The site-specific first microsolvation step of furan and some of its derivatives with methanol is explored to benchmark the ability of quantum-chemical methods to describe the structure, energetics, and vibrational spectrum at low temperature. Infrared and microwave spectra in supersonic jet expansions are used to quantify the docking preference and some relevant quantum states of the model complexes. Microwave spectroscopy strictly rules out in-plane docking of methanol as opposed to the top coordination of the aromatic ring. Contrasting comparison strategies, which emphasize either the experimental or the theoretical input, are explored. Within the harmonic approximation, only a few composite computational approaches are able to achieve a satisfactory performance. Deuteration experiments suggest that the harmonic treatment itself is largely justified for the zero-point energy, likely and by design due to the systematic cancellation of important anharmonic contributions between the docking variants. Therefore, discrepancies between experiment and theory for the isomer abundance are tentatively assigned to electronic structure deficiencies, but uncertainties remain on the nuclear dynamics side. Attempts to include anharmonic contributions indicate that for systems of this size, a uniform treatment of anharmonicity with systematically improved performance is not yet in sight.

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The first microsolvation step for furans: New experiments and benchmarking strategies.

The vibrational dynamics of the formic acid monomer (FAM) and dimer (FAD) is investigated from machine-learned potential energy surfaces at the MP2 (PESMP2) and transfer-learned (PESTL) to the CCSD(T) levels of theory. The normal mode (MAEs of 17.6 and 25.1 cm−1) and second order vibrational perturbation theory (VPT2, MAEs of 6.7 and 17.1 cm−1) frequencies from PESTL for all modes below 2000 cm−1 for FAM and FAD agree favourably with experiment. For the OH stretch mode the experimental frequencies are overestimated by more than 150 cm−1 for both FAM and FAD from normal mode calculations. Conversely, VPT2 calculations on PESTL for FAM reproduce the experimental OH frequency to within 22 cm−1. For FAD the VPT2 calculations find the high-frequency OH stretch at 3011 cm−1, compared with an experimentally reported, broad (∼100 cm−1) absorption band with center frequency estimated at ∼3050 cm−1. In agreement with earlier reports, MD simulations at higher temperature shift the position of the OH-stretch in FAM to the red, consistent with improved sampling of the anharmonic regions of the PES. However, for FAD the OH-stretch shifts to the blue and for temperatures higher than 1000 K the dimer partly or fully dissociates using PESTL. Including zero-point energy corrections from diffusion Monte Carlo simulations for FAM and FAD and corrections due to basis set superposition and completeness errors yields a dissociation energy of D0 = −14.23 ± 0.08 kcal mol−1 compared with an experimentally determined value of −14.22 ± 0.12 kcal mol−1.

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Transfer learned potential energy surfaces: accurate anharmonic vibrational dynamics and dissociation energies for the formic acid monomer and dimer.

Vibrational spectroscopy represents an active frontier for the identification and characterization of molecular species in the context of astrochemistry and astrobiology. As new missions will provide more data over broader ranges and at higher resolution, especially in the infrared region, which could be complemented with new spectrometers in the future, support from laboratory experiments and theory is crucial. In particular, computational spectroscopy is playing an increasing role in deepening our understanding of the origin and nature of the observed bands in extreme conditions characterizing the ISM or some planetary atmospheres, not easily reproducible on Earth. In this connection, the best compromise between reliability, feasibility and ease of interpretation is still a matter of concern due to the interplay of several factors in determining the final spectral outcome, with larger molecular systems and non-covalent complexes further exacerbating the dichotomy between accuracy and computational cost. In this context, second-order vibrational perturbation theory (VPT2) together with density functional theory (DFT) has become particularly appealing. The well-known problem of the reliability of exchange-correlation functionals, coupled with the treatment of resonances in VPT2, represents a challenge for the determination of standardized or "black-box" protocols, despite successful examples in the literature. With the aim of getting a clear picture of the achievable accuracy and reliability of DFT-based VPT2 calculations, a multi-step study will be carried out here. Beyond the definition of the functional, the impact of the basis set and the influence of the resonance treatment in VPT2 will be analyzed. For a better understanding of the computational aspects and the results, a short summary of vibrational perturbation theory and the overall treatment of resonances for both energies and intensities will be given.The first part of the benchmark will focus on small molecules, for which very accurate experimental and theoretical data are available, to investigate electronic structure calculation methods. Beyond the reliability of energies, widely used for such systems, the issue of intensities will also be investigated in detail. The best performing electronic structure methods will then be used to treat larger molecular systems, with more complex topologies and resonance patterns.

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Accuracy and Reliability in the Simulation of Vibrational Spectra: A Comprehensive Benchmark of Energies and Intensities issuing from Generalized Vibrational Perturbation Theory to Second Order (GVPT2)

The calculation of the anharmonic modes of small- to medium-sized molecules for assigning experimentally measured frequencies to the corresponding type of molecular motions is computationally challenging at sufficiently high levels of quantum chemical theory. Here, a practical and affordable way to calculate coupled-cluster quality anharmonic frequencies using second-order vibrational perturbation theory (VPT2) from machine-learned models is presented. The approach, referenced as "NN + VPT2", uses a high-dimensional neural network (PhysNet) to learn potential energy surfaces (PESs) at different levels of theory from which harmonic and VPT2 frequencies can be efficiently determined. The NN + VPT2 approach is applied to eight small- to medium-sized molecules (H2CO, trans-HONO, HCOOH, CH3OH, CH3CHO, CH3NO2, CH3COOH, and CH3CONH2) and frequencies are reported from NN-learned models at the MP2/aug-cc-pVTZ, CCSD(T)/aug-cc-pVTZ, and CCSD(T)-F12/aug-cc-pVTZ-F12 levels of theory. For the largest molecules and at the highest levels of theory, transfer learning (TL) is used to determine the necessary full-dimensional, near-equilibrium PESs. Overall, NN + VPT2 yields anharmonic frequencies to within 20 cm-1 of experimentally determined frequencies for close to 90% of the modes for the highest quality PES available and to within 10 cm-1 for more than 60% of the modes. For the MP2 PESs only ∼60% of the NN + VPT2 frequencies were within 20 cm-1 of the experiment, with outliers up to ∼150 cm-1, compared to the experiment. It is also demonstrated that the approach allows to provide correct assignments for strongly interacting modes such as the OH bending and the OH torsional modes in formic acid monomer and the CO-stretch and OH-bend mode in acetic acid.

Transfer Learning to CCSD(T): Accurate Anharmonic Frequencies from Machine Learning Models.

The higher-energy cis- as well as the global minimum trans-rotamers of the four H/D isotopologues of the formic acid monomer have been examined with Raman jet spectroscopy extending the vibrational gas phase reference database by eleven new cis-band positions for HCOOD, DCOOH, and DCOOD. With these new additions, all O–H/D, C–H/D, and CO stretching as well as the O–D in-plane bending vibrations of these higher-energy rotamers are known in addition to the previously determined C–O stretch and OH torsion of cis-HCOOH. Further, a comparison of the vibrational spectra of all four H/D isotopologues of the globally stable trans-rotamer of formic acid is shown to be very helpful in revealing similarities and differences in these systems, particularly with regard to Fermi resonances. Amongst the most prominent ones is the ν5/2ν9 resonance doublet of trans-HCOOH, for which we provide more insight into a recently suggested label switch of the resonance partners via the comparison of infrared and Raman jet spectra.

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Increasing the weights in the molecular work-out of cis- and trans-formic acid: extension of the vibrational database via deuteration.

Formic acid dimer as the prototypical doubly hydrogen-bonded gas-phase species is discussed from the perspective of the three translational and the three rotational degrees of freedom which are lost when two formic acid molecules form a stable complex. The experimental characterisation of these strongly hindered translations and rotations is reviewed, as are attempts to describe the associated fundamental vibrations, their combinations, and their thermal shifts by different electronic structure calculations and vibrational models. A remarkable match is confirmed for the combination of a CCSD(T)-level harmonic treatment and an MP2-level anharmonic VPT2 correction. Qualitatively correct thermal shifts of the vibrational spectra can be obtained from classical molecular dynamics in CCSD(T)-quality force fields. A detailed analysis suggests that this agreement between experiment and composite theoretical treatment is not strongly affected by fortuitous error cancellation but fully converged variational treatments of the six pair or intermolecular modes and their overtones and combinations in this model system would be welcome.

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Concerted Pair Motion Due to Double Hydrogen Bonding: The Formic Acid Dimer Case

Revisiting recently published Raman jet spectra of monomeric formic acid with accurate high order perturbative calculations based on two explicitly correlated coupled-cluster quality potential energy surfaces from the literature, we assign and add 11 new vibrational band centers to the trans-HCOOH database and 53 for its three deuterated isotopologs Profiting from the synergy between accurate calculations and symmetry information from depolarized Raman spectra, we reassign eight literature IR bands up to 4000 cm−1 Experimental detection of highly excited torsional states (ν9) of trans-HCOOH, such as 4ν9 and ν6 + 2ν9, reveals substantial involvement of the C–O stretch ν6 into the O–H bend/torsion resonance ν5/2ν9, which is part of a larger resonance polyad Depolarization and isotopic C-D substitution experiments further elucidate the nature of Raman peaks in the vicinity of the O–H stretching fundamental (ν1), which seem to be members of a large set of interacting states that can be identified and described with a polyad quantum number and that gain intensity via resonance mixing with ν1

The Raman jet spectrum of trans-formic acid and its deuterated isotopologs: Combining theory and experiment to extend the vibrational database.

Three energetically close pairs of vibrational states in glycolic acid are investigated by Raman spectroscopy in a supersonic jet to provide challenging benchmarks for vibrational and electronic st...

Glycolic Acid as a Vibrational Anharmonicity Benchmark.

When the lower frequency OH stretching fundamental of a water molecule is shifted to the 3500 cm-1 spectral range by the solvation of a carbonyl compound, in this case a ketone, its infrared intensity is shared with a dark state. It is shown by chemical and isotope substitution for more than a dozen systems that the location of this resonance is remarkably substitution-independent. Harmonic and anharmonic model calculations support its assignment to a combination of the water bending overtone and in-plane water libration. This previously unrecognized intramolecular-intermolecular coupling in single solvent water has a strength of 7-10 cm-1. It may have been sporadically observed before in a few other carbonyl compounds such as amides, without any previous exploration of its potential universality. The resulting generic picosecond energy redistribution channel for aqueous solutions may represent a slow counterpart and doorway model of what happens on a subpicosecond time scale when the hydrogen bonds become stronger, such as in carboxylic acid dimers or protonated water clusters.

Arman Nejad

Papers

Concerted Pair Motion Due to Double Hydrogen Bonding: The Formic Acid Dimer Case

Increasing the weights in the molecular work-out of cis- and trans-formic acid: extension of the vibrational database via deuteration.

The Raman jet spectrum of trans-formic acid and its deuterated isotopologs: Combining theory and experiment to extend the vibrational database.

Glycolic Acid as a Vibrational Anharmonicity Benchmark.

A Rather Universal Vibrational Resonance in 1:1 Hydrates of Carbonyl Compounds.