Volume 135, Issue 7, 21 August 2011

Recent reports indicate that the crystallization of clathrate hydrates occurs in multiple steps that involve amorphous intermediates and metastable clathrate crystals. The elucidation of the reaction coordinate for clathratecrystallization requires the use of order parameters able to identify the reactants, products, and intermediates in the crystallization pathway. Nevertheless, existing order parameters cannot distinguish between amorphous and crystalline clathrates or between different clathrate crystals. In this work, we present the first set of order parameters that discern between the sI and sII clathrate crystals, the amorphousclathrates, the blob of solventseparated guests and the liquidsolution. These order parameters can be used to monitor the advance of the crystallization and for the efficient implementation of methods to sample the rare clathratenucleation events in molecular simulations. We illustrate the use of these order parameters in the analysis of the growth and the dissolution of clathrate crystals and the spontaneous nucleation and growth of clathrates under conditions of high supercooling.
 COMMUNICATIONS


Communication: Vacuum ultraviolet laser photodissociation studies of small molecules by the vacuum ultraviolet laser photoionization timesliced velocitymapped ion imaging method
View Description Hide DescriptionWe demonstrate that the vacuum ultraviolet (VUV)photodissociation dynamics of N_{2} and CO_{2} can be studied using VUV photoionization with timesliced velocitymapped ion imaging (VUVPIVMI) detection. The VUV laser light is produced by resonant sum frequency mixing in Kr. N_{2} is used to show that when the photon energy of the VUV laser is above the ionization energy of an allowed transition of one of the product atoms it can be detected and characterized as the wavelength is varied. In this case a β parameter = 0.57 for the N(^{2}D°) was measured after exciting N_{2}(o ^{1}Π_{u}, v^{′} = 2, J^{′} = 2) ← N_{2}(X ^{1}Σ_{g} ^{+}, v^{″} = 0, J^{″} = 1). Studies with CO_{2} show that when there is no allowed transition, an autoionization resonance can be used for the detection of a product atom. In this case it is shown for the first time that the O(^{1}D) atom is produced with CO(^{1}Σ^{+}) at 92.21 nm. These results indicate that the VUV laser photodissociation combined with the VUVPIVMI detection is a viable method for studying the onephoton photodissociation from the ground state of simple molecules in the extreme ultraviolet and VUV spectral regions.

Communication: Toward ultrafast, reconfigurable logic in the nanoscale
View Description Hide DescriptionWe propose and illustrate numerically a class of nanoscale, ultrafast logic gates with the further advantage of reconfigurability. Underlying the operation of the gates and their versatility is the concept of polarization control of the electromagnetic energy propagating via metal nanoparticle arrays. Specifically, a set of different logic gates is shown to obtain from a single metal nanoparticle junction by modification of the polarization properties of the input light sources. Implications and extensions of the gates are discussed.

Communication: A new hybrid exchange correlation functional for bandgap calculations using a shortrange Gaussian attenuation (GaussianPerdue–Burke–Ernzerhof)
View Description Hide DescriptionWe have developed a new hybrid functional [GaussianPerdue–Burke–Ernzerhof (GauPBE)] that is suitable for the calculation of solid state bandgaps using a periodic boundary condition. The characteristic of this functional is the use of a Gaussian attenuation scheme (Gau) to include a shortrange Hartree–Fock (HF) exchange. This new functional can perform barrier height calculations with an accuracy comparable to the middlerange hybrid functional and bandgap calculations with an accuracy comparable to the Heyd–Scuseria–Ernzerhof (HSE) functional. However, the point is that the performance can be achieved using a Gaussian HF exchange, while the HISS functional calculates twice HFexchange integrations using an error function to obtain both performances. In addition, GauPBE functional can decrease the time cost of bandgap calculations by an average of 40% compared to the HSE functional.

Communication: Configuration interaction singles has a large systematic bias against chargetransfer states
View Description Hide DescriptionWe show that standard configuration interaction singles (CIS) has a systematic bias against chargetransfer(CT) states, wherein the computed vertical excitation energies for CT states are disproportionately too high (by >1 eV) as compared with nonCT states. We demonstrate this bias empirically for a set of chemical problems with both inter and intramolecular electron transfer, and then, for a small analytical model, we prove that this large difference in accuracy stems from the massive changes in electronic structure that must accompany longrange charge transfer. Thus far, the conclusion from this research is that, even in the context of wave functiontheory,CIS alone is insufficient for offering a balanced description of excited state surfaces (both CT and nonCT) and explicit electronelectron correlation must be included additionally (e.g., via CIS(D)) for chargetransfer applications.
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 ARTICLES

 Theoretical Methods and Algorithms

Secondorder nonadiabatic couplings from timedependent density functional theory: Evaluation in the immediate vicinity of JahnTeller/RennerTeller intersections
View Description Hide DescriptionFor a rigorous quantum simulation of nonadiabatic dynamics of electrons and nuclei, knowledge of not only the firstorder but also the secondorder nonadiabatic couplings (NACs) is required. Here, we propose a method to efficiently calculate the secondorder NAC from timedependent density functional theory (TDDFT), on the basis of the Casida ansatz adapted for the computation of firstorder NAC, which has been justified in our previous work and can be shown to be valid for calculating secondorder NAC between ground state and singly excited states within the TammDancoff approximation. Test calculations of the secondorder NAC in the immediate vicinity of JahnTeller and RennerTeller intersections show that calculation results from TDDFT, combined with modified linear response theory, agree well with the prediction from the JahnTeller/RennerTeller models. Contrary to the diverging behavior of the firstorder NAC near all types of intersection points, the Cartesian components of the secondorder NAC are shown to be negligibly small near RennerTeller glancing intersections, while they are significantly large near the JahnTeller conical intersections. Nevertheless, the components of the secondorder NAC can cancel each other to a large extent in JahnTeller systems, indicating the background of neglecting the secondorder NAC in practical dynamics simulations. On the other hand, it is shown that such a cancellation becomes less effective in an elliptic JahnTeller system and thus the role of secondorder NAC needs to be evaluated in the rigorous framework. Our study shows that TDDFT is promising to provide accurate data of NAC for full quantum mechanical simulation of nonadiabatic processes.

Wave frontray synthesis for solving the multidimensional quantum HamiltonJacobi equation
View Description Hide DescriptionA Cauchy initialvalue approach to the complexvalued quantum HamiltonJacobi equation (QHJE) is investigated for multidimensional systems. In this approach, ray segments foliate configuration space which is laminated by surfaces of constant action. The QHJE incorporates all quantum effects through a term involving the divergence of the quantum momentum function (QMF). The divergence term may be expressed as a sum of two terms, one involving displacement along the ray and the other incorporating the local curvature of the action surface. It is shown that curvature of the wave front may be computed from coefficients of the first and second fundamental forms from differential geometry that are associated with the surface. Using the expression for the divergence, the QHJE becomes a Riccatitype ordinary differential equation (ODE) for the complexvalued QMF, which is parametrized by the arc length along the ray. In order to integrate over possible singularities in the QMF, a stable and accurate Möbius propagator is introduced. This method is then used to evolve rays and wave fronts for four systems in two and three dimensions. From the QMF along each ray, the wave function can be easily computed. Computational difficulties that may arise are described and some ways to circumvent them are presented.

Nonhard sphere thermodynamic perturbation theory
View Description Hide DescriptionA nonhard sphere (HS) perturbation scheme, recently advanced by the present author, is elaborated for several technical matters, which are key mathematical details for implementation of the nonHS perturbation scheme in a coupling parameter expansion (CPE) thermodynamicperturbation framework. NVTMonte Carlo simulation is carried out for a generalized LennardJones (LJ) 2nn potential to obtain routine thermodynamic quantities such as excess internal energy, pressure, excess chemical potential, excess Helmholtz free energy, and excess constant volume heat capacity. Then, these new simulation data, and available simulation data in literatures about a hard core attractive Yukawa fluid and a Sutherland fluid, are used to test the nonHS CPE 3rdorder thermodynamicperturbation theory (TPT) and give a comparison between the nonHS CPE 3rdorder TPT and other theoretical approaches. It is indicated that the nonHS CPE 3rdorder TPT is superior to other traditional TPT such as van der Waals/HS (vdW/HS), perturbation theory 2 (PT2)/HS, and vdW/Yukawa (vdW/Y) theory or analytical equation of state such as mean spherical approximation (MSA)equation of state and is at least comparable to several currently the most accurate OrnsteinZernike integral equation theories. It is discovered that three technical issues, i.e., opening up new bridge function approximation for the reference potential, choosing proper reference potential, and/or using proper thermodynamic route for calculation of f _{ ex − ref }, chiefly decide the quality of the nonHS CPE TPT. Considering that the nonHS perturbation scheme applies for a wide variety of model fluids, and its implementation in the CPE thermodynamicperturbation framework is amenable to highorder truncation, the nonHS CPE 3rdorder or higher order TPT will be more promising once the abovementioned three technological advances are established.

Openshell reduced density matrix functional theory
View Description Hide DescriptionOpenshell reduced density matrix functionaltheory is established by investigating the domain of the exact functional. For spin states that are the ground state, a particularly simple set is found to be the domain. It cannot be generalized to other spin states. A number of conditions satisfied by the exact density matrix functional is formulated and tested for approximate functionals. The exact functional does not suffer from fractional spin error, which is the source of the static correlation error in dissociated molecules. We prove that a simple approximation (called the BuijseBaerends functional, Müller or square root functional) has a nonpositive fractional spin error. In the case of the H atom the error is zero. Numerical results for a few atoms are given for approximate density and density matrix functionals as well as a recently developed rangeseparated combination of both.

An O(N ^{3}) implementation of Hedin's GW approximation for molecules
View Description Hide DescriptionWe describe an implementation of Hedin's GW approximation for molecules and clusters, the complexity of which scales as O(N ^{3}) with the number of atoms. Our method is guided by two strategies: (i) to respect the locality of the underlying electronic interactions and (ii) to avoid the singularities of Green's functions by manipulating, instead, their spectral functions using fast Fourier transform methods. To take into account the locality of the electronic interactions, we use a local basis of atomic orbitals and, also, a local basis in the space of their products. We further compress the screened Coulomb interaction into a space of lower dimensions for speed and to reduce memory requirements. The improved scaling of our method with respect to most of the published methodologies should facilitate GW calculations for large systems. Our implementation is intended as a step forward towards the goal of predicting, prior to their synthesis, the ionization energies and electron affinities of the large molecules that serve as constituents of organic semiconductors.

Direct simulation of electron transfer using ring polymer molecular dynamics: Comparison with semiclassical instanton theory and exact quantum methods
View Description Hide DescriptionThe use of ring polymer molecular dynamics (RPMD) for the direct simulation of electron transfer(ET)reactiondynamics is analyzed in the context of Marcus theory, semiclassical instanton theory, and exact quantum dynamics approaches. For both fully atomistic and systembath representations of condensedphase ET, we demonstrate that RPMD accurately predicts both ETreaction rates and mechanisms throughout the normal and activationless regimes of the thermodynamic driving force. Analysis of the ensemble of reactive RPMD trajectories reveals the solvent reorganization mechanism for ET that is anticipated in the Marcus rate theory, and the accuracy of the RPMD rate calculation is understood in terms of its exact description of statistical fluctuations and its formal connection to semiclassical instanton theory for deeptunneling processes. In the inverted regime of the thermodynamic driving force, neither RPMD nor a related formulation of semiclassical instanton theory capture the characteristic turnover in the reaction rate; comparison with exact quantum dynamics simulations reveals that these methods provide inadequate quantization of the realtime electronicstate dynamics in the inverted regime.

Local explicitly correlated secondorder Møller–Plesset perturbation theory with pair natural orbitals
View Description Hide DescriptionWe explore using a pair natural orbital analysis of approximate firstorder pair functions as means to truncate the space of both virtual and complementary auxiliary orbitals in the context of explicitly correlated F12 methods using localised occupied orbitals. We demonstrate that this offers an attractive procedure and that only 10–40 virtual orbitals per significant pair are required to obtain secondorder valence correlation energies to within 1–2% of the basis set limit. Moreover, for this level of virtual truncation, only 10–40 complementary auxiliary orbitals per pair are required for an accurate resolution of the identity in the computation of the three and fourelectron integrals that arise in explicitly correlated methods.

Time scale separation leads to positiondependent diffusion along a slow coordinate
View Description Hide DescriptionWhen there is a separation of time scales, an effective description of the dynamics of the slow variables can be obtained by adiabatic elimination of fast ones. For example, for anisotropicLangevin dynamics in two dimensions, the conventional procedure leads to a Langevin equation for the slow coordinate that involves the potential of the mean force. The friction constant along this coordinate remains unchanged. Here, we show that a more accurate, but still Markovian, description of the slow dynamics can be obtained by using positiondependent friction that is related to the time integral of the autocorrelation function of the difference between the actual force and the mean force by a Kirkwoodlike formula. The result is generalized to many dimensions, where the slow or reaction coordinate is an arbitrary function of the Cartesian coordinates. When the fast variables are effectively onedimensional, the additional friction along the slow coordinate can be expressed in closed form for an arbitrary potential. For a cylindrically symmetric channel of varying cross section with winding centerline, our analytical expression immediately yields the multidimensional version of the ZwanzigBradley formula for the positiondependent diffusion coefficient.

The performance and relationship among rangeseparated schemes for density functional theory
View Description Hide DescriptionThe performance and relationship among different rangeseparated (RS) hybrid functional schemes are examined using the Coulombattenuating method (CAM) with different values for the fractions of exact HartreeFock (HF) exchange (α), longrange HF (β), and a rangeseparation parameter (μ), where the cases of α + β = 1 and α + β = 0 were designated as CA and CA0, respectively. Attenuated PBE exchangecorrelation functionals with α = 0.20 and μ = 0.20 (CAPBE) and α = 0.25 and μ = 0.11 (CA0PBE) are closely related to the LRCωPBEh and HSE functionals, respectively. Timedependent density functional theory calculations were carried out for a number of classes of molecules with varying degrees of chargetransfer(CT) character to provide an assessment of the accuracy of excitation energies from the CA functionals and a number of other functionals with different exchange hole models. Functionals that provided reasonable estimates for local and shortrange CT transitions were found to give large errors for longrange CT excitations. In contrast, functionals that afforded accurate longrange CTexcitation energies significantly overestimated energies for shortrange CT and local transitions. The effects of exchange hole models and parameters developed for RS functionals for CT excitations were analyzed in detail. The comparative analysis across compound classes provides a useful benchmark for CT excitations.

Accurate nonBornOppenheimer calculations of the complete pure vibrational spectrum of D_{2} with including relativistic corrections
View Description Hide DescriptionIn this work we report very accurate variational calculations of the complete pure vibrational spectrum of the D_{2} molecule performed within the framework where the BornOppenheimer (BO) approximation is not assumed. After the elimination of the centerofmass motion, D_{2} becomes a threeparticle problem in this framework. As the considered states correspond to the zero total angular momentum, their wave functions are expanded in terms of allparticle, onecenter, spherically symmetric explicitly correlated Gaussian functions multiplied by even nonnegative powers of the internuclear distance. The nonrelativistic energies of the states obtained in the nonBO calculations are corrected for the relativistic effects of the order of α^{2} (where α = 1/c is the fine structure constant) calculated as expectation values of the operators representing these effects.

Electron pair density in the lowest ^{1} and ^{1} states of H_{2}
View Description Hide DescriptionWe demonstrate and advocate the use of observable quantities derived from the twoelectron reduced density matrix – pair densities, conditional densities, and exchangecorrelation holes – as signatures of the type of electron correlation in a chemical bond. The prototype cases of the lowest ^{1} and ^{1} states of H_{2}, which exhibit large variation in types of bonding, ranging from strongly ionic to covalent, are discussed. Both the excited ^{1} and ^{1} states have been interpreted as essentially consisting of (natural) orbital configurations with an inner electron in a contracted 1sσ_{ g } orbital and an outer electron in a diffuse (united atom type, Rydberg) orbital. We show that nevertheless totally different correlation behavior is encountered in various states when comparing them at a common internuclear distance. Also when following one state along the internuclear distance coordinate, strong variation in correlation behavior is observed, as expected. Switches between ionic to covalent character of a state occur till very large distances (40 bohrs for states approaching the 1s3ℓ asymptotic limit, and 282 bohrs for states approaching the 1s4ℓ limit).

Ordinary differential equation for local accumulation time
View Description Hide DescriptionCell differentiation in a developing tissue is controlled by the concentration fields of signaling molecules called morphogens. Formation of these concentration fields can be described by the reactiondiffusion mechanism in which locally produced molecules diffuse through the patterned tissue and are degraded. The formation kinetics at a given point of the patterned tissue can be characterized by the local accumulation time, defined in terms of the local relaxation function. Here, we show that this time satisfies an ordinary differential equation. Using this equation one can straightforwardly determine the local accumulation time, i.e., without preliminary calculation of the relaxation function by solving the partial differential equation, as was done in previous studies. We derive this ordinary differential equation together with the accompanying boundary conditions and demonstrate that the earlier obtained results for the local accumulation time can be recovered by solving this equation.

CCSDPCM: Improving upon the reference reaction field approximation at no cost
View Description Hide DescriptionThe combination of the coupled cluster (CC) method with the polarizable continuum model (PCM) of solvation requires a much larger computational effort than gas phase CC calculations, since the PCM contribution depends nonlinearly on the CC reduced density: perturbation theoryenergy and density (PTED) scheme. An approximation can be introduced that neglects the “correlation” PCM contribution and only considers the “reference” PCM contribution to the free energy: PTE scheme. The PTE scheme is a computationally efficient strategy, since the cost is comparable to gas phase CC, but the difference in the free energy with respect to the PTED scheme can be significant. In this work, two intermediate approximations are presented, PTE(S) and PTES (where S stands for singles), which retain the computational efficiency of the PTE scheme while reducing the energy gap with the PTED scheme. PTE(S) only introduces an energy correction to the PTE free energy, while PTES introduces explicit PCM terms in the iterative solution of the CC equations. PTE(S) improves the PTE free energy, although such correction is small. PTES recovers 50%–80% of the PTEPTED difference and represents a promising approach to perform calculations in solution of CC quality at a cost comparable to gas phase CC. The expressions for the CCPTE(S) and PTES wave functions,free energy, and free energy analytical gradients are presented, and the methods are tested with numerical examples.
 Advanced Experimental Techniques

Structure determination of the nonlinear hydrocarbon chains C_{9}H_{3} and C_{11}H_{3} by deuterium labeling
View Description Hide DescriptionA systematic deuterium labeling experiment is presented that aims at an unambiguous determination of the geometrical ground state structure of the C_{9}H_{3} and C_{11}H_{3} hydrocarbon chains. Cavity ringdown spectroscopy and special plasma expansions constituting C/H, C/D, and C/H/D are used to record optical transitions of both species and their (partially) deuterated equivalents in the 19 000 cm^{−1} region. The number of observed bands, the quantitative determination of isotopic shifts, and supporting calculations show that the observed C_{9}H_{3} and C_{11}H_{3}spectra originate from HC_{4}(CH)C_{4}H and HC_{4}[C(C_{2}H)]C_{4}H species with C _{2v } symmetry. This result illustrates the potential of deuterium labeling as a useful approach to characterize the molecular structure of nonlinear hydrocarbon chains.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Explicitly correlated treatment of H_{2}NSi and H_{2}SiN radicals: Electronic structure calculations and rovibrational spectra
View Description Hide DescriptionVarious ab initio methods are used to compute the six dimensional potential energy surfaces (6DPESs) of the ground states of the H_{2}NSi and H_{2}SiN radicals. They include standard coupled cluster (RCCSD(T)) techniques and the newly developed explicitly correlated RCCSD(T)F12 methods. For H_{2}NSi, the explicitly correlated techniques are viewed to provide data as accurate as the standard coupled cluster techniques, whereas small differences are noticed for H_{2}SiN. These PESs are found to be very flat along the outofplane and some inplane bending coordinates. Then, the analytic representations of these PESs are used to solve the nuclear motions by standard perturbation theory and variational calculations. For both isomers, a set of accurate spectroscopic parameters and the vibrational spectrum up to 4000 cm^{−1} are predicted. In particular, the analysis of our results shows the occurrence of anharmonic resonances for H_{2}SiN even at low energies.

Highlevel ab initio potential energy surfaces and vibrational energies of H_{2}CS
View Description Hide DescriptionSixdimensional (6D) potential energy surfaces (PESs) of H_{2}CS have been generated ab initio using the recently proposed explicitly correlated (F12) singles and doubles coupled cluster method including a perturbational estimate of connected triple excitations, CCSD(T)F12b [T. B. Adler, G. Knizia, and H.J. Werner, J. Chem. Phys.127, 221106 (2007)] in conjunction with F12optimized correlation consistent basis sets. Coreelectron correlation, highorder correlation, scalar relativistic, and diagonal BornOppenheimer terms were included as additive highlevel (HL) corrections. The resulting 6D PESs were represented by analytical functions which were used in variational calculations of the vibrational term values below 5000 cm^{−1}. The best PESs obtained with and without the HL corrections, VQZ and VQZF12*, reproduce the fundamental vibrational wavenumbers with mean absolute deviations of 1.13 and 1.22 cm^{−1}, respectively. A detailed analysis of the effects of the HL corrections shows how the VQZF12 results benefit from error cancellation. The present purely ab initio PESs will be useful as starting points for empirical refinements towards an accurate “spectroscopic” PES of H_{2}CS.