Local hybrids

Separation of covalently bonded atoms into QM and MM regions introduces an unsatisfied valence in the QM region this can be satisfied by several different methods. In the frozen-orbital approach a strictly localized hybrid sp2 bond orbital containing a single electron is used at the QM/MM junction [29]. Fro-... 

These new combinations are just the localized hybrid orbitals for... 

It is known that, in the MO framework, the nondynamical electron correlation is accounted for by means of a so-called CASSCF calculation, which is nothing else than a full Cl in a given space of orbitals and electrons, in which the orbitals and the coefficients of the configurations are optimized simultaneously. If the active space includes all the valence orbitals and electrons, then the totality of the nondynamical correlation of the valence electrons is accounted for. In the VB framework, an equivalent VB calculation, defined with pure AOs or purely localized hybrid atomic orbitals (HAOs), would involve all the covalent and ionic structures that may possibly be generated for the molecule at hand. Note that the resulting covalent—ionic VB wave function would have the same dimension as the valence—CASSCF one (e.g., 1764 VB structures for methane, and 1764 MO SCF configurations in the CASSCF framework). 

If the size of an annelated ring decreases, its angular strain increases due to a more pronounced bending of local hybrid orbitals. It is credible, therefore, to expect larger distortions of the benzene fragment. This turns out to be true as evidenced by benzocy-clobutene 11 and benzocyclopropene 12 (Fig. 12). Their theoretical structural parame-... 

Figure 2. Schematic representation of the partitioning of an aspartate amino acid residue into QM and MM regions. The side chain (which may be involved in e.g. chemical reaction or binding) is treated QM (up to and including C(3). To account for the bond between Ca and C(3, a link atom (typically hydrogen) may be added toCp. Alternatively, a localized hybrid orbital on CP can be employed. Consideration must also be given as to which MM interactions to include between the MM and QM atoms, e.g. which bonded terms (for bonds, bond angles, dihedral angles, etc.) between the two regions. In the implementation of Fielder al. [41], all MM bonded terms involving at least one MM atom are retained.

Locality Hybrid and Black Red Pin Plains Eastern Silver black Green ... 

A second and more elegant approach is to use localized hybrid orbitals for the QM atoms at the junction. This method was used by Warshel and Levitt in their original work on lysozyme [14] and has been further devel-... 

We can think of the singlet state of a free carbene, in terms of localized hybrid orbitals, as a bent molecule (6) harboring three sp2 orbitals (one of which is doubly occupied and non-bonding) and an empty, perpendicularly-situated 2p orbital. A triplet carbene (really a diradical) would be a less bent species (7) with two singly-occupied, orthogonal 2p orbitals and two sp orbitals that are involved in bonding to substituents. 

These a bonds, which may be constructed either from delocalized a AO s or from localized hybrid atomic orbitals, are neglected in a 7r-electron approximation for the delocalized ir system. 

A different approach to this problem is offered by local hybrid (Lh) [93] or hyper-GGA... 

What differences and similarities exist among (a) atomic orbitals, (b) localized hybridized atomic orbitals according to valence bond theory, and (c) molecular orbitals ... 

SOC calculations were recently reported for two bicyclic biradicals 10 and 11 derived from barrelene [44] and for 1,/i-alkanediyls with n = 3 - 8, for which a unique alternation of SOC with the parity of the number of intervening bonds between the radical centers was found [35]. In addition, it was shown that omis-sion of H2 eq. (7) leads to less serious errors than confining the active space to two MOs (HOMO-LUMO), and a dissection of SOC values into local hybrid orbital contribution was described [35]. 

Pyramidalization affects SOC mainly through the in-plane component of the SOC vector, which increases particularly for small values of cf), since the increasing p part of the localized hybrid B is rotated by f into the x direction and yields a large overlap with the localized hybrid A. In the case of pyramidalization, however, the hybrids A and B remain parallel and SOC becomes practically zero for (]) = 0, since the coupling through is not possible in this case. 

C. Angeli, G. Del Re, and M. Persico Quasi-bond Orbitals from Maximum-Localization Hybrids for ab Initio Cl Calculations. Chem. Phys. Lett. 233, 102-110 (1995). 

Building procedure of maximum localization hybrid orbitals... 

Del Re s main achievements in his primary research field are marked by the well-known Del Re method for the determination of charges in molecules and by the introduction of maximum localization hybrids in the molecular orbital method. Both procedures have been used by researchers throughout the world. 

Partly for ease of visualization and predictive utility, the generalized anomeric effect is expressed by reference to localized, hybrid orbitals (Scheme 17, shown for a cyclic acetal). Mixing of the antiperiplanar (app)... 

Thermoplastics - long fiber-reinforced, textile-reinforced, woven mat-rein-forced or with local hybrid fiber reinforcement - will gain ground in the direction of large-scale production series and structural parts production. 

---