Boundary QM atoms

When a biomolecular system is separated into QM and MM regions one must usually cut amino acid side chains or the protein backbone at covalent bonds (Fig. 5.2 a). The construction of the covalent boundary between the QM and MM parts is key to accurate results from QM/MM calculations. Because there is no unique way to treat the covalent boundary, several different approaches have been described. In the first applications of coupled QM/MM simulations link atoms were used to create the covalent QM/MM boundary (Fig. 5.2b). Link atoms are atoms added to the QM part to fill the broken valences of the boundary QM atoms. These atoms are placed along the broken QM/MM bond at a distance appropriate for the QM bond added. The link atoms have usually been hydrogen atoms but methyl groups and pseudohalogen atoms have also been used [35]. 

At the same time such an approach seems quite artificial. Moreover, in Ref. [136] (cited by Ref. [121]) it is stated that the strong deviation of the link atom equilibrium position from the line connecting atoms forming covalent bond leads to serious problems. Moreover, the vibrational spectra calculated by the optimization of the link atom position method are worse than even the MM-force field derived. Also the QM/MM calculated proton affinity for small gas phase aluminosilicate clusters is very sensitive to the length of the bond between boundary QM atom and the hydrogen atom introduced [137]. The problems with positioning of link atoms are... 

To circumvent problems associated with the link atoms different approaches have been developed in which localized orbitals are added to model the bond between the QM and MM regions. Warshel and Levitt [17] were the first to suggest the use of localized orbitals in QM/MM studies. In the local self-consistent field (LSCF) method the QM/MM frontier bond is described with a strictly localized orbital, also called a frozen orbital [43]. These frozen orbitals are parameterized by use of small model molecules and are kept constant in the SCF calculation. The frozen orbitals, and the localized orbital methods in general, must be parameterized for each quantum mechanical model (i.e. energy-calculation method and basis set) to achieve reliable treatment of the boundary [34]. This restriction is partly circumvented in the generalized hybrid orbital (GHO) method [44], In this method, which is an extension of the LSCF method, the boundary MM atom is described by four hybrid orbitals. The three hybrid orbitals that would be attached to other MM atoms are fixed. The remaining hybrid orbital, which represents the bond to a QM atom, participates in the SCF calculation of the QM part. In contrast with LSCF approach the added flexibility of the optimized hybrid orbital means that no specific parameterization of this orbital is needed for each new system. 

Murphy et al. [34,45] have parameterized and extensively tested a QM/MM approach utilizing the frozen orbital method at the HF/6-31G and B3LYP/6-31G levels for amino acid side chains. They parameterized the van der Waals parameters of the QM atoms and molecular mechanical bond, angle and torsion angle parameters (Eq. 3, Hqm/mm (bonded int.)) acting across the covalent QM/MM boundary. High-level QM calculations were used as a reference in the parameterization and the molecular mechanical calculations were performed with the OPLS-AA force... 

In the structurally coupled QM/MM implementation of Zhang et al. [55, 56], in which the QM/MM boundary was treated by use of the pseudobond approach [55, 57], the QM/MM minimization of the QM part is combined with FEP calculations. In this procedure the energy profile of the enzyme reaction is first determined by use of QM/MM energy minimizations. The structures and charges of the QM atoms are then used, in the same manner as in the QM/FE method, to determine the role of environment on the energy profile of the reaction. In this way the effects of a large number of MM conformations of protein and solvent environment can be included in the total energies. 

HBoundary is the boundary Hamiltonian and it will consist of two parts — an operator for the interaction with the QM atoms, Boundary(QMp and an energy for the interaction with the MM atoms, Boundary(MM)-... 

The local self-consistent field (LSCF) method108 provides a clear and consistent framework for treating the boundary between covalently bonded QM and MM atoms. In the LSCF method, a strictly localized bond orbital, also often described as a frozen orbital, describes the electrons of the frontier bond. This frozen orbital is used at the QM/MM boundary, i.e. for the QM atom at the frontier between QM and MM regions. The electron density of the orbital is... 

Another approach to treating the boundary between covalently bonded QM and MM systems is the connection atom method,119 120 in which rather than a link atom, a monovalent pseudoatom is used. This connection atom is parameterized to give the correct behavior of the partitioned covalent bond. The connection atoms interact with the other QM atoms as a (specifically parameterized) QM atom, and with the other MM atoms as a standard carbon atom. This avoids the problem of a supplementary atom in the system, as the connection atom and the classical frontier atom are unified. However, the need to reparameterize for each type of covalent bond at a given level of quantum chemical theory is a laborious task.121 The connection atom method has been implemented for semiempirical molecular orbital (AMI and PM3)119 and density functional theory120 levels of theory. Tests carried out by Antes and Thiel to validate the connection atom method at the semiempirical level suggested that the connection atom approach is more accurate than the standard link atom approach.119... 

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