Volume 135, Issue 12, 28 September 2011

A first principles quantum mechanical calculation of the vibrational energy levels and transition frequencies associated with protons in stoichiometric LiNbO_{3}single crystal has been carried out. The hydrogen contaminated crystal has been approximated by a model one obtains by translating a supercell, i.e., a cluster of LiNbO_{3} unit cells containing a single H^{+} and a Li^{+} vacancy. Based on the supercell model an approximate Hamiltonian operator describing vibrations of the proton sublattice embedded in the host crystal has been derived. It is further simplified to a sum of uncoupled Hamiltonian operators corresponding to different wave vectors (s) and each describing vibrations of a quasiparticle (quasiproton). The three dimensional (3D) Hamiltonian operator of has been employed to calculate vibrational levels and transition frequencies. The potential energy surface (PES) entering this Hamiltonian operator has been calculated point wise on a large set of grid points by using density functional theory, and an analytical approximation to the PES has been constructed by nonparametric approximation. Then, the nuclear motion Schrödinger equation has been solved by employing the method of discrete variable representation. It has been found that the (quasi)H^{+} vibrates in a strongly anharmonic PES. Its vibrations can be described approximately as a stretching, and two orthogonal bending vibrations. The theoretically calculated transition frequencies agree within 1% with those experimentally determined, and they have allowed the assignment of one of the hitherto unassigned bands as a combination of the stretching and the bending of lower fundamental frequency.
 COMMUNICATIONS


Communication: Strong excitonic and vibronic effects determine the optical properties of Li_{2}O_{2}
View Description Hide DescriptionThe band structure and optical absorptionspectrum of lithium peroxide (Li_{2}O_{2}) is calculated from firstprinciples using the G_{0}W_{0} approximation and the BetheSalpeter equation, respectively. A strongly localized (Frenkel type) exciton corresponding to the π^{*}→σ^{*} transition on the O_{2} ^{−2} peroxide ion gives rise to a narrow absorption peak around 1.2 eV below the calculated bandgap of 4.8 eV. In the excited state, the internal O_{2} ^{−2} bond is significantly weakened due to the population of the σ^{*} orbital. As a consequence, the bond is elongated by almost 0.5 Å leading to an extreme Stokes shift of 2.6 eV. The strong vibronic coupling entails significant broadening of the excitonic absorption peak in good agreement with diffuse reflectance data on Li_{2}O_{2} which shows a rather featureless spectrum with an absorption onset around 3.0 eV. These results should be important for understanding the origin of the high potential losses and low current densities, which are presently limiting the performance of Liair batteries.

Communication: Drift velocity of Brownian particle in a periodically tapered tube induced by a timeperiodic force with zero mean: Dependence on the force period
View Description Hide DescriptionWe study the drift of a Brownian particle in a periodically tapered tube, induced by a longitudinal timeperiodic force of amplitude F that alternates in sign every halfperiod. The focus is on the velocity dependence on the force period, which is usually considered not tractable analytically. For large F we derive an analytical solution that gives the velocity as a function of the amplitude and the period of the force as well as the geometric parameters of the tube. The solution shows how the velocity decreases from its maximum value to zero as the force period decreases from infinity (adiabatic regime) to zero. Our analytical results are in excellent agreement with those obtained from 3D Brownian dynamics simulations.

 ARTICLES

 Theoretical Methods and Algorithms

Mayersampling Monte Carlo calculations of uniquely flexible contributions to virial coefficients
View Description Hide DescriptionWe present methods for computing contributions to the virial coefficients uniquely associated with molecular flexibility, and we demonstrate their use with application to the third, fourth, and fifth virial coefficients of unitedatom models of linear alkanes and methanol belonging to the suite of transferrable potentials for phase equilibria (TraPPEUA). We find that these uniquely flexible contributions are more difficult to compute than the remainder of the coefficient, especially for the conditions at which they appear to be most important. The significance of these contributions relative to the full virial coefficient grows with the number of sites (the size of the molecule), the number of molecules, and, to a certain extent, the temperature. The nature of the sitesite interactions is of great importance: the significance of the uniquely flexible contribution at third and fourth order is orders of magnitude larger for TraPPEUA methanol, which has Coulombic interactions, than for TraPPEUA propane, which does not, even though both models have three sites per molecule and comparable bending potentials. While the uniquely flexible contribution of TraPPEUA propane has a negligible impact on its thirdorder virialequationofstate estimate of the critical point, the uniquely flexible contribution of TraPPEUA methanol increases this estimate of its critical pressure by about 5%.

Hierarchical expansion of the kinetic energy operator in curvilinear coordinates for the vibrational selfconsistent field method
View Description Hide DescriptionA new hierarchical expansion of the kinetic energy operator in curvilinear coordinates is presented and modified vibrational selfconsistent field (VSCF) equations are derived including all kinematic effects within the mean field approximation. The new concept for the kinetic energy operator is based on manybody expansions for all matrix elements and its determinant. As a test application VSCF computations were performed on the H_{2}O_{2} molecule using an analytic potential (PCPSDE) and different hierarchical approximations for the kinetic energy operator. The results indicate that coordinatedependent reduced masses account for the largest part of the kinetic energy. Neither kinematic couplings nor derivatives of the matrix nor its determinant had significant effects on the VSCF energies. Only the zeropoint value of the pseudopotential yields an offset to absolute energies which, however, is irrelevant for spectroscopic problems.

A generalized mean field theory of coarsegraining
View Description Hide DescriptionA general mean field theory is presented for the construction of equilibrium coarsegrained models. Inverse methods that reconstruct microscopic models from low resolution experimental data can be derived as particular implementations of this theory. The theory also applies to the opposite problem of reduction, where relevant information is extracted from available equilibrium ensemble data. Additionally, a complementary approach is presented and problems of representability in coarsegrained modeling analyzed using information theoretic arguments. These problems are central to the construction of coarsegrained representations of complex systems, and commonly used coarsegraining methods and variational principles for coarsegraining are derived as particular cases of the general theory.

Marginal states in a cubic autocatalytic reaction
View Description Hide DescriptionMarginal steady state belongs to a special class of states in nonlinear dynamics. To realize this state we consider a cubic autocatalytic reactionA + 2B → 3B in a continuousstirredtankreactor, where the flow rate of the reactant A can be controlled to manipulate the dynamical behavior of the open system. We demonstrate that when the flow rate is weakly noisy the autocatalytic reaction admits of a steady state which is marginal in nature and is surrounded by infinite number of periodic trajectories. When the uncatalyzed reactionA → B is included in the reaction scheme, there exists a marginal steady state which is a critical state corresponding to the point of transition between the flow branch and the equilibrium branch, similar to gasliquidcritical point of transition. This state loses its stability in the weak noise limit.

Bond energy analysis revisited and designed toward a rigorous methodology
View Description Hide DescriptionThe present study theoretically revisits and numerically assesses twobody energy decomposition schemes including a newly proposed one. The new decomposition scheme is designed to make the equilibrium bond distance equivalent with the minimum point of bond energies. Although the other decomposition schemes generally predict the wrong order of the C–C bond strengths of C_{2}H_{2}, C_{2}H_{4}, and C_{2}H_{6}, the new decomposition scheme is capable of reproducing the C–C bond strengths. Numerical assessment on a training set of molecules demonstrates that the present scheme exhibits a stronger correlation with bonddissociation energies than the other decomposition schemes do, which suggests that the new decomposition scheme is a reliable and powerful analysis methodology.

Monte Carlo and eventdriven dynamics of Brownian particles with orientational degrees of freedom
View Description Hide DescriptionRecently, a simple scaling argument was introduced that allows us to map, with some precautions, Brownian and Monte Carlodynamics for spherical particles. Here, we extend the scaling to study systems that have orientational degrees of freedom and carefully asses its validity over a wide region of temperature and density. Our work allows us to devise a Brownian Monte Carlo algorithm that produces, to a good approximation, physically meaningful trajectories with a minimum programming effort, although at the expense of some sampling efficiency.

Mathematical analysis of the boundaryintegral based electrostatics estimation approximation for molecular solvation: Exact results for spherical inclusions
View Description Hide DescriptionWe analyze the mathematically rigorous BIBEE (boundaryintegral based electrostatics estimation) approximation of the mixeddielectric continuum model of molecular electrostatics, using the analytically solvable case of a spherical solute containing an arbitrary charge distribution. Our analysis, which builds on Kirkwood's solution using spherical harmonics, clarifies important aspects of the approximation and its relationship to generalized Born models. First, our results suggest a new perspective for analyzing fast electrostaticmodels: the separation of variables between material properties (the dielectric constants) and geometry (the solute dielectric boundary and charge distribution). Second, we find that the eigenfunctions of the reactionpotential operator are exactly preserved in the BIBEE model for the sphere, which supports the use of this approximation for analyzing chargecharge interactions in molecular binding. Third, a comparison of BIBEE to the recent GBε theory suggests a modified BIBEE model capable of predicting electrostatic solvation free energies to within 4% of a full numerical Poisson calculation. This modified model leads to a projectionframework understanding of BIBEE and suggests opportunities for future improvements.

Projected quasiparticle theory for molecular electronic structure
View Description Hide DescriptionWe derive and implement symmetryprojected HartreeFockBogoliubov (HFB) equations and apply them to the molecular electronic structure problem. All symmetries (particle number, spin, spatial, and complex conjugation) are deliberately broken and restored in a selfconsistent variationafterprojection approach. We show that the resulting method yields a comprehensive blackbox treatment of static correlations with effective oneelectron (meanfield) computational cost. The ensuing wave function is of multireference character and permeates the entire Hilbert space of the problem. The energy expression is different from regular HFB theory but remains a functional of an independent quasiparticle density matrix. All reduced density matrices are expressible as an integration of transition density matrices over a gauge grid. We present several proofofprinciple examples demonstrating the compelling power of projected quasiparticletheory for quantum chemistry.

Instanton calculations of tunneling splittings for water dimer and trimer
View Description Hide DescriptionWe investigate the ability of the recently developed ringpolymer instanton (RPI) method [J. O. Richardson and S. C. Althorpe, J. Chem. Phys.134, 054109 (2011)]10.1063/1.3530589 to treat tunneling in water clusters. We show that the RPI method is easy to extend to treat tunneling between more than two minima, using elementary graph theory. Tests of the method on water dimer and trimer yield a set of instanton periodic orbits which correspond to all known tunneling pathways in these systems. Splitting patterns obtained from the orbits are in good overall agreement with experiment. The agreement is closer for the deuterated than for the protonated clusters, almost certainly because the main approximation in the calculations is neglect of anharmonicity perpendicular to the tunneling path. All the calculations were performed on a desktop computer, which suggests that similar calculations will be possible on much larger clusters.

A parallelizable block cellular automaton for the study of diffusion of binary mixtures containing CO_{2} in microporous materials
View Description Hide DescriptionWe applied a method based on a block cellular automaton (BCA) algorithm to the study of diffusion of various binary mixtures adsorbed in a model microporous material, such as zeolite ZK4. Our aim was to test the capability of our model to cope with systems in which more than one species is present, using a set of parameters based on heuristic considerations from the molecular dynamics (MD) results present in the literature. A rigorous methodology for the assignment of suitable adsorption energies and diffusion activation barriers for our BCA has not been developed yet, nonetheless the results were quite interesting at this stage and we obtained a good qualitative agreement with MD data in the literature. The mixtures we investigated contain CO_{2}, which causes the socalled segregationeffect, a strong suppression of selfdiffusivity of coadsorbed species. This effect gives rise to relevant problems in the application of some well established and robust methods, while our model proved to be able to reproduce both the common features and the segregation anomaly in the trends of diffusion.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Ab initio potential energy surface and bound states for the Kr–OCS complex
View Description Hide DescriptionThe first ab initiopotential energy surface of the Kr–OCS complex is developed using the coupledcluster singles and doubles with noniterative inclusion of connected triples [CCSD(T)]. The mixed basis sets, augccpVTZ for the O, C, and S atom, and augccpVQZPP for the Kr atom, with an additional (3s3p2d1f) set of midbond functions are used. A potential model is represented by an analytical function whose parameters are fitted numerically to the single point energies computed at 228 configurations. The potential has a Tshaped global minimum and a local linear minimum. The global minimum occurs at R = 7.146 a _{0}, θ = 105.0° with energy of −270.73 cm^{−1}. Bound state energies up to J = 9 are calculated for three isotopomers ^{82}Kr–OCS, ^{84}Kr–OCS, and ^{86}Kr–OCS. Analysis of the vibrational wavefunctions and energies suggests the complex can exist in two isomeric forms: Tshaped and quasilinear. The calculated transition frequencies and spectroscopic constants of the three isotopomers are in good agreement with the experimental values.

Pulsed discharge jet electronic spectroscopy of the aluminum dicarbide (AlC_{2}) free radical
View Description Hide DescriptionLaserinduced fluorescence and wavelength resolved emission spectra of the ^{2}B_{2}– ^{2}A_{1} band system of the gas phase aluminum dicarbide free radical have been obtained using the pulsed discharge jet technique. The radical was produced by electron bombardment of a precursor mixture of trimethylaluminum in highpressure argon. The three vibrational frequencies of Tshaped AlC_{2} have been determined in both the combining states along with several of the anharmonicity constants. The band has been recorded with high resolution and rotationally analyzed. The spectrum is complicated by partially resolved spinrotation and aluminum hyperfine splittings. Where necessary, we have fixed the spinrotation constants used in the rotational analysis at the values predicted by density functional theory. The derived molecular structures are: (C–C) = 1.271(2) Å, (Al–C) = 1.926(1) Å, θ ^{″}(C–Al–C) = 38.5(2)°, (C–C) = 1.323(2) Å, (Al–C) = 1.934(1) Å, and θ ^{′}(C–Al–C) = 40.0(2)°. Unlike SiC_{2}, aluminum dicarbide shows no spectroscopic evidence of facile isomerization to the linear structure in the ground electronic state.

Physical properties of small water clusters in low and moderate electric fields
View Description Hide DescriptionLikely candidates for the lowest minima of water clusters (H_{2}O)_{N} for N ⩽ 20 interacting with a uniform electric field strength in the range E ⩽ 0.6 V/Å have been identified using basinhopping global optimization. Two waterwater model potentials were considered, namely TIP4P and the polarizable DangChang potential. The two models produce some consistent results but also exhibit significant differences. The cluster internal energy and dipole moment indicate two varieties of topological transition in the structure of the global minimum as the field strength is increased. The first takes place at low field strengths (0.1 V/Å<E < 0.2 V/Å) and reorganizes the hydrogenbonds to orient the water permanent dipoles along the field. The second type of transition occurs at larger field strengths (0.3 V/Å<E < 0.5 V/Å) and corresponds to an extensive structural reorganization, where several hydrogenbonds break as the cluster stretches along the field direction, the larger clusters (N > 10) usually forming helical structures.

Optical purification of a mixture of chiral forms by dimer formation
View Description Hide DescriptionWe introduce a readily executable method for the optical purification of “scalemic” (non 50%50%) mixtures of chiral molecules of opposite handedness (“enantiomers”). The method relies on the formation of two types of dimers, (RR or SS) “homodimers” and (RS) “heterodimers.” The selectivity is linked to the difference in sign recently discovered by us to exist between certain transitiondipole matrix elements of opposite enantiomers. This sign difference results in differences in spectral propensity rules: In homodimers, transitions from the ground state can only take place to inversion symmetricexcited states, while in the heterodimer the transitions are much more likely to proceed to antisymmetricexcited states (although for heterodimers weak transitions to symmetric states might exist). These opposing propensity rules fully explain the observed large differences in the spectra of homodimers vs. heterodimers, which exist despite the almost identical energy levels positions. We illustrate the general concepts by computationally demonstrating the optically induced enantiopurification of scalemic mixtures of the hydropropionic (lactic) acid.

Intramolecular vibrational dynamics in S_{1} pfluorotoluene. I. Direct observation of doorway states
View Description Hide DescriptionPicosecond timeresolved photoelectron spectroscopy is used to investigate intramolecular vibrational redistribution (IVR) following excitation of S_{1} 18a^{1} in pfluorotoluene (pFT) at an internal energy of 845 cm^{−1}, where ν_{18a} is a ring bending vibrational mode. Characteristic oscillations with periods of 8 ps and 5 ps are observed in the photoelectron signal and attributed to coupling between the initially excited zeroorder bright state and two doorway states. Values for the coupling coefficients connecting these three vibrational states have been determined. In addition, an exponential change in photoelectron signal with a lifetime of 17 ps is attributed to weaker couplings with a bath of dark states that play a more significant role during the latter stages of IVR. A tier model has been used to assign the most strongly coupled doorway state to S_{1} 17a^{1} 6a_{2} ^{′}, where ν_{17a} is a CH outofplane vibrational mode and 6a_{2} ^{′} is a methyl torsional level. This assignment signifies that a torsionvibration coupling mechanism mediates the observed dynamics, thus demonstrating the important role played by the methyl torsional mode in accelerating IVR.

Spectroscopy and thermochemistry of a jetcooled openshell polyene: 1,4pentadienyl radical
View Description Hide DescriptionThe 1,4pentadienyl (vinylallyl) radical has been observed for the first time by optical spectroscopy. An excitation spectrum is recorded on m/z 67 by resonant twocolor twophoton ionization spectroscopy. Several bands are observed with the origin transition identified at 19 449 cm^{−1}. The spectrum is assigned by a comparison with ab initio frequencies calculated at the CASPT2/ccpVTZ level of theory, with an accompanying FranckCondon calculation of the excitation spectrum, including Dushinsky mixing. The b 1 and a 2 outer C–C bond torsional modes are calculated to halve in frequency upon electronic excitation, bringing about their appearance in the excitation spectrum. This can be readily understood by considering the torsional sensitivity of the frontier molecular orbital energies. Highlevel quantum chemical calculations of the radical stabilization energy, resulting in a value of nearly 120 kJ mol^{−1}, provide quantitative confirmation that this radical is highly stabilized.

Low energy (0–10 eV) electron driven reactions in the halogenated organic acids CCl_{3}COOH, CClF_{2}COOH, and CF_{3}CHNH_{2}COOH (trifluoroalanine)
View Description Hide DescriptionNegative ion formation following resonant electron attachment to the three title molecules is studied by means of a beam experiment with mass spectrometric detection of the anions. All three molecules exhibit a pronounced resonance in the energy range around 1 eV which decomposes by the loss of a neutral hydrogen atom thereby generating the closed shell anion (M–H)^{−} (or RCOO^{−}), a reaction which is also a common feature in the nonsubstituted organic acids. The two chlorine containing molecules CCl_{3}COOH and CClF_{2}COOH exhibit an additional strong and narrow resonance at very low energy (close to 0 eV) which decomposes by the cleavage of the C–Cl bond with the excess charge finally localised on either of the two fragments Cl^{−} and (M–Cl)^{−}. This reaction is by two to three orders of magnitude more effective than hydrogen loss. Apart from these direct bond cleavages (C–Cl, O–H) resonant attachment of subexcitation electrons trigger additional remarkably complex unimolecular decompositions leading, e.g., to the formation of the bihalide ions ClHCl^{−} and ClHF^{−} from CCl_{3}COOH and CClF_{2}COOH, respectively, or the loss of a neutral CF_{2} unit from trifluoroalanine thereby generating the fluoroglycine radical anion. These reactions require substantial rearrangement in the transitory negative ion, i.e., the cleavage of different bonds and formation of new bonds. F^{−} from both chlorodifluoroacetic acid and trifluoroalanine is formed at comparatively low intensity (more than three orders of magnitude less than Cl^{−} from the chlorine containing molecules) and predominantly within a broad resonant feature around 7–8 eV characterised as core excited resonance.

Interplay between charge and vibrational delocalization in cationic helium clusters
View Description Hide DescriptionThe stable structures and low temperature thermodynamics of cationic helium clusters are investigated theoretically using a diatomicsinmolecules model for the potential energy surfaces and a computational framework in which both electronic and nuclear degrees of freedom are treated on a quantum mechanical footing. While the charge is generally carried by two atoms, vibrational delocalization significantly spreads out the charge over multiple isomers for clusters containing five or more helium atoms. Our calculations indicate that large clusters are essentially fluid with a welldefined solvation shell around the charged core.