The nuclear-spin-forbidden rovibrational transitions of water from first principles.

The water molecule occurs in two nuclear-spin isomers that differ by the value of the total nuclear spin of the hydrogen atoms, i.e., I = 0 for para-H2O and I = 1 for ortho-H2O. Spectroscopic transitions between rovibrational states of ortho and para water are extremely weak due to the tiny hyperfine nuclear-spin-rotation interaction of only ∼30 kHz and, so far, have not been observed. We report the first comprehensive theoretical investigation of the hyperfine effects and ortho-para transitions in H2 16O due to nuclear-spin-rotation and spin-spin interactions. We also present the details of our newly developed general variational approach to the simulation of hyperfine effects in polyatomic molecules. Our results for water suggest that the strongest ortho-para transitions with room-temperature intensities on the order of 10-31 cm/molecule are about an order of magnitude larger than previously predicted values and should be detectable in the mid-infrared ν2 and near-infrared 2ν1 + ν2 and ν1 + ν2 + ν3 bands by current spectroscopy experiments.

Picosecond pulse-shaping for strong three-dimensional field-free alignment of generic asymmetric-top molecules.

Fixing molecules in space is a crucial step for the imaging of molecular structure and dynamics. Here, we demonstrate three-dimensional (3D) field-free alignment of the prototypical asymmetric top molecule indole using elliptically polarized, shaped, off-resonant laser pulses. A truncated laser pulse is produced using a combination of extreme linear chirping and controlled phase and amplitude shaping using a spatial-light-modulator (SLM) based pulse shaper of a broadband laser pulse. The angular confinement is detected through velocity-map imaging of H+ and C2+ fragments resulting from strong-field ionization and Coulomb explosion of the aligned molecules by intense femtosecond laser pulses. The achieved three-dimensional alignment is characterized by comparing the result of ion-velocity-map measurements for different alignment directions and for different times during and after the alignment laser pulse to accurate computational results. The achieved strong three-dimensional field-free alignment of [Formula: see text] demonstrates the feasibility of both, strong three-dimensional alignment of generic complex molecules and its quantitative characterization.

Active learning of potential-energy surfaces of weakly bound complexes with regression-tree ensembles.

Several pool-based active learning (AL) algorithms were employed to model potential-energy surfaces (PESs) with a minimum number of electronic structure calculations. Theoretical and empirical results suggest that superior strategies can be obtained by sampling molecular structures corresponding to large uncertainties in their predictions while at the same time not deviating much from the true distribution of the data. To model PESs in an AL framework, we propose to use a regression version of stochastic query by forest, a hybrid method that samples points corresponding to large uncertainties while avoiding collecting too many points from sparse regions of space. The algorithm is implemented with decision trees that come with relatively small computational costs. We empirically show that this algorithm requires around half the data to converge to the same accuracy in comparison to the uncertainty-based query-by-committee algorithm. Moreover, the algorithm is fully automatic and does not require any prior knowledge of the PES. Simulations on a 6D PES of pyrrole(H2O) show that <15 000 configurations are enough to build a PES with a generalization error of 16 cm-1, whereas the final model with around 50 000 configurations has a generalization error of 11 cm-1.

Electric quadrupole transitions in carbon dioxide.

Recent advances in high sensitivity spectroscopy have made it possible, in combination with accurate theoretical predictions, to observe, for the first time, very weak electric quadrupole transitions in a polar polyatomic molecule of water. Here, we present accurate theoretical predictions of the complete quadrupole rovibrational spectrum of a non-polar molecule CO2, important in atmospheric and astrophysical applications. Our predictions are validated by recent cavity enhanced absorption spectroscopy measurements and are used to assign few weak features in the recent ExoMars Atmospheric Chemistry Suite mid-infrared spectroscopic observations of the Martian atmosphere. Predicted quadrupole transitions appear in some of the mid-infrared CO2 and water vapor transparency regions, making them important for detection and characterization of the minor absorbers in water- and CO2-rich environments, such as those present in the atmospheres of Earth, Venus, and Mars.

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.

Detection of electric-quadrupole transitions in water vapour near 5.4 and 2.5 µm.

Nowadays, the spectroscopic databases used for the modeling of Earth and planetary atmospheres provide only electric-dipole transitions for polyatomic molecules (H2O, CO2, N2O, CH4, O3…). Very recently, electric-quadrupole transitions have been detected in the high sensitivity cavity ring down spectrum (CRDS) of water vapour near 1.3 µm [A. Campargue et al., Phys. Rev. Res., 2020, 2, 023091, DOI: 10.1103/PhysRevResearch.2.023091]. This discovery paved the way to systematic searches of quadrupole transitions in water vapor and other polyatomic molecules. In the present work, on the basis of high accuracy ab initio predictions, H216O quadrupole lines are detected for the first time in the 5.4 µm and 2.5 µm regions where they are predicted to have their largest intensities (up to 10-26 cm per molecule). A total of twelve quadrupole lines are identified in two high sensitivity Fourier transform spectra recorded with a 1064 m path length. Ten lines in the 4030-4150 cm-1 region are assigned to the ν3 band while the lines near 1820 and 1926 cm-1 belong to the ν2 band. The derived line intensities which are largely above the dipole intensity cut-off of the standard spectroscopic databases, agree nicely with the theoretical predictions. We thus conclude that the calculated line list of quadrupole transitions, validated by the present measurements, should be incorporated in the spectroscopic databases.

The Effect of Nuclear-Quadrupole Coupling in the Laser-Induced Alignment of Molecules.

We present a theoretical study of the time-dependent laser alignment of molecules taking into account the hyperfine coupling due to nuclear-quadrupole interactions. The coupling of nuclear spins to the overall angular momentum of molecules significantly influences their rotational dynamics. Here, we systematically analyze the impact of the nuclear-quadrupole coupling on the rotational dynamics of the linear and the asymmetric-top diiodobenzene molecule induced by external laser fields. We explore different regimes of pulse shapes and laser-pulse intensities and detail under which conditions the quadrupole coupling cannot be neglected in the description of the laser alignment of molecules.

Variationally Computed IR Line List for the Methyl Radical CH3.

We present the first variational calculation of a hot-temperature ab initio line list for the CH3 radical. It is based on a high-level ab initio potential energy surface and dipole moment surface of CH3 in the ground electronic state. The ro-vibrational energy levels and Einstein A coefficients were calculated using the general-molecule variational approach implemented in the computer program TROVE. Vibrational energies and vibrational intensities are found to be in very good agreement with the available experimental data. The line list comprises 9 127 123 ro-vibrational states ( J ≤ 40) and 2 058 655 166 transitions, covering the wavenumber range up to 10 000 cm-1 and should be suitable for temperatures up to T = 1500 K.

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.

Laser-induced dynamics of molecules with strong nuclear quadrupole coupling.

We present a general variational approach for computing the laser-induced rovibrational dynamics of molecules, taking into account the hyperfine effects of the nuclear quadrupole coupling. The method combines the general variational approach TROVE (Theoretical Ro-Vibrational Energies), which provides accurate rovibrational hyperfine energies and wavefunctions for arbitrary molecules, with the variational method RichMol, designed for generalized simulations of the rovibrational dynamics in the presence of external electric fields. We investigate the effect of the nuclear quadrupole coupling on the short-pulse laser alignment of a prototypical molecule CFClBrI, which contains nuclei with large quadrupole constants. The influence of the nuclear quadrupole interactions on the postpulse molecular dynamics is negligible at early times, for the first several revivals; however, at longer time scales, the effect is entirely detrimental and strongly depends on the laser intensity. This effect can be explained by dephasing in the laser-excited rotational wavepacket due to irregular spacings between the hyperfine-split nuclear spin states across different rotational hyperfine bands.

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.

Treating linear molecule HCCH in calculations of rotation-vibration spectra.

Special treatment is required for ro-vibrational calculations involving polyatomic molecules of linear geometry in order to avoid singularities in the kinetic energy operator. Here we present a variational approach which allows calculations involving such configurations, with a set of 3N-5 linearized coordinates used to represent the vibrations. This approach has been implemented as part of the variational nuclear motion program TROVE (Theoretical ROVibrational Energies). A symmetry adapted basis set based on the Dnh symmetry point group is used. As an illustration of the 3N-5 model presented, TROVE has been used to compute an ab initio room temperature line list for C212H2 using symmetry-adapted ab initio potential energy (CCSD(T)-F12c/cc-pVQZ-F12) and dipole moment surfaces for the ground electronic state. Line positions and intensities (J ≤ 58, l < 8, covering the wavenumbers up to 10 000 cm-1) are compared against HITRAN-2016 and ASD-1000. Alternative methods for treating linear molecules and future work are discussed.

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.

Communication: General variational approach to nuclear-quadrupole coupling in rovibrational spectra of polyatomic molecules.

A general algorithm for computing the quadrupole-hyperfine effects in the rovibrational spectra of polyatomic molecules is presented for the case of ammonia (NH3). The method extends the general variational approach TROVE [J. Mol. Spectrosc. 245, 126-140 (2007)] by adding the extra term in the Hamiltonian that describes the nuclear quadrupole coupling, with no inherent limitation on the number of quadrupolar nuclei in a molecule. We applied the new approach to compute the nitrogen-nuclear-quadrupole hyperfine structure in the rovibrational spectrum of NH314. These results agree very well with recent experimental spectroscopic data for the pure rotational transitions in the ground vibrational and ν2 states and the rovibrational transitions in the ν1, ν3, 2ν4, and ν1 + ν3 bands. The computed hyperfine-resolved rovibrational spectrum of ammonia will be beneficial for the assignment of experimental rovibrational spectra, further detection of ammonia in interstellar space, and studies of the proton-to-electron mass variation.

Symmetry-Adapted Ro-vibrational Basis Functions for Variational Nuclear Motion Calculations: TROVE Approach.

We present a general, numerically motivated approach to the construction of symmetry-adapted basis functions for solving ro-vibrational Schrödinger equations. The approach is based on the property of the Hamiltonian operator to commute with the complete set of symmetry operators and, hence, to reflect the symmetry of the system. The symmetry-adapted ro-vibrational basis set is constructed numerically by solving a set of reduced vibrational eigenvalue problems. In order to assign the irreducible representations associated with these eigenfunctions, their symmetry properties are probed on a grid of molecular geometries with the corresponding symmetry operations. The transformation matrices are reconstructed by solving overdetermined systems of linear equations related to the transformation properties of the corresponding wave functions on the grid. Our method is implemented in the variational approach TROVE and has been successfully applied to many problems covering the most important molecular symmetry groups. Several examples are used to illustrate the procedure, which can be easily applied to different types of coordinates, basis sets, and molecular systems.

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 semi-classical approach to the calculation of highly excited rotational energies for asymmetric-top molecules.

We report a new semi-classical method to compute highly excited rotational energy levels of an asymmetric-top molecule. The method forgoes the idea of a full quantum mechanical treatment of the ro-vibrational motion of the molecule. Instead, it employs a semi-classical Green's function approach to describe the rotational motion, while retaining a quantum mechanical description of the vibrations. Similar approaches have existed for some time, but the method proposed here has two novel features. First, inspired by the path integral method, periodic orbits in the phase space and tunneling paths are naturally obtained by means of molecular symmetry analysis. Second, the rigorous variational method is employed for the first time to describe the molecular vibrations. In addition, we present a new robust approach to generating rotational energy surfaces for vibrationally excited states; this is done in a fully quantum-mechanical, variational manner. The semi-classical approach of the present work is applied to calculating the energies of very highly excited rotational states and it reduces dramatically the computing time as well as the storage and memory requirements when compared to the fullly quantum-mechanical variational approach. Test calculations for excited states of SO2 yield semi-classical energies in very good agreement with the available experimental data and the results of fully quantum-mechanical calculations.

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.

Detecting Chirality in Molecules by Linearly Polarized Laser Fields.

A new scheme for enantiomer differentiation of chiral molecules using a pair of linearly polarized intense ultrashort laser pulses with skewed mutual polarization is presented. The technique relies on the fact that the off-diagonal anisotropic contributions to the electric polarizability tensor for two enantiomers have different signs. Exploiting this property, we are able to excite a coherent unidirectional rotation of two enantiomers with a π phase difference in the molecular electric dipole moment. The approach is robust and suitable for relatively high temperatures of molecular samples, making it applicable for selective chiral analysis of mixtures, and to chiral molecules with low barriers between enantiomers. As an illustration, we present nanosecond laser-driven dynamics of a tetratomic nonrigid chiral molecule with short-lived chirality. The ultrafast time scale of the proposed technique is well suited to study parity violation in molecular systems in short-lived chiral states.