Volume 138, Issue 12, 28 March 2013
 COMMUNICATIONS


Communication: Growing room temperature ice with graphene
View Description Hide DescriptionWater becomes ordered in the form of hexagonal ice at room temperature under controlled humidity conditions upon confinement in the nanometer range between protective graphene sheets and crystalline (111) surfaces with hexagonal symmetry of the alkali earth fluoride BaF_{2}. Interfacial water/substrate pseudoepitaxy turns out to be a critical parameter since ice is only formed when the lattice mismatch is small, an observation based on the absence of ice on (111) surfaces of isostructural CaF_{2}

Communication: A new ab initio potential energy surface for HCl–H_{2}O, diffusion Monte Carlo calculations of D _{0} and a delocalized zeropoint wavefunction
View Description Hide DescriptionWe report a global, fulldimensional, ab initio potential energy surface describing the HCl–H_{2}O dimer. The potential is constructed from a permutationally invariant fit, using Morselike variables, to over 44 000 CCSD(T)F12b/augccpVTZ energies. The surface describes the complex and dissociated monomers with a total RMS fitting error of 24 cm^{−1}. The normal modes of the minima, lowenergy saddle point and separated monomers, the double minimum isomerization pathway and electronic dissociation energy are accurately described by the surface. Rigorous quantum mechanical diffusion Monte Carlo (DMC) calculations are performed to determine the zeropoint energy and wavefunction of the complex and the separated fragments. The calculated zeropoint energies together with a D _{ e } value calculated from CCSD(T) with a complete basis set extrapolation gives a D _{0} value of 1348 ± 3 cm^{−1}, in good agreement with the recent experimentally reported value of 1334 ± 10 cm^{−1}[B. E. Casterline, A. K. Mollner, L. C. Ch'ng, and H. Reisler, J. Phys. Chem. A114, 9774 (Year: 2010)10.1021/jp102532m]. Examination of the DMC wavefunction allows for confident characterization of the zeropoint geometry to be dominant at the C _{2v } doublewell saddle point and not the C _{ s } global minimum. Additional support for the delocalized zeropoint geometry is given by numerical solutions to the 1D Schrödinger equation along the imaginaryfrequency outofplane bending mode, where the zeropoint energy is calculated to be 52 cm^{−1} above the isomerization barrier. The D _{0} of the fully deuterated isotopologue is calculated to be 1476 ± 3 cm^{−1}, which we hope will stand as a benchmark for future experimental work.
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 ARTICLES

 Theoretical Methods and Algorithms

Analytical energy gradient used in variational BornOppenheimer calculations with allelectron explicitly correlated Gaussian functions for molecules containing one π electron
View Description Hide DescriptionAn algorithm for variational calculations of molecules with one π electron performed with allelectron explicitly correlated Gaussian (ECG) functions with floating centers is derived and implemented. The algorithm includes the analytic gradient of the BornOppenheimer electronic energy determined with respect to the ECG exponential parameters and the coordinates of the Gaussian centers. The availability of the gradient greatly accelerates the variational energy minimization. The algorithm is tested in calculations of four electronic excited states, c^{3}Π_{ u }, C^{1}Π_{ u }, i^{3}Π_{ g }, and I^{1}Π_{ g }, of the hydrogen molecule at a single internuclear distance specific to each state. With the use of the analytical energy gradient, the present calculations yield new, lowesttodate, variational energy upper bounds for all four states.

Hyperfine interaction mechanism of magnetic field effects in sequential fluorophore and exciplex fluorescence
View Description Hide DescriptionThe magnetic field effect on the fluorescence of the photoexcited electron acceptor, ^{1} A*, and the exciplex, ^{1}[D ^{+δ} A ^{−δ}] formed at contact of ^{1} A* with an electron donor ^{1} D, is theoretically explored in the framework of Integral Encounter Theory. It is assumed that the excited fluorophore is equilibrated with the exciplex that reversibly dissociates into the radicalion pair. The magnetic field sensitive stage is the spin conversion in the resulting geminate radicalion pair, ^{1, 3}[D ^{+}…A ^{−}] that proceeds due to hyperfine interaction. We confirm our earlier conclusion (obtained with a rate description of spin conversion) that in the model with a single nucleus spin 1/2 the magnitude of the Magnetic Field Effect (MFE) also vanishes in the opposite limits of low and high dielectric permittivity of the solvent. Moreover, it is shown that MFE being positive at small hyperfine interaction A, first increases with A but approaching the maximum starts to decrease and even changes the sign.

Direct evaluation of the saddle splay modulus of a liquidliquid interface using the classical mean field lattice model
View Description Hide DescriptionWe study the curvature dependence of the liquidliquid (liquidgas) interface using the wellknown mean field lattice model to estimate its rigidity parameters. The Gaussian or saddlesplay modulus is found by evaluating the curvature energy of an interface onto which a saddle shape is imposed as this occurs in an Im3m cubic phase. The resulting values are consistent with those found by the classical indirect route, wherein the Gaussian bending modulus results from combining the curvature dependences of the interfacial tension in cylindrical and spherical geometries.

An optimized semiclassical approximation for vibrational response functions
View Description Hide DescriptionThe observables of multidimensional infrared spectroscopy may be calculated from nonlinear vibrational response functions. Fully quantum dynamical calculations of vibrational response functions are generally impractical, while completely classical calculations are qualitatively incorrect at long times. These challenges motivate the development of semiclassical approximations to quantum mechanics, which use classical mechanical information to reconstruct quantum effects. The meantrajectory (MT) approximation is a semiclassical approach to quantum vibrational response functions employing classical trajectories linked by deterministic transitions representing the effects of the radiationmatter interaction. Previous application of the MT approximation to the thirdorder response function R ^{(3)}(t _{3}, t _{2}, t _{1}) demonstrated that the method quantitatively describes the coherence dynamics of the t _{3} and t _{1} evolution times, but is qualitatively incorrect for the waitingtime t _{2} period. Here we develop an optimized version of the MT approximation by elucidating the connection between this semiclassical approach and the doublesided Feynman diagrams (2FD) that represent the quantum response. Establishing the direct connection between 2FD and semiclassical paths motivates a systematic derivation of an optimized MT approximation (OMT). The OMT uses classical mechanical inputs to accurately reproduce quantum dynamics associated with all three propagation times of the thirdorder vibrational response function.

Lattice Boltzmann implementation of the threedimensional BenNaim potential for waterlike fluids
View Description Hide DescriptionWe develop a threedimensional lattice Boltzmann (LB) model accounting for directional interactions between waterlike molecules, based on the socalled BenNaim (BN) potential [A. BenNaim, Molecular Theory of Water and Aqueous Solutions: Part I: Understanding Water (World Scientific Publishing Company, Year: 2010); A. BenNaim, “Statistical mechanics of ‘waterlike’ particles in two dimensions. I. Physical model and application of the PercusYevick equation,” J. Chem. Phys.54, 3682 (Year: 1971)]10.1063/1.1675414. The waterlike molecules are represented by rigid tetrahedra, with two donors and two acceptors at the corners and interacting with neighboring tetrahedra, sitting on the nodes of a regular lattice. The tetrahedra are free to rotate about their centers under the drive of the torque arising from the interparticle potential. The orientations of the water molecules are evolved in time via an overdamped Langevin dynamics for the torque, which is solved by means of a quaternion technique. The resulting advectiondiffusionreaction equation for the quaternion components is solved by a LB method, acting as a dynamic minimizer for the global energy of the fluid. By adding thermal fluctuations to the torque equation, the model is shown to reproduce some microscopic features of real water, such as an average number of hydrogen bonds per molecules (HBs) between 3 and 4, in a qualitative agreement with microscopic water models. Albeit slower than a standard LB solver for ordinary fluids, the present scheme opens up potentially farreaching scenarios for multiscale applications based on a coarsegrained representation of the water solvent.

Complexscaled equationofmotion coupledcluster method with single and double substitutions for autoionizing excited states: Theory, implementation, and examples
View Description Hide DescriptionTheory and implementation of complexscaled variant of equationofmotion coupledcluster method for excitation energies with single and double substitutions (EOMEECCSD) is presented. The complexscaling formalism extends the EOMEECCSD model to resonance states, i.e., excited states that are metastable with respect to electron ejection. The method is applied to Feshbach resonances in atomic systems (He, H^{−}, and Be). The dependence of the results on oneelectron basis set is quantified and analyzed. Energy decomposition and wave function analysis reveal that the origin of the dependence is in electron correlation, which is essential for the lifetime of Feshbach resonances. It is found that oneelectron basis should be sufficiently flexible to describe radial and angular electron correlation in a balanced fashion and at different values of the scaling parameter, θ. Standard basis sets that are optimized for notcomplexscaled calculations (θ = 0) are not sufficiently flexible to describe the θdependence of the wave functions even when heavily augmented by additional sets.

Double excitations from modified Hartree Fock subsequent minimization scheme
View Description Hide DescriptionDoubly excited states have nowadays become important in technological applications, e.g., in increasing the efficiency of solar cells and therefore, their description using ab initio methods is a great theoretical challenge as double excitations cannot be described by linear response theories based on a single Slater determinant. In the present work we extend our recently developed HartreeFock (HF) approximation for calculating singly excited states[M. Tassi, I. Theophilou, and S. Thanos, Int. J. Quantum Chem.113, 690 (Year: 2013)10.1002/qua.24049] in order to allow for the calculation of doubly excited states. We describe the double excitation as two holes in the subspace spanned from the occupied HF orbitals and two particles in the subspace of virtual HF orbitals. A subsequent minimization of the energy results to the determination of the spin orbitals of both the holes and the particles in the occupied and virtual subspaces, respectively. We test our method, for various atoms, H_{2} and polyene molecules which are known to have excitations presenting a significant double excitation character. Importantly, our approach is computationally inexpensive.

Nonadiabatic anharmonic electron transfer
View Description Hide DescriptionThe effect of an inner sphere, local mode vibration on an electron transfer is modeled using the nonadiabatic transition probability (rate) expression together with both the anharmonic Morse and the harmonic oscillator potential. For an anharmonic inner sphere mode, a variational analysis uses harmonic oscillator basis functions to overcome the difficulties evaluating Morsemodel FranckCondon overlap factors. Individual matrix elements are computed with the use of new, fast, robust, and flexible recurrence relations. The analysis therefore readily addresses changes in frequency and/or displacement of oscillator minimums in the different electron transfer states. Direct summation of the individual Boltzmann weighted FranckCondon contributions avoids the limitations inherent in the use of the familiar hightemperature, Gaussian form of the rate constant. The effect of harmonic versus anharmonic inner sphere modes on the electron transfer is readily seen, especially in the exoergic, inverted region. The behavior of the transition probability can also be displayed as a surface for all temperatures and values of the driving force/exoergicity Δ = −ΔG. The temperature insensitivity of the transfer rate is clearly seen when the exoergicity equals the collective reorganization energy (Δ = Λ_{ s }) along a maximum ln (w) vs. Δ ridge of the surface. The surface also reveals additional regions for Δ where ln (w) appears to be insensitive to temperature, or effectively activationless, for some kinds of inner sphere contributions.

A combined quasicontinuum/Langevin equation approach to study the selfdiffusion dynamics of confined fluids
View Description Hide DescriptionIn this work, we combine our earlier proposed empirical potential based quasicontinuum theory, (EQT) [A. V. Raghunathan, J. H. Park, and N. R. Aluru, J. Chem. Phys.127, 174701 (Year: 2007)10.1063/1.2793070], which is a coarsegrained multiscale framework to predict the static structure of confined fluids, with a phenomenological Langevin equation to simulate the dynamics of confined fluids in thermal equilibrium. An attractive feature of this approach is that all the input parameters to the Langevin equation (mean force profile of the confined fluid and the static friction coefficient) can be determined using the outputs of the EQT and the selfdiffusivity data of the corresponding bulk fluid. The potential of mean force profile, which is a direct output from EQT is used to compute the mean force profile of the confined fluid. The density profile, which is also a direct output from EQT, along with the selfdiffusivity data of the bulk fluid is used to determine the static friction coefficient of the confined fluid. We use this approach to compute the mean square displacement and survival probabilities of some important fluids such as carbondioxide, water, and LennardJones argon confined inside slit pores. The predictions from the model are compared with those obtained using molecular dynamics simulations. This approach of combining EQT with a phenomenological Langevin equation provides a mathematically simple and computationally efficient means to study the impact of structural inhomogeneity on the selfdiffusion dynamics of confined fluids.

Spinadaptation and redundancy in statespecific multireference perturbation theory
View Description Hide DescriptionSpinadaptation of virtual functions in statespecific multireference perturbation theory is examined. Redundancy occurring among virtual functions generated by unitary group based excitation operators on a modelspace function is handled by canonical orthogonalization. The treatment is found to remove nonphysical kinks observed earlier on potential energy surfaces. Sensitivity analysis of the new approach confirms the elimination of the drastic increase in singular values of sensitivity matrices, reported earlier.

Quartic scaling secondorder approximate coupled cluster singles and doubles via tensor hypercontraction: THCCC2
View Description Hide DescriptionThe secondorder approximate coupled cluster singles and doubles method (CC2) is a valuable tool in electronic structure theory. Although the density fitting approximation has been successful in extending CC2 to larger molecules, it cannot address the steep scaling with the number of basis functions, N. Here, we introduce the tensor hypercontraction (THC) approximation to CC2 (THCCC2), which reduces the scaling to and the storage requirements to . We present an algorithm to efficiently evaluate the THCCC2 correlation energy and demonstrate its quartic scaling. This implementation of THCCC2 uses a gridbased leastsquares THC (LSTHC) approximation to the densityfitted electron repulsion integrals. The accuracy of the CC2 correlation energy under these approximations is shown to be suitable for most practical applications.

Semilocal and hybrid density embedding calculations of groundstate chargetransfer complexes
View Description Hide DescriptionWe apply the frozen density embedding method, using a full relaxation of embedded densities through a freezeandthaw procedure, to study the electronic structure of several benchmark groundstate chargetransfer complexes, in order to assess the merits and limitations of the approach for this class of systems. The calculations are performed using both semilocal and hybrid exchangecorrelation (XC) functionals. The results show that embedding calculations using semilocal XC functionals yield rather large deviations with respect to the corresponding supermolecular calculations. Due to a large error cancellation effect, however, they can often provide a relatively good description of the electronic structure of chargetransfer complexes, in contrast to supermolecular calculations performed at the same level of theory. On the contrary, when hybrid XC functionals are employed, both embedding and supermolecular calculations agree very well with each other and with the reference benchmark results. In conclusion, for the study of groundstate chargetransfer complexes via embedding calculations hybrid XC functionals are the method of choice due to their higher reliability and superior performance.

Accurate prediction of nuclear magnetic resonance shielding constants: Towards the accuracy of CCSD(T) complete basis set limit
View Description Hide DescriptionIn this work, we have calculated the nuclear magnetic resonance (NMR) shielding constants for 42 molecules at the levels of second order MøllerPlesset perturbation (MP2) and coupledcluster singles and doubles model augmented by perturbative corrections for triple excitations CCSD(T). Basis set extrapolations to the complete basis set (CBS) limit have been performed. A focalpoint analysis method for magnetic parameters was proposed here, which adds the [σ e (CCSD(T)) − σ e (MP2)] difference to the MP2/CBS number to approximate the corresponding CCSD(T)/CBS value. Systematical comparison has demonstrated the usefulness of this FPAM/CBS scheme.

Topology of classical molecular optimal control landscapes in phase space
View Description Hide DescriptionOptimal control of molecular dynamics is commonly expressed from a quantum mechanical perspective. However, in most contexts the preponderance of molecular dynamics studies utilize classical mechanical models. This paper treats laserdriven optimal control of molecular dynamics in a classical framework. We consider the objective of steering a molecular system from an initial point in phase space to a target point, subject to the dynamic constraint of Hamilton's equations. The classical control landscape corresponding to this objective is a functional of the control field, and the topology of the landscape is analyzed through its gradient and Hessian with respect to the control. Under specific assumptions on the regularity of the control fields, the classical control landscape is found to be free of traps that could hinder reaching the objective. The Hessian associated with an optimal control field is shown to have finite rank, indicating the presence of an inherent degree of robustness to control noise. Extensive numerical simulations are performed to illustrate the theoretical principles on (a) a model diatomic molecule, (b) two coupled Morse oscillators, and (c) a chaotic system with a coupled quartic oscillator, confirming the absence of traps in the classical control landscape. We compare the classical formulation with the mathematically analogous quantum statetostate transition probability control landscape.
 Atoms, Molecules, and Clusters

Vibrational and electronic excitations in fluorinated ethene cations from the ground up
View Description Hide DescriptionValence threshold photoelectron spectra of four fluorinated ethenes; C_{2}H_{3}F, 1,1C_{2}H_{2}F_{2}, C_{2}HF_{3}, and C_{2}F_{4} were recorded at the Swiss Light Source with 0.002 eV resolution. The adiabatic ionization energies were found to be 10.364 ± 0.007, 10.303 ± 0.005, 10.138 ± 0.007, and 10.110 ± 0.009 eV, respectively. The electronic ground state of each cation shows wellresolved multicomponent vibrational progressions, the dominant transitions being in the C=C stretching mode. Density functional theory based Franck–Condon simulations are used to model the vibrational structure and assign the spectra, sometimes revising previous assignments. An additional vibrational progression in the first photoelectron band of 1,1C_{2}H_{2}F_{2} indicates that the ground electronic state of the molecular ion is no longer planar. It is shown that ab initio vibrational frequencies together with the observed vibrational spacings do not always suffice to assign the spectra. In addition to symmetry rules governing the transitions, it is often essential to consider the associated Franck–Condon factors explicitly. Ionization to higher lying excited valence electronic states were also recorded by threshold ionization up to 23 eV photon energy. Equationofmotion coupled cluster with single and double substitutions for ionization potential (EOMIPCCSD/ccpVTZ) calculations confirmed historic electronic state assignments, and untangled the ever more congested spectra with increasing Fsubstitution. Previous attempts at illuminating the intriguing dissociative photoionization mechanism of fluorinated ethenes are reconsidered in view of new computational and experimental results. We show how nonstatistical Fatom loss from C_{2}H_{3}F^{+} is decoupled from the ground state dissociation dynamics in the energy range of its state. Both the statistical and the nonstatistical dissociation processes are mediated by a plethora of conical intersections.

Ab initio studies of atomic properties and experimental behavior of element 119 and its lighter homologs
View Description Hide DescriptionStatic dipole polarizabilities of element 119 and its singly charged cation are calculated, along with those of its lighter homologs, Cs and Fr. Relativity is treated within the 4component DiracCoulomb formalism and electron correlation is included by the single reference coupled cluster approach with single, double, and perturbative triple excitations (CCSD(T)). Very good agreement with available experimental values is obtained for Cs, lending credence to the predictions for Fr and element 119. The atomic properties in group1 are largely determined by the valence ns orbital, which experiences relativistic stabilization and contraction in the heavier elements. As a result, element 119 is predicted to have a relatively low polarizability (169.7 a.u.), comparable to that of Na. The adsorption enthalpy of element 119 on Teflon, which is important for possible future experimental studies of this element, is estimated as 17.6 kJ/mol, the lowest among the atoms considered here.

Photoelectron spectroscopy of the aluminum hydride anions: AlH_{2} ^{−}, AlH_{3} ^{−}, Al_{2}H_{6} ^{−}, Al_{3}H_{9} ^{−}, and Al_{4}H_{12} ^{−}
View Description Hide DescriptionWe report measurements of the negative ion photoelectron spectra of the simple aluminum hydride anions: AlH_{2} ^{−}, AlH_{3} ^{−}, Al _{2}H_{6} ^{−}, Al _{3}H_{9} ^{−}, and Al _{4}H_{12} ^{−}. From these spectra, we measured the vertical detachment energies of the anions, and we estimated the electron affinities of their neutral counterparts. Our results for AlH_{2} ^{−}, AlH_{3} ^{−}, and Al _{2}H_{6} ^{−} were also compared with previous predictions by theory.

Ion imaging study of dissociative charge transfer in the N_{2} ^{+} + CH_{4} system
View Description Hide DescriptionThe velocity map ion imaging method is applied to the dissociative charge transfer reactions of N_{2} ^{+} with CH_{4} studied in crossed beams. The velocity space images are collected at four collision energies between 0.5 and 1.5 eV, providing both product kinetic energy and angular distributions for the reaction products CH_{3} ^{+} and CH_{2} ^{+}. The general shapes of the images are consistent with long range electron transfer from CH_{4} to N_{2} ^{+} preceding dissociation, and product kinetic energy distributions are consistent with energy resonance in the initial electron transfer step. The branching ratio for CH_{3} ^{+}:CH_{2} ^{+} is 85:15 over the full collision energy range, consistent with literature reports.