A Bond-Based Machine Learning Model for Molecular Polarizabilities and A Priori Raman Spectra

The use of machine learning (ML) algorithms in molecular simulations has become commonplace in recent years. There now exists, for instance, a multitude of ML force field algorithms that have enabled simulations approaching ab initio level accuracy at time scales and system sizes that significantly exceed what is otherwise possible with traditional methods. Far fewer algorithms exist for predicting rotationally equivariant, tensorial properties such as the electric polarizability. Here, we introduce a kernel ridge regression algorithm for machine learning of the polarizability tensor. This algorithm is based on the bond polarizability model and allows prediction of the tensor components at the cost similar to that of scalar quantities. We subsequently show the utility of this algorithm by simulating gas phase Raman spectra of biphenyl and malonaldehyde using classical molecular dynamics simulations of these systems performed with the recently developed MACE-OFF23 potential. The calculated spectra are shown to agree very well with the experiments and thus confirm the expediency of our algorithm as well as the accuracy of the used force field. More generally, this work demonstrates the potential of physics-informed approaches to yield simple yet effective machine learning algorithms for molecular properties.

Wavepacket dynamical study of H-atom tunneling in catecholate monoanion: the role of intermode couplings and energy flow

We present a study of H-atom tunneling in catecholate monoanion through wavepacket dynamical simulations. In our earlier study of this symmetrical double-well system [Phys. Chem. Chem. Phys., 2022, 24, 10887], a limited number of transition state modes were identified as being important for the tunneling process. These include the imaginary frequency mode Q₁, the CO scissor mode Q₁₀, and the OHO bending mode Q₂₉. In this work, starting from non-stationary initial states prepared with excitations in these modes, we have carried out wavepacket dynamics in two and three dimensional spaces. We analyse the dynamical effects of the intermode couplings, in particular the role of energy flow between the studied modes on H-atom tunneling. We find that while Q₁₀ strongly modulates the donor-acceptor distance, it does not exchange energy with Q₁. However, excitation in Q₂₉ or Q₁ does lead to rapid energy exchange between these modes, which modifies the tunneling rate at early times.

Multidimensional H-atom tunneling in the catecholate monoanion

We present the catecholate monoanion as a new model system for the study of multidimensional tunneling. It has a symmetrical O-H double-well structure, and the H atom motion between the two wells is coupled to both low and high frequency modes with different strengths. With a view to studying mode-specific tunneling in the catecholate monoanion, we have developed a full (33) dimensional potential energy surface in transition state (TS) normal modes using a Distributed Gaussian Empirical Valence Bond (DGEVB) based approach. We have computed eigenstates in different subspaces using both unrelaxed and relaxed potentials based on the DGEVB model. With unrelaxed potentials, we present results up to 7D subspaces that include the imaginary frequency mode and six modes coupled to it. With relaxed potentials, we focus on the two most important coupling modes. The structures of the ground and vibrationally excited eigenstates are discussed for both approaches and mode-specific tunneling splitting and their trends are presented.

Vibrational Dynamics of the Intramolecular H-Bond in Acetylacetone Investigated with Transient and 2D IR Spectroscopy

Acetylacetone (AcAc) has proven to be a fruitful but highly challenging model system for the experimental and computational interrogation of strong intramolecular hydrogen bonds. Key questions remain, however, regarding the identity of the minimum-energy structure of AcAc and the dynamics of intramolecular proton transfer. Here, we investigate the OH/OD stretch and bend regions of the enol tautomer of AcAc and its deuterated isotopologue with transient absorption and 2D IR spectroscopy. The OH bend region reveals a single dominant diagonal transition near 1625 cm^-1 with intense cross peaks to lower-frequency modes, demonstrating highly mixed fingerprint transitions that contain OH bend character. The anharmonic coupling of the OH bend results in a highly elongated OH bend excited-state absorption transition that indicates a large manifold of OH bend overtone/combination bands in the OH stretch region that leads to strong bend-stretch Fermi resonance interactions. The OH and OD stretch regions consist of broad ground-state bleach signals, but there is no clear evidence of ω₂₁ excited-state absorptions due to rapid population relaxation arising from strong intramolecular coupling to bending, fingerprint, and low-frequency H-bond modes. Orientational relaxation dynamics persist for timescales longer than the vibrational lifetimes, with polarization anisotropy components decaying within approximately 2 and 10 periods of the O-O oscillation for the OH and OD stretch, respectively. The significant isotopic dependence of the orientational dynamics is discussed in the context of intramolecular mode coupling, diffusional processes, and contributions from proton/deuteron transfer dynamics.

UV Photochemistry of Acetylacetaldehyde Trapped in Cryogenic Matrices

The broad band UV photochemistry of acetylacetaldehyde, the hybrid form between malonaldehyde and acetylacetone (the two other most simple molecules exhibiting an intramolecular proton transfer), trapped in four cryogenic matrices, neon, nitrogen, argon, and xenon, has been studied by IRTF spectroscopy. These experimental results have been supported by B3LYP/6-311G++(2d,2p) calculations in order to get S₀ minima together with their harmonic frequencies. On those minima, we have also calculated their vibrationally resolved UV absorption spectra at the time-dependent DFT ωB97XD/6-311++G(2d,2p) level. After deposition, only the two chelated forms are observed while they isomerize upon UV irradiation toward nonchelated species. From UV irradiation effects we have identified several nonchelated isomers, capable, in turn, of isomerizing and fragmenting, even if this last phenomenon seems to be most unlikely due to cryogenic cages confinement. On the basis of these findings, we have attempted a first approach to the reaction path of electronic relaxation. It appeared that, as with acetylacetone, the path of electronic relaxation seems to involve triplet states.

Intramolecular hydrogen tunneling in 2-chloromalonaldehyde trapped in solid para-hydrogen

The internal dynamics of a 2-chloromalonaldehyde (2-ClMA) molecule, possessing a strong internal hydrogen bond (IHB), was examined by means of matrix isolation spectroscopy in a soft host: para-hydrogen (pH₂). 2-ClMA is a chlorinated derivative of malonaldehyde (MA), a model molecule in hydrogen transfer studies, better suited to low temperature experiments than its parent molecule. The infrared absorption spectra of 2-ClMA isolated in pH₂ exhibit temperature dependent structures which are explained as transitions occurring from split vibrational levels induced by hydrogen tunneling. The doublet components associated with higher and lower energy levels are changing reversibly with the increase/decrease of the matrix temperature. The ground state splitting is measured to be 7.9 ± 0.1 cm^-1. The presence of oH₂ impurities in the pH₂ matrix close to the neighborhood of the 2-ClMA molecule is found to quench the H tunneling. The data provide a powerful insight into the dynamical picture of intramolecular hydrogen tunneling in a molecule embedded in a very weakly perturbing environment.

Selective photoisomerisation of 2-chloromalonaldehyde

Isomerization of 2-chloromalonaldehyde (2-ClMA) is explored giving access to new experimental data on this derivative of malonaldehyde, not yet studied much. Experiments were performed isolating 2-ClMA in argon, neon, and para-hydrogen matrices. UV irradiation of the matrix samples induced isomerization to three open enolic forms including two previously observed along with the closed enolic form after deposition. IR spectra of these specific conformers were recorded, and a clear assignment of the observed bands was obtained with the assistance of theoretical calculations. UV spectra of the samples were measured, showing a blue shift of the π^* ← π absorption with the opening of the internal hydrogen bond of the most stable enol form. Specific sequences of UV irradiation at different wavelengths allowed us to obtain samples containing only one enol conformer. The formation of conformers is discussed. The observed selectivity of the process among the enol forms is analyzed.

Large amplitude motions within molecules trapped in solid parahydrogen

Molecules of the β-diketone and β-dialdehyde families were trapped in solid parahydrogen (pH2) to investigate the vibrational behavior of systems containing an intramolecular hydrogen bond (IHB). In the simplest β-diketone, acetylacetone (AcAc), H transfer related to the IHB is coupled with methyl torsions. In pH2, the study of nuclear spin conversion (NSC) in methyl groups allows the characterisation of the influence of these large amplitude motions on the vibrational modes. The deuteration of the OH group involved in the IHB has important consequences on the vibrational spectrum of the molecule and evidence of NSC in methyl groups is difficult to obtain. In the chlorine derivative (3-chloroacetylacetone), the H-transfer is no longer coupled with methyl torsion, and NSC has undetectable effects on the IR spectrum. A search of H tunnelling splitting in the IR spectra of β-dialdehydes trapped in pH2 was performed. A few modes of 2-chloromalonaldehyde appear as doublets and were assigned to tunnelling levels. The spectroscopic results related to large amplitude motions are detailed and discussed, highlighting puzzling effects.

2-Chloromalonaldehyde, a model system of resonance-assisted hydrogen bonding: vibrational investigation

The chelated enol isomer of 2-chloromalonaldehyde (2-ClMA) is experimentally characterized for the first time by IR and Raman spectroscopies. The spectra are obtained by trapping the molecule in cryogenic matrices and analyzed with the assistance of theoretical calculations. Experiments were performed in argon, neon and para-hydrogen matrices. The results highlight puzzling matrix effects, beyond site effects, which are interpreted as due to a tunneling splitting of the vibrational levels related to the proton transfer along the internal hydrogen bond (IHB). 2-ClMA is thus one of the very few molecules in which the H tunneling has been observed in cryogenic matrices. The comparison with its parent molecule (malonaldehyde) shows experimentally and theoretically the weakening of the IHB upon chlorination, with a reduced cooperative effect in the resonance assisted hydrogen bond. In addition, the Cl substitution induces an important stabilization of two open enol conformers. These two open forms appear in the spectra of as-deposited samples, meaning that, in contrast with other well-studied molecules of the same family (β-dialdehydes and β-diketones), they are present in the gas phase at room temperature.

UV and IR Photochemistries of Malonaldehyde Trapped in Cryogenic Matrices

UV and IR photochemistries of malonaldehyde, the simplest molecule exhibiting an intramolecular proton exchange, have been studied in four cryogenic matrices at 4.3 K, N₂, Ne, Ar, and Xe. Samples have been irradiated using a UV and IR OPO type tunable laser, and with a broad band UV mercury lamp. UV and IR spectra have been recorded and compared with theoretical calculations carried out at the SAC-CI/6-31++G(d,p) (UV transitions) and B3LYP/6-311++G(2d,2p) (IR spectra) levels of theory. After deposition, the intramolecularly H-bonded form is found exclusively, while several open forms are formed upon UV irradiation. These open forms show ability to interconvert upon UV irradiation too. Some of them are also able to isomerize upon selective IR irradiations. The whole set of results allowed us to identify seven isomers among the eight postulated. The photodynamics of the electronic relaxation of malonaldehyde have also been investigated. By following the decay or rise of suited specific vibrational bands in the IR spectra, and by comparing the results with an earlier study of the homologous acetylacetone, we deduced that the electronic relaxation of malonaldehyde proceeds through singlet states, most probably through a 3-fold conical intersection, as postulated from theoretical calculations. In contrast with acetylacetone, malonaldehyde does not show fragmentation after UV excitation.

NMR and IR Investigations of Strong Intramolecular Hydrogen Bonds

For the purpose of this review, strong hydrogen bonds have been defined on the basis of experimental data, such as OH stretching wavenumbers, νOH, and OH chemical shifts, δOH (in the latter case, after correction for ring current effects). Limits for O-H···Y systems are taken as 2800 > νOH > 1800 cm-1, and 19 ppm > δOH > 15 ppm. Recent results as well as an account of theoretical advances are presented for a series of important classes of compounds such as β-diketone enols, β-thioxoketone enols, Mannich bases, proton sponges, quinoline N-oxides and diacid anions. The O···O distance has long been used as a parameter for hydrogen bond strength in O-H···O systems. On a broad scale, a correlation between OH stretching wavenumbers and O···O distances is observed, as demonstrated experimentally as well as theoretically, but for substituted β-diketone enols this correlation is relatively weak.

Quantum Mechanical Investigation of Mode-Specific Tunneling upon Fundamental Excitation in Malonaldehyde

We present a quantum mechanical study of mode-specific tunneling upon fundamental excitation in malonaldehyde with a multidimensional theory that utilizes the saddle-point normal coordinates. We find that a ring-deformation normal mode is as essential as the well-known imaginary-frequency normal mode in the multidimensional investigation. The changes in tunneling splittings upon fundamental excitation are calculated. The results are competitive with those from a recently developed mixed classical-quantum method. Moreover, the results are qualitatively consistent with experiment for about half of all the modes.

Symmetry breaking in the axial symmetrical configurations of enolic propanedial, propanedithial, and propanediselenal: pseudo Jahn–Teller effect versus the resonance-assisted hydrogen bond theory

The origin of the symmetry breaking in the axial symmetrical configurations of enolic propanedial (1), propanedithial (2), and propanediselenal (3) have been investigated by means of time-dependence density functional theory and natural bond orbital interpretations. The results obtained at the quantum chemistry composite (G2MP2, CBS-QB3), ab initio molecular orbital (MP2/6-311++G**), and hybrid density functional theory (B3LYP/6-311++G**) levels of theory showed that the hydrogen-centered synchronous axial symmetrical (C2v) configurations of compounds 1–3 possessing the maximum π-electron delocalization within the M1=C2–C3=C4–M5–H6 keto-enol groups are less stable than their corresponding plane symmetrical (Cs) forms. Importantly, the symmetry breaking in the C2v configurations of the enol forms of compounds 1–3 to their corresponding plane symmetrical Cs configurations is due to the pseudo Jahn–Teller effect (PJTE) by mixing the ground A1 and excited B2 electronic states resulting in a PJT (A1 + B2) ⊗ b2 problem. We may expect that by the decrease of the energy gaps between reference states in the C2v forms that are involved in the PJTE decrease from compound 1 to compound 3, the PJT stabilization energy (PJTSE) may increase but the results obtained showed that the corresponding PJTSEs decrease. This fact can be justified by the increase of the electron delocalizations from the nonbonding orbitals of the C=M moieties to the antibonding orbitals of the H–M bonds, which leads to an increase of the π-electron delocalization within the M1=C2–C3=C4–M5–H6 keto-enol groups. In confrontation between the impacts of the resonance-assisted hydrogen bond and PJTE in the structural and configurational properties of compounds 1–3, PJTE has an overwhelming contribution and causes the symmetry breaking of the C2v configurations to their corresponding Cs forms. The correlations between the structural parameters, synchronicity indices, natural charges, PJTSEs, electron delocalizations, and the hardness of compounds 1–3 have been investigated.

Intra-residue interactions in proteins: interplay between serine or cysteine side chains and backbone conformations, revealed by laser spectroscopy of isolated model peptides

Intra-residue interactions play an important role in proteins by influencing local folding of the backbone. Taking advantage of the capability of gas phase experiments to provide relevant information on the intrinsic H-bonding pattern of isolated peptide chains, the intra-residue interactions of serine and cysteine residues, i.e., OH/SH···OC(i) C6 and NH(i···)O/S C5 interactions in Ser/Cys residues, are probed by laser spectroscopy of isolated peptides. The strength of these local side chain-main chain interactions, elegantly documented from their IR spectral features for well-defined conformations of the main chain, demonstrates that a subtle competition exists between the two types of intra-residue bond: the C6 H-bond is the major interaction with Ser, in contrast to Cys where C5 interaction takes over. The restricted number of conformers observed in the gas phase experiment with Ser compared to Cys (where both extended and folded forms are observed) also suggests a significant mediation role of these intra-residue interactions on the competition between the several main chain folding patterns.

Multidimensional Hamiltonian for tunneling with position-dependent mass

A multidimensional Hamiltonian for tunneling is formulated, based on the mode with imaginary frequency of the transition state as a reaction coordinate. To prepare it for diagonalization, it is transformed into a lower-dimension Hamiltonian by incorporating modes that move faster than the tunneling into a coordinate-dependent kinetic energy operator, for which a Hermitian form is chosen and tested for stability of the eigenvalues. After transformation to a three-dimensional form, which includes two normal modes strongly coupled to the tunneling mode, this Hamiltonian is diagonalized in terms of a basis set of harmonic oscillator functions centered at the transition state. This involves a sparse matrix which is easily partially diagonalized to yield tunneling splittings for the zero-point level and the two fundamental levels of the coupled modes. The method is tested on the well-known benchmark molecule malonaldehyde and a deuterium isotopomer, for which these splittings have been measured. Satisfactory agreement with experiment results is obtained.

Stretching and folding of 2-nanometer hydrocarbon rods

Linear alkanes CnH2n+2 in vacuum isolation are finite models for an infinite polyethylene chain. Using spontaneous Raman scattering in supersonic jet expansions for n = 13-21 in different spectral ranges, we determine the minimal chain length nh for the cohesion-driven folding of the preferred extended all-trans conformation into a hairpin structure. We treat fully stretched all-trans alkanes as molecular "nanorods" and derive Young's modulus E for the stretching of an isolated single-strand polyethylene fibre by extrapolating the longitudinal acoustic mode to infinite chain length. Two key quality parameters for accurate intra- and intermolecular force fields of hydrocarbons (nh = 18 ± 1, E = 305 ± 5 GPa) are thus derived with high accuracy from experimental spectroscopy.