Volume 116, Issue 13, 01 April 2002
 COMMUNICATIONS


Influence of a knot on the stretchinginduced crystallization of a polymer
View Description Hide DescriptionThe effect of stretching a polymer sample containing a single trefoil knot has been studied by computer simulationmolecular dynamics calculations. Under axial load that approximates a fiber extrusion process, the knot is found to nucleate crystallization of the sample, which occurs on the ns time scale. The extension of the strain field associated with the knot has been quantified.

Isotropic collision induced light scattering spectra from gaseous
View Description Hide DescriptionThe experimental binary isotropic collisioninduced light scatteringspectrum of the gaseous sulfur hexafluoride is measured in absolute units in the frequency range. The contribution of dipole–multipole mechanisms is computed in a semiclassical way. From comparison with experiment, the independent component of the dipole–octopole polarizabilitytensor is estimated. This evaluation is compared to a recent theoreticalab initio calculation.

Differential cross sections for reactions by direct imaging
View Description Hide DescriptionWe report a crossed molecular beam study of the reaction of with cyclohexane with velocity map imaging of the cyclohexyl radical product using single photonionization. The results represent the first direct measurement of the differential cross sections for ground state oxygen atom reactions with alkanes. The experimental approach has the advantage that the collision energy is not only well defined but also continuously tunable in a reasonable range. The results show that at 5.8 kcal/mol collision energy the products are mainly backward scattered, clearly confirming the anticipated rebound reaction mechanism. More surprising is the large fraction, nearly 60%, of the available energy partitioned into the internal degrees of freedom of the products.
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 ARTICLES

 Theoretical Methods and Algorithms

Robust wave function optimization procedures in quantum Monte Carlo methods
View Description Hide DescriptionThe energy variance optimization algorithm over a fixed ensemble of configurations in variational Monte Carlo often encounters problems of convergence. Being formally identical to a problem of fitting data, we reexamine it from a statistical maximumlikelihood point of view. We show that the assumption of an underlying Gaussian distribution of the local energy, implicit in the standard variance minimization scheme, is not theoretically nor practically justified, and frequently generates convergence problems. We propose alternative procedures for optimization of trial wave functions in quantum Monte Carlo and successfully test them by optimizing a trial wave function for the helium trimer.

A new reciprocal space based treatment of long range interactions on surfaces
View Description Hide DescriptionA new formalism designed to treat long range interactions on surfaces, systems which are infinitely replicated in two spatial directions but have finite extent in the third, is developed. The new formalism is based in reciprocal space and, thus, permits the facile extension of standard planewave based density functional theory, Ewald summation, and smooth particlemesh Ewald methods to handle surfaces efficiently. The method is tested on both model (body centered cubic lattices) and realistic problems (an icesurface with a defect and the 2×1 surface reconstruction of silicon) and found to be accurate, efficient, and a marked improvement on existing formulations in speed, accuracy, and utility.

Initial convergence of the perturbation series expansion for vibrational nonlinear optical properties
View Description Hide DescriptionAb initio Hartree–Fock and MP2 calculations of the longitudinal (hyper)polarizability—including the static electronic, static zeropoint vibrational average (ZPVA), and pure vibrational (static and dynamic) contributions—have been carried out on a set of seven typical medium size conjugated nonlinear optical (NLO) molecules. The ZPVA is obtained through firstorder in mechanical plus electrical anharmonicity. Based on physical “nuclear relaxation” considerations the individual (square bracket) terms that contribute to the pure vibrational (hyper)polarizability are then taken into account through third, fourth, or fifthorder depending upon the type of term. In order to carry out the correlated treatment, fieldinduced coordinates and a special finite field technique are utilized. Correlation leads to very substantial differences in the absolute and relative values of the various contributions. In comparison to the electronic term the ZPVA correction is usually small but in one case is over twothirds as large. On the other hand, both static and dynamic pure vibrational contributions are commonly of a magnitude that is comparable to, or are larger than, the electronic term. The higherorder pure vibration terms are often large. For dynamic processes they can be almost as important as the lowestorder terms; for static (hyper)polarizabilities they can be more important. Thus, for typical NLO molecules, the initial convergence behavior of the perturbation series in mechanical and electrical anharmonicity requires further investigation.

The asymptotic region of the Kohn–Sham exchange potential in molecules
View Description Hide DescriptionThe Kohn–Sham exchange potential is shown to approach on nodal surfaces of the energetically highest occupied orbital different asymptotic limits than in other regions. This leads to strong anisotropies and barrier–well structures in the nearasymptotic region. Effective exactexchange potentials, like the one obtained in the recently introduced localized Hartree–Fock method, exhibit the correct asymptotic limits and the accompanying structures in the nearasymptotic region. An efficient, accurate method for the calculation of the Slater potential and of effective exactexchange potentials in the asymptotic region is presented. The method is based on an asymptotic continuation of Kohn–Sham (KS) orbitals and is numerically stable up to arbitrary large distances from the molecule. It can easily be implemented in existing quantum chemistry codes employing Gaussian basis sets. The asymptotic region of effective exactexchange potentials is shown to be different from the various asymptotically corrected exchangecorrelation functionals and to strongly affect unoccupied KS orbitals. Results for small and mediumsize molecules are presented.

Basis set limit binding energies of dimers derived from basis set convergence of monomer energies
View Description Hide DescriptionThe basis set limit electronic binding energies of and at the MP2 and CCSD(T) level (coupled cluster single and double excitations with perturbative triples correction) were estimated through the extrapolation of two successive energies of the dimer with correlationconsistent augccpVXZ basis sets by where the convergence power p was derived from the basis set convergence behavior of the monomer (He, HF, and energies toward the known corresponding basis set limits. It is shown that the convergence behaviors of the correlationenergy of the monomer and dimer with correlationconsistentbasis sets closely resemble each other in these weakly bound systems, which is well demonstrated by the excellent agreement of the estimated basis set limit binding energies on this premise with the reference values in all cases. By contrast, the accuracy of a simple twopoint extrapolation scheme in estimating the binding energies of these complexes is shown to depend on the correlation level, basis set quality, and kind of interatomic or molecular interactions present in the system. For the extrapolation of correlationenergies of the dimer with augccpVDZ and augccpVTZ basis set by with the convergence power p determined from the basis set convergence behavior of the monomercorrelationenergies, the estimated MP2 binding energies for and are 19.5 7.00 and with the values in parentheses representing the exact basis set limit binding energies. The corresponding CCSD(T) binding energies for and are 30.8 7.19 and 7.86 respectively.

The dependence of nonadiabatic couplings on the origin of electron coordinates
View Description Hide DescriptionIt is shown both analytically and numerically for a number of examples that both radial and rotational nonadiabatic couplings within the standard adiabatic approach depend on the origin of the lightparticle coordinates and the ambiguity in the nonadiabatic couplings does not lead to ambiguity in the coupled channel equations. The examples considered are the nH, nD, quasimolecules, for which the nonadiabatic couplings can be calculated analytically, and the HeH molecule, for which ab initio calculations are carried out. Analytical formulas for couplings calculated with the shifted origin are derived. The coupled equations take their simplest form in Jacobi coordinates for which many nonadiabatic couplings are nonzero, even for such noninteracting systems as nH, nD, and These couplings are a fundamental feature of the adiabatic approach.

Firstorder properties for triplet excited states in the approximated coupled cluster model CC2 using an explicitly spin coupled basis
View Description Hide DescriptionAn implementation is reported for firstorder properties of excited triplet states within the approximate coupled clustermodel CC2 using an explicitly spin coupled basis for the triplet excitation manifold and the resolution of the identity (RI) approximation for the electron repulsion integrals. Results are presented for the change of the second moment of charge upon excitation in the valence and Rydberg states of benzene. Employing large basis sets with up to 828 functions, we obtain results close to the CC2 basis set limit and are able to resolve an uncertainty in the assignment of the lowest states. It is found that the often used measure for the single excitation contribution to excited states is not reliable for a comparison across different excitation operator manifolds. An alternative diagnostic is proposed which provides a unique measure for the single excitation contribution that is independent of the chosen representation of the excitation operator manifold.

A dynamical correlation functional
View Description Hide DescriptionThe purpose of this work is to search for a justifiable form for a molecular dynamiccorrelation functional. A detailed examination of Colle and Salvetti’s derivation of the LYP functional is presented. It is argued that the leading term is all important, and furthermore that it should account for αβ correlation. This term only depends upon the densities, and it has a truncation factor which is obtained from the size of the correlation hole. It is It reproduces the αβ correlation energies of (He–Ar) to a very high accuracy. The correlation functional which represents σσ correlation is more complex, because the two particle Hartree–Fock density matrix is zero at electron coalescence. The functional must therefore depend upon Using these and related arguments we have found a four parameter generalized gradient functional which appears to perform nearly as well as the LYP functional. However unlike the LYP functional, it has two identifiable terms for αβ correlation, and two identifiable terms for σσ correlation. Together with our previously derived exchange functional, we have therefore obtained an exchangecorrelation functional for molecular studies, the form for which can be more understandably justified. The performance of this new Generalized Gradient Approximation functional for molecular predictions is reported. It is a considerable improvement on the BLYP functional, and is in the category of an optimum Generalized Gradient functional. Finally the present status of the science of searching for exchangecorrelation functions is reviewed. It is suggested that it may not be possible to find a local functional which is significantly more accurate for chemistry than the presently used Generalized Gradient Approximation functionals.

Multicanonical parallel tempering
View Description Hide DescriptionWe present a novel implementation of the parallel tempering Monte Carlo method in a multicanonical ensemble. Multicanonical weights are derived by a selfconsistent iterative process using a Boltzmann inversion of global energy histograms. This procedure gives rise to a much broader overlap of thermodynamicproperty histograms; fewer replicas are necessary in parallel tempering simulations, and the acceptance of trial swap moves can be made arbitrarily high. We demonstrate the usefulness of the method in the context of a grandmulticanonical ensemble, where we use multicanonical simulations in energy space with the addition of an unmodified chemical potential term in particlenumber space. Several possible implementations are discussed, and the best choice is presented in the context of the liquid–gas phase transition of the LennardJones fluid. A substantial decrease in the necessary number of replicas can be achieved through the proposed method, thereby providing a higher efficiency and the possibility of parallelization.

Fewestswitches with time uncertainty: A modified trajectory surfacehopping algorithm with better accuracy for classically forbidden electronic transitions
View Description Hide DescriptionWe present a modification of Tully’s fewestswitches (TFS) trajectory surfacehopping algorithm (also called molecular dynamics with quantum transitions) that is called the fewestswitches with time uncertainty (FSTU) method. The FSTU method improves the selfconsistency of the fewestswitches algorithm by incorporating quantum uncertainty into the hopping times of classically forbidden hops. This uncertainty allows an electronic transition that is classically forbidden at some geometry to occur by hopping at a nearby classically allowed geometry if an allowed hopping point is reachable within the Heisenberg interval of time uncertainty. The increased accuracy of the FSTU method is verified using a challenging set of threebody, twostate test cases for which accurate quantummechanical results are available. The FSTU method is shown to be more accurate than the TFS method in predicting total nonadiabatic quenching probabilities and product branching ratios.

Density matrix variational theory: Application to the potential energy surfaces and strongly correlated systems
View Description Hide DescriptionThe density matrix variational theory (DMVT) algorithm developed previously [J. Chem. Phys. 114, 8282 (2001)] was utilized for calculations of the potential energy surfaces of molecules, CO, and The using the and conditions as subsidiary condition, reproduced the fullCI curves very accurately even up to the dissociation limit. The method described well the quasidegenerate states and the strongly correlated systems. On the other hand, the was not satisfactory especially in the dissociation limit and its potential curves were always repulsive. The size consistency of the method was discussed and the condition was found to be essential for the correct behavior of the potential curve. Further, we also examined the Weinhold–Wilson inequalities for the resultant 2RDM of calculations. Two linear inequalities were violated when the results were less accurate, suggesting that this inequality may provide a useful representability condition for the DMVT.

The energy as a functional of the charge density and the chargedensity susceptibility: A simple, exact, nonlocal expression for the electronic energy of a molecule
View Description Hide DescriptionSimple, new expressions relate the electronic potential energy and the total electronic energy E of a molecule to its averaged electron density the nonlocal chargedensity susceptibility the nuclear positions and the nuclear charges The expressions derived in this work are exact nonrelativistically, within the Born–Oppenheimer approximation. The results give a nonlocal form for the electronic energy in density functional theory. The virial theorem for a system with Coulomb forces is used to derive the expectation value of the kinetic energy in terms of the expectation values of the potential energy and the derivatives of the potential energy operator with respect to nuclear coordinates; gradient expansions of the kinetic energy functional are not needed. Exchange and correlation effects on and E are determined by an integral of the chargedensity susceptibility over imaginary frequencies. The results for and E are first derived by use of the fluctuationdissipation theorem and the symmetry properties of the chargedensity susceptibility with respect to a change in the sign of ω. Identical results are derived by integration of over imaginary frequencies and use of the closure relation.

Extending the polarizable continuum model to effective ab initio pair potentials in multicomponent solutions: A test on calcium–water and calcium–ammonia potentials
View Description Hide DescriptionThe use of the polarizable continuum model to develop ab initio effective pair potentials is extended to multicomponent solutions. The methodology takes into account nonadditivity effects on pair interactions computing wave functions perturbed by the solvent.–water and –ammonia potentials suitable for aqueous ammonia solutions are presented. These effective ab initio pair potentials present smaller binding energies with respect to strictly ab initio twobody potentials. The reduction is higher in –ammonia (28%) than in –water (22%) and brings to a small gap the difference between the binding energies of the two ligands with when solvent effects are considered. As a first test, metalligand clusters of different size and composition have been studied. The comparison with restricted Hartree–Fock ab initio calculations shows good agreement for the largest clusters considered. Results confirm that the presented methodology, based on the polarizable continuum model, describes in a proper way the interactions in the condensed phase, where the ion completes its coordination sphere. The cluster results also show that ammonia can displace water in the first ion coordination with a tendency to change the coordination number from 8 to 9 when the ion is fully surrounded by the former, the ninth ammonia molecule being positioned in an intermediate situation between the first and the second coordination shells.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Preferential solvation of in aqueous solutions containing ammonia: A molecular dynamics study
View Description Hide Descriptionaqueous solutions containing different proportions of ammonia have been studied by means of molecular dynamics simulations. Previously developed ab initio effective pair potentials, in the framework of the polarizable continuum model, and only tested at a cluster computation level, have been employed to describe ion–ligand interactions. Structural and dynamic changes present in the neighborhood of the ion as a function of the ammonia concentration have been followed. Results show a preferential solvation for ammonia, even at very low concentrations. For the pure aqueous solution, calcium ion is coordinated by eight water molecules, while the presence of ammonia favors an equilibrium between an octa and ennacoordinated situation when this ligand becomes predominant, confirming the prediction of cluster calculations. However, the increase in the coordination number is followed by an intrinsic loss of stability for the identifiable solvated structures because of the larger tendency of ammonia to participate in solvent exchange phenomena. Solvent exchange events show, for the most simple case (water–water exchange), a marked mechanistic variety.

Dissociative electron attachment to molecules in the gas phase and in rare gas solids
View Description Hide DescriptionMeasurements of dissociative electron attachment (DEA) cross sections in chloroalkanes and chlorofluoromethanes have shown strong correlations between the peak DEA cross sections and the vertical attachment energies (VAEs) of these compounds. We explore the extent to which these gas phase data can be used to predict such cross sections for molecules embedded within or on the surface of a Kr solid. Effective VAEs are computed that include polarization of the solid by the anion and effects due to electron motion in the lattice. Comparisons are made with recent surface and bulk measurements and show good agreement for both within and on the surface. Satisfactory agreement is found for in the bulk but not on the surface.

Ab initio allelectron fully relativistic Dirac–Fock selfconsistent field calculations for molecules of superheavy elements: Seaborgium hexabromide
View Description Hide DescriptionGargantuan ab initio allelectron fully relativistic Dirac–Fock (DF) and nonrelativistic (NR) Hartree–Fock (HF) limit selfconsistent field (SCF) molecular calculations are reported for at various Sg–Br bond distances assuming an octahedral geometry. Our fully relativistic Dirac–Fock and nonrelativistic HF calculations predict for bond distance of 2.52 and 2.59 Å, respectively. Both our DF and NR HF SCF calculations predict the ground state of to be bound, with the predicted atomization energy of 18.75 and 11.53 eV, respectively. A relativistic Dirac–Fock wave function predicts for larger atomization energy than the corresponding NR HF calculation. The vertical ionization potential of calculated with our DF and HF wave functions is almost the same, viz., 10.60 and 10.78 eV, respectively. This is due to the fact that the HOMO consists entirely of the combination of the AOs of the six Br ligands, for which relativistic effects are nominal. However, the vertical electron affinity calculated with our HF and DF wave function for is 5.35 and 3.80 eV, respectively. The calculated HF HOMO–LUMO gap of 7.74 eV is in fairly close agreement with that of 8.91 eV obtained from the corresponding DF relativistic MOs for These results can be understood in terms of the nature of the HOMOs and LUMOs calculated in our HF and DF calculations for Mulliken population analysis of our relativistic DF and HF wave functions yields a charge of 1.26 and 0.70, respectively on Sg in our DF wave function predicts to be more ionic (and less volatile) than that by the corresponding HF wave function. Our prediction of the bonddissociation energy of 44 and 72 kcal mol^{−1} with our NR HF and relativistic DF wave functions, respectively for is a first for a species of a superheavy transactinide element, as is our prediction of a positive electron affinity for with both our HF and DF wave functions.

An ab initio study of the ionization potentials and spectroscopy of europium atoms and ions
View Description Hide DescriptionThe first three ionization potentials of europium and the spectroscopy of the two lowest multiplets of have been calculated using ab initio spin–orbit configuration interaction techniques. To accomplish this, a new averaged relativistic effective core potential has been developed which leaves only the and in the valence space. A series of configuration interaction calculations were carried out up through single and partial double excitations with a doublezeta quality basis set. The computed ionization values have an absolute error of about 0.1 eV from the experimental values. The computed spectroscopy for the lowest multiplet of has a RMS error with experiment of about The computed spectroscopy for the first excited multiplet has a higher RMS error of about The computed center of gravity separation between the multiplet is underestimated by Comparisons between nonspin–orbit and spin–orbit configuration interaction calculations for the separations of the centers of gravity of multiplets are very favorable up through single and double excitations with differences of a tenth of an eV or less. The spin–orbit configuration interaction calculations are among the largest ever performed for lanthanides, with expansion lengths in excess of 1.9 million doublegroupadapted functions. The calculations were achieved by application of a new parallel spin–orbit configuration interaction component in the COLUMBUS Program System.