One of the key questions in electronic structure theory concerns the accuracy of the computed molecular quantities, including relative energies. The composite focal-point analysis (FPA) approach developed some two decades ago by us provides a clean way to determine the uncertainties of computed relative energies.
W. D. Allen, A. L. L. East, and A. G. Császár, Structures and Conformations of Non-Rigid Molecules, edited by J. Laane, M. Dakkouri, B. van der Veken and H. Oberhammer (Kluwer, Dordrecht, 1993), pp. 343-373.
A. G. Császár, W. D. Allen, and H. F. Schaefer, III, In Pursuit of the Ab Initio Limit for Conformational Energy Prototypes, J. Chem. Phys. 1998, 108, 9751-9764.
A. G. Császár, W. D. Allen, Y. Yamaguchi, and H. F. Schaefer III, Ab Initio Determination of Accurate Potential Energy Hypersurfaces for the Ground Electronic States of Molecules, in Computational Molecular Spectroscopy, 2000, eds. P. Jensen and P. R. Bunker, Wiley: New York.
A. G. Császár, G. Tarczay, M. L. Leininger, O. L. Polyansky, J. Tennyson, and W. D. Allen, Dream or Reality: Complete Basis Set Full Configuration Interaction Potential Energy Hypersurfaces, in Spectroscopy from Space, edited by J. Demaison, K. Sarka, and E. A. Cohen (Kluwer, Dordrecht, 2001), pp. 317-339.
NEAT is a simple and fast, weighted, linear least-squares refinement protocol and code for inverting the information contained in a network of quantum chemically computed 0 K reaction enthalpies. This inversion yields internally consistent 0 K enthalpies of formation for the species of the network. The refinement takes advantage of the fact that the accuracy of computed enthalpies depends strongly on the quantum-chemical protocol employed for their determination. Different protocols suffer from different sources of error; thus, the reaction enthalpies computed by them have “random” residual errors. Since it is much more natural for quantum-chemical energy and enthalpy results, including reaction enthalpies, to be based on the electronic ground states of the atoms and not on the historically preferred elemental states, and since these two possible protocols can be converted into each other straightforwardly, it is proposed that first-principles thermochemistry should employ the ground electronic states of atoms. In this scheme, called atom-based thermochemistry (AT), the enthalpy of formation of a gaseous compound corresponds simply to the total atomization energy of the species; it is always positive, and it reflects the bonding strength within the molecule. The inversion protocol developed and based on AT is termed NEAT, which represents the fact that the protocol proceeds from a network of computed reaction enthalpies toward atom-based thermochemistry, most directly to atom-based enthalpies of formation.
A. G. Császár and T. Furtenbacher, From a Network of Computed Reaction Enthalpies to Atom-Based Thermochemistry (NEAT), Chem. Eur. J. 2010, 16(16), 4826-4835.