Volume 135, Issue 9, 07 September 2011

Lowtemperature neutron scattering spectra of diammonium dodecahydroclosododecaborate [(NH_{4})_{2}B_{12}H_{12}] reveal two NH_{4} ^{+} rotational tunneling peaks (e.g., 18.5 μeV and 37 μeV at 4 K), consistent with the tetrahedral symmetry and environment of the cations. The tunneling peaks persist between 4 K and 40 K. An estimate was made for the tunnel splitting of the first NH_{4} ^{+} librational state from a fit of the observed groundstate tunnel splitting as a function of temperature. At temperatures of 50 K–70 K, classical neutron quasielastic scattering appears to dominate the spectra and is attributed to NH_{4} ^{+} cation jump reorientation about the four C_{3} axes defined by the N–H bonds. A reorientational activation energy of 8.1 ± 0.6 meV (0.79 ± 0.06 kJ/mol) is determined from the behavior of the quasielastic linewidths in this temperature regime. This activation energy is in accord with a change in NH_{4} ^{+} dynamical behavior above 70 K. A lowtemperature inelastic neutron scattering feature at 7.8 meV is assigned to a NH_{4} ^{+} librational mode. At increased temperatures, this feature drops in intensity, having shifted entirely to higher energies by 200 K, suggesting the onset of quasifree NH_{4} ^{+} rotation. This is consistent with neutrondiffractionbased model refinements, which derive very large thermal ellipsoids for the ammoniumion hydrogen atoms at room temperature in the direction of reorientation.
 COMMUNICATIONS


Communication: Probable scenario of the liquid–liquid phase transition of SnI_{4}
View Description Hide DescriptionWe have shown from in situ synchrotron xray diffraction measurements that there are two thermodynamically stable liquid forms of SnI_{4}, depending on the pressure. Based on the liquid–liquidcritical point scenario, our recent measurements suggest that the second critical point, if it exists, may be located in a region close to the point at which the melting curve of the crystalline phase abruptly breaks. This region is, unlike that of water, experimentally accessible with relative ease.

Communication: Theoretical exploration of Au^{+}+H_{2}, D_{2}, and HD reactive collisions
View Description Hide DescriptionA quasiclassical study of the endoergic Au ^{+}(^{1} S) + ) → AuH^{+} (^{2}Σ^{+}) + H(^{2} S) reaction, and isotopic variants, is performed to compare with recent experimental results [F. Li, C. S. Hinton, M. Citir, F. Liu, and P. B. Armentrout, J. Chem. Phys.134, 024310 (2011)]. For this purpose, a new global potential energy surface has been developed based on multireference configuration interaction ab initio calculations. The quasiclassical trajectory results show a very good agreement with the experiments, showing the same trends for the different isotopic variants of the hydrogen molecule. It is also found that the total dissociation into three fragments, Au ^{+}+H+H, is the dominant reaction channel for energies above the H2 dissociation energy. This results from a well in the entrance channel of the potential energy surface, which enhances the probability of H–Au–H insertion.
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 ARTICLES

 Theoretical Methods and Algorithms

Dispersion energy evaluated by using locally projected occupied and excited molecular orbitals for molecular interaction
View Description Hide DescriptionThe dispersion terms are evaluated with the perturbation theory based on the locally projected molecular orbitals. A series of model systems, including some of the S22 set, is examined, and the calculated binding energies are compared with the published results. The basis set dependence is also examined. The dispersion energy correction is evaluated by taking into account the double excitations only of the dispersion type electron configurations and is added to the 3rd order single excitation perturbation energy, which is a good approximation to the counterpoise (CP) corrected HartreeFock (HF) binding energy. The procedure is the approximate “CP corrected HF + D” method. It ensures that the evaluated binding energy is approximately free of the basis set superposition error without the CP procedure. If the augmented basis functions are used, the evaluated binding energies for the predominantly dispersionbound systems, such as rare gas dimers and halogen bonded clusters, agree with those of the reference calculations within 1 kcal mol^{−1} (4 kJ mol^{−1}). The limitation of the present method is also discussed.

A constrained approach to multiscale stochastic simulation of chemically reacting systems
View Description Hide DescriptionStochastic simulation of coupled chemical reactions is often computationally intensive, especially if a chemical system contains reactions occurring on different time scales. In this paper, we introduce a multiscale methodology suitable to address this problem, assuming that the evolution of the slow species in the system is well approximated by a Langevin process. It is based on the conditional stochastic simulation algorithm (CSSA) which samples from the conditional distribution of the suitably defined fast variables, given values for the slow variables. In the constrained multiscale algorithm (CMA) a single realization of the CSSA is then used for each value of the slow variable to approximate the effective drift and diffusion terms, in a similar manner to the constrained meanforce computations in other applications such as molecular dynamics. We then show how using the ensuing FokkerPlanck equation approximation, we can in turn approximate average switching times in stochastic chemical systems.

Accurate predictions of the energetics of silicon compounds using the multireference correlation consistent composite approach
View Description Hide DescriptionTheoretical studies, using the multireference correlation consistent composite approach (MRccCA), have been carried out on the ground and lowest lying spinforbidden excited states of a series of siliconcontaining systems. The MRccCA method is the multireference equivalent of the successful single reference ccCA method that has been shown to produce chemically accurate (within ±1.0 kcal mol^{−1} of reliable, wellestablished experiment) results. The percentage contributions of the SCF configurations to complete active space selfconsistent field wave functions together with the Frobenius norm of the t _{1} vectors and related D _{1} diagnostics of the coupledcluster single double wave function with the ccpVTZ basis set have been utilized to illustrate the multiconfigurational characteristics of the compounds considered. MRccCA incorporates additive terms to account for relativistic effects, atomic spinorbit coupling, scalar relativistic effects, and corevalence correlation. MRccCA has been utilized to predict the atomization energies, enthalpies of formation, and the lowest energy spinforbidden transitions for Si_{ n }X_{ m } (2 ≤ n + m ≥ 3 where n ≠ 0 and X = B, C, N, Al, P), silicon hydrides, and analogous compounds of carbon. The energetics of small silicon aluminides and phosphorides are predicted for the first time.

Secondorder perturbation theory with a density matrix renormalization group selfconsistent field reference function: Theory and application to the study of chromium dimer
View Description Hide DescriptionWe present a secondorder perturbation theory based on a density matrix renormalization group selfconsistent field (DMRGSCF) reference function. The method reproduces the solution of the complete active space with secondorder perturbation theory (CASPT2) when the DMRG reference function is represented by a sufficiently large number of renormalized manybody basis, thereby being named DMRGCASPT2 method. The DMRGSCF is able to describe nondynamical correlation with large active space that is insurmountable to the conventional CASSCF method, while the secondorder perturbation theory provides an efficient description of dynamical correlation effects. The capability of our implementation is demonstrated for an application to the potential energy curve of the chromium dimer, which is one of the most demanding multireference systems that require best electronic structure treatment for nondynamical and dynamical correlation as well as large basis sets. The DMRGCASPT2/ccpwCV5Z calculations were performed with a large (3d doubleshell) active space consisting of 28 orbitals. Our approach using largesize DMRG reference addressed the problems of why the dissociation energy is largely overestimated by CASPT2 with the small active space consisting of 12 orbitals (3d4s), and also is oversensitive to the choice of the zerothorder Hamiltonian.

Longrangecorrected hybrids using a rangeseparated PerdewBurkeErnzerhof functional and random phase approximation correlation
View Description Hide DescriptionWe build on methods combining a shortrange density functional approximation with a longrange random phase approximation [B. G. Janesko, T. M. Henderson, and G. E. Scuseria, J. Chem. Phys.130, 081105 (2009)10.1063/1.3090814] or secondorder screened exchange [J. Paier et al., J. Chem. Phys.132, 094103 (2010)10.1063/1.3317437] by replacing the rangeseparated local density approximation functional with a rangeseparated generalized gradient approximation functional in the short range. We present benchmark results that show a marked improvement in the thermodynamic tests over the previous local density approximationbased methods while retaining those methods’ excellent performance in van der Waals interactions.

Novel numerical method for calculating the pressure tensor in spherical coordinates for molecular systems
View Description Hide DescriptionWe propose a novel method for computing the pressure tensor along the radial axis of a molecular system with spherical symmetry. The proposed method uses the slice averaged pressure to improve the numerical stability and precision significantly. Simplified expressions of the local pressure are derived for a conventional molecular force field including nonbond, bond stretching, angle bending, and torsion interactions; these expressions are advantageous in terms of the computational cost. We also discuss an algorithm to avoid numerical singularity. Finally, the method is successfully applied to three different molecular systems, i.e., a water droplet in oil, a spherical micelle, and a liposome.

The spinpolarized extended Brueckner orbitals
View Description Hide DescriptionConventional natural and Brueckner orbitals (BOs) are rather frequently used for improving active orbital spaces in various configuration interaction (CI) approaches. However, the natural and Brueckner singledeterminant models per se fail to give an adequate picture of highly correlated and quasidegenerate states such as openshell singlet and dissociative states. We suggest the use of the spinpolarized extended BOs formally defining them in the same manner as in Löwdin's spinextended HartreeFock method. Such BO orbitals turn out to be quite flexible and particularly useful for analyzing highly correlated electronic states. It is shown that the extended BOs always exist, unlike the usual unrestricted BOs. We discuss difficulties related to violation of sizeconsistency for spin projected determinant models. The working algorithm is proposed for computing BOs within the full CI and related complete active space methodology. The extended BOs are analyzed in terms of the special densitylike matrices associated with spinup and spindown BO orbitals. From these density matrices, the corresponding spinpolarization diagrams are produced for effectively unpaired (essentially correlated) electrons. We illustrate the approach by calculations on cyclic hydrogen clusters (H4, H6, and H8), certain carbene diradicals and monoradicals, and lowlying excited states. The computations show that the BO spinprojected determinant provides a strong overlap with the multiconfigurational state even for quasidegenerate states and bond breaking processes.

Hybrid coupledcluster and perturbation method for extended systems of onedimensional periodicity
View Description Hide DescriptionA hybrid of the coupledcluster singles and doubles (CCSD) and secondorder Møller–Plesset perturbation (MP2) methods [M. Nooijen, J. Chem. Phys.111, 10815 (1999)10.1063/1.480445;A. D. Bochevarov and C. D. Sherrill, ibid.122, 234110 (2005);A. D. Bochevarov et al., ibid.125, 054109 (2006)] is formulated and implemented for onedimensional periodic extended systems, in which the excitation (T) amplitudes of active bands are determined iteratively by CCSD, while the T amplitudes of mixed active/inactive bands are held fixed at the firstorder Møller–Plesset perturbation values. The occupied and virtual bands near the Fermi level, which can cause instability in MP2 when they are (quasi)degenerate, are selected as active bands to be treated by CCSD, which can, in principle, resist such instability. Two contraction schemes of the T amplitudes (Contractions A and B) are considered. Contraction A is the one proposed for molecules and used also for extended systems because it is efficient for CCSD, but not necessarily so for the hybrid CCSD/MP2. Contraction B is introduced to be more optimally efficient for the hybrid CCSD/MP2 by maximizing the number of intermediate quantities made of the inactive T amplitudes and molecular integrals, which do not vary during CCSD iterations and are computed only once, stored, and reused. In an application to transpolyacetylene, a smooth transition of the results of the hybrid CCSD/MP2 is observed toward those of CCSD and MP2 by increasing and decreasing, respectively, the number of active bands. With the smallest active space, the hybrid CCSD/MP2 with Contractions A and B achieves a speedup by a factor of 360 and 520, respectively, relative to CCSD. When all of the occupied bands and about half of the virtual bands are active, the hybrid CCSD/MP2 can recover 98% of the CCSD correlation energy or half of the difference between CCSD and MP2 at less than a tenth of the usual CCSD cost.

Computer simulations of thermoshrinking polyelectrolyte gels
View Description Hide DescriptionIn this work, thermoresponsive polyelectrolytegels have been simulated using polymernetworks of diamondlike topology in the framework of the primitive model. Monte Carlo simulations were performed in the canonical ensemble and a wide collection of situations has been systematically analysed. Unlike previous studies, our model includes an effective solventmediated potential for the hydrophobic interaction between nonbonded polymer beads. This model predicts that the strength of the attractive hydrophobic forces increases with temperature, which plays a key role in the explanation of the thermoshrinking behaviour of many real gels. Although this hydrophobic model is simple (and it could overestimate the interactions at high temperature), our simulation results qualitatively reproduce several features of the swelling behaviour of real gels and microgels reported by experimentalists. This agreement suggests that the effective solventmediated polymerpolymer interaction used here is a good candidate for hydrophobic interaction. In addition, our work shows that the functional form of the hydrophobic interaction has a profound influence on the swelling behaviour of polyelectrolytegels. In particular, systems with weak hydrophobic forces exhibit discontinuous volume changes, whereas gels with strong hydrophobic forces do not show hallmarks of phase transitions, even for highly charged polyelectrolyte chains.
 Advanced Experimental Techniques

A method for the determination of speeddependent semiclassical vector correlations from sliced image anisotropies
View Description Hide DescriptionWe present analytical expressions relating the bipolar moment parameters of Dixon to the measured anisotropy parameters of different pump/probe geometry sliced ion images. In the semiclassical limit, when there is no significant coherent contribution from multiple excited states to fragment angular momentumpolarization, the anisotropy of the images alone is sufficient to extract the parameters with no need to reference relative image intensities. The analysis of sliced images is advantageous since the anisotropy can be directly obtained from the image at any radius without the need for 3Ddeconvolution, which is not applicable for most pump/probe geometries. This method is therefore ideally suited for systems which result in a broad distribution of fragment velocities. The bipolar moment parameters are obtained for NO_{2} dissociation at 355 nm using these equations, and are compared to the bipolar moment parameters obtained from a proven iterative fitting technique for crushed ion images. Additionally, the utility of these equations in extracting speeddependent bipolar moments is demonstrated on the recently investigated NO_{3} system.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Predicted thermochemistry and unimolecular kinetics of nitrous sulfide
View Description Hide DescriptionThe geometry of N_{2}S was obtained at the CCSD(T)/augccpV(T + d)Z level of theory and energies with coupledcluster single double triple (CCSD(T)) and basis sets up to augccpV(6 + d)Z. After correction for anharmonic zeropoint energy, corevalence correlation, correlation up to CCSDT(Q) and relativistic effects, D_{0} for the N–S bond is estimated as 71.9 kJ mol^{−1}, and the corresponding thermochemistry for N_{2}S is and with an uncertainty of ±2.5 kJ mol^{−1}. Using CCSD(T)/augccpV(T + d) theory the minimum energy crossing point between singlet and triplet potential energy curves is found at r(N–N) ≈ 1.105 Å and r(N–S) ≈ 2.232 Å, with an energy 72 kJ mol^{−1} above N_{2} + S(^{3}P). Application of Troe's unimolecular formalism yields the lowpressurelimiting rate constant for dissociation of N_{2}S k_{0} = 7.6 × 10^{−10} exp(−126 kJ mol^{−1}/RT) cm^{3} molecule^{−1} s^{−1} over 700–2000 K. The estimated uncertainty is a factor of 4 arising from unknown parameters for energy transfer between N_{2}S and Ar or N_{2} bath gas. The thermochemistry and kinetics were included in a mechanism for CO/H_{2}/H_{2}S oxidation and the conclusion is that little NO is produced via subsequent chemistry of NNS.

Comparative study of cluster Ag_{17}Cu_{2} by instantaneous normal mode analysis and by isothermal Browniantype molecular dynamics simulation
View Description Hide DescriptionWe perform isothermal Browniantype molecular dynamics simulations to obtain the velocity autocorrelation function and its time Fouriertransformed power spectral density for the metallic clusterAg_{17}Cu_{2}. The temperature dependences of these dynamical quantities from T = 0 to 1500 K were examined and across this temperature range the cluster melting temperature T _{ m } , which we define to be the principal maximum position of the specific heat is determined. The instantaneous normal modeanalysis is then used to dissect the cluster dynamics by calculating the vibrational instantaneous normal mode density of states and hence its frequency integrated value I _{ j } which is an ensemble average of all vibrational projection operators for the jth atom in the cluster. In addition to comparing the results with simulation data, we look more closely at the entities I _{ j } of all atoms using the point group symmetry and diagnose their temperature variations. We find that I _{ j } exhibit features that may be used to deduce T _{ m } , which turns out to agree very well with those inferred from the power spectral density and specific heat.

Comparative density functional theory and postHartreeFock (CCSD, CASSCF) studies on the electronic structure of halogen nitrites ClONO and BrONO using quantum chemical topology
View Description Hide DescriptionIn this paper, the electronic structures of cis and transClONO and BrONO are studied at the CCSD/augccpVTZ, CASSCF(14,12)/augccpVTZ, and B3LYP/augccpVTZ computational levels. For the Cl–O bond, topological analysis of the electron density field, ρ(r), shows the prevalence of the sharedelectron type bond (∇^{2} ρ _{(3,−1)} < 0). The Br–O bond, however, represents the closedshell interaction (∇^{2} ρ _{(3,−1)} > 0). Topological analysis of the electron localization function, η(r), and electron localizability indicator (ELID), ϒ _{D} ^{ σ }(r), shows that the electronic structure of the central N–O bond is very sensitive to both electron correlation improvements (coupledcluster single double (CCSD), CASSCF, density functional theory(DFT)) and bond length alteration. Depending on the method used, the N–O bond can be characterized as a “normal” N–O bond with a disynaptic V(N,O) basin (DFT); a protocovalent N–O bond with two monosynaptic, V(N) and V(O), basins (CCSD, CASSCF); or a new type, first discovered for FONO, characterized by a single monosynaptic, V(N) basin (CCSD, DFT). The total basin population oscillates between 0.46–0.96 e (CCSD) and 0.86–1.02 e (CASSCF). The X–O bond is described by the single disynaptic basin, V(X,O), with a basin population between 0.76 and 0.81 e (CCSD) or 0.77 and 0.85 e (CASSCF). Analysis of the localized electron detector distribution for the cisCl–O1–N=O2 shows a manifold in the Cl⋅⋅⋅O2 region, associated with decreased electron density.

“Adiabatichinderedrotor” treatment of the parahydrogenwater complex
View Description Hide DescriptionInspired by a recent successful adiabatichinderedrotor treatment for parahydrogen pH_{2} in CO_{2}–H_{2} complexes [H. Li, P.N. Roy, and R. J. Le Roy, J. Chem. Phys.133, 104305 (2010);H. Li, R. J. Le Roy, P.N. Roy, and A. R. W. McKellar, Phys. Rev. Lett.105, 133401 (2010)], we apply the same approximation to the more challenging H_{2}O–H_{2} system. This approximation reduces the dimension of the H_{2}O–H_{2} potential from 5D to 3D and greatly enhances the computational efficiency. The global minimum of the original 5D potential is missing from the adiabatic 3D potential for reasons based on solution of the hinderedrotor Schrödinger equation of the pH_{2}. Energies and wave functions of the discrete rovibrational levels of H_{2}O–pH_{2} complexes obtained from the adiabatic 3D potential are in good agreement with the results from calculations with the full 5D potential. This comparison validates our approximation, although it is a relatively cruder treatment for pH_{2}–H_{2}O than it is for pH_{2}–CO_{2}. This adiabatic approximation makes largescale simulations of H_{2}O–pH_{2} systems possible via a pairwise additive interaction model in which pH_{2} is treated as a pointlike particle. The poor performance of the diabatically spherical treatment of pH_{2} rotation excludes the possibility of approximating pH_{2} as a simple sphere in its interaction with H_{2}O.

The complex spectrum of a “simple” free radical: The  band system of the jetcooled boron difluoride free radical
View Description Hide DescriptionThe nearultraviolet band system of the jetcooled boron difluoride free radical has been studied by a combination of laserinduced fluorescence and single vibronic level wavelength resolved emission spectroscopies. The radical was produced in a supersonic discharge jet using a precursor mixture of 1%–3% of BF_{3} or ^{10}BF_{3} in high pressure argon. A large number of bands were found in the 340–286 nm region and assigned as transitions from the ground state to the lower RennerTeller component of the ^{2}Π excited state, based on our previous ab initio potential energy surface predictions, matching the emission spectra FranckCondon profiles of ^{11}BF_{2} and ^{10}BF_{2}, and comparison of observed and calculated boronisotope effects. Several bands have been rotationally analyzed providing ground state structural parameters of (BF) = 1.3102(9) Å and (FBF) = 119.7(6)°. The ground state totally symmetric vibrational energy levels of both boron isotopologues have also been measured and assigned up to energies of more than 8000 cm^{−1}. Although BF_{2} might be considered to be a “simple” free radical, understanding the details of its electronic spectrum remains a major challenge for both theory and experiment.

Rovibrational bound states of neon trimer: Quantum dynamical calculation of all eigenstate energy levels and wavefunctions
View Description Hide DescriptionExact quantum dynamics calculations of the eigenstate energy levels and wavefunctions for all bound rovibrational states of the Ne_{3} trimer (J = 0–18) have been performed using the ScalIT suite of parallel codes. These codes employ a combination of highly efficient methods, including phasespace optimized discrete variable representation, optimal separable basis, and preconditioned inexact spectral transform methods, together with an effective massive parallelization scheme. The Ne_{3} energy levels and wavefunctions were computed using a pairwise LennardJones potential. Jacobi coordinates were used for the calculations, but to identify just those states belonging to the totally symmetric irreducible representation of the G_{12} complete nuclear permutationinversion group, wavefunctions were plotted in hyperspherical coordinates. “Horseshoe” states were observed above the isomerization barrier, but the horseshoe localization effect is weaker than in Ar_{3}. The rigid rotor model is found to be applicable for only the ground and first excited vibrational states at low J; fitted rotational constant values are presented.

Variational quantum mechanical and active database approaches to the rotationalvibrational spectroscopy of ketene, H2CCO
View Description Hide DescriptionA variational quantum mechanical protocol is presented for the computation of rovibrational energy levels of semirigid molecules using discrete variable representation of the Eckart−Watson Hamiltonian, a complete, “exact” inclusion of the potential energy surface, and selection of a vibrational subspace. Molecular symmetry is exploited via a symmetryadapted Lanczos algorithm. Besides symmetry labels, zerothorder rigidrotor and harmonicoscillator quantum numbers are employed to characterize the computed rovibrational states. Using the computational molecular spectroscopy algorithm presented, a large number of rovibrational states, up to J = 50, of the ground electronic state of the parent isotopologue of ketene, H2 ^{12}C=^{12}C=^{16}O, were computed and characterized. Based on 12 references, altogether 3982 measured and assigned rovibrational transitions of H2 ^{12}C=^{12}C=^{16}O have been collected, from which 3194 were validated. These transitions form two spectroscopic networks (SN). The ortho and the para SNs contain 2489 and 705 validated transitions and 1251 and 471 validated energy levels, respectively. The computed energy levels are compared with energy levels obtained, up to J = 41, via an inversion protocol based on this collection of validated measured rovibrational transitions. The accurate inverted energy levels allow new assignments to be proposed. Some regularities and irregularities in the rovibrational spectrum of ketene are elucidated.

Rotational analysis and deperturbation of the A ^{2}Π → X ^{2}Σ^{+} and B ^{′} ^{2}Σ^{+} → X ^{2}Σ^{+} emission spectra of MgH
View Description Hide DescriptionDeperturbation analysis of the A ^{2}Π → X ^{2}Σ^{+} and B ^{′} ^{2}Σ^{+} → X ^{2}Σ^{+}emission spectra of ^{24}MgH is reported. Spectroscopic data for the v = 0 to 3 levels of the A ^{2}Π state and the v = 0 to 4 levels of the B ^{′} ^{2}Σ^{+} state were fitted together using a single Hamiltonian matrix that includes ^{2}Π and ^{2}Σ^{+} matrix elements, as well as offdiagonal elements coupling several vibrational levels of the two states. A Dunhamtype fit was performed and the resulting Y _{ l } _{,0} and Y _{ l } _{,1} coefficients were used to generate Rydberg–Klein–Rees (RKR) potential curves for the A ^{2}Π and the B ^{′} ^{2}Σ^{+} states. Vibrational overlap integrals were computed from the RKR potentials, and the offdiagonal matrix elements coupling the electronic wavefunctions (a ^{+} and b) were determined. Zero point dissociation energies (D _{0}) of the A ^{2}Π and B ^{′} ^{2}Σ^{+} states of ^{24}MgH were determined to be 12 957.5 ± 0.5 and 10 133.6 ± 0.5 cm^{−1}, respectively. Using the Y _{0,1} coefficients, the equilibrium internuclear distances (r _{ e }) of the A ^{2}Π and B ^{′} ^{2}Σ^{+} states were determined to be 1.67827(1) Å and 2.59404(4) Å, respectively.