A reaction surface Hamiltonian study of malonaldehyde

Nuclear quantum effects in gas-phase ethylene glycol

Path integral molecular simulations are used to explore the nuclear quantum effects (NQEs) on the structure, dihedral landscape and infrared spectrum of ethylene glycol. The simulations are carried out on a new reaction surface Hamiltonian-based model potential energy surface, with special focus on the role of the OCCO and HOCC dihedrals. In contrast with classical simulations, we analyse how the intramolecular interactions between the OH groups change due to zero-point effects as well as temperature. These are found to be weak. The NQEs on the free energy profile along the OCCO dihedral are analysed, where notable effects are seen at low temperatures and found to be correlated with the radii of gyration of the atoms. Finally, the power spectrum of the molecule from path integral simulations is compared with the experimental infrared spectrum, yielding a good agreement of band positions.

Nuclear quantum effects in gas-phase 2-fluoroethanol

Torsional motions along the FCCO and HOCC dihedrals lead to the five unique conformations of 2-fluoroethanol, of which the conformer that is gauche along both dihedrals has the lowest energy. In this work, we explore how nuclear quantum effects (NQEs) manifest in the structural parameters of the lowest energy conformer, in the intramolecular free energy landscape along the FCCO and HOCC dihedrals, and also in the infrared spectrum of the title molecule, through the use of path integral simulations. We have first developed a full dimensional potential energy surface using the reaction surface Hamiltonian framework. On this potential, we have carried out path integral molecular dynamics simulations at several temperatures starting from the minimum energy well to explore structural influences of NQEs including geometrical markers of the interaction between the OH and F groups. From the computed free energy landscapes, significant reduction of the torsional barrier is found at low temperature near the cis region of the dihedrals, which can be understood through the trends in the radii of gyration of the atomic ring polymers. We find that the inclusion of NQEs in the computation of infrared spectrum is important to obtain good agreement with the experimental band positions.

Smolyak Scheme for solving the Schrödinger equation: Application to Malonaldehyde in Full Dimensionality

In 1963 Smolyak introduced an approach to overcome the exponential scaling with respect to the number of variables of the direct product size [S. A. Smolyak Soviet Mathematics Doklady, 4, 240 (1963)]. The main idea is to replace a single large direct product by a sum of selected small direct products. It was first used in quantum dynamics in 2009 by Avila and Carrington [G. Avila and T. Carrington, J. Chem. Phys., 131, 174103 (2009)]. Since then, several calculations have been published by Avila and Carrington and by other groups. In the present study, and to push the limit to larger and more complex systems, this scheme is combined with the use of an on-the-fly calculation of the kinetic energy operator and a Block-Davidson procedure to obtain eigenstates in our home-made Fortran codes, ElVibRot and Tnum-Tana. This was applied to compute the tunneling splitting of malonaldehyde in full dimensionality (21D) using the potential of Mizukami et al. [W. Mizukami, S. Habershon, and D.P. Tew, J. Chem. Phys. 141, 1443-10 (2014)]. Our tunneling splitting calculations, 21.7±0.3 cm-1 and 2.9±0.1 cm-1 , show excellent agreement with the experimental values, 21.6 cm-1 and 2.9 cm-1 for the normal isotopologue and the mono-deuterated one, respectively.

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.

Analytical gradients for nuclear–electronic orbital multistate density functional theory: Geometry optimizations and reaction paths

Hydrogen tunneling plays a critical role in many biologically and chemically important processes. The nuclear–electronic orbital multistate density functional theory (NEO-MSDFT) method was developed to describe hydrogen transfer systems. In this approach, the transferring proton is treated quantum mechanically on the same level as the electrons within multicomponent DFT, and a nonorthogonal configuration interaction scheme is used to produce delocalized vibronic states from localized vibronic states. The NEO-MSDFT method has been shown to provide accurate hydrogen tunneling splittings for fixed molecular systems. Herein, the NEO-MSDFT analytical gradients for both ground and excited vibronic states are derived and implemented. The analytical gradients and semi-numerical Hessians are used to optimize and characterize equilibrium and transition state geometries and to generate minimum energy paths (MEPs), for proton transfer in the deprotonated acetylene dimer and malonaldehyde. The barriers along the resulting MEPs are lower when the transferring proton is quantized because the NEO-MSDFT method inherently includes the zero-point energy of the transferring proton. Analysis of the proton densities along the MEPs illustrates that the proton density can exhibit symmetric or asymmetric bilobal character associated with symmetric or slightly asymmetric double-well potential energy surfaces and hydrogen tunneling. Analysis of the contributions to the intrinsic reaction coordinate reveals that changes in the C–O bond lengths drive proton transfer in malonaldehyde. This work provides the foundation for future reaction path studies and direct nonadiabatic dynamics simulations of a wide range of hydrogen transfer reactions.

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.

Perturbing the O-H…O Hydrogen Bond in 1-oxo-3-hydroxy-2-propene

Ab initio MP2/aug'-cc-pVTZ calculations have been carried out to identify and characterize equilibrium structures and transition structures on the 1-oxo-3-hydroxy-2-propene: Lewis acid potential energy surfaces, with the acids LiH, LiF, BeH2, and BeF2. Two equilibrium structures, one with the acid interacting with the C=O group and the other with the interaction occurring at the O-H group, exist on all surfaces. These structures are separated by transition structures that present the barriers to the interconversion of the two equilibrium structures. The structures with the acid interacting at the C=O group have the greater binding energies. Since the barriers to convert the structures with interaction occurring at the O-H group are small, only the isomers with interaction occurring at the C=O group could be experimentally observed, even at low temperatures. Charge-transfer energies were computed for equilibrium structures, and EOM-CCSD spin-spin coupling constants 2hJ(O-O), 1hJ(H-O), and 1J(O-H) were computed for equilibrium and transition structures. These coupling constants exhibit a second-order dependence on the corresponding distances, with very high correlation coefficients.

On the separability of large-amplitude motions in anharmonic frequency calculations

Nuclear vibrational theories based upon the Watson Hamiltonian are ubiquitous in quantum chemistry, but are generally unable to model systems in which the wavefunction can delocalise over multiple energy minima, i.e. molecules that have low-energy torsion and inversion barriers. In a 2019 Chemical Reviews article, Puzzarini et al. note that a common workaround is to simply decouple these problematic modes from all other vibrations in the system during anharmonic frequency calculations. They also point out that this approximation can be "ill-suited", but do not quantify the errors introduced. In this work, we present the first systematic investigation into how separating out or constraining torsion and inversion vibrations within potential energy surface (PES) expansions affects the accuracy of computed fundamental wavenumbers for the remaining vibrational modes, using a test set of 19 tetratomic molecules for which high quality analytic potential energy surfaces and fully-coupled anharmonic reference fundamental frequencies are available. We find that the most effective and efficient strategy is to remove the mode in question from the PES expansion entirely. This introduces errors of up to +10 cm-1 in stretching fundamentals that would otherwise couple to the dropped mode, and ±5 cm-1 in all other fundamentals. These errors are approximately commensurate with, but not necessarily additional to, errors due to the choice of electronic structure model used in constructing spectroscopically accurate PES.

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.

Monitoring transient events in infrared spectra using local mode analysis

Time-resolved Fourier transformed infrared (FTIR) spectroscopy of chemical reactions is highly sensitive to minimal spatiotemporal changes. Structural features are decoded and represented in a comprehensible manner by combining FTIR spectroscopy with biomolecular simulations. Local mode analysis (LMA) is a tool to connect molecular motion based on a quantum mechanics simulation with infrared (IR) spectral features and vice versa. Here, we present the python-based software tool of LMA and demonstrate the novel feature of LMA to extract transient structural details and identify the related IR spectra at the case example of malonaldehyde (MA). Deuterated MA exists in two almost equally populated tautomeric states separated by a low barrier for proton transfer so IR spectra represent a mixture of both states. By state-dependent LMA, we obtain pure spectra for each tautomeric state occurring within the quantum mechanics trajectory. By time-resolved LMA, we obtain a clear view of the transition between states in the spectrum. Through local mode decomposition and the band-pass filter, marker bands for each state are identified. Thus, LMA is beneficial to analyze the experimental spectra based on a mixture of states by determining the individual contributions to the spectrum and motion of each state.

Toward a General Yet Effective Computational Approach for Diffusive Problems: Variable Diffusion Tensor and DVR Solution of the Smoluchowski Equation along a General One-Dimensional Coordinate

A generalization to arbitrary large amplitude motions of a recent approach to the evaluation of diffusion tensors [ J. Comput. Chem. , 2009 , 30 , 2 - 13 ] is presented and implemented in a widely available package for electronic structure computations. A fully black-box tool is obtained, which, starting from the generation of geometric structures along different kinds of paths, proceeds toward the evaluation of an effective diffusion tensor and to the solution of one-dimensional Smoluchowski equations by a robust numerical approach rooted in the discrete variable representation (DVR). Application to a number of case studies shows that the results issuing from our approach are identical to those delivered by previous software (in particular DiTe) for rigid scans along a dihedral angle, but can be improved by employing relaxed scans (i.e., constrained geometry optimizations) or even more general large amplitude paths. The theoretical and numerical background is robust and general enough to allow quite straightforward extensions in several directions (e.g., inclusion of reactive paths, solution of Fokker-Planck or stochastic Liouville equations, multidimensional problems, free-energy rather than electronic-energy driven processes).

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).

Harmonic bath averaged Hamiltonian: an efficient tool to capture quantum effects of large systems

Starting from a reaction path Hamiltonian, a suitably reduced harmonic bath averaged Hamiltonian is derived by averaging over all the normal mode coordinates. Generalization of the harmonic bath averaged Hamiltonian to any dimensions are performed and the feasibility to use a linear reaction path/surface are investigated and discussed. By use of a harmonic bath averaged Hamiltonian, the tunneling splitting and proton transfer dynamics of malonaldehyde is briefly discussed and shows that the harmonic bath averaged Hamiltonian is an efficient tool to capture quantum effects in larger systems.

A generalized reactive force field for nonlinear hydrogen bonds: hydrogen dynamics and transfer in malonaldehyde

Using molecular dynamics (MD) simulations, the spectroscopy and dynamics of malonaldehyde is investigated. To this end, the recently proposed molecular mechanics with proton transfer (MMPT) potential is generalized to nonlinear hydrogen bonds. The calculated properties for malonaldehyde in both gas and condensed phases, including equilibrium geometries, infrared spectra, tunneling splittings, and hydrogen transfer rates, compare well with previous experimental and computational works. In particular, by using a harmonic bath averaged (HBA) Hamiltonian, which is based on a reaction path Hamiltonian, it is possible to estimate the tunneling splitting in an efficient manner. It is found that a zero point corrected barrier of 6.7 kcal/mol and effective masses of 1.234 (i.e., 23.4% larger than the mass of a physical H-atom) and 1.117 (for the physical D-atom) are consistent with the measured splittings of 21.6 and 2.9 cm(-1), respectively. The HBA Hamiltonian also yields a pair of hydrogen transfer fundamentals at 1573 and 1267 cm(-1), similar to results obtained with a reaction surface Hamiltonian on a MP2/6-31G(**) potential energy surface. This amounts to a substantial redshift of more than 1000 cm(-1) which can be rationalized by comparison with weakly (HCO(+): rare gas) and strongly (H(2)O-H(+)-OH(2)) proton-bound systems. Hydrogen transfer rates in vacuum and water were determined from the validated MMPT potential and it is found that the solvent enhances the rate by a factor of 5 at 300 K. The rates of 2.4/ns and 10/ns are commensurate with previous density functional tight binding ab initio MD studies.

Combining the nuclear-electronic orbital approach with vibronic coupling theory: calculation of the tunneling splitting for malonaldehyde

The nuclear-electronic orbital (NEO) method is combined with vibronic coupling theory to calculate hydrogen tunneling splittings in polyatomic molecules. In this NEO-vibronic coupling approach, the transferring proton and all electrons are treated quantum mechanically at the NEO level, and the other nuclei are treated quantum mechanically using vibronic coupling theory. The dynamics of the molecule are described by a vibronic Hamiltonian in a diabatic basis of two localized nuclear-electronic states for the electrons and transferring proton. This ab initio approach is computationally practical and efficient for relatively large molecules, and the accuracy can be improved systematically. The NEO-vibronic coupling approach is used to calculate the hydrogen tunneling splitting for malonaldehyde. The calculated tunneling splitting of 24.5 cm(-1) is in excellent agreement with the experimental value of 21.6 cm(-1). This approach also enables the identification of the dominant modes coupled to the transferring hydrogen motion and provides insight into their roles in the hydrogen tunneling process.

Large curvature tunnelling on the reaction path

The reaction path Hamiltonian [J. Chem. Phys., 1980, 72(1), 99] has found few if any successful applications to the explicit treatment of hydrogen tunnelling dynamics in the limit of large path curvature which is typical for hydrogen exchange tunnelling. I argue hat this is due to fundamental limitations of the reaction path formulation. A two-dimensional model mimicking the intramolecular hydrogen transfer in malonaldehyde shows that commonly used approximations can produce misleading results. As a solution to the problem I propose a non-orthogonal representation of the Hamiltonian in terms of local harmonic oscillators distributed along the reaction path. In contrast to the usual reaction path Hamiltonian it has an exact variational limit for all curvatures. This distributed harmonic oscillator approach has the added advantages of stability against variations of the reaction path as well as the ability to treat bifurcating paths.