Volume 122, Issue 11, 15 March 2005
 ARTICLES

 Theoretical Methods and Algorithms

Elusive contribution of the experimental surface molecular electrostatic potential and promolecule approximation in the empirical estimate of the crystal density
View Description Hide DescriptionThe aim of this study is to probe the crystal density description in terms of pertinent molecular characteristics and properties. In this purpose, the electrostatic potential was derived from available experimental electron density multipole parameters of molecular compounds with different magnitudes. The surfaceelectrostatic potential has been analyzed through the positive and negative statistical variances. The surface of the molecule is here corresponding to particular isodensity values according to Bader’s topological theory. Following the successful Politzer’s method based on quantum mechanics calculations to empirically describe macroscopic properties, the crystal density was regressed on the molecular density and the surfaceelectrostatic potential variance. This latter appears to be a poor statistical descriptor of the crystal density when the experimentally derived electrostatic potential is used and it does not significantly improve the fit of to molecular density alone. Compared to Politzer’s approach based on gas phase isolated molecules, the experimental electrostatic potential is biased by the interactions in the crystal lattice. As an alternative to other sophisticated methods, the promolecule isodensity surface offers a quite useful and straightforward way to define the molecular volumes. The reported description of the crystal density for a set of 50 molecules using the promolecule approach yields satisfactory results.

Test of a nonempirical density functional: Shortrange part of the van der Waals interaction in raregas dimers
View Description Hide DescriptionIt is known that the nonempirical generalized gradient approximation (GGA) of Perdew, Burke, and Ernzerhof (PBE) provides a much more realistic description of the shortrange part of the van der Waals (vdW) interaction than does the local spin density (LSD) approximation. In the present work, the ability of the higherlevel nonempirical metaGGA of Tao, Perdew, Staroverov, and Scuseria (TPSS) to describe vdW interaction is tested selfconsistently in ten raregas dimers with . The oneparameter hybrid version (TPSSh) of the TPSS exchangecorrelation functional is also included in this test. Calculations show that both TPSS and TPSSh functionals correctly yield vdW bonds in these dimers and significantly improve the prediction of bond lengths, binding energies, and harmonic vibrational frequencies over LSD. The rather close agreement of TPSS with PBE for these dimers confirms a principle of the TPSS construction: preservation of the PBE largegradient behavior. More importantly, it suggests that TPSS can serve as a platform on which to construct a stillhigher level of nonempirical functionals. Compared with the PBE GGA, TPSS, and TPSSh yield a slightly weaker binding. As for normally bonded molecules, TPSSh yields the most accurate vibrational frequencies. The typically toolong bond lengths and toosmall binding energies of TPSS metaGGA suggest the need for some longrange vdW interaction correction even in this class of systems. The effect of basisset superposition error on the calculated properties of these vdW systems is investigated. We also show that the relatively strong anharmonic effects in the raregas dimers are described remarkably well by the Morse potential.

A proper approach for nonequilibrium molecular dynamics simulations of planar elongational flow
View Description Hide DescriptionWe present nonequilibrium molecular dynamics simulations of planar elongational flow (PEF) by an algorithm proposed by Tuckerman et al. [J. Chem. Phys. 106, 5615 (1997)] and theoretically elaborated by Edwards and Dressler [J. NonNewtonian, Fluid Mech. 96, 163 (2001)], which we shall call the properSLLOD algorithm, or for short. [For background on names of algorithms see W. G. Hoover, D. J. Evans, R. B. Hickman, A. J. C. Ladd, W. T. Ashurst, and B. Moran, Phys. Rev. A 22, 1690 (1980) and D. J. Evans and G. P. Morriss, Phys. Rev. A 30, 1528 (1984).] We show that there are two sources for the exponential growth in PEF of the total linear momentum of the system in the contracting direction, which has been previously observed using the socalled SLLOD algorithm. The first comes from the SLLOD algorithm itself, and the second from the implementation of the Kraynik and Reinelt [Int. J. Multiphase Flow18, 1045 (1992)] boundary conditions. Using the algorithm (to eliminate the first source) implemented with our simulation strategy (to eliminate the second) in PEF simulations, we no longer observe the exponential growth. By analyzing the equations of motion, we also demonstrate that both the SLLOD and the DOLLS algorithms are intrinsically unsuitable for representing a nonequilibrium system with elongational flow. However, the algorithm has a rigorously canonical structure in laboratory phase space, and thus can represent a nonequilibrium system not only for elongational flow but also for a general flow.

Multiconfiguration perturbation theory: Size consistency at second order
View Description Hide DescriptionA modified version of a previously elaborated multiconfiguration perturbation theory (MCPT) [Rolik et al.J. Chem. Phys.119, 1922 (2003)] is presented. In the modified formulation size consistency is ensured at second order in energy, by omitting projectors from the zero order Hamiltonian operator. This MCPT formulation is abbreviated as SC2MCPT (size consistent at second order). To ensure proper separability, we also require that energy denominators are constructed as differences of some oneparticle energies. A similar choice for energy denominators also renders the wellknown multireference Møller–Plesset (MRMP) energy size consistent at second order. The same thing applies to the related multireference perturbation theory by Witek, Nakano, and Hirao.

Quantum wave packet ab initio molecular dynamics: An approach to study quantum dynamics in large systems
View Description Hide DescriptionA methodology to efficiently conduct simultaneous dynamics of electrons and nuclei is presented. The approach involves quantum wave packet dynamics using an accurate banded, sparse and Toeplitz representation for the discrete free propagator, in conjunction with ab initiomolecular dynamics treatment of the electronic and classical nuclear degree of freedom. The latter may be achieved either by using atomcentered densitymatrix propagation or by using Born–Oppenheimer dynamics. The two components of the methodology, namely, quantum dynamics and ab initiomolecular dynamics, are harnessed together using a timedependent selfconsistent fieldlike coupling procedure. The quantum wave packet dynamics is made computationally robust by using adaptive grids to achieve optimized sampling. One notable feature of the approach is that important quantum dynamical effects including zeropoint effects, tunneling, as well as overbarrier reflections are treated accurately. The electronic degrees of freedom are simultaneously handled at accurate levels of density functional theory, including hybrid or gradient corrected approximations. Benchmark calculations are provided for proton transfer systems and the dynamics results are compared with exact calculations to determine the accuracy of the approach.

Twophoton absorption in the relativistic fourcomponent Hartree–Fock approximation
View Description Hide DescriptionA first implementation of the single residue of the quadratic response function in the fourcomponent Hartree–Fock approximation is presented. The implementation is based on a Kramers paired molecular orbital basis and takes full advantage of time and spatial symmetry reductions in a quaternion formulation—in analogy with the previous work on the quadratic response function [J. Chem. Phys.121, 6145 (2004)]. Sample calculations are given in terms of the monochromatic and coherent twophoton absorption cross sections in the noble gases. The relativistic twophoton selection rule allows for nonrelativistically spinforbidden transitions, and, even in neon, strong twophoton absorption is shown to occur for the transition. It is argued that relevant comparisons between nonrelativistic and relativistic calculations must be performed at the level of integrated absorption cross sections.

Leadingorder relativistic effects on nuclear magnetic resonance shielding tensors
View Description Hide DescriptionWe present perturbational ab initio calculations of the nuclearspindependent relativistic corrections to the nuclear magnetic resonance shielding tensors that constitute, together with the other relativistic terms reported by us earlier, the full leadingorder perturbational set of results for the oneelectron relativistic contributions to this observable, based on the (Breit–)Pauli Hamiltonian. These contributions are considered for the and molecules, as well as the noble gas (Ne, Ar, Kr, Xe, Rn) atoms. The corrections are evaluated using the relativistic and magnetic operators as perturbations on an equal footing, calculated using analytical linear and quadratic response theory applied on top of a nonrelativistic reference state provided by selfconsistent field calculations. The and heavyatom nuclear magnetic shieldingtensors are compared with four component, nearly basissetlimit Dirac–Hartree–Fock calculations that include positronic excitations, as well as available literature data. Besides the easy interpretability of the different contributions in terms of familiar nonrelativistic concepts, the accuracy of the present perturbational scheme is striking for the isotropic part of the shielding tensor, for systems including elements up to Xe.

Free energy profile along a discretized reaction path via the hyperplane constraint force and torque
View Description Hide DescriptionBy employing mechanical work analogies, we derive a convenient computational approach for evaluation of the free energy profile (FEP) along some discretized path defined as a sequence of hyperplanes. A hyperplane is fully specified by any of its point and a tangent vector. The FEP is obtained as an integral of two components. The translational component of the free energy is computed by integrating the hyperplane constraint force. The rotational component is evaluated via the hyperplane torque. Both ingredients—the constraint force and the hyperplane torque—are evaluated on each hyperplane independently. The integration procedure utilizes a set of reference points defining a point of rotation on each hyperplane, and these points can be chosen before or after the sampling takes place. A shift in the reference points redistributes the FEP contributions between the translational and rotational components. For systems where the FEP is dominated by the potential energy differences, reference points residing on the minimum energy path present a natural choice. We demonstrate the validity of our approach on two examples, a simple twodimensional (2D) potential, and a sevenatom LennardJones cluster. In each case, we compare the numerical FEP with the harmonic approximation estimates. Our results for the 2D potential are also verified by the data available in the literature. In both cases, the rotational component of the FEP represents a sizable contribution to the total FEP, so ignoring it would yield clearly incorrect results.

On dynamical tunneling and classical resonances
View Description Hide DescriptionThis work establishes a firm relationship between classical nonlinear resonances and the phenomenon of dynamical tunneling. It is shown that the classical phase space with its hierarchy of resonance islands completely characterizes dynamical tunneling and explicit forms of the dynamical barriers can be obtained only by identifying the key resonances. Relationship between the phase space viewpoint and the quantum mechanical superexchange approach is discussed in nearintegrable and mixed regularchaotic situations. For nearintegrable systems with sufficient anharmonicity the effect of multiple resonances, i.e., resonanceassistedtunneling, can be incorporated approximately. It is also argued that the presumed relation of avoided crossings to nonlinear resonances does not have to be invoked in order to understand dynamical tunneling. For molecules with low density of states the resonanceassisted mechanism is expected to be dominant.

Validation of the densityfunctional based tightbinding approximation method for the calculation of reaction energies and other data
View Description Hide DescriptionWe investigated the performance of the approximative density functional method DFTB versus BLYP and G2 with respect to zeropoint corrected reaction energies, vibrational frequencies, and geometry parameters for a set of 28 reactions and 22 representative molecules containing C, H, N, and O (DFTB—densityfunctional based tightbinding approximation). The DFTB reaction energies show a mean absolute deviation versus the G2 reference of only. The corresponding value for the vibrational frequencies amounts to versus BLYP/ccpVTZ. With very few exceptions bond lengths and angles are in excellent agreement with the results of higherlevel methods.

Dissipating the Langevin equation in the presence of an external stochastic potential
View Description Hide DescriptionIn the Langevin formalism, the delicate balance maintained between the fluctuations in the system and their corresponding dissipation may be upset by the presence of a secondary, spacedependent stochastic force, particularly in the lowfriction regime. In prior work, the latter was dissipated selfconsistently through an additional uniform (meanfield)friction [T. Shepherd and R. Hernandez, J. Chem. Phys.115, 2430 (2001).] An alternative approach to ensure that equipartition is satisfied relies on the use of a spacedependent friction while ignoring nonlocal correlations. The approach is evaluated with respect to its ability to maintain constant temperature for two simple onedimensional, stochastic potentials of mean force wherein the friction can be evaluated explicitly when there is no memory in the barriers. The use of a spacedependent friction is capable of providing qualitatively similar results to those obtained previously, but in extreme cases deviations from equipartition may be observed due to the neglect of the memory effects present in the stochastic potentials.

From molecular dynamics to hydrodynamics: A novel Galilean invariant thermostat
View Description Hide DescriptionThis paper proposes a novel thermostat applicable to any particlebased dynamic simulation. Each pair of particles is thermostated either (with probability ) with a pairwise Lowe–Andersen thermostat [C. P. Lowe, Europhys. Lett.47, 145 (1999)] or (with probability ) with a thermostat that is introduced here, which is based on a pairwise interaction similar to the Nosé–Hoover thermostat. When the pairwise Nosé–Hoover thermostat dominates (low ), the liquid has a high diffusion coefficient and low viscosity, but when the Lowe–Andersen thermostat dominates, the diffusion coefficient is low and viscosity is high. This novel Nosé–Hoover–Lowe–Andersen thermostat is Galilean invariant and preserves both total linear and angular momentum of the system, due to the fact that the thermostatic forces between each pair of the particles are pairwise additive and central. We show by simulation that this thermostat also preserves hydrodynamics. For the (noninteracting) ideal gas at , the diffusion coefficient diverges and viscosity is zero, while for it has a finite value. By adjusting probability , the Schmidt number can be varied by orders of magnitude. The temperature deviation from the required value is at least an order of magnitude smaller than in dissipative particle dynamics (DPD), while the equilibrium properties of the system are very well reproduced. The thermostat is easy to implement and offers a computational efficiency better than (DPD), with better temperature control and greater flexibility in terms of adjusting the diffusion coefficient and viscosity of the simulated system. Applications of this thermostat include all standard molecular dynamic simulations of dense liquids and solids with any type of force field, as well as hydrodynamic simulation of multiphase systems with largely different bulk viscosities, including surface viscosity, and of dilute gases and plasmas.

Combining smart darting with parallel tempering using Eckart space: Application to Lennard–Jones clusters
View Description Hide DescriptionThe smartdarting algorithm is a Monte Carlo based simulation method used to overcome quasiergodicity problems associated with disconnected regions of configurations space separated by high energy barriers. As originally implemented, the smartdarting method works well for clusters at low temperatures with the angular momentum restricted to zero and where there are no transitions to permutational isomers. If the rotational motion of the clusters is unrestricted or if permutational isomerization becomes important, the acceptance probability of darting moves in the original implementation of the method becomes vanishingly small. In this work the smartdarting algorithm is combined with the parallel tempering method in a manner where both rotational motion and permutational isomerization events are important. To enable the combination of parallel tempering with smart darting so that the smartdarting moves have a reasonable acceptance probability, the original algorithm is modified by using a restricted space for the smartdarting moves. The restricted space uses a bodyfixed coordinate system first introduced by Eckart, and moves in this Eckart space are coupled with local moves in the full dimensional space. The modified smartdarting method is applied to the calculation of the heat capacity of a sevenatom Lennard–Jones cluster. The smartdarting moves yield significant improvement in the statistical fluctuations of the calculated heat capacity in the region of temperatures where the system isomerizes. When the modified smartdarting algorithm is combined with parallel tempering, the statistical fluctuations of the heat capacity of a sevenatom Lennard–Jones cluster using the combined method are smaller than parallel tempering when used alone.

Matchingpursuit∕splitoperator Fouriertransform simulations of nonadiabatic quantum dynamics
View Description Hide DescriptionA rigorous and practical approach for simulations of nonadiabatic quantum dynamics is introduced. The algorithm involves a natural extension of the matchingpursuit∕splitoperator Fouriertransform (MP∕SOFT) method [Y. Wu and V. S. Batista, J. Chem. Phys.121, 1676 (Year: 2004)] recently developed for simulations of adiabatic quantum dynamics in multidimensional systems. The MP∕SOFT propagation scheme, extended to nonadiabatic dynamics, recursively applies the timeevolution operator as defined by the standard perturbation expansion to first, or secondorder, accuracy. The expansion is implemented in dynamically adaptive coherentstate representations, generated by an approach that combines the matchingpursuit algorithm with a gradientbased optimization method. The accuracy and efficiency of the resulting propagation method are demonstrated as applied to the canonical model systems introduced by Tully for testing simulations of dual curvecrossing nonadiabatic dynamics.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Experimental and theoretical investigation of the reaction
View Description Hide DescriptionThe rate coefficient of the reaction is determined in a quasistatic laserflash photolysis,laserinduced fluorescence system at low pressures . The radicals are produced via the quenching of (obtained by photolyzing ) with Xe whereas the H atoms are generated in a microwave discharge. The concentration profile is measured under pseudofirstorder condition, i.e., in the presence of a large excess of H atoms. The room temperature rate coefficient is determined to be . It is found to be independent of the pressure in the range considered in the present experiment. A global potential energy surface for the state is calculated with the internally contracted multireference configuration interaction method and the augmented correlation consistent polarized valence quadruple zeta atomic basis. The title reaction is investigated by classical trajectory calculations on this surface. The theoretical room temperature rate coefficient is . Using the thermodynamical data for the atoms and molecules involved, the rate coefficient for the reverse reaction,, is also calculated. At high temperatures it agrees well with the measured .

Accurate potential energy curves for , , and : Spectroscopy and transport coefficients
View Description Hide DescriptionWe calculate accurate potential energy curves for , , and , including the full counterpoise correction and allowing for spin–orbit effects. Comparison with previous curves is presented, where these are available. The three curves, , , and , are used to derive spectroscopic constants and to calculate the transport coefficients for moving in a bath of the respective rare gas. Conclusions are made based on a comparison with the available data.

Novel structures and energy spectra of hydroxylated based clusters: Searching for the magic cluster
View Description Hide DescriptionThe prominent mass peak resulting from the laser ablation of hydroxylated silica, attributed to magic cluster formation, is investigated employing global optimization with a dedicated interatomic potential and density functional calculations. The lowenergy spectra of cluster isomers are calculated for the closed shell clusters: and giving the likely global minima in each case. Based upon our calculated cluster structures and energetics, and further on the known experimental details, it is proposed that the abundant formation of clusters is largely dependent on the high stability of the ground state cluster. Both the and ground state clusters are found to exhibit cagelike structures with the latter containing a particularly unusual tetrahedrally fourcoordinated oxygen center not observed before in either bulk silica or silica clusters. The bare ground state cluster ion core is also found to have four tetrahedrally symmetric terminations making it a possible candidate, when combined with suitable cations, for extended clusterbased structures/materials.

Ab initio electron valence state perturbation theory study of the adiabatic transitions in carbonyl molecules: Formaldehyde, acetaldehyde, and acetone
View Description Hide DescriptionThe application of the recently developed secondorder electron valence state perturbation theory (NEVPT2) to small carbonyl molecules (formaldehyde, acetaldehyde, and acetone) is presented. The adiabatic transition energies are computed for the singlet and triplet , , and states performing a full geometry optimization of the relevant states at the single state CASSCF level and taking into account the zero point energy correction in the harmonic approximation. The agreement with the known experimental values and with previously published high level calculations confirms that NEVPT2 is an efficient tool to be used for the interpretation of molecular electronic spectra. Moreover, different insight into the nature of the excited states has been obtained. Some of the transitions presented here have never been theoretically computed previously [ and adiabatic transitions in acetaldehyde and acetone] or have been studied only using moderate level (single reference based) ab initio methods (all adiabatic transitions in acetaldehyde). In the present work a consistent disagreement between NEVPT2 and experiment has been found for the adiabatic transition in all molecules: this result is attributed to the low intensity of the transition to the first vibrational levels of the excited state. The singlet and triplet vertical transition energies are also reported for all the molecules.

First principles study of the carbon(silicon) doped clusters
View Description Hide DescriptionThe structural stability and physical properties have been studied for carbon(silicon) doped clusters using DMOL method based on densityfunctional theory.Doped clusters prefer to be icosahedron. Substitutional doping with a carbon or silicon impurity makes some clusters closed electronic shell, especially in icosahedral isomers. Substitutional doping of icosahedral clusters is found to be favorable at surface sites of clusters, especially for Sidoped cluster, which is very likely to be formed during the doping process. In addition, the structural distortions due to the doping are discussed.

Molecular alignment of ammonia studied by electronionion coincidence spectroscopy
View Description Hide DescriptionElectronionion coincidence measurements carried out at discrete resonances near the N threshold in ammonia are reported. The measured coincidence spectra show clear alignment of the molecule upon resonant coreelectron excitation. The coincidence data are analyzed to extract information about the molecule in the excited state by simulating the alignment and the dissociation processes. Dynamic changes in molecular geometry are found as the photon energy is scanned through the N resonance, whereas for the N state the geometry and kinetic energy released upon dissociation remain unchanged. The alignment of the coreexcited molecules is found to be preserved even in twostep dissociation processes.