Sigma and pi bonds

Here are the plots of a sigma and a pi bonds in H₂C=CH₂.

Sigma bond:  When atomic orbitals overlap end-to-end to result in a possitive overlap in the region along the 'bond' connecting the atoms.

Pi bond:  When atomic orbitals overlap side-to-side to result in two lopes above and below the 'bond' connecting the atoms.

The objective of this tutorial is to use ethane and ethyne to study the nature of sigma and pi bonds.

Procedure for using tools in Avisto: 

1. Use MolDesign to build ethane, H₃C-CH₃ and ethylene, H₂C=CH₂.  Make sure for ethane to have almost the ecclipse structure and ethylene to have the two CH2 groups almost perpendicular to each other.

2. Use Basic QChem Edu or Basic QChem tool, search for stable structures for both molecules.

3. User PsiViewer to view results.

A. Rotation about the C-C bond

Compare the potential curves.

Using the animation function in PsiViewer to view the energy changes as the two groups in ethane and ethylene rotate around the CC bond.  Rotation around the C-C bond costs about 4-5 kcal/mol in ethane as compared to more than 60 kcal/mol in ethylene.   This indicates rotation about a single bond is easy but rotation about a double bond is almost impossible.

B. Delocalized molecular orbitals

Use PsiViewer to plot the delocalized molecular orbitals for both molecules.

For ethylene, it is easy to distinguish the pi and

 pi* MO from the sigma orbitals.  However, for ethane there are only sigma MO's.  Since they are delocalized and thus are more difficult to make any physical interpretation.

C. Localized molecular orbitals

This time plots the localized molecular orbitals for both molecules.  Only occupied MO's can be localized and thus the orbital energy diagram in PsiViewer only shows the occupied localized MO's.

Localized MO's illustrate the physical interpretation of sigma and pi bonds much better than the delocalized MO's.

D. Orbital hybridization

Under the Files tab of PsiViewer, open the .out file and find the Sigma-Pi Bond-order matrix.

For ethane,

          SIGMA-PI BOND-ORDER MATRIX

                         S-SIGMA    P-SIGMA      P-PI     S-SIGMA    P-SIGMA      P-PI                                C  1       C  1       C  1       C  2       C  2       C  2------------------------------------------------------------------------------ S-SIGMA  C  1   0.992682 P-SIGMA  C  1   0.000000   2.930420   P-PI        C  1   0.000000   0.000000   0.014323 S-SIGMA  C  2   0.041160   0.199503   0.000000   0.992677 P-SIGMA  C  2   0.199540   0.562035   0.000000   0.000000   2.930439   P-PI        C  2   0.000000   0.000000   0.010963   0.000000   0.000000   0.014312 S-SIGMA  H  3   0.000003   0.000047   0.000059   0.250671   0.722904   0.001057 S-SIGMA  H  4   0.000003   0.000047   0.000059   0.250669   0.722906   0.001057 S-SIGMA  H  5   0.000003   0.000047   0.000059   0.250667   0.722911   0.001056 S-SIGMA  H  6   0.250648   0.722923   0.001061   0.000003   0.000048   0.000059 S-SIGMA  H  7   0.250662   0.722907   0.001063   0.000003   0.000048   0.000059 S-SIGMA  H  8   0.250664   0.722910   0.001059   0.000003   0.000047   0.000059

For C1 atom, 0.993 s orbital combined with 2.93 p orbitals to make four sp³ hybrid orbitals to form sigma bonds with three hydrogen atoms and the other carbon atom. Similar orbital hybridization is found for the other carbon atom. 

For ethylene,

          SIGMA-PI BOND-ORDER MATRIX

                           S-SIGMA    P-SIGMA    P-PI     S-SIGMA    P-SIGMA      P-PI                                C  1       C  1       C  1       C  2       C  2       C  2------------------------------------------------------------------------------ S-SIGMA  C  1   0.982162 P-SIGMA  C  1   0.000000   1.960084   P-PI       C  1   0.000000   0.000000   1.015587 S-SIGMA  C  2   0.105650   0.262808   0.000000   0.982162 P-SIGMA  C  2   0.262805   0.371888   0.000000   0.000000   1.960083   P-PI        C  2   0.000000   0.000000   1.013735   0.000000   0.000000   1.015587 S-SIGMA  H  3   0.000015   0.000394   0.000012   0.306841   0.662298   0.000913 S-SIGMA  H  4   0.000015   0.000395   0.000012   0.306833   0.662303   0.000914 S-SIGMA  H  5   0.306826   0.662311   0.000913   0.000015   0.000394   0.000012 S-SIGMA  H  6   0.306851   0.662287   0.000913   0.000015   0.000394   0.000012

For C1 atom, 0.982 of the 2s orbital combined with 1.96 2p orbitals to form three sp2 hybrid orbitals to form sigma bonds with hydrogen atoms and the other carbon atom.  It leaves one 2p to form the pi bond.