Frontier atom, hybridization

The MM subsystem in its turn also affects the parameters of the QM subsystem as any geometry variation in the MM subsystem induces changes in pseudo- and quasirotation angles defining hybridization of the frontier atom. The corrections to the QM one-center Hamiltonian parameters (in the linear approximation) are ... 

The quasitorque induced by the small variations of the one-center ES Vs is vanishing, thus resulting in no quasirotation of the hybridization tetrahedron. At the same time the pseudotorque appears due to the involvement of the frontier atom in the density redistribution within the QM part of the complex system. This contribution to the QM induced pseudotorque is collinear to the QM residing HO (m = 4). 

If these variations are taken into account in the calculations on the QM part of the complex system, the effect of the MM system on the parameters of the effective Hamiltonian for the QM part turns out to be taken into account in the first order. It should be stressed that changes in the hybridization of the frontier atom due to participation of one orbital in the QM subsystem are not taken into account in any of the existing QM/MM schemes. This effect is not very large, so the first-order correction for taking it into account seems to be adequate. 

An alternative, and perhaps more physically attractive, method is the localized bond orbital approach proposed by Rivail and co-workers and also suggested by Warshel and Levitt. In this method, the atomic orbital basis set located on the frontier QM atom is first transformed into hybrid orbitals which are aligned along the direction of the bonds of this atom. The hybrid orbital directly connected to the MM fragment will not be included in the SCF calculation, and its charge density, which is predetermined in a full QM calculation for the entire Y-X system or a much larger fragment than Y itself, is kept frozen. Thus, only three hybrid orbitals from the QM frontier atom enter into the QM system. 

Figure 6. Top 1-4 interactions between hybrid orbitals on neighboring Si atoms. Bottom The frontier orbitals of three conformers of SiJ0H<2 in the notation of Figure...

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. 

Fig. 2-12. Electron energy band formation of silicon crystals from atomic frontier orbitals number of silicon atoms in crystal r = distance between atoms rg = stable atom-atom distance in crystals, sp B8 = bonding band (valence band) of sp hybrid orbitals sp ABB = antibonding band (conduction band) of sp hybrid orbitals.

We start with Salem s treatment of the Walden inversion Frontier orbital approximation is assumed the major interaction is supposed to be that between the nucleophile s HOMO and the substrate s LUMO. Now, according to ab initio calculations, the latter is essentially an out-of-phase combination of a carbon hybrid atomic orbital 0c with a leaving group hybrid atomic orbital 0x- In the first approximation, the LUMO wave function may be written as ... 

This problem illustrates some of the limitations of rule 2 and the frontier orbital approximation. We begin by describing the carbonyl group in terms of an interaction between an sp2-hybridized C atom and an sp oxygen. We will place the molecule in the xy plane and orient the CO bond along the x-axis ... 

The derivatives of the energy correction (of the terms proportional to dP4rr and c)T4r) with respect to the angles J/ J/ yield additional quasi- and pseudotorques (K 4 and (V4, respectively) acting upon the hybridization tetrahedron of the frontier nitrogen atom ... 

For the majority of enzyme-catalysed reactions, covalently bonded parts of the system must be separated into QM and MM regions. There has been considerable research into methods for QM/MM partitioning of covalently bonded systems. Important methods include the local self-consistent field (LSCF) method,114115 and the generalized hybrid orbital (GHO) technique.116 Alternatively a QM atom (or QM pseudo-atom) can be added to allow a bond at the QM/MM frontier for example, the link atom method or the connection atom method. 

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