Semiempirical molecular orbital models based on the neglect of diatomic differential overlap approximation

• Published in: International journal of quantum chemistry Vol. 118; no. 24
• Main Authors: Husch, Tamara, Vaucher, Alain C., Reiher, Markus
• Format: Journal Article
• Language: English
• Published: Hoboken, USA John Wiley & Sons, Inc 15.12.2018; Wiley Subscription Services, Inc
• Subjects: Approximation; Chemistry; Computing time; Density functional theory; Differential equations; Electrons; Error compensation; Integrals; Molecular orbitals; NDDO approximation; Parameter identification; Parameter sensitivity; Physical chemistry; Quantum physics; semi‐empirical methods; Sensitivity analysis
• ISSN: 0020-7608; 1097-461X
• DOI: 10.1002/qua.25799

Semiempirical molecular orbital (SEMO) models based on the neglect of diatomic differential overlap (NDDO) approximation efficiently solve the self‐consistent field equations by rather drastic approximations. The computational efficiency comes at the cost of an error in the electron‐electron repulsion integrals. The error may be compensated by the introduction of parametric expressions to evaluate the electron‐electron repulsion integrals, the one‐electron integrals, and the core‐core repulsion. We review the resulting formalisms of popular NDDO‐SEMO models (such as the MNDO(/d), AM1, PMx, and OMx models) in a concise and self‐contained manner. We discuss the approaches to implicitly and explicitly describe electron correlation effects within NDDO‐SEMO models and we dissect strengths and weaknesses of the different approaches in a detailed analysis. For this purpose, we consider the results of recent benchmark studies. Furthermore, we apply bootstrapping to perform a sensitivity analysis for a selection of parameters in the MNDO model. We also identify systematic limitations of NDDO‐SEMO models by drawing on an analogy to Kohn‐Sham density functional theory. Semiempirical molecular orbital (SEMO) models based on the neglect of diatomic differential overlap (NDDO) approximation efficiently solve the self‐consistent field equations by rather drastic approximations. Their computational efficiency comes at the cost of an error in the electron‐electron repulsion integrals, sometimes compensated by the introduction of parametric expressions. This review compares the resulting formalisms, systematic limitations, and strength and weaknesses of the most popular NDDO‐SEMO models.