Efficient Ab Initio Calculation of Polyatomic Ro-vibrational Spectra: A Comparative Study of Discrete Variable Representations for NH ₂ with Non-Adiabatic Coupling

We theoretically investigated the rotational-vibrational (ro-vibrational) spectrum of the NH₂ molecule in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mover><mml:mi>X</mml:mi><mml:mo>~</mml:mo></mml:mover><mml:mn>2</mml:mn></mml:msup><mml:msup><mml:mi>A</mml:mi><mml:mo>″</mml:mo></mml:msup></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mover><mml:mi>A</mml:mi><mml:mo>~</mml:mo></mml:mover><mml:mn>2</mml:mn></mml:msup><mml:msup><mml:mi>A</mml:mi><mml:mo>'</mml:mo></mml:msup></mml:math> electronic states. Because the ground electronic state <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mover><mml:mi>X</mml:mi><mml:mo>~</mml:mo></mml:mover><mml:mn>2</mml:mn></mml:msup><mml:msup><mml:mi>A</mml:mi><mml:mo>″</mml:mo></mml:msup></mml:math> and the first excited state <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mover><mml:mi>A</mml:mi><mml:mo>~</mml:mo></mml:mover><mml:mn>2</mml:mn></mml:msup><mml:msup><mml:mi>A</mml:mi><mml:mo>'</mml:mo></mml:msup></mml:math> have nonlinear equilibrium geometries, the Renner-Teller (RT) effect plays a significant role in the ro-vibrational spectrum. By introducing the RT effect as an effective coupling potential of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mover><mml:mi>X</mml:mi><mml:mo>~</mml:mo></mml:mover><mml:mn>2</mml:mn></mml:msup><mml:msup><mml:mi>A</mml:mi><mml:mo>″</mml:mo></mml:msup></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mover><mml:mi>A</mml:mi><mml:mo>~</mml:mo></mml:mover><mml:mn>2</mml:mn></mml:msup><mml:msup><mml:mi>A</mml:mi><mml:mo>'</mml:mo></mml:msup></mml:math> states, the ro-vibrational spectra at different total angular momentum quantum numbers are calculated with the generalized Laguerre discrete variable representation (LDVR), Laguerre-Morse DVR (LMDVR), and Jacobi DVR (JDVR). Additionally, we conduct a comparative analysis of the efficiency of Laguerre, Laguerre-Morse, Jacobi, and conventional sine DVR in calculating the ro-vibrational spectra. The results of the ab initio calculations are presented in this work as well as the data and code for the potential energy surface (PES) part of the Hamiltonian with the RT effect.