Volume 136, Issue 7, 21 February 2012

In the first of a series of four papers on hydrogen under pressure, and its transitions from an initiating molecular state, we begin by defining carefully the problem, and setting the distance scale of interactions of protons and electrons in molecular aggregates of the first of the elements. Following a review of the experimental situation, in particular the phase diagram of hydrogen, in as much as it is known, and the behavior of its vibrons and rotons, we move onto the setting up of a numerical laboratory for probing the underlying physics and chemistry of interactions in hydrogen as the pressure increases. The laboratory consists of the preferred static structures emerging from calculations on the system in the range of 1 atm to 500 GPa, those of Pickard and Needs. The intermolecular (interpair) H···H separations naturally decrease with increasing pressure, first rapidly so, then more slowly. The intramolecular (intrapair) H–H distances vary over a much smaller scale (0.05 Å) as the pressure increases, first decreasing, then increasing, and finally decreasing. We define an equalization function to gauge the approach to equality of the first neighbor and shortest next neighbor H (proton) separations in this numerical laboratory. And we find that metallization is likely to occur before bond equalization.
 COMMUNICATIONS


Communication: Variational manybody expansion: Accounting for exchange repulsion, charge delocalization, and dispersion in the fragmentbased explicit polarization method
View Description Hide DescriptionA fragmentbased variational manybody (VMB) expansion method is described to directly account for exchange repulsion, charge delocalization (charge transfer) and dispersion interactions in the explicit polarization (XPol) method. The present VMB/XPol approach differs from other fragment molecular orbital (FMO) techniques in two major aspects. First, the wave function for the monomeric system is variationally optimized using standard XPol method, as opposed to the iterative update procedure adopted in FMO. Second, the mutual polarizations in the dimeric terms are also variationally determined, whereas singlepoint energy calculations of the individual dimers embedded in a static monomer field are used in FMO. The secondorder (twobody) VMB (VMB2) expansion method is illustrated on a series of water hexamer complexes and one decamer cluster, making use of HartreeFock theory, MP2, and the PBE1 and M06 density functionals to represent the monomer and dimer fragments. The computed binding energies are within 2 kcal/mol of the corresponding results from fully delocalized calculations. Energy decomposition analyses reveal specific dimeric contributions to exchange repulsion, charge delocalization, and dispersion. Since the wave functions for onebody and all twobody terms are variationally optimized in VMB2 and XPol, it is straightforward to obtain analytic gradient without the additional coupledperturbed HartreeFock step. Thus, the method can be useful for molecular dynamics simulations.

Communication: Translational Brownian motion for particles of arbitrary shape
View Description Hide DescriptionA single Brownian particle of arbitrary shape is considered. The timedependent translational mean square displacement W(t) of a reference point at this particle is evaluated from the Smoluchowski equation. It is shown that at times larger than the characteristic time scale of the rotational Brownian relaxation, the slope of W(t) becomes independent of the choice of a reference point. Moreover, it is proved that in the longtime limit, the slope of W(t) is determined uniquely by the trace of the translationaltranslational mobility matrix evaluated with respect to the hydrodynamic center of mobility. The result is applicable to dynamic light scatteringmeasurements, which indeed are performed in the longtime limit.
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 ARTICLES

 Theoretical Methods and Algorithms

Unraveling rotationvibration mixing in highly fluxional molecules using diffusion Monte Carlo: Applications to and H_{3}O^{+}
View Description Hide DescriptionA thorough examination of the use of fixednode diffusionMonte Carlo for the study of rotationvibration mixing in systems that undergo large amplitude vibrational motions is reported. Using as a model system, the overall accuracy of the method is tested by comparing the results of these calculations with those from converged variational calculations. The effects of the presence of a large amplitude inversion mode on rotationvibration mixing are considered by comparing the results with those for H_{3}O^{+}. Finally, analysis of the results of the fixednode diffusionMonte Carlo calculations performed in different nodal regions is found to provide clear indications of when some of the methodology's underlying assumptions are breaking down as well as provide physical insights into the form of the rotationvibration coupling that is most likely responsible.

Bifidelity fitting and optimization
View Description Hide DescriptionA common feature in computations of chemical and physical properties is the investigation of phenomena at different levels of computational accuracy. Less accurate computations are used to provide a relatively quick understanding of the behavior of a system and allow a researcher to focus on regions of initial conditions and parameter space where interesting phenomena are likely to occur. These inexpensive calculations are often discarded when more accurate calculations are performed. This paper demonstrates how computations at different levels of accuracy can be simultaneously incorporated to study chemical and physical phenomena with less overall computational effort than the most expensive level of computation. A smaller set of computationally expensive calculations is needed because the set of expensive calculations is correlated with the larger set of less expensive calculations. We present two applications. First, we demonstrate how potential energy surfaces can be fit by simultaneously using results from two different levels of accuracy in electronic structure calculations. In the second application, we study the optical response of metallic nanostructures. The optical response is generated with calculations at two different grid resolutions, and we demonstrate how using these two levels of computation in a correlated fashion can more efficiently optimize the response.

A generalized solidstate nudged elastic band method
View Description Hide DescriptionA generalized solidstate nudged elastic band (GSSNEB) method is presented for determining reaction pathways of solid–solid transformations involving both atomic and unitcell degrees of freedom. We combine atomic and cell degrees of freedom into a unified description of the crystal structure so that calculated reaction paths are insensitive to the choice of periodic cell. For the rocksalt to wurtzite transition in CdSe, we demonstrate that the method is robust for mechanisms dominated either by atomic motion or by unitcell deformation; notably, the lowestenergy transition mechanism found by our GSSNEB changes with cell size from a concerted transformation of the cell coordinates in small cells to a nucleation event in large cells. The method is efficient and can be applied to systems in which the force and stress tensor are calculated using density functional theory.

A rare event sampling method for diffusion Monte Carlo using smart darting
View Description Hide DescriptionWe identify a set of multidimensional potential energy surfaces sufficiently complex to cause both the classical parallel tempering and the guided or unguided diffusionMonte Carlo methods to converge too inefficiently for practical applications. The mathematical model is constructed as a linear combination of decoupled Double Wells [(DDW)_{ n }]. We show that the set (DDW)_{ n } provides a serious test for new methods aimed at addressing rare event sampling in stochastic simulations. Unlike the typical numerical tests used in these cases, the thermodynamics and the quantum dynamics for (DDW)_{ n } can be solved deterministically. We use the potential energy set (DDW)_{ n } to explore and identify methods that can enhance the diffusionMonte Carlo algorithm. We demonstrate that the smart darting method succeeds at reducing quasiergodicity for n ≫ 100 using just 1 × 10^{6} moves in classical simulations (DDW)_{ n }. Finally, we prove that smart darting, when incorporated into the regular or the guided diffusionMonte Carlo algorithm, drastically improves its convergence. The new method promises to significantly extend the range of systems computationally tractable by the diffusionMonte Carlo algorithm.

Efficient simultaneous reverse Monte Carlo modeling of pairdistribution functions and extended xrayabsorption fine structure spectra of crystalline disordered materials
View Description Hide DescriptionAn efficient implementation of simultaneous reverse Monte Carlo (RMC) modeling of pair distribution function (PDF) and EXAFSspectra is reported. This implementation is an extension of the technique established by Krayzman et al. [J. Appl. Cryst.42, 867 (2009)] in the sense that it enables simultaneous realspace fitting of xray PDF with accurate treatment of Qdependence of the scattering crosssections and EXAFS with multiple photoelectron scattering included. The extension also allows for atom swaps during EXAFS fits thereby enabling modeling the effects of chemical disorder, such as migrating atoms and vacancies. Significant acceleration of EXAFS computation is achieved via discretization of effective path lengths and subsequent reduction of operation counts. The validity and accuracy of the approach is illustrated on small atomic clusters and on 5500–9000 atom models of bccFe and αFe_{2}O_{3}. The accuracy gains of combined simultaneous EXAFS and PDF fits are pointed out against PDFonly and EXAFSonly RMC fits. Our modeling approach may be widely used in PDF and EXAFS based investigations of disordered materials.

Approaching the bulk limit with finite cluster calculations using local increments: The case of LiH
View Description Hide DescriptionFinitecluster calculations employing highlevel wavefunctionbased ab initio methods and extended atomicorbital basis sets are used to determine local energy increments for bulk LiH. It is shown that these increments can be converged with respect to cluster size and pointcharge embedding so as to yield bulk cohesive energies with an accuracy of better than 1 mE_{ h }, both at the HartreeFock and at correlated levels. Instrumental for the efficiency of the scheme is the introduction of nonorthogonal orbitals, at an intermediate stage.
 Advanced Experimental Techniques

Electronic states of cyclophanes with small bridges
View Description Hide DescriptionElectronic absorption and magnetic circular dichroism were recorded for five cyclophanes with ethano bridges: [2.2]paracyclophane, (1,2,4)[2.2.2]cyclophane, (1,2,4;1,2,5)[2.2.2]cyclophane, (1,2,3,4,5,6)(1,2,3,4,5,6)cyclophane, and trans[2.2]metacyclophane. Spectral and structuralanalyses were based on geometry optimization and calculations of transition energies, carried out using density functional theory methods. The assignments have been proposed for several electronic transitions observed in the region below 52 000 cm^{−1}. The observation of transitions which should be forbidden in the high D _{2h } symmetry [2.2]paracyclophane suggests a twisted ground state structure of D _{ 2 } symmetry, although the former structure with large amplitude vibrations at room temperature cannot be excluded. The PBE0 functional turned out to appropriately reproduce the interring distances and electronic transition energies.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Scattering resonances in slow NH_{3}–He collisions
View Description Hide DescriptionWe theoretically study slow collisions of NH_{3} molecules with He atoms, where we focus in particular on the observation of scattering resonances. We calculate statetostate integral and differential cross sections for collision energies ranging from 10^{−4} cm^{−1} to 130 cm^{−1}, using fully converged quantum closecoupling calculations. To describe the interaction between the NH_{3} molecules and the He atoms, we present a fourdimensional potential energy surface, based on an accurate fit of 4180 ab initio points. Prior to collision, we consider the ammonia molecules to be in their antisymmetric umbrella state with angular momentumj = 1 and projection k = 1, which is a suitable state for Stark deceleration. We find pronounced shape and Feshbach resonances, especially for inelastic collisions into the symmetric umbrella state with j = k = 1. We analyze the observed resonant structures in detail by looking at scatteringwavefunctions, phase shifts, and lifetimes. Finally, we discuss the prospects for observing the predicted scattering resonances in future crossed molecular beam experiments with a Starkdecelerated NH_{3}beam.

B80 and B101–103 clusters: Remarkable stability of the coreshell structures established by validated density functionals^{a)}
View Description Hide DescriptionPrompted by the very recent claim that the volleyballshaped B80fullerene[X. Wang, Phys. Rev. B82, 153409 (2010)] is lower in energy than the B80buckyball[N. G. Szwacki, A. Sadrzadeh, and B. I. Yakobson, Phys. Rev. Lett.98, 166804 (2007)] and coreshell structure[J. Zhao, L. Wang, F. Li, and Z. Chen, J. Phys. Chem. A114, 9969 (2010)], and inspired by the most recent finding of another coreshell isomer as the lowest energy B80 isomer [S. De, A. Willand, M. Amsler, P. Pochet, L. Genovese, and S. Goedecher, Phys. Rev. Lett.106, 225502 (2011)], we carefully evaluated the performance of the density functional methods in the energetics of boron clusters and confirmed that the coreshell construction (stuffed fullerene) is thermodynamically the most favorable structural pattern for B80. Our global minimum search showed that both B101 and B103 also prefer a coreshell structure and that B103 can reach the complete coreshell configuration. We called for great attention to the theoretical community when using density functionals to investigate boronrelated nanomaterials.

A femtosecond velocity map imaging study on Bband predissociation in CH_{3}I. II. The and vibronic levels
View Description Hide DescriptionFemtosecond timeresolved velocity map imagingexperiments are reported on several vibronic levels of the second absorption band (Bband) of CH_{3}I, including vibrational excitation in the ν_{2} and ν_{3} modes of the bound ^{3} R _{1}(E) Rydberg state. Specific predissociation lifetimes have been determined for the and vibronic levels from measurements of timeresolved I*(^{2} P _{1/2}) and CH_{3} fragment images, parent decay, and photoelectron images obtained through both resonant and nonresonant multiphoton ionization. The results are compared with our previously reported predissociation lifetime measurements for the band origin [Gitzinger et al., J. Chem. Phys.132, 234313 (2010)10.1063/1.3455207]. The result, previously reported in the literature, where vibrational excitation to the CI stretching mode (ν_{3}) of the CH_{3}I ^{3} R _{1}(E) Rydberg state yields a predissociation lifetime about four times slower than that corresponding to the vibrationless state, whereas predissociation is twice faster if the vibrational excitation is to the umbrella mode (ν_{2}), is confirmed in the present experiments. In addition to the specific vibrational state lifetimes, which were found to be 0.85 ± 0.04 ps and 4.34 ± 0.13 ps for the and vibronic levels, respectively, the time evolution of the fragment anisotropy and the vibrational activity of the CH_{3} fragment are presented. Additional striking results found in the present work are the evidence of ground state I(^{2} P _{3/2}) fragment production when excitation is produced specifically to the vibronic level, which is attributed to predissociationvia the Aband ^{1} Q _{1} potential energy surface, and the indication of a fast adiabatic photodissociation process through the repulsive Aband ^{3} A _{1}(4E) state, after direct absorption to this state, competing with absorption to the vibronic level of the ^{3} R _{1}(E) Rydberg state of the Bband.

Structure and dynamics of the electronically excited C 1 and D 0^{+} states of ArXe from highresolution vacuum ultraviolet spectra
View Description Hide DescriptionVacuum ultraviolet spectra of the C 1 ← X 0^{+} and D 0^{+} ← X 0^{+} band systems of ArXe have been recorded at high resolution. Analysis of the rotational structure of the spectra of several isotopomers, and in the case of Ar^{129}Xe and Ar^{131}Xe also of the hyperfine structure, has led to the derivation of a complete set of spectroscopic parameters for the C 1 and D 0^{+} states. The rovibrational energy level structure of the C 1 state reveals strong homogeneous perturbations with neighboring Ω = 1 electronic states. The analysis of isotopic shifts led to a reassignment of the vibrational structure of the C 1 state. The observation of electronically excited Xe fragments following excitation to the C state rotational levels of f parity indicates that the C state is predissociated by the electronic state of 0^{−} symmetry associated with the Ar(^{1}S0) + Xe( ) dissociation limit. The observed predissociation dynamics differ both qualitatively and quantitatively from the behavior reported in previous investigations. An adiabatic twostate coupling model has been derived which accounts for the irregularities observed in the rovibronic and hyperfine level structure of the C 1 state. The model predicts the existence of a second state of Ω = 1 symmetry, supporting several tunneling/predissociation resonances located ∼200 cm^{−1} above the C 1 state.

Recoil frame photoelectron angular distributions of BF_{3}: A sensitive probe of the shape resonance in the F 1s continuum
View Description Hide DescriptionRecoil frame photoelectron angular distributions (RFPADs) of BF_{3} molecules are presented over the energy region of the shape resonance in the F 1s continuum. Timedependent density functional theory calculations are also given to understand the shape resonance dynamics. The RFPADs have been compared with the theoretical calculations. It is found that the RFPADs calculated by the localized corehole model are in better agreement with the experimental, compared with those by the delocalized core hole. Dipole matrix elements and dipole prepared continuum wavefunctions show that the shape resonance in the F 1sionization continuum of BF_{3} is induced by ppartial waves as previously reported by Swanson et al. [J. Chem. Phys.75, 619 (1981)10.1063/1.442078]. However, due to the couplings with the other partial waves the feature characteristic of the ppartial waves has not been observed in the RFPADs.
 Condensed Phase Dynamics, Structure, and Thermodynamics: Spectroscopy, Reactions, and Relaxation

A fresh look at dense hydrogen under pressure. I. An introduction to the problem, and an index probing equalization of H–H distances
View Description Hide DescriptionIn the first of a series of four papers on hydrogen under pressure, and its transitions from an initiating molecular state, we begin by defining carefully the problem, and setting the distance scale of interactions of protons and electrons in molecular aggregates of the first of the elements. Following a review of the experimental situation, in particular the phase diagram of hydrogen, in as much as it is known, and the behavior of its vibrons and rotons, we move onto the setting up of a numerical laboratory for probing the underlying physics and chemistry of interactions in hydrogen as the pressure increases. The laboratory consists of the preferred static structures emerging from calculations on the system in the range of 1 atm to 500 GPa, those of Pickard and Needs. The intermolecular (interpair) H···H separations naturally decrease with increasing pressure, first rapidly so, then more slowly. The intramolecular (intrapair) H–H distances vary over a much smaller scale (0.05 Å) as the pressure increases, first decreasing, then increasing, and finally decreasing. We define an equalization function to gauge the approach to equality of the first neighbor and shortest next neighbor H (proton) separations in this numerical laboratory. And we find that metallization is likely to occur before bond equalization.

A fresh look at dense hydrogen under pressure. II. Chemical and physical models aiding our understanding of evolving H–H separations
View Description Hide DescriptionIn order to explain the intricate dance of intramolecular (intraprotonpair) H–H separations observed in a numerical laboratory of calculationally preferred static hydrogen structures under pressure, we examine two effects through discrete molecular models. The first effect, we call it physical, is of simple confinement. We review a salient model already in the literature, that of LeSar and Herschbach, of a hydrogen molecule in a spheroidal cavity. As a complement, we also study a hydrogen molecule confined along a line between two helium atoms. As the size of the cavity/confining distance decreases (a surrogate for increasing pressure), in both models the equilibrium proton separation decreases and the force constant of the stretching vibration increases. The second effect, which is an orbital or chemical factor, emerges from the electronic structure of the known molecular transition metal complexes of dihydrogen. In these the H–H bond is significantly elongated (and the vibron much decreased in frequency) as a result of depopulation of the σ _{ g } bonding molecular orbital of H_{2}, and population of the antibonding σ _{ u }* MO. The general phenomenon, long known in chemistry, is analyzed through a specific molecular model of three hydrogen molecules interacting in a ring, a motif found in some candidate structures for dense hydrogen.

A fresh look at dense hydrogen under pressure. III. Two competing effects and the resulting intramolecular HH separation in solid hydrogen under pressure
View Description Hide DescriptionA preliminary discussion of the general problem of localization of wave functions, and the way it is approached in theoretical condensed matter physics (Wannier functions) and theoretical chemistry (localized or fragment orbitals) is followed by an application of the ideas of Paper II in this series to the structures of hydrogen as they evolve under increasing pressure. The idea that emerges is that of simultaneously operative physical (reduction of available space by an increasingly stiff wall of neighboring molecules) and chemical (depopulation of the σ_{g} bonding molecular orbital of H_{2}, and population of the antibonding σ_{u}* MO) factors. The two effects work in the same direction of reducing the intermolecular separation as the pressure increases, but compete, working in opposite directions, in their effect on the intramolecular (nearest neighbor, intrapair) distance. We examine the population of σ_{g} and σ_{u}* MOs in our numerical laboratory, as well as the total electron transfer (small), and polarization (moderate, where allowed by symmetry) of the component H_{2} molecules. From a molecular model of two interacting H_{2} molecules we find a linear relationship between the electron transfer from σ_{g} to σ_{u}* of a hydrogen molecular fragment and the intramolecular HH separation, and that, in turn, allows us to estimate the expected bond lengths in H_{2} under pressure if the first effect (that of simple confinement) was absent. In essence, the intramolecular HH separations under pressure are much shorter than they would be, were there no physical/confinement effect. We then use this knowledge to understand how the separate E and PV terms contribute to hydrogen phase changes with increasing pressure.

A fresh look at dense hydrogen under pressure. IV. Two structural models on the road from paired to monatomic hydrogen, via a possible noncrystalline phase
View Description Hide DescriptionIn this paper, we examine the transition from a molecular to monatomic solid in hydrogen over a wide pressure range. This is achieved by setting up two models in which a single parameter δ allows the evolution from a molecular structure to a monatomic one of high coordination. Both models are based on a cubic Bravais lattice with eight atoms in the unit cell; one belongs to space group , the other to space group . In one moves from effective 1coordination, a molecule, to a simple cubic 6coordinated structure but through a very special point (the golden mean is involved) of 7coordination. In , the evolution is from 1 to 4 and then to 3 to 6coordinate. If one studies the enthalpy as a function of pressure as these two structures evolve (δ increases), one sees the expected stabilization of minima with increased coordination (moving from 1 to 6 to 7 in the structure, for instance). Interestingly, at some specific pressures, there are in both structures relatively large regions of phase space where the enthalpy remains roughly the same. Although the structures studied are always higher in enthalpy than the computationally best structures for solid hydrogen – those emerging from the Pickard and Needs or McMahon and Ceperley numerical laboratories – this result is suggestive of the possibility of a microscopically noncrystalline or “soft” phase of hydrogen at elevated pressures, one in which there is a substantial range of roughly equienthalpic geometries available to the system. A scaling argument for potential dynamic stabilization of such a phase is presented.

The structure of liquid Nmethyl pyrrolidone probed by xray scattering and molecular simulations
View Description Hide DescriptionThe structural properties of liquidNmethyl pyrrolidone have been investigated by combining energy dispersive xray diffraction experiments and molecular dynamics simulations with generalized AMBER force field. A very good agreement between theoretical and experimental diffraction patterns was achieved. The analysis of the radial distribution functions shows that the methylcarbonyl Hbond network observed in the crystal structure is partly preserved in the liquid structure.

Twopoint approximation to the Kramers problem with coloured noise
View Description Hide DescriptionWe present a method, founded on previous renewal approaches as the classical WilemskiFixman approximation, to describe the escape dynamics from a potential well of a particle subject to nonMarkovian fluctuations. In particular, we show how to provide an approximated expression for the distribution of escape times if the system is governed by a generalized Langevin equation (GLE). While we show that the method could apply to any friction kernel in the GLE, we focus here on the case of powerlaw kernels, for which extensive literature has appeared in the last years. The method presented (termed as twopoint approximation) is able to fit the distribution of escape times adequately for low potential barriers, even if conditions are far from Markovian. In addition, it confirms that nonexponential decays arise when a powerlaw friction kernel is considered (in agreement with related works published recently), which questions the existence of a characteristicreaction rate in such situations.