Volume 123, Issue 12, 22 September 2005
 ARTICLES

 Theoretical Methods and Algorithms

Calculation of spindensities within the context of density functional theory. The crucial role of the correlation functional
View Description Hide DescriptionIt is demonstrated that the LYP correlation functional is not suited to be used for the calculation of electron spin resonance hyperfine structure (HFS) constants, nuclear magnetic resonance spinspin coupling constants, magnetic, shieldings and other properties that require a balanced account of opposite and equalspin correlation, especially in the core region. In the case of the HFS constants of alkali atoms, LYP exaggerates oppositespin correlation effects thus invoking too strong inout correlation effects, an exaggerated spinpolarization pattern in the core shells of the atoms, and, consequently, too large HFS constants. Any correlation functional that provides a balanced account of opposite and equalspin correlation leads to improved HFS constants, which is proven by comparing results obtained with the LYP and the PW91 correlation functional. It is suggested that specific response properties are calculated with the PW91 rather than the LYP correlation functional.

Densityfunctional theorybased chemical reactivity indices in the HartreeFock method. I. Unrestricted HartreeFock method for a noninteger number of electrons
View Description Hide DescriptionCorrect evaluation of the reactivity indices, such as chemical potential, hardness, and Fukui function demands for the extension of the formalism beyond the integer particle picture. An ensemble approach is used as an extension of the unrestricted HartreeFock (UHF) method for noninteger electron number systems. A prescription is given for the construction of an ensemble Fock operator for a system with partially filled spinorbitals. The comparison between the ensemble HF method and the hyperHF method in terms of density matrices and spinorbitals is presented. The equivalence of the equiensemble case and the ensemble UHF case with unequal weight factors is shown.

DFTbased chemical reactivity indices in the HartreeFock method. II. Fukui function, chemical potential, and hardness
View Description Hide DescriptionA derivation of the densityfunctionaltheory (DFT) based reactivity indices in the ensemble unrestricted HartreeFock (eUHF) method is presented. The comparison between the properties of the reactivity indices evaluated in one and two sets of spinorbital approach of the eUHF and hyperunrestricted HartreeFock (UHF) methods are shown. All approaches give similar Fukui function irrespective of methodology used, but significantly differ for the global indices, containing important chemical information, and so their interpretation in terms of DFT based indices can be questionable. The calculation scheme for the indices using the first and secondorder coupled perturbed eHF equations is proposed. A method for the identification of the spinorbitals involved in the change of the total number of electrons is included. The illustrative examples (water and hydrogen cyanide) show that the groundstate(GS)properties of the electron systems can be predicted from the GSproperties of the electron systems with an accuracy comparable with the UHF calculations. The relaxation effect, important for the HCN system in which a change in the symmetry of the highestoccupied spinorbital occurs, is effectively predicted.

Spectroscopic effects of firstorder relativistic vibronic coupling in linear triatomic molecules
View Description Hide DescriptionIt has recently been shown that there exists, in addition to the wellknown nonrelativistic RennerTeller coupling, a linear (that is, of the first order in the bending distortion) vibroniccoupling mechanism of relativistic (that is, spinorbit) origin in electronic states of linear molecules [L. V. Poluyanov and W. Domcke, Chem. Phys.301, 111 (2004)]. The generic aspects of the relativistic linear vibroniccoupling mechanism have been analyzed in the present work by numerical calculations of the vibronic spectrum for appropriate models. The vibronic and spinorbit parameters have been determined by accurate ab initio electronicstructure calculations for the states of a series of triatomic radicals and radical cations. It is shown for the example of GeCH that the relativistic linear vibroniccoupling mechanism provides a quantitative explanation of the pronounced perturbations in the vibronic spectrum of the state of GeCH, which previously have been termed “Sears resonances” [S.G. He, H. Li, T. C. Smith, D. J. Clouthier, and A. J. Merer, J. Chem. Phys.119, 10115 (2003)]. The vibronic spectra of the series , , , and OBS illustrate the interplay of nonrelativistic and relativistic vibroniccoupling mechanisms in RennerTeller systems.

Spinunrestricted linearscaling electronic structure theory and its application to magnetic carbondoped boron nitride nanotubes
View Description Hide DescriptionWe present an extension of the densitymatrixbased linearscaling electronic structuretheory to incorporate spin degrees of freedom. When the spin multiplicity of the system can be predetermined, the generalization of the existing linearscaling methods to spinunrestricted cases is straightforward. However, without calculations it is hard to determine the spin multiplicity of some complex systems, such as many magnetic nanostuctures and some inorganic or bioinorganic molecules. Here we give a general prescription to obtain the spinunrestricted ground state of openshell systems. Our methods are implemented into the linearscaling tracecorrecting densitymatrix purification algorithm. The numerical atomicorbital basis, rather than the commonly adopted Gaussian basis functions, is used. The test systems include molecule and magnetic carbondoped boron nitride (BN)(5,5) and BN(7,6) nanotubes. Using the newly developed method, we find that the magnetic moments in carbondoped BNnanotubes couple antiferromagnetically with each other. Our results suggest that the linearscaling spinunrestricted tracecorrecting purification method is very powerful to treat large magnetic systems.

Allexchanges parallel tempering
View Description Hide DescriptionAn alternative exchange strategy for parallel tempering simulations is introduced. Instead of attempting to swap configurations between two randomly chosen but adjacent replicas, the acceptance probabilities of all possible swap moves are calculated a priori. One specific swap move is then selected according to its probability and enforced. The efficiency of the method is illustrated first on the case of two LennardJones (LJ) clusters containing 13 and 31 atoms, respectively. The convergence of the caloric curve is seen to be at least twice as fast as in conventional parallel tempering simulations, especially for the difficult case of . Further evidence for an improved efficiency is reported on the ergodic measure introduced by Mountain and Thirumalai [J. Phys. Chem.93, 6975 (1989)], calculated here for close to the melting point. Finally, tests on two simple spin systems indicate that the method should be particularly useful when a limited number of replicas are available.

Assessment of Gaussian3 and densityfunctional theories on the G3/05 test set of experimental energies
View Description Hide DescriptionThe G3/99 test set [L. A. Curtiss, K. Raghavachari, P. C. Redfern, and J. A. Pople, J. Chem. Phys.112, 7374 (2000)] of thermochemical data for validation of quantum chemical methods is expanded to include 78 additional energies including 14 enthalpies of formation of the first and secondrow nonhydrogen molecules, 58 energies of molecules containing the thirdrow elements K, Ca, and Ga–Kr, and 6 hydrogenbonded complexes. The criterion used for selecting the additional systems is the same as before, i.e., experimental uncertainties less than . This new set, referred to as the G3/05 test set, has a total of 454 energies. The G3 and G3X theories are found to have mean absolute deviations of 1.13 and , respectively, when applied to the G3/05 test set. Both methods have larger errors for the nonhydrogen subset of 79 species for which they have mean absolute deviations of 2.10 and , respectively. On all of the other types of energies the G3 and G3X methods are very reliable. The G3/05 test set is also used to assess densityfunctional methods including a series of new functionals. The most accurate functional for the G3/05 test set is B98 with a mean absolute deviation of , compared to for B3LYP. The latter functional has especially large errors for larger molecules with a mean absolute deviation of for molecules having 28 or more valence electrons. For smaller molecules B3LYP does as well or better than B98 and the other functionals. It is found that many of the densityfunctional methods have significant errors for the larger molecules in the test set.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

On the electron affinity of SiN and spectroscopic constants of
View Description Hide DescriptionAccurate spectroscopic constants and energetics were calculated for the two lowestlying states of SiN and employing the coupled cluster methodology and very large basis sets (up to doubly augmented sextuple quality) accounting also for core∕valence correlation, oneelectron DouglasKrollHess relativistic effects, and atomic spinorbit couplings. Our best estimate for the adiabatic electron affinity of SiN is , in very good agreement with the recent, experimentally determined value of . However, the calculated bond length of the state at the same level, , is smaller than the indirectly extracted experimental value of , pointing out that the latter value is either a bit overestimated or not as accurate as the error bar indicates. For the neutral SiN, all calculated data are in excellent agreement with previous accurate experimental results.

Bond selective dissociative electron attachment to thymine
View Description Hide DescriptionFreeelectron attachment to thymine and partially deuterated thymine, where D replaces H at all carbon atoms, is studied in the electron energy range from about . The formation of fragment anions that are formed by the loss of one or two H (D) atoms is analyzed as a function of the incident electron energy using a crossed electron/neutral beam apparatus in combination with a quadrupole mass spectrometer. By using partially deuterated thymine and quantumchemical calculation a bond selectivity for the loss of one and two hydrogen atoms is observed that is determined only by the kinetic energy of the incident electron.

Photodissociation dynamics of indole in a molecular beam
View Description Hide DescriptionPhotodissociation of indole at 193 and 248 nm under collisionfree conditions has been studied in separate experiments using multimass ion imaging techniques. H atom elimination was found to be the only dissociation channel at both wavelengths. The photofragment translational energy distribution obtained at 193 nm contains a fast and a slow component. Fiftyfour percent of indole following the 193 nm photoexcitation dissociate from electronically excited state, resulting in the fast component. The rest of 46% indole dissociate through the ground electronic state, giving rise to the slow component. A dissociation rate of , corresponding to the dissociation from the ground electronic state, was determined. Similar twocomponent translational energy distribution was observed at 248 nm. However, more than 80% of indole dissociate from electronically excited state after the absorption of 248 nm photons. A comparison with the potential energy surfaces from the ab initio calculation has been made.

Influence of vibrational energy flow on isomerization of flexible molecules: Incorporating nonRiceRamspergerKasselMarcus kinetics in the simulation of dipeptide isomerization
View Description Hide DescriptionThe conformationalisomerization of a dipeptide,acetyltryptophan methyl amide (NATMA), is studied computationally by including important dynamical corrections to RiceRamspergerKasselMarcus (RRKM) theory for the transition rate between pairs of isomers. The dynamical corrections arise from incomplete or sluggish vibrational energy flow in the dipeptide, a property suggested by the modeselective chemistry that has been observed by Dian et al. [J. Chem. Phys.120, 133 (2004)]. We compute the extent and rate of vibrational energy flow in NATMA quantum mechanically using local random matrix theory, which we then use to correct the RRKM theory rates. The latter rates are then introduced into a master equation to study the population dynamics of the dipeptide. Incomplete or slow vibrational energy flow is found to enhance the conformational selectivity of NATMA over RRKM estimates.

Elastic, quasielastic, and inelastic neutronscattering studies on the chargetransfer hexamethylbenzenetetracyanoquinodimethane complex
View Description Hide DescriptionThe 1:1 hexamethylbenzene tetracyanoquinodimethane complex shows a firstorder phase transition at (heating/cooling) with no change of the space group. The neutrondiffraction studies reveal that this transition is related to a freezing of the rotation of methyl groups. The results for enabled precise determination of configuration of complexes. The planes of and molecules from small angle (6°) so that the dicyanomethylene group approaches the molecule to a distance of . The conformation of methyl groups was exactly determined. The quasielastic neutronscattering spectra can be interpreted in terms of 120° jumps with different activation barrier in low and hightemperature phases, equal to 3.7 and , respectively. These values are lower than that for neat . The conclusion can be drawn that the methyl groups can reorient more freely in the complex. This conclusion is in agreement with the results of inelastic neutronscattering studies of lowfrequency modes assigned to torsional vibrations of methyl groups. These frequencies are lower than those for neat . The analyzed increase of frequencies of these modes as compared with free molecules can be interpreted as due to formation of unconventional hydrogen bonds which are more pronounced in crystals of neat than in those of . The lowfrequency librational modes can be treated as a sensitive measure of unconventional hydrogen bonds formed by the groups.

The NaK states: Theoretical and experimental studies of fine and hyperfine structure of rovibrational levels near the dissociation limit
View Description Hide DescriptionEarlier highresolution spectroscopic studies of the fine and hyperfine structure of rovibrational levels of the state of NaK have been extended to include high lying rovibrational levels with , of which the highest levels lie within of the dissociation limit. A potential curve is determined using the inverted perturbation approximation method that reproduces these levels to an accuracy of . For the largest values of , the outer turning points occur near , which is sufficiently large to permit the estimation of the coefficient for this state. The fine and hyperfine structure of the rovibrational levels has been fit using the matrix diagonalization method that has been applied to other states of NaK, leading to values of the spin–orbit coupling constant and the Fermi contact constant . New values determined for are consistent with values determined by a simpler method and reported earlier. The measured fine and hyperfine structure for in the range exhibits anomalous behavior whose origin is believed to be the mixing between the and states. The matrix diagonalization method has been extended to treat this interaction, and the results provide an accurate representation of the complicated patterns that arise. The analysis leads to accurate values for and for all values of . For higher , several rovibrational levels have been assigned, but the pattern of fine and hyperfine structure is difficult to interpret. Some of the observed features may arise from effects not included in the current model.

A sequential Monte Carlo quantum mechanics study of the hydrogenbond interaction and the solvatochromic shift of the transition of acrolein in water
View Description Hide DescriptionThe sequential Monte Carlo(MC) quantum mechanics (QM) methodology, using timedependent densityfunctional theory (TDDFT), is used to study the solvatochromic shift of the transition of transacrolein in water. Using structures obtained from the isothermalisobaric Metropolis MC simulation TDDFT calculations, within the B3LYP functional, are performed for the absorptionspectrum of acrolein in water. In the average acrolein makes one hydrogen bond with water and the hydrogenbond shell is responsible for 30% of the total solvatochromic shift, considerably less than the shift obtained for the minimumenergy configurations. MC configurations are sampled after analysis of the statistical correlation and 100 configurations are extracted for subsequent QM calculations. Allelectron TDDFT B3LYP calculations of the absorption transition including acrolein and all explicit solvent molecules within the first hydration shell, 26 water molecules, give a solvatochromic shift of . Using simple point charges to represent the solvent the shifts are calculated for the first, second, and third solvation shells. The results converge for the calculated shift of in very good agreement with the experimentally inferred result of . All average results presented are statistically converged.

Two ferromagnetic azidobridged copper(II) complexes studied by firstprinciple electronicstructure calculation
View Description Hide DescriptionThe electronic structures of two ferromagnetic polynuclear copper(II) complexes, derived from endtoend azido ligand and tridentate (NNN donor) Schiff base ligand, have been studied using the fullpotential linearized augmented planewave method based on the densityfunctional theory. They are (1) and (2). The result shows that the spin populations in these two complexes are mainly distributed on the equatorial planes of a square pyramidal that surround the copper(II) ions. There are large and positive spin populations on copper(II) ions, small and positive spin populations on the three nitrogen atoms of tridentate Schiff base ligand, and the two terminal nitrogen atoms of asymmetrical endtoend azido ligand, while weak and negative spin populations on the central nitrogen atoms of asymmetrical endtoend azido ligand. Ferromagnetic coupling through the asymmetrical azido ligand in these two complexes has been mainly attributed to the spin delocalization, also with weak spinpolarization effect.

Production of methyloxonium ion and its complexes in the coreexcited clusters: transfer from the carbonyl
View Description Hide DescriptionDissociation of free methylformate (MF), , and its clusters, , induced by corelevel excitation was studied near the oxygen edge by timeofflight fragmentmass spectroscopy. Besides the protonated clusters, with , we identified the production for another series of with as well as methyloxonium ion, , characteristic of hydrogen transfer reactions in the cationic clusters. Here, specifically labeled methylformated (MFD), was also used to examine the coreexcited dissociation mechanisms. Deuteriumlabeled experiments indicated that with low internal energies, partially generated after the core excitation, produces via a sitespecific deuterium transfer from the carbonyl in the molecular cation and that can be formed via the successive transfer of another deuterium from the neighbor molecule in the clusters. The deuteron (proton) transfer was also found to take place preferentially from the carbonyl of the neighbor molecule for the production of deuteronated , (protonated ), clusters. The minimal energy requirement paths were examined for dimer cation to support the present dissociation mechanisms of coreexcited clusters using ab initio molecularorbital calculations.

Vibrational coupling in carboxylic acid dimers
View Description Hide DescriptionThe vibrational level splitting in the ground electronic state of carboxylic acid dimers mediated by the doubly hydrogenbonded networks are investigated using pure and mixed dimers of benzoic acid with formic acid as molecular prototypes. Within the range, the frequencies for the fundamental and combination vibrations of the two dimers are experimentally measured by using dispersed fluorescence spectroscopy in a supersonic jet expansion. Densityfunctionaltheory calculations predict that most of the dimer vibrations are essentially inphase and outofphase combinations of the monomer modes, and many of such combinations show significantly large splitting in vibrational frequencies. The infrared spectrum of the jetcooled benzoic acid dimer, reported recently by Bakker et al. [J. Chem. Phys.119, 11180 (2003)], has been used along with the dispersed fluorescence spectra to analyze the coupled vibrational levels. Assignments of the dispersed fluorescence spectra of the mixed dimer are suggested by comparing the vibronic features with those in the homodimer spectrum and the predictions of densityfunctionaltheory calculation. The fluorescence spectra measured by excitations of the lowlying single vibronic levels of the mixed dimer reveal that the hydrogenbond vibrations are extensively mixed with the ring modes in the surface.

An empirical potentialenergy surface for the van der Waals complex including threebody effects
View Description Hide DescriptionAn empirical intermolecular potentialsurface is proposed for the complex, modeled as a sum of pairwise He–I Morse interactions plus a threebody interaction term. The potential reproduces with very good agreement the spectral blueshifts and vibrational predissociation lifetimes measured for in the range of vibrational excitations. In particular, the accuracy achieved in the description of the experimental data for high levels is attributed to the threebody interaction term included in the potential. The behavior of the potential surface with the I–I separation is analyzed and correlated with the experimental findings.

Complex polarization propagator method for calculation of dispersion coefficients of extended conjugated systems: The coefficients of polyacenes and
View Description Hide DescriptionThe frequencydependent polarizabilities and the dipoledipole dispersion coefficients for the first members of the polyacenes namely benzene, naphthalene, anthracene, and naphthacene as well as the fullerene have been calculated at the timedependent HartreeFock level and the timedependent densityfunctional theory level with the hybrid B3LYP exchangecorrelation functional. The dynamic polarizabilities at imaginary frequencies are obtained with use of the complex linear polarization propagator method and the coefficients are subsequently determined from the CasimirPolder relation. We report the first ab initio calculations of the coefficients for the molecules under consideration, and our recommended value for the dispersion coefficient of the fullerene is

The elimination of a hydrogen atom in
View Description Hide DescriptionBy a systematic examination on , with , 9, 10, and 15, we demonstrate that a hydrogen loss reaction can be initiated by a single sodium atom with water molecules. This reaction is similar to the wellknown sizedependent intracluster hydrogen loss in , which is isoelectronic to . However, with one less charge on than that on , the hydrogen loss for is characterized by a higher barrier and a more flexible solvation shell around the metal ion, although the reaction should be accessible, as the lowest barrier is around . Interestingly, the hydroxide ion produced in the process is stabilized by the solvation of molecules and the formation of an ion pair . The activation barrier is reduced as the unpaired electron in moves to higher solvation shells with increasing cluster size, and the reaction is not switched off for larger clusters. This is in sharp contrast to the reaction for , in which the ion is stabilized by direct coordination with and the reaction is switched off for , as the unpaired electron moved to higher solvation shells. Such a contrast illustrates the important link between microsolvation environment and chemical reactivity in solvation clusters.