MATRIX ALGEBRA and ORBITALS

Orbitals emerge from sophisticated algebraic manipulations of matrixes. "n": simultaneous linear equations in "n" unknowns are manipulated in the quantification and quantum mechanics of "n" orbitals. Once the LCAO orbitals are generated, then one can infer from them solutions to problems in chemical reactivity and bonding and conductivity. The orbitals emerge from simultaneous linear equations involving symmetry properties of molecules and extended structures...it is matrix algebra on a very large scale. And everything follows the rules laid down in Cotton's book for properties of acceptable wave functions. Extended Hueckel was the first such method of LCAO-MO's and LCAO-CO's.