High resolution jet-cooled infrared absorption spectra of (HCOOH)2, (HCOOD)2, and HCOOH—HCOOD complexes in 7.2 μm region

An Ab Initio Neural Network Potential Energy Surface for the Dimer of Formic Acid and Further Quantum Tunneling Dynamics

We construct a full-dimensional ab initio neural network potential energy surface (PES) for the isomerization system of the formic acid dimer (FAD). This is based upon ab initio calculations using the DLPNO-CCSD(T) approach with the aug-cc-pVTZ basis set, performed at over 14000 symmetry-unique geometries. An accurate fit to the obtained energies is generated using a general neural network fitting procedure combined with the fundamental invariant method, and the overall energy-weighted root-mean-square fitting error is about 6.4 cm^-1. Using this PES, we present a multidimensional quantum dynamics study on tunneling splittings with an efficient theoretical scheme developed by our group. The ground-state tunneling splitting of FAD calculated with a four-mode coupled method is in good agreement with the most recent experimental measurements. The PES can be applied for further dynamics studies. The effectiveness of the present scheme for constructing a high-dimensional PES is demonstrated, and this scheme is expected to be feasible for larger molecular systems.

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.

Double proton transfer in hydrated formic acid dimer: Interplay of spatial symmetry and solvent-generated force on reactivity

The double proton transfer (DPT) reaction in the hydrated formic acid dimer (FAD) is investigated at molecular-level detail. For this, a global and reactive machine learned (ML) potential energy surface (PES) is developed to run extensive (more than 100 ns) mixed ML/MM molecular dynamics (MD) simulations in explicit molecular mechanics (MM) solvent at MP2-quality for the solute. Simulations with fixed – as in a conventional empirical force field – and conformationally fluctuating – as available from the ML-based PES – charge models for FAD show a significant impact on the competition between DPT and dissociation of FAD into two formic acid monomers. With increasing temperature the barrier height for DPT in solution changes by about 10% (∼1 kcal mol⁻¹) between 300 K and 600 K. The rate for DPT is largest, ∼1 ns⁻¹, at 350 K and decreases for higher temperatures due to destabilisation and increased probability for dissociation of FAD. The water solvent is found to promote the first proton transfer by exerting a favourable solvent-induced Coulomb force along the O–H⋯O hydrogen bond whereas the second proton transfer is significantly controlled by the O–O separation and other conformational degrees of freedom. Double proton transfer in hydrated FAD is found to involve a subtle interplay and balance between structural and electrostatic factors.

Simulation of double proton transfer in formic acid dimer by reactive ML potential in explicit molecular mechanics water solvent.

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.

Slow monomer vibrations in formic acid dimer: Stepping up the ladder with FTIR and Raman jet spectroscopy

In an effort to extend the cold gas phase spectroscopic database of the cyclic formic acid dimer (FAD), we present and analyze the jet-cooled vibrational infrared and Raman spectrum of (HCOOH)₂ in the monomer fingerprint region between 600 and 1500 cm^-1. The present study bridges the gap between the intermolecular dimerization-induced and the carbonyl stretching fundamentals that have already been reexamined using jet-cooled or high-resolution spectroscopy. This completes the characterization of the jet-cooled vibrational (HCOOH)₂ spectrum below the complex OH (CH) stretching fundamentals, and we report resonance-induced FAD combination/overtone transitions that will serve as a valuable reference for a theoretical modeling of its vibrational dynamics. As a by-product, several new formic acid trimer fundamentals are identified in the jet spectra and assigned with the help of second-order vibrational perturbation theory (VPT2). The polar formic acid dimer still eludes detection in a supersonic jet, but we are able to estimate an experimental upper-bound of the polar dimer-to-trimer-to-cyclic dimer intensity ratio to about 1:10:100 under typical expansion conditions. Using VPT2 with resonance treatment (VPT2+K), we reinvestigate the notorious ν₂₂ resonance triad. Generally, we find that VPT2, which is, of course, inadequate for modeling the resonance-rich OH stretching spectrum of FAD, is performing very satisfactorily in predicting fundamental and two-quantum state term values for the slower modes below 1500 cm^-1. As these modes are the building blocks for the ultrafast energy dissipation in the OH stretching region, the present work opens the door for its quantitative understanding.

Double Proton Transfer Across a Table: The Formic Acid Dimer-Fluorobenzene Complex

Proton transfer via tunneling is a fundamental quantum‐mechanical phenomenon. We report rotational spectroscopy measurements of this process in the complex of the formic acid dimer with fluorobenzene. The assignment of the spectrum indicates that this complex exists in the form of a π–π stacked structure. Each rotational transition of the parent isotopologue exhibits splitting. Isotopic substitution experiments show that the spectral splitting results from double‐proton transfer tunneling in the formic acid dimer. Presence of fluorobenzene as a neighboring molecule does not quench the double proton transfer in the formic acid dimer but decreases its tunneling splitting from 341(3) MHz to 267.608(1) MHz. Calculations suggest that the presence of the weakly bounded fluorobenzene does not influence the activation energy of the proton transfer. The fluorobenzene is reoriented with respect to the formic acid dimer during the course of the reaction, slowing down the proton transfer motion.

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

The vibrational dynamics of the formic acid monomer (FAM) and dimer (FAD) is investigated from machine-learned potential energy surfaces at the MP2 (PES_MP2) and transfer-learned (PES_TL) 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 PES_TL 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 PES_TL 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 PES_TL. 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.

Neural network based PESs are constructed for formic acid monomer and dimer at the MP2 and transfer learned to the CCSD(T) level of theory. The PESs are used to study the vibrational dynamics and dissociation energy of the molecules.

A simplistic computational procedure for tunneling splittings caused by proton transfer

In this manuscript, we present an approach for computing tunneling splittings for large amplitude motions. The core of the approach is a solution of an effective one-dimensional Schrödinger equation with an effective mass and an effective potential energy surface composed of electronic and harmonic zero-point vibrational energies of small amplitude motions in the molecule. The method has been shown to work in cases of three model motions: nitrogen inversion in ammonia, single proton transfer in malonaldehyde, and double proton transfer in the formic acid dimer. In the current work, we also investigate the performance of different DFT and post-Hartree–Fock methods for prediction of the proton transfer tunneling splittings, quality of the effective Schrödinger equation parameters upon the isotopic substitution, and possibility of a complete basis set (CBS) extrapolation for the resulting tunneling splittings.

Theoretical Study of Proton Tunneling in the Imidazole-Imidazolium Complex

Proton tunneling in the hydrogen-bonded imidazole–imidazolium complex ion has been studied theoretically. Ab initio CASSCF/6-311++G(d,p) calculations concerning geometry optimization and vibrational frequencies have been carried out for equilibrium and transition state structures of the system. Two-dimensional double-well model potentials were constructed on the basis of ab initio results and used to analyze the proton dynamics in the hydrogen bond and the influence of the excitation of low-frequency hydrogen-bond vibrations on the proton tunneling splittings. The energy of tunneling-split vibrational sublevels of the high-frequency tunneling mode have been calculated for its ground and first excited vibrational state for the series of excitations of the coupled low-frequency intramolecular hydrogen-bond modes. The promoting and suppressing effect of the low-frequency modes on the proton splittings was shown in the ground and first excited vibrational state of the tunneling mode. The vibrational sublevels form the two separate semicontinuous bands between which the absorption transitions may occur. This mechanism explains the experimentally observed splitting and doublet-component broadening of the high-frequency N–H stretching infrared (IR) absorption band.

Efficient Quantum Mechanical Calculations of Mode-Specific Tunneling Splittings upon Fundamental Excitation in the Dimer of Formic Acid

The formic acid dimer (FAD) is an important benchmark system for understanding the double hydrogen transfer process. Most recently, Zhang et al. measured a few tunneling splittings upon fundamental excitation of FAD precisely (Zhang, Y. et al. J. Chem. Phys. 2017, 146, 244306); however, relevant theoretical studies are very limited. Here, we present a multidimensional quantum dynamics study on mode-specific tunneling splittings upon fundamental excitation in FAD with an efficient theoretical scheme developed by our group in which the process-oriented basis function customization strategy is combined with the preconditioned inexact spectral transform method. Various mode-specific tunneling splittings upon fundamental excitation are systematically calculated, and interesting mode-specific excitation effects on tunneling rate are identified. In particular, the calculated tunneling splittings for the ν₂₂ and ν₂₁ states are in good agreement with experiment, and the remarkable mode-specific suppression effects upon excitation should result from that the antisymmetric vibrational modes hinder the concerted double H-transfer. The present work is helpful to acquire a better understanding of the mode-specific excitation effects on tunneling processes.

Proton Transfer vs Complex Formation Channels in Ionized Formic Acid Dimer: A Direct Ab Initio Molecular Dynamics Study

Photoirradiation to a hydrogen-bonded system plays an important role in the initial DNA and enzyme damage processes. The formic acid (FA) dimer is a model compound of double proton transfer systems, such as DNA base pairs. In the present study, the reactions of the FA dimer cation, formed upon ionization of the neutral dimer, have been investigated by the direct ab initio molecular dynamics method. Two reaction channels were identified for the FA dimer cation: complex formation and proton transfer (PT). In the complex formation channel, the carbonyl oxygen atoms of the two FA monomers were bound symmetrically, and a face-to-face complex was formed. In the PT channel, the proton of FA⁺ was transferred to FA, forming the H⁺(HCOOH)--HCO₂ radical cation as product. At low temperature, the complex channel was dominant, whereas the PT channel increased with increasing temperature. The asymmetric spin distribution on the FA dimer cation exhibited a strong correlation with the PT channel.

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

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.

Double Proton Transfer in the Dimer of Formic Acid: An Efficient Quantum Mechanical Scheme

Double proton transfer plays an important role in biology and chemistry, such as with DNA base pairs, proteins and molecular clusters, and direct information about these processes can be obtained from tunneling splittings. Carboxylic acid dimers are prototypes for multiple proton transfer, of which the formic acid dimer is the simplest one. Here, we present efficient quantum dynamics calculations of ground-state and fundamental excitation tunneling splittings in the formic acid dimer and its deuterium isotopologues. These are achieved with a multidimensional scheme developed by us, in which the saddle-point normal coordinates are chosen, the basis functions are customized for the proton transfer process, and the preconditioned inexact spectral transform method is used to solve the resultant eigenvalue problem. Our computational results are in excellent agreement with the most recent experiments (Zhang et al., 2017; Li et al., 2019).

Soft experimental constraints for soft interactions: a spectroscopic benchmark data set for weak and strong hydrogen bonds

An experimental benchmark data base on rotational constants, vibrational properties and energy differences for weakly and more strongly hydrogen-bonded complexes and their constituents from the spectroscopic literature is assembled. It is characterized in detail and finally contracted to a more compact, discriminatory set (ENCH-51, for Experimental Non-Covalent Harmonic with 51 entries). The meeting points between theory and experiment consist of equilibrium rotational constants and harmonic frequencies and energies, which are back-corrected from experimental observables and are very easily accessible by quantum chemical calculations. The relative performance of B3LYP-D3, PBE0-D3 and M06-2X density functional theory predictions with a quadruple-zeta basis set is used to illustrate systematic errors, error compensation and selective performance for structural, vibrational and energetical observables. The current focus is on perspectives and different benchmarking methodologies, rather than on a specific theoretical method or a specific class of compounds. Extension of the data base in chemical, observable and quantum chemical method space is encouraged.

Mid-infrared quantum cascade laser spectroscopy of the Ar-NO complex: Fine and hyperfine structure

The rovibrational spectrum of the Ar-NO open-shell complex has been measured in the 5.3 µm region using distributed feed-back quantum lasers to probe the direct absorption in a slit-jet supersonic expansion. Five P-subbands, namely, P^'←P^″:1/2←3/2,1/2←1/2,3/2←1/2,5/2←3/2, and 7/2←5/2, are observed, with J up to 15.5. The hyperfine structure due to the nuclei spin of ¹⁴N (I = 1) can be partially resolved in the P^'←P^″:1/2←3/2,1/2←1/2, and 3/2←1/2 subbands. The fine structure of the observed spectrum is analyzed using a modified semi-rigid rotor Hamiltonian [W. M. Fawzy and J. T. Hougen, J. Mol. Spectrosc. 137, 154-165 (1989)] and an empirical Hamiltonian [Y. Kim and H. Meyer, Int. Rev. Phys. Chem. 20, 219-282 (2001)] separately. The hyperfine structure can be simulated successfully by including hyperfine terms to the semi-rigid rotor Hamiltonian. A linear J-dependence of the angle between the inertial a-axis of the complex and the intramolecular axis of the NO subunit is also introduced in order to model the strong structure relaxation effect in the P = 1/2 state.

Quantum approaches to vibrational dynamics and spectroscopy: is ease of interpretation sacrificed as rigor increases?

The subject of this Perspective is quantum approaches, beyond the harmonic approximation, to vibrational dynamics and IR spectroscopy.

IR Spectra of (HCOOH)2 and (DCOOH)2: Experiment, VSCF/VCI, and Ab Initio Molecular Dynamics Calculations Using Full-Dimensional Potential and Dipole Moment Surfaces

We report quantum VSCF/VCI and ab initio molecular dynamics (AIMD) calculations of the IR spectra of (HCOOH)₂ and (DCOOH)₂, using full-dimensional, ab initio potential energy and dipole moment surfaces (PES and DMS). These surfaces are fits, using permutationally invariant polynomials, to 13 475 ab initio CCSD(T)-F12a electronic energies and MP2 dipole moments. Here "AIMD" means using these ab initio potential and dipole moment surfaces in the MD calculations. The VSCF/VCI calculations use all (24) normal modes for coupling, with a four-mode representation of the potential. The quantum spectra align well with jet-cooled and room-temperature experimental spectra over the spectral range 600-3600 cm^-1. Analyses of the complex O-H and C-H stretch bands are made based on the mixing of the VSCF/VCI basis functions. The comparisons of the AIMD IR spectra with both experimental and VSCF/VCI ones provide tests of the accuracy of the AIMD approach. These indicate good accuracy for simple bands but not for the complex O-H stretch band, which is upshifted from experimental and VSCF/VCI bands by roughly 300 cm^-1. In addition to testing the AIMD approach, the PES, DMS, and VSCF/VCI calculations for formic acid dimer provide opportunities for testing other methods to represent high-dimensional data and other methods that perform postharmonic vibrational calculations.

Quantum and classical IR spectra of (HCOOH)2, (DCOOH)2 and (DCOOD)2 using ab initio potential energy and dipole moment surfaces

Full-dimensional (24 modes) quantum calculation of the IR spectrum of (DCOOD)₂, and comparison with classical MD one.