Volume 130, Issue 11, 21 March 2009
 ARTICLES

 Theoretical Methods and Algorithms

State specific equation of motion coupled cluster method in general active space
View Description Hide DescriptionThe state specific equation of motion coupled cluster (SSEOMCC) method is an internally contracted multireference approach, applicable to both ground and excited states. Attractive features of the method are as follows: (1) the SSEOMCC wave function is qualitatively correct and rigorously spin adapted, (2) both orbitals and dynamical correlation are optimized for the target state, (3) nondynamical correlation and differential orbital relaxation effects are taken care of by a diagonalization of the transformed Hamiltonian in the multireference configurationinteraction singles space, (4) only one and twoparticle density matrices of a completeactivespace selfconsistentfield reference state are needed to define equations for the cluster amplitudes, and (5) the method is invariant with respect to orbital rotations in core, active, and virtual subspaces. Prior applications focused on biradicallike systems, in which only one extra orbital is needed to construct the active space, and similarly, single bond breaking processes. In this paper, the applicability of the method is extended to systems of general active spaces. Studies on , , CO, and are carried out to gauge its accuracy. The convergence strategy is discussed in detail.

Uncertainties in scaling factors for ab initio vibrational zeropoint energies
View Description Hide DescriptionVibrational zeropoint energies (ZPEs) determined from ab initio calculations are often scaled by empirical factors. An empirical scaling factor partially compensates for the effects arising from vibrational anharmonicity and incomplete treatment of electron correlation. These effects are not random but are systematic. We report scaling factors for 32 combinations of theory and basis set, intended for predicting ZPEs from computed harmonic frequencies. An empirical scaling factor carries uncertainty. We quantify and report, for the first time, the uncertainties associated with scaling factors for ZPE. The uncertainties are larger than generally acknowledged; the scaling factors have only two significant digits. For example, the scaling factor for is (standard uncertainty). The uncertainties in the scaling factors lead to corresponding uncertainties in predicted ZPEs. The proposed method for quantifying the uncertainties associated with scaling factors is based upon the Guide to the Expression of Uncertainty in Measurement, published by the International Organization for Standardization. We also present a new reference set of 60 diatomic and 15 polyatomic “experimental” ZPEs that includes estimated uncertainties.

Transformation from angleaction variables to Cartesian coordinates for polyatomic reactions
View Description Hide DescriptionThe transformation from angleaction variables to Cartesian coordinates is an important step of the semiclassical description of bimolecular collisions and photofragmentations. The basic reason is that dynamical conditions corresponding to molecular beam experiments are ideally generated in angleaction variables, whereas the classical equations of motion are ideally solved in Cartesian coordinates by standard numerical approaches. To our knowledge, this transformation is available in the literature only for atomdiatom arrangements. The goal of the present work is to derive it for diatompolyatom ones. The analogous transformation for any type of arrangement may then be straightforwardly deduced from that presented here.

Excitation energies with timedependent density matrix functional theory: Singlet twoelectron systems
View Description Hide DescriptionTimedependent density functional theory in its current adiabatic implementations exhibits three striking failures: (a) Totally wrong behavior of the excited state surface along a bondbreaking coordinate, (b) lack of doubly excited configurations, affecting again excited state surfaces, and (c) much too low charge transferexcitation energies. We address these problems with timedependent density matrix functional theory (TDDMFT). For twoelectron systems the exact exchangecorrelation functional is known in DMFT, hence exact response equations can be formulated. This affords a study of the performance of TDDMFT in the TDDFT failure cases mentioned (which are all strikingly exhibited by prototype twoelectron systems such as dissociating and ). At the same time, adiabatic approximations, which will eventually be necessary, can be tested without being obscured by approximations in the functional. We find the following: (a) In the fully nonadiabatic (dependent, exact) formulation of linear response TDDMFT, it can be shown that linear response (LR)TDDMFT is able to provide exact excitation energies, in particular, the first order (linear response) formulation does not prohibit the correct representation of doubly excited states; (b) within previously formulated simple adiabatic approximations the bondingtoantibonding excited state surface as well as charge transfer excitations are described without problems, but not the double excitations; (c) an adiabatic approximation is formulated in which also the double excitations are fully accounted for.

Levels of selfconsistency in the approximation
View Description Hide DescriptionWe perform calculations on atoms and diatomic molecules at different levels of selfconsistency and investigate the effects of selfconsistency on total energies,ionization potentials, and particle number conservation. We further propose a partially selfconsistent scheme in which we keep the correlation part of the selfenergy fixed within the selfconsistency cycle. This approximation is compared to the fully selfconsistent results and to the and the approximations. Total energies,ionization potentials, and twoelectron removal energies obtained with our partially selfconsistent approximation are in excellent agreement with fully selfconsistent results while requiring only a fraction of the computational effort. We also find that selfconsistent and partially selfconsistent schemes provide ionization energies of similar quality as the values but yield better total energies and energy differences.

A MinMax selfconsistentfield approach for auxiliary density functional theory
View Description Hide DescriptionA MinMax selfconsistentfield (SCF) approach is derived in the framework of auxiliary density functional theory. It is shown that the SCF convergence can be guided by the fitting coefficients that arise from the variational fitting of the Coulomb potential. An incore direct inversion of the iterative subspace (DIIS) algorithm is presented. Due to its reduced memory demand this new incore DIIS method can be applied without overhead to very large systems with tens of thousands of basis and auxiliary functions. Due to the new DIIS error definition systems with fractional occupation numbers can be treated, too.

A study of the fixednode error in quantum Monte Carlo calculations of electronic transitions: The case of the singlet (CO) transition of the acrolein
View Description Hide DescriptionWe report fixednode diffusionMonte Carlo (FNDMC) calculations of the singlet (CO) vertical transition of acrolein. The impact of the fixednode approximation on the excitation energy is investigated. To do that, trial wave functions corresponding to various nodal patterns are used. They are constructed by using either a minimal completeactivespace selfconsistent field (CASSCF) calculation involving an oxygen lone pair and the (CO) molecular orbitals or a more complete set involving all the molecular orbitals expected to play a significant role in the excitation process. Calculations of both states have been performed with molecular orbitals optimized separately for each state via standard “state specific” CASSCF calculations or by using a common set of optimized orbitals [“state averaged” CASSCF calculations] whose effect is to introduce some important correlation between the nodal patterns of the two electronic states. To investigate the role of the basis set three different basis of increasing size have been employed. The comparative study based on the use of all possible combinations of basis sets, active spaces, and type of optimized molecular orbitals shows that the nodal error on the difference of energies is small when chemically relevant active space and stateaveragedtype CASSCF wave functions are used, although the fixednode error on the individual total energies involved can vary substantially. This remarkable result obtained for the acrolein suggests that FNDMC calculations based on a simple strategy (use of standard ab initiowave functions and no Monte Carlo optimization of molecular orbital parameters) could be a working computational tool for computing electronic transition energies for more general systems.

Efficient and accurate local approximations to coupledelectron pair approaches: An attempt to revive the pair natural orbital method
View Description Hide DescriptionCoupledelectron pair approximations (CEPAs) and coupledpair functionals (CPFs) have been popular in the 1970s and 1980s and have yielded excellent results for small molecules. Recently, interest in CEPA and CPF methods has been renewed. It has been shown that these methods lead to competitive thermochemical, kinetic, and structural predictions. They greatly surpass second order Møller–Plesset and popular density functional theory based approaches in accuracy and are intermediate in quality between CCSD and CCSD(T) in extended benchmark studies. In this work an efficient production level implementation of the closed shell CEPA and CPF methods is reported that can be applied to medium sized molecules in the range of 50–100 atoms and up to about 2000 basis functions. The internal space is spanned by localized internal orbitals. The external space is greatly compressed through the method of pair natural orbitals (PNOs) that was also introduced by the pioneers of the CEPA approaches. Our implementation also makes extended use of density fitting (or resolution of the identity) techniques in order to speed up the laborious integral transformations. The method is called local pair natural orbital CEPA (LPNOCEPA) (LPNOCPF). The implementation is centered around the concepts of electron pairs and matrix operations. Altogether three cutoff parameters are introduced that control the size of the significant pair list, the average number of PNOs per electron pair, and the number of contributing basis functions per PNO. With the conservatively chosen default values of these thresholds, the method recovers about 99.8% of the canonical correlation energy. This translates to absolute deviations from the canonical result of only a few . Extended numerical test calculations demonstrate that LPNOCEPA (LPNOCPF) has essentially the same accuracy as parent CEPA (CPF) methods for thermochemistry, kinetics, weak interactions, and potential energy surfaces but is up to 500 times faster. The method performs best in conjunction with large and flexible basis sets. These results open the way for largescale chemical applications.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Hydrogen multicenter bonds and reversible hydrogen storage
View Description Hide DescriptionA new strategy for reversible hydrogen storage based on the properties of hydrogen multicenter bonds is proposed. This is demonstrated by carrying out ab initio calculations of hydrogen saturation of titanium and bimetallic titaniumaluminum nanoclusters. Hydrogen saturation leads to the formation of exceptionally and energetically stable hydrogen multicenter bonds. The stabilization results from sharing of the hydrogen atom electron density with the frontier orbitals of the metal cluster. The strength of the hydrogen multicenter bonds can be modulated either by varying the degree of hydrogen loading or by suitable alloying. Modespecific infrared excitation of the vibrational modes associated with the multicenter hydrogen bonds can release the adsorbed hydrogen, thereby enabling efficient reversible hydrogen storage. The possible formation of hydrogen multicenter bonds involving titanium atoms and its implication to hydrogen adsorption/desorption kinetics in hydrogen cycled Tidoped is also discussed.

Theoretical studies of angleresolved ion yield spectra of coretovalence transitions of acetylene
View Description Hide DescriptionRecent experimental results on angleresolved photoionyield spectroscopy (ARPIS) spectra near the coretovalence excitation in acetylene show significant anisotropies in the spectral profile measured at 0° and 90° regarding to the polarization direction of xrayphotons. In the present work, a theoretical model is proposed to simulate the fine structure and anisotropy in ARPIS. This employs twodimensional potential energy surfaces of the ground and coreexcited states, as well as transition dipole moments, including symmetric and antisymmetric bending modes to account for Duschinsky effect. The ARPIS is simulated by evaluation of the ion flux, which is found as a projection of the excited state wave packet on a particular direction in the molecular frame. Numerical simulations explain qualitatively the angular dependence of the experimental spectra of the and transitions. The effects of the lifetime of the coreexcited state, the direction of the ion flux, and the transition dipole moment are discussed.

Quantum calculations of collisions: From ultracold to thermal energies
View Description Hide DescriptionWe present quantum dynamics of collisions between two para molecules from low to high collisionenergies (1 eV). The calculations are carried out using a quantum scattering code that solves the timeindependent Schrödinger equation in its full dimensionality without any decoupling approximations. The sixdimensional potential energy surface for the system developed by Boothroyd et al. [J. Chem. Phys.116, 666 (2002)] is used in the calculations. Elastic, inelastic, and statetostate cross sections as well as rate coefficients from to 400 K obtained from our calculations are compared with available experimental and theoretical results. Overall, good agreement is obtained with previous studies.

Photochemical reactions of the lowlying excited states of formaldehyde: intersystem crossings, characteristics of the and potential energy surfaces, and a global potential energy surface
View Description Hide DescriptionAccurate ab initio calculations using the multireference configuration interaction method have been performed to characterize the potential energy surfaces (PESs) of lowlying excited states ( and ) of formaldehyde and hydroxymethylene (HCOH) with emphasis on their isomerization,dissociation, and the possible role of the state in the nonadiabaticphotodissociation of . Two regions on the PES are found to contribute to the nonadiabatic transition to the ground state. Three minima on the seam of crossing (MSXs), (above the global minimum), are located in the HCOH region; they, however, are blocked by a highenergy isomerization transition state at . The other MSX discovered in the region is reachable with energy and strong spinorbit interaction; this may be a more important pathway for the to transition. A fulldimensional PES is generated for the state, fitted by a weighted leastsquares method employing a manybody expansion in which each term is a function of the internuclear distances and is invariant under permutations of like atoms. The single global function covers the formaldehyde and the HCOH regions as well as dissociation pathways. The high quality of the fitted PES is demonstrated by the small rootmeansquare fitting error of and the close agreement between the critical points from ab initio calculations and from the fitted PES.

Fragmentation of adenine under energy control
View Description Hide DescriptionWe present results on the fragmentation of adenine dication as a function of the excitation energy. The adenine molecule is charged and excited in a single collision with ion at 3 keV and the excitation energy distribution is obtained for each fragmentation channel by measuring the kinetic energy loss of the projectile. This method named collision induced dissociation under energy control is based on the formation of a negative scattered projectile as a result of double electron capture from the target molecule. Comparison between the main dissociation channels of singly and doubly charged adenine shows that fragmentation patterns are very similar consisting mainly of the successive emission of neutral HCN or . The energy distributions of the parent adenine dication and the kinetic energy release of the fragments measured for the most abundant fragmentation channels confirms the assumption of successive emission dynamics. A specific fragmentation pathway of the adenine requiring less energy than the usual successive emission of neutral HCN could be identified. It consists of the emission of a charged following on by the emission of a dimer of HCN (precisely ). This new channel, measured for a mean excitation energy of 8.4 eV for the adenine dication is very closed to the emission of HCN monomer measured at 7.9 eV. The implications of these results concern the formation of adenine in the sealedtube reaction of HCN with liquid ammonia as well as the possible formation of the adenine molecule in the interstellar medium. This last point is briefly discussed in relation to astrobiology and exobiology interests.

Investigation of the reactions of small neutral iron oxide clusters with methanol
View Description Hide DescriptionReactions of neutral iron oxide clusters (, , ) with methanol in a fast flow reactor are investigated by time of flight mass spectrometry. Detection of the neutral iron oxide cluster distribution and reaction intermediates and products is accomplished through single photon ionization by a 118 nm (10.5 eV) VUV laser. Partially deuterated methanol is employed to distinguish reaction products and reaction mechanisms. Three major reactions are identified experimentally: association with FeO; methanol dehydrogenation on and ; and formation. Density functional theory calculations are carried out to identify reaction products, and to explore the geometric and electronic structures of the iron oxide clusters, reaction intermediates, and transition states, and to evaluate reaction pathways. Neutral formaldehyde is calculated to be formed on and clusters. Hydrogen transfer from methanol to iron oxide clusters occurs first from the O–H moiety of methanol, and is followed by a hydrogen transfer from the C–H moiety of methanol. Computational results are in good agreement with experimental observations and reveal reaction mechanisms for neutral iron oxide clusters taking methanol to formaldehyde through various reaction intermediates. Based on the experimental results and the calculated reaction mechanisms and pathways, complete catalytic cycles are suggested for the heterogeneous reaction of to facilitated by an iron oxide catalyst.
 Condensed Phase Dynamics, Structure, and Thermodynamics: Spectroscopy, Reactions, and Relaxation

Electric field of Ions in solution probed by hyperRayleigh scattering
View Description Hide DescriptionThe electric field of dissolved ions accounts for the narrow spike at zero frequency shift, with the polarization signature of a polar longitudinal collective mode, in the high resolution hyperRayleigh light scattering (HRS) spectrum for liquid water and other polar solvents. This peak in the HRS spectrum probes both the structure factor and the fluctuation time for the ion charge density in solution. The experimental results for solutions are consistent with the Debye–Hückel charge structure factor and determine the diffusion coefficient and static local field factor.

Interaction between buoyancy and diffusiondriven instabilities of propagating autocatalytic reaction fronts. I. Linear stability analysis
View Description Hide DescriptionThe interaction between buoyancydriven and diffusiondriven instabilities that can develop along a propagating reaction front is discussed for a system based on an autocatalytic reaction. Twelve different cases are possible depending on whether the front is ascending or descending in the gravity field, whether the reactant is heavier or lighter than the products, and whether the reactant diffuses faster, slower, or at the same rate as the product. A linear stability analysis (LSA) is undertaken, in which dispersion curves (plots of the growth rate against wave number ) are derived for representative cases as well as an asymptotic analysis for small wave numbers. The results from the LSA indicate that, when the initial reactant is denser than the reaction products, upward propagating fronts remain unstable with the diffusiondriven instability enhancing this instability. Buoyantly stable downward propagating fronts become unstable when the system is also diffusionally unstable. When the initial reactant is lighter than the reaction products, any diffusionally unstable upward propagating front is stabilized by small buoyancy effects. A diffusionalinstability enhances the buoyant instability of a downward propagating front with there being a very strong interaction between these effects in this case.

Interaction between buoyancy and diffusiondriven instabilities of propagating autocatalytic reaction fronts. II. Nonlinear simulations
View Description Hide DescriptionThe nonlinear dynamics resulting from the interplay between diffusive and buoyancydriven Rayleigh–Taylor (RT) instabilities of autocatalytic traveling fronts are analyzed numerically for fronts ascending or descending in the gravity field and for various values of the relevant parameters, the Rayleigh numbers and of the reactant and autocatalytic product , respectively, and the ratio of the diffusion coefficients of the two key chemical species. The interaction between the coarseningdynamics characteristic of the RT instability and the fixed short wavelength dynamics of the diffusive instability leads in some parameter regimes to complex dynamics dominated by the irregular succession of birth and death of fingers. Large single convective fingers with a tip deformed by the short wavelength diffusive instability are also observed. If is sufficiently small and the RT instability is active, the concentration of the slower diffusing species can be convected to values above its fully reacted concentration. Experimental conditions that would allow the observation of the dynamics predicted here are described.

Physical and chemical effects on crystalline induced by 20 keV protons
View Description Hide DescriptionWe present laboratory studies on radiation chemistry, sputtering, and amorphization of crystalline induced by 20 keV protons at 80 K. We used infrared spectroscopy to identify , , and possibly , measure the fluence dependence of the fraction of crystalline and amorphous and of the production of and destruction of . Furthermore, using complementary techniques, we observe that the sputtering yield depends on fluence due to the buildup of radiation products in the sample. In addition, we find that the effective cross sections for the destruction of hydrogen peroxide and the production of water are very high compared to radiation chemical processes in water even though the fluence dependence of amorphization is nearly the same for the two materials. This result is consistent with a model of fast cooling of a liquid track produced by each projectile ion rather than with the disorder produced by the formation of radiolytic products.

Noncrystalline compact packings of hard spheres of two sizes: Bipyramids and the geometry of common neighbors
View Description Hide DescriptionInsight into the efficient filling of space in systems of binary spheres is explored using bipyramids consisting of tetrahedra sharing a common pair of spheres. Compact packings are sought in bipyramids consisting of larger hard spheres of unit radius and smaller hard spheres of radius . Seventyseven distinct compact bipyramids are found. The number of distinct compact bipyramids increases with the number of constituent tetrahedra. No compact bipyramids are found for and for . A topological instability eliminates compact packings for . Pentagonal bipyramids cover a larger range in than any other compact bipyramids studied.

Dipolar truncation in magicangle spinning NMR recoupling experiments
View Description Hide DescriptionQuantitative solidstate NMR distance measurements in strongly coupled spin systems are often complicated due to the simultaneous presence of multiple noncommuting spin interactions. In the case of zerothorder homonuclear dipolar recoupling experiments, the recoupled dipolar interaction between distant spins is attenuated by the presence of stronger couplings to nearby spins, an effect known as dipolar truncation. In this article, we quantitatively investigate the effect of dipolar truncation on the polarizationtransfer efficiency of various homonuclear recoupling experiments with analytical theory, numerical simulations, and experiments. In particular, using selectively labeled tripeptides, we compare the extent of dipolar truncation in model threespin systems encountered in protein samples produced with uniform and alternating labeling. Our observations indicate that while the extent of dipolar truncation decreases in the absence of directly bonded nuclei, twobond dipolar couplings can generate significant dipolar truncation of small, longrange couplings. Therefore, while alternating labeling alleviates the effects of dipolar truncation, and thus facilitates the application of recoupling experiments to large spin systems, it does not represent a complete solution to this outstanding problem.