Frontier bonds in QM/MM methods: A comparison of different approaches

A major complication in hybrid QM/MM methods is the treatment of the frontier between the quantum part, describing the reactive region, and the classical part, describing the environment. Two approaches to this problem, the "link atom" method and the "local self-consistent field" (LSCF) formalism, are compared in this paper. For this purpose, the LSCF formalism has been introduced into the CHARMM program. A detailed description of the two approaches is presented. The results of semiempirical calculations of deprotonation enthalpies and proton affinities of propanol and a tripeptide with different treatments of the frontier bond are compared. Particular emphasis is placed on the effect of an external charge. It is shown that the choice of the QM/MM electronic interactions included in the frontier region is of considerable importance in determining the electron distribution of the QM region and the overall energy. The link atom and LSCF methods are generally of similar accuracy if care is taken in the choice of the frontier between the QM and MM regions. QM and QM/MM geometry optimizations of ethane and butane are also compared. The introduction of a link atom in the frontier bond is shown to lead to distortions of the internal coordinates unless the frontier bond is treated in a special way. A number of practical points concerning the choice of the frontier between the QM and MM regions are presented. It is not advisable to remove classical charges from the interactions with a subset of the quantum atoms, as this can introduce significant errors in the energy computations. The presence of a large charge on the classical atom involved in the QM/MM frontier also adversely influences the energy, especially with the LSCF method, and it is therefore advised to select classical frontier atoms with small charges. Charged atoms which are not directly bound to the QM frontier but which are in its proximity are also shown to be a source of errors, and it is advised to introduce warning messages In QM-MM codes when such a situation arises.