# Accurate theoretical chemistry with coupled pair models

Frank Neese, Andreas Hansen, Frank Wennmohs, Stefan Grimme

*Accounts of Chemical Research 2009 May 19, 42 (5): 641-8*

19296607

Quantum chemistry has found its way into the everyday work of many experimental chemists. Calculations can predict the outcome of chemical reactions, afford insight into reaction mechanisms, and be used to interpret structure and bonding in molecules. Thus, contemporary theory offers tremendous opportunities in experimental chemical research. However, even with present-day computers and algorithms, we cannot solve the many particle Schrodinger equation exactly; inevitably some error is introduced in approximating the solutions of this equation. Thus, the accuracy of quantum chemical calculations is of critical importance. The affordable accuracy depends on molecular size and particularly on the total number of atoms: for orientation, ethanol has 9 atoms, aspirin 21 atoms, morphine 40 atoms, sildenafil 63 atoms, paclitaxel 113 atoms, insulin nearly 800 atoms, and quaternary hemoglobin almost 12,000 atoms. Currently, molecules with up to approximately 10 atoms can be very accurately studied by coupled cluster (CC) theory, approximately 100 atoms with second-order Møller-Plesset perturbation theory (MP2), approximately 1000 atoms with density functional theory (DFT), and beyond that number with semiempirical quantum chemistry and force-field methods. The overwhelming majority of present-day calculations in the 100-atom range use DFT. Although these methods have been very successful in quantum chemistry, they do not offer a well-defined hierarchy of calculations that allows one to systematically converge to the correct answer. Recently a number of rather spectacular failures of DFT methods have been found-even for seemingly simple systems such as hydrocarbons, fueling renewed interest in wave function-based methods that incorporate the relevant physics of electron correlation in a more systematic way. Thus, it would be highly desirable to fill the gap between 10 and 100 atoms with highly correlated ab initio methods. We have found that one of the earliest (and now almost forgotten) of this class of methods, the coupled-electron pair approximation (CEPA), performs exceedingly well in chemical applications. In this Account, we examine the performance of CEPA in chemical applications. One attractive feature of CEPA, in addition to its surprising accuracy that surpasses that of DFT and MP2 theory, is a simplicity that allows for straightforward and very efficient approximations and extensions to be developed; these are much more difficult or even impossible with the more rigorous CC theory. Thus, approximate CEPA methods can be implemented efficiently enough to allow for calculations on molecules of 50-100 atoms, perhaps the most common range in contemporary chemical research.

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