Generalized hybrids

Let us begin by sketching the general polyatomic formulation of hybridization from the NBO viewpoint. A general hybrid h/A) on atom A can be expanded in the complete orthonormal set of NAOs, (A) on this atom ... 

General hybrid orbital functions and natural bond angles... 

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. 

Akhmatskaya, E., Bou-Rabee, N., Reich, S. A comparison of generalized hybrid Monte Carlo methods with and without momentum flip. J. Comput. Phys. 2009, 228, 2256-65. 

The reason for expressing the relative contributions ofj and p in terms of the awkward-looking factors a/ 1/(1 + m) and Vm/(l + m) is that this form guarantees that the generalized hybrid A 1.9 will be normalized. (See Problem 1.7.) We have thus built in automatically one of the restraints on our hybrids. The quantity m is the hybridization index, and is the number that appears as the superscript in the standard designation of hybrid type. Thus an sp3 orbital, m = 3, always has the form... 

When considering ab initio methods as a part of a more general hybrid technique one has to remember that no counterpoise is built in the former to overcome its inherent limitations. Combining this - exact method - with any inevitably empirical classical scheme for the environment raises the question of the status of the result. We shall address this problem later when reviewing the corresponding hybrid techniques. 

Fig. 4.5 Film devices and circuits (a) thin-film resistors on glass and steatite substrates (b) thick-film resistor networks on snapstrate alumina substrate (c) various thick-film resistors (d) hybrid microcircuits. (Components kindly supplied by General Hybrid, C-MAC and...

For rationally constructing domain-swapped proteins, one consideration is whether to include a linker region between the two domains. In general, hybrids with two autonomously functioning domains require significant distance between the two domains so that they can fold and... 

The orbitals plotted in Figures 11 and 12 are generalized hybrids they are mainly defined on one atom but they show contributions also from neighbouring centres. 

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. 

Gao JL, P Amara, C Alhambra, MJ Field (1998) A generalized hybrid orbital (GHO) method for the treatment of boundary atoms in combined QM/MM calculations. J. Phys. Chem. A 102 (24) 4714-4721... 

Garcia-Viloca M, JL Gao (2004) Generalized hybrid orbital for the treatment of boundary atoms in combined quantum mechanical and molecular mechanical calculations using the semiempirical parameterized model 3 method. Theor. Chem. Acc. Ill (2-6) 280-286... 

Pu JZ, JL Gao, DG Truhlar (2004a) Combining self-consistent-charge density-functional tight-binding (SCC-DFTB) with molecular mechanics by die generalized hybrid orbital (GHO) method. J. Phys. Chem. A 108 (25) 5454-5463... 

Pu JZ, JL Gao, DG Truhlar (2005) Generalized hybrid-orbital method for combining density functional theory with molecular mechanicals. ChemPhysChem 6 (9) 1853—1865... 

Gao J, Truhlar DG (2004) Generalized Hybrid Orbital (GHO) Method for Combining Ab Initio Hartree-Fock Wave Functions with Molecular Mechanics. J. Phys. Chem. A 108 632-650... 

The local self-consistent field (LSCF) or fragment SCF method has been developed for treating large systems [105,134-139], in which the bonds at the QM/MM junction ( frontier bonds ) are described by strictly localized bond orbitals. These frozen localized bond orbitals are taken from calculations on small models, and remain unchanged in the QM/MM calculation. The LSCF method has been applied at the semiempirical level [134-137], and some developments for ab initio calculations have been made [139]. Gao et al. have developed a similar Generalized Hybrid Orbital method for semiempirical QM/MM calculations, in which the semiempirical parameters of atoms at the junction are modified to enhance the transferability of the localized bond orbitals [140]. Recent developments for ab initio QM/MM calculations include the method of Phillip and Friesner [141], who use Boys-localized orbitals in ab initio Hartree-Fock QM/MM calculations. These orbitals are again taken from calculations on small model systems, and kept frozen in QM/MM calculations. 

---