Localized molecular orbitals separation

The localized molecular orbital model (LMO) (39-41) treats the electrons and nuclei separately. The nuclear contribution is identical to eq. [26] with = Z e, the nuclear charge screened by the irmer shell electrons that are assumed to follow the nuclei. The local units for the contribution from the valence elec-... 

The Fermi hole for the reference electron at a bonded maxima in the VSCC of the carbon atom has the appearance of the density of a directed sp hybrid orbital of valence bond theory or of the density of a localized bonding orbital of molecular orbital theory. Luken (1982, 1984) has also discussed and illustrated the properties of the Fermi hole and noted the similarity in appearance of the density of a Fermi hole to that for a corresponding localized molecular orbital. We emphasize here again that localized orbitals like the Fermi holes shown above for valence electrons are, in general, not sufficiently localized to separate regions of space to correspond to physically localized or distinct electron pairs. The fact that the Fermi hole resembles localized orbitals in systems where physical localization of pairs is not found further illustrates this point. 

Note that a distinction is made between electrostatic and polarization energies. Thus the electrostatic term, Ue e, here refers to an interaction between monomer charge distributions as if they were infinitely separated (i.e., t/°le). A perturbative method is used to obtain polarization as a separate entity. The electrostatic and polarization contributions are expressed in terms of multipole expansions of the classical coulomb and induction energies. Electrostatic interactions are computed using a distributed multipole expansion up to and including octupoles at atom centers and bond midpoints. The polarization term is calculated from analytic dipole polarizability tensors for each localized molecular orbital (LMO) in the valence shell centered at the LMO charge centroid. These terms are derived from quantum calculations on the... 

Experimental chemistry is focused, in most cases, on molecules of a larger size than those for which fair calculations with correlation are possible. However, after thorough analysis of the situation, it turns out that the cost of the calculations does not necessarily increase very fast with the size of a molecule. Employing localized molecular orbitals and using the multipole expansion (see Appendix X available at booksite.elsevier.com/978-0-444-59436-5) of the integrals involving the orbitals separated in space causes, fa- elongated molecules, the cost of the post-Hartree-Fock calculations to scale linearly with the size of a molecule. It can he expected that if the methods described in... 

Fig. 1 Separation of the QM and MM subsystems by a frozen strictly localized molecular orbital (SLMO). QM and MM atoms are designated by Q and M, respectively. QMH is the QM host atom and MMH is the MM host atom, and the latter is also called frontier atom...

For large interchain separations (8 A < R < 30 A), the LCAO coefficients of a given molecular orbital are localized on a single chain, as intuitively expected. The lowest excited state of these dimers results from a destructive interaction of the two intrachain transition dipole moments, whereas a constructive interaction prevails for the second excited stale. This result is fully consistent with the molcc-... 

For planar unsaturated and aromatic molecules, many MO calculations have been made by treating the a and n electrons separately. It is assumed that the o orbitals can be treated as localized bonds and the calculations involve only the tt electrons. The first such calculations were made by Hiickel such calculations are often called Hiickel molecular orbital (HMO) calculations Because electron-electron repulsions are either neglected or averaged out in the HMO method, another approach, the self-consistent field (SCF), or Hartree-Fock (HF), method, was devised. Although these methods give many useful results for planar unsaturated and aromatic molecules, they are often unsuccessful for other molecules it would obviously be better if all electrons, both a and it, could be included in the calculations. The development of modem computers has now made this possible. Many such calculations have been made" using a number of methods, among them an extension of the Hiickel method (EHMO) and the application of the SCF method to all valence electrons. ... 

That is, it also reduces the long-range repulsions between the orbitals as much as possible. Thus, this localization method achieves three objectives concentration of the molecular orbitals, short-range separation of different orbitals, and long-range separation of different orbitals. 

---