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28 Mar 2013

Volume 138, Issue 12, Articles (12xxxx)

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J. Chem. Phys. 138, 124701 (2013); http://dx.doi.org/10.1063/1.4794685 (9 pages)

Luying Wang, Randall S. Dumont, and James M. Dickson
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back to top Theoretical Methods and Algorithms

Analytical energy gradient used in variational Born-Oppenheimer calculations with all-electron explicitly correlated Gaussian functions for molecules containing one π electron

Wei-Cheng Tung, Michele Pavanello, Keeper L. Sharkey, Nikita Kirnosov, and Ludwik Adamowicz

J. Chem. Phys. 138, 124101 (2013); http://dx.doi.org/10.1063/1.4795094 (11 pages)

Online Publication Date: 22 March 2013

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An algorithm for variational calculations of molecules with one π electron performed with all-electron explicitly correlated Gaussian (ECG) functions with floating centers is derived and implemented. The algorithm includes the analytic gradient of the Born-Oppenheimer 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, c3Πu, C1Πu, i3Πg, and I1Πg, 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, lowest-to-date, variational energy upper bounds for all four states.
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31.15.vj Electron correlation calculations for atoms and ions: excited states

Hyperfine interaction mechanism of magnetic field effects in sequential fluorophore and exciplex fluorescence

Dmitry V. Dodin, Anatoly I. Ivanov, and Anatoly I. Burshtein

J. Chem. Phys. 138, 124102 (2013); http://dx.doi.org/10.1063/1.4795576 (11 pages)

Online Publication Date: 22 March 2013

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The magnetic field effect on the fluorescence of the photoexcited electron acceptor, 1A*, and the exciplex, 1[D+δA−δ] formed at contact of 1A* with an electron donor 1D, 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 radical-ion pair. The magnetic field sensitive stage is the spin conversion in the resulting geminate radical-ion 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.
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33.50.Dq Fluorescence and phosphorescence spectra
82.20.Yn Solvent effects on reactivity
82.30.Cf Atom and radical reactions; chain reactions; molecule-molecule reactions
82.30.Lp Decomposition reactions (pyrolysis, dissociation, and fragmentation)
33.57.+c Magneto-optical and electro-optical spectra and effects
31.30.Gs Hyperfine interactions and isotope effects
31.70.Dk Environmental and solvent effects

Direct evaluation of the saddle splay modulus of a liquid-liquid interface using the classical mean field lattice model

F. A. M. Leermakers

J. Chem. Phys. 138, 124103 (2013); http://dx.doi.org/10.1063/1.4795607 (7 pages)

Online Publication Date: 22 March 2013

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We study the curvature dependence of the liquid-liquid (liquid-gas) interface using the well-known mean field lattice model to estimate its rigidity parameters. The Gaussian or saddle-splay 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.
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68.03.Cd Surface tension and related phenomena
68.05.Cf Liquid-liquid interface structure: measurements and simulations
62.10.+s Mechanical properties of liquids

An optimized semiclassical approximation for vibrational response functions

Mallory Gerace and Roger F. Loring

J. Chem. Phys. 138, 124104 (2013); http://dx.doi.org/10.1063/1.4795941 (11 pages)

Online Publication Date: 25 March 2013

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The 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 mean-trajectory (MT) approximation is a semiclassical approach to quantum vibrational response functions employing classical trajectories linked by deterministic transitions representing the effects of the radiation-matter interaction. Previous application of the MT approximation to the third-order response function R(3)(t3, t2, t1) demonstrated that the method quantitatively describes the coherence dynamics of the t3 and t1 evolution times, but is qualitatively incorrect for the waiting-time t2 period. Here we develop an optimized version of the MT approximation by elucidating the connection between this semiclassical approach and the double-sided 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 third-order vibrational response function.
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33.20.Tp Vibrational analysis
33.20.Ea Infrared spectra
31.15.-p Calculations and mathematical techniques in atomic and molecular physics

Lattice Boltzmann implementation of the three-dimensional Ben-Naim potential for water-like fluids

Nasrollah Moradi, Andreas Greiner, Francesco Rao, and Sauro Succi

J. Chem. Phys. 138, 124105 (2013); http://dx.doi.org/10.1063/1.4795008 (9 pages)

Online Publication Date: 26 March 2013

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We develop a three-dimensional lattice Boltzmann (LB) model accounting for directional interactions between water-like molecules, based on the so-called Ben-Naim (BN) potential [A. Ben-Naim, Molecular Theory of Water and Aqueous Solutions: Part I: Understanding Water (World Scientific Publishing Company, 2010); A. Ben-Naim, “Statistical mechanics of ‘waterlike’ particles in two dimensions. I. Physical model and application of the Percus-Yevick equation,” J. Chem. Phys. 54, 3682 (1971)]10.1063/1.1675414. The water-like 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 advection-diffusion-reaction 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 far-reaching scenarios for multiscale applications based on a coarse-grained representation of the water solvent.
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66.10.C- Diffusion and thermal diffusion
61.20.Ja Computer simulation of liquid structure

Complex-scaled equation-of-motion coupled-cluster method with single and double substitutions for autoionizing excited states: Theory, implementation, and examples

Ksenia B. Bravaya, Dmitry Zuev, Evgeny Epifanovsky, and Anna I. Krylov

J. Chem. Phys. 138, 124106 (2013); http://dx.doi.org/10.1063/1.4795750 (15 pages)

Online Publication Date: 26 March 2013

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Theory and implementation of complex-scaled variant of equation-of-motion coupled-cluster method for excitation energies with single and double substitutions (EOM-EE-CCSD) is presented. The complex-scaling formalism extends the EOM-EE-CCSD 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 one-electron 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 one-electron 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 not-complex-scaled calculations (θ = 0) are not sufficiently flexible to describe the θ-dependence of the wave functions even when heavily augmented by additional sets.
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31.15.bw Coupled-cluster theory
31.15.vj Electron correlation calculations for atoms and ions: excited states
32.80.Zb Autoionization

Double excitations from modified Hartree Fock subsequent minimization scheme

M. Tassi, Iris Theophilou, and S. Thanos

J. Chem. Phys. 138, 124107 (2013); http://dx.doi.org/10.1063/1.4797466 (8 pages)

Online Publication Date: 27 March 2013

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Doubly 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 Hartree-Fock (HF) approximation for calculating singly excited states [M. Tassi, I. Theophilou, and S. Thanos, Int. J. Quantum Chem. 113, 690 (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, H2 and polyene molecules which are known to have excitations presenting a significant double excitation character. Importantly, our approach is computationally inexpensive.
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31.15.xr Self-consistent-field methods
31.15.ag Excitation energies and lifetimes; oscillator strengths

Nonadiabatic anharmonic electron transfer

P. P. Schmidt

J. Chem. Phys. 138, 124108 (2013); http://dx.doi.org/10.1063/1.4795581 (16 pages)

Online Publication Date: 27 March 2013

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The 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 Morse-model Franck-Condon 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 Franck-Condon contributions avoids the limitations inherent in the use of the familiar high-temperature, 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 = Λs) 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.
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82.30.Fi Ion-molecule, ion-ion, and charge-transfer reactions
33.70.Ca Oscillator and band strengths, lifetimes, transition moments, and Franck-Condon factors
82.20.Db Transition state theory and statistical theories of rate constants

A combined quasi-continuum/Langevin equation approach to study the self-diffusion dynamics of confined fluids

T. Sanghi and N. R. Aluru

J. Chem. Phys. 138, 124109 (2013); http://dx.doi.org/10.1063/1.4796387 (9 pages)

Online Publication Date: 28 March 2013

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In this work, we combine our earlier proposed empirical potential based quasi-continuum theory, (EQT) [A. V. Raghunathan, J. H. Park, and N. R. Aluru, J. Chem. Phys. 127, 174701 (2007)10.1063/1.2793070], which is a coarse-grained 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 self-diffusivity 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 self-diffusivity 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 carbon-dioxide, water, and Lennard-Jones 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 self-diffusion dynamics of confined fluids.
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66.10.cg Mass diffusion, including self-diffusion, mutual diffusion, tracer diffusion, etc.
02.50.Cw Probability theory
62.10.+s Mechanical properties of liquids
61.20.Ja Computer simulation of liquid structure

Spin-adaptation and redundancy in state-specific multireference perturbation theory

Péter Jeszenszki, Péter R. Surján, and Ágnes Szabados

J. Chem. Phys. 138, 124110 (2013); http://dx.doi.org/10.1063/1.4795436 (14 pages) | Cited 1 time

Online Publication Date: 28 March 2013

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Spin-adaptation of virtual functions in state-specific multireference perturbation theory is examined. Redundancy occurring among virtual functions generated by unitary group based excitation operators on a model-space function is handled by canonical orthogonalization. The treatment is found to remove non-physical 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.
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31.15.xp Perturbation theory
31.50.-x Potential energy surfaces

Quartic scaling second-order approximate coupled cluster singles and doubles via tensor hypercontraction: THC-CC2

Edward G. Hohenstein, Sara I. L. Kokkila, Robert M. Parrish, and Todd J. Martínez

J. Chem. Phys. 138, 124111 (2013); http://dx.doi.org/10.1063/1.4795514 (10 pages) | Cited 1 time

Online Publication Date: 28 March 2013

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The second-order 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 O(N5) scaling with the number of basis functions, N. Here, we introduce the tensor hypercontraction (THC) approximation to CC2 (THC-CC2), which reduces the scaling to O(N4) and the storage requirements to O(N2). We present an algorithm to efficiently evaluate the THC-CC2 correlation energy and demonstrate its quartic scaling. This implementation of THC-CC2 uses a grid-based least-squares THC (LS-THC) approximation to the density-fitted electron repulsion integrals. The accuracy of the CC2 correlation energy under these approximations is shown to be suitable for most practical applications.
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31.15.bw Coupled-cluster theory
31.15.eg Exchange-correlation functionals (in current density functional theory)

Semilocal and hybrid density embedding calculations of ground-state charge-transfer complexes

S. Laricchia, E. Fabiano, and F. Della Sala

J. Chem. Phys. 138, 124112 (2013); http://dx.doi.org/10.1063/1.4795825 (12 pages) | Cited 1 time

Online Publication Date: 28 March 2013

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We apply the frozen density embedding method, using a full relaxation of embedded densities through a freeze-and-thaw procedure, to study the electronic structure of several benchmark ground-state charge-transfer 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 exchange-correlation (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 charge-transfer 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 ground-state charge-transfer complexes via embedding calculations hybrid XC functionals are the method of choice due to their higher reliability and superior performance.
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34.70.+e Charge transfer
31.15.eg Exchange-correlation functionals (in current density functional theory)

Accurate prediction of nuclear magnetic resonance shielding constants: Towards the accuracy of CCSD(T) complete basis set limit

Meng Sun, Igor Ying Zhang, Anan Wu, and Xin Xu

J. Chem. Phys. 138, 124113 (2013); http://dx.doi.org/10.1063/1.4796485 (9 pages)

Online Publication Date: 29 March 2013

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In this work, we have calculated the nuclear magnetic resonance (NMR) shielding constants for 42 molecules at the levels of second order Møller-Plesset perturbation (MP2) and coupled-cluster 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 focal-point analysis method for magnetic parameters was proposed here, which adds the [σe(CCSD(T)) − σe(MP2)] difference to the MP2/CBS number to approximate the corresponding CCSD(T)/CBS value. Systematical comparison has demonstrated the usefulness of this FPA-M/CBS scheme.
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31.15.bw Coupled-cluster theory
31.15.xp Perturbation theory
33.25.+k Nuclear resonance and relaxation

Topology of classical molecular optimal control landscapes in phase space

Carlee Joe-Wong, Tak-San Ho, Ruixing Long, Herschel Rabitz, and Rebing Wu

J. Chem. Phys. 138, 124114 (2013); http://dx.doi.org/10.1063/1.4797498 (15 pages)

Online Publication Date: 29 March 2013

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Optimal 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 laser-driven 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 state-to-state transition probability control landscape.
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33.80.-b Photon interactions with molecules
34.20.-b Interatomic and intermolecular potentials and forces, potential energy surfaces for collisions
31.15.-p Calculations and mathematical techniques in atomic and molecular physics
03.65.-w Quantum mechanics
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