Calculation of the Kirkwood–Frohlich correlation factor and dielectric constant of methanol using a statistical model and density functional theory

Abstract

The geometries of methanol monomer and methanol clusters, (CH₃OH) _m , m = 2–10, were optimized using the DFT/B3LYP/6-31++G(d,p) method. For each m > 2, a number of conformers were found to satisfy the optimization condition, showing no imaginary frequency in their calculated IR spectra. With increasing m, five- and six-membered rings begin to appear with open chain branches and the calculated IR spectra approach the experimentally observed IR spectrum of liquid methanol. Using the average energy of formation of one hydrogen bond and a statistical model, the Kirkwood–Frohlich (K–F) correlation factor (g) and dielectric constant (ε) were calculated for each methanol cluster. From a plot of ε versus cluster size (m), the bulk dielectric constant was obtained by extrapolation to m→∞. The value of g averaged over all conformers is in almost complete agreement with the g value obtained in an earlier molecular dynamics simulation study by Fonseca and Ladanyi [J. Chem. Phys. 93, 8148 (1990)]. Using this value of g in the K–F equation, the dielectric constant (ε) of methanol was calculated and found to be in fair agreement with (∼17% lower than) the experimental value and also with an earlier molecular dynamics simulation [Mol. Phys. 94, 435 (1998)]. The calculated ε follows the same trend in variation with temperature as the experimental ε in the range 288–318 K.

Keywords:

• dielectric constant
• methanol
• DFT
• quantum chemistry
• Kirkwood-Frohlich

Acknowledgements

ND thanks the CSIR for a senior research fellowship. The authors thank a referee for valuable comments and suggestions.

Notes

All figures can be viewed in colour online.