Molecular orbitals fragment

The analogy between the electronic structures of two isolobal fragments is, of course, still present if we consider their molecular orbitals. 

We start with the organic series CH3, CH2, and CH. Just as there were one, two, or three nonbonding hybrid orbitals, respectively in the valence-bond model, the electronic structure in terms of 

In contrast to hybrid orbitals, MO are adapted to molecular symmetry. Several features therefore arise that are new, compared to the previous description. First, even though the MO that are considered are always concentrated in the same region of space as the vacant site(s) of the tetrahedron, they do not always point directly towards these sites, except, of course, in the case of CH3 where there is only a single vacant site. For example, the shapes of the ai and b2 MO in the CH2 fragment mean that the two sites of the initial tetrahedron are equivalent for these two MO (5-7b), but neither orbital points along the direction of the 

We shall now consider the inorganic fragments that are the isolohal analogues of CH3, CH2, and CH, that is, the SBP 4 ML5, butterfly 4 ML4 and pyramidal 4 ML3 fragments ( 5.1.1), and compare the MO that are concentrated around the vacant site(s) following the homolytic rupture of one, two, or three bonds in the initial structure (tetrahedral CH4 or octahedral MLg). 

In the CH3 and 4 ML5 fragments, there is only one orbital of this type. It is totally symmetric (ai symmetry) in both cases (C3V for CH3 and C4V for ML5) (5-8), it points towards the vacant site (of the tetrahedron or of the octahedron) and of course it has axial symmetry with respect to the main symmetry axis (C3 and C4, respectively). These two orbitals are not identical— the first is an sp hybrid orbital, the second a polarized orbital—but they are very similar. Counting electrons, 

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Reactions in solution have been analyzed computationally using the QM/ MM method. Although the QM/MM method can treat chemical events in solution at a reasonable computational expense, it has the inherent limitation that nucleophilic participation by solvent molecules cannot be treated by the classical MM scheme. Thus, a full QM method is required to describe the hydrolysis mechanism of CH3 substrates. The fragment molecular orbital (FMO)-MD scheme,144 146 which treats the whole system in a full QM fashion, makes it possible to deal with solution reaction dynamics with a reasonable number of solvent molecules explicitly with the accuracy of the given QM level. 

Komeiji Y, Ishida T, Fedorov DG, Kitaura K (2007) Change in a protein s electronic structure induced by an explicit solvent An ab initio fragment molecular orbital study of ubiquitin. J Comput Chem 28 1750-1762... 

Large scale MP2 calculations with fragment molecular orbital scheme93... 

Fukuzawa K, Mochizuki Y, Tanaka S, Kitaura K, Nakano T. Molecular interactions between estrogen receptor and its ligand studied by the ab initio fragment molecular orbital method. J Phys Chem B Condens Matter Mater Surf Interfaces Biophys 2006 110 16102-10. 

S. Dapprich, G. Frenking, Investigation of donor-acceptor interactions A charge decomposition analysis using fragment molecular orbitals, /. Phys. Chem. 99 (1995) 9352. 

Fedorov DG, Ishida T, Uebayasi M, Kitaura K (2007) The fragment molecular orbital method... 

Fig. 40.7. Fragment molecular orbitals that produce the three-center/two-electron bonds (one of three by symmetry), which constitute the principal metal-to-metal bonding interactions of Ru3(CO)i2[Pd(PR3)].

To quantify our perturbational picture of the TM-H bond, we performed Density Functional calculations for a variety of complexes. For the optimized molecular geometries, we did a fragment molecular orbital analysis, as outlined in Scheme 1. The HOMO energies E, for the L M fragment, as well as the nd -IJj overlap terms S are displayed in Figure 2. 

Nagata, T, Fedorov, D. G., Kitaura, K., Gordon, M. S. [2009]. A Combined Effective Fragment Potential-Fragment Molecular Orbital Method. 1. The Energy Expression and Initial Applications, J. Chem. Phys., 131, 024101. 

Steinmann, C., Fedorov, D. G., Jensen, J. H. (2010], Effective Fragment Molecular Orbital Metliod A Merger of the Effective Fragment Potential and Fragment Molecular Orbital Methods,/. Phys. Chem. A, 114,8705-8712. 

Pruitt, S. R., Steinmann, C., Jensen, J. H., Gordon, M. S. (2013]. Fully Integrated Effective Fragment Molecular Orbital Method, /. Chem. Theory Comp., 9, 2235-2249. 

M. Chiba, D. G. Fedorov, and K. Kitaura. Polarizable continuum model with the fragment molecular orbital-based time-dependent density functionai theory./ Comput. Chem., 29 2667-2676, 2008. 

Keywords Model core potential Pseudopotential Scalar-relativistic effects ECP spin-orbit calculation Fragment molecular orbital... 

An important development related to the MCPs was the introduction of the model core potentials to the fragment molecular orbital (FMO) calculations [115]. The FMO/MCP method allows to carry out quantum mechanical calculations for large scale systems containing heavy metal atoms. 

Another acronym for this approach is FO (frontier orbital) theory. The acronym FMO is also used for the fragment molecular orbital method. See, for example, Fedorov, D. G. Kitaura, K. J. Phys. Chem. A 2007, 111, 6904. 

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