properties of systems that can be approximated using a mixed quantumclassical description. This approach is applied to studying vibrational pure dephasing of ground state molecular iodine in a rare gas matrix. The Feynman–Kleinert optimized harmonic approximation for the full system density operator is used to sample initial conditions for the bath degrees of freedom. This extremely efficient approach is compared to alternative initial condition sampling techniques at low temperatures where classical initial condition sampling yields dephasing rates that are nearly an order of magnitude too slow compared to quantum initial condition sampling and experimental results.

Formulation of improved basis sets for the study of polymer dynamics through diffusion theory methods
View Description Hide DescriptionIn this work a new method is proposed for the choice of basis functions in diffusion theory (DT) calculations. This method, named hybrid basis approach (HBA), combines the two previously adopted long time sorting procedure (LTSP) and maximum correlation approximation (MCA) techniques; the first emphasizing contributions from the long time dynamics, the latter being based on the local correlations along the chain. In order to fulfill this task, the HBA procedure employs a first order basis set corresponding to a high order MCA one and generates upper order approximations according to LTSP. A test of the method is made first on a melt of cis1,4polyisoprene decamers where HBA and LTSP are compared in terms of efficiency. Both convergence properties and numerical stability are improved by the use of the HBA basis set whose performance is evaluated on local dynamics, by computing the correlation times of selected bond vectors along the chain, and on global ones, through the eigenvalues of the diffusion operator . Further use of the DT with a HBA basis set has been made on a 71mer of syndiotactic trans1,2polypentadiene in toluene solution, whose dynamical properties have been computed with a high order calculation and compared to the “numerical experiment” provided by the molecular dynamics (MD) simulation in explicit solvent. The necessary equilibrium averages have been obtained by a vacuum trajectory of the chain where solvent effects on conformational properties have been reproduced with a proper screening of the nonbonded interactions, corresponding to a definite value of the mean radius of gyration of the polymer in vacuum. Results show a very good agreement between DT calculations and the MD numerical experiment. This suggests a further use of DT methods with the necessary input quantities obtained by the only knowledge of some experimental values, i.e., the mean radius of gyration of the chain and the viscosity of the solution, and by a suitable vacuum trajectory, with great savings in computational time required. This offers a theoretical bridge between the experimental static and dynamical properties of polymers.

Improved configuration space sampling: Langevin dynamics with alternative mobility
View Description Hide DescriptionWe present a new and efficient method for determining optimal configurations of a large number of interacting particles. We use a coarsegrained stochastic Langevin equation in the overdamped limit to describe the dynamics of this system and replace the standard mobility by an effective space dependent inverse Hessian correlation matrix. Due to the analogy of the drift term in the Langevin equation and the update scheme in Newton’s method, we expect accelerated dynamics or improved convergence in the convex part of the potential energy surface. The stochastic noise term, however, is not only essential for proper thermodynamic sampling but also allows the system to access transition states in the concave parts of . We employ a Broyden–Fletcher–Goldfarb–Shannon method for updating the local mobility matrix. Quantitative analysis for one and two dimensional systems shows that the new method is indeed more efficient than standard methods with constant effective friction. Due to the construction, our effective mobility adapts high values/low friction in configurations which are less optimal and low values/high friction in configurations that are more optimal.

Quantitative prediction of gasphase nuclear magnetic shielding constants
View Description Hide DescriptionBenchmark calculations of nuclear magnetic shielding constants are presented for a set of . Nearquantitative accuracy (ca. deviation from experiment) is achieved if (1) electron correlation is adequately treated by employing the coupledcluster singles and doubles (CCSD) model augmented by a perturbative correction for triple excitations [CCSD(T)], (2) large (uncontracted) basis sets are used, (3) gaugeincluding atomic orbitals are used to ensure gaugeorigin independence, (4) calculations are performed at accurate equilibrium geometries [obtained from CCSD(T)/ccpVTZ calculations correlating all electrons], and (5) vibrational averaging and temperature corrections via secondorder vibrational perturbation theory (VPT2) are included. For the CCSD(T)/13s9p4d3f calculations corrected for vibrational effects, mean and standard deviation from experiment are and , respectively. Less elaborate theoretical treatments result in larger errors. Consideration of relative shifts can reduce the mean deviation (through an appropriately chosen reference compound), but does not change the standard deviation. Densityfunctional theory calculations of absolute and relative nuclear magnetic shielding constants are found to be, at best, as accurate as the corresponding Hartree–Fock selfconsistentfield calculations and are not improved by consideration of vibrational effects. Molecular systems containing fluorineoxygen, fluorinenitrogen, and fluorinefluorine bonds are found to be more challenging than the other investigated molecules for the considered theoretical methods.

Hartree–Fock orbitals significantly improve the reaction barrier heights predicted by semilocal density functionals
View Description Hide DescriptionSemilocal density functional theory predictions for the barrier heights of representative hydrogen transfer, heavyatom transfer, and nucleophilic substitution reactions are significantly improved in nonselfconsistent calculations using Hartree–Fock orbitals. Orbitals from hybrid calculations yield related improvements. These results provide insight into compensating for oneelectron selfinteraction error in semilocal density functional theory.

Simple coupledcluster singles and doubles method with perturbative inclusion of triples and explicitly correlated geminals: The model
View Description Hide DescriptionTo approach the complete basis set limit of the “goldstandard” coupledcluster singles and doubles plus perturbative triples [CCSD(T)] method, we extend the recently proposed perturbative explicitly correlated coupledcluster singles and doubles method, [E. F. Valeev, Phys. Chem. Chem. Phys.8, 106 (2008)], to account for the effect of connected threeelectron correlations. The natural choice of the zerothorder Hamiltonian produces a perturbation expansion with rigorously separable secondorder energy corrections due to the explicitly correlated geminals and conventional triple and higher excitations. The resulting energy is defined as a sum of the standard CCSD(T) energy and an amplitudedependent geminal correction. The method is technically very simple: Its implementation requires no modification of the standard CCSD(T) program and the formal cost of the geminal correction is small. We investigate the performance of the openshell version of the method as a possible replacement of the standard completebasisset CCSD(T) energies in the high accuracy extrapolated ab initiothermochemistry model of Stanton et al. [J. Chem. Phys.121, 11599 (2004)]. Correlation contributions to the heat of formation computed with the new method in an basis set have mean absolute basis set errors of 2.8 and when is T and Q, respectively. The corresponding errors of the standard CCSD(T) method are 9.1, 4.0, and when , Q, and 5. Simple twopoint basis set extrapolations of standard CCSD(T) energies perform better than the explicitly correlated method for absolute correlation energies and atomization energies, but no such advantage found when computing heats of formation. A simple Schwenketype twopoint extrapolation of the energies with yields the most accurate heats of formation found in this work, in error on average by and at most by .

The multiscale coarsegraining method. I. A rigorous bridge between atomistic and coarsegrained models
View Description Hide DescriptionCoarsegrained (CG) models provide a computationally efficient method for rapidly investigating the long time and lengthscale processes that play a critical role in many important biological and soft matter processes. Recently, Izvekov and Voth introduced a new multiscale coarsegraining (MSCG) method [J. Phys. Chem. B109, 2469 (2005); J. Chem. Phys.123, 134105 (2005)] for determining the effective interactions between CG sites using information from simulations of atomically detailed models. The present work develops a formal statistical mechanical framework for the MSCG method and demonstrates that the variational principle underlying the method may, in principle, be employed to determine the manybody potential of mean force (PMF) that governs the equilibrium distribution of positions of the CG sites for the MSCG models. A CG model that employs such a PMF as a “potential energy function” will generate an equilibrium probability distribution of CG sites that is consistent with the atomically detailed model from which the PMF is derived. Consequently, the MSCG method provides a formal multiscale bridge rigorously connecting the equilibrium ensembles generated with atomistic and CG models. The variational principle also suggests a class of practical algorithms for calculating approximations to this manybody PMF that are optimal. These algorithms use computer simulation data from the atomically detailed model. Finally, important generalizations of the MSCG method are introduced for treating systems with rigid intramolecular constraints and for developing CG models whose equilibrium momentum distribution is consistent with that of an atomically detailed model.

The multiscale coarsegraining method. II. Numerical implementation for coarsegrained molecular models
View Description Hide DescriptionThe multiscale coarsegraining (MSCG) method [S. Izvekov and G. A. Voth, J. Phys. Chem. B109, 2469 (2005);J. Chem. Phys.123, 134105 (2005)] employs a variational principle to determine an interaction potential for a CG model from simulations of an atomically detailed model of the same system. The companion paper proved that, if no restrictions regarding the form of the CG interaction potential are introduced and if the equilibrium distribution of the atomistic model has been adequately sampled, then the MSCG variational principle determines the exact manybody potential of mean force (PMF) governing the equilibrium distribution of CG sites generated by the atomistic model. In practice, though, CG force fields are not completely flexible, but only include particular types of interactions between CG sites, e.g., nonbonded forces between pairs of sites. If the CG force field depends linearly on the force field parameters, then the vector valued functions that relate the CG forces to these parameters determine a set of basis vectors that span a vector subspace of CG force fields. The companion paper introduced a distance metric for the vector space of CG force fields and proved that the MSCG variational principle determines the CG force force field that is within that vector subspace and that is closest to the force field determined by the manybody PMF. The present paper applies the MSCG variational principle for parametrizing molecular CG force fields and derives a linear least squares problem for the parameter set determining the optimal approximation to this manybody PMF. Linear systems of equations for these CG force field parameters are derived and analyzed in terms of equilibrium structural correlation functions. Numerical calculations for a onesite CG model of methanol and a molecular CG model of the ionic liquid are provided to illustrate the method.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Evidence of an isomeric pair in furan…HCl: Fourier transform infrared spectroscopy and ab initio calculations
View Description Hide DescriptionFor the first time the coexistence of a  and a complex in the system has been observed, in the same supersonic expansion of a molecular jet seeded with argon (or helium) or in a flowcooled cell at . This is an exception to the third of the Legon–Miller rules which claims the structure to be the only one to exist. On the grounds of energetic considerations and band contour simulations, two observed bands at 2787.7 and of the HCl stretching frequency are assigned to the two complexes, recorded as Fourier transforminfrared spectra with a resolution between 0.2 and . Complementary calculations show that the use of the standard secondorder Møller–Plesset perturbation theory may be erroneous for such a complex, due of the overestimation of the dispersion contribution with respect to the electrostatic term. It is finally established that only a balanced version of the secondorder Møller–Plesset perturbation method, spincomponent scaledMP2, or a higher level of theory like a coupledcluster approach, can provide a reliable energetic analysis for this complex.