Volume 119, Issue 19, 15 November 2003
 ARTICLES

 Theoretical Methods and Algorithms

Robust control of quantum information
View Description Hide DescriptionErrors in the control of quantum systems may be classified as unitary, decoherent, and incoherent. Unitary errors are systematic, and result in a density matrix that differs from the desired one by a unitary operation. Decoherent errors correspond to general completely positive superoperators, and can only be corrected using methods such as quantum error correction. Incoherent errors can also be described, on average, by completely positive superoperators, but can nevertheless be corrected by the application of a locally unitary operation that “refocuses” them. They are due to reproducible spatial or temporal variations in the system’s Hamiltonian, so that information on the variations is encoded in the system’s spatiotemporal state and can be used to correct them. In this paper liquidstatenuclear magnetic resonance is used to demonstrate that such refocusing effects can be built directly into the control fields, where the incoherence arises from spatial inhomogeneities in the quantizing static magnetic field as well as the radiofrequency control fields themselves. Using perturbation theory, it is further shown that the eigenvalue spectrum of the completely positive superoperator exhibits a characteristic spread that contains information on the Hamiltonians’ underlying distribution.

Interpolating moving leastsquares methods for fitting potential energy surfaces: Detailed analysis of onedimensional applications
View Description Hide DescriptionWe present the basic formal and numerical aspects of higher degree interpolated moving leastsquares (IMLS) methods. For simplicity, applications of these methods are restricted to two onedimensional (1D) test cases: a Morse oscillator and a 1D slice of the potential energy surface. For these two test cases, we systematically examine the effect of parameters in the weight function (intrinsic to IMLS methods), the degree of the IMLS fit, and the number and placement of potential energy points. From this systematic study, we discover compact and accurate representations of potentials and their derivatives for firstdegree and higherdegree (up to nine degree) IMLS fits. We show how the number of ab initio points needed to achieve a given accuracy declines with the degree of the IMLS. We outline automatic procedures for ab initio point selection that can optimize this decline.

Transcorrelated method for electronic systems coupled with variational Monte Carlo calculation
View Description Hide DescriptionA Jastrow–Slatertype wave function is often used as a trial function for precise calculations of the total energy of electronic systems, where the correlation effect is taken into account by the Jastrow factor that directly depends on the distance between electrons. Since manybody integrals are inevitable there, the calculation totally depends on Monte Carlo sampling, and so, except for very simple cases, it is very difficult to optimize onebody wave functions in the Slater determinant which determine the nodal surfaces of the total wave function. Here we propose and demonstrate that the total wave function is efficiently optimized by coupling an ordinary variational Monte Carlo (VMC) technique with the transcorrelated method, in which the onebody wave functions are definitely obtained by solving Hartree–Focktype selfconsistentfield (SCF) equations derived from the similaritytransformed Hamiltonian. It is shown that the present method reproduces about 90% of the correlationenergy for heliumlike twoelectron systems He, and and gives much better results than the conventional VMC method using the Hartree–Fock orbitals for a Li atom, a Be atom, and a molecule. It is also shown that the orbital energy appearing in the SCF equations gives a good approximation to the ionization potential.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Timeresolved study of the symmetric reaction
View Description Hide DescriptionTimeresolvedphotoelectron spectroscopy of negative ions has been applied to study the title reaction as a model system for gas phase reactions. Starting from the precursor cluster the interaction of the reactants and is initiated by a pump pulse and the subsequent dynamics are observed with a delayed probe pulse used to detach the excess electron and measure their photoelectron spectra. Using two different pump photon energies, which lead to different amounts of internal energy available to the reaction complex, a number of dynamical features have been observed. For small internal excitation, the reactants only form stable, albeit vibrationally excited, complexes. However, with increased internal excitation, complexes are formed that exhibit biexponential decay back to and reactants with time scales of 0.8 and 10 ps. Similar dynamics are expected for entrance channel complex formed in the first step of a gas phase reaction.

Influence of collision energy on the reaction dynamics: A quasiclassical trajectory study involving four potential energy surfaces
View Description Hide DescriptionThe influence of collision energy on the dynamics of the atmospheric reaction was studied by means of the quasiclassical trajectory method. The four lowest potential energy surfaces (PESs) involved in the process were used in the calculations and PESs), and the nonadiabatic couplings between them were neglected. The dependence of the scalar and twovector properties of the reaction with was analyzed. Moreover, the different modes of reaction taking place were investigated. Although only one type of microscopic mechanism (abstraction) was found for the and PESs, two different modes of reaction (abstraction and insertion) were observed to coexist for the PES. For this PES, the abstraction mechanism is the most important one at room temperature, while the insertion mechanism increases its contribution to reactivity with (it accounts for about half of the reactivity above 0.5 eV).

Zero temperature quantum properties of small protonated water clusters
View Description Hide DescriptionThe study of the energetics and structure of small protonated water clusters has been carried out employing the OSS3 potential energy surface developed by Ojamae, Singer, and Shavitt [J. Chem. Phys. 109, 5547 (1998)]. By comparing it with accurate ab initio MP2 calculations for this allatom potential is also shown to reproduce quantitatively the geometry and the relative energetics of small neutral and protonated water clusters containing up to five molecules. To correct the total and binding energy for vibrational motion, the zero point energy of the clusters has been calculated by means of the harmonic approximation and by simulating the exact ground state using the diffusionMonte Carlo method. From these 0 K results, it appears that the anharmonicity accounts for a decrease (increase) of 1.5–5.5 mhartree (1.0–3.5 kcal/mol) in the total (binding) energy of the protonated clusters. Moreover, we found all the cyclic isomers of and to be unstable during the diffusionMonte Carlo simulations, and to convert into treelike or linear isomers. Employing the same interaction potential, we also simulated the ground state of to compute the proton binding energy to a water cluster. This quantity is decreased by roughly 12 mhartree (7.5 kcal/mol) by including the zero point energy correction to the total energy. The relevance of these findings with respect to the experimental detection and probing of the protonated water clusters is discussed.

An ab initio investigation on the vertical electron detachment energies of semiconductoralkali binary anions
View Description Hide DescriptionGroundstate structures of semiconductoralkali binary anions have been optimized using the secondorder Møller–Plesset perturbation (MP2) method and their vertical detachment energies predicted employing the outer valence Green’s function (OVGF) procedure. The calculated lowest detachment energies of anions composed of semiconductor Zintl anions and facecapping or edgebridging alkali cations exhibit maximums around 5, 9, and 10 and minimums at and 7, in overall agreement with the magic numbers observed for in timeofflightmass spectroscopy. The lowest detachment energies of series increase from Na, to Li with increasing electronegativities of the alkali atoms and decreased ionic bond lengths. Small ternary exhibit similar behavior to binary at the same sizes

Experimental evidence for the 7,7,8,8tetracyanoquinodimethane dianion in vacuo
View Description Hide DescriptionThe existence of the unsolvated 7,7,8,8tetracyanoquinodimethane (TCNQ) dianion is proved experimentally. The dianion was formed in 50keV collisions between TCNQ monoanions and sodium vapor. In the collision process, electron capture to the monoanion occurs with a cross section of about 1 Å^{2}. The lifetime of the dianion is estimated to be in the order of microseconds or longer as the flight time from the collision cell to the detector is 5 μs. The stability of the dianion was elucidated by density functional theory(DFT) and ab initio MP2 calculations. A selection of dissociationreactions have been studied theoretically and compared with the experimental results.

Ab initio quantum chemical calculations for fullerene cages with large holes
View Description Hide DescriptionOne of the important issues in endohedral fullerene chemistry is the generation of a suitable window for atoms or small molecules to enter into the fullerene cages. In this paper, the structure and stability of fullerenes possessing holes, formed by removing one or more adjacent atoms from the clusters, are examined via ab initio Hartree–Fock and density functional theory calculations. When vacancies are created in the cluster, some of the original 5 and 6member rings are destroyed, resulting in defect structures, containing larger rings (7, 8, and 9member rings) and abutting 5member rings. It was also found that the ground state is a singlet for the defect structure with two vacancies and a triplet for the defect structures with one or three vacancies. The vacancies decrease the cluster stability. However, among these defect structures, the twovacancy defect with a 7member ring is the most stable and has a hole with a sufficiently large diameter (3.22 Å) for atoms or small molecules to pass through. Therefore, this fullerene cage could provide an excellent cage for fullerene endohedral complexes and as a storage place for fuels (such as

Ab initio calculation of interaction nature of borazine dimer
View Description Hide DescriptionThe π/π interaction (stacking) and N(B)–H/π interaction of the borazine dimer were theoretically studied. In contrast to the benzene dimer, the gauche parallelstacked dimer of borazine was energetically minimum, and total interaction energy was about 1 kcal/mol more negative than that of the parallelstacked dimer of benzene. The gauche parallelstacked dimer of borazine was more stable than slipped parallelstacked dimers and Tshape dimers. The syn parallelstacked dimer of borazine was energetically unstable and it was less stable than the slipped syn parallelstacked structures. The electron correlation effect at higher than the secondorder Møller–Plesset (MP2) level on the molecular interaction energy was quite small. The dispersion term and the charge transfer term had large contribution in almost all the borazine dimer formations, except the syn parallelstacked dimer. In the case of syn parallelstacked dimer, contribution of the dispersion term was dominant. The electrostatic term had only small contribution for all the dimer formations.

Transition state spectroscopy of the excited electronic states of Li–HF
View Description Hide DescriptionIn this work the electronic spectrum is simulated and compared with the experimental one obtained by Hudson et al. [J. Chem. Phys. 113, 9897 (2000)]. High level ab initio calculations of three and one electronic states have been performed using a new atomic basis set and for a large number of nuclear configurations (about 6000). Four analytic global potential energy surfaces have been fitted. The spectrum involved very excited rovibrational states, close to the first dissociation limit, at high total angular momentum. Two different methods have been used, one based on bound state and the second one on wave packet calculations. Different alternatives have been used to simulate the relatively high temperatures involved. The agreement obtained with the experimental spectrum is very good allowing a very simple assignment of the peaks. They are due to bending progressions on the three excited electronic states. A simple model is used in which only rotational degrees of freedom are included, which simulates the spectrum in excellent agreement with the experimental one, providing a nice physical interpretation. Moreover, the remaining theoretical/experimental discrepancies have been attributed to nonadiabatic effects through the extension of this model to a diabatic representation of excited coupled electronic states.

Structural and thermochemical properties of the hydroxymethyl radical: A high precision ab initio study
View Description Hide DescriptionThe variational solution of the nuclear problem was performed by treatment of as a planar molecule with highly anharmonic vibrations. A sophisticated dynamic model to describe the structural flexibility of was applied. The detailed analysis of the rovibrational Hamiltonian is shown. The electron problem solution was obtained by use of the coupled cluster electron correlation technique and the augmented correlationconsistent polarized basis sets of triple and quadrupleζ qualities. The geometry and energy parameters were extrapolated to the complete basis set limit. The partition functions of were calculated by the explicit summation of vibrational and rotational levels. The heat of formation of was calculated by a study of the reaction using the augmented basis set of quintupleζ quality and the relativistic and corevalence corrections of the total energies. Some structural and thermodynamic properties of are reported.

The RennerTeller effect and Sears resonances in the ground state of the GeCH and GeCD free radicals
View Description Hide DescriptionThe vibrational energy levels of the jetcooled GeCH and GeCD radicals have been studied by a combination of laserinduced fluorescence and wavelengthresolved emission techniques. The radicals were produced in a pulsed electric discharge free jet expansion using methyltrichlorogermane and tetramethylgermane precursors. A reexamination of the weaker hot bands in the LIF spectrum has provided a more complete vibrational analysis of the upper state energy levels. The single vibronic level emission spectra obtained by pumping several bands of each isotopomer were analyzed to provide information on the lowlying ground state vibronic energy levels up to 3000 cm^{−1} above the zeropoint level. Strong interactions occur in these molecules between vibronic levels with the same value of P, but differing by one unit of such interactions were first described for NCS by Northrup and Sears [Mol. Phys. 71, 45 (1990)] and are conveniently called “Sears resonances.” The spectra of GeCH were further complicated by Fermi resonances between the bending and Ge–C stretching levels. Despite these difficulties, it proved possible to analyze the data using a standard RennerTeller model with the addition of Sears resonance coupling terms. The validity of the fitted parameters was tested using the isotope relations. The Sears resonance parameters for GeCH are much larger than those of NCS, a result of the much stronger vibronic coupling in the germanium methylidynes.

Fragmentation mechanisms of aqueous clusters charged with ions
View Description Hide DescriptionFragmentation processes of mesoscopic aqueous clusters charged with ions of similar sign are studied by computer simulations. In order to examine differences in the fragmentation that depend on the nature of the ions and the charge distribution, the clusters contain positive and or negative ions. Insight into the fragmentation mechanism is obtained by theories of activated processes. Critical to this approach is the use of a new reaction coordinate that captures the shape fluctuations of the droplet that are responsible for the reaction. Reversible work profiles for the reaction are constructed along the reaction coordinate, and dynamics is performed. The dynamics validates the use of the reaction coordinate, and shows diffusive barrier crossing. It is found that clusters with even number of charges fragment unevenly in contrast to analytical theories that predict even fission by considering only the energetic factors that determine the stability of chargeddroplets.

Improving ab initio infrared spectra of glucose–water complexes by considering explicit intermolecular hydrogen bonds
View Description Hide DescriptionIn this paper, using density functional theory, we show the effects of explicit intermolecular hydrogen bonds on infrared spectra of glucose–water complexes. The number of explicit water molecules ranges from four to nine, and we approximate the rest of other water molecules as a continuum medium. When eight or nine water molecules are considered explicitly, our computed spectra are in good agreement with the main features of the experimental one. However, in the cases of explicit water molecules less than eight, our computed spectra are not improved successfully. This suggests that in predicting infrared spectrum of glucose in water the effects of explicit water molecules around the glucose molecule are not negligible. We also discuss the numbers of intermolecular hydrogen bonds,spectral differences between α and β anomers, and the main features of normal modes in the 1000–1200 cm^{−1} region.

Large anharmonic effects in the infrared spectra of the symmetrical and complexes
View Description Hide DescriptionThe observed IR spectra of the and complexes display sequences of up to seven transitions in the region of the OH stretch fundamentals. This is indicative of strong anharmonic coupling between the OH stretch modes and one or more lowfrequency modes. Cubic force fields have been calculated for these two complexes using the MP2 method, and these have been used to calculate the vibrational spectra and to identify the key couplings responsible for the “extra” lines in the observed spectra. In addition, a simple adiabatic model involving the OH stretch and intermolecular rock vibrations is introduced and shown to account in an near quantitative manner for the structure in the OH stretch region of the spectra.

Modedependent vibrational autoionization of
View Description Hide DescriptionTripleresonance excitation and highresolution photoelectron spectroscopy were combined to study the mode dependence of vibrational autoionization in Rydberg states of Photoselection isolates vibrational autoionization via the symmetric stretching vibration, and the bending vibration, The previously characterized Fermi resonance between one quantum of and two quanta of [H. Matsui et al., J. Mol. Spectrosc. 175, 203 (1996)] allows the comparison of the vibrational autoionization matrix elements for these two modes. The squared matrix element for vibrational autoionization via the symmetric stretch is found to be approximately 35 times greater than that for the bend, which is also consistent with previous results. The results are discussed in terms of existing theoretical models for the autoionization process.

Vibrationally mediated dissociation dynamics of in the polyad
View Description Hide DescriptionVibrationally mediated photodissociation dynamics of jetcooled in the polyad is studied in a supersonic slit jet expansion. Single rotational states within in normal mode notation), and vibrational states of are selectively prepared with near IR overtone pumping, photodissociated at 193 nm, and the resulting nascent internal state distribution of OH fragments probed via laser induced fluorescence. Strong oscillations in rotational, spin–orbit, and lambdadoublet distributions are observed, often in remarkably close agreement with statetostate photodissociation studies from both higher and lower polyads. The influence of initially excited bending and levels of on spin–orbit, Λdoublet, and rotational distributions of OH is examined in detail. Several new dynamical trends are identified, for example, a clear propensity at high N for a strong versus inversion in the spin–orbit manifold, which reverses in the manifold, suggesting spin–orbit sensitive stereodynamics in the ejection process. Furthermore, the results highlight significant differences in photodissociation dynamics from gerade (e.g., versus ungerade (e.g., vibrational states, specifically with respect to branching ratios, and signaling a breakdown of the “spectator” model at low vibrational excitation.

Spectroscopic characterization of the first singlet excited state of
View Description Hide DescriptionUsing laser induced fluorescence(LIF) and resonance enhanced twophoton ionization (R2PI) spectroscopy, several vibrational bands of the perpendicular transition of the molecule have been rotationally resolved and analyzed to yield effective values. The estimated geometry of the state does not vary with (symmetric stretch mode), but increases and decreases slightly as (bending mode) increases. Extrapolation leads to an estimate for the (0,0,0) state of and for the potential minimum The strongly bent nature of the state is due to promotion of an pelectron from the strongly ionic, linear ground state to an molecular orbital which has Li/Li bonding character. The state thus has an approximately charge distribution, so that the ionic bonding is less strong than in the linear ground state, where (from this study and an earlier stimulationemission pumping study) In fact, the Li–Li distance in the state, ∼3.0 Å, is quite similar to that of the ion, so the bonding may be described as that of bound ionically to the ion.

A stateselected study of the proton transfer reaction using the pulsedfield ionization–photoelectron–secondary ion coincidence scheme
View Description Hide DescriptionThe endothermic proton transferreaction, is investigated over a broad range of reactant vibrational energies using the pulsedfield ionization–photoelectron–secondary ion coincidence (PFI–PESICO) scheme. For the lowest vibrational levels, and 1, a detailed translational energy dependence is also presented using a continuous approach for preparing reactant ions with monochromatic VUV. Sharp threshold onsets are observed, suggesting the importance of longlived intermediates or resonances. At a translational energy, absolute stateselected reaction cross sections are measured for all reactant vibrational levels For levels the cross sections grow rapidly with vibrational quantum, above which the cross sections saturate at a value of At levels the cross sections decline, probably due to competition with the dissociation channel. At a translational energy, absolute stateselected reaction cross sections are measured for reactant vibrational levels spanning the range between and 14. Cross section growth is observed from above which the cross sections no longer exhibit a steady trend. At cross sections are reported for vibrational levels covering the range between and 12. The cross sections are substantially lower at this high translational energy, however, they still exhibit a substantial vibrational enhancement below The present measurements are compared with quasiclassical trajectory(QCT) calculations. The comparison can be categorized by three distinct total energy regimes. For the experimental cross sections exceed the QCT results, consistent with important quantum effects at low energies. For excellent agreement is observed between the PFI–PESICO cross sections and the QCT calculations. At total energies exceeding 3 eV, the experimental results are generally higher, probably because QCT overpredicts competition from the dissociation channel.