Volume 129, Issue 14, 14 October 2008
 ARTICLES

 Theoretical Methods and Algorithms

Approximate treatment of higher excitations in coupledcluster theory. II. Extension to general singledeterminant reference functions and improved approaches for the canonical Hartree–Fock case
View Description Hide DescriptionThe theory and implementation of approximate coupledcluster (CC), in particular approximate CC singles, doubles, triples, and quadruples methods, are discussed for general singledeterminant reference functions. While the extension of iterative approximate models to the nonHartree–Fock case is straightforward, the generalization of perturbative approaches is not trivial. In contrast to the corresponding perturbative triples methods, there are additional terms required for nonHartree–Fock reference functions, and there are several possibilities to derive approximations to these terms. As it turns out impossible to develop an approach that is consistent with the canonical Hartree–Fockbased theory, several new approximations have been implemented and their performance for total energies and heats of formation has been assessed. The numerical results show that the performance of the methods does not depend strongly on the approximations assumed. Furthermore, the new perturbative quadruples methods, when applied to canonical Hartree–Fock reference functions, outperform at least for absolute energies the existing ones without increasing the computational costs.

A molecular dynamics study of the phase transition in bcc metal nanoparticles
View Description Hide DescriptionThe phase transition between liquid and solid phases in bodycentered cubic (bcc) metal nanoparticles of iron,chromium,molybdenum, and tungsten with size ranging from 2000 to 31250 atoms was investigated using a molecular dynamics simulation. The nucleation from an undercooled liquid droplet was observed during cooling in all nanoparticles considered. It was found that a nucleus was generated near one side of the particle and solidification spread toward the other side the during nucleation process. On the other hand, the surfacemelting and subsequent inward melting of the solid core of the nanoparticles were observed during heating. The depression of the melting point was proportional to the inverse of the particle radius due to the Gibbs–Thomson effect. On the other hand, the depression of the nucleation temperature during cooling was not monotonic with respect to the particle radius since the nucleation from an undercooled liquid depends on the event probability of an embryo or a nucleus.

Correlation between conductivity or diffusivity and activation energy in amorphous solids
View Description Hide DescriptionThere exist many investigations of ionic transport in a variety of glasses. These studies exhibit strong correlation between ionic conductivity and activation energy: Typically, it is found that higher conductivity is associated with lower activation energies and vice versa. Although there are explanations for this at a phenomenological level, there is no consistent physical picture to explain the correlation between conductivity and activation energy. We have carried out molecular dynamics simulation as a function of the size of the impurity atom or diffusant (both neutral and charged) in a host amorphous matrix. We find that there is a maximum in selfdiffusivity as a function of the size of the impurity atom suggesting that there is an appropriate size for which the diffusivity is maximum. The activation energy is found to be the lowest for this size of the impurity. A similar maximum has been previously found in other condensed phases, such as confined fluids and dense liquids, and has its origin in the levitation effect. The implications of this result for understanding ionic conductivity in glasses are discussed. Our results suggest that there is a relation between microscopic structure of the amorphous solid, diffusivity or conductivity, and activation energy. The nature of this relationship is discussed in terms of the levitation parameter showing that diffusivity is maximum when the size of the neck or doorway radius is comparable with the size of the diffusant. Our computational results here are in excellent agreement with independent experimental results of Nascimento et al. [Braz. J. Phys.35, 626 (2005)] that structural features of the glass are important in determining the ionic conductivity.

Correlation functions in quantized Hamilton dynamics and quantal cumulant dynamics
View Description Hide DescriptionQuantized Hamilton dynamics (QHD) [O. V. Prezhdo and Y. V. Pereverzev, J. Chem. Phys.113, 6557 (2000)] and quantal cumulant dynamics (QCD) [Shigeta et al., J. Chem. Phys.125, 244102 (2006)] are used to obtain a semiclassical description of twotime correlation functions (CFs). Generally, lowerorder CFs couple to higherorder CFs. The infinite hierarchy is terminated by a closure, which neglects higherorder irreducible correlators and provides an efficient approximation to quantum mechanics. The approach is illustrated with a simple nonlinear system, for which the real part of the classical CF continues a perfect oscillation and the imaginary part is identically zero. At little computational expense, the secondorder QHD/QCD approximation reproduces the real and imaginary parts of the quantummechanical CF.

Interpreting the Coulombfield approximation for generalizedBorn electrostatics using boundaryintegral equation theory
View Description Hide DescriptionThe importance of molecular electrostatic interactions in aqueous solution has motivated extensive research into physical models and numerical methods for their estimation. The computational costs associated with simulations that include many explicit water molecules have driven the development of implicitsolvent models, with generalizedBorn (GB) models among the most popular of these. In this paper, we analyze a boundaryintegral equation interpretation for the Coulombfield approximation (CFA), which plays a central role in most GB models. This interpretation offers new insights into the nature of the CFA, which traditionally has been assessed using only a single point charge in the solute. The boundaryintegral interpretation of the CFA allows the use of multiple point charges, or even continuous charge distributions, leading naturally to methods that eliminate the interpolation inaccuracies associated with the Still equation. This approach, which we call boundaryintegralbased electrostatic estimation by the CFA (BIBEE/CFA), is most accurate when the molecular charge distribution generates a smooth normal displacement field at the solutesolvent boundary, and CFAbased GB methods perform similarly. Conversely, both methods are least accurate for charge distributions that give rise to rapidly varying or highly localized normal displacement fields. Supporting this analysis are comparisons of the reactionpotential matrices calculated using GB methods and boundaryelementmethod (BEM) simulations. An approximation similar to BIBEE/CFA exhibits complementary behavior, with superior accuracy for charge distributions that generate rapidly varying normal fields and poorer accuracy for distributions that produce smooth fields. This approximation, BIBEE by preconditioning (BIBEE/P), essentially generates initial guesses for preconditioned Krylovsubspace iterative BEMs. Thus, iterative refinement of the BIBEE/P results recovers the BEM solution; excellent agreement is obtained in only a few iterations. The boundaryintegralequation framework may also provide a means to derive rigorous results explaining how the empirical correction terms in many modern GB models significantly improve accuracy despite their simple analytical forms.

Adsorption of inert gases including element 118 on noble metal and inert surfaces from ab initio Dirac–Coulomb atomic calculations
View Description Hide DescriptionThe interaction of the inert gases Rn and element 118 with various surfaces has been studied on the basis of fully relativistic ab initio Dirac–Coulomb CCSD(T) calculations of atomic properties. The calculated polarizability of element 118, 46.3 a.u., is the largest in group 18, the ionization potential is the lowest at 8.91 eV, and the estimated atomic radius is the largest, 4.55 a.u. These extreme values reflect, in addition to the general trends in the Periodic Table, the relativistic expansion and destabilization of the outer valence orbital. Van der Waals coefficients and adsorption enthalpies of Ne through element 118 on noble metals and inert surfaces, such as quartz, ice, Teflon, and graphite, were calculated in a physisorption model using the atomic properties obtained. The coefficients were shown to steadily increase in group 18, while the increase in from Ne to Rn does not continue to element 118: The large atomic radius of the latter element is responsible for a decrease in the interaction energy. We therefore predict that experimental distinction between Rn and 118 by adsorption on these types of surfaces will not be feasible. A possible candidate for separating the two elements is charcoal; further study is needed to test this possibility.

Multibody scattering, correlation, molecular conduction, and the 0.7 anomaly
View Description Hide DescriptionWe describe a new gridbased (or localized orbitalbased) method for treating the effects of exchange and correlation on electronic transmission through a molecular target where there are initially other bound electrons. Our algorithm combines the approaches of (i) solidstate gridbased algorithms using selfenergies and (ii) the complex Kohn method from electronmolecule scattering. For the general problem of a molecular target with electrons, our algorithm should ideally solve for electronic transmission with a computational cost scaling as , although the present implementation is limited to onedimensional problems. In this paper, we implement our algorithm to solve three onedimensional model problems involving two electrons: (i) Singlechannel resonant transmission through a doublebarrier well (DBW), where the target already contains one boundstate electron [Rejec et al., Phys. Rev. B67, 075311 (2003)]; (ii) multichannel resonant transmission through a DBW, where the incoming electron can exchange energy with the bound electron; (iii) transmission through a triplebarrier well (TBW), where the incoming electron can knock forward the bound electron, yielding a physical model of electronassisted electron transfer. This article offers some insight about the role and size of exchange and correlation effects in molecular conduction, where few such rigorous calculations have yet been made. Such multibody effects have already been experimentally identified in mesoscopic electron transport, giving rise to the “0.7 anomaly,” whereby electrons traveling through a narrow channel pair up as singlets and triplets. We expect the effect of electronic correlation to be even more visible for conduction through molecules, where electrons should partially localize into bonding and antibonding orbitals.

The relative entropy is fundamental to multiscale and inverse thermodynamic problems
View Description Hide DescriptionWe show that the relative entropy,, provides a fundamental and unifying framework for multiscale analysis and for inverse molecularthermodynamic problems involving optimization of a model system () to reproduce the properties of a target one (). We demonstrate that the relative entropy serves as a generating function for principles in variational meanfieldtheory and uniqueness and gives intuitive results for simple case scenarios in model development. Moreover, we suggest that the relative entropy provides a rigorous framework for multiscale simulations and offers new numerical techniques for linking models at different scales. Finally, we show that carries physical significance by using it to quantify the deviations of a threesite model of water from simple liquids, finding that the relative entropy, a thermodynamic concept, even predicts water’s kinetic anomalies.

Real space method for the electronic structure of onedimensional periodic systems
View Description Hide DescriptionWe present a real space pseudopotential method for calculating the electronic structure of onedimensional periodic systems such as nanowires. As an application of this method, we examine Hpassivated Si nanowires. The band structure and heat of formation of the Si nanowires are presented and compared to plane wave methods. Our method is able to offer the same accuracy as the traditional plane wave methods but offers a number of computational advantages such as faster convergence for heteropolar nanowires.

The role of dimensionality on the quenching of spinorbit effects in the optics of gold nanostructures
View Description Hide DescriptionBy firstprinciples timedependent densityfunctional calculations, we show the relevance of relativistic effects to shape the photoabsorption cross section of small goldclusters (, , and ) and small nanowires. The relativistic effects not only dictate the stabilization of planar geometries (as it has already been shown by treating the core electrons relativistically): The spinorbit coupling also has a strong impact in the absorption spectra (resonances and oscillator strengths). This is especially true for nanowires, where the effect of spin orbit is large and not substantially reduced with the chain length, in contrast to more compact goldclusters where this spinorbit effect tends to be quenched. These results have far reaching consequences in fields such as electronic transport, where goldnanowires are often used, but where spinorbit effects are generally disregarded.

Two complementary molecular energy decomposition schemes: The Mayer and Ziegler–Rauk methods in comparison
View Description Hide DescriptionIn the present paper we discuss and compare two different energy decomposition schemes: Mayer’s Hartree–Fock energy decomposition into diatomic and monoatomic contributions [Chem. Phys. Lett.382, 265 (2003)], and the Ziegler–Rauk dissociation energy decomposition [Inorg. Chem.18, 1558 (1979)]. The Ziegler–Rauk scheme is based on a separation of a molecule into fragments, while Mayer’s scheme can be used in the cases where a fragmentation of the system in clearly separable parts is not possible. In the Mayer scheme, the density of a free atom is deformed to give the oneatom Mulliken density that subsequently interacts to give rise to the diatomic interaction energy. We give a detailed analysis of the diatomic energy contributions in the Mayer scheme and a close look onto the oneatom Mulliken densities. The Mulliken density has a single large maximum around the nuclear position of the atom , but exhibits slightly negative values in the vicinity of neighboring atoms. The main connecting point between both analysis schemes is the electrostaticenergy. Both decomposition schemes utilize the same electrostaticenergy expression, but differ in how fragment densities are defined. In the Mayer scheme, the electrostatic component originates from the interaction of the Mulliken densities, while in the Ziegler–Rauk scheme, the undisturbed fragment densities interact. The values of the electrostaticenergy resulting from the two schemes differ significantly but typically have the same order of magnitude. Both methods are useful and complementary since Mayer’s decomposition focuses on the energy of the finally formed molecule, whereas the Ziegler–Rauk scheme describes the bond formation starting from undeformed fragment densities.

Solvent effects on optical properties of molecules: A combined timedependent density functional theory/effective fragment potential approach
View Description Hide DescriptionA quantum mechanics/molecular mechanics (QM/MM) type of scheme is employed to calculate the solventinduced shifts of molecular electronic excitations. The effective fragment potential (EFP) method was used for the classical potential. Since EFP has a density dependent functional form, in contrast with most other MM potentials, timedependent density functional theory (TDDFT) has been modified to combine TDDFT with EFP. This new method is then used to perform a hybrid QM/MM molecular dynamics simulation to generate a simulated spectrum of the vertical excitation energy of acetone in vacuum and with 100 water molecules. The calculated watersolvent effect on the vertical excitation energy exhibits a blueshift of the vertical excitation energy in acetone , which is in good agreement with the experimental blueshift.

Nonequilibrium fluctuationdissipation theorem of Brownian dynamics
View Description Hide DescriptionStudying the Brownian motion of a system driven by an external control from one macroscopic state to another macroscopic state, this paper presents the derivation of a nonlinear fluctuationdissipation theorem (FDT). The new FDT relates the nonequilibrium work to the equilibrium freeenergy difference in a very simple manner. It is valid wherever the Brownian dynamics is applicable. It recovers the wellknown Crooks fluctuation theorem (CFT) within the quasiequilibrium regime where the dissipative work is nearly zero. It will also be shown that the CFT’s fundamental assumption of microscopic reversibility is not obeyed in experiments such as mechanically unfolding biological molecules, in which the external driving forces depend on the system’s coordinates.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Rotational spectrum and molecular properties of
View Description Hide DescriptionThe rotational spectra of six isotopologues of pyridinexenon, two isotopes of the nitrogen atom ( and ) in pyridine with three isotopes of the rare gas atom (, , and ) have been measured by pulsed jet Fourier transformmicrowave spectroscopy. The complex has a structure with the xenon atom located in the plane of symmetry perpendicular to the aromatic ring plane. Its distance from the center of mass of pyridine is , and it is tilted—with respect to the principal axis of pyridine—by toward the N atom. The and nuclear quadrupole coupling constants have been determined for the isotopologues containing these nuclei. Information on the dynamics of the Xe van der Waals motions was obtained from the centrifugal distortion and from the changes in the planar moments of inertia in going from pyridine to .

Laser detection of spinpolarized hydrogen from HCl and HBr photodissociation: Comparison of H and halogenatom polarizations
View Description Hide DescriptionThermal HCl and HBr molecules were photodissociated using circularly polarized light, and the speeddependent spin polarization of the Hatom photofragments was measured using polarized fluorescence at . Both polarization components, described by the and parameters which arise from incoherent and coherent dissociation mechanisms, are measured. The values of the parameter, for both HCl and HBr photodissociation, are within experimental error of the predictions of both ab initio calculations and of previous measurements of the polarization of the halide cofragments. The experimental and ab initio theoretical values of the parameter show some disagreement, suggesting that further theoretical investigations are required. Overall, good agreement occurs despite the fact that the current experiments photodissociate molecules at , whereas previous measurements were conducted at rotational temperatures of about .

Vibrational energy transfer between and He at very low temperatures: Impulsive versus complex formation mechanisms assisted by tunneling through the centrifugal barrier
View Description Hide DescriptionThe temperature dependence of the statetostate vibrational relaxation rate constant for collisions between and He at very low kinetic energies was studied. The fluorescence from with indicates that in the temperature range of these states are populated by only one collision with He. The behavior of with temperature can be divided into two groups. The group with quantum changes shows scattering resonances in the low temperature region, with a general monotonical decrease of the rate constant with temperature, suggesting the importance of van der Waals interactions. This behavior is supported by the calculation of the probability of tunneling through the centrifugal barriers. For collisions in which 4–5 quanta are lost in a single event, there are no evidences of scattering resonances and the values of the relaxation rate constants could be determined only at the highest temperatures of this study. This suggests that relaxation occurs via impulsive collisions. The branching ratios for each channel are also temperature dependent and this behavior also suggests that the energy transfer mechanism changes with .

Theoretical investigation of intramolecular vibrational energy redistribution in HFCO and DFCO induced by an external field
View Description Hide DescriptionThe present paper is devoted to a full quantum mechanical study of the intramolecular vibrational energy redistribution in HFCO and DFCO. In contrast to our previous studies [Pasin et al., J. Chem. Phys.124, 194304 (2006)and 126, 024302 (2007)], the dynamics is now performed in the presence of an external timedependent field. This more closely reflects the experimental conditions. A sixdimensional dipole surface is computed. The multiconfiguration timedependent Hartree method is exploited to propagate the corresponding sixdimensional wave packets. Special emphasis is placed on the excitation of the outofplane bending vibration and on the dissociation of the molecule. In the case of DFCO, we predict that it is possible to excite the outofplane bending mode of vibration and to drive the dissociation to with only one laser pulse with a fixed frequency and without excitation of an electronic state.

An ab initio calculation of the vibronic energy levels of the and electronic states of
View Description Hide DescriptionIn the present study, the results of an ab initio calculation of the vibronic energy levels in the and electronic states of are reported. This work is motivated by recent measurements carried out by [Sunahori et al.J. Chem. Phys.128, 244311 (2008)]. The vertical electronic spectrum,excitation energies, bending potential curves, and spinorbit constants for the title molecule are computed by means of the stateaverage complete active space selfconsistent field and multireference configuration interaction approach. Vibronic energy levels of the and states are calculated with the help of a simple, effectively onedimensional model. The results of the present study strongly support the analysis of experimental data by Sunahori et al. and offer reliable predictions for experimental searches for heretofore unobserved electronic states.

Experimental interrogation of the multidimensional and intermolecular potential energy surfaces
View Description Hide DescriptionResonant twophoton excitation of the Tshaped and linear complexes is used to access the intermolecular vibrational levels bound within the and intermolecular potentials. The excitation utilizes different metastable intermolecular vibrational levels within the and potentials to access levels with varying intermolecular vibrational excitation in the ionpair states. In addition to providing data revealing properties of the and potentials, the transition energies of the observed features permit the relative binding energies of the Tshaped and linear groundstate conformers to be accurately measured. The binding energies of the Tshaped and linear conformers are 16.6(3) and , respectively. These values and the observed transition energies are then used to set the binding energies of the Tshaped complexes in the , , , and potentials as 13.4(3), 13.3(3), 41(1), and , respectively. Nonadiabatic coupling between specific intermolecular vibrational levels within the state and the molecular state is observed.

The mechanism of paramagnetic NMR relaxation produced by Mn(II): Role of orthorhombic and fourthorder zero field splitting terms
View Description Hide DescriptionMn(II) is a spin5/2 paramagnetic ion that mediates a characteristically large NMRparamagneticrelaxation enhancement (NMRPRE) of nuclear spins in solution. In the range of high magnetic field strengths (above about 0.3 T), where the electronic Zeeman interaction provides the largest term of the electron spin Hamiltonian,NMRrelaxation mechanism is well understood. In the lower field range, the physical picture is more complex because of the presence in the spin Hamiltonian of zero field splitting (ZFS) terms that are comparable to or greater than the Zeeman term. This work describes a systematic study of the relaxation mechanism in the low field range, particularly aspects involving the dependence of NMRPRE on the orthorhombic and fourthorder (, ) ZFS tensor components. It is shown that the fourfold and twofold fourthorder components exert large orientationdependent influences on the NMRPRE. Thus, fourthorder terms with magnitudes equal to only a few percent of the quadratic ZFS terms produce large changes in the shape of the magnetic field profile of the PRE. Effects arising from the orthorhombic quadratic ZFS term are much smaller than those of the fourthorder terms and can in most cases be neglected. However, effects due to and need to be included in simulations of low field data.