Volume 123, Issue 6, 08 August 2005
 ARTICLES

 Theoretical Methods and Algorithms

Relativistic dynamics of halfspin particles in a homogeneous magnetic field: An atom with nucleus of spin
View Description Hide DescriptionAn investigation of the relativistic dynamics of spin particles placed in an external, homogeneous magnetic field is carried out. The system can represent an atom with a fermion nucleus and electrons. Quantum electrodynamical interactions, namely, projected Briet and magnetic interactions, are chosen to formulate the relativistic Hamiltonian. The quasifreeparticle picture is retained here. The total pseudomomentum is conserved, and its components are distinct when the total charge is zero. Therefore, the centerofmass motion can be separated from the Hamiltonian for a neutral fermion system, leaving behind a unitarily transformed, effective Hamiltonian at zero total pseudomomentum. The latter operator represents the complete relativistic dynamics in relative coordinates while interaction is chosen through order . Each oneparticle part in the effective Hamiltonian can be brought to a separable form for positive and negativeenergy states by replacing the odd operator in it through two successive unitary transformations, one due to Tsai [Phys. Rev. D7, 1945 (1973)] and the other due to Weaver [J. Math. Phys.18, 306 (1977)]. Consequently, the projector changes and the interaction that involves the concerned particle also becomes free from the corresponding odd operators. When this maneuver is applied only to the nucleus, and the nonHermitian part of the transformed interaction is removed by another unitary transformation, a familiar form of the atomic relativistic Hamiltonian emerges. This operator is equivalent to . A good Hamiltonian for relativistic quantum chemical calculations, , is obtained by expanding the nuclear part of the atomic Hamiltonian through order for positiveenergy states. The operator is obviously an approximation to . When the same technique is used for all particles, and subsequently the nonHermitian terms are removed by suitable unitary transformations, one obtains a Hamiltonian that is equivalent to but is in a completely separable form. As the semidiscrete eigenvalues and eigenfunctions of the oneparticle parts are known, the completely separable Hamiltonian can be used in computation. A little more effort leads to the derivation of the correct atomic Hamiltonian in the nonrelativistic limit, . The operator is an approximation to . It not only retains the relativistic and radiative effects, but also directly exhibits the phenomena of electron paramagnetic resonance and nuclear magnetic resonance.

Decoupling and recoupling using continuouswave irradiation in magicanglespinning solidstate NMR: A unified description using bimodal Floquet theory
View Description Hide DescriptionThe application of two or more different timedependent coherent perturbations with, in general, incommensurable frequencies occurs quite commonly in NMR experiments. Here we develop a unified description of the entire class of experiments using bimodal Floquet theory and van Vleck–Primas perturbation theory. This treatment leads to a timeindependent effective Hamiltonian in Hilbert space and can be looked at as a generalization of average Hamiltonian theory to several incommensurate time dependencies. As a prototype experiment we treat the application of continuouswave (cw) radiofrequency irradiation in combination with magicangle sample spinning. Practically relevant examples of this type of experiments are heteronuclear spin decoupling and recoupling experiments using cw irradiation, e.g., rotaryresonance recoupling. Perturbations up to the third order must be taken into account to explain all experimentally observed resonance conditions.

Electronic decoherence time for nonBornOppenheimer trajectories
View Description Hide DescriptionAn expression is obtained for the electronic decoherence time of the reduced density electronic matrix in mixed quantumclassical moleculardynamics simulations. The result is obtained by assuming that decoherence is dominated by the time dependence of the overlap of minimumuncertainty packets and then maximizing the rate with respect to the parameters of the wave packets. The expression for the decay time involves quantities readily available in nonBornOppenheimer moleculardynamics simulations, and it is shown to have a reasonable form when compared with two other formulas for the decay time that have been previously proposed.

Investigation of isotope effects with the nuclearelectronic orbital approach
View Description Hide DescriptionThis paper addresses fundamental issues that arise in the application of the nuclearelectronic orbital (NEO) approach to systems with equivalent quantum nuclei. Our analysis illustrates that HartreeFock nuclear wave functions do not provide physically reasonable descriptions of systems comprised of equivalent lowspin fermions or equivalent bosons. The physical basis for this breakdown is that the ionic terms dominate due to the localized nature of the nuclear orbitals. Multiconfigurational wave functions that include only covalent terms provide physically reasonable descriptions of these types of systems. The application of the NEO approach to a variety of chemical systems is presented to elucidate the isotope effects on the geometries and electronic wave functions. Deuteration of hydrogen halides, water, ammonia, and hydronium ion decreases the bond length and the magnitude of negative partial atomic charge on the heavy atom. These results are consistent with experimental spectroscopic data. Deuteration at the beta position for formate anion and a series of amines increases the magnitude of negative partial atomic charge on the protonation site for the unprotonated species. This observation is consistent with the experimentally observed increase in basicity upon deuteration at the beta position for carboxylic acids and amines.

On the nature of the MøllerPlesset critical point
View Description Hide DescriptionIt has been suggested [F. H. Stillinger, J. Chem. Phys.112, 9711 (2000)] that the convergence or divergence of MøllerPlesset perturbation theory is determined by a critical point at a negative value of the perturbation parameter at which an electron cluster dissociates from the nuclei. This conjecture is examined using configurationinteraction computations as a function of and using a quadratic approximant analysis of the highorder perturbation series. Results are presented for the He, Ne, and Ar atoms and the hydrogen fluoride molecule. The original theoretical analysis used the true Hamiltonian without the approximation of a finite basis set. In practice, the singularity structure depends strongly on the choice of basis set. Standard basis sets cannot model dissociation to an electron cluster, but if the basis includes diffuse functions then it can model another critical point corresponding to complete dissociation of all the valence electrons. This point is farther from the origin of the plane than is the critical point for the electron cluster, but it is still close enough to cause divergence of the perturbation series. For the hydrogen fluoride molecule a critical point is present even without diffuse functions. The basis functions centered on the H atom are far enough from the F atom to model the escape of electrons away from the fluorine end of the molecule. For the Ar atom a critical point for a oneelectron ionization, which was not previously predicted, seems to be present at a positive value of the perturbation parameter. Implications of the existence of critical points for quantumchemical applications are discussed.

Multidimensional timedependent discrete variable representations in multiconfiguration Hartree calculations
View Description Hide DescriptionIn the multiconfiguration timedependent Hartree (MCTDH) approach, the wave function is expanded in timedependent basis functions, called singleparticle functions, to increase the efficiency of the wavepacket propagation. The correlation discrete variable representation (CDVR) approach, which is based on a timedependent discrete variable representation (DVR), can be employed to evaluate matrix elements of the potential energy. The efficiency of the MCTDH method can be further enhanced by using multidimensional singleparticle functions. However, up to now the CDVR approach could not be used in MCTDH calculations employing multidimensional singleparticle functions, since this would require a general multidimensional nondirectproduct DVR scheme. Recently, Dawes and Carrington presented a practical scheme to implement general nondirectproduct multidimensional DVRs [R. Dawes and T. Carrington, Jr., J. Chem. Phys.121, 726 (2004)]. The present work utilizes their scheme in the MCTDH/CDVR approach. The accuracy is tested using the photodissociation of NOCl as example. The results show that the CDVR scheme based on multidimensional timedependent DVRs allows for an accurate evaluation of the potential in MCTDH calculations with multidimensional singleparticle functions.

Systematically convergent basis sets for transition metals. I. Allelectron correlation consistent basis sets for the elements Sc–Zn
View Description Hide DescriptionSequences of basis sets that systematically converge towards the complete basis set (CBS) limit have been developed for the firstrow transition metal elements Sc–Zn. Two families of basis sets, nonrelativistic and DouglasKrollHess (DK) relativistic, are presented that range in quality from triple to quintuple. Separate sets are developed for the description of valence electron correlation ( and ; , 5) and valence plus outercore correlation ( and ; , 5), as well as these sets augmented by additional diffuse functions for the description of negative ions and weak interactions ( and ). Extensive benchmark calculations at the coupled cluster level of theory are presented for atomic excitation energies, ionization potentials, and electron affinities, as well as molecular calculations on selected hydrides (TiH, MnH, CuH) and other diatomics (TiF, ). In addition to observing systematic convergence towards the CBS limits, both electron correlation and scalar relativity are calculated to strongly impact many of the atomic and molecular properties investigated for these firstrow transition metal species.

A local correlation model that yields intrinsically smooth potentialenergy surfaces
View Description Hide DescriptionWe demonstrate an algorithm for computing local coupledcluster doubles (LCCD) energies that form rigorously smooth potentialenergysurfaces and which should be fast enough for application to large systems in the future. Like previous LCCD algorithms, our method solves iteratively for only a limited number of correlation amplitudes, treating the remaining amplitudes with secondorder perturbation theory. However, by employing bump functions, our method smoothes the transition from iteratively solved amplitude to perturbationtreated amplitude, invoking the implicit function theorem to prove that our LCCD energy is an infinitely differentiable function of nuclear coordinates. We make no explicit amplitude domains nor do we rely on the existence of atomcentered, redundant orbitals in order to get smooth potentialenergy curves. In fact, our algorithm employs only localized orthonormal occupied and virtual orbitals. Our approach should be applicable to many other electron correlation methods.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Collisional and photoinitiated reaction dynamics in the ground electronic state of Ca–HCl
View Description Hide Descriptionreactive collisions were studied for different rovibrational states of the HCl reactant using wavepacket calculations in reactant Jacobi coordinates. A recently proposed potentialenergy surface was used with a barrier of followed by a deep well. The possibility of an insertion mechanism due to this last well has been analyzed and it was found that once the wave packet passes over the barrier most of it goes directly to products, which shows that the reaction dynamics is essentially direct. It was also found that there is no significant change in the reaction efficiency as a function of the initial HCl rovibrational state, because CaHCl at the barrier has an only little elongated HCl bond. Near the threshold for reaction with , however, the reaction shows significant steric effects for . In a complementary study, the infrared excitation from the Ca–HCl van der Waals well was simulated. The spectrum thus obtained shows several series of resonances which correspond to quasibound states correlating to excited vibrations. The Ca–HCl binding energies of these quasibound states increase dramatically with , from , because the wave function spreads increasingly over larger HCl bond lengths. Thus it explores the region of the barrier saddle point and the deep insertion well. Although also the chargetransfer contribution increases with , the reaction probability for resonances of the manifold, which are well above the reaction threshold, is still negligible. This explains the relatively long lifetimes of these resonances. The reaction probability becomes significant at . Our simulations have shown that an experimental study of this type will allow a gradual spectroscopic probing of the barrier for the reaction.

FranckCondon analysis of the absorption and fluorescence spectra of all trans ,diphenylpolyenes with one to seven polyene double bonds
View Description Hide DescriptionFluorescence and absorption spectra have been measured for alltrans ,diphenylpolyenes with one to seven polyene double bonds in roomtemperature solution, along with the fluorescence spectra of those with one to six polyene double bonds in alkane matrices at 77 K. All the spectral data were fitted by sums of Gaussians to treat the FranckCondon envelopes of the measured spectra quantitatively. The FranckCondon analyses of the spectra in the harmonic limit revealed that the displacements of the CC and C–C stretching vibrational modes in the 2 Ag state relative to those in the ground state,, increase, while those in the state show a slight decrease with the increase of the polyene chain length. It is also shown that the bandwidths of the absorption and fluorescence spectra exhibit a monotonic decrease with the increase of the chain length.

The weakly bound He–HCCCN complex: Highresolution microwave spectra and intermolecular potentialenergy surface
View Description Hide DescriptionRotational spectra of the weakly bound He–HCCCN and He–DCCCN van der Waals complexes were observed using a pulsednozzle Fouriertransform microwave spectrometer in the 7–26GHz frequency region. Nuclear quadrupole hyperfine structures due to the and D nuclei (both with nuclearspin quantum number ) were resolved and assigned. Both strong and weaker type transitions were observed and the assigned transitions were used to fit the parameters of a distortable asymmetric rotor model. The dimers are floppy, near Tshaped complexes. Three intermolecular potentialenergysurfaces were calculated using the coupledcluster method with single and double excitations and noniterative inclusion of triple excitations. Boundstate rotational energy levels supported by these surfaces were determined. The quality of the potentialenergysurfaces was assessed by comparing the experimental and calculated transition frequencies and also the corresponding spectroscopic parameters. Simple scaling of the surfaces improved both the transition frequencies and spectroscopic constants. Five other recently reported surfaces [O. AkinOjo, R. Bukowski, and K. Szalewicz, J. Chem. Phys.119, 8379 (2003)], calculated using a variety of methods, and their agreement with spectroscopic properties of He–HCCCN are discussed.

Guided ionbeam studies of the reactions of with : Cobalt clusteroxide and dioxide bond energies
View Description Hide DescriptionThe kineticenergy dependence for the reactions of with is measured as a function of kinetic energy over a range of in a guided ionbeam tandem mass spectrometer. A variety of , , and product ions is observed, with the dioxide cluster ions dominating the products for all larger clusters.Reaction efficiencies of cations with are near unity for all but the dimer. Bond dissociation energies for both cobaltcluster oxides and dioxides are derived from threshold analysis of the energy dependence of the endothermic reactions using several different methods. These values show little dependence on cluster size for clusters larger than three atoms. The trends in this thermochemistry and the stabilities of oxygenated cobaltclusters are discussed. The bond energies of for larger clusters are found to be very close to the value for desorption of atomic oxygen from bulkphase cobalt.Rate constants for chemisorption on the cationic clusters are compared with results from previous work on cationic, anionic, and neutral cobaltclusters.

The effect of the torsional and stretching vibrations of on the reaction
View Description Hide DescriptionWe present a threedimensional quantum scattering model to treat reactions of the type . The model allows the torsional and the stretching degrees of freedom to be treated explicitly. Zeropoint energies of the remaining modes are taken into account in electronic structure calculations. An analytical potentialenergysurface was developed from a minimal number of ab initio geometry evaluations using the CCSD(T,full)/ccpVTZ//MP2(full)/ccpVTZ level of theory. The reaction is endothermic by and exhibits a vibrationally adiabatic barrier of . The results show that the torsional mode influences reactivity when coupled with the vibrational C–H stretching mode. We also found that ethyl radical products are formed internally excited in the torsional mode.

Geometries, stabilities, and electronic properties of differentsized clusters: A densityfunctional investigation
View Description Hide DescriptionThe clusters with different spin configurations have been systematically investigated by using the densityfunctional approach. The total energies, equilibrium geometries, growthpattern mechanisms, natural population analysis, etc., are discussed. The equilibrium structures of differentsized clusters can be determined by two evolution patterns. Theoretical results indicate that the most stable geometries, except , keep the analogous frameworks as the lowestenergy or the second lowestenergy clusters. However, for large clusters, Zr atom obviously disturbs the framework of silicon clusters, and the localized position of the transitionmetal (TM) Zr atom gradually varies from the surface insertion site to the concave site of the open silicon cage and to the encapsulated site of the sealed silicon cage. It should be mentioned that the lowestenergy sandwichlike geometry is not a sealed structure and appears irregular as compared with other . The growth patterns of clusters are concerned showing the Zrencapsulated structures as the favorable geometries. In addition, the calculated fragmentation energies of the clusters manifest that the magic numbers of stabilities are 6, 8, 10, 14, and 16, and that the fullerenelike is the most stable structure, which is in good agreement with the calculated atomic binding energies of and with available experimental and theoretical results. Natural population analysis shows that the natural charge population of Zr atom in the most stable structures exactly varies from positive to negative at the criticalsized cluster; furthermore, the charge distribution around the Zr atom appears clearly covalent in character for the small or middlesized clusters and metallic in character for the largesized clusters. Finally, the properties of frontier orbitals and polarizabilities of are also discussed.

Bound states and scattering resonances of OH–He
View Description Hide DescriptionThe OH–He complex has been observed using laser excitation of the transition. The bands of the complex were close to the monomer rotational lines that terminate on the , 1, and 2 levels of OH. The unresolved band associated with He·OH was redshifted from the OH parent line by , providing a direct measurement of . The complex features associated with and 2 were identified as scattering resonances. They have been assigned by comparison with resonance structures derived from closecoupling calculations. The ab initiopotential energy surface of H.S. Lee, A.B. McCoy, R.R. Toczylowski, and S.M. Cybulski, [J. Chem. Phys.113, 5736 (2000)] was used in these calculations. The level of agreement between the observed and predicted resonances indicated that the ab initiosurface is reasonably accurate.

Threshold collisioninduced dissociation of diatomic molecules: A case study of the energetics and dynamics of collisions with Ar and Xe
View Description Hide DescriptionThe energetics and dynamics of collisioninduced dissociation of with Ar and Xe targets are studied experimentally using guided ionbeam tandem mass spectrometry. The cross sections and the collision dynamics are modeled theoretically by classical trajectory calculations. Experimental apparent threshold energies are 2.1 and in excess of the thermochemicalbonddissociation energy for argon and xenon, respectively. Classical trajectory calculations confirm the observed threshold behavior and the dependence of cross sections on the relative kinetic energy. Representative trajectories reveal that the bonddissociation takes place on a short time scale of about in strong direct collisions. Collisioninduced dissociation is found to be remarkably restricted to the perpendicular approach of to the molecular axis of , while collinear collisions do not result in dissociation. The higher collisional energytransfer efficiency of xenon compared with argon is attributed to both mass and polarizability effects.

Solvation of sodiumchloride ion pair in water cluster at atmospheric conditions: Grand canonical ensemble Monte Carlo simulation
View Description Hide DescriptionOpen statistical ensemble simulations are used to study the mechanism of nucleation of atmospheric water on sodiumchloride ion pair in a wide range of temperature and relative humidity values. The extended simple pointcharge model is used for water molecules. Ionswater nonadditive interactions are taken into account by introducing the mutual polarization of ions and water in the field of each other. Gibbs freeenergy variations are calculated from paircorrelation function and used as a criterion for determining the possible stable states of the cluster. In this relation, it was found that the dissociation of ion pairs in water clusters occurs even at vapor pressures of only a few millibars. In the conditions under consideration solventseparated ionpair states are found to be more probable than contact ionpair configurations. The susceptibilities of water and ions are found to play an essential role in the stabilization of ions at large separations. The structure of ioninduced clusters is analyzed in terms of binary correlation functions. The nonpair interactions influence essentially the structure of ion solvation shells. The results of simulation show that the separation of the charges in water clusters containing simple ions can take place under atmospheric conditions.

Steric effects in statetostate scattering of OH by HCl
View Description Hide DescriptionIn this paper we address stereodynamical issues in the inelastic encounters between OH radicals and HCl . The experiments were performed in a crossed molecularbeam machine at the nominal collision energy of . Prior to the collisions, the OH molecules were selected using a hexapole in a welldefined rotational state , , , , , and subsequently oriented in a homogeneous electrical field. We have measured rotationally resolved relative cross sections for collisions in which OH is oriented with either the O side or the H side towards HCl, from which we have calculated the corresponding steric asymmetry factors . The results are presented in comparison with data previously obtained by our group for the inelastic scattering of OH by CO and studied under similar experimental conditions. The dissimilarity in the behavior of the system revealed by this comparison is explained on the basis of the difference in the anisotropy of the interaction potential governing the collisions. The interpretation of the data takes into account the specific features of both nonreactive and reactive parts of the potentialenergy surface. The results indicate that the scattering dynamics at this collision energy may be influenced by the HO–HCl van der Waals well and by reorientation effects determined by the longrange electrostatic forces and, furthermore, may involve reactive collisions.

Branching ratio deviations from statistical behavior in core photoionization
View Description Hide DescriptionAccurate calculations of carbonphotoionization cross sections have been performed at the density functional level with the Bspline linear combination of atomic orbitals approach. The molecules considered are FCCH, , FCCCN, , , and . The variation of the branching ratios relative to inequivalent C ionizations have been evaluated from threshold to about 100 eV photoelectron kinetic energy. Large deviations from the statistical ratios are observed at low energies, which remain often significant several tens of eV above threshold. The importance of taking into account core branching ratios for peak deconvolution and quantitative analysis, as well as an additional tool for structural information, is pointed out. Strong shape resonant effects are found to largely cancel in branching ratios. Their nature and variation along the series is analyzed in the framework of excitations into valence orbitals.

Structure and stability of : Experiment and diffusion quantum Monte Carlo theory with “on the fly” electronic structure
View Description Hide DescriptionNew data are reported for the massspectrometry fragmentation patterns of helium clusters, either pure or containing a Ne or an Ar atom. The patterns for and show clear evidence of structure, while those of do not. To better understand the surprising result for the fragments, diffusionquantum Monte Carlo (DMC) calculations of the energies and structural properties of these ions were performed using a diatomicsinmolecule (DIM) parametrization of the potential energy. Using DIM for electronic energy evaluation allows us to sample configurations even for a cluster as large as . The results of the DMC calculation are very surprising. For , the DMC random walkers rarely venture within of the minimum potential energy. Analysis of the resulting particle density distributions shows that the zeropoint energy does more than spread the wave function around the potentialenergy minima, resulting in very diffuse wave functions. For some of the clusters the quantum effects nearly exclude the region of the potential minimum from the overall wave function. An important result of this effect is that the incremental bonding energy of the helium atom varies quite smoothly with , for . This eliminates the expected shell structure and explains the lack of magicnumbertype features in the data.