Volume 136, Issue 16, 28 April 2012
Index of content:

A molecular understanding of how protein function is related to protein structure requires an ability to understand large conformational changes between multiple states. Unfortunately these states are often separated by high free energy barriers and within a complex energy landscape. This makes it very difficult to reliably connect, for example by allatom molecular dynamics calculations, the states, their energies, and the pathways between them. A major issue needed to improve sampling on the intermediate states is an order parameter – a reduced descriptor for the major subset of degrees of freedom – that can be used to aid sampling for the large conformational change. We present a method to combine information from molecular dynamics using nonlinear time series and dimensionality reduction, in order to quantitatively determine an order parameter connecting two largescale conformationally distinct protein states. This new method suggests an implementation for molecular dynamics calculations that may be used to enhance sampling of intermediate states.
 ARTICLES


Theoretical Methods and Algorithms

Towards the prediction of order parameters from molecular dynamics simulations in proteins
View Description Hide DescriptionA molecular understanding of how protein function is related to protein structure requires an ability to understand large conformational changes between multiple states. Unfortunately these states are often separated by high free energy barriers and within a complex energy landscape. This makes it very difficult to reliably connect, for example by allatom molecular dynamics calculations, the states, their energies, and the pathways between them. A major issue needed to improve sampling on the intermediate states is an order parameter – a reduced descriptor for the major subset of degrees of freedom – that can be used to aid sampling for the large conformational change. We present a method to combine information from molecular dynamics using nonlinear time series and dimensionality reduction, in order to quantitatively determine an order parameter connecting two largescale conformationally distinct protein states. This new method suggests an implementation for molecular dynamics calculations that may be used to enhance sampling of intermediate states.

New accurate reference energies for the G2/97 test set
View Description Hide DescriptionA recently proposed computational protocol is employed to obtain highly accurate atomization energies for the full G2/97 test set, which consists of 148 diverse molecules. This computational protocol is based on the explicitly correlated coupledcluster method with iterative single and double excitations as well as perturbative triple excitations, using quadrupleζ basis sets. Corrections for higher excitations and core/corevalence correlation effects are accounted for in separate calculations. In this manner, suitable reference values are obtained with a mean deviation of −0.75 kJ/mol and a standard deviation of 1.06 kJ/mol with respect to the active thermochemical tables. Often, in the literature, new approximate methods (e.g., in the area of density functional theory) are compared to, or fitted to, experimental heats of formation of the G2/97 test set. We propose to use our atomization energies for this purpose because they are more accurate on average.

Bennett's acceptance ratio and histogram analysis methods enhanced by umbrella sampling along a reaction coordinate in configurational space
View Description Hide DescriptionFree energy perturbation, a method for computing the free energy difference between two states, is often combined with nonBoltzmann biased sampling techniques in order to accelerate the convergence of free energy calculations. Here we present a new extension of the Bennett acceptance ratio (BAR) method by combining it with umbrella sampling (US) along a reaction coordinate in configurational space. In this approach, which we call Bennett acceptance ratio with umbrella sampling (BARUS), the conditional histogram of energy difference (a mapping of the 3Ndimensional configurational space via a reaction coordinate onto 1D energy difference space) is weighted for marginalization with the associated population density along a reaction coordinate computed by US. This procedure produces marginal histograms of energy difference, from forward and backward simulations, with higher overlap in energy difference space, rendering free energy difference estimations using BAR statistically more reliable. In addition to BARUS, two histogram analysis methods, termed Bennett overlapping histograms with US (BOHUS) and BennettHummer (linear) least square with US (BHLSUS), are employed as consistency and convergence checks for free energy difference estimation by BARUS. The proposed methods (BARUS, BOHUS, and BHLSUS) are applied to a 1dimensional asymmetric model potential, as has been used previously to test free energy calculations from nonequilibrium processes. We then consider the more stringent test of a 1dimensional strongly (but linearly) shifted harmonic oscillator, which exhibits no overlap between two states when sampled using unbiased Brownian dynamics. We find that the efficiency of the proposed methods is enhanced over the original Bennett's methods (BAR, BOH, and BHLS) through fast uniform sampling of energy difference space via US in configurational space. We apply the proposed methods to the calculation of the electrostatic contribution to the absolute solvation free energy (excess chemical potential) of water. We then address the controversial issue of ion selectivity in the K^{+}ion channel, KcsA. We have calculated the relative binding affinity of K^{+} over Na^{+} within a binding site of the KcsA channel for which different, though adjacent, K^{+} and Na^{+} configurations exist, ideally suited to these USenhanced methods. Our studies demonstrate that the significant improvements in free energy calculations obtained using the proposed methods can have serious consequences for elucidating biological mechanisms and for the interpretation of experimental data.

Inactive excitations in Mukherjee's statespecific multireference coupled cluster theory treated with internal contraction: Development and applications
View Description Hide DescriptionOne generic difficulty of most statespecific manybody formalisms using the JeziorskiMonkhorst ansatz: ψ = ∑_{μ}exp (T ^{μ})ϕ_{μ}⟩c _{μ} for the waveoperators is the large number of redundant cluster amplitudes. The number of cluster amplitudes up to a given rank is many more in number compared to the dimension of the Hilbert Space spanned by the virtual functions of up to the same rank of excitations. At the same time, all inactive excitations – though linearly independent – are far too numerous. It is well known from the success of the contracted multireference configuration interaction (MRCI(SD)) that, at least for the inactive double excitations, their model space dependence (μdependence) is weak. Considerable simplifications can thus be obtained by using a partially internally contracted description, which uses the physically appealing approximation of taking the inactive excitations T _{ i } to be independent of the model space labels (μindependent). We propose and implement in this paper such a formalism with internal contractions for inactive excitations (ICI) within Mukherjee's statespecific multireference coupled clustertheory (SSMRCC) framework (referred to from now on as the ICISSMRCC). To the extent the μindependence of T _{ i } is valid, we expect the ICISSMRCC to retain the conceptual advantages of sizeextensivity yet using a drastically reduced number of cluster amplitudes without sacrificing accuracy. Moreover, greater coupling is achieved between the virtual functions reached by inactive excitations as a result of the internal contraction while retaining the original coupling term for the μdependent excitations akin to the parent theory. Another major advantage of the ICISSMRCC, unlike the other analogous internally contracted theories, such as ICMRCISD, CASPT2, or MRMP2, is that it can use relaxed coefficients for the model functions. However, at the same time it employs projection manifolds for the virtuals obtained from inactive n holen particle (nhnp) excitations on the entire reference function containing relaxed model space coefficients. The performance of the method has been assessed by applying it to compute the potential energy surfaces of the prototypical H_{4}; to the torsional potential energy barrier for the cistrans isomerism in C_{2}H_{4} as well as that of N_{2}H_{2}, automerization of cyclobutadiene, single point energy calculation of CH_{2}, SiH_{2}, and comparing them against the SSMRCC results, benchmark full CI results, wherever available and those from the allied MR formalisms. Our findings are very much reminiscent of the experience gained from the ICMRCISD method.

Analysis of electronpositron wavefunctions in the nuclearelectronic orbital framework
View Description Hide DescriptionThe nuclearelectronic orbital explicitly correlated HartreeFock (NEOXCHF) approach is extended and applied to the positronic systems PsH, LiPs, and e^{+}LiH. In this implementation, all electrons and positrons are treated quantum mechanically, and all nuclei are treated classically. This approach utilizes molecular orbital techniques with Gaussian basis sets for the electrons and positrons and includes electronpositroncorrelation with explicitly correlated Gaussiantype geminal functions. An efficient strategy is developed to reduce the number of variational parameters in the NEOXCHF calculations. The annihilation rates, electron and positron densities, and electronpositron contact densities are compared to available results from higherlevel calculations. Our analysis illustrates that the NEOXCHF method produces qualitative to semiquantitative results for these properties at a relatively low computational cost by treating only the essential electronpositroncorrelation explicitly. The NEOHF method, which does not include explicit correlation and therefore is extremely efficient, is found to provide qualitatively accurate electronpositron contact densities for the e^{+}LiH system but not for the LiPs system. Thus, the utility of the NEOHF method for determining where annihilation occurs is system dependent and not generally reliable. The NEOXCHF method, however, provides a computationally practical and reliable approach for determining where annihilation will occur in positronic systems.

Density functional resonance theory: Complex density functions, convergence, orbital energies, and functionals
View Description Hide DescriptionAspects of density functional resonance theory (DFRT) [D. L. Whitenack and A. Wasserman, Phys. Rev. Lett.107, 163002 (2011)], a recently developed complexscaled version of groundstatedensity functional theory(DFT), are studied in detail. The asymptotic behavior of the complex density function is related to the complex resonance energy and system's threshold energy, and the function's local oscillatory behavior is connected with preferential directions of electron decay. Practical considerations for implementation of the theory are addressed including sensitivity to the complexscaling parameter, θ. In KohnSham DFRT, it is shown that almost all θdependence in the calculated energies and lifetimes can be extinguished via use of a proper basis set or fine grid. The highest occupied KohnSham orbital energy and lifetime are related to physical affinity and width, and the threshold energy of the KohnSham system is shown to be equal to the threshold energy of the interacting system shifted by a welldefined functional. Finally, various complexscaling conditions are derived which relate the functionals of groundstateDFT to those of DFRT via proper scaling factors and a nonHermitian couplingconstant system.

Hybrid finite element and Brownian dynamics method for diffusioncontrolled reactions
View Description Hide DescriptionDiffusion is often the rate determining step in many biological processes. Currently, the two main computational methods for studying diffusion are stochastic methods, such as Brownian dynamics, and continuum methods, such as the finite element method. This paper proposes a new hybrid diffusion method that couples the strengths of each of these two methods. The method is derived for a general multidimensional system, and is presented using a basic test case for 1D linear and radially symmetric diffusion systems.

Towards constructing multibit binary adder based on BelousovZhabotinsky reaction
View Description Hide DescriptionIt has been proposed that the spatial excitable media can perform a wide range of computational operations, from image processing, to path planning, to logical and arithmetic computations. The realizations in the field of chemical logical and arithmetic computations are mainly concerned with single simple logical functions in experiments. In this study, based on BelousovZhabotinsky reaction, we performed simulations toward the realization of a more complex operation, the binary adder. Combining with some of the existing functional structures that have been verified experimentally, we designed a planar geometrical binary adder chemical device. Through numerical simulations, we first demonstrated that the device can implement the function of a singlebit full binary adder. Then we show that the binary adder units can be further extended in plane, and coupled together to realize a twobit, or even multibit binary adder. The realization of chemical adders can guide the constructions of other sophisticated arithmetic functions, ultimately leading to the implementation of chemical computer and other intelligent systems.

Projected Hartree–Fock theory
View Description Hide DescriptionProjected Hartree–Fock (PHF) theory has a long history in quantum chemistry. PHF is here understood as the variational determination of an Nelectron broken symmetry Slater determinant that minimizes the energy of a projected state with the correct quantum numbers. The method was actively pursued for several decades but seems to have been abandoned. We here derive and implement a “variation after projection” PHF theory using techniques different from those previously employed in quantum chemistry. Our PHF methodology has modest meanfield computational cost, yields relatively simple expressions, can be applied to both collinear and noncollinear spin cases, and can be used in conjunction with deliberate symmetry breaking and restoration of other molecular symmetries like complex conjugation and point group. We present several benchmark applications to dissociation curves and singlettriplet energy splittings, showing that the resulting PHF wavefunctions are of high quality multireference character. We also provide numerical evidence that in the thermodynamic limit, the energy in PHF is not lower than that of brokensymmetry HF, a simple consequence of the lack of size consistency and extensivity of PHF.

On the existence of a natural common gaugeorigin for the calculation of magnetic properties of atoms and molecules via gaugeless basis sets
View Description Hide DescriptionIt is proven that, within the conventional approach using a common origin and gaugeless basis sets for the calculation of atomic magnetizability and Larmor current density induced by an external magnetic field, the natural gauge origin coincides with the nucleus. Recipes for defining an optimal gauge origin for the calculation of magnetizability and magnetic shielding at the nuclei of a molecule are given. Within the common origin approach, the paramagnetic contributions to the components of magnetic tensors of a molecule are represented by a minimum number of nonvanishing parameters if the gauge origin is chosen at a point characterized by the total molecular symmetry, e.g., the center of electronic charge for magnetizabilities. It is shown that total values of diagonal components of the magnetic shieldingtensor at a nucleus I in a molecule, as well as separate diamagnetic and paramagnetic contributions, calculated via the common origin method, are origin independent for a number of local point group symmetries.The diagonal components (and the average value) of depend on the gauge origin only for nuclear site symmetries C _{1}, C _{ s }, C _{ n }, C _{ nv }, n = 2, 3…. Grouptheoretical methods show interesting features, e.g., for S _{4} local symmetry, in a coordinate transformation, the paramagnetic contribution to the zz component and to the trace of the shielding tensor is origin independent, whereas the xx and yy components mix into one another, in such a way that their sum remains constant.

Fast and spectrally accurate Ewald summation for 2periodic electrostatic systems
View Description Hide DescriptionA new method for Ewald summation in planar/slablike geometry, i.e., systems where periodicity applies in two dimensions and the last dimension is “free” (2P), is presented. We employ a spectral representation in terms of both Fourier series and integrals. This allows us to concisely derive both the 2P Ewald sum and a fast particle mesh Ewald (PME)type method suitable for largescale computations. The primary results are: (i) close and illuminating connections between the 2P problem and the standard Ewald sum and associated fast methods for full periodicity; (ii) a fast, O(N log N), and spectrally accurate PMEtype method for the 2P kspace Ewald sum that uses vastly less memory than traditional PME methods; (iii) errors that decouple, such that parameter selection is simplified. We give analytical and numerical results to support this.

A new model of chemical bonding in ionic melts
View Description Hide DescriptionWe developed a new physical model to predict macroscopic properties of inorganic molten systems using a realistic description of interatomic interactions. Unlike the conventional approach, which tends to overestimate viscosity by several times, our systems consist of a set of ions with an admixture of neutral atoms. The neutral atom subsystem is a consequence of the covalent/ionic state reduction, occurring in the liquid phase. Comparison of the calculated macroscopic properties (shear viscosity and selfdiffusion constants) with the experiment demonstrates good performance of our model. The presented approach is inspired by a significant degree of covalent interaction between the alkali and chlorine atoms, predicted by the coupled cluster theory.

Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Anisotropic hot electron emission from fullerenes
View Description Hide DescriptionPhotoelectron spectra for fullerenes C_{60} and C_{70} ionized using 800 nm laser pulses with pulse durations from 120 to 1000 fs show thermal electron kinetic energy distributions but they also exhibit angular anisotropy with respect to the laser light polarization. The effective temperature of electrons, measured along the laser polarization direction, is significantly higher than in the perpendicular direction. We explain this observation by considering that the emission of the thermal electrons is uncorrelated with the phase of the laser pulse, unlike directly ionized electrons, and, depending on the time of emission, they may experience an additional “kick” from the vector potential of the laser field when they are emitted from the molecule.

Will water act as a photocatalyst for cluster phase chemical reactions? Vibrational overtoneinduced dehydration reaction of methanediol
View Description Hide DescriptionThe possibility of water catalysis in the vibrational overtoneinduced dehydration reaction of methanediol is investigated using ab initio dynamical simulations of small methanediolwater clusters. Quantum chemistry calculations employing clusters with one or two water molecules reveal that the barrier to dehydration is lowered by over 20 kcal/mol because of hydrogenbonding at the transition state. Nevertheless, the simulations of the reaction dynamics following OHstretch excitation show little catalytic effect of water and, in some cases, even show an anticatalytic effect. The quantum yield for the dehydration reaction exhibits a delayed threshold effect where reaction does not occur until the photonenergy is far above the barrier energy. Unlike thermally induced reactions, it is argued that competition between reaction and the irreversible dissipation of photonenergy may be expected to raise the dynamical threshold for the reaction above the transition state energy. It is concluded that quantum chemistry calculations showing barrier lowering are not sufficient to infer water catalysis in photochemical reactions, which instead require dynamical modeling.

The lowestlying electronic singlet and triplet potential energy surfaces for the HNO–NOH system: Energetics, unimolecular rate constants, tunneling and kinetic isotope effects for the isomerization and dissociation reactions
View Description Hide DescriptionThe lowestlying electronic singlet and triplet potential energy surfaces (PES) for the HNO–NOH system have been investigated employing high level ab initio quantum chemical methods. The reaction energies and barriers have been predicted for two isomerization and four dissociationreactions. Total energies are extrapolated to the complete basis set limit applying focal point analyses. Anharmonic zeropoint vibrational energies, diagonal BornOppenheimer corrections, relativistic effects, and core correlation corrections are also taken into account. On the singlet PES, the ^{1}HNO ^{1}NOH endothermicity including all corrections is predicted to be 42.23 ± 0.2 kcal mol^{−1}. For the barrierless decomposition of ^{1}HNO to H + NO, the dissociation energy is estimated to be 47.48 ± 0.2 kcal mol^{−1}. For ^{1}NOH H + NO, the reaction endothermicity and barrier are 5.25 ± 0.2 and 7.88 ± 0.2 kcal mol^{−1}. On the triplet PES the reaction energy and barrier including all corrections are predicted to be 7.73 ± 0.2 and 39.31 ± 0.2 kcal mol^{−1} for the isomerizationreaction^{3}HNO ^{3}NOH. For the triplet dissociationreaction (to H + NO) the corresponding results are 29.03 ± 0.2 and 32.41 ± 0.2 kcal mol^{−1}. Analogous results are 21.30 ± 0.2 and 33.67 ± 0.2 kcal mol^{−1} for the dissociationreaction of ^{3}NOH (to H + NO). Unimolecular rate constants for the isomerization and dissociationreactions were obtained utilizing kinetic modeling methods. The tunneling and kinetic isotope effects are also investigated for these reactions. The adiabatic singlet–triplet energy splittings are predicted to be 18.45 ± 0.2 and 16.05 ± 0.2 kcal mol^{−1} for HNO and NOH, respectively. Kinetic analyses based on solution of simultaneous firstorder ordinarydifferential rate equations demonstrate that the singlet NOH molecule will be difficult to prepare at room temperature, while the triplet NOH molecule is viable with respect to isomerization and dissociationreactions up to 400 K. Hence, our theoretical findings clearly explain why ^{1}NOH has not yet been observed experimentally.

Nanosecond simulations of the dynamics of C_{60} excited by intense nearinfrared laser pulses: Impulsive Raman excitation, rearrangement, and fragmentation
View Description Hide DescriptionImpulsive Raman excitation of C_{60} by single or double pulses of nearinfrared wavelength λ = 1800 nm was investigated by using a timedependent adiabatic state approach combined with the density functional theory method. We confirmed that the vibrational energy stored in a Raman active mode of C_{60} is maximized when T _{p} ∼ T _{vib}/2 in the case of a single pulse, where T _{p} is the pulse length and T _{vib} is the vibrational period of the mode. In the case of a double pulse, mode selective excitation can be achieved by adjusting the pulse interval τ. The energy of a Raman active mode is maximized if τ is chosen to equal an integer multiple of T _{vib} and it is minimized if τ is equal to a halfinteger multiple of T _{vib}. We also investigated the subsequent picosecond or nanosecond dynamics of StoneWales rearrangement (SWR) and fragmentation by using the densityfunctional based tightbinding semiempirical method. We present how SWRs are caused by the flow of vibrational kinetic energy on the carbonbond network of C_{60}. In the case where the h_{g}(1) prolateoblate mode is initially excited, the number of SWRs before fragmentation is larger than in the case of a_{g}(1) mode excitation for the same excess vibrational energy. Fragmentation by C_{2} ejection C_{60} → C_{58} + C_{2} is found to occur from strained, fused pentagon/pentagon defects produced by a preceding SWR, which confirms the earliest mechanistic speculations of Smalley et al. [J. Chem. Phys.88, 220 (1988)]. The fragmentation rate of C_{2} ejection in the case of h_{g}(1) mode excitation does not follow a statistical description as employed for instance in the RiceRamspergerKassel (RRK) theory, whereas the rate for a_{g}(1) mode excitation does follow the prediction by RRK. We also found for the h_{g}(1) mode excitation that the nonstatistical nature affects the distribution of barycentric velocities of fragments C_{58} and C_{2}. This result suggests that it is possible to control rearrangement and subsequent bond breaking in a “nonstatistical” way by initial selective mode excitation.

Scattering of nitrogen molecules by silver atoms
View Description Hide DescriptionWe present a quantal study of the rotationally elastic and inelastic scattering of Ag and N_{2}, with the nitrogen molecule treated as a rigid rotor. The twodimensional potential energy surface of the AgN_{2} complex is obtained ab initio by means of the spin unrestricted coupledcluster method with single, double, and perturbative triple excitations. The global minimum is found to be located at an internuclear distance of 8.13 a _{0} and an angle of 127.2°. The longrange part of the potential is constructed from the dynamic electric dipole polarizabilities of Ag and N_{2}. Elastic, excitation, and relaxation cross sections and rates are calculated for energies between 0.1 and 5000 cm^{−1}. The momentum transfer cross sections and rates are also computed. Finally, we compare the cross sections for Ag–N_{2} and Na–N_{2} to explore the possibility of using silver instead of sodium in experimental tests.

Depolarization of rotational angular momentum in CN(A^{2}Π, v = 4) + Ar collisions
View Description Hide DescriptionAngular momentum depolarization and population transfer in CN(A^{2}Π, v = 4, j, F _{1} e) + Ar collisions have been investigated both experimentally and theoretically. Groundstate CN(X^{2}Σ^{+}) molecules were generated by pulsed 266nm laser photolysis of ICN in a thermal (nominally 298 K) bath of the Ar collision partner at a range of pressures. The translationally thermalized CN(X) radicals were optically pumped to selected unique CN(A^{2}Π, v = 4, j = 2.5, 3.5, 6.5, 11.5, 13.5, and 18.5, F _{1} e) levels on the AX (4,0) band by a pulsed tunable dye laser. The prepared level was monitored in a collinear geometry by cw frequencymodulated(FM) spectroscopy in stimulated emission on the CN(AX) (4,2) band. The FM lineshapes for co and counterrotating circular pump and probe polarizations were analyzed to extract the time dependence of the population and (to a good approximation) orientation (tensor rank K = 1 polarization). The corresponding parallel and perpendicular linear polarizations yielded population and alignment (K = 2). The combined population and polarizationmeasurements at each Ar pressure were fitted to a 3level kinetic model, the minimum complexity necessary to reproduce the qualitative features of the data. Rate constants were extracted for the total loss of population and of elastic depolarization of ranks K = 1 and 2. Elastic depolarization is concluded to be a relatively minor process in this system. Complementary full quantum scattering (QS) calculations were carried out on the best previous and a new set of ab initio potential energy surfaces for CN(A)–Ar. Collisionenergydependent elastictensor and depolarization cross sections for ranks K = 1 and 2 were computed for CN(A^{2}Π, v = 4, j = 1.5–10.5, F _{1} e) rotational/finestructure levels. In addition, integral cross sections for rotationally inelastic transitions out of these levels were computed and summed to yield total population transfer cross sections. These quantities were integrated over a thermal collisionenergy distribution to yield the corresponding rate constants. A complete masterequation simulation using the QS results for the selected initial level j = 6.5 gave close, but not perfect, agreement with the nearexponential experimental population decays, and successfully reproduced the observed multimodal character of the polarization decays. On average, the QS population removal rate constants were consistently 10%–15% higher than those derived from the 3level fit to the experimental data. The QS and experimental depolarization rate constants agree within the experimental uncertainties at low j, but the QS predictions decline more rapidly with j than the observations. In addition to providing a sensitive test of the achievable level of agreement between stateofthe art experiment and theory, these results highlight the importance of multiple collisions in contributing to phenomenological depolarization using any method sensitive to both polarized and unpolarized molecules in the observed level.

Gasphase calorimetry of protonated water clusters
View Description Hide DescriptionProtonated water clusters with 60 to 79 molecules have been studied by nanocalorimetry. The technique is based on multicollision excitations of the accelerated clusters with helium. The caloric curves indicate transitions that resemble those of water clusters charged by an excess electron, but the transition temperatures of the protonated clusters are higher.

Dissociative electron attachment resonances in ammonia: A velocity slice imaging based study
View Description Hide DescriptionNegative ion resonance states of ammonia are accessed upon capture of electrons with energy 5.5 eV and 10.5 eV, respectively. These resonance states dissociate to produce H^{−} and fragment anions via different fragmentation channels. Using the velocity slice imaging technique, we measured the angular and kinetic energy distribution of the fragment H^{−} and anions with full 0–2π angular coverage across the two resonances. The scattered H^{−} ions at both resonances show variation in their angular distribution as a function of the kinetic energy indicating geometric rearrangement of ion due to internal excitations and differ from the equilibrium geometry of the neutral molecule. The second resonance at 10.5 eV shows strong forwardbackward asymmetry in the scattering of H^{−} and fragment ions. Based on the angular distributions of the H^{−} ions, the symmetry of the resonances at 5.5 eV and 10 .5 eV are determined to be A_{1} and E, respectively, within C_{3v } geometry.
