Fragment SCF method

The most convenient manner to describe these regions is to use a basis of strictly localized molecular orbitals (SLMOs). The SLMOs can be expressed as linear combinations of normalized atomic hybrid orbitals as in Eqs. (4.B-4.4) of Sect. 4.3. 

The coefficients Z , etc. determine the direction and s-character of the hybrids. The optimal calculation of these parameters is a difficult task and several procedures are known in the literature for this purpose [221, 222]. For the present purposes it is sufficient to invoke the chemical intuition and start with a set of hybrids with standard s-characters and directed along the bonds. Since such hybrids are not orthogonal on each atomic center (except in the case of some special bond angles), a consecutive Lowdin-orthogonalization allows one to readjust their 5-characters and bond directions. 

Once we have the proper hybrid orbitals a zeroth-order wave function can be constructed from all occupied two-centre SLMOs. To optimize their coefficients (the bond polarities) the following coupled set of 2 x 2 secular equations can be derived [26, 220] 

The first and second term in Eq. (6.23) stand for the interaction between electrons of the i-th bond and those for other bonds within the inner (I, D and C) and outer (T) regions, respectively. The last sum comes from region T, containing N bonds and is an additive constant. 

Once we have optimized parameters of the SLMOs the molecular orbitals for region C can be expanded on this basis set and a secular equation can be written for the derivation of expansion coefficients. Its dimensionality is determined by the size of region C alone. The molecular orbitals can be written as 

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For lowering the CPU time of SCF calculations for large molecules, the fragment SCF method [74] can also be used. 

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 electron repulsion integrals ij kl) are obtained formally from Eq. (6.24) by replacing etc. by (p,-, etc. The Fragment SCF method has been implemented at the CNDO level of approximation and applied to the conformational study of the catalytic triad in serine proteases [223]. 

F(r) was also computed from ab initio wave functions in the framework of the HF/SCF method using 3-21G and 6-31G basis sets due to the large size ofLR-B/081, the calculation has as yet been performed on isolated molecular fragments, adopting a geometry based on molecular dimensions from X-ray diffraction studies. 

The main difference between the two testbenches is the fact that the second of the two uses an orthogonal basis and so some of the steps in the SCF method are omitted. The relevant program fragment in the full calculation is... 

A short summary of the SCF-MI method is presented here for the simplest case of two interacting closed-shell monomers A and B. A full account of the theory is given elsewhere [11] and its generalization to interaction of an open shell with an arbitrary number of closed shell fragments has recently appeared [19]. 

Gianinetti, E., Vandoni, I., Famulari, A. and Raimondi, M (1998) Extension ofthe SCF-MI method to the case of K fragments one of which is an open-shell system, Adv. Quantum Chem., 31,251-266. 

We have already presented [17,18] the SCF-Ml (Self Consistent Field for Molecular Interactions) method, based on the idea that BSSE can be avoided a priori provided the MOs of each fragment are expanded only using basis functions located on each subsystem. In the present work we propose a multiconfiguration extension (MCSCF-MI) of the same technique, particularly suited to deal with systems for which proton transfer processes must be considered. 

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