The recently introduced complete basis set, CBS-Q, model chemistry is modified to use B3LYP hybrid density functional geometries and frequencies, which give both improved reliability (maximum error for the G2 test set reduced from 3.9 to 2.8 kcal/mol) and increased accuracy (mean absolute error reduced from 0.98 to 0.87 kcal/mol), with little penalty in computational speed. The use of a common method for geometries and frequencies makes the modified model applicable to transition states for chemical reactions.

It is shown that localization is necessary to preserve size consistency in nonlinear extrapolations of molecular energies. We demonstrate that the unphysical behavior of Mulliken populations obtained from extended basis set wave functions can lead to incomplete localization of orbitals by the Pipek–Mezey population localization method, and introduce a modification to correct this problem. The new localization procedure, called minimum population localization, is incorporated into the CBS-QB3 and the new CBS-4M model chemistries, and their performance is assessed on the G2/97 test set. The errors found for CBS-QB3 are comparable with those for the G3 and G3(MP2) (mean absolute deviation of 1.10, 0.94, and 1.21 kcal/mol, respectively, on the G2/97 test set). The CBS-4M is less accurate than the other models (mean absolute deviation of 3.26 kcal/mol on the G2/97 test set), but can be applied to much larger systems. The modified localization method resolves several problem cases found with CBS-4 and improves the reliability of CBS-QB3.

Articles you may be interested inExtension of complete basis set model chemistries to molecules containing third row atoms Ga-Kr

The major source of error in most ab initio calculations of molecular energies is the truncation of the one-electron basis set. An open-shell complete basis set (CBS) model chemistry, based on the unrestricted Hartree–Fock (UHF) zero-order wave function, is defined to include corrections for basis set truncation errors. The total correlation energy for the first-row atoms is calculated using the unrestricted Mo/ller–Plesset perturbation theory, the quadratic configuration interaction (QCI) method, and the CBS extrapolation. The correlation energies of the atoms He, Li, Be, B, C, N, O, F, and Ne, calculated using atomic pair natural orbital (APNO) basis sets, vary from 85.1% to 95.5% of the experimental correlation energies. However, extrapolation using the asymptotic convergence of the pair natural orbital expansions retrieves from 99.3% to 100.6% of the experimental correlation energies for these atoms. The total extrapolated energies (ESCF+Ecorrelation) are then in agreement with experiment to within ±0.0012 hartree (root-mean-square deviation) and represent the most accurate total energy calculations yet reported for the first-row atoms.

The major source of error in most ab initio calculations of molecular energies is the truncation of the one-electron basis set. Extrapolation to the complete basis set second-order (CBS2) limit using the N−1 asymptotic convergence of N-configuration pair natural orbital (PNO) expansions can be combined with the use of relatively small basis sets for the higher-order (i.e., MP3, MP4, and QCI) correlation energy to develop cost effective computational models. Following this strategy, three new computational models denoted CBS-4, CBS-q, and CBS-Q, are introduced. The mean absolute deviations (MAD) from experiment for the 125 energies of the G2 test set are 2.0, 1.7, and 1.0 kcal/mol, respectively. These results compare favorably with the MAD for the more costly G2(MP2), G2, and CBS-QCI/APNO models (1.6, 1.2, and 0.5 kcal/mol, respectively). The error distributions over the G2 test set are indistinguishable from Gaussian distribution functions for all six models, indicating that the rms errors can be interpreted in the same way that experimental uncertainties are used to assess reliability. However, a broader range of examples reveals special difficulties presented by spin contamination, high molecular symmetry, and localization problems in molecules with multiple lone pairs on the same atom. These characteristics can occasionally result in errors several times the size expected from the Gaussian distributions. Each of the CBS models has a range of molecular size for which it is the most accurate computational model currently available. The largest calculations reported for these models include: The CBS-4 heat of formation of tetranitrohydrazine (91.5±5 kcal/mol), the CBS-4 and CBS-q isomerization energies for the conversion of azulene to naphthalene (ΔHcalc=−35.2±1.0 kcal/mol, ΔHexp=−35.3±2.2 kcal/mol), and the CBS-Q heat of formation of SF6 (ΔHcalc=−286.6±1.3 kcal/mol, ΔHexp=−288.3±0.2 kcal/mol). The CBS-Q value for the dissociation energy of a C–H bond in benzene (113.1±1.3 kcal/mol) is also in agreement with the most recent experimental result (112.0±0.6 kcal/mol). The CBS-QCI/APNO model is applicable to the prediction of the C–H bond dissociation energies for the primary (100.7±0.7 kcal/mol calc.) and secondary (97.7±0.7 kcal/mol calc., 97.1±0.4 kcal/mol exp.) hydrogens of propane.