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We present an efficient approach for generating highly accurate molecular potential energy surfaces (PESs) using self-correcting, kernel ridge regression (KRR) based machine learning (ML). We introduce structure-based sampling to automatically assign nuclear configurations from a pre-defined grid to the training and prediction sets, respectively. Accurate high-level \textit{ab initio} energies are required only for the points in the training set, while the energies for the remaining points are provided by the ML model with negligible computational cost. The proposed sampling procedure is shown to be superior to random sampling and also eliminates the need for training several ML models. Self-correcting machine learning has been implemented such that each additional layer corrects errors from the previous layer. The performance of our approach is demonstrated in a case study on a published high-level \textit{ab initio} PES of methyl chloride with 44,819 points. The ML model is trained on sets of different size and then used to predict the energies for tens of thousands of nuclear configurations within seconds. The resulting datasets are utilized in variational calculations of the vibrational energy levels of CH$_3$Cl. By using both structure-based sampling and self-correction, the size of the training set can be kept small (e.g. 10\% of the points) without any significant loss of accuracy. In \textit{ab initio} rovibrational spectroscopy, it is thus possible to reduce the number of computationally costly electronic structure calculations through structure-based sampling and self-correcting KKR-based machine learning by up to 90\%.

Numerous accidental near-degeneracies exist between the $2\nu_2$ and $\nu_4$ rotation-vibration energy levels of ammonia. Transitions between these two states possess significantly enhanced sensitivity to a possible variation of the proton-to-electron mass ratio $\mu$. Using a robust variational approach to determine the mass sensitivity of the energy levels along with accurate experimental values for the energies, sensitivity coefficients have been calculated for over 350 microwave, submillimetre and far infrared transitions up to $J\!=\!15$ for $^{14}$NH$_3$. The sensitivities are the largest found in ammonia to date. One particular transition, although extremely weak, has a sensitivity of $T=-16,738$ and illustrates the huge enhancement that can occur between close-lying energy levels. More promising however are a set of previously measured transitions with $T=-32$ to $28$. Given the astrophysical importance of ammonia, the sensitivities presented here confirm that $^{14}$NH$_3$ can be used exclusively to constrain a spatial or temporal variation of $\mu$. Thus, certain systematic errors which affect the ammonia method can be eliminated. For all transitions analyzed we provide frequency data and Einstein A coefficients to guide future laboratory and astronomical observations.

A new dipole moment surface (DMS) for methyl chloride has been generated at the CCSD(T)/aug-cc-pVQZ(+d for Cl) level of theory. To represent the DMS, a symmetry-adapted analytic representation in terms of nine vibrational coordinates has been developed and implemented. Variational calculations of the infrared spectrum of CH$_3$Cl show good agreement with a range of experimental results. This includes vibrational transition moments, absolute line intensities of the $\nu_1$, $\nu_4$, $\nu_5$ and $3\nu_6$ bands, and a rotation-vibration line list for both CH$_{3}{}^{35}$Cl and CH$_{3}{}^{37}$Cl including states up to $J=85$ and vibrational band origins up to $4400{\,}$cm$^{-1}$. Across the spectrum band shape and structure are well reproduced and computed absolute line intensities are comparable with highly accurate experimental measurements for certain fundamental bands. We thus recommend the DMS for future use.

A new nine-dimensional potential energy surface (PES) and dipole moment surface (DMS) for silane have been generated using high-level \textit{ab initio} theory. The PES, CBS-F12$^{\,\mathrm{HL}}$, reproduces all four fundamental term values for $^{28}$SiH$_4$ with sub-wavenumber accuracy, resulting in an overall root-mean-square (rms) error of $0.63{\,}$cm$^{-1}$. The PES is based on explicitly correlated coupled cluster calculations with extrapolation to the complete basis set limit, and incorporates a range of higher-level additive energy corrections to account for core-valence electron correlation, higher-order coupled cluster terms, and scalar relativistic effects. Systematic errors in computed intra-band rotational energy levels are reduced by empirically refining the equilibrium geometry. The resultant Si-H bond length is in excellent agreement with previous experimental and theoretical values. Vibrational transition moments, absolute line intensities of the $\nu_3$ band, and the infrared spectrum for $^{28}$SiH$_4$ including states up to $J=20$ and vibrational band origins up to $5000{\,}$cm$^{-1}$ are calculated and compared with available experimental results. The DMS tends to marginally overestimate the strength of line intensities. Despite this, band shape and structure across the spectrum are well reproduced and show good agreement with experiment. We thus recommend the PES and DMS for future use.

The mass sensitivity of the vibration-rotation-inversion transitions of H$_3{}^{16}$O$^+$, H$_3{}^{18}$O$^+$, and D$_3{}^{16}$O$^+$ is investigated variationally using the nuclear motion program TROVE~\citep{TROVE:2007}. The calculations utilize new high-level \textit{ab initio} potential energy and dipole moment surfaces. Along with the mass dependence, frequency data and Einstein A coefficients are computed for all transitions probed. Particular attention is paid to the $\Delta|k|=3$ and $\Delta|k-l|=3$ transitions comprising the accidentally coinciding $|J,K\!=\!0,v_2\!=\!0^+\rangle$ and $|J,K\!=\!3,v_2\!=\!0^-\rangle$ rotation-inversion energy levels. The newly computed probes exhibit sensitivities comparable to their ammonia and methanol counterparts, thus demonstrating their potential for testing the cosmological stability of the proton-to-electron mass ratio. The theoretical TROVE results are in close agreement with sensitivities obtained using the nonrigid and rigid inverter approximate models, confirming that the \textit{ab initio} theory used in the present study is adequate.

Two new nine-dimensional potential energy surfaces (PESs) have been generated using high-level \textit{ab initio} theory for the two main isotopologues of methyl chloride, CH$_{3}{}^{35}$Cl and CH$_{3}{}^{37}$Cl. The respective PESs, CBS-35$^{\,\mathrm{HL}}$ and CBS-37$^{\,\mathrm{HL}}$, are based on explicitly correlated coupled cluster calculations with extrapolation to the complete basis set (CBS) limit, and incorporate a range of higher-level (HL) additive energy corrections to account for core-valence electron correlation, higher-order coupled cluster terms, scalar relativistic effects, and diagonal Born-Oppenheimer corrections. Variational calculations of the vibrational energy levels were performed using the computer program TROVE, whose functionality has been extended to handle molecules of the form XY$_3$Z. Fully converged energies were obtained by means of a complete vibrational basis set extrapolation. The CBS-35$^{\,\mathrm{HL}}$ and CBS-37$^{\,\mathrm{HL}}$ PESs reproduce the fundamental term values with root-mean-square errors of $0.75$ and $1.00{\,}$cm$^{-1}$ respectively. An analysis of the combined effect of the HL corrections and CBS extrapolation on the vibrational wavenumbers indicates that both are needed to compute accurate theoretical results for methyl chloride. We believe that it would be extremely challenging to go beyond the accuracy currently achieved for CH$_3$Cl without empirical refinement of the respective PESs.

Accurate \textit{ab initio} calculations on the rotation-vibration spectrum of methyl fluoride (\ce{CH3F}) are reported. A new nine-dimensional potential energy surface (PES) and dipole moment surface (DMS) have been generated using high-level electronic structure methods. Notably, the PES was constructed from explicitly correlated coupled cluster calculations with extrapolation to the complete basis set limit and considered additional energy corrections to account for core-valence electron correlation, higher-order coupled cluster terms beyond perturbative triples, scalar relativistic effects, and the diagonal Born-Oppenheimer correction. The PES and DMS are evaluated through robust variational nuclear motion computations of pure rotational and vibrational energy levels, the equilibrium geometry of \ce{CH3F}, vibrational transition moments, absolute line intensities of the $\nu_6$ band, and the rotation-vibration spectrum up to $J=40$. The computed results show excellent agreement with a range of experimental sources, in particular the six fundamentals are reproduced with a root-mean-square error of 0.69~cm$^{-1}$. This work represents the most accurate theoretical treatment of the rovibrational spectrum of \ce{CH3F} to date.

A new nine-dimensional potential energy surface (PES) for methane has been generated using state-of-the-art \textit{ab initio} theory. The PES is based on explicitly correlated coupled cluster calculations with extrapolation to the complete basis set limit and incorporates a range of higher-level additive energy corrections. These include: core-valence electron correlation, higher-order coupled cluster terms beyond perturbative triples, scalar relativistic effects and the diagonal Born-Oppenheimer correction. Sub-wavenumber accuracy is achieved for the majority of experimentally known vibrational energy levels with the four fundamentals of $^{12}$CH$_4$ reproduced with a root-mean-square error of $0.70{\,}$cm$^{-1}$. The computed \textit{ab initio} equilibrium C{--}H bond length is in excellent agreement with previous values despite pure rotational energies displaying minor systematic errors as $J$ (rotational excitation) increases. It is shown that these errors can be significantly reduced by adjusting the equilibrium geometry. The PES represents the most accurate \textit{ab initio} surface to date and will serve as a good starting point for empirical refinement.

A comprehensive study of the mass sensitivity of the vibration-rotation-inversion transitions of $^{14}$NH$_3$, $^{15}$NH$_3$, $^{14}$ND$_3$, and $^{15}$ND$_3$ is carried out variationally using the TROVE approach. Variational calculations are robust and accurate, offering a new way to compute sensitivity coefficients. Particular attention is paid to the $\Delta k=\pm 3$ transitions between the accidentally coinciding rotation-inversion energy levels of the $\nu_2=0^+,0^-,1^+$ and $1^-$ states, and the inversion transitions in the $\nu_4=1$ state affected by the "giant" $l$-type doubling effect. These transitions exhibit highly anomalous sensitivities, thus appearing as promising probes of a possible cosmological variation of the proton-to-electron mass ratio $\mu$. Moreover, a simultaneous comparison of the calculated sensitivities reveals a sizeable isotopic dependence which could aid an exclusive ammonia detection., Comment: 18 pages, 2 figures, 10 tables

A new nine-dimensional (9D), \textit{ab initio} electric dipole moment surface (DMS) of methane in its ground electronic state is presented. The DMS is computed using an explicitly correlated coupled cluster CCSD(T)-F12 method in conjunction with an F12-optimized correlation consistent basis set of the TZ-family. A symmetrized molecular bond representation is used to parameterise the 9D DMS in terms of sixth-order polynomials. Vibrational transition moments as well as band intensities for a large number of IR-active vibrational bands of $^{12}$CH$_4$ are computed by vibrationally averaging the \textit{ab initio} dipole moment components. The vibrational wavefunctions required for these averages are computed variationally using the program TROVE and a new `spectroscopic' $^{12}$CH$_4$ potential energy surface. The new DMS will be used to produce a hot line list for $^{12}$CH$_4$., Comment: J. Molec. Spectrosc. (submitted)