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GAMESS WORKSHOP:
The Energy Profile for the Formation of Formaldehyde to Hydroxycarbene


Purpose:

GAMESS and MacMolPlt software is unlike Chem3D's spring-and-ball, classic mechanical calculations (MM2) because it calculates the energies of a molecule's electrons using quantum mechanics (Schrodinger equations, Hessians, etc.).  The purpose of this exercise is to become familiar with its use. 

The ground states (optimized geometries) of structural isomers HCOH (a carbene) and H2CO (formaldehyde, a ketone) and the transition structure that connects them at the HF/3-21G level of theory were calculated using GAMESS.  The difference in energy for the two isomers and the activation energy barrier (energy difference with the transition state energy) was also calculated.

Energy Profile of Reaction and Pictures of Geometries:

energy profile of reaction

optimized geometry of carbene

1. HYDROXYCARBENE  
Energy: -113.1463 Hartrees = -71,000.43471 kcal/ mole

carbene's lewis structure
 Saddlepoint for the transition state
2. TRANSITION STATE
Energy: -113.0501 Hartrees = -70940.06825 kcal/ mole

lewis structure of the transition state
 optimized geometry of formaldehyde
 3. FORMALDEHYDE
Energy: -113.2218 Hartrees = -71047.81172 kcal/ mole

lewis structure of formaldehyde

The predicted difference in energy between the hydroxycarbene and the formaldehyde isomers is -47.4 kcal/ mole as shown in the energy profile graph.  The activation energy barrier from hydroxycarbene to the transition state is 60.4 kcal/ mol.  The activation energy barrier from formaldehyde to the transition state is 107.8 kcal/ mol.

An analysis of the geometric structures and the lewis structures for the two isomers and the transition state gives a good explanation for the observed energies. 

1) The formaldehyde isomer is the lowest energy molecule--all molecules have filled valence shells and zero formal charges.
2) The hydroxycarbene has greater energy because, judging from its resonance structures, the highly electronegative oxygen has a partial positive formal charge (indicating a lower electron density than what is desirable) and the carbon is not completely satisfied with a full octet--this leads to a highly reactive, higher energy molecule.
3) The transition state is the highest energy state where hydrogen is pushed toward the carbon atom and is in the process of forming a bond with carbon and breaking its bond with oxygen... leading to a highly strained pseudo-ring structure.  The formal charges in the Lewis structure further represent the instability of the electron arrangement in the transition state.