Full-Dimensional Quantum Calculations of Vibrational Levels of NH<sub>4</sub><sup>+</sup> and Isotopomers on An Accurate Ab Initio Potential Energy Surface

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We report a new full-dimensional variational algorithm to calculate rovibrational spectra of polyatomic molecules using an exact quantum mechanical Hamiltonian. The rovibrational Hamiltonian of system is derived in a set of orthogonal polyspherical coordinates in the body-fixed frame. It is expressed in an explicitly Hermitian form. The Hamiltonian has a universal formulation regardless of the choice of orthogonal polyspherical coordinates and the number of atoms in molecule, which is suitable for developing a general program to study the spectra of many polyatomic systems. An efficient coupled-state approach is also proposed to solve the eigenvalue problem of the Hamiltonian using a multi-layer Lanczos iterative diagonalization approach via a set of direct product basis set in three coordinate groups: radial coordinates, angular variables, and overall rotational angles. A simple set of symmetric top rotational functions is used for the overall rotation whereas a potential-optimized discrete variable representation method is employed in radial coordinates. A set of contracted vibrationally diabatic basis functions is adopted in internal angular variables. Those diabatic functions are first computed using a neural network iterative diagonalization method based on a reduced-dimension Hamiltonian but only once. The final rovibrational energies are computed using a modified Lanczos method for a given total angular momentum J, which is usually fast. Two numerical applications to CH4 and H2CO are given, together with a comparison with previous results.

An exact variational method to calculate rovibrational spectra of polyatomic molecules with large amplitude motion

2016

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Sub-Doppler slit jet infrared spectroscopy of astrochemically relevant cations: The NH stretching mode in ND3H+

Chang

Scrape

Nesbitt

2018

High-resolution rotationally resolved spectra of the N–H stretch vibrational mode (ν1) of jet-cooled ND3H+ ions are collected and analyzed in a sub-Doppler slit-jet infrared spectrometer. The isotopomeric ammonium ions are generated by proton transfer from H3+ to ND3 in a discharge of an ND3/H2 gas mixture, whereby the slit jet expansion cools the nascent ND3H+ ions into lower rotational states. Rotational assignments are confirmed by four-line combination differences that agree to within the spectrometer precision (9 MHz). Based on precision two-line ground-state combination differences and a symmetric top Hamiltonian, the B, DJ, and DJK rotational constants for the ground vibrational state of ND3H+ are determined with high precision for the first time. Approximate rotational constants for the ν1 excited state are also determined, with a band origin at 3316.8425(19) cm−1 and in remarkable (∼0.1 cm−1) agreement with high level anharmonic theoretical predictions by Guo and co-workers [J. Phys. Chem. A, 120, 2185 (2016)]. Our results allow us to predict several low-J pure rotational transitions of ND3H+, which we hope will support future studies of this important ion in laboratory and astronomical rotational spectroscopy.

Suppressed-Doppler slit jet infrared spectroscopy of astrochemically relevant cations: ν1 and ν4 NH stretching modes in NH3D+

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Chang²,

Nesbitt

2019

A suppressed-Doppler (Δν = 180 MHz) infrared spectrum of monodeuterated ammonium ions (NH3D+) has been obtained for the ν1 (symmetric) and ν4 (degenerate) N–H stretch bands via direct absorption high resolution IR laser spectroscopy in a planar slit jet discharge expansion. The ion is efficiently generated by H3+ protonation of NH2D in a discharge mixture of H2/NH2D, with the resulting expansion rapidly cooling the molecular ions into low rotational states. The first high-resolution infrared spectrum of ν1 is reported, as well as many previously unobserved transitions in the ν4 rovibrational manifold. Simultaneous observation of both ν1 and ν4 permits elucidation of both the vibrational ground and excited state properties of the ion, including rigorous benchmarking of band origins against high-level anharmonic ab initio theory as well as determination of the ν1:ν4 intensity ratio for comparison with bond-dipole model predictions. Ground-state combination differences from this work and earlier studies permit the rotational constants of NH3D+ to be determined to unprecedented accuracy, the results of which support previous laboratory and astronomical assignment of the 10–00 pure rotational transition and should aid future searches for other rotational transitions as well.