Description of pentacoordinated phosphorus under an external electric field: which basis sets and semi-empirical methods are needed?

Phosphate transfer reactions are ubiquitous in nature and play fundamental roles in ATP hydrolysis and protein phosphorylation processes. The mechanisms of these reactions involve a pentacoordinated phosphorus atom that can be an intermediate or a transition state. These structures are very sensitive to both internal and external electrostatic effects and their description with quantum mechanical methods is challenging. We have investigated the variations of geometry an energetics under an external electric field for two different molecules and their transition states of formation. The DFT method, with the mPW1PW91 functional employing several basis sets, and different semi-empirical methods have been tested. Compared to zero-field cases, one needs more extended basis sets to achieve the same precision. A good compromise for large systems is the 6-31 + G(d). Many semi-empirical methods are unable to describe polarisation effects in pentacoordinated structures. The best methods to describe geometries are PM6 and AM1/d-PhoT and for energetics AM1/d-PhoT. Methods without d orbitals have poorer performances but the best among those is the AM1 parametrization of Arantes et al.