species containing first-row, second-row, and third row main group elements. G4 theory is an improved modification of the earlier approach G3 theory. The modifications to G3- theory are the change in an estimate of the Hartree–Fock energy limit, an expanded polarization set for the large basis set calculation, use of CCSD(T) energies, use of geometries from density functional theory and zero-point energies, and two added higher level correction parameters. According to the developers, this theory gives significant improvement over G3-theory. The G4 and the related G4MP2 methods have been extended to cover transition metals. A variant of G4MP2, termed G4(MP2)-6X, has been developed with an aim to improve the accuracy with essentially identical quantum chemistry components. It applies scaling to the energy components in addition to using the HLC. In the G4(MP2)-XK method that is related to G4(MP2)-6X, the Pople-type basis sets are replaced with customized Karlsruhe-type basis sets. In comparison with G4(MP2)-6X, which covers main-group elements up to krypton, G4(MP2)-XK is applicable to main-group elements up to radon. Feller-Peterson-Dixon approach (FPD) Unlike fixed-recipe, "model chemistries", the FPD approach consists of a flexible sequence of (up to) 13 components that vary with the nature of the chemical system under study and the desired accuracy in the final results. In most instances, the primary component relies on coupled cluster theory, such as CCSD(T), or configuration interaction theory combined with large Gaussian basis sets (up through aug-cc-pV8Z, in some cases) and extrapolation to the complete basis set limit. As with some other approaches, additive corrections for core/valence, scalar relativistic and higher order correlation effects are usually included. Attention is paid to the uncertainties associated with each of the components so as to permit a crude estimate of the uncertainty in the overall results. Accurate structural parameters and vibrational frequencies are a natural byproduct of the method. While the computed molecular properties can be highly accurate, the computationally intensive nature of the FPD approach limits the size of the chemical system to which it can be applied to roughly 10 or fewer first/second row atoms. The FPD Approach has been heavily benchmarked against experiment. When applied at the highest possible level, FDP is capable to yielding a root-mean-square (RMS) deviation with respect to experiment of 0.30 kcal/mol (311 comparisons covering atomization energies, ionization potentials, electron affinities and proton affinities). In terms of equilibrium, bottom-of-the-well structures, FPD gives an RMS deviation of 0.0020 Å