Local self consistent field

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. 

The first reported approach along these lines was the localized self-consistent-field (LSCF) method of Ferenczy et al. (1992), originally described for the NDDO level of theory. In this case, the auxiliary region consists of a single frozen orbital on each QM boundary atom. 

Thdry, V., Rinaldi, D., Rivail, J.-L., Maigret, B., and Ferenczy, G. G. 1994. Quantum Mechanical Computations on Very Large Molecular Systems The Local Self-consistent Field Method , J. Comput. Chem., 15, 269. 

V. Thery, D. Rinaldi, J. L. Rivail, B. Maigret and G. G. Ferenczy, Quantum-mechanical computations on very large molecular-systems - the local self-consistent-field method, J. Comput. Chem., 15 (1994) 269-282. 

Models of this type are present in the literature. The simplest ones are based on the use of local orbitals. It is the local self-consistent field (LSCF) approach [216,231, 265,266]. In it the chemical bonds between QM and MM regions are represented by strictly local bond orbitals (SLBOs). The BOs can be obtained by the a posteriori localization procedures known in the literature. The localized orbitals thus obtained have some degree of delocalization, i.e. they have non-zero contributions of the AOs centered on the atoms not incident to a given bond (or a lone pair) ascribed to this particular BO. These contributions are the so-called tails of the localized orbitals and neglecting them yields the strictly local BOs (SLBOs) which are used in the LSCF scheme. The QM part of the system is described by a set of delocalized MOs while the boundary is modeled by the frozen SLBOs. 

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. 

Assfeld X, JL Rivail (1996) Quantum chemical computations on parts of large molecules The ab initio local self consistent field method. Chem. Phys. Lett. 263 (1-2) 100-106... 

Gorb LG, Rivail JL, Thery V, Rinaldi D (1996) Modification of the local self-consistent field method for modeling surface reactivity of covalent solids, Int J Quant Chem 60 313—324... 

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. 

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 strategy to separate the QM part from the MM one is to freeze the pair of electrons in the broken bond (assumed to be a single bond). This has been suggested first by Warshel and Levitt [22] and the method has been developed recently at the semiempirical [23,241 and ab initio levels [26-281 as the local self-consistent field (LSCF) method. 

Assfeld X, Ferre N, Rivail JL. The local self consistent field. Principles and applications to combined QM/MM computations on biomacromolecular systems. In Gao J, Thompson MA, eds. Combined Quantum Mechanical and Molecular Mechanical Methods. ACS Symposium Series 712. Washington, DC American Chemical Society, 1998 234-239. 

Edwards beautiful and promising approach, utilizing functional integral techniques, was reviewed in detail, emphasizing his derivation of the existence of localized states through the introduction of a symmetrybreaking local self-consistent field. 

Abstract Hybrid methods, combining the accuracy of Quantum Mechanics and the potency of Molecular Mechanics, the so-called QM/MM methods, arise from the desire of theoretician chemists to study electronic phenomena in large molecular systems. In this contribution, a focus, on the Physics and Chemistry on which theses methods are based on, is given. The advantages, flaws, and limitations of each type of methods are exposed. A special emphasis is put on the Local Self-Consistent Field method, developed in our group. The latest developments are detailed and illustrated by chosen examples. 

Finally, the third class of approaches encompasses all methods dealing with frozen electronic density (see Fig. 1.1c). Generally, the electronic density is obtained from orbitals (hybrid orbitals or localized molecular orbitals) determined on small molecules which contain the bond of interest [9,19,20], It is then possible to cut bonds of any polarity (P-0 in DNA for example), or multiphcity. It is even possible to cnt peptide bond, which represent a serious advantage for the study of proteins. The universality of these methods is however accompanied by an inherent coding complexity. Among these methods, the Local Self-Consistent Field approach (LSCF) developed in our group since more than fifteen years is detailed in the next section. 

Monari A, Rivail J-L, Assfeld X (2013) Theoretical modelling of large molecular systems. Advances in the local self consistent field method for mixed quantum mechanics/molecular mechanics calculations. Acc Chem Res 46 596-603... 

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