Volume 121, Issue 14, 08 October 2004
 COMMUNICATIONS


Rovibrational product state distribution for inelastic collisions
View Description Hide DescriptionExperimental measurements of rovibrational product state distributions for the inelastic scattering process are presented and compared with the results of quasiclassical and quantum mechanical calculations. Agreement between theory and experiment is almost quantitative. Two subtle trends are found: the relative amount of energy in product rotational excitation decreases slightly with increasing collision energy and increases slightly with increasing product vibrational excitation. These trends are the reverse of what has been found for reactive scattering in which the opposite trends are much more pronounced.
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 ARTICLES

 Theoretical Methods and Algorithms

A closedshell coupledcluster treatment of the Breit–Pauli firstorder relativistic energy correction
View Description Hide DescriptionFirstorder relativistic corrections to the energy of closedshell molecular systems are calculated, using all terms in the twocomponent Breit–Pauli Hamiltonian. In particular, we present the first implementation of the twoelectron Breit orbit–orbit integrals, thus completing the firstorder relativistic corrections within the twocomponent Pauli approximation. Calculations of these corrections are presented for a series of small and light molecules, at the Hartree–Fock and coupledcluster levels of theory. Comparisons with fourcomponent Dirac–Coulomb–Breit calculations demonstrate that the full Breit–Pauli energy corrections represent an accurate approximation to a fully relativistic treatment of such systems. The Breit interaction is dominated by the spin–spin interaction, the orbit–orbit interaction contributing only about 10% to the total twoelectron relativistic correction in molecules consisting of light atoms. However, the relative importance of the orbit–orbit interaction increases with increasing nuclear charge, contributing more than 20% in

A semiclassical study of wave packet dynamics in anharmonic potentials
View Description Hide DescriptionClassical and semiclassical methods are developed to calculate and invert the wave packet motion measured in pumpprobe experiments. With classical propagation of the Wigner distribution of the initial wave packet created by the pump pulse, we predict the approximate probe signal with slightly displaced recurrence peaks, and derive a set of firstorder canonical perturbation expressions to relate the temporal features of the signal to the characteristics of the potential surface. A reduced dynamics scheme based on the Gaussian assumption leads to the correct center of mass motion but does not describe the evolution of the shape of the wave packet accurately. To incorporate the quantum interference into classical trajectories, we propose a finalvalue representation semiclassical method, specifically designed for the purpose of computing pumpprobe signals, and demonstrate its efficiency and accuracy with a Morse oscillator and two kinetically coupled Morse oscillators. For the case of onecolor pump probe, a simple phasespace quantization scheme is devised to reproduce the temporal profile at the leftturning point without actual wave packet propagation, revealing a quantum mechanical perspective of the nearly classical pumpprobe signal.

Linear scaling computation of the Fock matrix. VII. Parallel computation of the Coulomb matrix
View Description Hide DescriptionWe present parallelization of a quantumchemical treecode [J. Chem. Phys. 106, 5526 (1997)] for linear scaling computation of the Coulomb matrix. Equal time partition [J. Chem. Phys. 118, 9128 (2003)] is used to load balance computation of the Coulomb matrix. Equal time partition is a measurement based algorithm for domain decomposition that exploits small variation of the density between selfconsistentfield cycles to achieve load balance. Efficiency of the equal time partition is illustrated by several tests involving both finite and periodic systems. It is found that equal time partition is able to deliver 91%–98% efficiency with 128 processors in the most time consuming part of the Coulomb matrix calculation. The current parallel quantum chemical tree code is able to deliver 63%–81% overall efficiency on 128 processors with fine grained parallelism (less than two heavy atoms per processor).

Single molecule conductivity: The role of junctionorbital degeneracy in the artificially high currents predicted by ab initio approaches
View Description Hide DescriptionA priori evaluations, using Hartree–Fock selfconsistentfield (SCF) theory or densityfunctional theory(DFT), of the current passing between two electrodes through a single bridging molecule result in predicted conductivities that may be up to one to two orders of magnitude larger than observed ones. We demonstrate that this is, in part, often due to the improper application of the computational methods. Conductivity is shown to arise from tunneling between junction states of the electrodes through the molecule; these states are inherently either quasi twofold or fourfold degenerate and always comprise the (highest occupied molecular orbital) HOMO band at the Fermi energy of the system. Frequently, in previous cluster based molecular conduction calculations, closedshell SCF or Kohn–Sham DFT methods have been applied to systems that we demonstrate to be intrinsically open shell in nature. Such calculations are shown to induce artificial HOMOLUMO (LUMO—lowest unoccupied molecular orbital) band splittings that Landauerbased formalisms for steadystate conduction interpret as arising from extremely rapid throughmolecule tunneling at the Fermi energy, hence, overestimating the lowvoltage conductivity. It is demonstrated that these shortcomings can be eliminated, dramatically reducing calculated current magnitudes, through the alternate use of electronicstructure calculations based on the spinrestricted openshell formalism and related multiconfigurational SCF of DFT approaches. Further, we demonstrate that most anomalies arising in DFT implementations arise through the use of hybrid density functionals such as B3LYP. While the enhanced bandgap properties of these functionals have made them the defacto standard in molecular conductivity calculations, we demonstrate that it also makes them particularly susceptible to openshell anomalies.

Extrapolating bound state data of anions into the metastable domain
View Description Hide DescriptionComputing energies of electronically metastable resonance states is still a great challenge. Both scattering techniques and quantum chemistry based methods are very time consuming. Here we investigate two more economical extrapolation methods. Extrapolating bound states energies into the metastable region using increased nuclear charges has been suggested almost 20 years ago. We critically evaluate this attractive technique employing our complex absorbing potential/Green’s function method that allows us to follow a bound state into the continuum. Using the resonance of and the resonance of as examples, we found that the extrapolation works suprisingly well. The second extrapolation method involves increasing of bond lengths until the sought resonance becomes stable. The keystone is to extrapolate the attachment energy and not the total energy of the system. This method has the great advantage that the whole potential energy curve is obtained with quite good accuracy by the extrapolation. Limitations of the two techniques are discussed.

Mixedsector intermediate Hamiltonian Fockspace coupled cluster approach
View Description Hide DescriptionAn alternative formulation of the intermediate Hamiltonian Fockspace coupled cluster scheme developed before is presented. The methodological and computational advantages of the new formulation include the possibility of using a model space with determinants belonging to different Fockspace sectors. This extends the scope of application of the multireference coupled cluster method, and makes possible the use of quasiclosed shells (e.g., as reference states. Representative applications are described, including electron affinities of group14 atoms, ionization potentials of group15 elements, and ionization potentials and excitation energies of silver and gold. Excellent agreement with experiment (a few hundredths of an electronvolt) is obtained, with significant improvement (by a factor of 5–10 for states) over Fockspace coupled cluster results. Many states not reachable by the Fockspace approach can now be studied.

Effective potential in density matrix functional theory
View Description Hide DescriptionIn the previous paper it was shown that in the ground state the diagonal of the spin independent secondorder density matrix can be determined by solving a single auxiliary equation of a twoparticle problem. Thus the problem of an arbitrary system with even electrons can be reduced to a twoparticle problem. The effective potential of the twoparticle equation contains a term of completely kinetic origin. Virial theorem and hierarchy of equations are derived for and simple approximations are proposed. A relationship between the effective potential of the shape functionequation and the potential is established.

Divideandconquer local correlation approach to the correlation energy of large molecules
View Description Hide DescriptionA divideandconquer local correlation approach for correlationenergy calculations on large molecules is proposed for any postHartreeFock correlation method. The main idea of this approach is to decompose a large system into various fragments capped by their local environments. The total correlationenergy of the whole system can be approximately obtained as the summation of correlationenergies from all capped fragments, from which correlationenergies from all adjacent caps are removed. This approach computationally achieves linear scaling even for mediumsized systems. Our test calculations for a wide range of molecules using the 631G or basis set demonstrate that this simple approach recovers more than 99.0% of the conventional secondorder MøllerPlesset perturbation theory and coupled cluster with single and double excitations correlationenergies.

Timedependent fourcomponent relativistic density functional theory for excitation energies
View Description Hide DescriptionTimedependent fourcomponent relativistic density functional theory within the linear response regime is developed for calculating excitation energies of heavy element containing systems. Since spin is no longer a good quantum number in this context, we resort to timereversal adapted Kramers basis when deriving the coupled DiracKohnSham equation. The particular implementation of the formalism into the Beijing density functional program package utilizes the multipolar expansion of the induced density to facilitate the construction of the induced Coulomb potential. As the first application, pilot calculations on the valence excitation energies and fine structures of the rare gas (Ne to Rn) and Group 12 (Zn to Hg) atoms are reported. To the best of our knowledge, it is the first time to be able to account for spin–orbit coupling within timedependent density functional theory for excitation energies.

HamiltonJacobi equation for the leastaction/leasttime dynamical path based on fast marching method
View Description Hide DescriptionClassical dynamics can be described with Newton’s equation of motion or, totally equivalently, using the HamiltonJacobi equation. Here, the possibility of using the HamiltonJacobi equation to describe chemical reactiondynamics is explored. This requires an efficient computational approach for constructing the physically and chemically relevant solutions to the HamiltonJacobi equation; here we solve HamiltonJacobi equations on a Cartesian grid using Sethian’s fast marching method [J. A. Sethian, Proc. Natl. Acad. Sci. USA 93, 1591 (1996)]. Using this method, we can—starting from an arbitrary initial conformation—find reaction paths that minimize the action or the time. The method is demonstrated by computing the mechanism for two different systems: a model system with four different stationary configurations and the reaction. Leasttime paths (termed brachistochrones in classical mechanics) seem to be a suitable chioce for the reaction coordinate, allowing one to determine the key intermediates and final product of a chemical reaction. For conservative systems the HamiltonJacobi equation does not depend on the time, so this approach may be useful for simulating systems where important motions occur on a variety of different time scales.

Multiresolution quantum chemistry in multiwavelet bases: Hartree–Fock exchange
View Description Hide DescriptionIn a previous study [R. J. Harrison et al., J. Chem. Phys. (in press)] we reported an efficient, accurate multiresolution solver for the Kohn–Sham selfconsisitent field (KSSCF) method for general polyatomic molecules. This study presents an efficient numerical algorithm to evalute Hartree–Fock (HF) exchange in the multiresolution SCF method to solve the HF equations. The algorithm employs fast integral convolution with the Poission kernel in the nonstandard form, screening the sparse multiwavelet representation to compute results of the integral operator only where required by the nonlocal exchange operator. Localized molecular obitals are used to attain near linear scaling. Results for atoms and molecules demonstrate reliable precision and speed. Calculations for small water clusters demonstrate a total cost to compute the HF exchange potential for all occpuied MOs scaling as

Analysis of cooperativity and localization for atomic rearrangements
View Description Hide DescriptionWe propose measures of localization and cooperativity for the analysis of atomic rearrangements. We show that for both clusters and bulk material cooperative rearrangements usually have significantly lower barriers than uncooperative ones, irrespective of the degree of localization. We also find that previous methods used to sample stationary points are biased towards rearrangements of particular types. Linear interpolation between local minima in doubleended transition state searches tends to produce cooperative rearrangements, while random perturbations of all the coordinates, as sometimes used in singleended searches, have the opposite effect.

Parallel, linearscaling buildingblock and embedding method based on localized orbitals and orbitalspecific basis sets
View Description Hide DescriptionWe present a linear scaling method for the energy minimization step of semiempirical and firstprinciples Hartree–Fock and Kohn–Sham calculations. It is based on the selfconsistent calculation of the optimum localized orbitals of any localization method of choice and on the use of orbitalspecific basis sets. The full set of localized orbitals of a large molecule is seen as an orbital mosaic where each tessera is made of only a few of them. The orbital tesserae are computed out of a set of embedded cluster pseudoeigenvalue coupled equations which are solved in a buildingblock selfconsistent fashion. In each iteration, the embedded cluster equations are solved independently of each other and, as a result, the method is parallel at a high level of the calculation. In addition to full system calculations, the method enables to perform simpler, much less demanding embedded cluster calculations, where only a fraction of the localized molecular orbitals are variational while the rest is frozen, taking advantage of the transferability of the localized orbitals of a given localization method between similar molecules. Monitoring single point energy calculations of large poly(ethylene oxide) molecules and three dimensional carbon monoxide clusters using an extended Hückel Hamiltonian are presented.

Complete structural and magnetic characterization of biological radicals in solution by an integrated quantum mechanical approach: Glycyl radical as a case study
View Description Hide DescriptionAn integrated quantum mechanical approach for the structural and magnetic characterization of flexible free radicals in solution has been applied to a model of the glycyl radical engaged in peptidic chains. The hyperfine couplings computed using hybrid density functionals and purposely tailored basis sets are in good agreement with experiment when vibrational averaging effects from low frequency motions and solvent effects (both direct H bonding and bulk) are taken into the proper account. The gtensor shows a smaller dependence on the specific form of the density functional, the extension of the basis set over a standard doubleζ+polarization level, vibrational averaging, and bulk solvent effects. However, hydrogen bridges with solvent molecules belonging to the first solvation shell play a significant role. Together with their intrinsic interest, our results show that a comprehensive and reliable computational approach is becoming available for the complete characterization of openshell systems of biological interest in their natural environment.

Twocomponent relativistic methods for the heaviest elements
View Description Hide DescriptionDifferent generalized DouglasKroll transformed Hamiltonians 2,…,5) proposed recently by Hess et al. are investigated with respect to their performance in calculations of the spin–orbit splittings. The results are compared with those obtained in the exact infiniteorder twocomponent (IOTC) formalism which is fully equivalent to the fourcomponent Dirac approach. This is a comprehensive investigation of the ability of approximate methods to correctly predict the spin–orbit splittings. On comparing the results with the IOTC (Dirac) data one finds that the calculated spin–orbit splittings are systematically improved with the increasing order of the DK approximation. However, even the highestorder approximate twocomponent DK5 scheme shows certain deficiencies with respect to the treatment of the spin–orbit coupling terms in very heavy systems. The meaning of the removal of the spindependent terms in the socalled spinfree (scalar) relativistic methods for manyelectron systems is discussed and a computational investigation of the performance of the spinfree and IOTC methods for manyelectron Hamiltonians is carried out. It is argued that the spinfree IOTC rather than the DiracCoulomb results give the appropriate reference for other spinfree schemes which are based on approximate twocomponent Hamiltonians. This is illustrated by calculations of spinfree and IOTC total energies, expectation values, ionization potentials, and electron affinities of heavy atomic systems.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Reactivity of and with and
View Description Hide DescriptionWe have investigated, both theoretically and experimentally, the reactions of naphthylium and dnaphthylium ions with and Cross sections as functions of the collision energy have been measured for a variety of reaction channels. Theoretical calculations have been carried out at the density functional theory level which utilizes the hybrid functional B3LYP and the splitvalence basis set. The key features of the potential energy surfaces and the relevant thermochemical parameters have been calculated and they provide insights on the reaction mechanisms. The bimolecular reactivity of with is dominated by the production of naphthalene cation The reaction is not a direct atomabstraction process, but instead it proceeds via the formation of a stable intermediate complex of σ type geometry, with a significant mobility of hydrogen along the ring. This mobility allows the scrambling of the hydrogen atoms and causes the successive statistical fragmentation of the complex into a variety of product channels. Elimination of one H(D) atom appears to be favored over elimination of one or HD molecule. Alternatively, the intermediate complex can be stabilized either by collision with a third body or by emission of a photon.

Ab initio and kinetic calculations for the reactions of Cl with
View Description Hide DescriptionThe direct hydrogen abstraction reactions of Cl atom with have been studied systematically using ab initio molecular orbital theory. Geometries have been optimized at the MP2 level with basis set, has been used in the final single point energy calculation. The kinetic calculations of these reactions have been explored using the canonical variational transition (CVT) state theory method with smallcurvature tunneling (SCT) effect correction over the temperature range of 200–2000 K. The CVT/SCT rate constants exhibit typical nonArrhenius behavior and threeparameter ratetemperature formulas have been fitted for the reactions of Cl with and respectively (in unit of cm^{3} molecule^{−1} s^{−1}). The calculated CVT/SCT rate constants are in agreement with the available experimental values.

Cyclic I. An accurate potential energy surface for the ground doublet electronic state up to the energy of the conical intersection
View Description Hide DescriptionA sophisticated adiabatic ground electronic state potential energy surface for a pure nitrogen ring (cyclic molecule is constructed based on extensive highlevel ab initio calculations and accurate threedimensional spline representation. Most of the important features of the potential energy surface are presented using various reduced dimensionality slices in internal hyperspherical coordinates as well as full dimensional isoenergy surfaces. Very significant geometric phase effects are predicted in the spectra of rotationalvibrational states of cyclic

The effect of kinematic parameters on inelastic scattering of glyoxal
View Description Hide DescriptionThe effect of kinematic parameters (relative velocity relative momentum and relative energy on the rotational and rovibrational inelastic scatterings of transglyoxal has been investigated by colliding glyoxal seeded in He or Ar with target gases He, or Ne at different scattering angles in crossed supersonic beams. The inelastic spectra for target gases He and acquired with two different sets of kinematic parameters revealed no significant differences. This result shows that kinematic factors have the major influence in the inelastic scattering channel competition whereas the intermolecular potential energy surface plays only a secondary role. The welldefined exponential dependence of relative cross sections on exchanged angular momentum identifies angular momentum as the dominant kinematic factor in collisioninduced rotationally and rovibrationally inelastic scatterings. This is supported by the behavior of the relative inelastic cross sections data in a “slope” representation. In this form, the data show a trend nearly independent of the target gas identity. Representations involving and show trends specific to the target gas.