Combined bond-polarization basis sets for accurate determination of dissociation energies. II. Basis set superposition error as a function of the parent basis set

The effect of the parent basis set on the basis set superposition error caused by bond functions is investigated systematically. An important difference between BSSE at the SCF and correlated levels is pointed out. Three new basis sets are defined, denoted 6-311 + G(d,p)B, 6-311 + G(2d,p)B, and 6-311 + G(2df,p)B. BSSE for the first-row hydrides seems to increase uniformly with increasing atomic number of the central atom. Expansion of the valence part of the basis set from 6-31G to 6-311G, as well as adding f functions, has a significant effect on the BSSE. Additional BSSEs incurred by bond functions are less than or equal to 1 kcal/mol for the 6-311 + G(2df,p)B basis set. For the dissociation energies of the first-row hydride species, agreement with experiment within only a few kcal/mol can be obtained even without resorting to isogyric reaction cycles. For high-quality calculations, adding bond functions seems to have definite advantages over expanding the polarization space beyond the [2d1f] level.     

MCSCF study of singlet oxygen addition to ethenol—a model of photooxidation reactions of unsaturated and aromatic compounds bearing hydroxy groups

The reaction path of singlet (¹Δ_g) oxygen addition to ethenol (vinyl alcohol)—a model of the reactions of singlet oxygen with aromatic and unsaturated compounds bearing the hydroxy groups—has been studied by means of MCSCF calculations, using various active spaces and basis sets. The effects of dynamic correlation (at the PT2 level) and basis set superposition error (BSSE) on relative energies were also investigated. It was found that including polarization functions is necessary to obtain geometries of the oxygen moiety consistent with the available experimental data. Two possible reaction products were considered: 1-hydroxy-1,2-dioxethane (peroxide) and 2-hydroperoxyethanal-1 (hydroperoxide); their energies are 24.1 and 36.6 kcal/mol (44.1 and 78.2 kcal/mol with the PT2 contribution and BSSE correction) below the dissociation limit, respectively (all energies reported here refer to the 6-31G** basis set and an active space composed of eight orbitals and ten electrons). A common stage of both reactions is the formation of a peralcoxyl intermediate with one of the oxygen atoms attached to the unsubstituted carbon atom; the energies of the respective transition state and that of the intermediate are 30.2 and 18.7 kcal/mol (15.9 and 10.3 kcal/mol with the PT2 contribution and BSSE correction) above the dissociation limit, respectively. The energy of this transition state is the dominant energy barrier to the reaction. The intermediate can then undergo conversion to the dioxethane product, to the perepoxide intermediate, or via a proton transfer, directly to the hydroperoxide, the last route being the most probable one. The perepoxide intermediate, after a proton transfer, also readily gives the hydroperoxide. It was also found that the unimolecular conversion from dioxethane to hydroperoxide via a proton transfer from the hydroxy group accompanied with ring cleavage requires an activation energy of at least 56 kcal/mol, making this reaction path highly improbable. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 1668–1681, 1997     

Basis sets for molecular interactions. 2. Application to H3N?HF,H3N?HOH,H2O?HF, (NH3)2, and H3CH?OH2

Modifications of the standard 6-31G** basis set as recommended in the accompanying paper are found to markedly lower the basis set superposition error (BSSE) in the title complexes, in contrast to enlargement to a triple-ζ scheme or by addition of a diffuse sp shell or a second set of d-functions without prior optimization, all of which lead to BSSE increase. After appropriate correction for correlation and superposition effects, all basis sets (with the exception of the standard 6-31G** and 6-311G** with their very large BSSE) predict the cyclic geometry of NH₃ dimer to be more stable than the linear arrangement. Correlation and BSSE can shift the equilibrium intermolecular distance in H₃CH-OH₂ by up to 0.4 Å. Failure to correct for superposition error leads to a drastic exaggeration of both the SCF and MP2 components of the interaction energy in this complex. Much better estimates are furnished by our recommended basis sets with their smaller superposition errors.     

Compact contracted Gaussian-type basis sets for halogen atoms. Basis-set superposition effects on molecular properties

Compact, contracted Gaussian basis sets for halogen atoms are generated and tested in ab initio molecular calculations. These basis sets have similar structure to that of Huzinaga and co-workers' (HTS ) sets; however, they give both better atomic total energies and better properties of atomic valence orbitals. These sets, after splitting of valence orbitals and augmenting with polarization functions, provide molecular results that agree well with those given by extended calculations. Basis set superposition error (BSSE ) is calculated using the counterpoise method. BSSE has only slight influence on calculated equilibrium geometry, shape of potential curve, and electric properties (dipole and quadrupole moments) of molecules. However, atomization energies may be significantly changed by the BSSE .     

Ab initio investigation on stability and properties of XYCO... HZ complexes. II: Post hartree-fock studies on H2CO... HF

Ab initio MP2 level of theory in conjunction with three basis sets of a triple-zeta quality was applied to study the molecular geometry and stability of the H₂CO... HF complex. An interaction energy predicted for this system at the highest, MP4(SDTQ)/6-311 + +G(2df, 2pd)//MP2/6-311 + +G(2df, 2pd), level corrected for the BSSE and ZPE contributions amounts to -4.85 kcal/ mol. BSSE contributes significantly to the interaction energies at all applied levels. Reliable MP2/ 6-311 + +G(2df, 2pd) level harmonic vibrational frequencies, IR intensities, and the predicted isotopic shifts upon deuteration and¹⁸O substitution are presented in order to facilitate experimental studies on the IR spectrum of the title complex.     

Post-Hartree-Fock and DFT level studies on the Cl2CO …︁ Cl2 complex: Accurate molecular parameters,harmonic vibrational frequencies,and interaction energies

The Cl₂CO …︁ Cl₂ complex was studied using ab initio post-Hartree-Fock theory at the MP2 and MP4 levels and, for comparison, the DFT method with 6-311G(2d), 6-311 + G(2d), and Sadlej's medium-size polarized (MSPBS) basis sets. A potential energy search recovered a planar minimum-energy structure characterized by a bent conformation. For this weakly bound complex, the interaction energy corrected for the basis set superposition error amounted to − 0.88, − 1.09, − 1.43, and − 0.38 kcal/mol at the MP4(SDTQ)/6-311G(2d), MP4(SDTQ)/6-311 + G(2d), MP4(SDTQ)/MSPBS, and DFT(Becke3LYP)/6-311 + G(2d) levels of theory, respectively. Two highly symmetrical forms, linear and T-shaped, correspond to transition-state conformers. The analysis of harmonic vibrational frequencies and potential energy distribution was performed at the MP2 and DFT levels with the 6-311 + G(2d) basis set. © 1996 John Wiley & Sons, Inc.     

The C2H 3 + cation and its interaction with HF

The structure and stability of classical and bridged C₂H ₃ ⁺ is reinvestigated. The SCF and CEPA-PNO computations performed with flexibles andp basis sets including twod-sets on carbon confirm our previous results. We find the protonated acetylene structure to be more stable than the vinyl cation by 3.5–4 kcal/mol. The energy barrier for the interconversion of these two structures is at most a few tenths of a kcal/mol. The equilibrium SCF geometries of Weberet al. [15] are affected insignificantly by further optimization at the CEPA-PNO level. Several structures for the interaction of C₂H ₃ ⁺ with HF have been investigated at the SCF level. With our largest basis set which includes a complete set of polarization functions we find a remarkable levelling of the stabilities of most of the structures. In these cases the stabilization energy ΔE ranges from −10 to −13 kcal/mol.     

Characterization of the potential energy surfaces of two small but challenging noncovalent dimers: (P2)2 and (PCCP)2

This work characterizes eight stationary points of the P₂ dimer and six stationary points of the PCCP dimer, including a newly identified minimum on both potential energy surfaces. Full geometry optimizations and corresponding harmonic vibrational frequencies were computed with the second‐order Møller–Plesset (MP2) electronic structure method and six different basis sets: aug‐cc‐pVXZ, aug‐cc‐pV(X+d)Z, and aug‐cc‐pCVXZ where X = T, Q. A new L‐shaped structure with C₂ symmetry is the only minimum for the P₂ dimer at the MP2 level of theory with these basis sets. The previously reported parallel‐slipped structure with C_2h symmetry and a newly identified cross configuration with D₂ symmetry are the only minima for the PCCP dimer. Single point energies were also computed using the canonical MP2 and CCSD(T) methods as well as the explicitly correlated MP2‐F12 and CCSD(T)‐F12 methods and the aug‐cc‐pVXZ (X = D, T, Q, 5) basis sets. The energetics obtained with the explicitly correlated methods were very similar to the canonical results for the larger basis sets. Extrapolations were performed to estimate the complete basis set (CBS) limit MP2 and CCSD(T) binding energies. MP2 and MP2‐F12 significantly overbind the P₂ and PCCP dimers relative to the CCSD(T) and CCSD(T)‐F12 binding energies by as much as 1.5 kcal mol^?1 for the former and 5.0 kcal mol^?1 for the latter at the CBS limit. The dominant attractive component of the interaction energy for each dimer configuration was dispersion according to several symmetry‐adapted perturbation theory analyses. © 2014 Wiley Periodicals, Inc.     

A theoretical determination of the dissociation energy of the nitric oxide dimer

Summary Multi-reference CI methods have been applied to determine the dissociation energy and structure of thecis-N₂O₂ molecule. The convergence of the theoretical result has been checked with respect to a systematic expansion of the one-electron basis set and the multi-reference CI wave function. The best calculated value, 13.8 kJ/mol, is in agreement with the experimental value, 12.2 kJ/mol. It has been obtained with an extended ANO-type basis set [6s5p3d2f], including the effect of the basis set superposition error (BSSE) in the geometry optimization, and additional effects, such as the electron correlation of core electrons and relativistic corrections, using the average coupled pair functional (ACPF) approach. The optimal geometry computed at this level was found to be:r(NN)=2.284 Å,r(NO)=1.149 Å, and s5p3d2f] basis set, the BSSE was found to be 2 kJ/mol.     

Non-empirical LCAO-MO-SCF calculations of the electronic structure of SiF2

Non-empirical LCAO-MO-SCF calculations on SiF₂ using two Gaussian basis sets are reported. The larger basis set gives a calculated geometry in good agreement with experiment. The effect on the energy and population analysis of optimization of the Si 3d exponent was investigated. 3d orbitals are found to be much less important in the bonding than in the isoelectronic molecule SO₂.     

Structure of Mn2(CO)10 and Mn2(CO)9: Insights from ab initio calculations

Optimization of the Mn–Mn distance in Mn₂(CO)₁₀ with various basis sets of at least doublezeta quality results in Mn–Mn bond lengths in the range of 3.07–3.15 Å, 0.2–0.25 Å longer than the experimental value of 2.895 Å. Incrementing the basis set with diffuse p functions (exponent 0.0332) on the carbon atoms improves the calculated bond length to a value of 2.876 Å at the CI level, as a consequence of a charge transfer between each Mn atom and the equatorial carbonyls of the other Mn atom. For Mn₂(CO)₉ four structures have been studied at the SCF and CI levels with assumed geometries. The structure with a symmetric bridging carbonyl turns to be much higher in energy at the SCF level. The two structures which are purely metal–metal bonded [corresponding to the departure of an axial or equatorial carbonyl from Mn₂(CO)₁₀] are nearly degenerate in energy and more stable than the structure with a semibridging carbonyl by 5 kcal/mol at the SCF level and 10–11 kcal/mol at the CI level (seemingly at variance with the conclusions of matrix experiments that favor the semibridging structure).     

SCF,MP2, and CEPA-1 calculations on the OH ‥ O hydrogen bonded complexes (H2O)2 and (H2O-H2CO)

Counterpoise corrected ab initio calculations are reported for (H₂O)₂ and H₂O-H₂CO. Geometry searches were done in the moment-optimized basis DZP' at the SCF, MP2, and CEPA-1 levels of theory, followed by more accurate single-point calculations in basis ESPB, which includes bondfunctions to saturate the dispersion energy. The final equilibrium binding energies obtained are ?4.7 ±0.3 kcal/mol for a near-linear (H₂O)₂ structure and ?4.6 ±0.3 kcal/mol for a strongly bent HOH ‥ OCH₂ structure. The energy difference between these systems is much smaller than in all previous ab initio work. Cyclic (C_2h) and bifurcated (C_2v) transition structures for (H₂O)₂ are located at 1.0 ±0.1 kcal/mol and 1.9 ±0.3 kcal/mol above the global minimum, respectively. A new partitioning scheme is presented that rigorously partitions the MP2 correlation interaction energy in intra and intermolecular (dispersion) contributions. These terms are large (up to 2 kcal/mol) but of opposite sign for most geometries studied and hence their overall effect upon the final structures is relatively small. The relative merits of the MP2 and CEPA-1 approaches are discussed are discussed and it is concluded that for economical reasons MP2 is to be preferred, especially for larger systems.     

A Systemic DFT Study on Several 5<Emphasis Type="Italic">d</Emphasis>-Electron Element Dimers: Hf<Subscript>2</Subscript>, Ta<Subscript>2</Subscript>, Re<Subscript>2</Subscript>, W<Subscript>2</Subscript>, and Hg<Subscript>2</Subscript>

Eleven kinds of density functionals in conjunction with three different basis sets are employed to investigate the homonuclear 5d-electron dimers: Hf₂, Ta₂, Re₂, W₂ and Hg₂. The computed bond lengths, vibrational frequencies and dissociation energies of these molecules are used to compare with available experimental data to find the appropriate combination of functional and basis set. The different functionals and basis sets favor different ground electronic state for Hf₂ and Re₂ molecules, indicating that these two dimers are sensitive to the functionals used. The molecular properties of Hg₂ dimer depend strongly on both functionals and basis sets used. It is found that the BP86 and PBEPBE functionals are generally successful in describing the 5d-electron dimers. For the ground states of these dimers, the bonding patterns are determined by natural bond orbital (NBO) analysis. Natural electron configurations show that the 6s and 5d orbitals in the bonding atoms hybrid with each other for the studied dimers except for Hg₂.     

Ab Initio and Quantum Chemical Topology studies on the isomerization of HONO to HNO2. Effect of the basis set in QCT

The article focus on the isomerization of nitrous acid HONO to hydrogen nitryl HNO₂. Density functional (B3LYP) and MP2 methods, and a wide variety of basis sets, have been chosen to investigate the mechanism of this reaction. The results clearly show that there are two possible paths: 1) Uncatalysed isomerisation, trans‐HONO → HNO₂, involving 1,2‐hydrogen shift and characterized by a large energetic barrier 49.7 ÷ 58.9 kcal/mol, 2) Catalysed double hydrogen transfer process, trans‐HONO + cis‐HONO → HNO₂ + cis‐HONO, which displays a significantly lower energetic barrier in a range of 11.6 ÷ 18.9 kcal/mol. Topological analysis of the Electron Localization Function (ELF) shows that the hydrogen transfer for both studied reactions takes place through the formation of a ‘dressed’ proton along the reaction path. 1 Use of a wide variety of basis sets demonstrates a clear basis set dependence on the ELF topology of HNO₂. Less saturated basis sets yield two lone pair basins, V₁(N), V₂(N), whereas more saturated ones (for example aug‐cc‐pVTZ and aug‐cc‐pVQZ) do not indicate a lone pair on the nitrogen atom. Topological analysis of the Electron Localizability Indication (ELI‐D) at the CASSCF (12,10) confirms these findings, showing the existence of the lone pair basins but with decreasing populations as the basis set becomes more saturated (0.35e for the cc‐pVDZ basis set to 0.06e for the aug‐cc‐pVTZ). This confirms that the choice of basis set not only can influence the value of the electron population at the particular atom, but can also lead to different ELF topology. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Coupled cluster,B2PLYP and M06-2X investigation of the thermochemistry of five-membered nitrogen containing heterocycles,furan, and thiophene

Herein, the thermochemical properties of five-membered rings heterocycles were studied employing the CCSD(T) methodology coupled with the correlation consistent basis sets and including corrections for relativistic and core-valence effects as well as anharmonicities of the potentials. For pyrrole, furan, imidazole, pyrazole, 1H-1,2,4-triazole, and 1H-tetrazole, the mean absolute deviation (MAD) of the \Updelta \textH_{\textf, 2 9 8}^\texto \Updelta {\text{H}}_{{{\text{f}}, 2 9 8}}^{\text{o}} , computed at the CCSD(T) level, is 0.5 kcal/mol with respect to the experimental values. In the case of 1H-1,2,3-triazole, 2H-1,2,3-triazole, 4H-1,2,3-triazole, 4H-1,2,4-triazole, 2H-tetrazole, and pentazole, we propose the following \Updelta \textH_{\textf, 2 9 8}^\texto \Updelta {\text{H}}_{{{\text{f}}, 2 9 8}}^{\text{o}} : 62.6, 59.2, 85.0, 54.2, 77.7, and 107.5 kcal/mol, respectively. For thiophene, we revisit our previous result and propose a value of 26.0 kcal/mol. The theoretical estimations were used to study the performance of the M06-2X and B2PLYP functionals. Also, the convergence toward the complete basis set limit (CBS) was analyzed. M06-2X did not show a smooth convergence toward the CBS limit. Particularly, for the cc-pVTZ and cc-pVQZ basis sets, some problems were detected. Yet, along the cc-pVQZ, cc-pV5Z, and cc-pV6Z basis sets, the TAE smoothly decreased. The diminution of the TAE upon increase in basis set was not expected because the opposite behavior is more frequently observed. The MAD of the total atomization energies determined at the M06-2X level was 0.42 kcal/mol, with respect to the CCSD(T) results. In the case of the double hybrid B2PLYP functional, a smooth convergence toward the CBS limit was detected, even though the performance seriously degradated when the basis set was increased. At the CBS limit, the MAD with respect to the CCSD(T) TAEs was 8.26 kcal/mol.     

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.