Atomic orbitals methods

Feynman model. The Feynman approach, or LCAO (hnear combination of atomic orbitals) method, assumes that a wavefunction of valence electrons i// in a metal is a linear combination of atomic functions ... 

K. Wolinski, J. F. Hinton and P. Pulay, Efficient implementation of the gauge-independent atomic orbital method for NMR chemical-shift calculations. J. Am. Chem. Soc., 1990, 112,8251-8260. 

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. 

Ditchfield, R. Self-consistent perturbation theory of diamagnetism. I. A gage-invariant LCAO(linear combination of atomic orbitals) method for NMR chemical shifts, Mol. Phys. 1974, 27, 789-807. 

Bullett, D. W. (1987). Applications of atomic-orbital methods to the structure and properties of complex transition-metal compounds. Phys. Chem. Mineral. 14, 485-91. 

Chelikowsky, J. R., and S. G. Louie (1984). First principles linear combination of atomic orbitals methods for the cohesive and structural properties of solids Application to diamond. Phys. Rev. B29, 3470-81. 

Theory delocalization energy by the atomic orbital method. 

Summary Comments for the Linear Combination of Atomic Orbitals Method and Diatomic Molecules... 

It is convenient to have a word for the space-dependent part of a wave function for one electron, to distinguish it from the whole wave function which includes reference to the spin. Orbital is the customary word. Such a function as the Is wave function, obtained by solving Schrodinger s equation for an atom, is called an atomic orbital. Such functions as the wave functions used in the last chapter for the hydrogen-molecule ion are called molecular orbitals. The foregoing method of approximation in a many-electron problem is therefore often called the atomic orbital method. 

The question now arises, why does the molecular orbital method afford four possibilities, three with spins paired, whereas the atomic orbital method seemed to yield only two possibilities, one with spins paired The answer comes from looking at a way of approximating ag and wave functions on the two atoms, which you used before. This way of approximating molecular orbitals is often called the LCAO approximation the linear combination of atomic orbitals. Fig. 6.8 shows cross-sections of A and 5. Clearly A + B looks like og (Fig. 6.7) and A — B looks like <7U. By using these approximations, the four functions of Table 6.1 can be rewritten into the forms shown in Table 6.2. When the products in Table 6.2 are expanded, and the results are compared with (6.1), the four functions take the forms shown in Table 6.3. 

These forms now call attention to two combinations of the atomic orbitals that were neglected in the earlier pursuit of the atomic orbital method the combinations, 4(1)., 4(2) and 5(1). 5(2). Clearly the states that these combinations represent are those in which both electrons with spins paired, are on one or the other proton the ionic states H H+ and H+H (Fig. 6.9). It is altogether probable that an approximation to the true wave function... 

This method is called the LCAO (Linear Combination of Atomic Orbitals) method. The electron density p(7) becomes ... 

What we have just described has its counterpart in a mathematical treatment called the LCAO (linear combination of atomic orbitals) method. In the LCAO treatment, wave functions for the atomic orbitals are combined in a linear fashion (by addition or subtraction) in order to obtain new wave functions for the molecular orbitals. 

---