A highly accurate potential energy surface for carbonyl sulphide (OCS): how important are the ab initio calculations?

Ab initio quantum chemical methods can produce accurate molecular potential energy surfaces (PESs) capable of predicting the fundamental vibrational wavenumbers to within 1 cm-1. However, for high-resolution applications this is simply not good enough and empirical refinement is necessary, i.e. adjusting the PES to better match laboratory spectroscopic data. Here, the impact of the underlying ab initio calculations is rigorously investigated within the context of empirical refinement. For carbonyl sulphide (OCS), state-of-the-art electronic structure calculations are employed to construct higher- and lower-level ab initio PESs, which are then empirically refined in near-identical procedures. The initial ab initio calculations are shown to considerably affect the accuracy of the final refined PES, with an order-of-magnitude improvement in computed rotation-vibration energy levels achieved for OCS. In demonstrating this, the most accurate PES of the electronic ground state of OCS is produced, reproducing the fundamentals with a root-mean-square error (RMSE) of 0.004 cm-1, and 884 rovibrational energy levels below 14 000 cm-1 with an RMSE of 0.060 cm-1.

VIB5 database with accurate ab initio quantum chemical molecular potential energy surfaces.

High-level ab initio quantum chemical (QC) molecular potential energy surfaces (PESs) are crucial for accurately simulating molecular rotation-vibration spectra. Machine learning (ML) can help alleviate the cost of constructing such PESs, but requires access to the original ab initio PES data, namely potential energies computed on high-density grids of nuclear geometries. In this work, we present a new structured PES database called VIB5, which contains high-quality ab initio data on 5 small polyatomic molecules of astrophysical significance (CH3Cl, CH4, SiH4, CH3F, and NaOH). The VIB5 database is based on previously used PESs, which, however, are either publicly unavailable or lacking key information to make them suitable for ML applications. The VIB5 database provides tens of thousands of grid points for each molecule with theoretical best estimates of potential energies along with their constituent energy correction terms and a data-extraction script. In addition, new complementary QC calculations of energies and energy gradients have been performed to provide a consistent database, which, e.g., can be used for gradient-based ML methods.

Theoretical rovibronic spectroscopy of the calcium monohydroxide radical (CaOH).

The rovibronic (rotation-vibration-electronic) spectrum of the calcium monohydroxide radical (CaOH) is of interest to studies of exoplanet atmospheres and ultracold molecules. Here, we theoretically investigate the Ã2Π-X̃2Σ+ band system of CaOH using high-level ab initio theory and variational nuclear motion calculations. New potential energy surfaces (PESs) are constructed for the X̃2Σ+ and Ã2Π electronic states along with Ã-X̃ transition dipole moment surfaces (DMSs). For the ground X̃2Σ+ state, a published high-level ab initio PES is empirically refined to all available experimental rovibrational energy levels up to J = 15.5, reproducing the observed term values with a root-mean-square error of 0.06 cm-1. Large-scale multireference configuration interaction calculations using quintuple-zeta quality basis sets are employed to generate the Ã2Π state PESs and Ã-X̃ DMSs. Variational calculations consider both Renner-Teller and spin-orbit coupling effects, which are essential for a correct description of the spectrum of CaOH. Computed rovibronic energy levels of the Ã2Π state, line list calculations up to J = 125.5, and an analysis of Renner-Teller splittings in the ν2 bending mode of CaOH are discussed.

Detecting handedness of spatially oriented molecules by Coulomb explosion imaging.

We present a new technique for detecting chirality in the gas phase: Chiral molecules are spatially aligned in three dimensions by a moderately strong elliptically polarized laser field. The momentum distributions of the charged fragments, produced by laser-induced Coulomb explosion, show distinct three-dimensional orientation of the enantiomers when the laser polarization ellipse is rotated by a non-right angle with respect to the norm vector of the detector plane. The resulting velocity-map-image asymmetry is directly connected to the enantiomeric excess and to the absolute handedness of molecules. We demonstrated our scheme computationally for camphor (C10H16O), with its methyl groups as marker fragments, using quantum-mechanical simulations geared toward experimentally feasible conditions. Computed sensitivity to enantiomeric excess is comparable to other modern chiroptical approaches. The present method can be readily optimized for any chiral molecule with an anisotropic polarizability tensor by adjusting the polarization state and intensity profile of the laser field.

Hierarchical machine learning of potential energy surfaces.

We present hierarchical machine learning (hML) of highly accurate potential energy surfaces (PESs). Our scheme is based on adding predictions of multiple Δ-machine learning models trained on energies and energy corrections calculated with a hierarchy of quantum chemical methods. Our (semi-)automatic procedure determines the optimal training set size and composition of each constituent machine learning model, simultaneously minimizing the computational effort necessary to achieve the required accuracy of the hML PES. Machine learning models are built using kernel ridge regression, and training points are selected with structure-based sampling. As an illustrative example, hML is applied to a high-level ab initio CH3Cl PES and is shown to significantly reduce the computational cost of generating the PES by a factor of 100 while retaining similar levels of accuracy (errors of ∼1 cm-1).

Theoretical rotation-vibration spectroscopy of cis- and trans-diphosphene (P2H2) and the deuterated species P2HD.

Growing astronomical interest in phosphorous (P) chemistry is stimulating the search for new interstellar P-bearing molecules, a task requiring detailed knowledge of the microwave and infrared molecular spectrum. In this work, we present comprehensive rotation-vibration line lists of the cis- and trans-isomers of diphosphene (P2H2). The line lists have been generated using robust, first-principles methodologies based on newly computed, high-level ab initio potential energy and dipole moment surfaces. Transitions are considered between states with energies up to 8000 cm-1 and total angular momentum J ≤ 25. These are the first-ever line lists to be reported for P2H2, and they should significantly facilitate future spectroscopic characterization of this system. The deuterated species trans-P2HD and the effect of its dynamic dipole moment on the rovibrational spectrum are also discussed.

The rotation-vibration spectrum of methyl fluoride from first principles.

Accurate ab initio calculations on the rotation-vibration spectrum of methyl fluoride (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 CH3F, vibrational transition moments, absolute line intensities of the ν6 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 CH3F to date.

Field-Induced Diastereomers for Chiral Separation.

A novel approach for the state-specific enantiomeric enrichment and the spatial separation of enantiomers is presented. Our scheme utilizes techniques from strong-field laser physics-specifically an optical centrifuge in conjunction with a static electric field-to create a chiral field with defined handedness. Molecular enantiomers experience unique rotational excitation dynamics, and this can be exploited to spatially separate the enantiomers using electrostatic deflection. Notably, the rotational-state-specific enantiomeric enhancement and its handedness are fully controllable. To explain these effects, the conceptual framework of field-induced diastereomers of a chiral molecule is introduced and computationally demonstrated through robust quantum-mechanical simulations on the prototypical chiral molecule propylene oxide (C_{3}H_{6}O), for which ensembles with an enantiomeric excess of up to 30% were obtained.

Climbing the Rotational Ladder to Chirality.

Molecular chirality is conventionally understood as space-inversion-symmetry breaking in the equilibrium structure of molecules. Less well known is that achiral molecules can be made chiral through extreme rotational excitation. Here, we theoretically demonstrate a clear strategy for generating rotationally induced chirality: An optical centrifuge rotationally excites the phosphine molecule (PH_{3}) into chiral cluster states that correspond to clockwise (R enantiomer) or anticlockwise (L enantiomer) rotation about axes almost coinciding with single P─H bonds. The application of a strong dc electric field during the centrifuge pulse favors the production of one rotating enantiomeric form over the other, creating dynamically chiral molecules with permanently oriented rotational angular momentum. This essential step toward characterizing rotationally induced chirality promises a fresh perspective on chirality as a fundamental aspect of nature.

RichMol: A general variational approach for rovibrational molecular dynamics in external electric fields.

In this paper, a general variational approach for computing the rovibrational dynamics of polyatomic molecules in the presence of external electric fields is presented. Highly accurate, full-dimensional variational calculations provide a basis of field-free rovibrational states for evaluating the rovibrational matrix elements of high-rank Cartesian tensor operators and for solving the time-dependent Schrödinger equation. The effect of the external electric field is treated as a multipole moment expansion truncated at the second hyperpolarizability interaction term. Our fully numerical and computationally efficient method has been implemented in a new program, RichMol, which can simulate the effects of multiple external fields of arbitrary strength, polarization, pulse shape, and duration. Illustrative calculations of two-color orientation and rotational excitation with an optical centrifuge of NH3 are discussed.

Structure-based sampling and self-correcting machine learning for accurate calculations of potential energy surfaces and vibrational levels.

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 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 ab initio PES of methyl chloride with 44 819 points. The ML model is trained on sets of different sizes 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 CH3Cl. 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 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 KRR-based machine learning by up to 90%.

Simulating electric field interactions with polar molecules using spectroscopic databases.

Ro-vibrational Stark-associated phenomena of small polyatomic molecules are modelled using extensive spectroscopic data generated as part of the ExoMol project. The external field Hamiltonian is built from the computed ro-vibrational line list of the molecule in question. The Hamiltonian we propose is general and suitable for any polar molecule in the presence of an electric field. By exploiting precomputed data, the often prohibitively expensive computations associated with high accuracy simulations of molecule-field interactions are avoided. Applications to strong terahertz field-induced ro-vibrational dynamics of PH3 and NH3, and spontaneous emission data for optoelectrical Sisyphus cooling of H2CO and CH3Cl are discussed.

A highly accurate ab initio potential energy surface for methane.

A new nine-dimensional potential energy surface (PES) for methane has been generated using state-of-the-art 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)CH4 reproduced with a root-mean-square error of 0.70 cm(-1). The computed 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 ab initio surface to date and will serve as a good starting point for empirical refinement.

Accurate ab initio vibrational energies of methyl chloride.

Two new nine-dimensional potential energy surfaces (PESs) have been generated using high-level ab initio theory for the two main isotopologues of methyl chloride, CH3 (35)Cl and CH3 (37)Cl. The respective PESs, CBS-35( HL), and CBS-37( 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 3Z. Fully converged energies were obtained by means of a complete vibrational basis set extrapolation. The CBS-35( HL) and CBS-37( 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 CH3Cl without empirical refinement of the respective PESs.

A global potential energy surface and dipole moment surface for silane.

A new nine-dimensional potential energy surface (PES) and dipole moment surface (DMS) for silane have been generated using high-level ab initio theory. The PES, CBS-F12(HL), reproduces all four fundamental term values for (28)SiH4 with sub-wavenumber accuracy, resulting in an overall root-mean-square 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 ν3 band, and the infrared spectrum for (28)SiH4 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.