Volume 126, Issue 23, 21 June 2007
 COMMUNICATIONS


Long range influence of an excess proton on the architecture of the hydrogen bond network in largesized water clusters
View Description Hide DescriptionInfrared spectra of completely sizeselected protonated water clusters are reported for clusters ranging from to 100. The behavior of the dangling OH stretch bands shows that the hydrogen bond structure in is uniquely different to that of up to the size of , at least. This finding indicates that the presence of an excess proton creates a characteristic morphology in the hydrogen bond network architecture of more than 100 surrounding water molecules.
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 ARTICLES

 Theoretical Methods and Algorithms

Berry phase approach to longitudinal dipole moments of infinite chains in electronicstructure methods with local basis sets
View Description Hide DescriptionThe authors provide a reformulation of the modern theory of polarization for onedimensional stereoregular polymers, at the level of the single determinant HartreeFock and KohnSham methods within a basis set of local orbitals. By starting with localization of oneelectron orbitals, their approach naturally arrives to the Berry phases of Bloch orbitals. Then they describe a novel numerical algorithm for evaluation of longitudinal dipole moments, computationally more convenient than those presently implemented within the local basis periodic codes. This method is based on the straightforward evaluation of the usual direct space dipole matrix elements between local orbitals, as well as overlap matrices between wave functions at two neighboring points of the reciprocal space mesh. The practical behavior of the algorithm and its convergence properties with respect to the point mesh density are illustrated in benchmark calculations for water chains and fluorinated transpolyacetylene.

An ab initio study of the photodissociation. I. Potential energy surfaces
View Description Hide DescriptionThe multireference spinorbit (SO) configuration interaction (CI) method in its contracted SOCI version is employed to calculate twodimensional potential energy surfaces for the ground and lowlying excited states of relevant to the photodissociation process in its absorption band. The computed equilibrium geometry for the ground state, as well as vibrational frequencies for the umbrella and symmetric stretch modes, are found to be in good agreement with available experimental data. The state converging to the excited limit is found to possess a shallow minimum of strongly shifted to larger internuclear distances relative to the ground state. This makes a commonly employed singleexponent approximation for analysis of the fragmentation dynamics unsuitable. The state dissociating to the same atomic limit is calculated to lie too high in the FranckCondon region to have any significant impact on the band absorption. The computed vertical excitation energies for the , , and states indicate that the band spectrum must lie approximately between 33 000 and , i.e., between 225 and . This result is in very good agreement with the experimental findings. The lowest Rydberg states are computed to lie at and correspond to the leading configuration. They are responsible for the vacuum ultraviolet absorption lines found experimentally beyond the band spectrum at and higher.

An ab initio study of the photodissociation. II. Transition moments and vibrational state control of the quantum yields
View Description Hide DescriptionMultireference spinorbit configuration interaction calculations of transition moments from the ground state to the , , and excited states responsible for the absorption band of are reported and employed for an analysis of the photofragmentation in this system. Contrary to what is usually assumed, the , , and transition moments are found to be strongly dependent on the C–I fragmentation coordinate. The sign of this dependence is opposite for the parallel and perpendicular transitions, which opens an opportunity for vibrational state control of the photodissociation product yields. The computed absorption intensity distribution and the quantum yield as a function of excitation energy are analyzed in comparison with existing experimental data, and good agreement between theory and experiment is found. It is predicted that significantly higher quantum yield values may be achieved when vibrationally hot molecules are excited in the appropriate spectral range. It is shown that vibrational state control of the branching ratio in the alkyl (hydrogen) iodide photodissociation has an electronic rather than a dynamic nature: Due to a different electron density distribution at various molecular geometries, one achieves a more efficient excitation of a particular fragmentation channel rather than influences the dynamics of the decay process.

Quantum similarity study of atoms: A bridge between hardness and similarity indices
View Description Hide DescriptionA hardness based similarity index for studying the quantum similarity for atoms is analyzed. The investigation of hardness and Fukui functions of atoms leads to the construction of a quantum similarity measure, which can be interpreted as a quantified comparison of chemical reactivity of atoms. Evaluation of the new measure reveals periodic tendencies throughout Mendeleev’s table. Moreover on the diagonal the global hardness was recovered. Considering a corresponding quantum similarity index reveals that renormalization of the measure can mask periodic patterns. The hardness was calculated for atoms with nuclear charge , using the best single configuration electron density functions available. Different hardness kernels were used and the importance of the different contributions to the kernel was investigated. The atomic selfsimilarities constructed in this way show a fair correlation with experimental atomic polarizability.

Energyconsistent pseudopotentials for quantum Monte Carlo calculations
View Description Hide DescriptionThe authors present scalarrelativistic energyconsistent HartreeFock pseudopotentials for the maingroup elements. The pseudopotentials do not exhibit a singularity at the nucleus and are therefore suitable for quantum Monte Carlo (QMC) calculations. They demonstrate their transferability through extensive benchmark calculations of atomic excitation spectra as well as molecular properties. In particular, they compute the vibrational frequencies and binding energies of 26 first and secondrow diatomic molecules using postHartreeFock methods, finding excellent agreement with the corresponding allelectron values. They also show their pseudopotentials give superior accuracy than other existing pseudopotentials constructed specifically for QMC. Finally, valence basis sets of different sizes ( with for first and second rows, and for third to fifth rows) optimized for our pseudopotentials are also presented.

A causal look into the quantum Talbot effect
View Description Hide DescriptionA wellknown phenomenon in both optics and quantum mechanics is the socalled Talbot effect. This near field interference effect arises when infinitely periodic diffracting structures or gratings are illuminated by highly coherent light or particle beams. Typical diffraction patterns known as quantum carpets are then observed. Here the authors provide an insightful picture of this nonlocal phenomenon as well as its classical limit in terms of Bohmian mechanics, also showing the causal reasons and conditions that explain its appearance. As an illustration, theoretical results obtained from diffraction of thermal He atoms by both slit arrays and weak corrugated surfaces are analyzed and discussed. Moreover, the authors also explain in terms of what they call the TalbotBeeby effect how realistic interaction potentials induce shifts and distortions in the corresponding quantum carpets.

Dwell time of a Brownian molecule in a microdomain with traps and a small hole on the boundary
View Description Hide DescriptionWe calculate the mean time a Brownian particle spends in a domain with traps and the number of bonds it makes before escaping through a small hole in the boundary. This mean time, called the Dwell time, depends on the backward binding rate (with the trap, e.g., scaffolding molecules), the mean time to reach the trap (forward binding rate), and the size of the hole. We estimate the mean and variance of the number of bonds made prior to exit. In a biochemical context, a quantitative signal occurs when the mean number of bonds exceeds a certain threshold, which may initiate a cascade of chemical reactions that have physiological consequences. We apply the present results to obtain estimates of the mean time a Brownian receptor spends inside a synaptic domain, when it moves freely by lateral diffusion on the membrane of a neuron and interacts at a synapse with scaffolding molecules.

Revisiting the calculation of condensed Fukui functions using the quantum theory of atoms in molecules
View Description Hide DescriptionThe analysis of previously reported shortcomings of the condensed Fukui functions obtained making use of the quantum theory of atoms in molecules indicates these drawbacks are due to the inadequacy of the definition employed to compute them and not to the partitioning. A new procedure, which respects the mathematical definition and solves these problems, is presented for the calculation of condensed Fukui functions for atomic basins defined according to the quantum theory of atoms in molecules. It is tested in a set of , which includes the most controversial reported cases.

Intermittent search process and teleportation
View Description Hide DescriptionThe authors study an intermittent search process combining diffusion and “teleportation” phases in a dimensional spherical continuous system and in a regular lattice. The searcher alternates diffusive phases, during which targets can be discovered, and fast phases (teleportation) which randomly relocate the searcher, but do not allow for target detection. The authors show that this alternation can be favorable for minimizing the time of first discovery, and that this time can be optimized by a convenient choice of the mean waiting times of each motion phase. The optimal search strategy is explicitly derived in the continuous case and in the lattice case. Arguments are given to show that much more general intermittent motions do provide optimal search strategies in dimensions. These results can be useful in the context of heterogeneous catalysis or in various biological examples of transport through membrane pores.

Real time correlation function in a single phase space integral beyond the linearized semiclassical initial value representation
View Description Hide DescriptionIt is shown how quantum mechanical time correlation functions [defined, e.g., in Eq. (1.1)] can be expressed, without approximation, in the same form as the linearized approximation of the semiclassical initial value representation (LSCIVR), or classical Wigner model, for the correlation function [cf. Eq. (2.1)], i.e., as a phase space average (over initial conditions for trajectories) of the Wigner functions corresponding to the two operators. The difference is that the trajectories involved in the LSCIVR evolve classically, i.e., according to the classical equations of motion, while in the exact theory they evolve according to generalized equations of motion that are derived here. Approximations to the exact equations of motion are then introduced to achieve practical methods that are applicable to complex (i.e., large) molecular systems. Four such methods are proposed in the paper—the full Wigner dynamics (full WD) and the second order WD based on “Wigner trajectories” [H. W. Lee and M. D. Scully, J. Chem. Phys.77, 4604 (1982)] and the full DonosoMartens dynamics (full DMD) and the second order DMD based on “DonosoMartens trajectories” [A. Donoso and C. C. Martens, Phys. Rev. Lett.8722, 223202 (2001)]—all of which can be viewed as generalizations of the original LSCIVR method. Numerical tests of the four versions of this new approach are made for two anharmonic model problems, and for each the momentum autocorrelation function (i.e., operators linear in coordinate or momentum operators) and the force autocorrelation function (nonlinear operators) have been calculated. These four new approximate treatments are indeed seen to be significant improvements to the original LSCIVR approximation.

Ab initio electron propagators in molecules with strong electronphonon interaction. I. Phonon averages
View Description Hide DescriptionAb initio electron propagators in molecular systems with strong electronelectron and electronphonon interactions are considered to study molecular electronic properties. This research is important in electron transfer reactions where the electron transition is not considered any longer as a single electron transfer process or in temperature dependences of currentvoltage characteristics in molecular wires or aggregates. To calculate electron Green’s functions, the authors apply a small polaron canonical transformation that intrinsically contains strong electronphonon effects. According to this transformation, the excitation energies of the noninteracting Hamiltonian are shifted down by the relaxation (solvation) energy for each state. The electronelectron interaction is also renormalized by the electronphonon coupling. For some values of the electronphonon coupling constants, the renormalized Coulomb integrals can be negative resulting in the attraction between two electrons. Within this transformation, they develop a diagrammatic expansion for electron Green’s function in which the electronphonon interaction is included into the multiple phononcorrelation functions. The multiple phononcorrelation functions are exactly found. It is pointed out that Wick’s theorem for such correlation functions is invalid. Consequently, there is no Dyson equation for electron Green’s functions. The proposed approach can be considered for future method developments for quantum chemical calculations that include strong nonadiabatic (nonBornOppenheimer) effects.

Geminal model chemistry III: Partial spin restriction
View Description Hide DescriptionThe authors define an ab initio electronic structure model that uses partial spin restriction. It is an intermediate case between the socalled spinrestricted and spinunrestricted formulations, which are popular in electronic structure methodology. Partial spin restriction arises naturally when the wave function is represented as an antisymmetrized product of twoelectron functions, as it is done in generalized valence bond and antisymmetrized product of strongly orthogonal geminal theories. The authors show that the new model is size consistent, and it improves the description of transition metal compounds.

One and twocenter physical space partitioning of the energy in the density functional theory
View Description Hide DescriptionA conceptually new approach is introduced for the decomposition of the molecular energy calculated at the density functional theory level of theory into sum of one and twoatomic energy components, and is realized in the “fuzzy atoms” framework. (Fuzzy atoms mean that the threedimensional physical space is divided into atomic regions having no sharp boundaries but exhibiting a continuous transition from one to another.) The new scheme uses the new concept of “bond order density” to calculate the diatomic exchange energy components and gives them unexpectedly close to the values calculated by the exact (HartreeFock) exchange for the same KohnSham orbitals.

Longrange corrected density functional study on weakly bound systems: Balanced descriptions of various types of molecular interactions
View Description Hide DescriptionThe longrange correction scheme for the density functional theory, combined with a van der Waals functional, is examined for its applicability to a wide variety of weakly bonded complexes including dispersion, dipoleinduced dipole, dipoledipole, and hydrogenbonded complexes. The present method is able to describe geometries and binding energies of all these complexes accurately. Explicit inclusion of the longrange exchange and dispersioninteractions is found to be important for the balanced description of various kinds of weak interactions. The present method is a promising alternative for highlevel ab initio methods in calculations of large and complex systems, because it gives equally correct descriptions for various types of molecular interactions with much less computational cost.

Use of nuclear stiffness in search for a maximum hardness principle and for the softest states along the chemical reaction path: A new formula for the energy third derivative
View Description Hide DescriptionNuclear stiffness, expressed as a hardness derivative, appears to be a good measure of the slope of global hardness. The authors analyze molecular states for which hardness has a maximum value. Maximum hardness principle (MHP) has been discussed. At the ground statehardness function does not obtain a maximum value versus spatial coordinates within a constant number of electrons , but is so within constant chemical potential constraint. The authors apply this feature to evaluate an energy third derivative . MHP has been analyzed via symmetry considerations of nuclear stiffness and nuclear reactivity. Nuclear stiffness has been also applied to study the hardness profile for a chemical reaction. In this case, the authors seek molecular states for which hardness is at a minimum. They have examined systems for which they have recently obtained regional chemical potentials [P. Ordon and A. Tachibana, J. Mol. Model.11, 312 (2005); J. Chem. Sci.117, 583 (2005)]. The transition state is found not to be the softest along the chemical reaction path. Nuclear stiffness reflects well the softest conformation of a molecule, which has been found independently along the intrinsic reaction coordinate profile. Electronic energydensity [A. Tachibana, J. Mol. Mod.11, 301 (2005)] has been used to visualize the reactivity difference between the softest state and the transition state.

Exact functional derivative of the nonadditive kineticenergy bifunctional in the longdistance limit
View Description Hide DescriptionWe have investigated the functional derivative of the nonadditive kineticenergy bifunctional, which appears in the embedding potential that is used in the frozendensity embedding formalism, in the limit that the separation of the subsystems is large. We have derived an exact expression for this kineticenergy component of the embedding potential and have applied this expression to deduce its exact form in this limit. Comparing to the approximations currently in use, we find that while these approximations are correct at the nonfrozen subsystem, they fail completely at the frozen subsystem. Using test calculations on two model systems, a complex and a cluster of aminocoumarin C151 surrounded by 30 water molecules, we show that this failure leads to a wrong description of unoccupied orbitals, which can lead to convergence problems caused by too lowlying unoccupied orbitals and which can further have serious consequences for the calculation of response properties. Based on our results, a simple correction is proposed, and we show that this correction is able to fix the observed problems for the model systems studied.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Contribution of water dimer absorption to the millimeter and far infrared atmospheric water continuum
View Description Hide DescriptionWe present a rigorous calculation of the contribution of water dimers to the absorption coefficient in the millimeter and far infrared domains, over a wide range of temperatures. This calculation relies on the explicit consideration of all possible transitions within the entire rovibrational bound state manifold of the dimer. The water dimer is described by the flexible 12dimensional potential energy surface previously fitted to far IR transitions [C. Leforestier et al., J. Chem. Phys.117, 8710 (2002)], and which was recently further validated by the good agreement obtained for the calculated equilibrium constant with experimental data [Y. Scribano et al., J. Phys. Chem. A.110, 5411 (2006)]. Transition dipole matrix elements were computed between all rovibrational states up to an excitation energy of , and rotational quantum numbers. It was shown by explicit calculations that these matrix elements could be extrapolated to much higher values . Transitions to vibrational states located higher in energy were obtained from interpolation of computed matrix elements between a set of initial states spanning the range and all vibrational states up to the dissociation limit . We compare our calculations with available experimental measurements of the water continuum absorption in the considered range. It appears that water dimers account for an important fraction of the observed continuum absorption in the millimeter region . As frequency increases, their relative contribution decreases, becoming small at the highest frequency considered .

Statistical modeling of sequential collisioninduced dissociation thresholds
View Description Hide DescriptionThermochemistry determined from careful analysis of the energy dependence of cross sections for collisioninduced dissociation (CID) reactions has primarily come from the primary dissociation channel. Higher order dissociations generally have thresholds measured to be higher than the thermodynamic limit because of the unknown internal and kinetic energy distributions of the primary products. A model that utilizes statistical theories for energydependent unimolecular decomposition to estimate these energy distributions is proposed in this paper. This permits a straightforward modeling of the cross sections for both primary and secondary dissociation channels. The model developed here is used to analyze data for , , complexes, chosen because the thermochemistry previously determined by threshold CID studies agrees well with values from theory and equilibrium high pressure mass spectrometry. The model is found to reproduce the cross sections with high fidelity and the threshold values for secondary processes are found to be in excellent agreement with literature values. Furthermore, relative thresholds for higher order dissociation processes appear to provide accurate thermodynamic information as well.

Binding in transition metal complexes: Reduced multireference coupledcluster study of the ( to Cu) compounds
View Description Hide DescriptionThe recently developed reduced multireference coupledcluster method with singles and doubles (RMR CCSD), which is perturbatively corrected for triples [RMR CCSD(T)], is employed to compute binding energies of nine transition metal ions with . Unlike analogous compounds involving maingroup elements, the ( to Cu)transition metal complexes often exhibit a nonnegligible multireference character. The authors thus employ the RMR CCSD(T) method, which represents an extension of the standard singlereference (SR) CCSD(T) method and can account for multireference effects, while employing only small reference spaces. In this way the role of quasidegeneracy effects on the binding energies of these complexes can be assessed at a higher SD(T) level than is possible with the widely used ab initio methods, namely, with the standard SR CCSD(T) approach, and provide a new benchmark for these quantities. The difference between the RMR and the standard CCSD(T) methods becomes particularly evident when considering nonequilibrium geometries.