The electron affinity of Al13H cluster: high level ab initio study

Al₁₃H clusters have been considered candidates for cluster assembled materials. Here we have carried out benchmark calculations for the Al₁₃H cluster, both neutral and anionic, with the aim of verifying the nature of stationary points on the potential energy surface, studying dynamics of H atom and determining an adiabatic electron affinity. A range of correlated methods applied include second-order perturbation theory (MP2), spin-component-scaled MP2, coupled electron pair (CEPA) and coupled cluster singles and doubles with perturbative triple corrections (CCSD(T)). These methods are used in combination with the correlation consistent basis sets through aug-cc-pVTZ including extrapolation to the complete basis set (CBS) limit. Performance of several different flavours of density functional theory (DFT) such as generalised gradient approximation (GGA), hybrid GGA, meta-GGA and hybrid-meta-GGA is assessed with respect to the ab initio correlated reference data. The harmonic force constant analysis is systematically performed with the MP2 and DFT methods. The MP2 results show that for neutral Al₁₃H only the hollow structure is a potential energy minimum, with the bridged structure being a transition state for the H shift from the hollow site to the adjacent hollow site. The CCSD(T)/aug-cc-pVTZ (CCSD(T)/CBS) estimate of the energy barrier to this H shift is 2.6 (2.9) kcal/mol, implying that the H atom movement over the Al₁₃H cluster surface is facile. By contrast, the DFT force constant analysis results suggest additional terminal and bridged minima structures. For the anion Al₁₃H^?, exhibiting ‘stiffer’ potential energy surface compared to the neutral, the existence of the hollow and terminal isomers is consistent with the earlier photoelectron spectroscopy assignment. The adiabatic electron affinity of Al₁₃H is determined to be 2.00 and 1.95 eV (the latter including the ΔZPE correction) based on the CCSD(T) energies extrapolated to the CBS limit, whereas the respective CCSD(T)/CBS thermodynamic EA values are 2.79 and 2.80 eV.     

Enthalpy difference between conformations of normal alkanes: effects of basis set and chain length on intramolecular basis set superposition error

The quantum chemistry of conformation equilibrium is a field where great accuracy (better than 100?cal?mol^?1) is needed because the energy difference between molecular conformers rarely exceeds 1000–3000?cal?mol^?1. The conformation equilibrium of straight-chain (normal) alkanes is of particular interest and importance for modern chemistry. In this paper, an extra error source for high-quality ab initio (first principles) and DFT calculations of the conformation equilibrium of normal alkanes, namely the intramolecular basis set superposition error (BSSE), is discussed. In contrast to out-of-plane vibrations in benzene molecules, diffuse functions on carbon and hydrogen atoms were found to greatly reduce the relative BSSE of n-alkanes. The corrections due to the intramolecular BSSE were found to be almost identical for the MP2, MP4, and CCSD(T) levels of theory. Their cancelation is expected when CCSD(T)/CBS (CBS, complete basis set) energies are evaluated by addition schemes. For larger normal alkanes (N?>?12), the magnitude of the BSSE correction was found to be up to three times larger than the relative stability of the conformer; in this case, the basis set superposition error led to a two orders of magnitude difference in conformer abundance. No error cancelation due to the basis set superposition was found. A comparison with amino acid, peptide, and protein data was provided.     

Atmospheric chemistry of diazomethane – an experimental and theoretical study

The kinetics of the O₃, OH and NO₃ radical reactions with diazomethane were studied in smog chamber experiments employing long-path FTIR and PTR-ToF-MS detection. The rate coefficients were determined to be k _CH2NN+O3?=?(3.2?±?0.4)?×?10^?17 and k _CH2NN+OH?=?(1.68?±?0.12)?×?10^?10 cm³ molecule^?1 s^?1 at 295?±?3?K and 1013?±?30 hPa, whereas the CH₂NN?+?NO₃ reaction was too fast to be determined in the static smog chamber experiments. Formaldehyde was the sole product observed in all the reactions. The experimental results are supported by CCSD(T*)-F12a/aug-cc-pVTZ//M062X/aug-cc-pVTZ calculations showing the reactions to proceed exclusively via addition to the carbon atom. The atmospheric fate of diazomethane is discussed.     

The gas phase oxidation of HCOOH by Cl and NH2 radicals. Proton coupled electron transfer versus hydrogen atom transfer*

ABSTRACT

The reaction of formic acid (HCOOH) with chlorine atom and amidogen radical (NH₂) have been investigated using high level theoretical methods such BH&HLYP, MP2, QCISD, and CCSD(T) with the 6–311?+?G(2df,2p), aug-cc-pVTZ, aug-cc-pVQZ and extrapolation to CBS basis sets. The abstraction of the acidic and formyl hydrogen atoms of the acid by the two radicals has been considered, and the different reactions proceed either by a proton coupled electron transfer (pcet) and hydrogen atom transfer (hat) mechanisms. Our calculated rate constant at 298?K for the reaction with Cl is 1.14?×?10^?13?cm³?molecule^?1?s^?1 in good agreement with the experimental value 1.8?±?0.12/2.0?×?10^?13?cm³?molecule^?1?s^?1 and the reaction proceeds exclusively by abstraction of the formyl hydrogen atom, via hat mechanism, producing HOCO+ClH. The calculated rate constant, at 298?K, for the reaction with NH₂ is 1.71?×?10^?15?cm³?molecule^?1?s^?1, and the reaction goes through the abstraction of the acidic hydrogen atom, via a pcet mechanism, leading to the formation of HCOO+NH₃.     

Physisorption and dissociative chemisorption of H2 on sub-nanosized Al$_{13}^{-}$ anion cluster: ab initio study

We have studied the interaction of Al₁₃^-_{13}^{-} anion cluster with H₂. Both the long range interaction and dissociative adsorption have been examined using the established correlated ab initio methods, MP2 and CCSD(T), in conjunction with the augmented correlation consistent basis sets up to aug-cc-pVTZ. The formation of the weakly bound (physisorbed) end-on anion complex Al₁₃^-_{13}^{-}...H₂ is predicted for the interacting Al...H distances of 3.95 ? with the H-H axis pointing towards the ‘hollow’ site of Al₁₃^-_{13}^{-} and binding energy (D_e)D_{e}) of 0.7 kcal/mol at the estimated complete basis set (CBS) limit of CCSD(T). The barrier height for H₂ dissociation on Al₁₃^-_{13}^{-} of 41.6 (42.9) kcal/mol calculated at the ZPVE-corrected CCSD(T)/aug-cc-pVTZ (estimated CCSD(T)/CBS) level is at least twice as large as that evaluated by us for a dissociative adsorption of H₂ on an open-shell Al₁₃ neutral cluster. To our knowledge, this report presents the first “benchmark” quality study of the physisorption and dissociative chemisorption of molecular hydrogen on Al₁₃^-_{13}^{-} anion cluster.     

Mechanistic and kinetics study of the gas phase reactions of methyltrifluoroacetate with OH radical and Cl atom

Theoretical investigations are carried out on the title reactions by means of ab initio and DFT methods. The optimized geometries, frequencies and minimum energy path are obtained at MPWB1K/6-31+G(d,p) level. Single point energy calculations are performed at MP2 and QCISD(T) levels of theory. Energetics were further refined by calculating the energy of the species with a high level G2(MP2) method. The rate constant of the two reactions are calculated at 298?K and 1?atm using Canonical Transition State Theory (CTST) utilizing the ab initio data obtained during the present study. The rate constant values are found to be 5.5?×?10^?14 and 5.9?×?10^?14?cm³ molecule^?1 s^?1, respectively which are in good agreement with the experimental data.     

A coupled cluster study of the magnetisability,rotational g-tensor and quadrupole moment of NF3, PF3 and AsF3

ABSTRACT

A coupled-cluster investigation of magnetic and electric properties of NF₃, PF₃ and AsF₃ provides for a comparison with recent experimental data. For PF₃, achieving reliable values for the magnetisability and rotational g-tensor of PF₃ has been particularly challenging. We report the most accurate calculations to date for PF₃; for the vibrationally corrected anisotropic magnetisability, our extrapolated CCSD(T)/CBS value of ?0.290 a.u is within the uncertainty limits of the most recent experimental value of ?0.286 ± 0.042 a.u. For the rotational g-tensor of PF₃, agreement between theory and experiment for the g_⊥ component is excellent (deviation of less than 0.0006 a.u.). However, the g_|| component remains problematic even though our vibrationally corrected CCSD(T)/CBS value of ?0.0387 a.u is in closer agreement with the recently revised experimental value of ?0.0470 ± 0.0020 a.u. than the original value of ?0.0815 ± 0.0020 a.u. The origin of the remaining discrepancy remains unclear. Dipole and quadrupole moments have also been investigated.     

Theoretical characterization of the HSOH,H2SO and H2OS isomers

The HSOH, H₂SO and H₂OS isomers have been investigated employing the CCSD(T) methodology and the cc-pV(X + d)Z X = 3,4,5,6 basis sets. The anharmonic force fields have been calculated to predict the fundamental vibrational frequencies, rotational constants, vibration–rotation corrections, anharmonic corrections to zero-point energies, and structural parameters. In addition to this, a spectroscopic characterization of the deuterated isomers D₂SO and D₂OS was performed. At the CCSD(T)/CBS limit and including corrections for scalar relativistic, spin orbit and core-valence correlation effects, the estimated enthalpies of formation are ?28.1 ± 1, ?12.3 ± 1, and 10.1 ± 1 kcal/mol for HSOH, H₂SO and H₂OS, respectively. Finally, we discuss the problems faced during the extrapolation to the CBS limit of the properties investigated.     

Explicitly correlated benchmark calculations on C8H8 isomer energy separations: how accurate are DFT,double-hybrid,and composite ab initio procedures?

Accurate isomerization energies are obtained for a set of 45 C₈H₈ isomers by means of the high-level, ab initio W1-F12 thermochemical protocol. The 45 isomers involve a range of hydrocarbon functional groups, including (linear and cyclic) polyacetylene, polyyne, and cumulene moieties, as well as aromatic, anti-aromatic, and highly-strained rings. Performance of a variety of DFT functionals for the isomerization energies is evaluated. This proves to be a challenging test: only six of the 56 tested functionals attain root mean square deviations (RMSDs) below 3?kcal?mol^?1 (the performance of MP2), namely: 2.9 (B972-D), 2.8 (PW6B95), 2.7 (B3PW91-D), 2.2 (PWPB95-D3), 2.1 (ωB97X-D), and 1.2 (DSD-PBEP86) kcal?mol^?1. Isomers involving highly-strained fused rings or long cumulenic chains provide a ‘torture test’ for most functionals. Finally, we evaluate the performance of composite procedures (e.g. G4, G4(MP2), CBS-QB3, and CBS-APNO), as well as that of standard ab initio procedures (e.g. MP2, SCS-MP2, MP4, CCSD, and SCS-CCSD). Both connected triples and post-MP4 singles and doubles are important for accurate results. SCS-MP2 actually outperforms MP4(SDQ) for this problem, while SCS-MP3 yields similar performance as CCSD and slightly bests MP4. All the tested empirical composite procedures show excellent performance with RMSDs below 1?kcal?mol^?1.     

Coupled cluster study of NMR shielding constants and spin-rotation constants in SiH4, PH3 and H2S molecules

Ab initio methods are applied to analyse the NMR shielding constants and spin-rotation constants in SiH₄, PH₃ and H₂S molecules. The electron correlation effects are studied applying the MP2 and coupled cluster perturbation approaches. The basis set convergence is examined at the same time, and the final results for the equilibrium geometries are obtained at the CCSD(T)/cc-pCVQZ level. Zero-point vibrational and temperature contributions are computed at the SCF, MP2 and CCSD level of approximation. In addition, for the shielding constants we also estimate the relativistic effects, to determine total values of the shielding of the third-row nuclei in the studied molecules. Our final results for the shielding constants at 300?K are σ (²⁹Si in SiH₄)?=?482.35?ppm, σ (³¹P in PH₃)?=?611.64?ppm and σ (³³S in H₂S)?=?736.13?ppm. These values, together with estimated corrections and error bars, can be used to determine absolute NMR shielding scales for the heavy nuclei.     

用从头算方法研究GeCl2分子的非谐振力场和光谱常数

用从头算方法的MP2和CCSD（T）方法结合cc-pVTZ基组计算了二氯化锗同位素（⁷⁰GeCl₂、⁷²GeCl₂和⁷⁶GeCl₂）分子的平衡结构、光谱常数和非谐振力场.二氯化锗的几何结构、转动常数、振转相互作用常数、谐频、非谐振常数、四次和六次离心畸变常数、三次和四次力常数的计算结果与实验结果符合较好,二氯化锗分子的同位素效应较小,可能的原因是Ge同位素的质量变化相对较小.两种方法计算的结果均与实验结果符合,但CCSD（T）方法比MP2计算结果的偏差稍大一些,可能的原因是CCSD（T）方法在描述过共价Cl原子的电子相关时不够充分.     

Electron correlation and the stability of substituted alkenes

Isomerization energies for hexenes (C₆H₁₂) were evaluated with ab initio (Hartree–Fock (HF), MP2, SCS‐MP2, and CCSD(T)) and several density functional approximation (DFA) methods. CCSD(T)/6‐311+G(2d,p) energies were taken as a benchmark standard. The HF method incorrectly predicts that monosubstituted alkenes are more stable than multiply‐substituted alkenes. DFAs generally predict the correct stability trends of alkenes (mono‐, < di‐, < tri‐, < tetra‐substituted alkenes) but errors in popular functionals, such as B3LYP, can be as large as errors found for alkane hydrocarbon thermochemistries. Some of the HF error is traced back to deficiencies in modeling 1,3‐geminal and 1,4‐vicinal alkyl–alkyl group interactions, called vinylbranches, and changes in C? C and C? H bond types (sp³–sp² C? C to sp³–sp³ C? C and sp³ C? H to sp² C? H). The latter is shown to be more significant. Comparison of CCSD(T) energies of trans‐2‐butene with 2‐methylpropylene and cis‐2‐butene suggests that geminal vinylbranches are stabilizing while vicinal vinylbranches are destabilizing. B3LYP and other DFAs have much smaller errors than HF theory due to inclusion of correlation energy that better reproduces bond type changes. Copyright © 2011 John Wiley & Sons, Ltd.     

Ab initio potential energy surface and intermolecular vibrational frequency of C3-He complex

The intermolecular potential energy surface for C₃–He complex has been constructed using supermolecular CCSD(T) and MP4 methods. The potential surfaces have been calculated for 27 values of R ranging from 2.8 to 8.0 Å and 19 values of θ equally spaced between 0° and 180°. Both CCSD(T) and MP4 potentials have similar global behaviors. The global minimum in each of the potentials corresponds to the slightly distorted T-shaped geometry. On the basis of these two potentials, the intermolecular vibrational energies and wavefunctions were calculated. The energy level pattern of the vdW vibrational states was predicted for C₃–He complex. The zero point bending motion of this complex has a range of 180°. The calculated fundamental frequency of vdW bending is 3.16 cm^?1 at CCSD(T) level, and 5.38 cm^?1 at the MP4 level. In addition, we have also constructed the intermolecular potential energy surface with C₃ bending coordinate of 160° by using supermolecular CCSD(T) method. Two local minima including arrow-shaped and Y-shaped configurations were determined. The rotational constants of three C₃–He structures including T-shaped, arrow-shaped and Y-shaped configurations at CCSD(T) level were also reported.     

Joint theoretical and experimental study of the gas‐phase elimination kinetics of tert‐butyl ester of carbamic,N, N‐dimethylcarbamic,N‐hydroxycarbamic acids and 1‐(tert‐butoxycarbonyl)‐imidazole

The gas‐phase elimination kinetics of the title compounds were carried out in a static reaction system and seasoned with allyl bromide. The working temperature and pressure ranges were 200–280 °C and 22–201.5 Torr, respectively. The reactions are homogeneous, unimolecular, and follow a first‐order rate law. These substrates produce isobutene and corresponding carbamic acid in the rate‐determining step. The unstable carbamic acid intermediate rapidly decarboxylates through a four‐membered cyclic transition state (TS) to give the corresponding organic nitrogen compound. The temperature dependence of the rate coefficients is expressed by the following Arrhenius equations: for tert‐butyl carbamate logk₁ (s^?1) = (13.02 ± 0.46) – (161.6 ± 4.7) kJ/mol(2.303 RT)^?1, for tert‐butyl N‐hydroxycarbamate logk₁ (s^?1) = (12.52 ± 0.11) – (147.8 ± 1.1) kJ/mol(2.303 RT)^?1, and for 1‐(tert‐butoxycarbonyl)‐imidazole logk₁ (s^?1) = (11.63 ± 0.21)–(134.9 ± 2.0) kJ/mol(2.303 RT)^?1. Theoretical studies of these elimination were performed at Møller–Plesset MP2/6‐31G and DFT B3LYP/6‐31G(d), B3LYP/6‐31G(d,p) levels of theory. The calculated bond orders, NBO charges, and synchronicity (Sy) indicate that these reactions are concerted, slightly asynchronous, and proceed through a six‐membered cyclic TS type. Results for estimated kinetic and thermodynamic parameters are discussed in terms of the proposed reaction mechanism and TS structure. Copyright © 2007 John Wiley & Sons, Ltd.     

Quantum chemical studies of the OH-initiated oxidation reactions of propenols in the presence of O2

ABSTRACT

The atmospheric oxidation mechanisms of 1- and 2-propenol initiated by OH radical have been theoretically investigated at the CCSD(T)//BH&;HLYP/6-311?+?+G(d,p) level of theory. Conventional transition state theory was employed to predict the rate constants for the initial reaction channels. The calculations clearly indicate that OH-addition channels contribute maximum to the total reaction, both for 1- and 2-propenol, while H-abstraction channels can be neglected at the temperature range of 220–520?K. The calculated total rate constants at 298?K are 1.66?×?10^?11 and 7.69?×?10^?12 cm³?molecule^?1?s^?1 respectively for 1- and 2-propenol, which are in reasonable agreement with the experimental values of similar systems (vinyl ethers?+?OH reactions). The deduced Arrhenius expressions are k(OH?+?1-propenol)?=?1.43?×?10^?12 exp[(743.7?K)/T] and k(OH?+?2-propenol)?=?2.86?×?10^?12 exp[(310.5?K)/T] cm³?molecule^?1?s^?1. Under atmospheric condition, the OH-addition intermediates (CH₃C?HCH(OH)₂, CH₃CH(OH)C?H(OH), CH₃CH(OH)₂?CH₂, CH₃?C(OH)CH₂(OH)) are likely to react rapidly with O₂, the theoretically identified major products for 1-propenol are HCOOH, CH₃CHO and CH₃CH(OH)CHO, and the dominant products for 2-propenol are CH₃COOH, HCHO and CH₃COCH₂OH, both companied with the regeneration of OH and HO₂ radicals (crucial reactive radicals in the atmosphere).     

Prediction and characterisation of a chalcogen···π interaction with acetylene as a potential electron donor in XHS···HCCH and XHSe···HCCH (X = F,Cl, Br,CN, OH,OCH3, NH2, CH3) σ-hole complexes

It is well-known that many covalently bonded atoms of group VI have specific positive regions of electrostatic potential (σ-holes) through which they can interact with Lewis bases. This interaction is called ‘chalcogen bond’ by analogy with halogen bond and hydrogen bond. In this study, ab initio calculations are performed to predict and characterise chalcogen···π interactions in XHS···HCCH and XHSe···HCCH complexes, where X = F, Cl, Br, CN, OH, OCH₃, NH₂, CH₃. For the complexes studied here, XHS(Se) and HCCH are treated as a Lewis acid and a Lewis base, respectively. The CCSD(T)/aug-cc-pVTZ interaction energies of this type of σ-hole bonding range from ?1.18 to ?4.83 kcal/mol. The calculated interaction energies tend to increase in magnitude with increasing positive electrostatic potential on the extension of X–S(Se) bond. The stability of chalcogen···π complexes is attributed mainly to electrostatic and correlation effects. The nature of chalcogen···π interactions is unveiled by means of the atoms in molecules, natural bond orbital, and electron localisation function analyses.     

A high level computational study of the CH4/CF4 dimer: how does it compare with the CH4/CH4 and CF4/CF4 dimers?

The interaction within the methane–methane (CH₄/CH₄), perfluoromethane–perfluoromethane (CF₄/CF₄) methane–perfluoromethane dimers (CH₄/CF₄) was calculated using the Hartree–Fock (HF) method, multiple orders of Møller–Plesset perturbation theory [MP2, MP3, MP4(DQ), MP4(SDQ), MP4(SDTQ)], and coupled cluster theory [CCSD, CCSD(T)], as well as the PW91, B97D, and M06-2X density functional theory (DFT) functionals. The basis sets of Dunning and coworkers (aug-cc-pVxZ, x?=?D, T, Q), Krishnan and coworkers [6-311++G(d,p), 6-311++G(2d,2p)], and Tsuzuki and coworkers [aug(df, pd)-6-311G(d,p)] were used. Basis set superposition error (BSSE) was corrected via the counterpoise method in all cases. Interaction energies obtained with the MP2 method do not fit with the experimental finding that the methane–perfluoromethane system phase separates at 94.5?K. It was not until the CCSD(T) method was considered that the interaction energy of the methane–perfluoromethane dimer (?0.69?kcal?mol^?1) was found to be intermediate between the methane (?0.51?kcal?mol^?1) and perfluoromethane (?0.78?kcal?mol^?1) dimers. This suggests that a perfluoromethane molecule interacts preferentially with another perfluoromethane (by about 0.09?kcal?mol^?1) than with a methane molecule. At temperatures much lower than the CH₄/CF₄ critical solution temperature of 94.5?K, this energy difference becomes significant and leads perfluoromethane molecules to associate with themselves, forming a phase separation. The DFT functionals yielded erratic results for the three dimers. Further development of DFT is needed in order to model dispersion interactions in hydrocarbon/perfluorocarbon systems.     

Computational studies of the halooxyhalocarbenes XOCX (X = F,Cl)

Ab initio calculations at the B3LYP, MP2, MP4 and CCSD(T) levels of theory were performed to predict the stability of the halooxyhalocarbenes, XOCX (X = F, Cl). The calculations indicate that the nonlinear FOCF molecule is stable with an energy 16 kJ mol^?1 below the energy of possible reacting fragments F₂ and CO. However, a nonlinear equilibrium structure for ClOCCl was located, but it was found to be about 192 kJ mol^?1 higher in energy than the energy of Cl₂ and CO. The charge distribution in these molecules was analysed using the atoms in molecules (AIM) method.     

Conformational and structural studies of n‐propylamine from temperature dependent Raman and far infrared spectra of xenon solutions and ab initio calculations

The Raman and infrared spectra (4000 to 50 cm^–1) of the gas, liquid or solution, and solid have been recorded of n‐propylamine, CH₃CH₂CH₂NH₂. Variable temperature (−60 to −100 °C) studies of the Raman (1175 to 625 cm^–1) and far infrared (600 to 10 cm^–1) spectra dissolved in liquid xenon were carried out. From these data, the five possible conformers were identified and their relative stabilities obtained with enthalpy difference relative to trans–trans (Tt) for trans–gauche (Tg) of 79 ± 9 cm^–1 (0.9 ± 0.1 kJ/mol); for Gg of 91 ± 26 cm^–1 (1.08 ± 0.3 kJ/mol); for Gg′ of 135 ± 21 cm^–1 (1.61 ± 0.2 kJ/mol); for Gt of 143 ± 11 cm^–1 (1.71 ± 0.1 kJ/mol). The percentage of the five conformers is estimated to be 18% for the Tt, 24 ± 1% for Tg, 23 ± 3% for Gg, 18 ± 1% for Gg′ and 18 ± 1% for Gt at ambient temperature. The conformational stabilities have been predicted from ab initio calculations utilizing several different basis sets up to aug‐cc‐pVTZ from both second‐order Møller–Plesset (MP2, full) and density functional theory calculations by the Becke, three‐parameter, Lee–Yang–Parr method. Vibrational assignments were provided for the observed bands for all five conformers, which are supported by MP2(full)/6‐31G(d) ab initio calculations to predict harmonic force constants, wavenumbers, infrared intensities, Raman activities and depolarization ratios for both conformers. Estimated r₀ structural parameters were obtained from adjusted MP2(full)/6‐311+G(d,p) calculations. The results are discussed and compared with the corresponding properties of some related molecules. Copyright © 2012 John Wiley & Sons, Ltd.     

Theoretical study of rearrangements in water dimer and trimer

The global minimum and transition states for the acceptor-tunnelling, donor-acceptor interchange and bifurcation tunnelling rearrangements of the water dimer, and the single-flip, bifurcation and concerted proton transfer processes in the water trimer have been reinvestigated. Our analysis of the tunnelling splittings and spectroscopy is based on ab initio calculations at the computational level of second-order M?ller-Plesset (MP2) theory with basis sets of aug-cc-pVXZ quality (X = D, T, Q for the dimer; X = D, T for the trimer). In both water dimer and trimer, the binding energy, barrier heights, intermonomer distances, and harmonic frequencies converge smoothly as the size of the basis set increases. In the water dimer, the binding energy was evaluated as 5.09kcal mol^?1, while the activation energies are 0.52 (acceptor-tunnelling) 0.79 (donor-acceptor interchange), and 1.94 kcal mol^?1 (bifurcation tunnelling) at the MP2/aug-cc-pVQZ level. In the water trimer, the binding energy was evaluated as 16.29 kcal mol^?1, while the activation energies are 0.28 (single-flip), 2.34 (bifurcation), and 26.36 (proton transfer) kcal mol^?1 at the MP2/aug-cc-pVTZ level.