A Theoretical Study of the Rearranging Trans-HCOH to H2CO via Quantum Tunneling with DFT and WKB Approximation

Abstract

We attempt to study the stability of trans-HCOH molecule using density functional theory (DFT). Experimentally, trans-HCOH rearranges to H2CO with half life two hours in temperature at 11K whereby quantum tunneling makes the rearrangement possible. We begin from determination of reaction path from trans-HCOH to H2CO followed by its corresponding energy barrier using DFT. Then, we use Wentzel-Kramers-Brillouin (WKB)approximation to get probability of quantum tunneling hence we are able to calculate the rearrangement rate and the half life. To prove the rearrangement is not triggered by internal thermal energy, we calculate rearrangement rate based on the Arrhenius equation. Our calculations predict the halflife of trans-HCOH is 151 minutes (2.5 hours) via quantum tunneling and infinity via internal thermal energy which agrees with the experiment.