Density functional calculations of thermochemical equilibria

Computationally practical quantum-mechanical methods are needed in order to determine the ideal-gas thermodynamic properties of moderate-size molecules. In this work, we attempt to utilize density functional theory with B3LYP functional to calculate thermodynamic quantities of organic molecules of moderate sizes and to apply the results to characterize the thermochemical equilibria of industrially important amines systems. It was found that the B3LYP calculations with the 6-31G** basis set systematically underestimate the heat of combustion. A molecular-size-dependent scaling factor was then defined to systematically scale up thr calculated heat of combustion. yielding good agreement with the well-established tabulated data. The heat of formation can be readily derived from the scaled heat of combustion. We show that single point energy calculations with the 6-311++G** basis set using the geometries and vibrational frequencies obtained at the 6-31G** level can greatly improve the quality of the calculated heats of formation. The calculated entropy and heat capacity are in good agreement with the tabulated values. The calculated Gibbs free energy of a molecule is also consistent with the tabulated data over a wide temperature range with the inaccuracy mainly resulting from the uncertainty of heat of formation. The calculated Gibbs free energy changes used to characterize the chemical equilibria in amine syntheses are in general within 2 kcal/mol difference from the tabulated data. The error is magnified in the calculated equilibrium constants.