Basis set effects on the stability of the Cl2O3 isomers using B3P86 and B3LYP methods of density functional theory

Four Cl₂O₃ isomers have been calculated using density functional theory with B3P86 and B3LYP functionals and various basis sets. The energy hypersurfaces of Cl₂O₃ are very flat and the relative energies of the isomers which have hypervalent characters such as ClOCl(O)O and ClClO₃ are strongly dependent on the basis sets. The stability for Cl₂O₃ isomers are in the order of (1)ClOOOCl(C_s), (2)ClOOOCl(C₂), (3)ClClO₃ and (4)ClOCl(O)O with ClOCl(O)O being most stable. We suggest that at least the cc-pV6Z(-ghi) basis set for Cl and the cc-pVTZ basis set for O are required to obtain reliable relative stabilities of Cl₂O₃ isomers with hypervalent characters.     

The use of MIDI basis set at the correlated level

The H₂O + H₂O, the NH₃ + NH₃, the BH₃ + H₂O and the Ne + Ne systems have been studied in the supermolecule approach, using several medium sized basis sets (especially the so-called MIDI basis set). The calculations have been carried out by the use of localized molecular orbitals (LMOs).

The dispersion interaction energies have been computed by a new method (Kozmutza and Kapuy; Int. J. Quantum Chem., 38 (1990) 665), whose essence lies in the use of LMO contributions at the correlated level.

The method proposed seems to be useful for the H₂O + H₂O, the NH₃ + NH₃, and the Ne + Ne systems at different intermolecular distances, using the MIDI basis, but fails in describing correctly the correlation energy for the BH₃ + H₂O system.     

New scale factors for harmonic vibrational frequencies using the B3LYP density functional method with the triple-zeta basis set 6-311+G(d,p)

We have calculated optimal frequency scaling factors for the B3LYP/ 6-311+G(d,p) method for fundamental vibrational frequencies on the basis of a set of 125 molecules. Using the new scaling factor, the vibrational frequencies calculated with the triple-zeta basis set 6-311+G(d,p) give significantly better accuracy than those calculated with the double-zeta 6-31G(d) basis set. Scale factors were also determined for low-frequency vibrations using the molecular set of 125 molecules and for zero-point energies using a smaller set of 40 molecules. We have studied the effect on the calculated vibrational frequencies for various combinations of diffuse and polarization functions added to the triple-zeta 6-311G basis set. The 6-311+G(d,p) basis set is found to give almost converged frequencies for most molecules, and we conclude that our optimum scaling factors are valid for the basis sets 6-311G(d,p) to 6-311++G(3df,3pd). The new scale factors are 0.9679 for vibrational frequencies, 1.0100 for low-frequency vibrations, and 0.9877 for zero-point vibrational energies.     

FTIR and computational studies of pure and water containing SO3 species in solid argon matrices

The FT infrared spectrum in the 4000–400 cm⁻¹ range of SO₃ vapors, matrix isolated in argon and in water doped argon solid layers, is reported. Vibrational bands are assigned to pure SO₃ monomeric and polymeric species and to SO₃H₂O complexes, on the basis of theoretical B3LYP and MP2 calculations employing the aug-cc-pVTZ basis sets. The spectroscopic evidence suggests that in addition to the monomer, both the dimeric and the cyclic trimeric (SO₃)_n complexes are the only other SO₃ forms present in the matrix. The spectra also indicate the presence of the 1:1 and the 1:2 SO₃·H₂O complexes as well as traces of H₂S₂O₇ and water complexed H₂SO₄, but no evidence for a stable 2:1 SO₃H₂O complex was found. The occurrence of the various species is discussed in the light of their calculated energies.     

The 6-31B(d) basis set and the BMC-QCISD and BMC-CCSD multicoefficient correlation methods

Three new multicoefficient correlation methods (MCCMs) called BMC-QCISD, BMC-CCSD, and BMC-CCSD-C are optimized against 274 data that include atomization energies, electron affinities, ionization potentials, and reaction barrier heights. A new basis set called 6-31B(d) is developed and used as part of the new methods. BMC-QCISD has mean unsigned errors in calculating atomization energies per bond and barrier heights of 0.49 and 0.80 kcal/mol, respectively. BMC-CCSD has mean unsigned errors of 0.42 and 0.71 kcal/mol for the same two quantities. BMC-CCSD-C is an equally effective variant of BMC-CCSD that employs Cartesian rather than spherical harmonic basis sets. The mean unsigned error of BMC-CCSD or BMC-CCSD-C for atomization energies, barrier heights, ionization potentials, and electron affinities is 22% lower than G3SX(MP2) at an order of magnitude less cost for gradients for molecules with 9-13 atoms, and it scales better (N6 vs N,7 where N is the number of atoms) when the size of the molecule is increased.     

The performance of B3-LYP density functional theory in describing SN2 reactions at saturated carbon

The performance of the B3-LYP variant of density functional theory when used in conjunction with the 6-31G(d) and 6-311 + G(3df, 2p) basis sets in describing the prototypical gas-phase S_N2 reactions of Cl⁻ + CH₃Cl and CH₃Br has been examined in detail. Reasonable values of the complexation energies (ΔH_comp) for the ion-molecule complexes formed in these reactions are obtained. However, the overall (ΔH_ovr^#) and central (ΔH_cent^#) barriers for these reactions calculated using the B3-LYP functional are significantly underestimated when compared with G2(+) or experimental results. This implies that the B3-LYP energies for the Cl(H₃C)Cl⁻ (D_3h) and Cl(H₃C)Br⁻ (C_3v) transition structures are relatively too low. The B3-LYP errors appear to be systematic, with similar errors being found for corresponding quantities for the two reactions examined.     

Binding energies of germanium clusters, Gen (n = 2−5)

Gaussian-2 (G2) theory for third-row non-transition elements is used to calculate energies of germanium clusters, Ge_n (n = 2−5). The G2 energies are used to derive accurate binding energies for the clusters. The results for Ge₂ and Ge₃ are in agreement with experiment while there is some disagreement for Ge₄ and Ge₅. The binding energies are also calculated using the B3LYP density functional method with the 6–311 + G(3df,2p) basis set and compared with the G2 results and experiment.     

The 6-31G++ basis set: An economical basis set for correlated wavefunctions

The 6-31G ⁺⁺ basis set is described. This basis set is very similar to the existing 6-31G ^** set but is somewhat smaller through the use of five (rather than six) second-order Gaussians (d functions) and has polarization function exponents optimized for correlated rather than Hartree–Fock wavefunctions. The performance of 6-31G ⁺⁺ is compared with that of the 6-31G ^** and 6-31G ^** basis sets through calculation of the geometries and atomization energies for the set of molecules LiH, FH, H₂O, NH₃, CH₄, N₂, CO, HCN, and HCCH.     

Thermochemistry of the higher chlorine oxides ClOx (x=3, 4) and Cl2Ox (x=3–7)†

Heats of formation for ClO₃, ClO₄, Cl₂O₃, Cl₂O₄, Cl₂O₅, Cl₂O₆ and Cl₂O₇ molecules are determined at the B3LYP, B3PW91, mPW1PW91 and B1LYP levels of the density functional theory employing a series of extended basis sets, and using Gaussian-3 model chemistries. Modified Gaussian-3 calculations, which employ accurate B3LYP/6-311+G(3d2f) molecular geometries and vibrational frequencies, were also performed. Heats of formation were calculated from both total atomization energies and isodesmic reaction schemes. The latter method in conjunction with Gaussian-3 models leads to the most reliable results. The best values at 298 K for ClO₃, ClO₄, Cl₂O₃ and Cl₂O₄ as derived from an average of G3//B3LYP and G3//B3LYP/6-311+G(3d2f) calculations are 43.1, 54.8, 31.7 and 37.4 kcal mol⁻¹. From calculations carried out at the G3(MP2)//B3LYP and G3(MP2)//B3LYP/6-311+G(3d2f) levels, heats of formation for Cl₂O₅, Cl₂O₆ and Cl₂O₇ are predicted to be 53.2, 52.2 and 61.5 kcal mol⁻¹. All best values are reproduced within 1 kcal mol⁻¹ by using mPW1PW91/6-311+G(3d2f) isodesmic energies. Enthalpy changes for relevant Cl–O bond fission reactions are reported. Comparisons with previous thermodynamics data are made.     

Investigation of the use of B3LYP zero-point energies and geometries in the calculation of enthalpies of formation

The use of B3LYP/6–31G^* zero-point energies and geometries in the calculation of enthalpies of formation has been investigated for the enlarged G2 test set of 148 molecules [J. Chem. Phys. 106 (1997) 1063]. A scale factor of 0.96 for the B3LYP zero-point energies gives an average absolute deviation nearly the same as scaled HF/6–31G^* zero-point energies for G2, G2(MP2), and B3LYP/6–311 + G(3df,2p) enthalpies. A scale factor of 0.98, which has been recommended in some studies, increases the average absolute deviation by about 0.2 kcal/mol. Geometries from B3LYP/6–31G^* are found to do as well as MP2/6–31G^* geometries in the calculation of the enthalpies of formation.     

Basis set dependence of the vibrational wavenumbers of the out-of-plane modes of conjugated π-electron ring systems

Basis set dependence of the vibrational wavenumbers of out-of-plane modes calculated at the MP2 level of ab initio molecular orbital theory is examined for benzene, p-benzoquinodimethane, p-benzoquinone, furan, and thiophene. Various polarization functions up to (3df,p) are used in combination with the 6-31G and 6-311G basis sets. It is shown that, especially in the case of normal modes with alternate out-of-plane motions of the carbon atoms (such as the ν₄ (b_2g) mode of benzene), the calculated wavenumbers depend strongly on the exponents (_d) of the d functions on the carbon atoms. It is therefore necessary to include d functions with an optimum exponent (_d0.4) on the carbon atoms to obtain reasonable out-of-plane vibrational force fields. In a few cases (such as the ν₁₆ (a₂) mode of furan), inclusion of a set of f functions on the carbon atoms has some effects on the calculated wavenumbers of out-of-plane modes. However, unless the basis set contains an optimum set of d functions, inclusion of a set of f functions does not improve the agreement between the observed and calculated vibrational wavenumbers. As a case with an exaggerated effect of basis set, it is shown that the wavenumber of the ν₄₁ (b_2g) mode of the planar optimized structure of p-benzoquinodimethane is calculated to be imaginary by using the 6-311G(d,p) or 6-311G(df,p) basis set at the MP2 level. For all the molecules treated in the present study, reasonable out-of-plane vibrational force fields are obtained by using the 6-31G(2df,p) and 6-311G(2df,p) basis sets.     

Parameterization of a B3LYP specific correction for non-covalent interactions and basis set superposition error on a gigantic dataset of CCSD(T) quality non-covalent interaction energies

A vast number of non-covalent interaction energies at the counterpoise corrected CCSD(T) level have been collected from the literature to build a diverse new dataset. The whole dataset, which consists of 2027 CCSD(T) energies, includes most of the published data at this level. A large subset of the data was then used to train a novel, B3LYP specific, empirical correction scheme for non-covalent interactions and basis set superposition error (abbreviated as B3LYP-MM). Results obtained with our new correction scheme were directly compared to benchmark results obtained with B3LYP-D3(1) and M06-2X(2) (two popular density functions designed specifically to accurately model non-covalent interactions). For non-covalent complexes dominated by dispersion or dipole-dipole interactions all three tested methods give accurate results with the medium size aug-cc-pVDZ(3-6) basis set with MUE's of 0.27 (B3LYP-MM), 0.32 (B3LYP-D3) and 0.47 kcal/mol (M06-2X) (with explicit counterpoise corrections). These results validate both B3LYP-D3 and M06-2X for interactions of this type using a much larger data set than was presented in prior work. However, our new dispersion correction scheme shows some clear advantages for dispersion and dipole-dipole dominated complexes with the small LACVP* basis set, which is very popular in use due to its low associated computational cost: The MUE for B3LYP-MM with the LACVP* basis set for this subset of complexes (without explicit counterpoise corrections) is only 0.28 kcal/mol, compared to 0.65 kcal/mol for M06-2X or 1.16 kcal/mol for B3LYP-D3. Additionally, our new correction scheme also shows major improvements in accuracy for hydrogen-bonded systems and for systems involving ionic interactions, for example cation-π interactions. Compared to B3LYP-D3 and M06-2X, we also find that our new B3LYP-MM correction scheme gives results of higher or equal accuracy for a large dataset of conformer energies of di- and tripeptides, sugars, and cysteine.     

Basis set effects on the intermolecular interaction of the H2-H2 system obtained using ab initio molecular orbital calculations with the Møller-Plesset perturbation correction

The intermolecular interaction potential of the H₂-H₂ system was calculated by an ab initio molecular orbital method using several basis sets (up to 6-31 lG(3pd)) with inclusion of the electron correlation correction of the Møller-Plesset perturbation method and the basis set superposition error (BSSE) correction of the counterpoise method in order to evaluate the basis set effect. The calculated interaction energies depend strongly on the basis set used. Whereas the interaction energies of the repulsive and coulombic energy components calculated at the Hartree-Fock level are not affected by a change of basis set, the dispersion energy component depends strongly on the basis set used. Parameters of an exp-6-1 type non-bonding interaction potential were optimized on the basis of the MP4(SDTQ)/6-311G(3p) level intermolecular interaction energies of the H₂-H₂ system.     

Effect of SO2 on the NO Oxidation over NiO/γAl2O3 Catalyst

NO is the dominant component of NO_x. It can be easily oxidized to NO₂ over active catalysts in the oxidizing exhaust gases. And then, the high reactive NO₂ can be removed completely further through adsorption or absorption approach. However, SO₂,another main contaminant in the exhaust, is well known to poison the oxidative catalysts. A strong deactivation for metal oxides supported on Al₂O₃ was found when catalysts had been exposed to the gas containing 500ppm SO₂. It was also reported that the inhibition effect of SO₂ was enhanced at low temperatures. But recently, some studies declare that the oxidation of propane can be promoted over Pt/γ-Al₂O₃ if a small amount of SO₂ (20 ppm) is present in the feed gas^[1]. Jang et al. have also found that SO₂ has a promoting effect for the oxidation of NO to NO₂ over CO₃O₄/γ-Al₂O₃ catalyst^[2]. These observations are meaningful because the existence of SO₂ in the oxidizing exhaust is often inevitable and the problem of catalyst deactivation by SO₂ has puzzled researchers for a long time.     

Chemical reactivity and selectivity using Fukui functions: basis set and population scheme dependence in the framework of B3LYP theory

The use of Fukui functions for the site selectivity of the formaldehyde molecule for nucleophilic, electrophilic and radical attacks has been made with special emphasis to the dependence of Fukui values on the basis sets as well as population schemes in the framework of B3LYP theory. Out of the five population schemes selected viz., Mulliken population analysis, natural population analysis, CHELP, CHELPG and atoms in molecules (AIM), it is found that the CHELPG and AIM schemes predict precise reactive site with less dependency on the basis sets. Charges derived from Hirshfeld partitioning, calculated using the BLYP/dnd method (implemented in the DMOL³ package), provide non-negative Fukui values for all the molecular systems considered in this study. Supporting results have been obtained for acetaldehyde and acetone molecules at the 6-31+G** basis set level. These results support the fact that high Fukui values correspond to soft–soft interaction sites. On the other hand, the correlation of the low Fukui value to the hard–hard interaction site merits further investigation. Received: 10 November 2001 / Accepted: 6 March 2002 / Published online: 13 June 2002     

On synthesis, structure, and thermal stability of mercury and lead sulfates and oxide sulfates

Reactions between HgO, PbO, or PbO₂ and 2.5–95 wt.% H₂SO₄ are studied at temperatures up to the boiling point of the acid. Depending on the oxide reactant, the H₂SO₄ concentration, and synthesis temperature, HgSO₄, Hg₃O₂(SO₄), PbSO₄ and Pb₂O(SO₄) are obtained as identified reaction products. The thermal stability of HgSO₄, Hg₃O₂(SO₄), PbSO₄, Pb₂O(SO₄), and PbO₂ is examined and the results supplement and modify earlier findings. The redetermined crystal structure of Hg₃O₂(SO₄) on the basis of powder neutron diffraction data shows that its space group (P3₁) is of lower symmetry than earlier reported (P3₁2₁).     

On the effectiveness of CCSD(T) complete basis set extrapolations for atomization energies

The leading cause of error in standard coupled cluster theory calculations of thermodynamic properties such as atomization energies and heats of formation originates with the truncation of the one-particle basis set expansion. Unfortunately, the use of finite basis sets is currently a computational necessity. Even with basis sets of quadruple zeta quality, errors can easily exceed 8 kcal/mol in small molecules, rendering the results of little practical use. Attempts to address this serious problem have led to a wide variety of proposals for simple complete basis set extrapolation formulas that exploit the regularity in the correlation consistent sequence of basis sets. This study explores the effectiveness of six formulas for reproducing the complete basis set limit. The W4 approach was also examined, although in lesser detail. Reference atomization energies were obtained from standard coupled-cluster singles, doubles, and perturbative triples (CCSD(T)) calculations involving basis sets of 6ζ or better quality for a collection of 141 molecules. In addition, a subset of 51 atomization energies was treated with explicitly correlated CCSD(T)-F12b calculations and very large basis sets. Of the formulas considered, all proved reliable at reducing the one-particle expansion error. Even the least effective formulas cut the error in the raw values by more than half, a feat requiring a much larger basis set without the aid of extrapolation. The most effective formulas cut the mean absolute deviation by a further factor of two. Careful examination of the complete body of statistics failed to reveal a single choice that out performed the others for all basis set combinations and all classes of molecules.     

Energy correctors for accurate prediction of molecular energies

Energy correctors are introduced for the calculation of molecular energies of compounds containing first row atoms (Li-F) to modify ab initio molecular orbital calculations of energies to better reproduce experimental results. Four additive correctors are introduced to compensate for the differences in the treatment of molecules with different spin multiplicities and multiplicative correctors are also calculated for the electronic and zero-point vibrational energies. These correctors, individually and collectively yield striking improvements in the atomization energies for several ab initio methods. We use as training set the first row subset of molecules from the G1 basis of molecules; when the correctors are applied to other molecules not included in the training set, selected from the G3 basis, similar improvements in the atomization energies are obtained. The special case of the B3PW91/cc-pVTZ yields an average error of 1.2 kcal/mol, which is already within a chemical accuracy and comparable to the Gaussian-n theories accuracy. The very inexpensive B3PW91/6-31G** yields an average error of 2.1 kcal/mol using the correctors. Methods considered unsuitable for energetics such as HF and LSDA yield corrected energies comparable to those obtained with the best highly correlated methods.