Volume 123, Issue 18, 08 November 2005
 ARTICLES

 Theoretical Methods and Algorithms

Multipolebased integral estimates for the rigorous description of distance dependence in twoelectron integrals
View Description Hide DescriptionWe derive multipolebased integral estimates (MBIE) as rigorous and tight upper bounds to fourcenter twoelectron integrals in order to account for the distance decay between the charge distributions, which is missing in the Schwarz screening commonly used in ab initio methods. Our screening criteria are valid for all angular momenta and can be formulated for any order of multipoles. We have found the expansion limited to dipoles to be sufficiently tight for estimating the integrals in HartreeFock and densityfunctional theories, while the screening effort is negligible. For, e.g., a DNA fragment with 1052 atoms and 10 674 basis functions the exchange part is faster by a factor of 2.1 as compared to the Schwarz screening both within our linear exchange scheme, whereas a smaller factor of 1.3 is gained for the Coulomb part within the continuous fast multipole method. Most importantly, our new MBIE screening is perfectly suited to exploit the strong distance decay of electroncorrelation effects of at least in atomicorbitalbased formulations of correlation methods.

Rigorous integral screening for electron correlation methods
View Description Hide DescriptionWe derive rigorous multipolebased integral estimates (MBIE) in order to account for the distance dependence occurring in atomicorbital (AO) formulations of electron correlationtheory, where our focus is on AOMP2 theory within a Laplace scheme. We find for the exact transformed integral products an extremely early onset of a linearscaling behavior and a very small number of significant products. To preselect the significant integral products we adapt our MBIE method as rigorous upper bound. In this way it is possible to exploit the favorable scaling behavior observed and to reduce the scaling of estimated products asymptotically to linear, without sacrificing accuracy or reliability. By separating Coulomb and exchangetype contractions only halftransformed integrals need to be computed. Furthermore, our scheme of rigorously preselecting transformed integral products via MBIE seems to offer particularly interesting perspectives for a direct formation of half or fully transformed integrals by using multipole expansions and auxiliary basis sets.

Transition state theory: Variational formulation, dynamical corrections, and error estimates
View Description Hide DescriptionTransition state theory(TST) is revisited, as well as evolutions upon TST such as variational TST in which the TST dividing surface is optimized so as to minimize the rate of recrossing through this surface and methods which aim at computing dynamical corrections to the TSTtransitionrate constant. The theory is discussed from an original viewpoint. It is shown how to compute exactly the mean frequency of transition between two predefined sets which either partition phase space (as in TST) or are taken to be wellseparated metastable sets corresponding to longlived conformation states (as necessary to obtain the actual transitionrate constants between these states). Exact and approximate criterions for the optimal TST dividing surface with minimum recrossing rate are derived. Some issues about the definition and meaning of the free energy in the context of TST are also discussed. Finally precise error estimates for the numerical procedure to evaluate the transmission coefficient of the TST dividing surface are given, and it is shown that the relative error on scales as when is small. This implies that dynamical corrections to the TSTrate constant can be computed efficiently if and only if the TST dividing surface has a transmission coefficient which is not too small. In particular, the TST dividing surface must be optimized upon (for otherwise is generally very small), but this may not be sufficient to make the procedure numerically efficient (because the optimal dividing surface has maximum , but this coefficient may still be very small).

Twodimensional crossspectral correlation analysis and its application to timeresolved Fourier transform emission spectra of transient radicals
View Description Hide DescriptionA spectralanalysis method, based on the generalized twodimensional (2D) vibrational spectra correlation analysis, is developed for deciphering the correlation among the spectral peaks of two differentspectra. This 2D crossspectral correlation (2DCSC) analysis is aimed at revealing the vibrational features associated with a common species in two spectra, each obtained from a system containing multiple species with at least one common species. The crossspectral correlation is based on the premise that the spectral features of the same species should have the same time and frequency responses toward similar perturbations. The effectiveness of the crossspectral correlation analysis is first illustrated with model systems, with spectral peaks decaying linearly or exponentially with time, before being applied to analyzingtimeresolvedemission spectra obtained, by a Fourier transform IR spectrometer, for samples consisting of the vibrationally excited transient cyanooxomethyl radical (OCCN). 2DCSC among the three different sets of timeresolvedspectra collected following the photodissociation of three different precursor molecules of OCCN, respectively, allows the identification of the CN and CO stretching modes of this radical.

Relativistic DMRG calculations on the curve crossing of cesium hydride
View Description Hide DescriptionOver the past few years, it has been shown in various studies on small molecules with only a few electrons that the densitymatrix renormalization group (DMRG) method converges to results close to the full configurationinteraction limit for the total electronic energy. In order to test the capabilities of the method for molecules with complex electronic structures, we performed a study on the potentialenergy curves of the ground state and the first excited state of symmetry of the cesium hydride molecule. For cesium relativistic effects cannot be neglected, therefore we have used the generalized arbitraryorder DouglasKrollHess protocol up to tenth order, which allows for a complete decoupling of the Dirac Hamiltonian. Scalarrelativistic effects are thus fully incorporated in the calculations. The potential curves of the cesium hydride molecule feature an avoided crossing between the ground state and the first excited state, which is shown to be very well described by the DMRG method. Compared to multireference configurationinteraction results, the potential curves hardly differ in shape, for both the ground state and the excited state, but the total energies from the DMRG calculations are in general consistently lower. However, the DMRG energies are as accurate as corresponding coupled clusterenergies at the equilibrium distance, but convergence to the full configurationinteraction limit is not achieved.

Weak intermolecular interactions calculated with diffusion Monte Carlo
View Description Hide DescriptionThe performance of fixed node diffusion Monte Carlo (FNDMC) for weakly interacting molecules is investigated. The effect of Gaussian basis sets on the asymptotic description of the molecular orbitals which is crucial for a successful importance sampling is analyzed for the example of the hydrogen atom. We find that accurate reference binding energies of the water, the ammonia, and the Tshaped as well as the paralleldisplaced benzene dimer are correctly reproduced by FNDMC. The binding energies for the benzene dimers are and , respectively. The description of the methane dimer which has the smallest binding energy and a quite large intermolecular distance requires a more flexible basis set of diffuse quadruple quality in order to prevent sampling errors.

The accuracy of ab initio molecular geometries for systems containing secondrow atoms
View Description Hide DescriptionThe performance of the standard hierarchy of ab initio models—that is, Hartree–Fock theory, secondorder Møller–Plesset theory,coupledcluster singlesanddoubles theory, and coupledcluster singlesdoublesapproximatetriples theory—in combination with correlationconsistentbasis sets is investigated for equilibrium geometries of molecules containing secondrow elements. From an analysis on a collection of (yielding statistical samples of 41 bond distances and 13 bond angles), the statistical errors (mean deviation, mean absolute deviation, standard deviation, and maximum absolute deviation) are established at each level of theory. The importance of core correlation is examined by comparing calculations in the frozencore approximation with calculations where all electrons are correlated.

Calculations of twophoton chargetransfer excitations using Coulombattenuated densityfunctional theory
View Description Hide DescriptionIn this work, we show that an implementation of Coulombattenuated densityfunctional theory leads to considerably better prospects than hitherto for modeling twophoton absorption cross sections for chargetransfer species. This functional, which corrects for the effect of poor asymptotic dependence of commonly used functionals, essentially brings down the widely different results for larger chargetransfer species between HartreeFock and densityfunctional theory (DFT)B3LYP into a closer range. The Coulombattenuated functional, which retains the best aspects of the HartreeFock and DFTB3LYP methods, proves to be very promising for further modeling design of multiphotonmaterials with technical applications.

The interaction of and with noble metal surfaces: Electronic level alignment and the origin of the interface dipole
View Description Hide DescriptionThe electronic interaction of two molecules, the aromatic benzene and the saturated hydrocarbon cyclohexane with a Cu(111) surface, have been determined using precise, ab initio electronic structure calculations. For the interaction of these adsorbates with the substrate, we present a detailed analysis and decomposition of various individual chemical mechanisms that contribute. A novel aspect of this analysis is the use of chargedensity difference contour plots to graphically display the chemistry. A wavefunctionbased approach was used in order to avoid problems when the presently most commonly employed approach, densityfunctional theory, is applied to weakly chemisorbed molecules, where the interaction is dominated by van der Waals forces. The present information are not only relevant with regard to understanding the chemistry going on when molecules are adsorbed on a Cusurface but also have important consequences with regard to charge injection in molecular electronic devices, e.g., organic fieldeffect transistors and organic lightemitting diodes.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Phasespace reaction network on a multisaddle energy landscape: HCN isomerization
View Description Hide DescriptionBy using the HCN/CNH isomerizationreaction as an illustrative vehicle of chemical reactions on multisaddle energy landscapes, we give explicit visualizations of molecular motions associated with a straightthrough reaction tube in the phase space inside which all reactive trajectories pass from one basin to another, with eliminating recrossing trajectories in the configuration space. This visualization provides us with a chemical intuition of how chemical species “walk along” the reactionrate slope in the multidimensional phase space compared with the intrinsic reaction path in the configuration space. The distinct nonergodic features in the two different HCN and CNH wells can be easily demonstrated by a section of Poincaré surface of section in those potential minima, which predicts in a priori the pattern of trajectories residing in the potential well. We elucidate the global phasespace structure which gives rise to the nonMarkovian dynamics or the dynamical correlation of sequential multisaddle chemical reactions. The phasespace structure relevant to the controllability of the product state in chemical reactions is also discussed.

Ab initio calculation of the interaction potentials in the quintet, triplet, and singlet states
View Description Hide DescriptionWe present the ab initiopotentialenergysurfaces of the NH–NH complex that correlate with two NH molecules in their electronic ground state. Three distinct potentialenergysurfaces, split by exchange interactions, correspond to the coupling of the and electronic spins of the monomers to dimer states with , 1, and 2. Exploratory calculations on the quintet , triplet , and singlet states and their exchange splittings were performed with the valence bond selfconsistentfield method that explicitly accounts for the nonorthogonality of the orbitals on different monomers. The potential surface of the quintet state, which can be described by a single Slater determinant reference function, was calculated at the coupled cluster level with single and double excitations and noniterative treatment of the triples. The triplet and singlet states require multiconfiguration reference wave functions and the exchange splittings between the three potential surfaces were calculated with the complete active space selfconsistentfield method supplemented with perturbative configuration interaction calculations of second and third orders. Full potentialenergysurfaces were computed as a function of the four intermolecular Jacobi coordinates, with an augccpVTZ basis on the N and H atoms and bond functions at the midpoint of the intermolecular vector . An analytical representation of these potentials was given by expanding their dependence on the molecular orientations in coupled spherical harmonics, and representing the dependence of the expansion coefficients on the intermolecular distance by the reproducing kernel Hilbert space method. The quintet surface has a van der Waals minimum of depth at for a linear geometry with the two NH electric dipoles aligned. The singlet and triplet surfaces show similar, slightly deeper, van der Waals wells, but when is decreased the weakly bound NH dimer with and converts into the chemically bound diimide (also called diazene) molecule with only a small energy barrier to overcome.

Dissociation processes of and studied by threshold photoelectronphotoion coincidence measurements
View Description Hide DescriptionA timeofflight (TOF) ion mass spectrum in coincidence with threshold photoelectrons was measured in the photon energy region between the first and second dissociation limits of to examine the decay processes of the state. The measured TOF spectrum reveals that fragment ions are produced through dissociation of the repulsive state, which can be formed by the decay process of the state accompanied with emission of photons. The potentialenergy curve of the state is deduced with detailed analysis of the observed TOF spectrum, in which the radiative lifetime of the state was also derived to be . Additionally, evidence of the dissociation process of ions was obtained in the same photon energy region, where the dominant channel is .

Extensive ab initio study of the electronic states of including spinorbit coupling
View Description Hide DescriptionThe effect of different basis sets for calculation of the spectroscopic constants of the ground state of sulfur monochloride was analyzed using scalar relativistic multireference configuration interaction with single and double excitations plus Davidson correction. Then the generally contracted allelectronic correlationconsistent polarized valence quintuple zeta basis sets were selected to compute the electronic states of including 12 valence and 9 Rydberg states. The spinorbit coupling effect was calculated via the state interaction approach with the full BreitPauli Hamiltonian. This effect splits these states into states. Potentialenergy curves of all these states are plotted with the help of the avoided crossing rule between the electronic states of the same symmetry. The structural properties of these states are analyzed. Spectroscopic constants of bound excited states that have never been observed in experiment are obtained. The transition dipole moments and the FranckCondon factors of several transitions from lowlying bound excited states to the ground state were also calculated.

Selective OD bond dissociation of HOD: Photodissociation of vibrationally excited HOD in the state
View Description Hide DescriptionExclusively selective OD bonddissociation of HOD has been demonstrated by the ultraviolet photodissociation at through the fourth overtone state of the OD stretching mode . Branching ratio between the OH and OD bonddissociation channels has been determined by detecting H and D atoms, utilizing a resonanceenhanced multiphoton ionization (REMPI) process. The OD bonddissociation has been solely observed with the branching ratio , which has been determined by the detection limit for the H atom. Timedependent wavepacket calculations reveal two important features for the highly selective OD bonddissociation: (1) strong localmode character of the state and (2) limitation of the total excitation energy lower than the saddle point between the OH and OD dissociation channels in the state. Additionally, the recoil velocity and angular distribution of the nascent D atom are roughly evaluated by analyzing the Dopplerresolved REMPI spectrum. Based on these results, the dynamics of the selective OD dissociation has been discussed in detail.

Structure and electronic properties of highly charged and fullerenes
View Description Hide DescriptionWe present a theoretical study of the structure and electronic properties of positively charged and fullerenes. Electronic energies and optimum geometries have been obtained using densityfunctional theory with the B3LYP functional for exchange and correlation. We have found that closed and semiclosedshell ions (, 5, and 10) preserve the original icosahedral symmetry of neutral . For other charges, significant distortions have been obtained. The fullerenes are, in general, less symmetric, being the closest to the spherical shape. Most fullerenes follow Hund’s rule for spin multiplicity, while most fullerenes are more stable with the lowest spin multiplicity. The calculated ionization potentials for both kinds of fullerenes increase almost linearly with charge, except in the vicinity of and . We have also explored the region of the potentialenergy surface of that leads to asymmetric fission. Minima and transition states corresponding to the last steps of the fission process have been obtained. This has led us to conclude that, for , emission is the preferred fragmentation channel, whereas, for higher values, emission of two charged atomic fragments is more favorable. The corresponding fission barrier vanishes for .
 Condensed Phase Dynamics, Structure, and Thermodynamics: Spectroscopy, Reactions, and Relaxation

Why is hydrofluoric acid a weak acid?
View Description Hide DescriptionThe infrared vibrational spectra of amorphous solid water thin films doped with at reveal a strong continuous absorbance in the range. This socalled Zundel continuum is the spectroscopic hallmark for aqueous protons. The extensive ionic dissociation of at such low temperature suggests that the reaction enthalpy remains negative down to . These observations support the interpretation that dilute aqueous solutions behave as weak acids largely due to the large positive reaction entropy resulting from the structure making character of the hydrated fluoride ion.

A new insight on the structural changes of linear quadrupole liquids
View Description Hide DescriptionMoleculardynamics simulations for linear quadrupoleliquids are presented. The study is carried out for two different molecular lengths at constant density and a number of temperatures and quadrupole moments. All the simulated thermodynamic states correspond to the condensed phases and some of them show typical features of a solid structure. Furthermore, a change on the preferred intermolecular orientation in the liquid phase is observed from a shifted parallel molecular arrangement to a perpendicular orientation as the quadrupole raises. This change depends on the quadrupole moment as well as on the molecular length and is put in relation with the solid structure of different “diatomic” molecules such as nitrogen, ethane, and acetylene. The appearance of a plastic solid phase at low quadrupole moment and density is also justified. A thoroughly discussion about the availability of classical perturbation theories for this kind of systems is presented.

Investigating pressure effects on structural and dynamical properties of liquid methanol with manybody interactions
View Description Hide DescriptionMoleculardynamics simulations utilizing a manybody potential was used to study the pressure dependence of structural and dynamical properties for liquid methanol. The liquid density as a function of pressure agreed well with experiment, and a combination of radial and angular distribution functions were used to analyze molecular structure. From these distribution functions, it was observed that hydrogen bond strength increased with increasing pressure. This observation coincided with an increase in the molecular dipole as a function of pressure, having a significant effect on the observed increased hydrogen bond strength. Also, methanols were found to more strongly favor exactly two hydrogen bonds, with fewer methanols of zero, one, or three hydrogen bonds present at higher pressures. Furthermore, a majority of the compression with increased pressure was found to occur in regions perpendicular to the methanol hydrogenoxygen bond vector. This was the case despite hydrogenoxygen nonbonded distances between hydrogen bonding species being shorter, but their stiffer oxygenhydrogen(nonbonded) oxygen angle offsets this, resulting in their oxygenoxygen distances being relatively unaffected. The methanol translational diffusion decreased significantly with increased pressure, while the rotational diffusion decreased at a similar magnitude around the oxygenhydrogen and oxygencarbon bond vectors, despite having very different overall diffusion. Finally, the hydrogen bond lifetime increased significantly with pressure, owing to the increased hydrogen bond strength, and the slower translational and rotational dynamics.

Global thermodynamics of hydrophobic cavitation, dewetting, and hydration
View Description Hide DescriptionPure water experimental and simulation results are combined to predict the thermodynamics of cavity formation, spanning atomic to macroscopic length scales, over the entire ambient liquid temperature range. The resulting cavityequation of state is used to quantify dewetting excess contributions to cavity formation thermodynamics and construct a thermodynamic perturbation theory of hydrophobic hydration. Predictions are compared with large cavity simulations and experimental raregas hydration thermodynamics data (for , , , , , and ). Key findings include the strong temperature dependence of the critical length scale for hydrophobic dewetting and the evaluation of fundamental solutesolvent interaction contributions to raregas hydration chemical potentials.

Collision as a way of forming bimetallic nanoclusters of various structures and chemical compositions
View Description Hide DescriptionIn the present work, a new way to obtain bimetallic nanoclusters of different structures and chemical compositions is proposed, which is based on computer simulations. Collision processes between two metal clusters of different natures are simulated through moleculardynamics simulations using manybody potentials. Diverse diffusion mechanisms and structures can be observed, depending on the metals combined and the initial kinetic energies. The nanostructures we have found are coreshell , alloyed , and threeshell onionlike (.