Volume 123, Issue 3, 15 July 2005
 ARTICLES

 Theoretical Methods and Algorithms

Hybrid approach for ab initio molecular dynamics simulation combining energy density analysis and shorttime Fourier transform: Energy transfer spectrogram
View Description Hide DescriptionWe propose a new analysis technique for specifying molecular vibrational modes related with intramolecular and/or intermolecular energy transfer in ab initiomolecular dynamics simulation of chemical reaction. The technique combines the shorttime Fourier transform method with energy density analysis, which partitions the quantum chemical potential energy in the system into atomic contributions. The image obtained by the combined scheme, termed an energy transfer spectrogram (ETS), enables us to understand the dynamics of energy transfer by timefrequency representation. The time change of the local energy is quite important in chemical reactions. In order to assess the performance of the ETS, its application to the collision reaction between two carbon dioxide molecules is shown.

A refined ring polymer molecular dynamics theory of chemical reaction rates
View Description Hide DescriptionWe further develop the ring polymermolecular dynamics (RPMD) method for calculating chemical reaction rates [I. R. Craig and D. E. Manolopoulos, J. Chem. Phys.122, 084106 (2005)]. We begin by showing how the rate coefficient we obtained before can be calculated in a more efficient way by considering the side functions of the ringpolymer centroids, rather than averaging over the side functions of the individual ringpolymer beads. This has two distinct advantages. First, the statistics of the phasespace average over the ringpolymer coordinates and momenta are greatly improved. Second, the resulting fluxside correlation function converges to its longtime limit much more rapidly. Indeed the shorttime limit of this fluxside correlation function already provides a “quantum transition state theory” approximation to the final rate coefficient. In cases where transition state recrossing effects are negligible, and the transition state dividing surface is put in the right place, the RPMD rate is therefore obtained almost instantly. We then go on to show that the longtime limit of the new fluxside correlation function, and hence the fully converged RPMD reaction rate, is rigorously independent of the choice of the transition state dividing surface. This is especially significant because the optimum dividing surface can often be very difficult to determine for reactions in complex chemical systems.

Quantitative molecular thermochemistry based on path integrals
View Description Hide DescriptionThe calculation of thermochemical data requires accurate molecular energies and heat capacities. Traditional methods rely upon the standard harmonic normalmode analysis to calculate the vibrational and rotational contributions. We utilize pathintegral Monte Carlo for going beyond the harmonic analysis and to calculate the vibrational and rotational contributions to ab initio energies. This is an application and an extension of a method previously developed in our group [J. Chem. Phys.118, 1596 (2003)].

Absolute free energy calculations by thermodynamic integration in four spatial dimensions
View Description Hide DescriptionAn optimized technique for calculating the excess chemical potential of small molecules in dense liquids and the binding affinity of molecular ligands to biomolecules is reported. In this method, a molecular species is coupled to the system of interest via a nonphysical fourth spatial dimension through which insertion or extraction can be carried out [R. Pomès, E. Eisenmesser, C. B. Post et al., J. Chem. Phys.111, 3387 (1999)]. Molecular simulations are used to compute the potential of mean force (PMF) acting on the solute molecule in the fourth dimension. The excess chemical potential of that molecule is obtained as the difference in the PMF between fully coupled and fully decoupled systems. The simplicity, efficiency, and generality of the method are demonstrated for the calculation of the hydration free energies of water and methanol as well as sodium, cesium, and chloride ions. A significant advantage over other methods is that the 4DPMF approach provides a single effective and general route for decoupling all nonbonded interactions (i.e., both LennardJones and Coulombic) at once for both neutral and charged solutes. Direct calculation of the mean force from thermodynamic integration is shown to be more computationally efficient than calculating the PMF from umbrella sampling. Statistical error analysis suggests a simple strategy for optimizing sampling. The detailed analysis of systematic errors arising from the truncation of Coulombic interactions in a solventdroplet of finite size leads to straightforward corrections to ionic hydration free energies.

Simulations of one and twoelectron systems by BeadFourier path integral molecular dynamics
View Description Hide DescriptionThe BeadFourier path integral molecular dynamics technique introduced earlier [S. D. Ivanov, A. P. Lyubartsev, and A. Laaksonen, Phys. Rev. E67066710 (2003)] is applied for simulation of electrons in the simplest molecules: molecular hydrogen, helium atom, and their ions. Special attention is paid to the correct description of electrons in the core region of a nucleus. In an attempt to smooth the Coulomb potential at small distances, a recipe is suggested. The simulation results are in excellent agreement with the analytical solution for the “harmonic helium atom”, as well as with the vibrational potential of the molecule and He ionization energies. It is demonstrated, that the BeadFourier path integral molecular dynamics technique is able to provide the accuracy required for the description of electron structure and chemical bonds in cases when electron exchange effects need not be taken into account.

Atomic spinorbit pseudopotential definition and its relation to the different relativistic approximations
View Description Hide DescriptionA critical analysis of usual shapeconsistent spinorbit pseudopotential extraction procedures is presented, considering the basic requirements of the atomic pseudopotentials. It is based on a perturbative analysis of both reference allelectron Dirac–Coulomb and pseudopotential calculations by means of the formalism developed by Lindgren and Morrisson. In the light of this analysis, we propose a new hybrid extraction of spinorbit pseudopotentials, taking advantage of both shapeconsistent and energyconsistent procedures. These new pseudopotentials are extracted and checked for the ground state of the halogens.

Combining the latticesum and reactionfield approaches for evaluating longrange electrostatic interactions in molecular simulations
View Description Hide DescriptionA new scheme, the latticesumemulated reactionfield (LSERF) method, is presented that combines the latticesum (LS) and reactionfield (RF) approaches for evaluating electrostaticinteractions in molecular simulations. More precisely, the LSERF scheme emulates a RF calculation (based on an atomic cutoff) via the LS machinery. This is achieved by changing the form of the electrostaticinteractions in a standard LS calculation (Coulombic) to the form corresponding to RF electrostatics (Coulombic plus quadratic reactionfield correction term, truncated at the cutoff distance). It is shown (both analytically and numerically) that in the limit of infinite reciprocalspace accuracy, (i) the LSERF scheme with a finite reactionfield cutoff and a given reactionfield permittivity is identical to the RF scheme with the same parameters (and an atomic cutoff), and (ii) the LSERF scheme is identical to the LS scheme in the limit of an infinite reactionfield cutoff, irrespective of the reactionfield permittivity. This new scheme offers two key advantages: (i) from a conceptual point of view, it shows that there is a continuity between the RF and LS schemes and unifies them into a common framework; (ii) from a practical point of view, it allows us to perform RF calculations with arbitrarily large reactionfield cutoff distances for the same computational costs as a corresponding LS calculation. The optimal choice for the cutoff will be the one that achieves the best compromise between artifacts arising from the dielectric heterogeneity of the system (short cutoff) and its artificial periodicity (long cutoff). The implementation of the LSERF method is extremely easy, requiring only very limited modifications of any standard LS code. For practical applications to biomolecular systems, the use of the LSERF scheme with large reactionfield cutoff distances is expected to represent a significant improvement over the current RF simulations involving comparatively much shorter cutoffs.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Theoretical and experimental studies of the infrared rovibrational spectrum of
View Description Hide DescriptionRovibrational spectra of the complex in the fundamental band of have been observed using a tunable infrared laser to probe a pulsed supersonic jet expansion, and calculated using five coordinates that specify the positions of the He atoms with respect to the NNO molecule, a product basis, and a Lanczos eigensolver. Vibrational dynamics of the complex are dominated by the torsional motion of the two He atoms on a ring encircling the molecule. The resulting torsional states could be readily identified, and they are relatively uncoupled to other He motions up to at least . Good agreement between experiment and theory was obtained with only one adjustable parameter, the band origin. The calculated results were crucial in assigning many weaker observed transitions because the effective rotational constants depend strongly on the torsional state. The observed spectra had effective temperatures around 0.7 K and involved transitions with , with and 1, and (with one possible exception) with . Mixing of the torsionrotation states is small but significant: some transitions with were predicted to have appreciable intensity even assuming that the dipole transition moment coincides perfectly with the NNO axis. One such transition was tentatively assigned in the observed spectra, but confirmation will require further work.

and , , excited states of boron isoelectronic series from explicitly correlated wave functions
View Description Hide DescriptionFor some members of the boron isoelectronic series and starting from explicitly correlated wave functions, six lowlying excited states have been studied. Three of them arise from the configuration, and the other three from the , , configurations. This work follows a previous one on both the ground state and the four excited states coming from the configuration. Energies, one and twobody densities in position space and some other twobody properties in position and momentum spaces have been obtained. A systematic analysis of the energetic ordering of the states as a function of the total orbital angular momentum and spin is performed in terms of the electronnucleus and electronelectron potential energies and the role of the angular correlation is discussed. All calculations have been carried out by using the Monte Carlo algorithm.

Photodissociation of the water dimer: Threedimensional quantum dynamics studies on diabatic potentialenergy surfaces
View Description Hide DescriptionThe results are presented of threedimensional model studies of the photodissociation of the water dimer following excitation in the first absorption band. Diabatic potentialenergy surfaces are used to investigate the photodissociation following excitation of the hydrogen bond donor molecule and of the hydrogen bond acceptor molecule. In both cases, the degrees of freedom considered are the two OHstretch modes of the molecule being excited, and the dimer stretch vibration. The diabatic potentials are based on adiabatic potential surfaces computed with the multireference configurationinteraction method, and the dynamics of dissociation was studied using the timedependent wavepacket method. The dynamics calculations yield a donor spectrum extending over roughly the same range of frequencies as the spectrum of the water monomer computed at the same level of theory. The acceptor spectrum has the same width as the monomerspectrum, but is shifted to the blue by . The dimer spectrum obtained by averaging the donor and the acceptor spectrum is broader than the monomerspectrum, with the center of the dimer first absorption band shifted to the blue by about relative to the monomer band. Our reduced dimensionality calculations do not find the red tail predicted for the dimer first absorption band by Harvey et al. [J. Chem. Phys.109, 8747 (1998)]. This conclusion also holds if preexcitation of the dimer stretch vibration with one or two quanta is considered.

Aminomethanol water elimination: Theoretical examination
View Description Hide DescriptionThe mechanism for the formation of hexamethylenetetraamine predicts the formation of aminomethanol from the addition of ammonia to formaldehyde. This molecule subsequently undergoes unimolecular decomposition to form methanimine and water. Aminomethanol is the predicted precursor to interstellar glycine, and is therefore of great interest for laboratory spectroscopic study, which would serve as the basis for observational searches. The height of the water loss barrier is therefore useful in the determination of an appropriate experimental approach for spectroscopic characterization of aminomethanol. We have determined the height of this barrier to be at ambient temperatures. In addition, we have determined the infinitepressure Rice–Ramsperger–Kassel–Marcus unimolecular decomposition rate to be at , indicating gasphase kinetic stability for typical laboratory and hot core temperatures. Therefore, spectroscopic characterization of and observational searches for this molecule should be straightforward provided an efficient formation mechanism can be found.

Gasphase electronic spectra of and rings
View Description Hide DescriptionThe electronic spectra of and in the range have been detected in the gas phase by a massselective resonant twocolor twophotonionization technique coupled to a laser ablation source. The spectra were assigned to several electronic systems of monocyclic cumulenic isomers with a symmetry for and for , based on timedependentdensityfunctional calculations and reactivity with respect to . The best cooling conditions were achieved with Kr as the buffer gas, and the origin of the transition of at shows a pair of broadbands spaced by . The next electronic transitions exhibited much broader, (in the visible) to (in ultraviolet range), features. The spectrum of exhibits an absorption pattern similar to , except that the narrow features to the red are missing; the oscillator strength of the transition is predicted to be low.

Electronic structure and magnetic properties of small manganese oxide clusters
View Description Hide DescriptionTo investigate the electronic structure and magnetic properties of manganese oxide clusters, we carried out firstprinciples electronic structure calculations for small MnO clusters. Among various structural and magnetic configurations of the clusters, the bulklike [111]antiferromagnetic ordering is found to be favored energetically, while the surface atoms of the clusters exhibit interesting electronic and magnetic characteristics which are different from their bulk ones. The distinct features of the surface atoms are mainly attributed to the reduction of Mn coordination numbers and the bondlength contractions in the clusters, which may serve as a key factor for the understanding of physical and chemical properties of magnetic oxide nanoparticles.

Photofragment angular momentum distribution beyond the axial recoil approximation: The role of molecular axis rotation
View Description Hide DescriptionWe present the quantummechanical expressions for the recoil angle dependence of the photofragment multipole moments which explicitly treat the role of molecular axis rotation on the electronic angular momentumpolarization of the fragments. The paper generalizes the result of Siebbeles et al. [J. Chem. Phys.100, 3610 (1994)] to the case of dissociation of rotating molecules. The electronic wave function of the molecule was used in the adiabatic bodyframe representation. The obtained rigorous expressions for the fragment state multipoles have been explicitly derived from the scattering wavefunction formalism and then simplified using the quasiclassical approximation in the high limit. Possible radial and Coriolisnonadiabatic interactions have been taken into consideration. It is shown that the rotation of the molecular axis is described by a number of rotation factors which depend on the rank of the incidentphoton polarization matrix, on the dissociation mechanism, and on the classical angle of rotation of the molecular axis .
 Condensed Phase Dynamics, Structure, and Thermodynamics: Spectroscopy, Reactions, and Relaxation

Nature of the entropy versus selfdiffusivity plot for simple liquids
View Description Hide DescriptionThe empirical relation between the selfdiffusion coefficient and the excess entropy of a liquid is studied here in the context of theoretical model calculation. The coefficient is dependent on the interaction potential and shows a crossover at an intermediate density, where cooperative dynamics become more important. Around this density a departure from the Stokes–Einstein relation is also observed. The above relation between entropy and diffusion is also tested for the scaled total diffusion coefficient in a binary mixture.

Relaxation dynamics in solutions
View Description Hide DescriptionThe highfrequency dynamics of solutions has been investigated by inelastic xray scattering. The measurements have been performed as a function of the concentration in the range at fixed temperature . The results have been compared with similar data in pure water and pure hydrogen fluoride . A viscoelasticanalysis of the data highlights the presence of a relaxation process characterized by a relaxation time and a strength directly related to the presence of a hydrogenbond network in the system. The comparison with the data on water and hydrogen fluoride shows that the structural relaxation time continuously decreases at increasing concentration of hydrogen fluoride passing from the value for water to the one for hydrogen fluoride , which is three times smaller. This is the consequence of a gradual decreasing number of constraints of the hydrogenbond networks in passing from one liquid to the other.

NMR relaxation parameters of a LennardJones fluid from moleculardynamics simulations
View Description Hide DescriptionEnsembles of soft spheres or of LennardJones atoms were studied by molecular dynamics at reduced temperatures from 0.8 to 3, and radial distribution functions,diffusion coefficients, and magnetic dipoledipole correlation functions were measured as functions of system size. The expected relation between the values of the correlation functions at zero lag time and the integrals of the radial distribution was verified for each system. The measured correlation functions were compared with theoretical expressions derived by [Ayant et al., J. Phys. (Paris)36, 991 (1975)] and by [Hwang and Freed, J. Chem. Phys.63, 4017 (1975)]. It was shown that, in order to recover the longtime behavior characteristic of diffusioncontrolled relaxation processes, the simulation must comprise at least 10 000 particles. By fitting the simulation results to the HwangFreed function, independent values of the diffusion coefficient were obtained, similar but not identical to those computed using the GreenKubo formalism. The spectral densities of the dipoledipole interaction were computed as Fourier transforms of the correlation functions. These quantities are less sensitive to model imperfections and reproduce quite well the values derived from theory. The dimensionless spinlattice and spinspin relaxation rates were derived from the spectral densities. It was shown that the spinlattice (longitudinal) relaxation rate goes through a maximum as the temperature increases, while the spinspin (transverse) rate decreases monotonously.

Generalized Langevin theory on the dynamics of simple fluids under external fields
View Description Hide DescriptionA theory on the time development of the density and current fields of simple fluids under an external field is formulated through the generalized Langevin formalism. The theory is applied to the linear solvation dynamics of a fixed solute regarding the solute as the external field on the solvent. The solutesolventsolvent threebody correlation function is taken into account through the hypernettedchain integral equation theory, and the time correlation function of the random force is approximated by that in the absence of the solute. The theoretical results are compared with those of moleculardynamics (MD) simulation and the surrogate theory. As for the transient response of the density field, our theory is shown to be free from the artifact of the surrogate theory that the solvent can penetrate into the repulsive core of the solute during the relaxation. We have also found a large quantitative improvement of the solvation correlation function compared with the surrogate theory. In particular, the shorttime part of the solvation correlation function is in almost perfect agreement with that from the MD simulation, reflecting that the shorttime expansion of the theoretical solvation correlation function is exact up to with the exact threebody correlation function. A quantitative improvement is found in the longtime region, too. Our theory is also applied to the forceforce time correlation function of a fixed solute, and similar improvement is obtained, which suggests that our present theory can be a basis to improve the modecoupling theory on the solutediffusion.

Phase and interface behaviors in typeI and typeV LennardJones mixtures: Theory and simulations
View Description Hide DescriptionDensity gradient theory (DGT) and moleculardynamics (MD) simulations have been used to predict subcritical phase and interface behaviors in typeI and typeV equalsize LennardJones mixtures. TypeI mixtures exhibit a continuum critical line connecting their pure critical components, which implies that their subcritical phase equilibria are gas liquid. TypeV mixtures are characterized by two critical lines and a heteroazeotropic line. One of the two critical lines begins at the more volatile pure component critical point up to an upper critical end point and the other one comes from the less volatile pure component critical point ending at a lower critical end point. The heteroazeotropic line connects both critical end points and is characterized by gasliquidliquid equilibria. Therefore, subcritical states of this type exhibit gasliquid and gasliquidliquid equilibria. In order to obtain a correct characterization of the phase and interface behaviors of these types of mixtures and to directly compare DGT and MD results, the global phase diagram of equalsize LennardJones mixtures has been used to define the molecular parameters of these mixtures. According to our results, DGT and MD are two complementary methodologies able to obtain a complete and simultaneous prediction of phase equilibria and their interfacial properties. For the type of mixtures analyzed here, both approaches have shown excellent agreement in their phase equilibrium and interfaceproperties in the full concentration range.

TwoGaussian excitations model for the glass transition
View Description Hide DescriptionWe develop a modified “twostate” model with Gaussian widths for the site energies of both ground and excited states, consistent with expectations for a disordered system. The thermodynamic properties of the system are analyzed in configuration space and found to bridge the gap between simple twostate models (“logarithmic” model in configuration space) and the random energy model (“Gaussian” model in configuration space). The Kauzmann singularity given by the random energy model remains for very fragile liquids but is suppressed or eliminated for stronger liquids. The sharp form of constantvolume heat capacity found by recent simulations for binary mixed LennardJones and softsphere systems is reproduced by the model, as is the excess entropy and heat capacity of a variety of laboratory systems, strong and fragile. The ideal glass in all cases has a narrow Gaussian, almost invariant among molecular and atomic glassformers, while the excitedstate Gaussian depends on the system and its width plays a role in the thermodynamic fragility. The model predicts the possibility of firstorder phase transitions for fragile liquids. The analysis of laboratory data for toluene and terphenyl indicates that fragile liquids resolve the Kauzmann paradox by a firstorder transition from supercooled liquid to idealglass state at a temperature between and Kauzmann temperature extrapolated from experimental data. We stress the importance of the temperature dependence of the energy landscape, predicted by the fluctuationdissipation theorem, in analyzing the liquid thermodynamics.