Extended Huckel Theory—Hoffmans EHT Method

Hoffman s extended Huckel theory, EHT (Hoffman, 1963), includes all bonding orbitals in the secular matrix rather than just all n bonding orbitals. This inclusion increases the complexity of the calculations so that they are not practical without a computer. The basis set is a linear combination that includes only valence orbitals 

The orbitals used for methane, for example, are four Is Slater orbitals of hydrogen and one 2s and three 2p Slater orbitals of carbon, leading to an 8 x 8 secular matrix. Slater orbitals are systematic approximations to atomic orbitals that are widely used in computer applications. We will investigate Slater orbitals in more detail in later chapters. 

We fill the secular matrix H with elements Hy over the entire set of valence orbitals. The diagonal elements are 

After diagonalization of the EHT matrix, the lowest 4 orbitals have an energy sum of about —70 eV. The electronic energy for these doubly occupied orbitals is 2(—70) = — 140 eV. The energy gain of the molecule relative to its atoms is —140 — ( — 110) = —30eV = —690 kcal mol (1 eV = 23 kcal mol ) therefore, the molecule is stable relative to its atoms. We can envision an energy cycle with three steps (Eig. 7-5)  

Completely independent core positive ions and electrons come together from infinite separation to form 1 C atom and 4 H atoms. One electron per atomic orbital brings about a total energy change of — 110 eV. 

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