A computationally efficient and reliable bond order measure

Bond order indexes are useful measures that connect quantum mechanical results with chemical understanding. One of these measures, the natural bond order index, based on the natural resonance theory procedure and part of the natural bond orbital analysis tools, has been proved to yield reliable results for many systems. The procedure's computational requirements, nevertheless, scales so highly with the number of functions in the basis set and the delocalization of the system, that the calculation of this bond order is limited to small or medium size molecules. We present in this work a bond order index, the first order perturbation theory bond order (fopBO), which is based on and strongly connected to the natural bond orbital analysis tools. We present the methodology for the calculation of the fopBO index and a number of test calculations that shows that it is as reliable as the natural bond orbital index, with the same weak sensitivity to variations among commonly used basis sets and, as opposed to the natural bond order index, suitable for the study of large systems, such as most of those of biological interest.