Critical test of quantum cluster equilibrium theory: Formic acid at B3LYP/6-31+G* hybrid density functional level

Abstract

The recently developed quantum cluster equilibrium (QCE) theory is used at the B3LYP/6-31+G* level of hybrid density functional theory to calculate the equilibrium cluster populations for formic acid vapor, whose quantitative cluster composition was determined by Coolidge and others through precise spectroscopic and vapor-density measurements over a wide range of temperature and pressure. Unlike previous experimental tests of QCE theory in which T,P-dependent cluster polpulations enter only indirectly (e.g., through convolutions with calculated cluster spectroscopic properties, yielding comparison with inhomogeneously braodened “average” spectral features), the present comparison is able to directly test the QCE population distributions. Nearly exact agreement between theory and experiment is found over the entire span of measurements, confirming that QCE theory satisfactorily predicts the T,P-dependent concentrations of individual cluster species, as well as the cruder population-weighted averages that enter less-sensitive comparisons with experiment.