Volume 134, Issue 12, 28 March 2011

The stimulated Raman component of the pumpprobe spectrum of transNmethylacetamide obtained in response to two soft xray pulses is calculated by treating the core excitations at the Hartree–Fock staticexchange level. The signal reveals the dynamics of valenceelectron wave packets prepared and detected in the vicinity of a selected atom (either nitrogen or oxygen). The evolving electronic charge density as well as electronic coherence of the doorway and the window created by the two pulses are visualized using a timedependent basis set of natural orbitals, which reveals that the wave packets consist of several entangled valence particle–hole pairs.
 COMMUNICATIONS


Communication: Xray scattering from ionic liquids with pyrrolidinium cations
View Description Hide DescriptionWe report the structure functions obtained from xray scattering experiments on a series of four homologous ionic liquids. The ionic liquids are 1alkyl1methylpyrrolidinium cations paired with the bis(trifluoromethylsulfonyl)amide anion, with alkyl chain lengths of n = 4, 6, 8, and 10. The structure functions display two intense diffraction peaks for values of the scattering vector q in the range from 0.6 to 1.5 Å^{−1} for all samples. Both diffraction peaks shift to lower values of q for increasing temperature. First sharp diffraction peaks are observed in the structure functions for q < 0.5 Å^{−1} for liquids with n = 6, 8, and 10.

Communication: Propagator for diffusive dynamics of an interacting molecular pair
View Description Hide DescriptionWe introduce a new method of solution for the Fredholm integral equations of the second kind. The method would be useful when the direct iterative approach leads to a divergent perturbation series solution. By using the method, we obtain an accurate expression of the propagator for diffusive dynamics of a pair of particles interacting via an arbitrary central potential and hydrodynamic interaction. We test the accuracy of the propagator expression by calculating the diffusioncontrolled geminate and bimolecular reaction rates. It is shown that our propagator expression provides very accurate results for the whole time region.

Communication: Identification of the molecule–metal bonding geometries of molecular nanowires
View Description Hide DescriptionMolecular nanowires in which a single molecule bonds chemically to two metal electrodes and forms a stable electrically conducting bridge between them have been studied intensively for more than a decade. However, the experimental determination of the bonding geometry between the molecule and electrodes has remained elusive. Here we demonstrate by means of ab initio calculations that inelastic tunneling spectroscopy (IETS) can determine these geometries. We identify the bonding geometries at the gold–sulfur interfaces of propanedithiolate molecules bridging goldelectrodes that give rise to the specific IETS signatures that were observed in recent experiments.

Communication: Single crystal xray diffraction observation of hydrogen bonding between 1propanol and water in a structure II clathrate hydrate
View Description Hide DescriptionSingle crystal xray crystallography is used to detect guest–host hydrogen bonding in structure II (sII) binary clathrate hydrate of 1propanol and methane. Xray structural analysis shows that the 1propanol oxygen atom is at a distance of 2.749 and 2.788 Å from the closest clathrate hydrate water oxygen atoms from a hexagonal face of the large sII cage. The 1propanol hydroxyl hydrogen atom is disordered and at distances of 1.956 and 2.035 Å from the closest cage water oxygen atoms. These distances are compatible with guest–water hydrogen bonding. The C–C–C–O torsional angle in 1propanol in the cage is 91.47° which corresponds to a staggered conformation for the guest. Molecular dynamics studies of this system demonstrated guest–water hydrogen bonding in this hydrate. The molecular dynamics simulations predict most probable distances for the 1propanol–water oxygen atoms to be 2.725 Å, and the average C–C–C–O torsional angle to be ∼59° consistent with a gauche conformation. The individual cage distortions resulting from guest–host hydrogen bonding from the simulations are rather large, but due to the random nature of the hydrogen bonding of the guest with the 24 water molecules making up the hexagonal faces of the large sII cages, these distortions are not observed in the xray structure.

Communication: The effect of dispersion corrections on the melting temperature of liquid water
View Description Hide DescriptionThe melting temperature (T _{ m }) of liquid water with the Becke–Lee–Yang–Parr (BLYP) density functional including dispersion corrections (BLYPD) and the Tholetype, version 3 (TTM3F) abinitio based flexible, polarizable classical potential is reported via constant pressure and constant enthalpy (NPH) molecular dynamics simulations of an iceI _{h}liquid coexisting system. Dispersion corrections to BLYP lower T _{ m } to about 360 K, a large improvement over the value of T _{ m } > 400 K previously obtained with the original BLYP functional under the same simulation conditions. For TTM3F, T _{ m } = 248 K from classical molecular dynamics simulations.
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 ARTICLES

 Theoretical Methods and Algorithms

Simulation and visualization of attosecond stimulated xray Raman spectroscopy signals in transNmethylacetamide at the nitrogen and oxygen Kedges
View Description Hide DescriptionThe stimulated Raman component of the pumpprobe spectrum of transNmethylacetamide obtained in response to two soft xray pulses is calculated by treating the core excitations at the Hartree–Fock staticexchange level. The signal reveals the dynamics of valenceelectron wave packets prepared and detected in the vicinity of a selected atom (either nitrogen or oxygen). The evolving electronic charge density as well as electronic coherence of the doorway and the window created by the two pulses are visualized using a timedependent basis set of natural orbitals, which reveals that the wave packets consist of several entangled valence particle–hole pairs.

An improved dynamic Monte Carlo model coupled with Poisson equation to simulate the performance of organic photovoltaic devices
View Description Hide DescriptionWe describe a new dynamic Monte Carlo model to simulate the operation of a polymerblend solar cell; this model provides major improvements with respect to the one we developed earlier [J. Phys. Chem. B 114, 36 (2010)] by incorporating the Poisson equation and a charge thermoactivation mechanism. The advantage of the present approach is its capacity to deal with a nonuniform electrostatic potential that dynamically depends on the charge distribution. In this way, the unbalance in electron and hole mobilities and the spacecharge induced potential distribution can be treated explicitly. Simulations reproduce well the experimental IV curve in the dark and the opencircuit voltage under illumination of a polymerblend solar cell. The dependence of the photovoltaic performance on the difference in electron and hole mobilities is discussed.

Quantum mechanical generalized phaseshift approach to atomsurface scattering: A Feshbach projection approach to dealing with closed channel effects
View Description Hide DescriptionWe have developed a new method for solving quantum dynamical scattering problems, using the timeindependent Schrödinger equation (TISE), based on a novel method to generalize a “oneway” quantum mechanical wave equation, impose correct boundary conditions, and eliminate exponentially growing closed channel solutions. The approach is readily parallelized to achieve approximate N ^{2} scaling, where N is the number of coupled equations. The full twoway nature of the TISE is included while propagating the wave function in the scattering variable and the full Smatrix is obtained. The new algorithm is based on a “Modified Cayley” operator splitting approach, generalizing earlier work where the method was applied to the timedependent Schrödinger equation. All scattering variable propagation approaches to solving the TISE involve solving a Helmholtztype equation, and for more than one degree of freedom, these are notoriously illbehaved, due to the unavoidable presence of exponentially growing contributions to the numerical solution. Traditionally, the method used to eliminate exponential growth has posed a major obstacle to the full parallelization of such propagation algorithms. We stabilize by using the Feshbach projection operator technique to remove all the nonphysical exponentially growing closed channels, while retaining all of the propagating open channel components, as well as exponentially decaying closed channel components.

Interpolation by fast Wigner transform for rapid calculations of magnetic resonance spectra from powders
View Description Hide DescriptionWe introduce a novel interpolation strategy, based on nonequispaced fast transforms involving spherical harmonics or Wigner functions, for efficient calculations of powder spectra in (nuclear) magnetic resonancespectroscopy. The fast Wigner transform (FWT) interpolation operates by minimizing the timeconsuming calculation stages, by sampling over a small number of Gaussian spherical quadrature (GSQ) orientations that are exploited to determine the spectral frequencies and amplitudes from a 10–70 times larger GSQ set. This results in almost the same orientational averaging accuracy as if the expanded grid was utilized explicitly in an order of magnitude slower computation. FWT interpolation is applicable to spectral simulations involving any timeindependent or timedependent and noncommuting spin Hamiltonian. We further show that the merging of FWT interpolation with the wellestablished ASG procedure of Alderman, Solum and Grant [J. Chem. Phys.134, 3717 (1986)] speeds up simulations by 2–7 times relative to using ASG alone (besides greatly extending its scope of application), and between 1–2 orders of magnitude compared to direct orientational averaging in the absence of interpolation. Demonstrations of efficient spectral simulations are given for several magicangle spinning scenarios in NMR, encompassing halfinteger quadrupolar spins and homonuclear dipolarcoupled ^{13}C systems.

Thermodynamics of water entry in hydrophobic channels of carbon nanotubes
View Description Hide DescriptionExperiments and computer simulations demonstrate that water spontaneously fills the hydrophobic cavity of a carbon nanotube. To gain a quantitative thermodynamic understanding of this phenomenon, we use the recently developed two phase thermodynamics method to compute translational and rotational entropies of confined water molecules inside singlewalled carbon nanotubes and show that the increase in energy of a water molecule inside the nanotube is compensated by the gain in its rotational entropy. The confined water is in equilibrium with the bulk water and the Helmholtz free energy per water molecule of confined water is the same as that in the bulk within the accuracy of the simulation results. A comparison of translational and rotational spectra of water molecules confined in carbon nanotubes with that of bulk water shows significant shifts in the positions of the spectral peaks that are directly related to the tube radius.

A fully simultaneously optimizing genetic approach to the highly excited coupledcluster factorization problem
View Description Hide DescriptionIn this article we report on the coupledcluster factorization problem. We describe the first implementation that optimizes (i) the contraction order for each term, (ii) the identification of reusable intermediates, (iii) the selection and factoring out of common factors simultaneously, considering all projection levels in a single step. The optimization is achieved by means of a genetic algorithm. Taking a onetermatatime strategy as reference our factorization yields speedups of up to 4 (for intermediate excitation levels, smaller basis sets). We derive a theoretical lower bound for the highest order scaling cost and show that it is met by our implementation. Additionally, we report on the performance of the resulting highly excited coupledcluster algorithms and find significant improvements with respect to the implementation of Kállay and Surján [J. Chem. Phys.115, 2945 (2001)]10.1063/1.1383290 and comparable performance with respect to MOLPRO’s handwritten and dedicated open shell coupled cluster with singles and doubles substitutions implementation [P. J. Knowles, C. Hampel, and H.J. Werner, J. Chem. Phys.99, 5219 (1993)10.1063/1.465990].

Entanglement of polar molecules in pendular states
View Description Hide DescriptionIn proposals for quantum computers using arrays of trapped ultracold polar molecules as qubits, a strong external field with appreciable gradient is imposed in order to prevent quenching of the dipole moments by rotation and to distinguish among the qubit sites. That field induces the molecular dipoles to undergo pendular oscillations, which markedly affect the qubit states and the dipole–dipole interaction. We evaluate entanglement of the pendular qubit states for two linear dipoles, characterized by pairwise concurrence, as a function of the molecular dipole moment and rotational constant, strengths of the external field and the dipole–dipole coupling, and ambient temperature. We also evaluate a key frequency shift, △ω, produced by the dipole–dipole interaction. Under conditions envisioned for the proposed quantum computers, both the concurrence and △ω become very small for the ground eigenstate. In principle, such weak entanglement can be sufficient for operation of logic gates, provided the resolution is high enough to detect the △ω shift unambiguously. In practice, however, for many candidate polar molecules it appears a challenging task to attain adequate resolution. Simple approximate formulas fitted to our numerical results are provided from which the concurrence and △ω shift can be obtained in terms of unitless reduced variables.

NMR shielding tensors from auxiliary density functional theory
View Description Hide DescriptionThe working equations for the calculation of NMR shielding tensors in the framework of auxiliary density functional theory are derived. It is shown that in this approach the numerical integration over gaugeincluding atomic orbitals can be avoided without the loss of accuracy. New integral recurrence relations for the required analytic electricfieldtype integrals are derived. The computational performance of the resulting formalism permits shielding tensor calculations of systems with more than 1000 atoms and 15 000 basis functions.

Analytical treatment of biased diffusion in tubes with periodic dead ends
View Description Hide DescriptionEffective mobility and diffusion coefficient of a particle in a tube with identical periodic dead ends characterize the motion on large time scale, when the particle displacement significantly exceeds the tube period. We derive formulas that show how these transport coefficients depend on the driving force and the geometric parameters of the system. Numerical tests show that values of the transport coefficients obtained from Brownian dynamics simulations are in excellent agreement with our theoretical predictions.

Attaining persistent fieldfree control of open and closed quantum systems
View Description Hide DescriptionPersistent quantum control (PQC) aims to maintain an observable objective value over a period of time following the action of an applied field. This paper assesses the feasibility of achieving PQC for arbitrary finitelevel systems and observables. The analysis is carried out independent of the particular method used for state preparation. The PQC behavior is optimized over the set of physically accessible prepared states for both open and closed systems. The quality of observable value persistence in the postcontrol period was found to vary with the required duration of persistence, the system temperature, the chosen observable operator, and the energy levels of the system. The alignment of a rigid diatomic rotor is studied as a model system. The theoretical estimates of PQC behavior are encouraging and suggest feasible exploration in the laboratory using currently available technology.

Cost reduction of highorder coupledcluster methods via activespace and orbital transformation techniques
View Description Hide DescriptionWe discuss several techniques which have the potential to decrease the computational expenses of highorder coupledcluster (CC) methods with a reasonable loss in accuracy. In particular, the CC singles, doubles, and triples (CCSDT) as well as the CC singles, doubles, triples, and perturbative quadruples [CCSDT(Q)] methods are considered, which are frequently used in highprecision model chemistries for the calculation of iterative triples and quadruples corrections. First, we study the possibilities for using active spaces to decrease the computational costs. In this case, an active space is defined and some indices of cluster amplitudes are restricted to be in the space. Second, the application of transformed virtual orbitals is investigated. In this framework, to reduce the computation time the dimension of the properly transformed virtual oneparticle space is truncated. We have found that the orbital transformation techniques outperform the activespace approaches. Using the transformation techniques, the computational time can be reduced in average by an order of magnitude without significant loss in accuracy. It is demonstrated that highorder CC calculations are possible for considerably larger systems than before using the implemented techniques.

NonMarkovian finitetemperature twotime correlation functions of system operators: Beyond the quantum regression theorem
View Description Hide DescriptionAn extremely useful evolution equation that allows systematically calculating the twotime correlation functions (CF's) of system operators for nonMarkovian open (dissipative) quantum systems is derived. The derivation is based on perturbative quantum master equation approach, so nonMarkovian open quantum systemmodels that are not exactly solvable can use our derived evolution equation to easily obtain their twotime CF's of system operators, valid to second order in the system–environment interaction. Since the form and nature of the Hamiltonian are not specified in our derived evolution equation, our evolution equation is applicable for bosonic and/or fermionic environments and can be applied to a wide range of system–environment models with any factorized (separable) system–environment initial states (pure or mixed). When applied to a general model of a system coupled to a finitetemperature bosonic environment with a system coupling operator L in the system–environment interaction Hamiltonian, the resultant evolution equation is valid for both L = L† and L ≠ L† cases, in contrast to those evolution equations valid only for L = L† case in the literature. The derived equation that generalizes the quantum regression theorem (QRT) to the nonMarkovian case will have broad applications in many different branches of physics. We then give conditions on which the QRT holds in the weak system–environment coupling case and apply the derived evolution equation to a problem of a twolevel system (atom) coupled to the finitetemperature bosonic environment (electromagnetic fields) with L ≠ L†.

Linearity condition for orbital energies in density functional theory: Construction of orbitalspecific hybrid functional
View Description Hide DescriptionThis study proposes a novel approach to construct the orbitalspecific (OS) hybrid exchangecorrelation functional by imposing the linearity condition: , where E, ε_{ i }, and f _{ i } represent the total energy, orbital energy, and occupation number of the ith orbital. The OS hybrid exchangecorrelation functional, of which the OS Hartree–Fock exchange (HFx) portion is determined by the linearity condition, reasonably reproduces the ionization potentials not only from valence orbitals but also from core ones in a sense of Koopmans’ theorem. The obtained shortrange HFx portions are consistent with the parameters empirically determined in core–valence–Rydberg–Becke3–parameter–Lee–Yang–Parr hybrid functional [Nakata et al., J. Chem. Phys., 124, 094105 (2006); ibid, 125, 064109 (2006)10.1063/1.2227379].

Compact wave functions for the beryllium isoelectronic series, Li^{−} to Ne^{6+}: A standard Hylleraas approach
View Description Hide DescriptionVariational calculations have been carried out for the ground states of several members of the beryllium isoelectronic series using a standard Hylleraas approach involving Slatertype basis functions. The species examined are Li^{−}, Be, B^{+}, C^{2+}, N^{3+}, O^{4+}, F^{5+}, and Ne^{6+}. For each species, the nonrelativistic energy, the electronic density at the nucleus, the expectation value 〈∇ _{ i }·∇ _{ j }〉, the moments for n = −1, 1, 2, and 3, and for n = −1, 1, and 2, are reported. With relatively compact basis sets, the ground state energies are obtained with uncertainties ranging from 50 parts per million to just under 4 parts per million.

Fully analytic energy gradient in the fragment molecular orbital method
View Description Hide DescriptionThe Zvector equations are derived and implemented for solving the response term due to the external electrostatic potentials, and the corresponding contribution is added to the energy gradients in the framework of the fragment molecular orbital (FMO) method. To practically solve the equations for large molecules like proteins, the equations are decoupled by taking advantage of the local nature of fragments in the FMO method and establishing the selfconsistent Zvector method. The resulting gradients are compared with numerical gradients for the test molecular systems: (H_{2}O)_{64}, alanine decamer, hydrated chignolin with the protein data bank (PDB) ID of 1UAO, and a Trpcage miniprotein construct (PDB ID: 1L2Y). The computation time for calculating the response contribution is comparable to or less than that of the FMO selfconsistent charge calculation. It is also shown that the energy gradients for the electrostatic dimer approximation are fully analytic, which significantly reduces the computational costs. The fully analytic FMO gradient is parallelized with an efficiency of about 98% on 32 nodes.