Abstract: Proton transfer is the most general and important reaction in chemistry. This work presented a sextic function to describe the potential energy surface(PES) of proton transfer. The picture of the sextic function V(R,γ)=R⁶+2(R⁴+(γ²+μ)R² is a double-well curve, when γ and μ satisfy specific conditions. Moreover, its corresponding Schrdinger equation has exactly analytic solutions via transformation. But to the generally used quartic function V(R)=A(R⁴-BR²), the corresponding Schrdinger equation can′t be solved exactly. Combined this potential function with one-dimensional double-well model and variational method, the energy splitting of the ground state of 9-hydroxyphenalenone, which is a typical system of intramolecular proton transfer, was studied in this work. The structure and energy were calculated with density-functional theory(DFT) at the B3P86/6-311G level for the equilibrium configuration and the transition state. The produced barrier height was 722.85 cm^-1. The energy splitting obtained Δ_H(0)=86.13 cm^-1 was satisfactorily compared with the experimental observations and other theoretical values.

Key words: Proton transfer, Energy splitting, Solvable potential function, Double-well model