Volume 129, Issue 19, 21 November 2008
 ARTICLES

 Theoretical Methods and Algorithms

Precision shooting: Sampling long transition pathways
View Description Hide DescriptionThe kinetics of collective rearrangements in solution, such as protein folding and nanocrystalphase transitions, often involve free energy barriers that are both long and rough. Applying methods of transition path sampling to harvest simulated trajectories that exemplify such processes is typically made difficult by a very low acceptance rate for newly generated trajectories. We address this problem by introducing a new generation algorithm based on the linear short time behavior of small disturbances in phase space. Using this “precision shooting” technique, arbitrarily small disturbances can be propagated in time, and any desired acceptance ratio of shooting moves can be obtained. We demonstrate the method for a simple but computationally problematic isomerization process in a dense liquid of soft spheres. We also discuss its applicability to barriercrossing events involving metastable intermediate states.

Optimized effective potentials from arbitrary basis sets
View Description Hide DescriptionWe investigate the use of a regularized optimized effective potential (OEP) energy functional and curve procedure [T. HeatonBurgess, F. A. Bulat, and W. Yang, Phys. Rev. Lett.98, 256401 (2007)] for determining physically meaningful OEPs from arbitrary combinations of finite orbital and potential basis sets. The important issue of the manner in which the optimal regularization parameter is determined from the curve perspective is reconsidered with the introduction of a rigorous measure of the quality of the potential generated—that being, the extent to which the Ghosh–Parr exchange energy virial relation is satisfied along the curve. This approach yields nearly identical potentials to our previous work employing a minimum derivative condition, however, gives rise to slightly lower exactexchange total energies. We observe that the groundstateenergy and orbital energies obtained from this approach, either with balanced or unbalanced basis sets, yield meaningful potentials and energies which are in good comparison to other (a priori balanced) finite basis OEP calculations and experimental ionization potentials. As such, we believe that the regularized OEP functional approach provides a computationally robust method to address the numerical stability issues of this often illposed problem.

Optimal alignment control of a nonpolar molecule through nonresonant multiphoton transitions
View Description Hide DescriptionAlignment control of an ensemble of nonpolar molecules is numerically studied by means of optimal control simulation. A nitrogen molecule that is modeled by a quantum rigid rotor is adopted. Controlled rotational wave packets are created through nonresonant optical transitions induced by polarizability coupling. Optimal pulses are designed to achieve the alignment control at a specified time in the absence/presence of external static fields in zero and finitetemperature cases, as well as to maintain an aligned state. When maintaining an aligned state over a specified time interval is chosen as a target, the control mechanism is primarily attributed to a dynamical one. Multiple optimal solutions that lead to virtually the same control achievement are found, which are consistent with the topology of the quantum control landscape.

Coarse grained open system quantum dynamics
View Description Hide DescriptionWe show that the quantum dynamics of a system comprised of a subspace coupled to a larger subspace can be recast as a reduced set of “coarse grained” ordinary differential equations with constant coefficients. These equations can be solved by a single diagonalization of a general complex matrix. The method makes no assumptions about the strength of the couplings between the and the subspaces, nor is there any limitation on the initial population in . The utility of the method is demonstrated via computations in three following areas: molecular compounds, photonicmaterials, and condensed phases.

A noniterative perturbative triples correction for the spinflipping and spinconserving equationofmotion coupledcluster methods with single and double substitutions
View Description Hide DescriptionA noniterative triples correction for the equationofmotion coupledcluster method with single and double substitutions (CCSD) is presented. The correction is derived by secondorder perturbation treatment of the similaritytransformed CCSD Hamiltonian. The spinconserving variant of the correction is identical to the triples correction of Piecuch and coworkers [Mol. Phys.104, 2149 (2006)] derived within methodofmoments framework and is not size intensive. The spinflip variant of the correction is size intensive. The performance of the correction is demonstrated by calculations of electronic excitation energies in methylene, nitrenium ion, cyclobutadiene, ortho, meta, and parabenzynes, 1,2,3tridehydrobenzene, as well as C–C bond breaking in ethane. In all cases except cyclobutadiene, the absolute values of the correction for energy differences were 0.1 eV or less. In cyclobutadiene, the absolute values of the correction were as large as 0.4 eV. In most cases, the correction reduced the errors against the benchmark values by about a factor of 2–3, the absolute errors being less than 0.04 eV.

Perturbative calculation of spinorbit splittings using the equationofmotion ionizationpotential coupledcluster ansatz
View Description Hide DescriptionSpinorbit splittings for states are calculated within coupledcluster (CC) theory via firstorder degenerate perturbation theory. Using the equationofmotion CC variant for ionization potentials (EOMIPCC), the two components of the considered state are treated in a balanced way by generating both radical states via annihilation of one electron out of the CC wave function of the corresponding anion. We report on the implementation of the described approach within the CC singles and doubles approximation. To ensure computational efficiency, an atomic meanfield approximation for the spinorbit integrals is used, resulting in a formulation in terms of oneelectron transitiondensity matrices. Calculations for radicals (, S, Se) lead to satisfactory agreement with experiment. For systems that within an EOMIPCC treatment can only be reached from a triplet reference state (e.g., CF and ) the influence of spin contamination is found to be negligible.

Magnetic exchange couplings from noncollinear spin density functional perturbation theory
View Description Hide DescriptionWe propose a method for the evaluation of magnetic exchange couplings based on noncollinear spin density functional calculations. The method employs the second derivative of the total Kohn–Sham energy of a single reference state, in contrast to approximations based on Kohn–Sham total energy differences. The advantage of our approach is twofold: It provides a physically motivated picture of the transition from a lowspin to a highspin state, and it utilizes a perturbation scheme for the evaluation of magnetic exchange couplings. The latter simplifies the way these parameters are predicted using first principles: It avoids the nontrivial search for different spin states that needs to be carried out in energy difference methods, and it opens the possibility of “blackboxifying” the extraction of exchange couplings from density functional theory calculations. We present proof of concept calculations of magnetic exchange couplings in the H–He–H model system and in an oxovanadium bimetallic complex where the results can be intuitively rationalized.

Optical absorption of small silver clusters: ,
View Description Hide DescriptionWe present a joint theoretical and experimental investigation of the absorption spectra of silverclusters . The experimental spectra of clusters isolated in an Ar matrix are compared with the calculated ones in the framework of the timedependent density functional theory. The analysis of the molecular transitions indicates that the electrons are responsible for the optical response of small clusters while the electrons play a crucial role in the optical excitations for larger values.

An efficient implementation for determining volume polarization in selfconsistent reaction field theory
View Description Hide DescriptionAn efficient algorithm of the surface and volume polarization for electrostatics (SVPE) method in selfconsistent reaction field (SCRF) theory, denoted by SV(1)PE, has been proposed to simulate direct volume polarization potential with a single layer of point charges outside the solute cavity while the indirect effects of volume polarization on surfacepolarization are still simulated with multiple layers of point charges. The free energies of solvation calculated using the SV(1)PE algorithm (implemented in GAUSSIAN03) reproduce the corresponding values calculated using the standard SVPE implementation within an error of only when the solute cavity is defined by the standard solute charge isodensity contour. The SV(1)PE results are much less sensitive to the used cavity size in comparison with the wellestablished surface and simulated volume polarization for electrostatics [SS(V)PE] method which simulates volume polarization through an additional surface charge distribution on the cavitysurface. The SCRF calculations using the SV(1)PE method are more efficient than those using the original SVPE method.

Firstprinciples study of thermal and electronactivated dissociation of acetone on Si(001)
View Description Hide DescriptionUsing firstprinciples densityfunctional calculations, we investigate the reaction of acetone on the Si(001) surface, which exhibits the conversion from a kinetically controlled reaction to thermodynamically controlled one by means of thermal anneal or the highly confined electron beam of the scanning tunneling microscopy(STM) tip. We identified the four different reaction pathways forming not only two kinds of di structures on top of a single Si dimer (termed as the cycloaddition structure) and across the ends of two adjacent Si dimers but also two bridgebonded dissociative structures (termed the “endbridge” and “dimerbridge” structures) involving two adjacent Si dimers. Our calculated energy profiles for the reaction pathways show not only that formation of the cycloaddition structure is kinetically favored because of its lowenergy barrier, but also that, as temperature increases, the kinetically favored cycloaddition structure is converted to the more thermodynamically stable endbridge and dimerbridge structures via an intermediate state where the O atom forms a dative bond to the down Si atom of the buckled dimer. In addition, we find that the Si–C bonding (antibonding) states of the cycloaddition structure appear at about 1–2 (2–3) eV below (above) the Fermi level, in which injected holes (electrons) through the STM tip can be created (trapped) to give rise to a Si–C bond breakage. These results manifest that the kinetically controlled reaction of acetone on Si(001) is associated with the cycloaddition structure, rather than the cleavage structure proposed by a recent STM experiment.

On the accuracy of densityfunctional theory exchangecorrelation functionals for H bonds in small water clusters. II. The water hexamer and van der Waals interactions
View Description Hide DescriptionSecond order Møller–Plesset perturbation theory at the complete basis set limit and diffusion quantum Monte Carlo are used to examine several low energy isomers of the water hexamer. Both approaches predict the socalled prism to be the lowest energy isomer, followed by cage, book, and cyclic isomers. The energies of the four isomers are very similar, all being within . These reference data are then used to evaluate the performance of several densityfunctional theory exchangecorrelation (xc) functionals. A subset of the xc functionals tested for smaller water clusters [I. Santra et al., J. Chem. Phys.127, 184104 (2007)] has been considered. While certain functionals do a reasonable job at predicting the absolute dissociation energies of the various isomers (coming within ), none predict the correct energetic ordering of the four isomers nor does any predict the correct low total energy isomer. All xc functionals tested either predict the book or cyclic isomers to have the largest dissociation energies. A manybody decomposition of the total interactionenergies within the hexamers leads to the conclusion that the failure lies in the poor description of van der Waals (dispersion) forces in the xc functionals considered. It is shown that the addition of an empirical pairwise (attractive) correction to certain functionals allows for an improved energetic ordering of the hexamers. The relevance of these results to densityfunctional simulations of liquid water is also briefly discussed.

Quantum trajectory calculations for bipolar wavepacket dynamics in one dimension
View Description Hide DescriptionQuantum trajectory methods (QTMs) hold great promise as a potential means of obtaining dynamical insight and computational scaling similar to classical trajectory simulations but in an exact quantum dynamical context. To date, the development of QTMs has been stymied by the “node problem”—highly nonclassical and numerically unstable trajectories that arise when the wavepacket density exhibits substantial interference oscillations. In a recent paper, however [B. Poirier, J. Chem. Phys.128, 164115 (2008)], a “bipolar decomposition,” , was introduced for onedimensional (1D) wavepacket dynamics calculations such that the component densities are slowly varying and otherwise interferencefree, even when itself is highly oscillatory. The bipolar approach is thus ideally suited to a QTM implementation, as is demonstrated explicitly in this paper. Two model 1D benchmark systems exhibiting substantial interference are considered—one with more “quantum” system parameters and the other more classicallike. For the latter, more challenging application, synthetic QTM results are obtained and found to be extremely accurate, as compared to a corresponding fixedgrid calculation. Ramifications of the bipolar QTM approach for the classical limit and also for multidimensional applications, are discussed.

Nonlinear quantum time correlation functions from centroid molecular dynamics and the maximum entropy method
View Description Hide DescriptionA new approach for the calculation of nonlinear quantum time correlation functions within the pathintegral centroid dynamics formalism is presented. This approach combines information on the realtime dynamics obtained from centroid molecular dynamics with classical operators with information on the corresponding imaginarytime dynamics obtained from pathintegral molecular dynamics. Nonlinear quantum correlation functions in the high and low temperature regimes computed for model potentials are in remarkably good agreement with the corresponding exact results, suggesting that the method represents an effective and accurate approach for the investigation of general quantum time correlation functions in systems with many degrees of freedom.

Exact integral constraint requiring only the groundstate electron density as input on the exchangecorrelation force for spherical atoms
View Description Hide DescriptionFollowing some studies of by earlier workers for the density functional theory(DFT) onebody potential generating the exact groundstate density, we consider here the special case of spherical atoms. The starting point is the differential virial theorem, which is used, as well as the Hiller–Sucher–Feinberg [Phys. Rev. A18, 2399 (1978)] identity to show that the scalar quantity paralleling the above vector integral, namely, , is determined solely by the electron density at the nucleus for the like atoms He and Be. The force is then related to the derivative of the exchangecorrelation potential by terms involving only the external potential in addition to . The resulting integral constraint should allow some test of the quality of currently used forms of . The article concludes with results from the differential virial theorem and the Hiller–Sucher–Feinberg identity for the exact manyelectron theory of spherical atoms, as well as for the DFT for atoms such as Ne with a closed shell.

The CCSD(T) complete basis set limit for Ne revisited
View Description Hide DescriptionRecent estimates of the CCSD(T)(FC) limit for the neon atom ( and ) are refined. Reexamination of the basis set convergence of the separate selfconsistent field, , , CCSD–MP2, and (T) components of the valence CCSD(T) energy gives a complete basis set limit of . This can now be used as an improved benchmark to calibrate more approximate calculations.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Analysis of polyatomic molecules using high resolution coherent twodimensional spectroscopy: Application to nitrogen dioxide
View Description Hide DescriptionThe peaksorting capabilities of high resolution coherent twodimensional (2D) spectroscopy provide a new way of dealing with severe rotational congestion. This paper describes the application of this technique to the polyatomic molecule, . is a primary component of photochemical smog and has a notoriously complex and congested spectrum that extends from the infrared to the ultraviolet regions. This spectrum is infamous for having an unusually high density of peaks and very few regular patterns. However, the coherent 2D spectrum of shows a network consisting of numerous Xshaped patterns that mark the locations of vibronic origins. This paper describes how peak sorting leads to the formation of such patterns and how peak coupling can be used to conduct a rotational analysis of congested areas in the visible spectrum of .

Melting scenario in metallic clusters
View Description Hide DescriptionThe isothermal Browniantype molecular dynamics simulation has been applied to study the melting behavior of bimetallic clusters. It was found that the specific heat and Lindermannlike parameter customarily used in bulk system to describe solidliquidtransition show incongruity in the predicted melting temperature . The underlying mechanisms that lead to the incompatibility of separately deduced from these two quantities were analyzed further. To gain insight into the melting behavior, we calculated in addition the velocity autocorrelation function and its Fourier transform, the power spectrum, and extracted from them the . It appears that the inferred from the latter quantities is closer to that deduced from the principal peak position of specific heat. Two bimetallic clusters, namely, and , were selected for a thorough investigation. In the context of cluster morphology, we scrutinized the atomic distributions of , , and and effected a comparative study between a bimetallic cluster and a pure cluster so as to learn from comparison the differences in the thermal reaction of atoms, in particular, the impurity atom in the bimetallic cluster. On analyzing the dynamical data, we observed at a lower temperature migrational relocation of atoms whose dynamics was superimposed at an intermediate temperature by permutations between atoms, and at a higher temperature , liquidlike or even gaslike behavior.

Kinetic and theoretical study of the reaction of Cl atoms with a series of linear thiols
View Description Hide DescriptionThe reactions of Cl with a series of linear thiols: 1propanethiol , 1butanethiol , and 1pentanethiol were investigated as a function of temperature (in the range of ) and pressure (in the range of ) by laser photolysisresonance fluorescence. Only 1propanethiol has previously been studied, but at of total pressure. The derived Arrhenius expressions obtained using our kinetic data were as follows: , , and (in units of ). Moreover, a theoretical insight into mechanisms of these reactions has also been pursued through ab initio Möller–Plesset secondorder perturbation treatment calculations with basis set. Optimized geometries have been obtained for transition states and molecular complexes appearing along the different reaction pathways. Furthermore, molecular energies have been calculated at QCISD(T) level in order to get an estimation of the activation energies. Finally, the nature of the molecular complexes and transitions states is analyzed by using kineticpotential and natural bond orbital total energy decomposition schemes.

Photodissociation dynamics of methyl formate at 193.3 nm: Branching ratios, kineticenergy distributions, and angular anisotropies of products
View Description Hide DescriptionWe investigated the photodissociation dynamics of methyl formated at 193.3 nm in a molecularbeam apparatus using undulator radiation as an ionization source. We measured kineticenergy distributions, spatial angular anisotropies, and branching ratios of all photofragments. Fractions of energy release into product translation were calculated from the kineticenergy distributions. Four primary dissociation pathways to asymptotes , , , and were identified; their branching ratios were determined to be 0.73, 0.06, 0.13, and 0.08, respectively. The former two dissociation paths were discernible in the timeofflight spectra of fragment with a signal at . Nominal products DCO and were unobservable as DCO in state dissociated to and internally hot decomposed to . Products DCO and have angular anisotropy parameter but other products have nearly isotropic angular distributions with . Nonadiabatic transitions might play an important role in fragmentation of methyl formate irradiated at 193.3 nm.

The multiconfigurationalreference internally contracted configuration interaction/complete basis set study of the excited states of the trifluoride anion
View Description Hide DescriptionThe multiconfigurationalreference internally contracted configuration interaction (MRCI)/augccpVQZbased computational protocol was employed to search for the minima of the potential energy surface of the lowlying singlet and triplet electronic states of the trifluoride anion in the , , , and symmetry groups. The bound state was located ( and ), which was predicted to lie less than 1 eV above the ground state by both the MRCI and equationofmotion coupledcluster singles, doubles and triples approaches [the MRCI adiabatic excitation energy extrapolated to the complete basis set (CBS) limit was 0.91 eV]. The latter value is proposed as a reliable estimate of the singlettriplet energy gap in . The vertical transitions from the state were analyzed in terms of the reorganization of electrons leading to the excited states and the corresponding MRCI/CBS excitation energies.