Vibrational tuning of the Hydrogen transfer in malonaldehyde – a combined FTIR and Raman jet study†

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.

MC-QTAIM analysis reveals an exotic bond in coherently quantum superposed malonaldehyde

The proton between the two oxygen atoms of the malonaldehyde molecule experiences an effective double-well potential in which the proton's wavefunction is delocalized between the two wells. Herein we employ a state-of-the-art multi-component quantum theory of atoms in molecules partitioning scheme to obtain the molecular structure, i.e. atoms in molecules and bonding network, from the superposed ab initio wavefunctions of malonaldehyde. In contrast to the familiar clamped-proton portrayal of malonaldehyde, in which the proton forms a hydrogen basin, for the superposed states the hydrogen basin disappears and two novel hybrid oxygen-hydrogen basins appear instead, with an even distribution of the proton population between the two basins. The interaction between the hybrid basins is stabilizing thanks to an unprecedented mechanism. This involves the stabilizing classical Coulomb interaction of the one-proton density in one of the basins with one-electron density in the other basin. This stabilizing mechanism yields a bond foreign to the known bonding modes in chemistry.

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 Tunneling Spectra of Molecules with Asymmetric Wells: A Combined Vibrational Configuration Interaction and Instanton Approach

A combined approach that uses the vibrational configuration interaction (VCI) and semiclassical instanton theory was developed to study vibrational tunneling spectra of molecules with multiple wells in full dimensionality. The method can be applied to calculate low-lying vibrational states in the systems with an arbitrary number of minima, which are not necessarily equal in energy or shape. It was tested on a two-dimensional double-well model system and on malonaldehyde, and the calculations reproduced the exact quantum mechanical (QM) results with high accuracy. The method was subsequently applied to calculate the vibrational spectrum of the asymmetrically deuterated malonaldehyde with nondegenerate vibrational frequencies in the two wells. The spectrum is obtained at a cost of single-well VCI calculations used to calculate the local energies. The interactions between states of different wells are computed semiclassically using the instanton theory at a comparatively negligible computational cost. The method is particularly suited to systems in which the wells are separated by large potential barriers and tunneling splittings are small, for example, in some water clusters, when the exact QM methods come at a prohibitive computational cost.

Hydrogen Delocalization in an Asymmetric Biomolecule: The Curious Case of Alpha-Fenchol

Rotational microwave jet spectroscopy studies of the monoterpenol α-fenchol have so far failed to identify its second most stable torsional conformer, despite computational predictions that it is only very slightly higher in energy than the global minimum. Vibrational FTIR and Raman jet spectroscopy investigations reveal unusually complex OH and OD stretching spectra compared to other alcohols. Via modeling of the torsional states, observed spectral splittings are explained by delocalization of the hydroxy hydrogen atom through quantum tunneling between the two non-equivalent but accidentally near-degenerate conformers separated by a low and narrow barrier. The energy differences between the torsional states are determined to be only 16(1) and 7(1) cm-1hc for the protiated and deuterated alcohol, respectively, which further shrink to 9(1) and 3(1) cm-1hc upon OH or OD stretch excitation. Comparisons are made with the more strongly asymmetric monoterpenols borneol and isopinocampheol as well as with the symmetric, rapidly tunneling propargyl alcohol. In addition, the third-in contrast localized-torsional conformer and the most stable dimer are assigned for α-fenchol, as well as the two most stable dimers for propargyl alcohol.

Predicting OH stretching fundamental wavenumbers of alcohols for conformational assignment: different correction patterns for density functional and wave-function-based methods

A model is presented for the prediction of OH stretching fundamental wavenumbers of alcohol conformers in the gas phase by application of a small set of empirical anharmonicity corrections to calculations in the harmonic approximation. In contrast to the popular application of a uniform scaling factor, the local chemical structure of the alcohol is taken into account to greatly improve accuracy. Interestingly, different correction patterns emerge for results of hybrid density functional (B3LYP-D3 and PBE0-D3) and wave-function-based methods (SCS-LMP2, LCCSD(T*)-F12a and CCSD(T)-F12a 1D). This raises questions about electronic structure deficiencies in these methods and differences in anharmonicity between alcohols. After its initial construction on the basis of literature assignments the model is tested with Raman jet spectroscopy of propargyl alcohol, cyclohexanol, borneol, isopinocampheol and 2-methylbutan-2-ol. For propargyl alcohol a spectral splitting attributed to tunneling is resolved. PBE0-D3 is identified as a well performing and broadly affordable electronic structure method for this model. A mean absolute error of 1.3 cm-1 and a maximum absolute error of 3 cm-1 result for 46 conformers of 24 alcohols in a 60 cm-1 range, when a single parameter is adjusted separately for each alcohol substitution class (methanol, primary, secondary, tertiary).

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.

Quantum momentum distribution and quantum entanglement in the deep tunneling regime

In this paper, we consider the momentum operator of a quantum particle directed along the displacement of two of its neighbors. A modified open-path path integral molecular dynamics is presented to sample the distribution of this directional momentum distribution, where we derive and use a new estimator for this distribution. Variationally enhanced sampling is used to obtain this distribution for an example molecule, malonaldehyde, in the very low temperature regime where deep tunneling happens. We find no secondary feature in the directional momentum distribution and that its absence is due to quantum entanglement through a further study of the reduced density matrix.

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.

Spectral Signatures of Proton-Transfer Dynamics at the Cusp of Low-Barrier Hydrogen Bonding

Despite their importance in diverse chemical and biochemical processes, low-barrier hydrogen bonds remain elusive targets to classify and interpret spectroscopically. Here the correlated nature of hydrogen bonding and proton transfer in the low-barrier regime has been probed for the ground and excited electronic states of 6-hydroxy-2-formylfulvene by acquiring jet-cooled fluorescence spectra of the parent and monodeuterated isotopologs. While excited-state profiles reveal regular vibronic patterns devoid of obvious dynamical signatures, their ground-state counterparts display a radically altered energy landscape characterized by spectral bifurcations comparable in magnitude to typical vibrational spacings (>100 cm^-1). Quantitative analyses yield unusual deuterium kinetic isotope effects that straddle limiting values attributed to above-barrier vibration and below-barrier tunneling of the proton adjoining donor/acceptor sites. Our findings provide compelling experimental evidence for ultrafast hydron-migration events commensurate with the onset of low-barrier hydrogen bonding and afford a trenchant glimpse of molecular phenomena taking place at the "tipping point" between disparate dynamical regimes.

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.

Theoretical study of the C-H/O-H stretching vibrations in malonaldehyde

IR and Raman spectra of the malonaldehyde molecule and its deuterated analogues were calculated in the B3LYP/cc-pVQZ approximation. Anharmonicity effects were taken into account both in the context of a standard model of the second order perturbation theory and by constructing the potential energy surfaces (PES) with a limited number of dimensions using the Cartesian coordinates of the hydroxyl hydrogen atom and the stretching coordinates of С-Н, C-D, O-H, and O-D bonds. It was shown that in each of the two equivalent forms of the molecule, besides the global minimum, an additional local minimum at the PES is formed with the energy more than 3,000 cm(-1) higher than the energy in the global minimum. Calculations carried out by constructing the 2D and 3D PESs indicate a high anharmonicity level and multiple manifestations of the stretching О-Н vibrations, despite the fact that the model used does not take into account the splitting of the ground-state and excited vibrational energy levels. In particular, the vibration with the frequency 3,258 cm(-1) may be associated with proton transfer to the region of a local minimum of energy. Comparing the results obtained with the experimental data presented in the literature allowed us to propose a new variant of bands assignments in IR and Raman spectra of the molecule in the spectral region 2,500-3,500 cm(-1).

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.

Calculations of Mode-Specific Tunneling of Double-Hydrogen Transfer in Porphycene Agree with and Illuminate Experiment

We report a theoretical study of mode-specific tunneling splittings in double-hydrogen transfer in trans-porphycene. We use a novel, mode-specific "Qim path method", in which the reaction coordinate is the imaginary-frequency normal mode of the saddle point separating the equivalent minima. The model considers all 108 normal modes and uses no adjustable parameters. The method gives the ground vibrational-state tunneling splitting, as well the increase in the splitting upon excitation of certain modes, in good agreement with experiment. Interpretation of these results is also transparent with this method. In addition, predictions are made for mode excitations not investigated experimentally. Results for d1 and d2 isotopolgues are also in agreement with experiment.