Volume 125, Issue 1, 07 July 2006
 COMMUNICATIONS


Free energy, entropy and volume of activation for electron transfer reactions in a polar solvent
View Description Hide DescriptionA continuum theory with account of cavity size fluctuations is employed to study free energy, volume and entropy of activation for nonadiabaticelectron transfer(ET)reactions in polar solvents. By using a twosphere cavity description, model calculations are performed for charge separation and recombination processes in acetonitrile under ambient conditions. It is found that the cavity size at the transition state varies with the free energy of reaction as well as with the thermodynamic conditions. In contrast to the Marcus theory predictions, the volume and entropy of activation show a monotonic behavior with the free energy of reaction and a strong correlation with each other. For example, for a given ET process, the volume and entropy of activation have the same sign. Their values for the charge separation and recombination processes are opposite in sign. These findings are in good qualitative agreement with measurements.
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 ARTICLES

 Theoretical Methods and Algorithms

The influence of correlation on the interpretation of Hund’s multiplicity rule: A quantum Monte Carlo study
View Description Hide DescriptionA systematic quantum Monte Carlo study of atoms (C, N, O) and atoms (Si, P, S) is performed to investigate the influence of correlation on the interpretation of Hund’s multiplicity rule, which is an extension of our previous study of the carbon atom [J. Chem. Phys.121, 7144 (2004)] to heavier atoms. The accuracy in the present study is significantly improved as compared with the previous study. A detailed analysis of the correlation contribution to individual energy components of the total energy is given beyond the selfconsistent HartreeFock calculation. The stability of the highest spinmultiplicity state of all the atoms is ascribed to the greater electronnucleus attraction energy that is gained at the cost of increasing the electronelectron repulsion energy as well as the kinetic energy. The present study demonstrates that correlation does not change the above conclusion due to the HartreeFock theory to support Boyd’s less screening mechanism.

Femtosecond laser pulse control of multidimensional vibrational dynamics: Computational studies on the pyrazine molecule
View Description Hide DescriptionThe multiconfiguration timedependent Hartree (MCTDH) method is combined with the optimal control theory(OCT) to study femtosecond laser pulse control of multidimensional vibrational dynamics. Simulations are presented for the widely discussed threeelectroniclevel vibronic coupling model of pyrazine either in a three or four vibrational coordinate version. Thus, for the first time OCT is applied to a fourcoordinate system. Different control tasks are investigated and also some general aspects of the OCTMCTDH method combination are analyzed.

A critical assessment of the use of compliance constants as bond strength descriptors for weak interatomic interactions
View Description Hide DescriptionInverse compliance constants (inverse diagonal elements of the inverse Hessian matrix) have frequently been proposed as replacements for regular internal coordinate force constants, as the former are invariant to the choice of internal coordinates while the latter are not. Recently, Grunenberg and coworkers have proposed using compliance constants as descriptors of bond strength, primarily based on their invariance properties. This article critically assesses the use of compliance constants as bond strength descriptors, highlighting reasons why their use for this purpose is considered inappropriate, particularly for weak bonding interactions.

Semiquantal analysis of hydrogen bond
View Description Hide DescriptionThe semiquantal timedependent Hartree (SQTDH) theory is applied to the coupled Morse and modified LippincottSchroeder (LS) model potentials of hydrogen bond. The structural correlation between the heavy atoms distance and the proton position, the geometric isotope effect, the energy of hydrogen bondformation, and the proton vibrational frequency shift are examined in a broad range of structural parameters. In particular, the geometric isotope effect is found to depend notably on the choice of the potential model, for which the LS potential gives the isotope shift of the heavy atoms distance in the range of , in quantitative agreement with the experimental findings from assortment of hydrogen bonding crystals. The fourthorder expansion approximation to the semiquantal extended potential was confirmed to be highly accurate in reproducing the full SQTDH results. The approximation is computationally efficient and flexible enough to be applied to general models of hydrogen bond.

Embedding wave function theory in density functional theory
View Description Hide DescriptionWe present a framework for embedding a highly accurate coupledcluster calculation within a larger density functional calculation. We use a perturbative buffer to help insulate the coupledcluster region from the rest of the system. Regions are defined, not in real space, but in Hilbert space, though connection between the two can be made by spatial localization of singleparticle orbitals. Relations between our embedding approach and some similar techniques are discussed. We present results for small sample systems for which we can extract essentially exact results, demonstrating that our approach seems to work quite well and is generally more reliable than some of the related approaches due to the introduction of additional interaction terms.

Exact KohnSham versus HartreeFock in momentum space: Examples of twofermion systems
View Description Hide DescriptionThe question of how density functional theory(DFT) compares with HartreeFock (HF) for the computation of momentumspace properties is addressed in relation to systems for which (near) exact KohnSham (KS) and HF oneelectron matrices are known. This makes it possible to objectively compare HF and exact KS and hence to assess the potential of DFT for momentumspace studies. The systems considered are the Moshinsky [Am. J. Phys.36, 52 (1968)] atom, Hooke’s atom, and light twoelectron ions, for which expressions for correlated density matrices or momentum densities have been derived in closed form. The results obtained show that it is necessary to make a distinction between true and approximate DFTs.

Selected configuration interaction with truncation energy error and application to the Ne atom
View Description Hide DescriptionSelected configuration interaction (SCI) for atomic and molecular electronic structure calculations is reformulated in a general framework encompassing all CI methods. The linked cluster expansion is used as an intermediate device to approximate CI coefficients of disconnected configurations (those that can be expressed as products of combinations of singly and doubly excited ones) in terms of CI coefficients of lowerexcited configurations where each is a linear combination of configurationstatefunctions (CSFs) over all degenerate elements of . Disconnected configurations up to sextuply excited ones are selected by Brown’s energy formula, , with determined from coefficients of singly and doubly excited configurations. The truncation energy error from disconnected configurations, , is approximated by the sum of of all discarded . The remaining (connected) configurations are selected by thresholds based on natural orbital concepts. Given a model CI space , a usual upper bound is computed by CI in a selected space , and , where is a residual error which can be calculated by welldefined sensitivity analyses. An SCI calculation on Ne ground state featuring 1077 orbitals is presented. Convergence to within near spectroscopic accuracy is achieved in a model space of CSFs ( determinants) containing up to quadruply excited CSFs. Accurate energy contributions of quintuples and sextuples in a model space of CSFs are obtained. The impact of SCI on various orbital methods is discussed. Since can readily be calculated for very large basis sets without the need of a CI calculation, it can be used to estimate the orbital basis incompleteness error. A method for precise and efficient evaluation of is taken up in a companion paper.

Selectdivideandconquer method for largescale configuration interaction
View Description Hide DescriptionA selectdivideandconquer variational method to approximate configuration interaction (CI) is presented. Given an orthonormal set made up of occupied orbitals (HartreeFock or similar) and suitable correlation orbitals (natural or localized orbitals), a large electron target space is split into subspaces. , of dimension , contains all configurations with attributes (energy contributions, etc.) above thresholds ; the CI coefficients in remain always free to vary. accommodates with attributes above . An eigenproblem of dimension for is solved first, after which the last rows and columns are contracted into a single row and column, thus freezing the last CI coefficients hereinafter. The process is repeated with successive chosen so that corresponding CI matrices fit random access memory (RAM). Davidson’s eigensolver is used times. The final energy eigenvalue (lowest or excited one) is always above the corresponding exact eigenvalue in . Threshold values regulate accuracy; for largedimensional , high accuracy requires to be solved outside RAM. From there on, however, usually a few Davidson iterations in RAM are needed for each step, so that Hamiltonian matrixelement evaluation becomes rate determining. One accuracy is achieved for an eigenproblem of order , involving nonzero matrix elements, and Slater determinants.

FranckCondon factors based on anharmonic vibrational wave functions of polyatomic molecules
View Description Hide DescriptionFranckCondon (FC) integrals of polyatomic molecules are computed on the basis of vibrational selfconsistentfield (VSCF) or configurationinteraction (VCI) calculations capable of including vibrational anharmonicity to any desired extent (within certain molecular size limits). The anharmonic vibrational wave functions of the initial and final states are expanded unambiguously by harmonic oscillator basis functions of normal coordinates of the respective electronic states. The anharmonic FC integrals are then obtained as linear combinations of harmonic counterparts, which can, in turn, be evaluated by established techniques taking account of the Duschinsky rotations, geometry displacements, and frequency changes. Alternatively, anharmonic wave functions of both states are expanded by basis functions of just one electronic state, permitting the FC integral to be evaluated directly by the GaussHermite quadrature used in the VSCF and VCI steps [Bowman et al., Mol. Phys.104, 33 (2006)]. These methods in conjunction with the VCI and coupledcluster with singles, doubles, and perturbative triples [CCSD(T)] method have predicted the peak positions and intensities of the vibrational manifold in the photoelectron band of with quantitative accuracy. It has revealed that two weakly visible peaks are the result of intensity borrowing from nearby states through anharmonic couplings, an effect explained qualitatively by VSCF and quantitatively by VCI, but not by the harmonic approximation. The photoelectron band of is less accurately reproduced by this method, likely because of the inability of CCSD(T)/ccpVTZ to describe the potential energy surface of openshell with the same high accuracy as in .

On correlated electronnuclear dynamics using timedependent density functional theory
View Description Hide DescriptionWe discuss possibilities and challenges for describing correlated electron and nuclear dynamics within a surfacehopping framework using timedependent density functional theory (TDDFT) for the electron dynamics. We discuss the recent surfacehopping method proposed by Craig et al. [Phys. Rev. Lett.95, 163001 (2005)] that is based on KohnSham potential energy surfaces. Limitations of this approach arise due to the KohnSham surfaces generally having different gradients than the true TDDFTcorrected ones. Two mechanisms of the linear response procedure cause this effect: we illustrate these with examples.

A semiclassical hybrid approach to many particle quantum dynamics
View Description Hide DescriptionWe analytically derive a correlated approach for a mixed semiclassical many particle dynamics, treating a fraction of the degrees of freedom by the multitrajectory semiclassical initial value method of Herman and Kluk [Chem. Phys.91, 27 (1984)] while approximately treating the dynamics of the remaining degrees of freedom with fixed initial phase space variables, analogously to the thawed Gaussian wave packet dynamics of Heller [J. Chem. Phys.62, 1544 (1975)]. A first application of this hybrid approach to the well studied SecrestJohnson [J. Chem. Phys.45, 4556 (1966)] model of atomdiatomic collisions is promising. Results close to the quantum ones for correlation functions as well as scattering probabilities could be gained with considerably reduced numerical effort as compared to the full semiclassical HermanKluk approach. Furthermore, the harmonic nature of the different degrees of freedom can be determined a posteriori by comparing results with and without the additional approximation.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Experimental control of excitation flow produced by delayed pulses in a ladder of molecular levels
View Description Hide DescriptionWe study a method for controlling the flow of excitation through decaying levels in a threelevel ladder excitation scheme in molecules. Like the stimulated Raman adiabatic passage (STIRAP), this method is based on the control of the evolution of adiabatic states by a suitable delayed interaction of the molecules with two radiation fields. However, unlike STIRAP, which transfers a population between two stable levels and via a decaying intermediate level through the interaction of partially overlapping pulses (usually in a linkage), here the final level is not long lived. Therefore, the population reaching level decays to other levels during the transfer process. Thus, rather than controlling the transfer into level , we control the flow of the population through this level. In the present implementation a laser couples a degenerate rovibrational level in the ground electronic state , , to the intermediate level , , , which in turn is linked to the final level , , by a laser , from which decay occurs to vibrational levels in the electronic and states. As in STIRAP, the maximum excitation flow through level is observed when the laser precedes the laser. We study the influence of the laser parameters and discuss the consequences of the detection geometry on the measured signals. In addition to verifying the control of the flow of population through level we present a procedure for the quantitative determination of the fraction of molecules initially in the ground level which is driven through the final level . This calibration method is applicable for any stepwise excitation.

Steering population flow in coherently driven lossy quantum ladders
View Description Hide DescriptionWe present a detailed theory of a technique for the adiabatic control of the population flow through a preselected decaying excited level in a threelevel ladder quantum system, as was experimentally demonstrated recently by GarciaFernandez et al. [Phys. Rev. Lett.95, 043001 (2005)]. Specifically, we consider a threestate excitation chain of bound states, 123, of successively increasing excitation energy, in which probability loss via fluorescence occurs from states 2 and 3. We describe a laser excitation scheme that can, by adjustment of laser parameters, alter at will the relative fraction of population that, starting from state 1, is ultimately lost through states 2 and 3. We present analytical results for the conditions under which quasiadiabatic passage can take place.

Geometrical and electronic structures of
View Description Hide DescriptionThe structural and electronic properties of binary clusters have been investigated by density functional theory with relativistic effective core potentials. The results indicate that Au atoms tend to occupy the surface of clusters ( and ). As a result, segregation of small or big bimetallic clusters can be explained according to the atomic mass. The binding energies of the most stable clusters increase with increasing . The vertical ionization potentials of the most stable clusters show oddeven oscillations with changing . The possible dissociation channels of the clusters considered are also discussed.

Quantum mechanical and quasiclassical investigations of the time domain nonadiabatic dynamics of close to the bottom of the conical intersection
View Description Hide DescriptionWe use the effective Hamiltonian that we recently fitted against the first 306 experimentally observed vibronic transitions of [Joyeux et al., J. Chem. Phys.119, 5923 (2003)] to investigate the time domain nonadiabaticdynamics of this molecule on the coupled and electronic states, using both quantum mechanical and quasiclassical techniques. From the quantum mechanical point of view, we show that the transfer of population to the electronic ground state originating from a wave packet launched on the excited state occurs in a stepwise fashion. The evolution of wave packets launched on the electronic ground state is instead more complex because the crossing seam is located close to the bottom of the electronic excited state. We next use the mapping formalism, which replaces the discrete electronic degrees of freedom by continuous ones, to obtain a classical description of the coupled electronic states. We propagate Gaussian swarms of trajectories to show that this approach can be used to calculate the populations in each electronic state. We finally propose a very simple trajectory surface hopping model, which assumes that trajectories have a constant probability to jump onto the other state in a particular region of the phase space and a null hopping probability outside from this region. Quasiclassical calculations show that this model enables a precise estimation of complex quantities, as for example the projection of the instantaneous probability density on given planes.

Preferential site occupancy of krypton atoms on free argoncluster surfaces
View Description Hide DescriptionArgon clusters have been doped with krypton atoms in a pickup setup and investigated by means of ultraviolet and xray photoelectron spectroscopy (UPS and XPS). The width of the krypton surface feature in the XPSspectra from mixed krypton/argon clusters has been studied and found to be narrower than in the case of homogeneous krypton clusters. By considering known spectral broadening mechanisms of the cluster features and the electron binding energy shift of the clustersurface feature relative to the atomic signal, we conclude that krypton adatoms preferentially occupy highcoordination surface sites on the argon hostcluster.

Slow electron velocitymap imaging photoelectron spectra of the methoxide anion
View Description Hide DescriptionHigh resolution anion photodetachmentspectra are presented for the methoxide anion and its fully deuterated counterpart. The spectra were obtained with slow electron velocitymap imaging. Improved electron affinities are determined for as and for as . The spectra resolve many features associated with spinorbit and vibronic coupling that were not seen in previous photodetachment studies. Photoelectron angular distributions taken as a function of detachment wavelength for the ground vibronic state transitions are recorded and are consistent with the removal of a nonbonding, type electron localized on the oxygen atom. Several hot bands and sequence bands are observed for the first time, providing insight into the vibrational structure of the methoxide anion. The results are compared to recent calculations of the anion photoelectron spectra that incorporate bilinear coupling terms among the methoxy vibrational modes and are found to be in reasonable agreement.

Termolecular kinetics for the recombination reaction: A unique test of quantum rate theory
View Description Hide DescriptionThe roomtemperature termolecular rate constants,, for the (, , Ar) recombination reaction have been measured by the technique, and are reported for moderator gas pressures of up to (densities ). The experimental relaxation rates reveal an unusual signature, in being dominated by the electron spinrotation interaction in the MuCO∙ radical that is formed in the addition step. In moderator, , only about 30% higher than found in Ar or He. The experimental results are compared with theoretical calculations carried out on the WernerKellerSchinke (WKS) surface [Keller et al., J. Chem. Phys.105, 4983 (1996)], within the framework of the isolated resonance model (IRM). The positions and lifetimes of resonance states are obtained by solving the complex Hamiltonian for the nonrotating MuCO system, using an method, with an absorbing potential in the asymptotic region. Accurate values of the vibrational bound and resonance states of MuCO reveal unprecedented isotope effects in comparisons with HCO, due to the remarkable effect of replacing H by the very light Mu atom . Due to its pronounced zeropoint energy shift, there are only two bound states in MuCO. Contributions from nonzero states to the termolecular rate constants are evaluated through the shifting approximation, with rotational constants evaluated at the potential minimum. The value of the important constant used in this approximation was supported by accurate calculations, from which was obtained by numerical evaluation. The calculations presented here, with a “weak collision factor” , indicative of the very sparse density of MuCO states, give a very good account of both the magnitude and pressure dependence of the experimental rates, but only when the fact that the two initially bound states become resonances for is taken into account. This is the first time in IRM calculations of atommolecule recombination reactions where states have proven to be so important, thus providing a truly unique test of quantum rate theory.

Excess electron localization sites in neutral water clusters
View Description Hide DescriptionWe present approximate pseudopotential quantummechanical calculations of the excess electron states of equilibrated neutral water clusters sampled by classical molecular dynamics simulations. The internal energy of the clusters are representative of those present at temperatures of 200 and . Correlated electronic structure calculations are used to validate the pseudopotential for this purpose. We find that the neutral clusters support localized, bound excess electron ground states in about 50% of the configurations for the smallest cluster size studied , and in almost all configurations for larger clusters . The state is always exterior to the molecular frame, forming typically a diffuse surface state. Both cluster size and temperature dependence of energetic and structural properties of the clusters and the electron distribution are explored. We show that the stabilization of the electron is strongly correlated with the preexisting instantaneous dipole moment of the neutral clusters, and its ground stateenergy is reflected in the electronic radius. The findings are consistent with electron attachment via an initial surface state. The hypothetical spectraldynamics following such attachment is also discussed.