High-accuracy solution of the rovibrational Schrödinger equation for triatomic molecules

Abstract

Modern meteorological studies and atmospheric monitoring are placing stringent requirements on the accuracy of high-resolution molecular spectroscopy at infrared and visible wavelengths. Experimental progress towards accurately determining infrared line centers to within kilohertz and line intensities to better than sub-promille accuracy requires corresponding progress in theoretical determinations. Recently, it has been demonstrated that modern rovibrational programs for diatomic molecules (DUO and LEVEL) can solve the Schrödinger equation with an accuracy of 1 part in 10${}^8$ by analysis of numerical solutions of exactly solvable problems. The demand for such agreement in triatomic calculations is pressing. Nine to ten digit convergence for computed CO${}_2$ rovibrational energy levels is demonstrated herein using a variety of available variational nuclear motion programs based on the use of exact (within the Born–Oppenheimer approximation) kinetic energy operators. The programs DVR3D, in both Radau and Jacobi coordinates, EVEREST, RV3 and TROVE are compared. The agreement achieved corresponds to about 0.00005 cm${}^{-1}$  which sets a new benchmark for accuracy. A comparison of DVR3D and EVEREST also shows agreement for computed Einstein A coefficients at the sub-percent level for the majority of transitions.