Volume 123, Issue 2, 08 July 2005
 ARTICLES

 Theoretical Methods and Algorithms

A postHartree–Fock model of intermolecular interactions
View Description Hide DescriptionIntermolecular interactions are of great importance in chemistry but are difficult to model accurately with computational methods. In particular, Hartree–Fock and standard densityfunctional approximations do not include the physics necessary to properly describe dispersion. These methods are sometimes corrected to account for dispersion by adding a pairwise term, with dispersion coefficients dependent on the atoms involved. We present a postHartree–Fock model in which coefficients are generated by the instantaneous dipole moment of the exchange hole. This model relies on occupied orbitals only, and involves only one, universal, empirical parameter to limit the dispersion energy at small interatomic separations. The model is extensively tested on isotropic coefficients of 178 intermolecular pairs. It is also applied to the calculation of the geometries and binding energies of 20 intermolecular complexes involving dispersion, dipoleinduced dipole, dipole–dipole, and hydrogenbonding interactions, with remarkably good results.

NonBorn–Oppenheimer treatment of the Hookean molecule
View Description Hide DescriptionWe show that the exact nonBorn–Oppenheimer Schrödinger equation for the Hookean diatomic molecule (a twoproton, twoelectron system where the electronproton interaction is harmonic while the protonproton and electronelectron interactions are Coulombic) can be decoupled into equations describing the relative motion of the electrons, the relative motion of nuclei, the motion of a collective mode representing a threedimensional harmonic oscillator, and the motion of a free particle expressed as a linear combination of the individual centerofmass coordinates of the nuclei and electrons. Analytic solutions to the relative motion of electrons can be readily obtained for the given values of the harmonic coupling constant. However, exact analytic solutions to the equation for the relative motion of the nuclei cannot be obtained simultaneously due to the fact that the harmonic constants in these two equations are coupled. For this reason, we present for the relative nuclear motion approximate analytic wave functions, one of them obtained variationally and the other by a series solution where the coefficients are determined recursively. We also explore a variational solution to the Taylorseries expansion of the nuclear interaction potential. Properties of the electronic and nuclear intracule densities are examined at different values of the coupling constant. An interesting result of the present nonBorn–Oppenheimer treatment of this harmonic model is the fact that the relative nuclear motion occurs in a highly correlated regime. This leads in a natural way to a spatial localization of the nuclei akin to Wigner electronic crystallization.

Basis set convergence studies of Hartree–Fock calculations of molecular properties within the resolution of the identity approximation
View Description Hide DescriptionWithin the resolution of the identity (RI) method, the convergence of the Hartree–Fock (HF) total molecular energy and the multipole moments in the course of the combined regular expansion of the molecular and auxiliary (RI) basis sets is studied. Dunning’s series is used for both the molecular and the RI basis sets. The results show the calculated quantities converge to the HF limit when both the molecular and the RI basis sets are expanded from correlationconsistent polarized valence double zeta to correlationconsistent polarized valence sextuple zeta. Combinations of molecular/RI basis sets sufficient for convergence of the total energy and of the multipole moments at various accuracy levels have been determined. A measure of the RI basis set incompleteness is suggested and discussed. As it is significantly faster than the standard HF algorithm for small and midsize molecules, the RIHF method, together with appropriate expanding series of both molecular and RI basis sets, provide an efficient tool to estimate and control the error of the Hartree–Fock calculations due to the finite basis set.

Hybrid Monte Carlo implementation of the Fourier path integral algorithm
View Description Hide DescriptionThis paper formulates a hybrid Monte Carlo implementation of the Fourier path integral (FPIHMC) approach with partial averaging. Such a hybrid Monte Carlo approach allows one to generate collective moves through configuration space using molecular dynamics while retaining the computational advantages associated with the Fourier path integral Monte Carlo method. In comparison with the earlier Metropolis Monte Carlo implementations of the FPI algorithm, the present HMC method is shown to be significantly more efficient for quantum LennardJones solids and suggests that such algorithms may prove useful for efficient simulations of a range of atomic and molecular systems.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Electronphonon interactions in photoinduced excited electronic states in fluoroacenes
View Description Hide DescriptionThe electronphonon coupling constants in the photoinduced excited electronic states in fluoroacenes are estimated and compared with those in the monoanions and cations . The values are much larger than the and values in fluoroacenes. Furthermore, the Coulomb pseudopotential values for the excited electronic states are estimated to be smaller than those for the monoanions and cations. The complete phase patterns difference between the highest occupied molecular orbitals (HOMOs) and the lowest unoccupied molecular orbitals (LUMOs) is the main reason why the electronphonon coupling constants and the values are larger and smaller, respectively, in the photoinduced excited electronic states than in the monoanions and cations. The possible electron pairing and Bose–Einstein condensation in the excited electronic states of fluoroacenes are discussed. Because of larger electronphonon coupling constants and smaller values in the excited electronic states than in the charged states, the conditions under which the electronelectron interactions become attractive can be more easily realized, in principle, in the excited electronic states than in the charged states in fluoroacenes. The values hardly change by H–F substitution, even though the and values significantly increase by H–F substitution in acenes. Antibonding interactions between carbon and fluorine atoms in the HOMO and LUMO are the main reason why the values hardly change by H–F substitution in acenes.

Molecularbeam study of the waterhelium system: Features of the isotropic component of the intermolecular interaction and a critical test for the available potentialenergy surfaces
View Description Hide DescriptionWe report molecularbeam measurements of the total integral cross sections for the scattering of water molecules by helium atoms. A combined analysis of the new experimental data together with available differential cross section results has allowed an accurate determination of the isotropic component of the interaction potential for this prototypical system. The potential well shows a depth of at a distance between He and the center of mass of the water molecule of . An effective isotropic longrange attraction constant , including both dispersion and induction contributions, has also been determined. The most recent and accurate ab initiopotentialenergysurfaces have been tested against these new experimental results.

Experimental and theoretical studies of the quenching of by
View Description Hide DescriptionQuenching mechanisms of the and states in collision with the nitrogen molecule are studied by laserinduced fluorescence spectroscopy and by a quantum chemical calculation. The state is observed to be efficiently quenched to the state detected as intense emission. The state is efficiently quenched to the and states detected as and emissions, respectively. The potentialenergysurfaces for the states show a large number of conical intersections and avoided crossings resulting from the couplings between the ionic and covalent configurations. There are a large number of stable excited states, and we give here the spectroscopic constants for the lowest two stable isomers correlating to .

Accurately solving the electronic Schrödinger equation of atoms and molecules using explicitly correlated multireference configuration interaction. VII. The hydrogen fluoride molecule
View Description Hide DescriptionWe compute the potentialenergy curve of the hydrogen fluoride molecule (HF) using a novel variant of the explicitly correlated multireference averaged coupledpair functional method with a carefully selected basis set and reference space. After correcting for scalar relativistic effects and spinorbit coupling, the potential is used to compute the dissociation energy, the equilibrium bond distance, the harmonic frequency, the anharmonicity, and the vibrational levels up to the dissociation limit. The errors in the equilibrium geometry constants compare favorably with the most elaborate (single reference) calculations of the literature. Starting at the region of , where the covalent HF bond begins to break and where singlereference methods become impractical, our potential begins to slightly underestimate the atomic interaction, which is reflected in an estimated error in the well depth of .

Multipolar polarizabilities of the sodium atom by a variationally stable procedure
View Description Hide DescriptionWe present a formalism that combines a semiempiricalmodel potential with a secondorder energy correction variationally stable method to evaluate the multipolar dynamic polarizabilities of the sodium atom. In this framework, the up to were calculated achieving good precision including the resonance domains of .

Observation of the state of methylene by opticaloptical double resonance
View Description Hide DescriptionWe report the observation of the rotationally resolved spectrum of the state of via sequential singlephoton absorptions at visible and nearinfrared wavelengths. Direct absorption from the lowest singlet state to occurs in the near UV, but it is weak because it corresponds to a two electron transition between the dominant single configuration approximations to the electronic wave functions. Some absorption lines in the system were originally reported in 1966 [G. Herzberg and J. W. C. Johns, Proc. R. Soc. London, Ser. A295, 107 (1966)], but the weak spectra could not be assigned at the time. Interest in the state was rekindled by recent ab initio results [S. N. Yurchenko, P. Jensen, Y. Li, R. J. Buenker, and P. R. Bunker, J. Mol. Spectrosc.208, 136 (2001)] which prompted the present work. The new spectra provide accurate energies for rotational levels in the level of the state, and permit assignment of most of the line positions measured by Herzberg and Johns. The doubleresonance technique used may be easily extended to the measurement of lower rovibrational levels in the electronic state and possibly also to access the state which is theoretically expected to lie at similar energies but, for symmetry reasons, is not accessible from the lowest singlet state in a single electricdipole transition.

A new scheme for determining the intramolecular sevenmembered ring hydrogenbonding energies of glycine and alanine peptides
View Description Hide DescriptionIn this paper a new scheme was proposed to calculate the intramolecular hydrogenbonding energies in peptides and was applied to calculate the intramolecular sevenmembered ring hydrogenbonding energies of the glycine and alanine peptides. The densityfunctional theory and methods and the secondorder MøllerPlesset perturbation theory method were used to calculate the optimal geometries and frequencies of glycine and alanine peptides and related structures. , , and MP2/augccpVTZ methods were then used to evaluate the singlepoint energies. It was found that the , , and methods yield almost similar structural parameters for the conformers of the glycine and alanine dipeptides. MP2/augccpVTZ predicts that the intramolecular sevenmembered ring hydrogenbonding strength has a value of in glycine dipeptide and 5.73 and in alanine dipeptides, while the steric repulsive interactions of the sevenmembered ring conformers are in glycine dipeptide and 6.62 and in alanine dipeptides. It was also found that gives as accurate intramolecular hydrogenbonding energies and steric repulsive interactions as the much more costly MP2/augccpVTZ does.

Anisotropic dipole polarizability of transition metal atoms: , , , and ions: ,
View Description Hide DescriptionDipole polarizabilitytensor components and quadrupole moments of transitionmetal atoms Sc, Ti, V, Ni, and Cu and ions and are computed using finite field complete active space selfconsistent field and multireference configuration interaction ab initio methods. Perpendicular components of the dipole polarizabilitytensor are calculated from equations involving only parallel components of the polarizabilitytensor and its average value. Mean polarizability and polarizabilityanisotropy decrease in the Sc–Ni series. Relativistic effects are accounted for with the DouglasKroll Hamiltonian. The consequences of the anisotropicproperties of these atoms to their interactions with spherically symmetric rare gases are also discussed.

Shape resonances as poles of the semiclassical Green’s function obtained from pathintegral theory: Application to the autodissociation of the state
View Description Hide DescriptionIt is known that onedimensional potentials, , with a local minimum and a finite barrier towards tunneling to a free particle continuum, can support a finite number of shape resonance states. Recently, we reported a formal derivation of the semiclassical Green’s function,, for such , with one and two local minima, which was carried out in the framework of the theory of path integrals [Th. G. Douvropoulos and C. A. Nicolaides, J. Phys. B35, 4453 (2002);J. Chem. Phys.119, 8235 (2003)]. The complex poles of represent the energies and the tunneling rates of the unstable states of . By analyzing the structure of , here it is shown how one can compute the energy, , and the radiationless width, , of each resonance state beyond the WentzelKramersBrillouin approximation. In addition, the energy shift, , due to the interaction with the continuum, is given explicitly and computed numerically. The dependence of the accuracy of the semiclassical calculation of and of on the distance from the top of the barrier is demonstrated explicitly. As an application to a real system, we computed the vibrational energies, , and the lifetimes, , of the , , 1, 2, 3, 4, and , 1, 2, 3, states, which autodissociate to the continuum. We employed the that was computed by Wolniewicz [J. Phys. B32, 2257 (1999)], which was reported as being accurate, over a large range of values of , to a fraction of . For example, for , the results for the lowest and highest vibrational levels for the state are level, below the barrier top, ; level, below the barrier top, . A brief presentation is also given of the quantal methods (and their results) that were applied previously for these shape resonances, such as the amplitude, the exterior complex scaling, and the lifetime matrix methods.

Onephoton massanalyzed threshold ionization spectroscopy of : Extensive bending progression, reduced steric effect, and spinorbit effect in the cation
View Description Hide DescriptionOnephoton massanalyzed threshold ionization (MATI) spectrum of was obtained using coherent vacuumultraviolet radiation generated by fourwave differencefrequency mixing in Kr. Unlike investigated previously, a very extensive bending (Br–C–I) progression was observed. Vibrational frequencies of were measured from the spectra and the vibrational assignments were made by utilizing frequencies calculated by the densityfunctionaltheory (DFT) method using relativistic effective core potentials with and without the spinorbit terms. A noticeable spinorbit effect on the vibrational frequencies was observed from the DFT calculations, even though its influence was not so dramatic as in . A simple explanation based on the bonding characteristics of the molecular orbitals involved in the ionization is presented to account for the above differences between the MATI spectra of and . The 00 band of the spectrum could be identified through the use of combined data from calculations and experiments. The adiabatic ionization energy determined from the position of this band was , which was significantly smaller than the vertical ionization energy reported previously.

Theoretical study of guanine–Cu and uracil–Cu (neutral, anionic, and cationic). Is it possible to carry out a photoelectron spectroscopy experiment?
View Description Hide DescriptionThe structure and bonding of guanine–Cu and uracil–Cu (neutral, anionic, and cationic) are discussed on the basis of the calculated structures and energies. The interaction of the metal atom with guanine and uracil has been analyzed using the B3LYP densityfunctional approach. The removal of one electron from the neutral complexes produces the stabilization of one of the isomers, while the addition of one electron leads to a system where the metal atom is weakly bounded to guanine or uracil, according to the metalbases bond distance that is long (2.29–2.90). For guanine–Cu and uracil–Cu, the vertical ionization energy of the anion is close to the dissociation energy of one hydrogen atom from guanine–Cu or uracil–Cu. In these cases, it could be possible to produce the detachment of one electron from the anion and also the removal of one hydrogen atom. This is important since the photoelectron spectroscopy of atomic or mixedatomic cluster anions has proven to be a very effective tool in the study of small systems. For the analysis of copper atoms with DNA bases such as guanine and uracil, it is expected that the photoelectron spectra of the anionbases complexes strongly resemble the spectrum of , just shifted to higher electron binding energies due to the product stabilization. Hopefully, this information will be useful for the experimental groups.

Spectroscopic characterization of a molecule with a weak bond: The BrOO radical
View Description Hide DescriptionPure rotational spectra of the BrOO radical for the and isotopomers have been observed using a Fourier transform microwave spectrometer. The radical was produced in a supersonic jet by discharging a mixture gas containing bromine and oxygen diluted in argon. type rotational transitions are observed for , with spin doublings and hyperfine splittings due to the nuclear spin of the bromine atom. Highlevel ab initio calculations by RCCSD(T) and MRCI have also been performed, and results are compared with the experimental data. Molecular structure of BrOO has been discussed based on the present experimental data, supplemented by the tendency among the halogen peroxide series and the results of the ab initio calculations; the Br–O bond is found to be anomalously long and weak. Systematic comparisons with other halogen peroxides have revealed anomalous nature of the X–O ( atom) bonds for this series of radicals.

The and systems: molecular properties, isomerization, and energetics
View Description Hide DescriptionThe isomer pair and related cations have been studied by means of a highly accurate level of theory. For all the species investigated the nearequilibrium potential energy surface has been calculated using the coupled cluster method in conjunction with correlation consistent basis sets ranging in size from quadruple to sextuple zeta. After extrapolation to the complete basis set limit, additional corrections due to corevalence correlation and scalar relativistic effects have also been included. Consequently, the molecular and spectroscopic properties as well as the ionization potentials and dissociation energies have been predicted to high accuracy. Isomerization path and energy for both radical and cationic species have also been investigated. Finally, the anharmonic vibrational frequencies have been employed in order to obtain zeropoint corrections to ionization potentials,dissociation energies, and isomerization barriers: and ; and ; , and .

Experimental and theoretical study on gasphase ion/molecule reactions of silver trimer cation, , with 12crown4
View Description Hide DescriptionThe reaction mechanisms of silver trimer cation, , with 12crown4 (12C4) were studied experimentally and theoretically. Using a cylindrical ion traptimeofflightmass spectrometer, gasphase ion/molecule reactions of with 12C4 were observed. Metalligand complexes of , and , and of and , were observed as the reaction intermediates and terminal products, respectively. The formations of the and complexes indicated that the neutral dimer had been eliminated from the trimer cation. From the results of ab initio calculations at the HF/LanL2DZ level of theory and the experiments, it is suggested that three 12C4 molecules can attach to through consecutive reactions and that neutral can be easily eliminated from .
 Condensed Phase Dynamics, Structure, and Thermodynamics: Spectroscopy, Reactions, and Relaxation

Hardsphere radial distribution function again
View Description Hide DescriptionA theoretically based closedform analytical equation for the radial distribution function,, of a fluid of hard spheres is presented and used to obtain an accurate analytic representation. The method makes use of an analytic expression for the short and longrange behaviors of , both obtained from the PercusYevick equation, in combination with the thermodynamic consistency constraint. Physical arguments then leave only three parameters in the equation of that are to be solved numerically, whereas all remaining ones are taken from the analytical solution of the PercusYevick equation.

Line of percolation in supercritical water
View Description Hide DescriptionThe percolation transition of the hydrogenbonded clusters of molecules is investigated in supercritical water by Monte Carlocomputer simulations. Simulations have been performed at four thermodynamic state points located above the supercritical extension of the vaporliquid coexistence curve on the phase diagram and at four state points located below this curve. It is found in a temperature range of a few hundred Kelvin that the extension of the vaporliquid coexistence curve separates the supercritical thermodynamic states in which the water molecules form infinite hydrogenbonded clusters from those in which the hydrogenbonded clusters are isolated oligomers. However, the difference between the size of the hydrogenbonded clusters at thermodynamic states located at the two sides of the extension of the coexistence curve is found to decrease with increasing temperature, and the present results suggest that this difference is likely to vanish at high enough temperatures.