SUPPLEMENTARY – 3

Generate the Molecular Orbitals for CH4(Td), CH4(D4h) and Cyclopropane using semi-empirical module with the AM1 (Austin Model 1) Hamiltonian using HyperChem7.5.

Please take the help from “Instructions to use HyperChem 7.5’ and Assignment – 1 to build and calculate the molecules. Assignment – 1 gives the information to generate the MOs.

AM1 is an improved version of MNDO (Modified Neglect of Diatomic Overlap) method. The MNDO is based on the NDDO (Neglect of Diatomic Differential Overlap) approximation and in turn NDDO an improvement version of INDO (Intermediate Neglect of Differential Overlap) method. INDO itself is an improvement on the CNDO (Complete Neglect of Differential Overlap) approximation. There are several such semi-empirical LCAO MO methods, developed for specific purposes.

In the assignment-2 we would like to concentrate on the results that are computed using the AM1 Hamiltonian. The molecular wave function is described by the LCAO (Linear Combination of Atomic Orbitals) approximation. AM1 uses s and p atomic orbitals like MNDO and the modified core repulsion function with additional Gaussian terms (Ref: J.Am.Chem.Soc., 1985, 107, 3902-3909. Also see the E-book at the library web page).

AM1 is parameterized for the following atoms:

H, B, C, N, O, F, Na, Mg, Al, Si, P, S, Cl, ZN, Ge, Br, Sn, I, and Hg.

AM1 is a good general method for quick compuation of structure and energetics of organic compound. The parameters for phosphorous and sulfur are not very good.

Stabilization of planar tetra coordinate carbon: -

As an example to learn the use of MO theory to design molecules with the specific geometries required, we will consider this problem. The arrangement of atoms in space for carbon chemistry was proposed by Jacobus Henricus van't Hoff when he was barely 22 years of age. The original title of the publication is “Proposal for the Extension of Current Chemical Structural Formulas into Space, together with Related Observation on the Connection between Optically Active Power and the Chemical Constitution of Organic Compounds.” He received the very first Noble prize (1901) in chemistry.

In 1874, van't Hoff and Le Bel discovered independently that tetracoordinate carbon prefers tetrahedral arrangements of the four substituents. The idea of arrangement of atoms in space introduced new perceptions in building the molecular structures of different kinds by chemists. In the late 1960's chemists started considering the possibility that compounds might be found with planar rather than tetrahedral tetracoordinate carbons. The literature based on this concept continues to grow! Now we will see the arrangement of atoms in space, as well as atomic orbitals in space. The simplest model to investigate is methane so that the concepts can be illustrated. Methane has 1s (H), 2s, 2px, 2py and 2pz (C) valence atomic orbitals as shown below.

We will arrange these atomic orbitals in space mainly in square planar, and tetrahedral fashion and we will see the structural deformations that are anticipated.

The construction of D4h CH4 (square planar arrangement) and the Td CH4 (tetrahedral arrangement) is as follows.

CH4 in square planar (D4h)

CH4 in tetrahedral shape (Td)

The correlation diagram between the bonding MOs of square planar and tetrahedral CH4 is as follows: -

During the D4h to Td distortion, the two degenerate energy levels in D4h are destabilized due to the overlap between the p orbital on carbon and the two hydrogen s orbitals is decreased. But the HOMO (Highest Occupied Molecular Orbital) is stabilized because the p orbital now mixes with the s orbital so that a directed C-H bonding orbital is obtained.

If we observe the bonding picture in D4h the HOMO is nonbonding where as in Td all the three degenerate MOs are bonding. Please check the bond order; CH4 has 8 electrons (four from carbon and four from hydrogen atoms). In D4h only six of them participate in bonding: the other two are nonbonding electrons. So there are only three bonding molecular orbitals, but CH4 has four bonds. That is these bonds are not two-center two-electron bonds (2c-2e). However it should be possible to stabilize the planar tetracoordinate carbon. The following factors are useful in stabilizing the planar tetracoordinate carbon (i) delocalizing the lone pair by p conjugation (ii) providing more electron density to carbon by s donation (iii) enforced reduction of the angle around planar tetracoordinate carbon atom by means of small rings. (Text Book No.5 by Albright et al).

To utilize the nonbonding electron pair as in (i) we should substitute electron-withdrawing groups such as Li, BH2 BeH2 etc., due to simultaneous operation of s donating and p accepting effects. If the vacant orbital on the substituent atom or group is parallel the to nonbonded orbital then the planar tetra coordinate carbon will be more stabilized than when the group is perpendicular to the nonbonded orbital.

The other way of stabilizing planar tetracoordinate carbon is by making the carbon atom a part of a small ring i.e. by bringing the internal angle closer to that in square-planar arrangement than in the tetrahedral arrangement. The examples are as follows.

The electron withdrawing groups can be incorporated into the ring structure or they can be introduced as external substituents.

Another geometry that is to be considered for CH4, the square pyramid. The square pyramidal geometry (C4v) is preferred than the square planar geometry (D4h).

The correlation energy diagram between square pyramidal (C4v), square planar (D4h) and tetrahedral (Td) carbon is as follows.