Volume 118, Issue 3, 15 January 2003
 COMMUNICATIONS


Timeresolved photoelectron imaging of the photodissociation of
View Description Hide DescriptionTimeresolved photoelectron imaging is presented as a new method for the study of anion dynamics. Timedependent photoelectron energy spectra and angular distributions are extracted from images taken during the dissociation of at 793 nm, and used to follow in detail the dissociation dynamics from 0–1 ps.

Oxygen adsorption on graphite and nanotubes
View Description Hide DescriptionWe study the binding of molecular oxygen to a graphene sheet and to a (8,0) single walled carbon nanotube, by means of spinunrestricted densityfunctional calculations. We find that triplet oxygen retains its spinpolarized state when interacting with graphene or the nanotube. This leads to the formation of a weak bond with essentially no charge transfer between the molecule and the sheet or tube, as one would expect for a physisorptive bond. This result is independent on the approximation used for the exchangecorrelation functional. The binding strength, however, depends strongly on the functional, reflecting the inability of current approximation functionals to deal correctly with dispersion forces. Gradientcorrected functionals yield very weak binding at distances around 4 Å, whereas local density functional results yield substantially stronger binding for both graphene and the nanotube at distances of less than 3 Å. The picture of oxygen physisorption is not substantially altered by the presence of topological defects such as 5–7 Stone–Wales pairs.
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 ARTICLES

 Theoretical Methods and Algorithms

A Lorentzian function based spectral filter for calculating the energy of excited bound states in quantum mechanics
View Description Hide DescriptionIn this paper, we study a Lorentzian function based spectral filter suitable for computing highly excited bound states of a quantum system. Using this filter, we have derived an expression for spectral intensities and also implemented a filter diagonalization scheme. We have used a Chebyshev polynomial based series expansion of the filter operator, and this allows us to accomplish a partial resummation of the double series analytically when computing the necessary matrix elements; this saves considerable computational effort. The exponential damping term in the Lorentzian provides a convenient control over the resolution of the computed spectrum in the spectral intensity plot. As a numerical test, we have computed eigenvalues and spectral intensities of a model Hamiltonian in an arbitrary energy window. For situations where eigenvalues are distributed nonuniformly we suggest a computational protocol, which judiciously combines the spectral intensity information with the filter diagonalization method. This protocol is efficient only with the Lorentzian filter studied here.

Quasirelativistic theory for the magnetic shielding constant. I. Formulation of Douglas–Kroll–Hess transformation for the magnetic field and its application to atomic systems
View Description Hide DescriptionA twocomponent quasirelativistic theory based on the Douglas–Kroll–Hess (DKH) transformation has been developed to study magnetic properties of molecules. The proposed Hamiltonian includes the relativistic magnetic vector potential in the framework of the DKH theory, and is applicable to the calculations of magnetic properties without further expansion in powers of By combining with the finiteperturbation theory and the generalizedUHF method, new pictures of the magnetic shielding constant are derived. We apply the theory to calculations of the magnetic shielding constants of He isoelectronic systems, Ne isoelectronic systems, and noble gas atoms. The results of the present theory compare well with those of the fourcomponent Dirac–Hartree–Fock calculations; the differences were within 3%. We note that the quasirelativistic theory that handles the magnetic vector potential at a nonrelativistic level greatly underestimates the relativistic effect. The socalled “picture change” effect is quite important for the magnetic shielding constant of heavy elements. The change in the orbital picture plays a significant role in the valenceorbital magnetic response as well as the coreorbital one. The effect of the finite nucleus is also studied using Gaussian nucleus model. The present theory reproduces the correct behavior of the finitenucleus effect that has been reported with the Dirac theory. In contrast, the nonrelativistic theory and the quasirelativistic theory with the nonrelativistic vector potential underestimate the finitenucleus effect.

Quasirelativistic theory for magnetic shielding constants. II. Gaugeincluding atomic orbitals and applications to molecules
View Description Hide DescriptionQuasirelativistic theory of magnetic shielding constants based on the Douglas–Kroll–Hess transformation of the magnetic potential presented in a previous paper is extended to molecular systems that contain heavy elements. The gaugeincluding atomic orbital method is adapted to the quasirelativistic Hamiltonian to allow originindependent calculations. The present theory is applied to the proton and halogen magnetic shielding constants of hydrogen halides and the magnetic shielding constants and chemical shifts of mercury dihalides and methyl mercury halides. While the relativistic correction to the magnetic interaction term has little effect on the protonmagnetic shielding constants, this correction is a dominant origin of the heavy atom shifts of the magnetic shielding constants of heavy halogens and mercury. The basis setdependence of mercury shielding constants is quite large in the relativistic calculation; it is important to use the basis functions that are optimized by the relativistic method to properly describe the relativistic effect. The relativistic correction to the magnetic interaction term is quite important for mercury dihalides in which the relativistic effects from mercury and halogen are strongly coupled. Without this correction, we obtain quite incorrect results. The origin of the chemical shifts in mercury dihalides is the spin–orbit interaction from heavy halogens. In methyl mercury halides, the paramagnetic shielding term as well as the spin–orbit interaction from heavy halogens dominates the chemical shifts.

Angular momentum in solidharmonicGaussian integral evaluation
View Description Hide DescriptionSolidharmonic derivatives of generalized Gaussian functions—exponential functions of a scalar argument that has no third derivatives with respect to any nuclear coordinate—are evaluated for three, four, and five centers without coupling any of the original angular momenta. Generalized Gaunt coefficients arise in this approach. They represent scalar coupling of all angular momenta lost from cross differentiation. All formulas are independent of all original angular momenta, which aids the evaluation of all integrals involving centers at one time. Recurrence relations are given for the generalized Gaunt coefficient. The methods of Racah are used to obtain the coefficients that transform the generalized Gaunt coefficients into a representation in which the angular momentum lost due to cross differentiation are arbitrarily coupled, and thus show directly that the generalized Gaunt coefficients always represent scalar coupling. More intermediate information can be reused if the coupled generalized Gaunt coefficients are used to evaluate all the integrals involving a given set of centers.

Application of timedependent currentdensityfunctional theory to nonlocal exchangecorrelation effects in polymers
View Description Hide DescriptionWe provide a successful approach towards the solution of the longstanding problem of the large overestimation of the static polarizability of conjugated oligomers obtained using the local density approximation within densityfunctional theory. The local approximation is unable to describe the highly nonlocal exchange and correlation effects found in these quasionedimensional systems. Timedependent currentdensityfunctional theory enables us to describe ultranonlocal exchangecorrelation effects within a local current description. Recently a brief account was given of the application of the Vignale–Kohn currentfunctional [G. Vignale and W. Kohn, Phys. Rev. Lett. 77, 2037 (1996)] to the axial polarizability of oligomer chains [M. van Faassen, P. L. de Boeij, R. van Leeuwen, J. A. Berger, and J. G. Snijders, Phys. Rev. Lett. 88, 186401 (2002)]. With the exception of the model hydrogen chain, our results were in excellent agreement with best available wavefunction methods. In the present work we further outline the underlying theory and describe how the Vignale–Kohn functional was implemented. We elaborate on earlier results and present new results for the oligomers of polyethylene, polysilane, polysilene, polymethineimine, and polybutatriene. The adiabatic local density approximation gave good results for polyethylene, which were slightly modified by the Vignale–Kohn functional. In all other cases the Vignale–Kohn functional gave large improvements upon the adiabatic local density approximation. The Vignale–Kohn results were in agreement with best available data from wave function methods. We further analyze the hydrogen chain model for different bond length alternations. In all these cases the Vignale–Kohn correction upon the adiabatic local density approximation was too small. Arguments are given that further improvements of the functional are needed.

Usefulness of the Colle–Salvetti model for the treatment of the nondynamic correlation
View Description Hide DescriptionIn this work, the behavior of the Colle–Salvetti correlation functional is examined for strongly correlated systems with nonnegligible nondynamic effects. Used with an appropriate multideterminantal wave function, it is able to reproduce accurately previous multireference coupledcluster results for the problem of the automerization of cyclobutadiene, as well as to provide the correct energetical profiles for diatomic molecules under dissociation. The results confirm the current quality of the functional for complicated chemical problems, in spite of the fact that the functional does not satisfy some known exact properties.

A general method for implementing vibrationally adiabatic mixed quantumclassical simulations
View Description Hide DescriptionAn approach for carrying out vibrationally adiabatic mixed quantumclassical molecular dynamics simulations is presented. An appropriate integration scheme is described for the vibrationally adiabatic equations of motion of a diatomic solute in a monatomic solvent and an approach for calculating the adiabatic energy levels is presented. Specifically, an iterative Lanczos algorithm with full reorthogonalization is used to solve for the lowest few vibrational eigenvalues and eigenfunctions. The eigenfunctions at one time step in a mixed quantumclassical trajectory are used to initiate the Lanczos calculation at the next time step. The basis set size is reduced by using a potentialoptimized discrete variable representation. As a demonstration the problem of a homonuclear diatomic molecule in a rare gas fluid in Ar) has been treated. The approach is shown to be efficient and accurate. An important advantage of this approach is that it can be straightforwardly applied to polyatomic solutes that have multiple vibrational degreesoffreedom that must be quantized.

Local hybrid functionals
View Description Hide DescriptionWe present a novel approach for constructing hybrid functionals by using a local mix of regular density functional theory(DFT) exchange and exact Hartree–Fock (HF) exchange. This local hybrid approach is computationally feasible for a wide range of molecules. In this work, the local mix of HF and DFT exchange is driven by the ratio of the Weizsäcker kinetic energy density, with τ, the exact kinetic energy density. This particular choice of local mix yields 100% of exact exchange in oneelectron regions. Dissociation energy curves, binding energies, and equilibrium geometries for twocenter, threeelectron symmetric radical cations can be modeled accurately using this scheme. We also report encouraging results for reaction energy barriers, and somewhat disappointing atomization energies for the small G2 set.

Selfguided enhanced sampling methods for thermodynamic averages
View Description Hide DescriptionIn the selfguided molecular dynamics (SGMD) simulation method, a continuously updated average force is used to bias the motions of the system. The method appears to sample the configuration space of a number of complex systems more efficiently than ordinary molecular dynamics, and it was argued that it yields canonical averages of observable quantities with only negligible errors. We analyze the dynamic mapping associated with the SGMD algorithm and find that the dynamics lacks reversibility because the effective potential that governs the motion is a functional of the trajectory rather than a function of the coordinates (i.e., the dynamics is not uniquely specified by the initial conditions but depends on past history as well). This irreversibility is shown to result in substantial errors in canonical averages for model systems. Motivated by this analysis, we introduce an alternative selfguided scheme (the momentumenhanced hybrid Monte Carlo method) that does converge to the canonical distribution in principle. The method differs from the original SGMD algorithm in that momenta, rather than forces, are averaged to bias the initial choice of momenta at each step in a hybrid Monte Carlo procedure. The relation of the method to other enhanced sampling algorithms is discussed.

Efficient thermal rate constant calculation for rare event systems
View Description Hide DescriptionWe present an efficient method for computing thermal reaction rate constants that can be applied to systems in which transitions from reactant to product are infrequent. The method can be applied to highdimensional, disordered systems which exhibit too many transition states to be identified, and for which useful reaction coordinates cannot be easily defined. The focus of our method is the time correlation function the normalized partition function for trajectories that begin in the reactant region and end in the product region after a time the time derivative of is the reaction rate constant, We use an umbrella potential to select initial positions from improbable regions of the reactant configuration space. We then compute directly by choosing random thermal momenta and asking if the resulting dynamical trajectory reaches the product region in time Since dynamical trajectories are run on the true potential energy surface, without the umbrella, recrossing effects are included correctly. The initial condition bias introduced by the umbrella is removed by a weighting factor. We test the method on a simple two dimensional model potential and on a model for the isomerization of a diatomic in a Weeks–Chandler–Andersen fluid, and show that it gives accurate and precise rates with substantial reduction in computer time.

Ab initio molecular dynamics with a continuum solvation model
View Description Hide DescriptionWe present an implementation of the conductorlike screening model (COSMO) within the framework of Car–Parrinello ab initiomolecular dynamics. In order to obtain the accurate forces needed for energyconserving dynamics, analytic derivatives with respect to the atomic positions are required for all energy terms. We use a steep, but continuous surface function that effectively switches the surface charges off when they are not exposed on the molecular surface. This allows us to construct the cavity surface in such a way that the required analytic derivatives of the surface charges and surface segments are always available. Furthermore, we treat the surface charges as fictitious dynamic variables within the extended Lagrangian approach, solving the electrostatic problem determining the charges “on the fly” as the system evolves in time. Our implementation makes it possible to perform energyconserving ab initiomolecular dynamics simulations in which continuum solvation is included. It provides solvation energies within the accuracy expected for a COSMO implementation at the densityfunctional level and allows one to study special features of reactivity that can only be observed at finite temperature in solution.

On the optimization of Gaussian basis sets
View Description Hide DescriptionA new procedure for the optimization of the exponents, of Gaussian basis functions, is proposed and evaluated. The direct optimization of the exponents is hindered by the very strong coupling between these nonlinear variational parameters. However, expansion of the logarithms of the exponents in the orthonormal Legendre polynomials, of the index, j: yields a new set of wellconditioned parameters, and a complete sequence of wellconditioned exponent optimizations proceeding from the eventempered basis set to a fully optimized basis set The error relative to the exact numerical selfconsistent field limit for a sixterm expansion is consistently no more than 25% larger than the error for the completely optimized basis set. Thus, there is no need to optimize more than six wellconditioned variational parameters, even for the largest sets of Gaussian primitives.

Method for the ab initio calculation of intermolecular potentials of ionic clusters: Test on Rg=He, Ne, Ar
View Description Hide DescriptionThe interactionenergy of a cationic complex can be computed as the sum of the interactionenergy of the neutral complex A–B and the geometry dependent difference in the ionization potentials of the complex A–B and the molecule B, with ionization potentials calculated by the outer valence Green’s function method. We test this method by computing the intermolecular potentialenergy of the complexes and for linear and Tshaped geometries. Onedimensional potential energy cuts were analyzed with emphasis on the asymptotic behavior. Results obtained by this method have been compared to interactionenergies of the complex computed directly by the partially spinrestricted single and double excitation coupled cluster method with perturbative triples. For the weakly bound complexes and the differences are only a few percent at small intermolecular distances but become significant for separations around the equilibrium distance and larger. Scaling the long range induction coefficients to match accurately known values significantly improves the agreement: the resulting interaction potentials are accurate to within a few percent at all intermolecular separations. For the complex the method produces less accurate results for small intermolecular distances but the binding in is very strong and for small R this system cannot be considered a weakly bound complex anymore.

Manybody effects in nonadiabatic molecular theory for simultaneous determination of nuclear and electronic wave functions: Ab initio NOMO/MBPT and CC methods
View Description Hide DescriptionWe have investigated the manybody effects in a molecular theory to determine simultaneously nuclear and electronic wave functions without the Born–Oppenheimer (BO) approximation. We first apply the manybody perturbationtheory using the electron–nucleus and nucleus–nucleus interactions to the nonBO theory and show the importance of the electron–nucleus correlation rather than the nucleus–nucleus one. We next combine the nonBO theory with the coupled cluster double and Brueckner double methods using the oneelectron plus onenucleus excitation operators.

Equationofmotion coupled cluster method with full inclusion of the connected triple excitations for ionized states: IPEOMCCSDT
View Description Hide DescriptionThe equationofmotion (EOM) coupled cluster (CC) method with full inclusion of the connected triple excitations for ionizationenergies has been formulated and implemented. Using proper factorization of the three and fourbody parts of the effective Hamiltonian, an efficient computational procedure has been proposed for IPEOMCCSDT which at the EOM level requires nohigherthan scaling. The method is calibrated by the evaluation of the valence vertical ionization potentials for CO, and molecules for several basis sets up to 160 basis functions. At the basis set limit, errors vary from 0.0 to 0.2 eV, compared to “experimental” vertical ionization potentials.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Core shell excitation of 2propenal (acrolein) at the and edges: An experimental and ab initio study
View Description Hide DescriptionThe carbon and oxygen Kshell spectra of gaseous 2propenal (acrolein) have been measured using the innershell electron energy loss spectroscopy method. Large scale ab initioconfiguration interaction calculations have been carried out to enable firm assignments of the observed bands. The overall shapes of the spectra are similar to previous low resolution monolayer and multilayer phases NEXAFS spectra recorded by photoabsorption of synchrotron radiation, but the spectral bands are much better resolved than the earlier ones. The spectra are dominated by excitation of type states and by interaction between the and orbitals.

Understanding highly excited states via parametric variations
View Description Hide DescriptionHighly excited vibrational states of an isolated molecule encode the vibrational energy flow pathways in the molecule. Recent studies have had spectacular success in understanding the nature of the excited states mainly due to the extensive studies of the classical phase space structures and their bifurcations. Such detailed classicalquantum correspondence studies are presently limited to two or quasitwodimensional systems. One of the main reasons for such a constraint has to do with the problem of visualization of relevant objects like surface of sections and Wigner or Husimi distributions associated with an eigenstate. This necessitates various alternative techniques which are more algebraic than geometric in nature. In this work we introduce one such method based on parametric variation of the eigenvalues of a Hamiltonian. It is shown that the level velocities are correlated with the phase space nature of the corresponding eigenstates. A semiclassical expression for the level velocities of a single resonance Hamiltonian is derived which provides theoretical support for the correlation. We use the level velocities to dynamically assign the highly excited states of a modelspectroscopic Hamiltonian in the mixed phase space regime. The effect of bifurcations on the level velocities is briefly discussed using a recently proposed spectroscopic Hamiltonian for the HCP molecule.

Infrared emission spectra of BeH and BeD
View Description Hide DescriptionHigh resolution infrared emission spectra of beryllium monohydride and monodeuteride have been recorded. The molecules were generated in a furnacedischarge source, at 1500 °C and 333 mA discharge current, with beryllium metal and a mixture of helium and hydrogen or deuterium gases. Approximately 160 BeH lines and 167 BeD lines for the vibrational bands to were observed in the spectra and spectroscopic constants were determined. The Dunham constants and Born–Oppenheimer breakdown constants were obtained in a combined fit of the BeH and BeD data. The equilibrium rotational constants for BeH and BeD were found to be 10.319 59(3) cm^{−1} and 5.688 29(2) cm^{−1}, respectively, while the equilibrium vibrational constants are 2061.416(3) and 1529.956(3) cm^{−1}. The equilibrium distance was determined to be 1.342 436(2) Å for BeH.