Oxidative addition of the ethane C-C bond to Pd. An ab initio benchmark and DFT validation study

We have computed a state-of-the-art benchmark potential energy surface (PES) for the archetypal oxidative addition of the ethane C-C bond to the palladium atom and have used this to evaluate the performance of 24 popular density functionals, covering LDA, GGA, meta-GGA, and hybrid density functionals, for describing this reaction. The ab initio benchmark is obtained by exploring the PES using a hierarchical series of ab initio methods [HF, MP2, CCSD, CCSD(T)] in combination with a hierarchical series of five Gaussian-type basis sets, up to g polarization. Relativistic effects are taken into account either through a relativistic effective core potential for palladium or through a full four-component all-electron approach. Our best estimate of kinetic and thermodynamic parameters is -10.8 (-11.3) kcal/mol for the formation of the reactant complex, 19.4 (17.1) kcal/mol for the activation energy relative to the separate reactants, and -4.5 (-6.8) kcal/mol for the reaction energy (zero-point vibrational energy-corrected values in parentheses). Our work highlights the importance of sufficient higher angular momentum polarization functions for correctly describing metal-d-electron correlation. Best overall agreement with our ab initio benchmark is obtained by functionals from all three categories, GGA, meta-GGA, and hybrid DFT, with mean absolute errors of 1.5 to 2.5 kcal/mol and errors in activation energies ranging from -0.2 to -3.2 kcal/mol. Interestingly, the well-known BLYP functional compares very reasonably with a slight underestimation of the overall barrier by -0.9 kcal/mol. For comparison, with B3LYP we arrive at an overestimation of the overall barrier by 5.8 kcal/mol. On the other hand, B3LYP performs excellently for the central barrier (i.e., relative to the reactant complex) which it underestimates by only -0.1 kcal/mol.     

Ab initio and DFT benchmark study for nucleophilic substitution at carbon (SN2@C) and silicon (SN2@Si)

To obtain a set of consistent benchmark potential energy surfaces (PES) for the two archetypal nucleophilic substitution reactions of the chloride anion at carbon in chloromethane (S(N)2@C) and at silicon in chlorosilane (S(N)2@Si), we have explored these PESes using a hierarchical series of ab initio methods [HF, MP2, MP4SDQ, CCSD, CCSD(T)] in combination with a hierarchical series of six Gaussian-type basis sets, up to g polarization. Relative energies of stationary points are converged to within 0.01 to 0.56 kcal/mol as a function of the basis-set size. Our best estimate, at CCSD(T)/aug-cc-pVQZ, for the relative energies of the [Cl(-), CH(3)Cl] reactant complex, the [Cl-CH(3)-Cl](-) transition state and the stable [Cl-SiH(3)-Cl](-) transition complex is -10.42, +2.52, and -27.10 kcal/mol, respectively. Furthermore, we have investigated the performance for these reactions of four popular density functionals, namely, BP86, BLYP, B3LYP, and OLYP, in combination with a large doubly polarized Slater-type basis set of triple-zeta quality (TZ2P). Best overall agreement with our CCSD(T)/aug-cc-pVQZ benchmark is obtained with OLYP and B3LYP. However, OLYP performs better for the S(N)2@C overall and central barriers, which it underestimates by 2.65 and 4.05 kcal/mol, respectively. The other DFT approaches underestimate these barriers by some 4.8 (B3LYP) to 9.0 kcal/mol (BLYP).     

Energy landscapes of nucleophilic substitution reactions: a comparison of density functional theory and coupled cluster methods

We have carried out a detailed evaluation of the performance of all classes of density functional theory (DFT) for describing the potential energy surface (PES) of a wide range of nucleophilic substitution (SN2) reactions involving, amongst others, nucleophilic attack at carbon, nitrogen, silicon, and sulfur. In particular, we investigate the ability of the local density approximation (LDA), generalized gradient approximation (GGA), meta-GGA as well as hybrid DFT to reproduce high-level coupled cluster (CCSD(T)) benchmarks that are close to the basis set limit. The most accurate GGA, meta-GGA, and hybrid functionals yield mean absolute deviations of about 2 kcal/mol relative to the coupled cluster data, for reactant complexation, central barriers, overall barriers as well as reaction energies. For the three nonlocal DFT classes, the best functionals are found to be OPBE (GGA), OLAP3 (meta-GGA), and mPBE0KCIS (hybrid DFT). The popular B3LYP functional is not bad but performs significantly worse than the best GGA functionals. Furthermore, we have compared the geometries from several density functionals with the reference CCSD(T) data. The same GGA functionals that perform best for the energies (OPBE, OLYP), also perform best for the geometries with average absolute deviations in bond lengths of 0.06 A and 0.6 degrees, even better than the best meta-GGA and hybrid functionals. In view of the reduced computational effort of GGAs with respect to meta-GGAs and hybrid functionals, let alone coupled cluster, we recommend the use of accurate GGAs such as OPBE or OLYP for the study of SN2 reactions.     

Ab initio benchmark study for the oxidative addition of CH4 to Pd: importance of basis-set flexibility and polarization

To obtain a state-of-the-art benchmark potential energy surface (PES) for the archetypal oxidative addition of the methane C-H bond to the palladium atom, we have explored this PES using a hierarchical series of ab initio methods (Hartree-Fock, second-order M?ller-Plesset perturbation theory, fourth-order M?ller-Plesset perturbation theory with single, double and quadruple excitations, coupled cluster theory with single and double excitations (CCSD), and with triple excitations treated perturbatively [CCSD(T)]) and hybrid density functional theory using the B3LYP functional, in combination with a hierarchical series of ten Gaussian-type basis sets, up to g polarization. Relativistic effects are taken into account either through a relativistic effective core potential for palladium or through a full four-component all-electron approach. Counterpoise corrected relative energies of stationary points are converged to within 0.1-0.2 kcal/mol as a function of the basis-set size. Our best estimate of kinetic and thermodynamic parameters is -8.1 (-8.3) kcal/mol for the formation of the reactant complex, 5.8 (3.1) kcal/mol for the activation energy relative to the separate reactants, and 0.8 (-1.2) kcal/mol for the reaction energy (zero-point vibrational energy-corrected values in parentheses). This agrees well with available experimental data. Our work highlights the importance of sufficient higher angular momentum polarization functions, f and g, for correctly describing metal-d-electron correlation and, thus, for obtaining reliable relative energies. We show that standard basis sets, such as LANL2DZ+1f for palladium, are not sufficiently polarized for this purpose and lead to erroneous CCSD(T) results. B3LYP is associated with smaller basis set superposition errors and shows faster convergence with basis-set size but yields relative energies (in particular, a reaction barrier) that are ca. 3.5 kcal/mol higher than the corresponding CCSD(T) values.     

Ab initio and analytic intermolecular potentials for Ar-CH(3)OH

Ab initio calculations at the CCSD(T)/aug-cc-pVTZ level of theory were used to characterize the Ar-CH(3)OH intermolecular potential energy surface (PES). Potential energy curves were calculated for four different Ar + CH(3)OH orientations and used to derive an analytic function for the intermolecular PES. A sum of Ar-C, Ar-O, Ar-H(C), and Ar-H(O) two-body potentials gives an excellent fit to these potential energy curves up to 100 kcal mol(-1), and adding an additional r(-n) term to the Buckingham two-body potential results in only a minor improvement in the fit. Three Ar-CH(3)OH van der Waals minima were found from the CCSD(T)/aug-cc-pVTZ//MP2/aug-cc-pVTZ calculations. The structure of the global minimum is in overall good agreement with experiment (X.-C. Tan, L. Sun and R. L. Kuczkowski, J. Mol. Spectrosc., 1995, 171, 248). It is T-shaped with the hydroxyl H-atom syn with respect to Ar. Extrapolated to the complete basis set (CBS) limit, the global minimum has a well depth of 0.72 kcal mol(-1) with basis set superposition error (BSSE) correction. The aug-cc-pVTZ basis set gives a well depth only 0.10 kcal mol(-1) smaller than this value. The well depths of the other two minima are within 0.16 kcal mol(-1) of the global minimum. The analytic Ar-CH(3)OH intermolecular potential also identifies these three minima as the only van der Waals minima and the structures predicted by the analytic potential are similar to the ab initio structures. The analytic potential identifies the same global minimum and the predicted well depths for the minima are within 0.05 kcal mol(-1) of the ab initio values. Combining this Ar-CH(3)OH intermolecular potential with a potential for a OH-terminated alkylthiolate self-assembled monolayer surface (i.e., HO-SAM) provides a potential to model Ar + HO-SAM collisions.     

Low-lying isomers of the B9(-) boron cluster: the planar molecular wheel versus three-dimensional structures

The B(9)(-) cluster was found previously to be an unprecedented molecular wheel containing an octacoordinate planar boron with D(8h) symmetry in a combined photoelectron spectroscopy (PES) and theoretical study [H. J. Zhai et al., Angew. Chem., Int. Ed. 42, 6004 (2003)]. However, the PES spectra of B(9)(-) exhibit minor features that cannot be explained by the global minimum D(8h) structure, suggesting possible contributions from low-lying isomers at finite temperatures. Here we present Car-Parrinello molecular dynamics with simulated annealing simulations to fully explore the potential energy surface of B(9)(-) and search for low-lying isomers that may account for the minor PES features. We performed density functional theory (DFT) calculations with different exchange-correlation functionals and ab initio calculations at various levels of theory with different basis sets. Two three-dimensional low-lying isomers were found, both of C(s) symmetry, 6.29 (C(s)-2) and 10.23 (C(s)-1) kcal/mol higher in energy than the D(8h) structure at the highest CCSD(T) level of theory. Calculated detachment transitions from the C(s)-2 isomer are in excellent agreement with the minor features observed in the PES spectra of B(9)(-). The B(9)(-) cluster proves to be a challenge for most DFT methods and the calculated relative energies strongly depend on the exchange-correlation functionals, providing an excellent example for evaluating the accuracies of various DFT methods.     

Interpolating moving least-squares methods for fitting potential energy surfaces: an application to the H2CN unimolecular reaction

Classical trajectories have been used to compute rates for the unimolecular reaction H2CN-->H+HCN on a fitted ab initio potential energy surface (PES). The ab initio energies were obtained from CCSD(T)/aug-cc-pvtz electronic structure calculations. The ab initio energies were fitted by the interpolating moving least-squares (IMLS) method. This work continues the development of the IMLS method for producing ab initio PESs for use in molecular dynamics simulations of many-atom systems. A dual-level scheme was used in which the preliminary selection of data points was done using a low-level theory and the points used for fitting the final PES were obtained at the desired higher level of theory. Classical trajectories were used on various low-level IMLS fits to tune the fit to the unimolecular reaction under study. Procedures for efficiently picking data points, selecting basis functions, and defining cutoff limits to exclude distant points were investigated. The accuracy of the fitted PES was assessed by comparing interpolated values of quantities to the corresponding ab initio values. With as little as 330 ab initio points classical trajectory rate constants were converged to 5%-10% and the rms error over the six-dimensional region sampled by the trajectories was a few tenths of a kcal/mol.     

Rozen's epoxidation reagent, CH3CN.HOF: a theoretical study of its structure, vibrational spectroscopy, and reaction mechanism

Rozen's epoxidation reagent, CH(3)CN.HOF, and a prototype epoxidation reaction employing it, have been subjected to an extensive ab initio and density functional study. Its anharmonic force field reveals a very strong red shift for the OH stretch and a strong blue shift for the HOF bend, in semiquantitative agreement with experiment. The very strong hydrogen bond (8.20 kcal/mol at the W1 level) not only serves to stabilize the reactant but also considerably lowers the barrier height for epoxidation of ethylene. Moreover, the reaction byproduct HF is found to act autocatalytically. The OH moiety acquires HO(+) character in the transition state. Our W1 benchmark data for the reaction profile allow the performance of various DFT functionals to be assessed. In general, "kinetics" functionals overestimate barrier heights, the BMK functional less so than the others. The B1B95 and TPSS33B95 meta-GGA functionals both perform very well, whereas general-purpose hybrid GGAs underestimate barrier heights. The simple PBE0 functional does reasonably well.     

Ab initio, density functional theory, and continuum solvation model prediction of the product ratio in the S(N)2 reaction of NO2(-) with CH3CH2Cl and CH3CH2Br in DMSO solution

The reaction pathways for the interaction of the nitrite ion with ethyl chloride and ethyl bromide in DMSO solution were investigated at the ab initio level of theory, and the solvent effect was included through the polarizable continuum model. The performance of BLYP, GLYP, XLYP, OLYP, PBE0, B3PW91, B3LYP, and X3LYP density functionals has been tested. For the ethyl bromide case, our best ab initio calculations at the CCSD(T)/aug-cc-pVTZ level predicts product ratio of 73% and 27% for nitroethane and ethyl nitrite, respectively, which can be compared with the experimental values of 67% and 33%. This translates to an error in the relative DeltaG* of only 0.17 kcal mol(-1). No functional is accurate (deviation <0.5 kcal mol(-1)) for predicting relative DeltaG*. The hybrid X3LYP functional presents the best performance with deviation 0.82 kcal mol(-1). The present problem should be included in the test set used for the evaluation of new functionals.     

Magnitude of the CH/pi interaction in the gas phase: experimental and theoretical determination of the accurate interaction energy in benzene-methane

The accurate CH/pi interaction energy of the benzene-methane model system was experimentally and theoretically determined. In the experiment, mass analyzed threshold ionization spectroscopy was applied to the benzene-methane cluster in the gas phase, prepared in a supersonic molecular beam. The binding energy in the neutral ground state of the cluster, which is regarded as the CH/pi interaction energy for this model system, was evaluated from the dissociation threshold measurements of the cluster cation. The experimentally determined binding energy (D(0)) was 1.03-1.13 kcal/mol. The interaction energy of the model system was calculated by ab initio molecular orbital methods. The estimated CCSD(T) interaction energy at the basis set limit (D(e)) was -1.43 kcal/mol. The calculated binding energy (D(0)) after the vibrational zero-point energy correction (1.13 kcal/mol) agrees well with the experimental value. The effects of basis set and electron correlation correction procedure on the calculated CH/pi interaction energy were evaluated. Accuracy of the calculated interaction energies by DFT methods using BLYP, B3LYP, PW91 and PBE functionals was also discussed.     

Computational study of the reactions of methanol with the hydroperoxyl and methyl radicals. 1. Accurate thermochemistry and barrier heights

The reactions of CH(3)OH with the HO(2) and CH(3) radicals are important in the combustion of methanol and are prototypes for reactions of heavier alcohols in biofuels. The reaction energies and barrier heights for these reaction systems are computed with CCSD(T) theory extrapolated to the complete basis set limit using correlation-consistent basis sets, both augmented and unaugmented, and further refined by including a fully coupled treatment of the connected triple excitations, a second-order perturbative treatment of quadruple excitations (by CCSDT(2)(Q)), core-valence corrections, and scalar relativistic effects. It is shown that the M08-HX and M08-SO hybrid meta-GGA density functionals can achieve sub-kcal mol(-1) agreement with the high-level ab initio results, identifying these functionals as important potential candidates for direct dynamics studies on the rates of these and homologous reaction systems.     

An ab initio correlated study of the potential energy surface for the HOBr.H2O complex

The potential energy surface (PES) for the HOBr.H(2)O complex has been investigated using second- and fourth-order M?ller-Plesset perturbation theory (MP2, MP4) and coupled cluster theory with single and doubles excitations (CCSD), and a perturbative approximation of triple excitations (CCSD-T), correlated ab initio levels of theory employing basis sets of triple zeta quality with polarization and diffuse functions up to the 6-311++G(3dp,3df ) standard Pople's basis set. Six stationary points being three minima, two first-order transition state (TS) structures and one second-order TS were located on the PES. The global minimum syn and the anti equilibrium structure are virtually degenerated [DeltaE(ele-nuc) approximately 0.3 kcal mol(-1), CCSD-T/6-311++G(3df,3pd) value], with the third minima being approximately 4 kcal mol(-1) away. IRC analysis was performed to confirm the correct connectivity of the two first-order TS structures. The CCSD-T/6-311++G(3df,3pd)//MP2/6-311G(d,p) barrier for the syn<-->anti interconversion is 0.3 kcal mol(-1), indicating that a mixture of the syn and anti forms of the HOBr.H(2)O complex is likely to exist.     

Dynamics of the O(3P) + CH4 → OH + CH3 reaction is similar to that of a triatomic reaction

The O((3)P) + CH(4) reaction has been investigated using the quasi-classical trajectory (QCT) method and an ab initio pseudotriatomic potential energy surface (PES). This has been mainly motivated by very recent experiments which support the reliability of the triatomic modeling even at high collision energy ( = 64 kcal mol(-1)). The QCT results agree rather well with the experiments (translational and angular distributions of products); i.e., the ab initio pseudotriatomic modeling "captures" the essence of the reaction dynamics, although the PES was not optimized for high E(col). Furthermore, similar experiments on the O((3)P) + CD(4) reaction at moderate E(col) (12.49 kcal mol(-1)) have also been of a large interest here and, under these softer reaction conditions, the QCT method leads to results which are almost in quantitative agreement with experiments. The utility of the ab initio pseudotriatomic modeling has also been recognized for other analogous systems (X + CH(4)) but with very different PESs.     

A new "spectroscopic" potential energy surface for formaldehyde in its ground electronic state

We report a new "spectroscopic" potential energy surface (PES) of formaldehyde (H(2)(12)C(16)O) in its ground electronic state, obtained by refining an ab initio PES in a least-squares fitting to the experimental spectroscopic data for formaldehyde currently available in the literature. The ab initio PES was computed using the CCSD(T)/aug-cc-pVQZ method at 30 840 geometries that cover the energy range up to 44 000 cm(-1) above equilibrium. Ro-vibrational energies of formaldehyde were determined variationally for this ab initio PES by means of the program TROVE [Theoretical ROtation-Vibration Energies; S. N. Yurchenko, W. Thiel, and P. Jensen, J. Mol. Spectrosc. 245, 126 (2007)]. The parameter values in the analytical representation of the PES were optimized in fittings to 319 ro-vibrational energies with J = 0, 1, 2, and 5. The initial parameter values in the fittings were those of the ab initio PES, the ro-vibrational eigenfunctions obtained from this PES served as a basis set during the fitting process, and constraints were imposed to ensure that the refined PES does not deviate unphysically from the ab initio one in regions of configuration space not sampled by the experimental data. The resulting refined PES, referred to as H(2)CO-2011, reproduces the available experimental J ≤ 5 data with a root-mean-square error of 0.04 cm(-1).     

Assessment of the accuracy of density functionals for prediction of relative energies and geometries of low-lying isomers of water hexamers

Water hexamers provide a critical testing ground for validating potential energy surface predictions because they contain structural motifs not present in smaller clusters. We tested the ability of 11 density functionals (four of which are local and seven of which are nonlocal) to accurately predict the relative energies of a series of low-lying water hexamers, relative to the CCSD(T)/aug'-cc-pVTZ level of theory, where CCSD(T) denotes coupled cluster theory with an interative treatment of single and double excitations and a quasi-perturbative treatment of connected triple excitations. Five of the density functionals were tested with two different basis sets, making a total of 16 levels of density functional theory (DFT) tested. When single-point energy calculations are carried out on geometries obtained with second-order M?ller-Plesset perturbation theory (MP2), only three density functionals, M06-L, M05-2X, and M06-2X, are able to correctly predict the relative energy ordering of the hexamers. These three functionals predict that the range of energies spanned by the six isomers is 3.2-5.6 kcal/mol, whereas the other eight functionals predict ranges of 1.0-2.4 kcal/mol; the benchmark value for this range is 3.1 kcal/mol. When the hexamers are optimized at each level of theory, all methods are able to reproduce the MP2 geometries well for all isomers except the boat and bag isomers, and DFT optimization changes the energy ordering for seven of the 16 methods tested. The addition of zero-point energy changes the energy ordering for all of the density functionals studied except for M05-2X and M06-2X. The variation in relative energies predicted by the different methods highlights the necessity for exercising caution in the choice of density functionals used in future studies. Of the 11 density functionals tested, the most accurate results for energies were obtained with the PWB6K, MPWB1K, and M05-2X functionals.     

Quantum chemical assessment of the binding energy of CuO+

We present a detailed theoretical investigation on the dissociation energy of CuO(+), carried out by means of coupled cluster theory, the multireference averaged coupled pair functional (MR-ACPF) approach, diffusion quantum Monte Carlo (DMC), and density functional theory (DFT). At the respective extrapolated basis set limits, most post-Hartree-Fock approaches agree within a narrow error margin on a D(e) value of 26.0 kcal mol(-1) [coupled-cluster singles and doubles level augmented by perturbative triples corrections, CCSD(T)], 25.8 kcal mol(-1) (CCSDTQ via the high accuracy extrapolated ab initio thermochemistry protocol), and 25.6 kcal mol(-1) (DMC), which is encouraging in view of the disaccording data published thus far. The configuration-interaction based MR-ACPF expansion, which includes single and double excitations only, gives a slightly lower value of 24.1 kcal mol(-1), indicating that large basis sets and triple excitation patterns are necessary ingredients for a quantitative assessment. Our best estimate for D(0) at the CCSD(T) level is 25.3 kcal mol(-1), which is somewhat lower than the latest experimental value (D(0) = 31.1 ± 2.8 kcal mol(-1)[semicolon] reported by the Armentrout group) [Int. J. Mass Spectrom. 182/183, 99 (1999)]. These highly correlated methods are, however, computationally very demanding, and the results are therefore supplemented with those of more affordable DFT calculations. If used in combination with moderately-sized basis sets, the M05 and M06 hybrid functionals turn out to be promising candidates for studies on much larger systems containing a [CuO](+) core.     

Small clusters of aluminum and tin: highly correlated calculations and validation of density functional procedures

We present results of molecular electronic structure treatments of multireference configuration interaction (MRCI) type for clusters Al(n) and Sn(n) in the range up to n = 4, and of coupled cluster singles and doubles with perturbative triples corrections (CCSD(T)) type in the range up to n = 10. Basis sets of quadruple zeta size are employed, computed energy differences, such as cohesive energies, E(coh), or dissociation energies for the removal of a single atom, D(e), differ from the complete basis set limit by only a few 0.01 eV. MRCI and CCSD(T) results are then compared to those obtained from density functional theory (DFT) treatments, which show that all computational procedures agree with the general features of D(e) and E(coh). The best agreement of DFT with CCSD(T) is found for the meta-GGA (generalized gradient approximation) TPSS (Tao, Perdew, Staroverov, Scuseria) for which D(e) differs from CCSD(T) by at most 0.15 eV for Al(n) and 0.21 eV for Sn(n). The GGA PBE (Perdew, Burke, Ernzerhof) is slightly poorer with maximum deviations of 0.23 and 0.24 eV, whereas hybrid functionals are not competitive with GGA and meta-GGA functionals. A general conclusion is that errors of D(e) and/or energy differences of isomers computed with DFT procedures may easily reach 0.2 eV and errors for cohesive energies E(coh) 0.1 eV.     

Structure of the boronic acid dimer and the relative stabilities of its conformers

Despite the widespread use of boronic acids in materials science and as pharmaceutical agents, many aspects of their structure and reactivity are not well understood. In this research the boronic acid dimer, [HB(OH)(2)](2), was studied by second-order M?ller-Plesset (MP2) perturbation theory and coupled cluster methodology with single and double excitations (CCSD). Pople split-valence 6-31+G*, 6-311G**, and 6-311++G** and Dunning-Woon correlation-consistent cc-pVDZ, aug-cc-pVDZ, cc-pVTZ, and aug-cc-pVTZ basis sets were employed for the calculations. A doubly hydrogen-bonded conformer (1) of the dimer was consistently found to be lowest in energy; the structure of 1 was planar (C(2h)) at most computational levels employed but was significantly nonplanar (C(2)) at the MP2/6-311++G** and CCSD/6-311++G** levels, the result of an intrinsic problem with Pople-type sp-diffuse basis functions on heavy atoms. The dimerization energy, enthalpy, and free energy for the formation of (1) from the exo-endo conformer of the monomer were -10.8, -9.2, and +1.2 kcal/mol, respectively, at the MP2/aug-cc-pVTZ level. Several other hydrogen-bonded conformers of the dimer were local minima on the potential energy surface (PES) and ranged from 2 to 5 kcal/mol higher in energy than 1. Nine doubly OH-bridged conformers, in which the boron atoms were tetracoordinated, were also local minima on the PES, but they were all greater than 13 kcal/mol higher in energy than 1; doubly H-bridged structures proved to be transition states. MP2 and CCSD results were compared to those from the BLYP, B3LYP, OLYP, O3LYP, PBE1PBE, and TPSS functionals with the 6-311++G** and aug-cc-pVTZ basis sets; the PBE1PBE functional performed best relative to the MP2 and CCSD results. Self-consistent reaction field (SCRF) calculations predict that boronic acid dimerization is less favorable in solution than in vacuo.