Assessing Permutationally Invariant Polynomial and Symmetric Gradient Domain Machine Learning Potential Energy Surfaces for H3O2.

The singly hydrated hydroxide anion OH-(H2O) is of central importance to a detailed molecular understanding of water; therefore, there is strong motivation to develop a highly accurate potential to describe this anion. While this is a small molecule, it is necessary to have an extensive data set of energies and, if possible, forces to span several important stationary points. Here, we assess two machine-learned potentials, one using the symmetric gradient domain machine learning (sGDML) method and one based on permutationally invariant polynomials (PIPs). These are successors to a PIP potential energy surface (PES) reported in 2004. We describe the details of both fitting methods and then compare the two PESs with respect to precision, properties, and speed of evaluation. While the precision of the potentials is similar, the PIP PES is much faster to evaluate for energies and energies plus gradient than the sGDML one. Diffusion Monte Carlo calculations of the ground vibrational state, using both potentials, produce similar large anharmonic downshift of the zero-point energy compared to the harmonic approximation of the PIP and sGDML potentials. The computational time for these calculations using the sGDML PES is roughly 300 times greater than using the PIP one.

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.

Nuclear Quantum Effects in Hydroxide Hydrate Along the H-Bond Bifurcation Pathway.

Path integral (PI) simulations are used to explore nuclear quantum effects (NQEs) in hydroxide hydrate and its perdeuterated isotopomer along the H-bond bifurcation pathway. Toward this, a new potential energy surface using the symmetric gradient domain machine learning method with ab initio data at the CCSD(T)/aug-cc-pVTZ level is built. From PI umbrella sampling (US) simulations, free energy profiles along the bifurcation coordinate are explored as a function of temperature. At ambient temperature, the bifurcation barrier is increased upon inclusion of NQEs. At low temperatures in the deep tunneling regime, the barrier is strongly decreased and flattened. These trends are examined, and the role of the O-O distance is also investigated through two-dimensional US simulations.

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.

Excited-state proton transfer in a 2-aminopyridine dimer: a surface hopping study.

We present a theoretical investigation of the excited-state intermolecular proton transfer process in a 2-aminopyridine dimer. Previous experimental and theoretical studies on this doubly hydrogen bonded system have attributed an ultrafast 50 fs timescale to the process at low excitation wavelengths and have shown that it involves access to the charge transfer (CT) states of the dimer. We have carried out a trajectory-based surface hopping study of the proton transfer process. To this end, we have further studied the key intersections between locally excited (LE) and CT states that facilitate the proton transfer as well as the eventual ground state return at the XMS-CASPT2 level of theory. The dynamical simulations to investigate the charge transfer-driven event are performed at both the XMS-CASPT2 and TDDFT levels of theory. Trajectories are initiated from the excited states that are either already of CT character or become so upon a short extension of the NH bond. This kind of dynamics is found to be ultrafast with a timescale of about 100 fs, where the dimer rapidly accesses the LE/CT intersection regions en route to single proton transfer. After the transfer, some trajectories are also able to reach the ground state as well through a non-adiabatic transition. In contrast, trajectories that are initiated on an LE state remain on states of that character and do not show proton transfer. However, additionally providing 3 or 4 quanta of initial excitation to the NH stretch was found to promote CT state-driven proton transfer in the dimer.

N-H photodissociation dynamics of electronically excited aniline: a three dimensional time-dependent quantum wavepacket study.

We have simulated the dynamics of 1πσ* state-mediated nonadiabatic N-H bond dissociation in photo-excited aniline (C6H5NH2). A three electronic state diabatic model potential, involving the ground, 1ππ*, and 1πσ* diabatic states, and focussing on the NH2 degrees of freedom alone is constructed using XMS-CASPT2 energies. Using a kinetic energy operator in the polyspherical framework, wavepacket dynamics in three vibrational modes, viz. NH stretch, NH2 out-of-plane wag and torsion, is carried out using the Chebyshev propagation scheme. For optically bright 1ππ* excitation, the wavepacket can access the 1πσ*/1ππ* and 1ππ/1πσ* conical intersections that lie en route to dissociation. For both intersections, NH2 out-of-plane wag and torsional motions are the most dominant coupling coordinates. Carrying out dynamics with initial wavepackets varying in excitation in the three degrees of freedom, we probe their roles in the evolution of the state populations, probability densities, and product branching for the NH dissociation process.

Alkyl hydrogen atom abstraction reactions of the CN radical with ethanol.

We present a study of the abstraction of alkyl hydrogen atoms from the ß and α positions of ethanol by the CN radical in solution using the Empirical Valence Bond (EVB) method. We have built separate 2 × 2 EVB models for the Hß and Hα reactions, where the atom transfer is parameterized using ab initio calculations. The intra- and intermolecular potentials of the reactant and product molecules were modelled with the General AMBER Force Field, with some modifications. We have carried out the dynamics in water and chloroform, which are solvents of contrasting polarity. We have computed the potential of mean force for both abstractions in each of the solvents. They are found to have a small and early barrier along the reaction coordinate with a large energy release. Analyzing the solvent structure around the reaction system, we have found two solvents to have little effect on either reaction. Simulating the dynamics from the transition state, we also study the fate of the energies in the HCN vibrational modes. The HCN molecule is born vibrationally hot in the CH stretch in both reactions and additionally in the HCN bends for the Hα abstraction reaction. In the early stage of the dynamics, we find that the CN stretch mode gains energy at the expense of the energy in CH stretch mode.

Isotopic fractionation in proteins as a measure of hydrogen bond length.

If a deuterated molecule containing strong intramolecular hydrogen bonds is placed in a hydrogenated solvent, it may preferentially exchange deuterium for hydrogen. This preference is due to the difference between the vibrational zero-point energy for hydrogen and deuterium. It is found that the associated fractionation factor Φ is correlated with the strength of the intramolecular hydrogen bonds. This correlation has been used to determine the length of the H-bonds (donor-acceptor separation) in a diverse range of enzymes and has been argued to support the existence of short low-barrier H-bonds. Starting with a potential energy surface based on a simple diabatic state model for H-bonds, we calculate Φ as a function of the proton donor-acceptor distance R. For numerical results, we use a parameterization of the model for symmetric O-H⋯O bonds [R. H. McKenzie, Chem. Phys. Lett. 535, 196 (2012)]. We consider the relative contributions of the O-H stretch vibration, O-H bend vibrations (both in plane and out of plane), tunneling splitting effects at finite temperature, and the secondary geometric isotope effect. We compare our total Φ as a function of R with NMR experimental results for enzymes, and in particular with an earlier model parametrization Φ(R), used previously to determine bond lengths.

Effect of quantum nuclear motion on hydrogen bonding.

This work considers how the properties of hydrogen bonded complexes, X-H⋯Y, are modified by the quantum motion of the shared proton. Using a simple two-diabatic state model Hamiltonian, the analysis of the symmetric case, where the donor (X) and acceptor (Y) have the same proton affinity, is carried out. For quantitative comparisons, a parametrization specific to the O-H⋯O complexes is used. The vibrational energy levels of the one-dimensional ground state adiabatic potential of the model are used to make quantitative comparisons with a vast body of condensed phase data, spanning a donor-acceptor separation (R) range of about 2.4-3.0 Å, i.e., from strong to weak hydrogen bonds. The position of the proton (which determines the X-H bond length) and its longitudinal vibrational frequency, along with the isotope effects in both are described quantitatively. An analysis of the secondary geometric isotope effect, using a simple extension of the two-state model, yields an improved agreement of the predicted variation with R of frequency isotope effects. The role of bending modes is also considered: their quantum effects compete with those of the stretching mode for weak to moderate H-bond strengths. In spite of the economy in the parametrization of the model used, it offers key insights into the defining features of H-bonds, and semi-quantitatively captures several trends.

A multi-sheeted three-dimensional potential-energy surface for the H-atom photodissociation of phenol.

Extending the previous work of Lan et al. [J. Chem. Phys., 122, 224315 (2005)], a multi-state potential model for the H atom photodissociation is presented. All three "disappearing coordinates" of the departing H atom have been considered. Ab initio CASSCF computations have been carried out for the linear COH geometry of C(2v) symmetry, and for several COH angles with the OH group in the ring plane and also perpendicular to the ring plane. By keeping the C6H5O fragment frozen in a C(2v)-constrained geometry throughout, we have been able to apply symmetry-based simplifications in the constructions of adiabatic model. This model is able to capture the overall trends of twelve adiabats at both torsional limits for a wide range of COH bend angles.

Vibrational symmetry breaking of NO3- in aqueous solution: NO asymmetric stretch frequency distribution and mean splitting.

We apply a solute-solvent approach to a theoretical study of vibrational symmetry breaking in aqueous NO(3)(-) solution. Experimental infrared and Raman spectra have shown that the NO asymmetric stretches, which are degenerate for the isolated anion, are split by 35-60 cm(-1) in dilute solution. As an initial step to calculating the spectra, we have computed the distribution of energies, or the "static spectrum", and the resulting mean splitting of the two NO asymmetric stretch eigenstates in an aqueous milieu. These have been obtained in a two-mode treatment that considers only the NO asymmetric stretch mode pair as well as a full six-mode treatment. In both sets of calculations, six eigenstates, namely, the ground state, the two NO asymmetric stretch fundamentals, and its three overtones, were determined to suffice for converged energy distributions and mean splittings. The couplings between these six states are driven by the solvent forces on the anion's modes, which were extracted from molecular dynamics simulations. The solvent forces on the two central modes were found to give rise to a majority of the computed mean splitting of 21.7 cm(-1). The distribution of NO asymmmetric stretch excitation energies with these two modes alone was found to have a Maxwell-Boltzmann shape. The solvent forces on the in-plane bends were found to modestly reduce the splitting size and slightly alter the width of the parent distribution. The symmetric stretch force was found to have no effect on the splitting but instead resulted in a widening on the distribution shape. The force gradients were found to have a weak effect on both the eigenvalue distribution and the mean splitting.

Vibrational relaxation of OH and CH fundamentals of polar and nonpolar molecules in the condensed phase.

Studies of vibrational energy flow in various polar and nonpolar molecules that follows the ultrafast excitation of the CH and OH stretch fundamentals, modeled using semiclassical methods, are reviewed. Relaxation rates are calculated using Landau-Teller theory and a time-dependent method, both of which consider a quantum mechanical solute molecule coupled to a classical bath of solvent molecules. A wide range of decay rates are observed, ranging from 1 ps for neat methanol to 50 ps for neat bromoform. In order to understand the flow rates, it is argued that an understanding of the subtle mixing between the solute eigenstates is needed and that solute anharmonicities are critical to facilitating condensed phase vibrational relaxation. The solvent-assisted shifts of the solute vibrational energy levels are seen to play a critical role of enhancing or decreasing lifetimes.

Charge transfer and OH vibrational frequency red shifts in nitrate-water clusters.

A theoretical study of charge transfer (CT) characteristics in nitrate (NO3(-)) anion-water complexes is presented, together with those for the halides, F-, Cl-, and Br-, for comparison. The relation between the vibrational frequency red shifts of the hydrogen (H)-bonded OH stretches and CT from the anion to the water molecule, established in previous work for the one-water complexes of the halides, is studied for both the one- and six-water nitrate complexes and is extended to the six-water case for the halides. In NO3(-) x H2O, the water molecule receives about as much charge as that in Br- x H2O. In a result consistent with aqueous phase infrared experiments [Bergström, P. A.; Lindgren, J.; Kristiansson, O. J. Phys. Chem. 1991, 95, 8575-8580], the CT and OH red shift in NO3(-) x 6 H2O are found to be smaller than those for all of the six-water halide complexes, despite the presence of three H-bonding sites. The inability of the nitrate anion to effect substantial CT lies in the preservation of the pi-system being energetically favored over charge localization and enhancement of the strengths of the multiple H-bonds.

Vibrational relaxation of the CH stretch fundamental in liquid CHBr3.

In continuation of our work on haloforms, the decay of CH stretch excitation in bromoform is modeled using molecular dynamics simulations. An intermolecular force field is obtained by fitting ab initio energies at select CHBr3 dimer geometries to a potential function. The solvent forces on vibrational modes obtained in the simulation are used to compute relaxation rates. The Landau-Teller approach points to a single acceptor state in the initial step of CH stretch relaxation. The time scale for this process is found to be 50-90 ps, which agrees well with the experimental value of 50 ps. The reason for the selectivity of the acceptor is elaborated. Results from a time-dependent approach to the decay rates are also discussed.

Combination of perturbative and variational methods for calculating molecular spectra: calculation of the upsilon=3-5 CH stretch overtone spectrum of CHF3.

Highly excited states of the CHF3 molecule belonging to the third, fourth, and fifth Fermi polyad are calculated using a combination of the Van Vleck perturbation theory and a variational treatment. The perturbation theory preconditions the Hamiltonian matrix by transforming away all couplings except those between nearly degenerate states. This transformation is implemented so that eigenvalues can be found with significantly smaller matrices than that which would be needed in the original normal mode representation. Even with preconditioning, at the energies as high as 3-5 quanta in the CH stretch, it is not possible to directly diagonalize the Hamiltonian matrix due to the large basis sets required. Iterative methods, particularly the block-Davidson method, are explored for finding the eigenvalues. The methods are compared and the advantages discussed.

Time scales and pathways of vibrational energy relaxation in liquid CHBr3 and CDBr3.

Molecular dynamics simulations are used in conjunction with Landau-Teller, fluctuating Landau-Teller, and time-dependent perturbation theories to investigate energy flow out of various vibrational states of liquid CHBr3 and CDBr3. The CH stretch overtone is found to relax with a time scale of about 1 ps compared to the 50 ps rate for the fundamental. The relaxation pathways and rates for the CD stretch decay in CDBr3 are computed in order to understand the changes arising from deuteration. While the computed relaxation rate agrees well with experiments, the pathway is found to be more complex than anticipated. In addition to the above channels for CH(D) stretch relaxation that involve only the hindered translations and rotations of the solvent, routes involving off-resonant and resonant excitations of solvent vibrational modes are also examined. Finally, the decay of energy from low frequency states to near-lying solute states and solvent vibrations are studied.

Relaxation of the CH stretch in liquid CHBr3: solvent effects and decay rates using classical nonequilibrium simulations.

This article addresses two questions regarding the decay of the CH stretch in liquid CHBr3. The first is whether the initial steps of the relaxation primarily involve energy redistribution within the excited molecule alone. Gas phase quantum mechanical and classical calculations are performed to examine the role of the solvent in this process. At the fundamental excitation level, it is found that CH stretch decay is, in fact, strongly solvent driven. The second question is on the applicability of a fully classical approach to the calculation of CH stretch condensed phase decay rates. To this end, nonequilibrium molecular dynamics simulations are performed. The results are compared with quantum mechanical rates computed previously. The two methods are found to be in fair agreement with each other. However, care must be exercised in the interpretation of the classical results.

Combined perturbative-variational investigation of the vibrations of CHBr(3) and CDBr(3).

A full dimensional vibrational treatment of CHBr(3) and CDBr(3) using Van Vleck perturbation theory followed by a variational calculation is presented. The calculation of a force field, and its adjustment for better match with experiment, is discussed. The computed eigenstates and spectral features are compared to experiment. Changes in intensities of the nu(1) and 2nu(4) bands upon simple alterations of the dipole moment expansion are described.