Accurate Treatment of Energetics and Geometry of Carbon and Hydrocarbon Compounds within Tight-Binding Model

Performance of B3LYP Density Functional Methods for a Large Set of Organic Molecules

Testing of the commonly used hybrid density functional B3LYP with the 6-31G(d), 6-31G(d,p), and 6-31+G(d,p) basis sets has been carried out for 622 neutral, closed-shell organic compounds containing the elements C, H, N, and O. The focus is comparison of computed and experimental heats of formation and isomerization energies. In addition, the effect of an empirical dispersion correction term has been evaluated and found to improve agreement with the experimental data. For the 622 compounds, the mean absolute errors (MAE) in the heats of formation are 3.1, 2.6, 2.7, and 2.4 kcal/mol for B3LYP/6-31G(d), B3LYP/6-31G(d,p), B3LYP/6-31+G(d,p), and B3LYP/6-31+G(d,p) with the dispersion correction. A diverse set of 34 isomerizations highlights specific issues of general interest, such as performance on differences in steric effects, conjugation, and bonding. The corresponding MAEs for the isomerizations are 2.7, 2.4, 2.2, and 1.9 kcal/mol. Improvement is obtained for isomerizations of amines and alcohols when both polarization and diffuse functions are used, but the overstabilization of linear alkanes compared to branched isomers can be relieved only with the dispersion correction. Besides the insights on DFT methods, the study also aimed to quantify the gains in accuracy that can be achieved by replacing energetics from NDO-based semiempirical methods with DFT results. Since the MAEs obtained with the PDDG/PM3 method for the 622 heats of formation and 34 isomerizations are 2.8 and 2.3 kcal/mol, negligible advantage in accuracy for the B3LYP-based methods emerged in the absence of the dispersion corrections.

Application of the Computationally Efficient Self-Consistent-Charge Density-Functional Tight-Binding Method to Magnesium-Containing Molecules

The geometric properties, ionization potentials, heats of formation, incremental binding energies, and protonation energies for up to 75 magnesium-containing compounds have been studied using the self-consistent-charge density-functional tight-binding method (SCC-DFTB), the complete-basis set (CBS-QB3) method, traditional B3LYP density-functional theory, and a number of modern semiempirical methods such as Austin Model 1 (AM1), modified neglect of diatomic overlap without and with inclusion of d functions (MNDO, MNDO/d), and the Parametric Method 3 (PM3) and its modification (PM5). The test set contains some widely varying chemical motifs including ionic or covalent, closed-shell or radical compounds, and many biologically relevant complexes. Geometric data are compared to experiment, if available, and otherwise to previous high-level ab initio calculations or the present B3LYP results. SCC-DFTB is found to predict bond lengths to high accuracy, with the root-mean-square (RMS) error being less than half that found for the other semiempirical methods. However, SCC-DFTB performs very poorly for absolute heats of formation, giving an RMS error of 29 kcal mol(-1), but for this property B3LYP and the other semiempirical methods also yield poor but useful results with errors of 12-22 kcal mol(-1). Nevertheless, SCC-DFTB does provide useful results for biologically relevant chemical-process energies such as protonation energies (RMS error 10 kcal mol(-1), with the range 6-19 kcal mol(-1) found for the other semiempirical methods) and ligation energies (RMS error 9 kcal mol(-1), less than the errors of 12-23 kcal mol(-1) found for the other semiempirical methods). SCC-DFTB is shown to provide a computationally expedient means of calculating properties of magnesium compounds, providing results with at most double the inaccuracy of the high-quality but dramatically more-expensive B3LYP method.

Comparison of SCC-DFTB and NDDO-Based Semiempirical Molecular Orbital Methods for Organic Molecules

Extensive testing of the SCC-DFTB method has been performed, permitting direct comparison to data available for NDDO-based semiempirical methods. For 34 diverse isomerizations of neutral molecules containing the elements C, H, N, and O, the mean absolute errors (MAE) for the enthalpy changes are 2.7, 3.2, 5.0, 5.1, and 7.2 kcal/mol from PDDG/PM3, B3LYP/6-31G(d), PM3, SCC-DFTB, and AM1, respectively. A more comprehensive test was then performed by computing heats of formation for 622 neutral, closed-shell H, C, N, and O-containing molecules; the MAE of 5.8 kcal/mol for SCC-DFTB is intermediate between AM1 (6.8 kcal/mol) and PM3 (4.4 kcal/mol) and significantly higher than for PDDG/PM3 (3.2 kcal/mol). Similarly, SCC-DFTB is found to be less accurate for heats of formation of ions and radicals; however, it is more accurate for conformational energetics and intermolecular interaction energies, though none of the methods perform well for hydrogen bonds with strengths under ca. 7 kcal/mol. SCC-DFTB and the NDDO methods all reproduce MP2/cc-pVTZ molecular geometries with average errors for bond lengths, bond angles, and dihedral angles of only ca. 0.01 A, 1.5 degrees , and 3 degrees . Testing was also carried out for sulfur containing molecules; SCC-DFTB currently yields much less accurate heats of formation in this case than the NDDO-based methods due to the over-stabilization of molecules containing an SO bond.