Volume 117, Issue 23, 15 December 2002
 ARTICLES

 Theoretical Methods and Algorithms

Designing reversible measure invariant algorithms with applications to molecular dynamics
View Description Hide DescriptionA new method for generating measure invariant algorithms is presented. This method is based on a reformulation of the equations of molecular dynamics. These new equations are nonHamiltonian but have a normal form which guarantees that the invariant measure is the canonical one for the new variables. Furthermore, from this normal form, one can easily build algorithms to integrate these equations. Using a Trottertype factorization of the classical Liouville propagator, we build (time) reversible measure invariant integrators as successive direct translations. We apply this method to propose new algorithms to generate the Nosé–Hoover chain dynamics and the isothermalisobaric dynamics. We also give a measure invariant integrator for the generalized Gaussian moment thermostating dynamics recently introduced by Liu and Tuckerman. Finally, we present numerical results which show comparable performances with previously proposed algorithms.

Validation and assessment of an accurate approach to the correlation problem in density functional theory: The Kriger–Chen–Iafrate–Savin model
View Description Hide DescriptionIn the present paper, we validate and assess a correlation functional based on the socalled meta generalized gradient approximation, whose form and parameters are entirely derived only from firstprinciples criteria. In particular, we have carried out a detailed comparison with the most common, parametrized correlation functionals. Next, we propose a new model in which the correlation functional proposed by Kriger, Chen, Iafrate, and Savin is integrated in a hybrid Hartree–Fock/density functional theory scheme. In such approach only one, or two in the G2optimized version, parameters are adjusted on experimental data, all the others being derived from purely theoretical considerations. The results obtained for a set of molecular properties, including Hbonded complexes, proton transfer model, reaction and magnetic properties, are satisfactory and comparable, if not better, with those delivered by the most common functionals including heavy parametrization. The way in which the whole functional is derived and the few empirical parameters used make the new exchange–correlation functional widely applicable.

On quantum trajectories and an uncertainty relation
View Description Hide DescriptionWe discuss quantum trajectories from the point of view of Bohm and Wyatt. We find that the theory can be formally written in terms of a field (probability) a position and an average momentum in a density operator which is normalized and Hermitian, but not positive definite. One consequence of this is that the theory obeys, in a natural way, a formal relation for these averages. We interpret this as a consistency requirement for a trajectory in space–time with a position x and an average momentum which allows a space–time description. We show that a momentum space form can be written in terms of a field (probability) a momentum and an average position We briefly discuss potential chemical applications of quantum trajectories in the theory of chemical dynamics, kinetics, and local field theory.

Pseudo Jahn–Teller origin of instability of molecular highsymmetry configurations: Novel numerical method and results
View Description Hide DescriptionThe pseudo Jahn–Teller (PJT) effect as the only source of instability of molecular highsymmetry configurations in nondegenerate states is given a deeper insight by means of a novel method of ab initio evaluation of the vibronic and nonvibronic contributions to the curvature of the adiabatic potential energy surface in the direction of distortion. The method overcomes two essential difficulties: (1) the low accuracy in calculation of because of the singularities at the nuclei where existing basis sets yield inadequate results, and (2) the lack of sufficiently accurate data on excited states (including the continuum spectrum) for calculation of This is achieved by summing up the contributions of the excited states to result in expressions with only the ground statewave function and its derivatives, and excluding the singularities by canceling mutually compensating diagonal matrix elements in and After these essential changes is no longer a small difference between two large numbers, and it can be calculated with reasonable accuracy, while the separation of allows one to reveal the PJT origin of the instability: the direction of distortion for which the negative value overcomes the positive one. A further insight into the origin of the instability is reached by estimating the relative contribution of the most active excited states for different distortions (and for the same distortions in similar compounds), since the contribution of the continuum states (the largest part of does not affect the bonding and hence the differences in Illustrative numerical calculations were carried out on several series of molecular systems: planar C, Si, planar octahedral Cr, and octahedral and

On using potential, gradient, and Hessian data in least squares fits of potentials: Application and tests for
View Description Hide DescriptionWe present a novel, leastsquares fitting approach to obtain a representation of a potential energy surface using potential, gradient, and Hessian data. The method is described in detail and then tested for in two ways. In the first test a global, analytical potential is used to generate the data at 7 and 11 configurations. A comparison of the accuracy of the fit against the exact surface is made, as is a comparison of lowlying vibrational states. In the second test, Density Functional theory(DFT) calculations of the potential, gradient, and Hessian are performed at 7 and 11 configurations to obtain fits. The predictions of the fits are compared to 125 new DFT calculations of the energies and a conventional fit to them, both directly and in vibrational calculations.

Interelectronic angle densities of atoms
View Description Hide DescriptionIn manyelectron systems, the interelectronic angle density represents the probability density function for the interelectronic angle spanned by position vectors and of any two electrons to be It is shown that in general the interelectronic angle density is expressed by a linear combination of Legendre polynomials Explicit formulas for the expansion coefficients are presented for atoms described by determinantal wave functions. The results are applied to the 102 atoms He through Lr in their ground states within the Hartree–Fock framework, and the expansion coefficients as well as the average interelectronic angles are reported.

Benchmark calculations on highdimensional Henon–Heiles potentials with the multiconfiguration time dependent Hartree (MCTDH) method
View Description Hide DescriptionWe present quantum dynamical simulations on generalized, highdimensional Henon–Heiles potentials. The calculations can serve as benchmark results for other, approximative methods. Especially, we will give a comparison with semiclassical and Gaussian wave packet Monte Carlo calculations from two other groups. The scaling behavior of the multiconfiguration time dependent Hartree method with the dimensionality of the problem is investigated and discussed.

Electron correlation and noninteracting representability in density functional theory: The Be isoelectronic series
View Description Hide DescriptionReference densities from accurate configuration interactionwave functions for the beryllium isoelectronic series were used to solve the Kohn–Sham equations using a constrained search that minimizes the kinetic energy. For in the series, a single Kohn–Sham determinant is sufficient to give the minimum kinetic energy. For higher Z a single Kohn–Sham determinant produces eigenvalues that are lower than the eigenvalues, and a kinetic energy that is not the minimum that can be obtained from an antisymmetric wave function that produces the reference density. Fractional occupation numbers are required to obtain the minimum kinetic energy, and at the minimum kinetic energy the and eigenvalues become equal. Values of the optimal occupation numbers approach 0.09 for high Z.

Development of firstprinciples interaction model potentials. An application to the study of the bromide hydration
View Description Hide DescriptionThis work presents the development of firstprinciples bromide ion–water interaction potentials using the mobile charge density in harmonic oscillatorstype model. This model allows for a flexible and polarizable character of the interacting molecules and has already been parametrized for water–water interactions. The prospected potential energy surfaces of the bromide ionwater system were computed quantummechanically at Hartree–Fock and Møller–Plesset secondorder perturbation levels. In addition to the ion–solvent molecule pair, structures formed by the anion and two or three water molecules were considered in order to include many body effects. Minimizations of hydrated bromide clusters in gas phase and Monte Carlo computations of bromide aqueous solutions were performed to test the new potentials. Both structural and thermodynamic properties have been studied in detail and compared to the available experimental and theoretical values. From these comparisons, it was concluded the importance of including basis set superposition error corrections for the twobody interactions, and the small role of both electron correlation on the threebody terms and the fourbody terms. Monte Carlo simulation results have also been used to investigate if the presence of the anion significantly affects the intramolecular geometry of the water molecules and the degree of disruption of the water solvent structure in its vicinity.

A novel perturbationbased complete active space–selfconsistentfield algorithm: Application to the direct calculation of localized orbitals
View Description Hide DescriptionA complete active space–selfconsistentfield (CAS–SCF) algorithm based on molecular orbitals that conserve their physical nature during the iterative process is proposed. The algorithm consists of an iterative procedure based on the imposition of the generalized Brillouin theorem to a complete active spaceconfiguration interactionwave function. At convergence, the wave function is identical to the corresponding one obtained using canonical CAS–SCF orbitals, provided the nature of the active space is the same. If localized guess orbitals are used, the locality property is conserved by the final orbitals. Test calculations illustrate the interest of the proposed approach, that permits to control the nature of the active space.

Optimization of quantum mechanical molecular mechanical partitioning schemes: Gaussian delocalization of molecular mechanical charges and the double link atom method
View Description Hide DescriptionTwo new techniques for modeling chemical processes in condensed phases with combined quantum mechanical and molecular mechanical (QM/MM) potentials are introduced and tested on small, model compounds. The first technique, the double link atom (DLA) method, is an extension of the traditional, single link atom (SLA) method to avoid some of the problems with the latter method. These problems are primarily electrostatic, as the SLA method can produce an unphysical overall charge or dipole. The second technique, the delocalized Gaussian MM charge (DGMM) method, is an empirical way to include the delocalized character of the electron density of atoms in the MM region. This can be important for the electrostatic interaction of the QM region with nearby atoms in the MM region, and it can simplify the rules governing which classical interactions are included in the energies and forces. Even for very short distances, the DGMM method does not require the neglect of the MM host in the QM calculation. The DGMM method can be used for modeling reactions in solution, and it can be combined with methods such as the link atom, frozen orbital, or pseudopotential methods for terminating the QM region at a covalent bond. The DLA and the DGMM methods have been combined effectively. Presented here are tests on small, model systems that mimic properties important for reactions in proteins, in particular rotational barriers, proton affinities, and deprotonation energies. The new methods yield improved energetics for model compounds, visàvis a pointMMcharge and SLA treatment.

Accurate correlation consistent basis sets for molecular core–valence correlation effects: The second row atoms Al–Ar, and the first row atoms B–Ne revisited
View Description Hide DescriptionCorrelation consistent basis sets for accurately describing core–core and core–valence correlation effects in atoms and molecules have been developed for the second row atoms Al–Ar. Two different optimization strategies were investigated, which led to two families of core–valence basis sets when the optimized functions were added to the standard correlation consistent basis sets In the first case, the exponents of the augmenting primitive Gaussian functions were optimized with respect to the difference between allelectron and valence–electron correlated calculations, i.e., for the core–core plus core–valence correlation energy. This yielded the family of basis sets, which are analogous to the sets developed previously for the first row atoms [D. E. Woon and T. H. Dunning, Jr., J. Chem. Phys. 103, 4572 (1995)]. Although the sets exhibit systematic convergence to the allelectron correlation energy at the complete basis set limit, the intershell (core–valence) correlation energy converges more slowly than the intrashell (core–core) correlation energy. Since the effect of including the core electrons on the calculation of molecular properties tends to be dominated by core–valence correlation effects, a second scheme for determining the augmenting functions was investigated. In this approach, the exponents of the functions to be added to the sets were optimized with respect to just the core–valence (intershell) correlation energy, except that a small amount of core–core correlation energy was included in order to ensure systematic convergence to the complete basis set limit. These new sets, denoted weighted core–valence basis sets significantly improve the convergence of many molecular properties with Optimum sets for the firstrow atoms were also developed and show similar advantages. Both the and basis sets were benchmarked in coupled cluster [CCSD(T)] calculations on a series of second row homonuclear diatomic molecules and as well as on selected diatomic molecules involving first row atoms (CO, SiO, PN, and BCl). For the calculation of core correlation effects on energetic and spectroscopic properties, the basis sets are recommended over the ones.

Are the maximum hardness and minimum polarizability principles always obeyed in nontotally symmetric vibrations?
View Description Hide DescriptionIn a recent paper [J. Am. Chem. Soc. 123, 7951 (2001)] we have shown for the first time the existence of molecules with nontotally symmetric vibrational modes that break the maximum hardness (MHP) and minimum polarizability (MPP) principles. We present here an extension of this previous work by devising a mathematical procedure that helps to determine the nontotally symmetric molecular distortions of a given molecule that do not follow the MPP or the MHP. This methodology is based on the diagonalization of the Hessian matrix of the polarizability or the hardness with respect to the vibrational normal coordinates. For a relatively large series of molecules, we have carried out diagonalizations of the Hessian matrix of the polarizability to determine the molecular distortions with a more marked MPP or antiMPP character. From the results obtained, we have derived a set of simple rules that allow to predict a priori without calculations the existence of vibrational modes that break the MPP. With respect to the MHP, the results strongly depend on the method of calculation, but the same rules are useful to predict the existence of vibrational modes that disobey the MHP when the Koopmans’ approximation is used to calculate the hardness.

On the use of ab initio interaction energies for the accurate calculation of thermodynamic properties
View Description Hide DescriptionIt is of interest to predict the thermodynamic properties and phase behavior of a substance from quantumchemical calculations of intermolecular interaction energies followed by molecular simulations. However, while quantumchemical methods can be quite accurate, they do not provide an exact solution to Schrödinger’s equation (excluding full CI) and additional errors arise when fitting energies to analytic potential functions. The purpose of this communication is to provide an understanding and quantification of the sensitivity of the calculated properties to changes (or uncertainties) in different parts of the potential function. For this purpose, Gibbs ensemble Monte Carlo simulations were used to determine the effects on phase behavior of small perturbations to various regions of the model LennardJones 12–6 potential. The results indicate that repulsive energies play a limited role in determining the phase behavior and critical properties, while the attractive energies strongly affect the critical temperature, critical pressure, saturation densities, and vapor pressure. The critical density is most strongly affected by the location at which the potential is zero. However, when the phase behavior and second virial coefficient are scaled by the critical properties calculated for each potential, the results obey a corresponding states relation. These results are used to understand and predict variations in the calculated phase behavior for intermolecular potentials obtained using various strategies to fit ab initiocalculated interaction energies. The knowledge obtained is used to provide accurate predictions for neon based on quantumchemical energies and a recommended fitting strategy. We also show that threebody nonadditivity effects are largely unimportant for neon.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Water vapor millimeter wave foreign continuum: A Lanczos calculation in the coordinate representation
View Description Hide DescriptionThe water vapor foreigncontinuum absorption has been calculated theoretically from first principles for the millimeter wavespectral region as a function of frequency f and temperature T. The calculations are made using the Lanczos algorithm by writing the resolvent operator as continued fractions. In order to guarantee the quick convergence of the continued fractions, the line space of is divided into two subspaces: one consists of the positive resonance lines and the other the negative ones. By ignoring the coupling between them, is expressed as a sum of two continued fractions. The parameters appearing in each of the fractions are functions of the matrix elements of powers of the Liouville operator L between the starting vectors spanning the corresponding subspaces. In the present work, we have taken into account all powers of L up to 5. With the coordinate representation in which the orientations of the collision pair are chosen as the basis functions in Hilbert space, the anisotropic interaction potential is diagonal, and calculations of the matrix elements are transformed to multidimensional integrations. The latter are evaluated with the Monte Carlo method. In order to reduce the lengthy calculations, we assume that the anisotropic potential has rotational symmetry about the Z axis of and consists of the longrange dipole–quadrupole part and a shortrange repulsive site–site model. Once the parameters of the continued fractions are known, one can calculate the poles and residues and then carry out the ensemble average over the translational motion. Within the quasistatic approximation, one can treat the latter classically and obtain contributions to the absorption coefficient at the poles. Finally, the absorption coefficient at frequency f can be derived by an interpolation method. The results are fitted to a simple function of f and T, and are compared with experimental data and with two different versions of Liebe’s empirical model. In general, the theoretical results are in good agreement with the experiment. Meanwhile, the magnitudes of the theoretical absorption are between those of the 1989 and 1993 versions, but the temperature dependence is closer to the latter one.

Density functional theory investigation of gold cluster geometry and gasphase reactivity with
View Description Hide DescriptionWe have conducted a density functional theory investigation into the gasphase reactivity of small goldcluster ions in the interest of understanding goldcluster reactivity in several catalytic systems. Previously unreported geometries for and anions are obtained and reported from geometry optimizations. Predicted values of the vertical detachment energy match well with experiment, as does a rough simulation of its ultraviolet photoelectron spectrum—we found that comparison of predicted spectra with experimental data is a more sensitive analysis of geometry differences. Several binding sites for with different energies are identified on but we show that the strongest binding site and orientation is predicted by frontier orbital theory. In addition, weakly stable adsorbed states for on the anion clusters and are predicted in agreement with frontier orbital theory. The calculated binding energies are consistent with the experimentally observed patterns in adsorption of on anionic Auclusters. The binding energy for to was calculated to be 19 kcal/mol, higher than for to either (4 kcal/mol) or (5 kcal/mol), and the calculated O–O bond length was found to increase from its gasphase value of 1.27 angstroms to 1.38 angstroms when adsorbed on the cluster, approaching the calculated bond length of 1.41 angstroms for the gasphase superoxide ion

HPO does not follow Walsh’s rules! Improved molecular structures from the spectroscopy of jetcooled HPO and DPO
View Description Hide DescriptionThe electronic spectra of jetcooled HPO and DPO have been studied using the techniques of pulsed discharge jet, laserinduced fluorescence, and wavelength resolved emission spectroscopy. All of the vibrational frequencies in the ground and excited states have been obtained for both isotopomers and vibrational force fields have been determined for both states. Rotational analysis of the highresolution band spectrum of DPO has yielded the first rotational constants of the deuterated species. By combining the rotational constants of DPO with literature values for the rotational constants of HPO, we have derived reliable structures of HPO in the combining states with estimated equilibrium values of and The decrease in the bond angle on electronic excitation is contrary to predictions based on Walsh diagrams. A quantitative ab initio study shows that the variation of the orbital energies with bond angle differs in the ground and excited states of HPO, and these differences account for the anomalous change in bond angle on electronic excitation.

Experimental and computational study of the new gaseous molecules OMnF and
View Description Hide DescriptionThe new gaseous species OMnF and were identified and studied by hightemperature Knudsen Cell Mass Spectrometry. Their thermochemical atomization energies were derived through the study of several allgas equilibria in the temperature range 1735–1913 K. FTIR matrix isolation experiments together with ab initio and density functional calculations were performed to determine the molecular parameters, bond distances, and vibrational frequencies of and The results allowed us to evaluate a set of thermal functions for the new species that were used in the evaluation of the equilibrium data. The proposed atomization energies and enthalpies of formation are and

The application of a vacuum ultraviolet Fourier transform spectrometer and synchrotron radiation source to measurements of: V. The β(11,0) band of NO
View Description Hide DescriptionThe β(11,0) band of NO was measured at high resolution (0.06 cm^{−1}) by the vacuum ultraviolet Fourier transformspectrometer from Imperial College, London, using synchrotron radiation at the Photon Factory, KEK, Japan, as a continuum light source. Such resolution facilitates a line by line analysis of the NO β(11,0) band which yields accurate rotational line positions and term values as well as the photoabsorption cross sections. The molecular constants of the level are found to be and The sum of the line strengths for all rotational transitions of the NO β(11,0) band is determined as corresponding to a band oscillator strength of

Ab initio study of –silicon clusters
View Description Hide DescriptionWe report on the energetics of clusters. By means of ab initio calculations based on the local density approximation to the density functional theory, we have investigated stable and metastable structures of and clusters. In each case, we show that silicon preferentially binds to over a carbon–carbon double bond, in accordance with calculations on the interaction of with silicon surfaces. This bonding is characterized by a partial charge transfer from silicon to We show that the interaction between and silicon is local and not perturbed by the addition of more clusters or molecules. The binding energy for stable and metastable systems is high enough (several eV) to open the prospect of synthesizing nanostructured films from the unit. Furthermore, in all three cases, the silicon position on a fivefold symmetry axis is found to be a metastable position. The nature and structure of nanostructured films resulting from the deposition of these clusters is qualitatively discussed.