Highly excited vibrational levels of methane up to 10 300 cm⁻¹: Comparative study of variational methods

In this work, we report calculated vibrational energy levels of the methane molecule up to 10 300 cm⁻¹. Two potential energy surfaces constructed in quite different coordinate systems with different analytical representations are employed in order to evaluate the uncertainty of vibrational predictions. To calculate methane energy levels, we used two independent techniques of the variational method. One method uses an exact kinetic energy operator in internal curvilinear coordinates. Another one uses an expansion of Eckart-Watson nuclear motion Hamiltonian in rectilinear normal coordinates. In the Icosad range (up to five vibrational quanta bands–below 7800 cm⁻¹), the RMS standard deviations between calculated and observed energy levels were 0.22 cm⁻¹ and 0.41 cm⁻¹ for these two quite different approaches. For experimentally well-known 3v₃ sub-levels, the calculation accuracy is estimated to be ∼1 cm⁻¹. In the Triacontad range (7660-9188 cm⁻¹), the average error of the calculation is about 0.5 cm⁻¹. The accuracy and convergence issues for higher energy ranges are discussed.