Benchmark of density functional theory methods on the prediction of bond energies and bond distances of noble-gas containing molecules

We have tested three pure density functional theory (DFT) functionals, BLYP, MPWPW91, MPWB95, and ten hybrid DFT functionals, B3LYP, B3P86, B98, MPW1B95, MPW1PW91, BMK, M05-2X, M06-2X, B2GP-PLYP, and DSD-BLYP with a series of commonly used basis sets on the performance of predicting the bond energies and bond distances of 31 small neutral noble-gas containing molecules. The reference structures were obtained using the CCSD(T)∕aug-cc-pVTZ theory and the reference energies were based on the calculation at the CCSD(T)∕CBS level. While in general the hybrid functionals performed significantly better than the pure functionals, our tests showed a range of performance by these hybrid functionals. For the bond energies, the MPW1B95∕6-311+G(2df,2pd), BMK∕aug-cc-pVTZ, B2GP-PLYP∕aug-cc-pVTZ, and DSD-BLYP∕aug-cc-pVTZ methods stood out with mean unsigned errors of 2.0-2.3 kcal∕mol per molecule. For the bond distances, the MPW1B95∕6-311+G(2df,2pd), MPW1PW91∕6-311+G(2df,2pd), and B3P86∕6-311+G(2df,2pd), DSD-BLYP∕6-311+G(2df,2pd), and DSD-BLYP∕aug-cc-pVTZ methods stood out with mean unsigned errors of 0.008-0.013 A? per bond. The current study showed that a careful selection of DFT functionals is very important in the study of noble-gas chemistry, and the most recommended methods are MPW1B95∕6-311+G(2df,2pd) and DSD-BLYP∕aug-cc-pVTZ.     

Benchmark calculations on the adiabatic ionization potentials of M-NH(3) (M=Na,Al,Ga,In,Cu,Ag)

The ground states of the M-NH(3) (M=Na,Al,Ga,In,Cu,Ag) complexes and their cations have been studied with density functional theory and coupled cluster [CCSD(T)] methods. The adiabatic ionization potentials (AIPs) of these complexes are calculated, and these are compared to results from high-resolution zero-electron kinetic energy photoelectron spectroscopy. By extrapolating the CCSD(T) energies to the complete basis set (CBS) limit and including the core-valence, scalar relativistic, spin-orbit, and zero-point corrections, the CCSD(T) method is shown to be able to predict the AIPs of these complexes to better than 6 meV or 0.15 kcal/mol. 27 exchange-correlation functionals, including one in the local density approximation, 13 in the generalized gradient approximation (GGA), and 13 with hybrid GGAs, were benchmarked in the calculations of the AIPs. The B1B95, mPW1PW91, B98, B97-1, PBE1PBE, O3LYP, TPSSh, and HCTH93 functionals give an average error of 0.1 eV for all the complexes studied, with the B98 functional alone yielding a maximum error of 0.1 eV. In addition, the calculated metal-ammonia harmonic stretching frequencies with the CCSD(T) method are in excellent agreement with their experimental values, whereas the B3LYP method tends to underestimate these stretching frequencies. The metal-ammonia binding energies were also calculated at the CCSD(T)/CBS level, and are in excellent agreement with the available experimental values considering the error limits, except for Ag-NH(3) and Ag(+)-NH(3), where the calculations predict stronger bond energies than measured by about 4 kcal/mol, just outside the experimental error bars of +/-3 kcal/mol.     

Testing the performance of density functionals for the calculation of energetic properties of complex-forming radical-molecule reactions

The performance of some popular and some more recent density functional methods for the calculation of energies of stationary points on the potential surfaces of radical-molecule reactions was examined. The functionals studied are B3-LYP, BH&H, BH&H-LYP, MPW1K, MPWB1K, TPSS, TPSSh, BB1K, M05 and M05-2X, in conjunction with nine different AO basis sets. The reaction energies, barrier heights and the relative energies of the pre-and post-reaction complexes were compared with those obtained at the CCSD(T)/CBS limit for the reactions of OH radicals with HOOH and CH₃OOH. Very poor barrier heights are provided by the B3-LYP, TPSS and TPSSh functionals. The best overall performance was obtained with the BB1K, MPW1K and MPWB1K functionals. In these reactions all of the studied functionals provide converged results only if they are used with large basis sets like aug-cc-pVTZ and def2-TZVP. The data show that before relying on a functional for a specific reaction, it is desirable to make some test calculations on the performance. The same functional can predict some relative energies very well and some others very poorly even in systems including chemically similar reactants.     

Design of density functionals that are broadly accurate for thermochemistry, thermochemical kinetics, and nonbonded interactions

This paper develops two new hybrid meta exchange-correlation functionals for thermochemistry, thermochemical kinetics, and nonbonded interactions. The new functionals are called PW6B95 (6-parameter functional based on Perdew-Wang-91 exchange and Becke-95 correlation) and PWB6K (6-parameter functional for kinetics based on Perdew-Wang-91 exchange and Becke-95 correlation). The resulting methods were comparatively assessed against the MGAE109/3 main group atomization energy database, against the IP13/3 ionization potential database, against the EA13/3 electron affinity database, against the HTBH38/4 and NHTBH38/04 hydrogen-transfer and non-hydrogen-transfer barrier height databases, against the HB6/04 hydrogen bonding database, against the CT7/04 charge-transfer complex database, against the DI6/04 dipole interaction database, against the WI7/05 weak interaction database, and against the new PPS5/05 pi-pi stacking interaction database. From the assessment and comparison of methods, we draw the following conclusions, based on an analysis of mean unsigned errors: (i) The PW6B95, MPW1B95, B98, B97-1, and TPSS1KCIS methods give the best results for a combination of thermochemistry and nonbonded interactions. (ii) PWB6K, MPWB1K, BB1K, MPW1K, and MPW1B95 give the best results for a combination of thermochemical kinetics and nonbonded interactions. (iii) PWB6K outperforms the MP2 method for nonbonded interactions. (iv) PW6B95 gives errors for main group covalent bond energies that are only 0.41 kcal (as measured by mean unsigned error per bond (MUEPB) for the MGAE109 database), as compared to 0.56 kcal/mol for the second best method and 0.92 kcal/mol for B3LYP.     

Assessment of density functionals for pi systems: Energy differences between cumulenes and poly-ynes; proton affinities, bond length alternation, and torsional potentials of conjugated polyenes; and proton affinities of conjugated Shiff bases

Woodcock et al. [J. Phys. Chem. A 2002, 106, 11923] pointed out that no density functional was able to obtain the correct sign of the relative energies of the allene and propyne isomers of C3H4 and that density functional theory (DFT) predicts that poly-ynes are insufficiently stabilized over cumulenes for higher homologues. In the present work, we show that the recent M05 density functional predicts the correct ordering of allene and propyne and gives a mean unsigned error (MUE) of only 1.8 kcal/mol for the relative energies of the two isomers of C3H4, C5H4, and C7H4. Two other recent functionals, M05-2X and PWB6K, also give reasonably low MUEs, 2.7 and 3.0 kcal/mol, respectively, as compared to 6.2 kcal/mol for the popular B3LYP functional. Another challenging problem for density functionals has been a tendency to overpolarize conjugated pi systems. We test this here by considering proton affinities of conjugated polyenes and conjugated Schiff bases. Again M05-2X performs quite well, with MUEs of 2.1 and 3.9 kcal/ mol, respectively, as compared to 5.8 and 5.9 kcal/mol for B3LYP. Averaged over the three problems, M05-2X has a MUE of 3.0 kcal/mol, the BMK functional of Boese et al. has an MUE of 3.2 kcal/mol, and M05 has an MUE of 5.1 kcal/mol. Twenty-two other tested functionals have MUEs of 5.2-8.1 kcal/mol averaged over the three test problems. Both M05 and M05-2X do quite well, compared to other density functionals, for torsion potentials in butadiene and styrene, and M05 does very well for bond length alternation in conjugated polyenes. Since the M05 functional has broad accuracy for main group and transition metal chemistry and M05-2X has broad accuracy for main group chemistry, we conclude that significant progress is being made in improving the performance of DFT across a wide range of problem types.     

The MC‐DFT approach including the SCS‐MP2 energies to the new minnesota‐type functionals

We have applied the multicoefficient density functional theory (MC‐DFT) to four recent Minnesota functionals, including M06‐2X, M08‐HX, M11, and MN12‐SX on the performance of thermochemical kinetics. The results indicated that the accuracy can be improved significantly using more than one basis set. We further included the SCS‐MP2 energies into MC‐DFT, and the resulting mean unsigned errors (MUEs) decreased by approximately 0.3 kcal/mol for the most accurate basis set combinations. The M06‐2X functional with the simple [6–311+G(d,p)/6–311+G(2d,2p)] combination gave the best performance/cost ratios for the MC‐DFT and MC‐SCS‐MP2|MC‐DFT methods with MUE of 1.58 and 1.22 kcal/mol, respectively. © 2014 Wiley Periodicals, Inc.     

Accurate bond dissociation enthalpies by using doubly hybrid XYG3 functional

In this work, we examine the performance of XYG3, a newly developed doubly hybrid density functional (Zhang, Xu, and Goddard III, Proc Natl Acad Sci USA 2009, 106, 4963), to calculate covalent bond dissociation enthalpy (BDE). We use 5 atoms, 32 molecular radicals, and 116 closed-shell molecules to set up 142 bond dissociation reactions. For the total of 148 heats of formation (HOFs) and 142 BDEs, XYG3 leads to mean absolute deviations (MADs) of 1.45 and 1.87 kcal/mol, respectively. In comparison with some other functionals, MADs for HOFs are 2.31 (M06-2X), 2.98 (B2PLYP-D), 3.04 (BMK), 3.96 (B3LYP), 4.47 (B2PLYP), 5.42 (B2GP-PLYP), 6.46 (PBE0), and 29.93 kcal/mol (B3P86), and the corresponding errors for BDEs are 2.06 (M06-2X), 2.25 (BMK), 2.51 (B2PLYP-D), 2.89 (B2GP-PLYP), 3.30 (B3P86), 3.44 (B2PLYP), 3.87 (PBE0), and 6.14 kcal/mol (B3LYP).     

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).     

Approximations to complete basis set-extrapolated, highly correlated non-covalent interaction energies

The first-principles calculation of non-covalent (particularly dispersion) interactions between molecules is a considerable challenge. In this work we studied the binding energies for ten small non-covalently bonded dimers with several combinations of correlation methods (MP2, coupled-cluster single double, coupled-cluster single double (triple) (CCSD(T))), correlation-consistent basis sets (aug-cc-pVXZ, X = D, T, Q), two-point complete basis set energy extrapolations, and counterpoise corrections. For this work, complete basis set results were estimated from averaged counterpoise and non-counterpoise-corrected CCSD(T) binding energies obtained from extrapolations with aug-cc-pVQZ and aug-cc-pVTZ basis sets. It is demonstrated that, in almost all cases, binding energies converge more rapidly to the basis set limit by averaging the counterpoise and non-counterpoise corrected values than by using either counterpoise or non-counterpoise methods alone. Examination of the effect of basis set size and electron correlation shows that the triples contribution to the CCSD(T) binding energies is fairly constant with the basis set size, with a slight underestimation with CCSD(T)∕aug-cc-pVDZ compared to the value at the (estimated) complete basis set limit, and that contributions to the binding energies obtained by MP2 generally overestimate the analogous CCSD(T) contributions. Taking these factors together, we conclude that the binding energies for non-covalently bonded systems can be accurately determined using a composite method that combines CCSD(T)∕aug-cc-pVDZ with energy corrections obtained using basis set extrapolated MP2 (utilizing aug-cc-pVQZ and aug-cc-pVTZ basis sets), if all of the components are obtained by averaging the counterpoise and non-counterpoise energies. With such an approach, binding energies for the set of ten dimers are predicted with a mean absolute deviation of 0.02 kcal/mol, a maximum absolute deviation of 0.05 kcal/mol, and a mean percent absolute deviation of only 1.7%, relative to the (estimated) complete basis set CCSD(T) results. Use of this composite approach to an additional set of eight dimers gave binding energies to within 1% of previously published high-level data. It is also shown that binding within parallel and parallel-crossed conformations of naphthalene dimer is predicted by the composite approach to be 9% greater than that previously reported in the literature. The ability of some recently developed dispersion-corrected density-functional theory methods to predict the binding energies of the set of ten small dimers was also examined.     

Accurate Interaction Energies of CO2 with the 20 Naturally Occurring Amino Acids

We have performed a series of highly accurate calculations between CO₂ and the 20 naturally occurring amino acids for the investigation of the attractive noncovalent interactions. Different nucleophilic groups present in the amino acid structures were considered (α-NH₂, COOH, side groups), and the stronger binding sites were identified. A database of accurate reference interactions energies was compiled as computed by explicitly-correlated coupled-cluster singles-and-doubles, together with perturbative triples extrapolated to the complete-basis-set limit. The CCSD(F12)(T)/CBS reference values were used for comparing a variety of popular density functionals with different basis sets. Our results show that most density functionals with the triple-zeta basis set def2-TZVPP align with the CCSD(F12)(T)/CBS reference values, but errors range from 0.1 kcal/mol up to 1.0 kcal/mol.     

Computational studies on the ground and excited states of BrOOBr

In this work, theoretical computations for the ground and excited states of BrOOBr have been performed at high-level ab initio molecular orbital theories. The ground-state geometries of BrOOBr in different forms (trans, cis, and twist form) have been optimized at the couple-cluster CCSD(T) level of theory with cc-pVTZ and aug-cc-pVTZ basis sets, which indicates that at CCSD(T)/cc-pVTZ level of theory, the twist form is 4.96 kcal/mol more stable than the trans form and 10.67 kcal/mol more stable than the cis form; at the CCSD(T)/aug-cc-pVTZ basis set the twist form is 4.33 kcal/mol more stable than the trans form and 9.54 kcal/mol more stable than the cis form. The vertical excitation energies and potential-energy curves for the singlet and triplet low-lying excited states of BrOOBr were calculated at both the complete active space self-consistent-field (CASSCF) level of theory and the multireference internally contracted configuration interaction (MRCI) level of theory. The differences of potential-energy curves at CASSCF and MRCI levels of theory are found for the BrOOBr excited states. At CASSCF level of theory, none of the BrOOBr excited states are bound. However, at MRCI level of theory, all the BrOOBr states studied in this work are bound or slightly bound at the Frank-Condon region. In addition, the scalar relativistic effect and the spin-orbital coupling effect on the vertical excitation energies of the electronic states of BrOOBr were estimated.     

Revision of the dissociation energies of mercury chalcogenides--unusual types of mercury bonding.

Mercury chalcogenides HgE (E=O, S, Se, etc.) are described in the literature to possess rather stable bonds with bond dissociation energies between 53 and 30 kcal mol(-1), which is actually difficult to understand in view of the closed-shell electron configuration of the Hg atom in its ground state (...4f(14)5d(10)6s(2)). Based on relativistically corrected many body perturbation theory and coupled-cluster theory [IORAmm/MP4, Feenberg-scaled IORAmm/MP4, IORAmm/CCSD(T)] in connection with IORAmm/B3LYP theory and a [17s14p9d5f]/aug-cc-pVTZ basis set, it is shown that the covalent HgE bond is rather weak (2-7 kcal mol(-1)), the ground state of HgE is a triplet rather than a singlet state, and that the experimental bond dissociation energies have been obtained for dimers (or mixtures of monomers, dimers, and even trimers) Hg2E2 rather than true monomers. The dimers possess association energies of more than 100 kcal mol(-1) due to electrostatic forces between the monomer units. The covalent bond between Hg and E is in so far peculiar as it requires a charge transfer from Hg to E (depending on the electronegativity of E) for the creation of a single bond, which is supported by electrostatic forces. However, a bonding between Hg and E is reduced by strong lone pair-lone pair repulsion to a couple of kcal mol(-1). Since a triplet configuration possesses somewhat lower destabilizing lone pair energies, the triplet state is more stable. In the dimer, there is a Hg-Hg pi bond of bond order 0.66 without any a support. Weak covalent Hg-O interactions are supported by electrostatic bonding. The results for the mercury chalcogenides suggests that all experimental dissociation energies for group-12 chalcogenides have to be revised because of erroneous measurements.     

CO oxidation catalyzed by a single gold atom: benchmark calculations and the performance of DFT methods

Quantum chemical calculations were carried out on CO oxidation catalyzed by a single gold atom. To investigate the performance of density functional theory (DFT) methods, 42 DFT functionals have been evaluated and compared with high-level wavefunction based methods. It was found that in order to obtain accurate results the functionals used must treat long range interaction well. The double-hybrid mPW2PLYP and B2PLYP functionals are the two functionals with best overall performance. CAM-B3LYP, a long range corrected hybrid GGA functional, also performs well. On the other hand, the popular B3LYP, PW91, and PBE functionals do not show good performance and the performance of the latter two are even at the bottom of the 42 functionals. Our accurate results calculated at the CCSD(T)/aug-cc-pVTZ//mPW2PLYP/aug-cc-pVTZ level of theory indicate that Au atom is a good catalysis for CO oxidation. The reaction follows the following mechanism where CO and O(2) adsorb on Au atom forming an Au(OCOO) intermediate and subsequently O(2) transfer one oxygen atom to CO to form CO(2) and AuO. Then AuO reacts with CO to form another CO(2) to complete the catalytic cycle. The overall energy barrier at 0 K for the first CO oxidation step (Au + CO + O(2)→ AuO + CO(2)) is just 4.8 kcal mol(-1), and that for the second CO oxidation step (AuO + CO → Au + CO(2)) is just 1.6 kcal mol(-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.     

Stabilisation energy of C(6)H(6)...C(6)X(6) (X = F, Cl, Br, I, CN) complexes: complete basis set limit calculations at MP2 and CCSD(T) levels

Stabilisation energies of stacked structures of C(6)H(6)...C(6)X(6) (X = F, Cl, Br, CN) complexes were determined at the CCSD(T) complete basis set (CBS) limit level. These energies were constructed from MP2/CBS stabilisation energies and a CCSD(T) correction term determined with a medium basis set (6-31G**). The former energies were extrapolated using the two-point formula of Helgaker et al. from aug-cc-pVDZ and aug-cc-pVTZ Hartree-Fock energies and MP2 correlation energies. The CCSD(T) correction term is systematically repulsive. The final CCSD(T)/CBS stabilisation energies are large, considerably larger than previously calculated and increase in the series as follows: hexafluorobenzene (6.3 kcal mol(-1)), hexachlorobenzene (8.8 kcal mol(-1)), hexabromobenzene (8.1 kcal mol(-1)) and hexacyanobenzene (11.0 kcal mol(-1)). MP2/SDD** relativistic calculations performed for all complexes mentioned and also for benzene[dot dot dot]hexaiodobenzene have clearly shown that due to relativistic effects the stabilisation energy of the hexaiodobenzene complex is lower than that of hexabromobenzene complex. The decomposition of the total interaction energy to physically defined energy components was made by using the symmetry adapted perturbation treatment (SAPT). The main stabilisation contribution for all complexes investigated is due to London dispersion energy, with the induction term being smaller. Electrostatic and induction terms which are attractive are compensated by their exchange counterparts. The stacked motif in the complexes studied is very stable and might thus be valuable as a supramolecular synthon.     

Model identity SN2 reactions CH3X + X- (X = F, Cl, CN, OH, SH, NH2, PH2): Marcus theory analyzed

The structures of seven gas phase identity S(N)2 reactions of the form CH(3)X + X(-) have been characterized with seven distinct theoretical methods: RHF, B3LYP, BLYP, BP86, MP2, CCSD, and CCSD(T), in conjunction with basis sets of double and triple zeta quality. Additionally, the energetics of said reactions have been definitively computed using focal point analyses utilizing extrapolation to the one-particle limit for the Hartree-Fock and MP2 energies using basis sets of up to aug-cc-pV5Z quality, inclusion of higher order correlation effects [CCSD and CCSD(T)] with basis sets of aug-cc-pVTZ quality, and additional auxiliary terms for core correlation and scalar relativistic effects. Final net activation barriers for the reactions are E(b)(F,F)= -0.8, E(b)(Cl,Cl)= 1.6, E(b)(CN,CN)= 28.7, E(b)(OH,OH)= 14.3, E(b)(SH,SH)= 13.8, E(b)(NH2,NH2)= 28.6, and E(b)(PH2,PH2)= 25.7 kcal mol(-1). General trends in the energetics, specifically the performance of the density functionals, and the component energies of the focal point analyses are discussed. The utility of classic Marcus theory as a technique for barrier predictions has been carefully analyzed. The standard Marcus theory results show disparities of up to 9 kcal mol(-1) with respect to explicitly computed results. However, when alternative approaches to Marcus theory, independent of the well-depths, are considered, excellent performance is achieved, with the largest deviations being under 3 kcal mol(-1).     

How accurate are electronic structure methods for actinoid chemistry?

The CASPT2, CCSD, and CCSD(T) levels of wave function theory and seven density functionals were tested against experiment for predicting the ionization potentials and bond dissociation energies of actinoid monoxides and dioxides with their cations. The goal is to guide future work by enabling the choice of an appropriate method when performing calculations on actinoid-containing systems. We found that four density functionals, namely MPW3LYP, B3LYP, M05, and M06, and three levels of wave function theory, namely CASPT2, CCSD, and CCSD(T), give similar mean unsigned errors for actinoid?Coxygen bond energies and for ionization potentials of actinoid oxides and their cations.     

Ab initio and density functional theory reinvestigation of gas-phase sulfuric acid monohydrate and ammonium hydrogen sulfate

We have calculated the thermochemical parameters for the reactions H(2)SO(4) + H(2)O <--> H(2)SO(4).H(2)O and H(2)SO(4) + NH(3) <--> H(2)SO(4).NH(3) using the B3LYP and PW91 functionals, MP2 perturbation theory and four different basis sets. Different methods and basis sets yield very different results with respect to, for example, the reaction free energies. A large part, but not all, of these differences are caused by basis set superposition error (BSSE), which is on the order of 1-3 kcal mol(-1) for most method/basis set combinations used in previous studies. Complete basis set extrapolation (CBS) calculations using the cc-pV(X+d)Z and aug-cc-pV(X+d)Z basis sets (with X = D, T, Q) at the B3LYP level indicate that if BSSE errors of less than 0.2 kcal mol(-1) are desired in uncorrected calculations, basis sets of at least aug-cc-pV(T+d)Z quality should be used. The use of additional augmented basis functions is also shown to be important, as the BSSE error is significant for the nonaugmented basis sets even at the quadruple-zeta level. The effect of anharmonic corrections to the zero-point energies and thermal contributions to the free energy are shown to be around 0.4 kcal mol(-1) for the H(2)SO(4).H(2)O cluster at 298 K. Single-point CCSD(T) calculations for the H(2)SO(4).H(2)O cluster also indicate that B3LYP and MP2 calculations reproduce the CCSD(T) energies well, whereas the PW91 results are significantly overbinding. However, basis-set limit extrapolations at the CCSD(T) level indicate that the B3LYP binding energies are too low by ca. 1-2 kcal/mol. This probably explains the difference of about 2 kcal mol(-1) for the free energy of the H(2)SO(4) + H(2)O <--> H(2)SO(4).H(2)O reaction between the counterpoise-corrected B3LYP calculations with large basis sets and the diffusion-based experimental values of S. M. Ball, D. R. Hanson, F. L Eisele and P. H. McMurry (J. Phys. Chem. A. 2000, 104, 1715). Topological analysis of the electronic charge density based on the quantum theory of atoms in molecules (QTAIM) shows that different method/basis set combinations lead to qualitatively different bonding patterns for the H(2)SO(4).NH(3) cluster. Using QTAIM analysis, we have also defined a proton transfer degree parameter which may be useful in further studies.