Formic Acid Dimer Research Articles

Nonadiabatic Hydrogen Tunneling Dynamics for Multiple Proton Transfer Processes with Generalized Nuclear-Electronic Orbital Multistate Density Functional Theory.

Proton transfer and hydrogen tunneling play key roles in many processes of chemical and biological importance. The generalized nuclear-electronic orbital multistate density functional theory (NEO-MSDFT) method was developed in order to capture hydrogen tunneling effects in systems involving the transfer and tunneling of one or more protons. The generalized NEO-MSDFT method treats the transferring protons quantum mechanically on the same level as the electrons and obtains the delocalized vibronic states associated with hydrogen tunneling by mixing localized NEO-DFT states in a nonorthogonal configuration interaction scheme. Herein, we present the derivation and implementation of analytical gradients for the generalized NEO-MSDFT vibronic state energies and the nonadiabatic coupling vectors between these vibronic states. We use this methodology to perform adiabatic and nonadiabatic dynamics simulations of the double proton transfer reactions in the formic acid dimer and the heterodimer of formamidine and formic acid. The generalized NEO-MSDFT method is shown to capture the strongly coupled synchronous or asynchronous tunneling of the two protons in these processes. Inclusion of vibronically nonadiabatic effects is found to significantly impact the double proton transfer dynamics. This work lays the foundation for a variety of nonadiabatic dynamics simulations of multiple proton transfer systems, such as proton relays and hydrogen-bonding networks.

Thermodynamics of the gas-phase dimerization of formic acid: Fully anharmonic finite temperature calculations at the CCSD(T) and many DFT levels.

A proof-of-concept study is undertaken to demonstrate the utility of the machine learning combined with the thermodynamic perturbation theory (MLPT) to test the accuracy of electronic structure methods in finite-temperature thermodynamic calculations. As a test example, formic acid dimer is chosen, which is one of the systems included in the popular benchmark set S22 [Jurečka et al., Phys. Chem. Chem. Phys. 8, 1985-1993 (2006)]. Starting from the explicit molecular dynamics and thermodynamic integration performed at the PBE + D2 level, the MLPT is used to obtain fully anharmonic dimerization free and internal energies at the reference quality CCSD(T) level and 19 different density functional approximations, including GGA, meta-GGA, non-local, and hybrid functionals with and without dispersion corrections. Our finite-temperature results are shown to be both qualitatively and quantitatively different from those obtained using the conventional benchmarking strategy based on fixed structures. The hybrid functional HSE06 is identified as the best performing approximate method tested, with the errors in free and internal energies of dimerization being 36 and 41meV, respectively.

Analysis of Site Energies and Excitonic Couplings: The Role of Symmetry and Polarization.

An excitonic coupling model is developed based on an equation-of-motion coupled cluster combined with the fragment molecular orbital method. The effects of polarization and excitonic coupling on the splitting of quasi-degenerate levels in systems containing multiple chromophores are elucidated on dimers of formaldehyde, water, formic acid, hydrogen fluoride, and carbon monoxide. It is shown that the level structure is mainly determined by the mutual polarization of chromophores and to a lesser extent by the excitonic coupling. The role of symmetry in excitonic coupling in dimers is discussed. The excitonic coupling between all residues in the photoactive yellow protein (PDB: 2PHY) is analyzed.

Transfer learning of hyperparameters for fast construction of anisotropic GPR models: design and application to the machine-learned force field FFLUX.

The polarisable machine-learned force field FFLUX requires pre-trained anisotropic Gaussian process regression (GPR) models of atomic energies and multipole moments to propagate unbiased molecular dynamics simulations. The outcome of FFLUX simulations is highly dependent on the predictive accuracy of the underlying models whose training entails determining the optimal set of model hyperparameters. Unfortunately, traditional direct learning (DL) procedures do not scale well on this task, especially when the hyperparameter search is initiated from a (set of) random guess solution(s). Additionally, the complexity of the hyperparameter space (HS) increases with the number of geometrical input features, at least for anisotropic kernels, making the optimization of hyperparameters even more challenging. In this study, we propose a transfer learning (TL) protocol that accelerates the training process of anisotropic GPR models by facilitating access to promising regions of the HS. The protocol is based on a seeding-relaxation mechanism in which an excellent guess solution is identified by rapidly building one or several small source models over a subset of the target training set before readjusting the previous guess over the entire set. We demonstrate the performance of this protocol by building and assessing the performance of DL and TL models of atomic energies and charges in various conformations of benzene, ethanol, formic acid dimer and the drug fomepizole. Our experiments suggest that TL models can be built one order of magnitude faster while preserving the quality of their DL analogs. Most importantly, when deployed in FFLUX simulations, TL models compete with or even outperform their DL analogs when it comes to performing FFLUX geometry optimization and computing harmonic vibrational modes.

Ultrafast Proton Transfer and Contact Ion-Pair Formation in Formic Acid Clusters.

The ultrafast proton transfer dynamics of homogeneous formic acid clusters (FA)n, n < 10, are investigated with femtosecond time-resolved mass spectrometry. We monitor the proton transfer pathway following Rydberg state electronic relaxation and find that successful ion pair formation increases logarithmically with cluster size. Ab initio calculations demonstrate similar excitation/relaxation behavior for each cluster, revealing a contact ion pair forms between two molecules composing the cluster before finally a formate anion (HCOO-) is dissociated by the probe pulse. The sub-ps time scale for rearrangement and proton transfer increases almost linearly with cluster size, requiring ∼67 fs per additional formic acid molecule and ranging from 213 ± 51 fs for the trimer to 667 ± 116 fs for FA9. The near-linear trends measured for both rearrangement lifetime and ion pair formation suggest that proton transfer is unlikely in the formic acid dimer but becomes prominent in small clusters.

Generalized Nuclear-Electronic Orbital Multistate Density Functional Theory for Multiple Proton Transfer Processes.

Proton transfer and hydrogen tunneling play pivotal roles in many chemical and biological processes. The nuclear-electronic orbital multistate density functional theory (NEO-MSDFT) approach was developed to describe hydrogen tunneling systems within the multicomponent NEO framework, where the transferring proton is quantized and treated with molecular orbital techniques on the same level as the electrons. Herein, the NEO-MSDFT framework is generalized to an arbitrary number of quantum protons to allow applications to systems involving the transfer and tunneling of multiple protons. The generalized NEO-MSDFT approach is shown to produce delocalized, bilobal proton densities and accurate tunneling splittings for fixed geometries of the formic acid dimer and asymmetric substituted variants, as well as the porphycene molecule. Investigation of a protonated water chain highlights the applicability of this approach to proton relay systems. This work provides the foundation for nuclear-electronic quantum dynamics simulations of a wide range of multiple proton transfer processes.

Intermolecular Charge Transfer Induced Fragmentation of Formic Acid Dimers.

We investigate the intermolecular nonradiative charge transfer process in a double hydrogen-bonded formic acid (FA) dimer, initiated by electron-collision induced double ionization of one FA molecule. Through fragment ions and electron coincident momentum measurements and abinitio calculations, we obtain direct evidence that electron transfer from the neighboring FA molecule to fill one of the two vacancies occurs by a potential energy curve crossing of FA^{++}+FA with FA^{+}+FA^{+*} curves, forming an electronic excited state of dicationic dimers. This process causes the breaking of two hydrogen bonds and subsequently the cleavage of C─H and C─O covalent bonds in the dimers, which is expected to be a general phenomenon occurring in molecular complexes and can have important implications for radiation damage to biological matter.

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.

Quantum dynamics calculations on isotope effects of hydrogen transfer isomerization in formic acid dimer

We present a quantum dynamics study on the isotope effects of hydrogen transfer isomerization in the formic acid dimer, and this is achieved by multidimensional dynamics calculations with an efficient quantum mechanical theoretical scheme developed by our group, on a full-dimensional neural network ab initio potential energy surface. The ground-state and fundamental tunneling splittings for four deuterium isotopologues of formic acid dimer are considered, and the calculated results are in very good general agreement with the available experimental measurements. Strong isotope effects are revealed, the mode-specific fundamental excitation effects on the tunneling rate are evidently influenced by the deuterium substitution of H atom with the substitution on the OH bond being more effective than on the CH bond. Our studies are helpful for acquiring a better understanding of isotope effects in the double-hydrogen transfer processes.

Infrared action spectroscopy of the deprotonated formic acid trimer, trapped in helium nanodroplets.

Hydrogen bonding interactions are essential in the structural stabilization and physicochemical properties of complex molecular systems, and carboxylic acid functional groups are common participants in these motifs. Consequently, the neutral formic acid (FA) dimer has been extensively investigated in the past, as it represents a useful model system to investigate proton donor-acceptor interactions. The analogous deprotonated dimers, in which two carboxylate groups are bound by a single proton, have also served as informative model systems. In these complexes, the position of the shared proton is mainly determined by the proton affinity of the carboxylate units. However, very little is known about the nature of the hydrogen bonding interactions in systems containing more than two carboxylate units. Here we report a study on the deprotonated (anionic) FA trimer. IR spectra are recorded in the 400-2000 cm-1 spectral range by means of vibrational action spectroscopy of FA trimer ions embedded in helium nanodroplets. Characterization of the gas-phase conformer and assignment of the vibrational features is achieved by comparing the experimental results with electronic structure calculations. To assist in the assignments, the 2H and 18O FA trimer anion isotopologues are also measured under the same experimental conditions. Comparison between the experimental and computed spectra, especially the observed shifts in spectral line positions upon isotopic substitution of the exchangeable protons, suggests that the prevalent conformer, under the experimental conditions, exhibits a planar structure that resembles the crystalline structure of formic acid.

Study on depolymerization kinetics of formic acid dimers in binary mixture.

In this study, polarization Raman spectra were collected for binary mixtures of formic acid/methanol and formic acid/acetonitrile with different volume fractions. The broad band of formic acid in the CO vibration region was divided into four vibration peaks, corresponding to CO symmetric and anti-symmetric stretching vibration from cyclic dimer, CO stretching from open dimer, and CO stretching from the free monomer. The experiments showed that as the volume fraction of formic acid in the binary mixture decreased, the cyclic dimer gradually converted to the open dimer, and at a volume fraction of 0.1, fully depolymerized into monomer form (free monomer, solvated monomer, and hydrogen bonding monomer clusters with solvent). The contribution percentage of the total CO stretching intensity of each structure at different concentrations was quantitatively calculated using high resolution infrared spectroscopy, and the results were consistent with the conclusions predicted by polarization Raman spectroscopy. Concentration-triggered 2D-COS synchronous and asynchronous spectra also confirmed the kinetics of formic acid diluted in acetonitrile. This work provides a spectroscopic method for studying the structure of organic compounds in solution and concentration-triggering kinetics in mixtures.

Limited Formation of CO3+ through Strong-Field Ionization and Coulomb Explosion of Formic Acid Clusters.

Femtosecond laser pulses are utilized to drive multiple ionization in gas-phase formic acid clusters (FA)n. Experimental measurements of the kinetic energy release (KER) of the ions through Coulomb explosion are studied using time-of-flight mass spectrometry and compared to the values recorded from molecules. Upon interacting with 200 fs linearly polarized laser pulses of 400 nm, formic acid clusters facilitate the formation of higher charge states than the formic acid dimer, reaching both C3+ and O3+ and also increasing the KER values to several hundred electronvolts in magnitude for such ions. At a lower laser intensity (3.8 × 1014 W/cm2), we record an enhancement in the signal of the (FA)5(H2O)H+ cluster, which suggests that it has a higher stability, in agreement with previous studies. A molecular dynamics simulation of the Coulomb explosion shows that the highly charged atomic ions arise from larger clusters, whereas the production of CO3+ is more likely to arise from the molecular case. Thus, the relative production of CO3+ is reduced in comparison to the highly charged ions upon clustering and is likely due to the higher ionization levels achieved, which facilitate dissociation.

Modeling the Solvation and Acidity of Carboxylic Acids Using an Ab Initio Deep Neural Network Potential.

Formic and acetic acid constitute the simplest of carboxylic acids, yet they exhibit fascinating chemistry in the condensed phase such as proton transfer and dimerization. The go-to method of choice for modeling these rare events have been accurate but expensive ab initio molecular dynamics simulations. In this study, we present a deep neural network potential trained using accurate ab initio data that can be used in tandem with enhanced-sampling methods to perform an efficient exploration of the free-energy surface of aqueous solutions of weak carboxylic acids. In particular, we show that our model captures proton dissociation and provides a good estimate of the pKa, as well as the dimerization of formic and acetic acid. This provides a suitable starting point for applications in different research areas where computational efficiency coupled with the accuracy of ab initio methods is required.

Production of Metastable CO3+ through the Strong-Field Ionization and Coulomb Explosion of Formic Acid Dimer

Femtosecond laser pulses are utilized to drive multiple ionization of formic acid dimers and the resulting ions are studied using time-of-flight mass spectrometry. The interaction of formic acid dimer with 200 fs linearly polarized laser pulses of 400 nm with intensities of up to 3.7 × 1015 W/cm2 produces a metastable carbon monoxide trication. Experimental kinetic energy release (KER) measurements of the ions are consistent with molecular dynamics simulations of the Coulomb explosion of a formic acid dimer and suggest that no significant movement occurs during ionization. KER values were recorded as high as 44 eV for CO3+, in agreement with results from a classical Molecular Dynamics simulation of fully ionized formic acid dimers. Potential energy curves for CO3+ are calculated using the multireference configuration interaction (MRCI+Q) method to confirm the existence of an excited metastable 2Σ state with a significant potential barrier with respect to dissociation. This combined experimental and theoretical effort reveals the existence of metastable CO3+ through direct observation for the first time.

Quantum Rényi entropy by optimal thermodynamic integration paths

Despite being a well-established operational approach to quantify entanglement, Rényi entropy calculations have been plagued by their computational complexity. We introduce here a theoretical framework based on an optimal thermodynamic integration scheme, where the Rényi entropy can be efficiently evaluated using regularizing paths. This approach avoids slowly convergent fluctuating contributions and leads to low-variance estimates. In this way, large system sizes and high levels of entanglement in model or first-principles Hamiltonians are within our reach. We demonstrate this approach in the one-dimensional quantum Ising model and perform an evaluation of entanglement entropy in the formic acid dimer, by discovering that its two shared protons are entangled even above room temperature.Received 29 December 2021Accepted 9 June 2022DOI:https://doi.org/10.1103/PhysRevResearch.4.L032002Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasChemical Physics & Physical ChemistryEntanglement entropyPath integralsQuantum phase transitionsTechniquesMonte Carlo methodsCondensed Matter, Materials & Applied PhysicsQuantum InformationStatistical Physics

Improved proton-transfer barriers with van der Waals density functionals: Role of repulsive non-local correlation.

Proton-transfer (PT) between organic complexes is a common and important biochemical process. Unfortunately, PT energy barriers are difficult to accurately predict using density functional theory (DFT); in particular, using the generalized gradient approximation (GGA) tends to underestimate PT barriers. Moreover, PT typically occurs in environments where dispersion forces contribute to the cohesion of the system; thus, a suitable exchange-correlation functional should accurately describe both dispersion forces and PT barriers. This paper provides benchmark results for the PT barriers of several density functionals, including several variants of the van der Waals density functional (vdW-DF). The benchmark set comprises small organic molecules with inter- and intra-molecular PT. The results show that replacing GGA correlation with a fully non-local vdW-DF correlation increases the PT barriers, making it closer to the quantum chemical reference values. In contrast, including non-local correlations with the Vydrov-Voorhis method or dispersion-corrections at the DFT-D3 or the Tkatchenko-Scheffler level has barely any impact on the PT barriers. Hybrid functionals also increase and improve the energies, resulting in an excellent performance of hybrid versions of vdW-DF-cx and vdW-DF2-B86R. For the formic acid dimer PT system, we analyzed the GGA exchange and non-local correlation contributions. The analysis shows that the repulsive part of the non-local correlation kernel plays a key role in the PT energy barriers predicted with vdW-DF.

Concerted Double Hydrogen-Bond Breaking by Intermolecular Coulombic Decay in the Formic Acid Dimer.

Hydrogen bonds are ubiquitous in nature and of fundamental importance to the chemical and physical properties of molecular systems in the condensed phase. Nevertheless, our understanding of the structural and dynamical properties of hydrogen-bonded complexes in particular in electronic excited states remains very incomplete. Here, by using formic acid (FA) dimer as a prototype of DNA base pair, we investigate the ultrafast decay process initiated by removal of an electron from the inner-valence shell of the molecule upon electron-beam irradiation. Through fragment-ion and electron coincident momentum measurements and ab initio calculations, we find that de-excitation of an outer-valence electron at the same site can initiate ultrafast energy transfer to the neighboring molecule, which is in turn ionized through the emission of low-energy electrons. Our study reveals a concerted breaking of double hydrogen-bond in the dimer initiated by the ultrafast molecular rotations of two FA+ cations following this nonlocal decay mechanism.

Free Energy Profiles of Proton Transfer Reactions: Density Functional Benchmark from Biased Ab Initio Dynamics.

By coupling an enhanced sampling algorithm with an orbital-localized variant of Car-Parrinello molecular dynamics, the so-called atomic centered density matrix propagation model, we reconstruct the free energy profiles along reaction pathways using different density functional approximations (DFAs) ranging from locals to hybrids. In particular, we compare the computed free energy barrier height of proton transfer (PT) reactions to those obtained by a more traditional static approach, based on the intrinsic reaction coordinate (IRC), for two case systems, namely malonaldehyde and formic acid dimer. The obtained results show that both the IRC profiles and the potentials of mean force, derived from biased dynamic trajectories, are very sensitive to the density functional approximation applied. More precisely, we observe that, with the notable exception of M06-L, local density functionals always strongly underestimate the reaction barrier heights. More generally, we find that also the shape of the free energy profile is very sensitive to the density functional choice, thus highlighting the effect, often neglected, that the choice of DFA has also in the case of dynamics simulations.

Matrix-isolation infrared study of acetaldehyde: Host-dependent vibrational features

The infrared spectra of acetaldehyde were measured in inert gas matrices (Ar, Kr, and N2). The vibrational features were dependent on the host atoms. In particular, in the CO stretching region, the fundamental band (ν4) is bifurcated for Ar, whereas it remains isolated for Kr and N2. The bifurcation could be interpreted as a Fermi-diad where host–guest interactions in the Ar matrix cause the accidental energy tuning of ν4 and 2ν9 levels, which is in contrast with the energy detuning observed for the formic acid dimers reported previously [J. Chem. Phys. 128 (2008) 114310.].

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 (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.