Models in theoretical chemistry: training and verification

Michael G. Medvedev

N.D. Zelinsky Institute of Organic Chemistry of Russian Academy of Sciences, Leninsky prospect 47, 119991 Moscow, Russian Federation


Models allow scientists to depict reality and make advance predictions. For example, on the outcome of a chemical reaction diminishing the number of required experimental setups. The main concern regarding models is, however, their reliability: sometimes models make wrong predictions; although, there are also cases when models have corrected experimental interpretations. The central limitation of practical ab initio quantum chemical models (Hartree-Fock, Coupled Cluster, etc.) is their neglect for higher-order electron interaction effects. In most cases, the method’s wielder knows exactly, which effects the method accounts for, and which it omits. On the other hand, more empirical models, such as density functional theory (DFT) or semi-empirical methods, incorporate knowledge from the training dataset. This makes them machine-learning models with all the corresponding pros and cons. In this talk, we will discuss various Machine Learning concepts and their manifestations in the history of DFT methods development. In particular, we shall consider the case when DFT methods became worse (less physically correct) when trained to become better (have lower errors in energies) [1], as well as the question, whether to believe DeepMind in the assertion that their DM21 functional is accurate for fractional-electron systems [2]. Supported by Russian Science Foundation grant # 22-73-10124. 1. Medvedev M.G., Bushmarinov I.S., Sun J., Perdew J.P., Lyssenko K.A. Density functional theory is straying from the path toward the exact functional // Science. – 2017. – Vol. 355, Ή 6320. – P. 49–52. – DOI: 10.1126/science.aah5975. 2. Kirkpatrick J., McMorrow B., Turban D.H.P., Gaunt A.L., Spencer J.S., Matthews A.G.D.G., Obika A., Thiry L., Fortunato M., Pfau D., Castellanos L.R., Petersen S., Nelson A.W.R., Kohli P., Mori-Sánchez P., Hassabis D., Cohen A.J. Pushing the frontiers of density functionals by solving the fractional electron problem // Science. – 2021. – Vol. 374, Ή 6573. – P. 1385–1389. – DOI: 10.1126/science.abj6511.