Molecular orbital-linear combination

The present article is an attempt to review those studies of pyridinelike heterocycles (mono-azines) and, to a lesser extent, their analogues and derivatives that have interpreted the behavior and estimated various physico-chemical properties of the compounds by the use of data calculated by the simplest version of the MO LCAO (molecular orbital, linear combination of atomic orbitals) method (both molecular orbital energies and expansion coefficients). In this review, attention is focused upon the use of the simple method because it has been applied to quite extensive sets of compounds and to the calculation of the most diverse properties. On the other hand, many fewer compounds and physico-chemical properties have been investigated by the more sophisticated methods. Such studies are referred to without being discussed in detail. In a couple of years, we believe, the extent of the applications of such methods will also be wide enough to warrant a detailed review. 

A very simple procedure was proposed by Del Re 87 for representing the <7 bonds in saturated compounds. Its essential features are as follows, (a) Treat each bond as a two-electron problem, (b) Describe each electron in the bond by a molecular orbital linear combination of... 

Up to this point nothing changes. The next assumption extends the above treatment of atoms to molecules. Within it the molecular orbitals - linear combinations of the atomic core orbitals with zero overlap - are taken to be the molecular core orbitals and are assumed to be filled. This allows one to write... 

In order to solve the Kohn-Sham equations (Eqn. (2)) we used the molecular orbital-linear combination of atomic orbitals (MO-LCAO) approach. The molecular wave functions 0j are expanded the symmetry adapted orbitals Xj) which are also expanded in terms of the atomic orbitals... 

In order to further describe the molecular wavefunctions or the molecular orbitals. Linear Combinations of Atomic Orbitals (LCAO) are normally used (LCAO method). Such a method of solution is possible since the directional dependence of the spherical-harmonic functions for the atomic orbitals can be used. The Pauli principle can be applied to the single-electron molecular orbitals and by filling the states with the available electrons the molecular electron configurations are attained. Coupling of the angular momenta of the open shell then gives rise to molecular terms. 

SCF-MO- Self-consistent field-molecular orbital-linear combination of atomic LCAO orbitals... 

Of the various methods of approximating the correct molecular orbitals, we shall discuss only one- the linear combination of atomic orbitals (LCAO) method. We assume that we can approximate the correct molecular orbitals by combining the atomic orbitals of the atoms that form the molecule. The rationale is that most of the time the electrons will be nearer and hence controlled by oneor the other of the two nuclei, and when this is so, the molecular orbital should be very nearly the same as the atomic orbital for that atom. The basic process is the same as the one wc employed in constructing hybrid atomic orbitals except that now we are combining orbitals on different atoms to form new orbitals that are associated with the entire molecule. We... 

The molecular orbital approach to chemical bonding rests on the notion that, as electrons in atoms occupy atomic orbitals, electrons in molecules occupy molecular orbitals. Just as our first task in writing the electron configuration of an atom is to identify the atomic orbitals that are available to it, so too must we first describe the orbitals available to a molecule. In the molecular orbital method this is done by representing molecular orbitals as combinations of atomic orbitals, the linear combination of atomic orbitals-molecular orbital (LCAO-MO) method. 

LCAO (Linear Combination of Atomic Orbitals) It is simple and qualitative approximation which can explain the formation of molecular orbitals by combination of atomic orbitals. 

LCAO method A method of calculation of molecular orbitals based upon the concept that the molecular orbital can be expressed as a linear combination of the atomic orbitals. 

B3.1.5.2 THE LINEAR COMBINATIONS OF ATOMIC ORBITALS TO FORM MOLECULAR ORBITALS EXPANSION OF THE SPIN ORBITALS... 

HMO theory is named after its developer, Erich Huckel (1896-1980), who published his theory in 1930 [9] partly in order to explain the unusual stability of benzene and other aromatic compounds. Given that digital computers had not yet been invented and that all Hiickel s calculations had to be done by hand, HMO theory necessarily includes many approximations. The first is that only the jr-molecular orbitals of the molecule are considered. This implies that the entire molecular structure is planar (because then a plane of symmetry separates the r-orbitals, which are antisymmetric with respect to this plane, from all others). It also means that only one atomic orbital must be considered for each atom in the r-system (the p-orbital that is antisymmetric with respect to the plane of the molecule) and none at all for atoms (such as hydrogen) that are not involved in the r-system. Huckel then used the technique known as linear combination of atomic orbitals (LCAO) to build these atomic orbitals up into molecular orbitals. This is illustrated in Figure 7-18 for ethylene. 

ITyperChem uses the Linear Combination of Atomic Orhilals-Molecular Orbital (LCAO-MO) approximation for all of itsah initio sem i-empirical melh ods. If rg, represen is a molecular orbital and... 

To com pnte molecular orbitals, yon must give them mathematical Torm. The usual approach is to expand them as a linear combination ofkiiown function s, such as th e atom ic orbitals oT th e con stit-... 

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