What is NBO analysis and how is it useful?

Natural bond orbital (NBO) analysis is one of many available options for 'translating' computational solutions of Schrodinger's wave equation into the familiar language of chemical bonding concepts. In this Review, we first address the title questions by describing characteristic features that distinguish NBO from alternative analysis methodologies (e.g. of QTAIM or EDA type) and answering criticisms that have been raised in specific chemical applications. We then address the general 'usefulness' of NBO analysis in the context of widely accepted philosophical criteria, including (i) broad consistency, both internally and with respect to known experimental data, (ii) multi-faceted predictive capacity, including numerical model predictions of specific properties, general correlative and statistical regression relationships, and 'risky' falsifiable predictions of previously unknown chemical phenomena, and (iii) general pedagogical value, promoting organisation, unification, and orderly rationalisation of chemical knowledge. Specific chemical topics chosen for discussion include controversial H center dot center dot center dot H 'bond lines' in bay-type hydrocarbon species; carbene ligation of coinage metals; resonance-type bonding of noble gas hydrides; NBO descriptors in Hammett-type quantitative structure-activity relationships; nature of conventional and 'anti-electrostatic' hydrogen bonding interactions; multi-centre bonding in 'aromatic' Al-4((2-)), Lewis-like hybridisation picture of non-VSEPR geometry and high-order multiple bonding in transition metal species; resonance origin of the '18e rule'; and localised (symmetry-independent) prediction of Jahn-Teller effects in free radical chemistry. We conclude with hints of some directions for future extensions of NBO methods.