New rovibrational kinetic energy operators using polyspherical coordinates for polyatomic molecules

What It Takes to Compute Highly Accurate Rovibrational Line Lists for Use in Astrochemistry

ConspectusWe review the Best Theory + Reliable High-Resolution Experiment (BTRHE) strategy for obtaining highly accurate molecular rovibrational line lists with InfraRed (IR) intensities. The need for highly accurate molecular rovibrational line lists is twofold: (a) assignment of the many rovibrational lines for common stable molecules especially those that exhibit a large amplitude motion, such as NH₃, or have a high density of states such as SO₂; and (b) characterization of the atmospheres of exoplanets, which will be one of the main areas of research in astronomy in the coming decades. The first motivation arises due to the need to eliminate lines due to common molecules in an astronomical observation in order to identify lines from new molecules, while the second motivation arises due to the need to obtain accurate molecular opacities in order to characterize the atmosphere of an exoplanet. The BTRHE strategy first consists of using high-quality ab initio quantum-chemical methods to obtain a global potential energy surface (PES) and dipole moment surface (DMS) that contains the proper physics. The global PES is then refined using a subset of the reliable high-resolution experimental data. The refined PES then gives energy-level predictions to an accuracy similar to the reproduction accuracy of the experimental data used in the refinement step in the interpolation region (i.e., within the range of the experimental data used in the refinement step). The accuracy of the energy levels will slowly degrade as they are extrapolated to spectral regions beyond the high-resolution experimental data used in the refinement step. However, because the degradation is slow, the predicted energy levels can be used to assign new high-resolution experiments, and the data from these can then be used in a subsequent refinement step. In this way, the global PES eventually can yield highly accurate energy levels for all desired spectral regions including to very high energies and high J values. We show that IR intensities computed with the BTRHE rovibrational wave functions and the DMS can be very accurate provided one has minimized the fitting error of the DMS and tested the completeness of the DMS. Some examples of our work on NH₃, CO₂, and SO₂ are given to highlight the usefulness of the BTRHE strategy and to provide ideas on how to further improve its predictive power in the future. In particular, it is shown how successive refinement steps, once new high-resolution data are available, can lead to PESs that yield highly accurate transition energies to larger spectral regions. The importance of including nonadiabatic corrections to reduce the J-dependence of errors for H-containing molecules is shown with work on NH₃. Another very important aspect of the BTRHE approach is the consistency across isotopologues, which allows for highly accurate line lists for any isotopologue once one is obtained for the main isotopologue (which has more high-resolution data available for refinement).

Derivation of ρ-dependent coordinate transformations for nonrigid molecules in the Hougen-Bunker-Johns formalism

In this paper, we report a series of transformations for the construction of a Hamiltonian model for nonrigid polyatomic molecules in the framework of the Hougen-Bunker-Johns formalism (HBJ). This model is expressed in normal mode coordinates for small vibrations and in a specific coordinate ρ to describe the large amplitude motion. For the first time, a general procedure linking the "true" curvilinear coordinates to ρ is proposed, allowing the expression of the potential energy part in the same coordinate representation as the kinetic energy operator, whatever the number of atoms. A Lie group-based method is also proposed for the derivation of the reference configuration in the internal axis system. This work opens new perspectives for future high-resolution spectroscopy studies of nonrigid, medium-sized molecules using HBJ-type Hamiltonians. Illustrative examples and computation of vibrational energy levels on semirigid and nonrigid molecules are given to validate this method.

High-accuracy water potential energy surface for the calculation of infrared spectra

Transition intensities for small molecules such as water and CO₂ can now be computed with such high accuracy that they are being used to systematically replace measurements in standard databases. These calculations use high-accuracy ab initio dipole moment surfaces and wave functions from spectroscopically determined potential energy surfaces (PESs). Here, an extra high-accuracy PES of the water molecule (H₂¹⁶O) is produced starting from an ab initio PES which is then refined to empirical rovibrational energy levels. Variational nuclear motion calculations using this PES reproduce the fitted energy levels with a standard deviation of 0.011 cm^-1, approximately three times their stated uncertainty. The use of wave functions computed with this refined PES is found to improve the predicted transition intensities for selected (problematic) transitions. A new room temperature line list for H₂¹⁶O is presented. It is suggested that the associated set of line intensities is the most accurate available to date for this species.This article is part of the theme issue 'Modern theoretical chemistry'.

Rovibrational molecular hamiltonian in mixed bond-angle and umbrella-like coordinates

A new exact quantum mechanical rovibrational Hamiltonian operator for molecules exhibiting large amplitude inversion and torsion motions is derived. The derivation is based on a division of a molecule into two parts: a frame and a top. The nuclei of the frame only are used to construct a molecular system of axes. The inversion motion of the frame is described in the umbrella-like coordinates, whereas the torsion motion of the top is described by the nonstandard torsion angle defined in terms of the nuclear vectors and one of the molecular axes. The internal coordinates chosen take into account the properties of the inversion and torsion motions. Vibrational s and rotational Omega vectors obtained for the introduced internal coordinates determine the rovibrational tensor G defined by simple scalar products of these vectors. The Jacobian of the transformation from the Cartesian to the internal coordinates considered and the G tensor specify the rovibrational Hamiltonian. As a result, the Hamiltonian for penta-atomic molecules like NH2OH with one inverter is presented and a complete set of the formulas necessary to write down the Hamiltonian of more complex molecules, like NH2NH2 with two inverters, is reported. The approach considered is essentially general and sufficiently simple, as demonstrated by derivation of a polyatomic molecule Hamiltonian in polyspherical coordinates, obtained by other methods with much greater efforts.