Maximum overlap method

To account for this phenomenon the hybrids used in the bond polarization calculations were described in agreement with an idea taken from the maximum overlap method (17). Atomic hybrids with a rigid relative orientation were optimized so that the overlap of the hybrids that form a bond is at maximum. The estimated... 

Separate initial state and final core-hole state calculations provided ASCF values of the CEBEs. The maximum overlap method [67, 68] was used to prevent variational collapse of the final hole state. This simply replaces the usual aufbau criterion for occupying orbitals in each iteration with a criterion that the occupied orbitals be selected to overlap as much as possible with those of the previous iteration. The Ahhichs VTZ basis set [69] was used, based on the very good results it provided in a recent MCSCF-... 

Gilbert ATB, Besley NA, Gill PMW (2008) Self-consistent field calculations of excited states using the maximum overlap method (MOM). J Phys C3iem A 112 13164-13171... 

M. Randid, Hybridization by the maximum overlap method, Int. J. Quantum Chem. 8 (1974) 643-676. 

Randic and Maksi6 have reviewed the maximum-overlap method of describing the hybridization of bonded atoms, and a number of cyclopropane and cyclobutane derivatives are included. The method has also been applied to benzocyclopropene and benzocyclobutene. One measure of the hybridization of the bonding orbitals of carbon is the magnitude of the and... 

Nevertheless, even direct minimization remains vulnerable to variational collapse, since the newly-occupied MO of the anion is subject to a different potential as compared to virtual MOs that might be nearby in energy. Subsequent SCF iterations can therefore modify the energetic ordering of the MOs, and in such cases, it is unclear which MOs should be the occupied ones at the next SCF iteration. The maximum overlap method (MOM) offers a possible solution to this problem, and a more refined version of the orbital relaxation technique. 

While CCSD(T), MP2, DFT, and so on are appropriate for bound anions, theoretical description of metastable anions requires specialized techniques. Many of these techniques are well-established but have seen far less use as compared to bound-state quantum chemistry. In this chapter, we have discussed a variety of techniques (the maximum overlap method, CCR, and stabilization methods) that are all based, at some level, on modifications to bound-state quantum chemistry that can be implemented as reasonably straightforward modifications of standard bound-state quantum chemistry codes. It is this author s hope that this review of such methods for temporary anion resonances will prompt renewed and increased interest in these techniques. 

A. T. B. Gilbert, N. A. Besley, and P. M. W. Gill,/. Phys. Chem. A, 112, 13164-13171 (2008). Self-Consistent Field Calculations of Excited States Using the Maximum Overlap Method (MOM). 

Theoretical considerations in the same fashion enable predication of the possible configuration of the transition state. Eq. (3.25 b) for the multicentre interaction is utilized. Hoffmann and Woodward 136> used such methods to explain the endo-exo selectivity of the Diels-Alder reaction (Fig. 7.28). The maximum overlapping criteria of the Alder rule is in this case valid. The prevalence of the endo-addition is experimentally known 137>. 

W = AG. Of course, this relation can be tested only in the region of work values along the work axis where both distributions (forward and reverse) overlap. An overlap between the forward and reverse distributions is hardly observed if the molecules are pulled too fast or if the number of pulls is too small. In such cases, other statistical methods (Rennet s acceptance ratio or maximum likelihood methods. Section IV.B.3) can be applied to get reliable estimates of AG. The validity of the CFT has been tested in the case of the RNA hairpin CD4 previously mentioned and the three-way junction RNA molecule as well. Figure 9c,d and Fig. 10c show results for these two molecules. 

---