Fast Near Ab Initio Potential Energy Surfaces Using Machine Learning.

A machine-learning based approach for evaluating potential energies for quantum mechanical studies of properties of the ground and excited vibrational states of small molecules is developed. This approach uses the molecular-orbital-based machine learning (MOB-ML) method to generate electronic energies with the accuracy of CCSD(T) calculations at the same cost as a Hartree-Fock calculation. To further reduce the computational cost of the potential energy evaluations without sacrificing the CCSD(T) level accuracy, GPU-accelerated Neural Network Potential Energy Surfaces (NN-PES) are trained to geometries and energies that are collected from small-scale Diffusion Monte Carlo (DMC) simulations, which are run using energies evaluated using the MOB-ML model. The combined NN+(MOB-ML) approach is used in variational calculations of the ground and low-lying vibrational excited states of water and in DMC calculations of the ground states of water, CH5+, and its deuterated analogues. For both of these molecules, comparisons are made to the results obtained using potentials that were fit to much larger sets of electronic energies than were required to train the MOB-ML models. The NN+(MOB-ML) approach is also used to obtain a potential surface for C2H5+, which is a carbocation with a nonclassical equilibrium structure for which there is currently no available potential surface. This potential is used to explore the CH stretching vibrations, focusing on those of the bridging hydrogen atom. For both CH5+ and C2H5+ the MOB-ML model is trained using geometries that were sampled from an AIMD trajectory, which was run at 350 K. By comparison, the structures sampled in the ground state calculations can have energies that are as much as ten times larger than those used to train the MOB-ML model. For water a higher temperature AIMD trajectory is needed to obtain accurate results due to the smaller thermal energy. A second MOB-ML model for C2H5+ was developed with additional higher energy structures in the training set. The two models are found to provide nearly identical descriptions of the ground state of C2H5+.

Using Diffusion Monte Carlo Wave Functions to Analyze the Vibrational Spectra of H7O3+ and H9O4.

An approach for evaluating spectra from ground state probability amplitudes (GSPA) obtained from diffusion Monte Carlo (DMC) simulations is extended to improve the description of excited state energies and allow for coupling among vibrational excited states. This approach is applied to studies of the protonated water trimer and tetramer, and their deuterated analogs. These ions provide models for solvated hydronium, and analysis of these spectra provides insights into spectral signatures of proton transfer in aqueous environments. In this approach, we obtain a separable set of internal coordinates from the DMC ground state probability amplitude. A basis is then developed from products of the DMC ground state wave function and low-order polynomials in these internal coordinates. This approach provides a compact basis in which the Hamiltonian and dipole moment matrix are evaluated and used to obtain the spectrum. The resulting spectra are in good agreement with experiment and in many cases provide comparable agreement to the results obtained using much larger basis sets. In addition, the compact basis allows for interpretation of the spectral features and how they evolve with cluster size and deuteration.

GPU-Accelerated Neural Network Potential Energy Surfaces for Diffusion Monte Carlo.

Diffusion Monte Carlo (DMC) provides a powerful method for understanding the vibrational landscape of molecules that are not well-described by conventional methods. The most computationally demanding step of these calculations is the evaluation of the potential energy. In this work, a general approach is developed in which a neural network potential energy surface is trained by using data generated from a small-scale DMC calculation. Once trained, the neural network can be evaluated by using highly parallelizable calls to a graphics processing unit (GPU). The power of this approach is demonstrated for DMC simulations on H2O, CH5+, and (H2O)2. The need to include permutation symmetry in the neural network potentials is explored and incorporated into the molecular descriptors of CH5+ and (H2O)2. It is shown that the zero-point energies and wave functions obtained by using the neural network potentials are nearly identical to the results obtained when using the potential energy surfaces that were used to train the neural networks at a substantial savings in the computational requirements of the simulations.

Isolating the Contributions of Specific Network Sites to the Diffuse Vibrational Spectrum of Interfacial Water with Isotopomer-Selective Spectroscopy of Cold Clusters.

Decoding the structural information contained in the interfacial vibrational spectrum of water requires understanding how the spectral signatures of individual water molecules respond to their local hydrogen bonding environments. In this study, we isolated the contributions for the five classes of sites that differ according to the number of donor (D) and acceptor (A) hydrogen bonds that characterize each site. These patterns were measured by exploiting the unique properties of the water cluster cage structures formed in the gas phase upon hydration of a series of cations M+·(H2O)n (M = Li, Na, Cs, NH4, CH3NH3, H3O, and n = 5, 20-22). This selection of ions was chosen to systematically express the A, AD, AAD, ADD, and AADD hydrogen bonding motifs. The spectral signatures of each site were measured using two-color, IR-IR isotopomer-selective photofragmentation vibrational spectroscopy of the cryogenically cooled, mass selected cluster ions in which a single intact H2O is introduced without isotopic scrambling, an important advantage afforded by the cluster regime. The resulting patterns provide an unprecedented picture of the intrinsic line shapes and spectral complexities associated with excitation of the individual OH groups, as well as the correlation between the frequencies of the two OH groups on the same water molecule, as a function of network site. The properties of the surrounding water network that govern this frequency map are evaluated by dissecting electronic structure calculations that explore how changes in the nearby network structures, both within and beyond the first hydration shell, affect the local frequency of an OH oscillator. The qualitative trends are recovered with a simple model that correlates the OH frequency with the network-modulated local electron density in the center of the OH bond.

Guided Diffusion Monte Carlo: A Method for Studying Molecules and Ions That Display Large Amplitude Vibrational Motions.

Diffusion Monte Carlo provides an effective and efficient approach for calculating ground state properties of molecular systems based on potential energy surfaces. The approach has been shown to require increasingly large ensembles when intra- and intermolecular vibrations are weakly coupled. We recently proposed a guided variant of diffusion Monte Carlo to address these challenges for water clusters [Lee, V. G. M.; McCoy, A. B. J. Phys. Chem. A 2019, 123, 8063-8070]. In the present study, we extend this approach and apply it to more strongly bound molecular ions, specifically CH5+ and H+(H2O)n=1-4. For the protonated water systems, we show that the guided DMC approach that was developed for studies of (H2O)n can be used to describe the OH stretches and HOH bends in the solvating water molecules, as well as the free OH stretches in the hydronium core. For the hydrogen bonded OH stretches in the H3O+ core of H+(H2O)n and the CH stretches in CH5+, we develop adaptive guiding functions based on the instantaneous structure of the ion of interest. Using these guiding functions, we demonstrate that we are able to obtain converged zero-point energies and ground state wave functions using ensemble sizes that are as small as 10% the size that is needed to obtain similar accuracy from unguided calculations.

Disentangling the Complex Vibrational Mechanics of the Protonated Water Trimer by Rational Control of Its Hydrogen Bonds.

The vibrational spectrum of the protonated water trimer, H+(H2O)3, is surprisingly complex, with many strong features in the expected region of the fundamentals associated with two H-bonded OH groups on the H3O+ core ion. Here we follow how the bands in this region of the spectrum evolve when the energies of the fundamentals in the H-bonded OH stretches are systematically increased by the attachment of increasingly strongly bound "tag" molecules (He, Ar, D2, N2, CO, and H2O) to the free OH position on the hydronium core ion of H+(H2O)3, as well as by replacement of the hydrogen atom in the nonbonded OH group on hydronium with methyl and ethyl groups. This allows for the incremental transformation of the complex band pattern observed in H+(H2O)3 into that of the "Eigen" structure of the protonated water tetramer. Differences among the trajectories of the various bands provide an empirical way to disentangle features primarily due to the displacements of the OH stretches bound to the hydronium core from those arising from anharmonic coupling to states involving one or more quanta in lower frequency modes. The latter are found to be dramatically enhanced when the nominal frequencies of the intermolecular OH stretching modes approach those of the intramolecular bends of the H3O+ and H2O constituents in both H and D isotopologues.

Spectral signatures of proton delocalization in H+(H2O)n=1-4 ions.

Couplings involving large amplitude vibrations in H+(H2O)n (n = 1-4) are explored using several theoretical approaches. These include harmonic treatments, analysis of harmonically coupled anharmonic oscillator (HCAO) models of the OH stretching vibrations, vibrational perturbation theory (VPT2) in internal coordinates, and diffusion Monte Carlo (DMC). It is found that couplings between shared proton stretches and HOH bends can lead to normal modes that are significantly mixed in character. Couplings between the various OH stretching vibrations are much weaker, and the OH stretches are well-described by harmonically coupled anharmonic oscillator models. Anharmonic couplings and the role of these large amplitude vibrations are further explored using DMC and VPT2. Based on the results of these calculations, it is found that all of the H+(H2O)n ions considered in this study display several different types of large amplitude vibrational motions even in their ground states. In the case of H7O3+, degenerate VPT2 calculations indicate that there are large couplings between the shared proton stretch and various lower frequency vibrations that correspond to motions that break the ionic hydrogen bonds. This leads to vibrational eigenstates that have contributions from several zero-order states.

Tag-Free and Isotopomer-Selective Vibrational Spectroscopy of the Cryogenically Cooled H9O4+ Cation with Two-Color, IR-IR Double-Resonance Photoexcitation: Isolating the Spectral Signature of a Single OH Group in the Hydronium Ion Core.

We report vibrational spectra of the cryogenically cooled H9O4+ cation along with those of the D2 tagged HD8O4+ isotopomers using two variations on a two-color, IR-IR double-resonance photoexcitation scheme. The spectrum of the isolated H9O4+ ion consists of two sharp features in the OH stretching region that indicate exclusive formation of the "Eigen" cation, the H3O+·(H2O)3 isomer that corresponds to the filled hydration shell around the hydronium ion. Consistent with this structural assignment, the spectrum of the HD8O4+ isotopologue is resolved into contributions from two isotopomers: one with the single OH group on one of the three solvent water molecules and another in which it resides on the hydronium core ion. The latter spectrum is dominated by a broad feature assigned to the isolated hydronium OH stretching fundamental with an envelope that is similar to that displayed by the H3O+·(H2O)3 isotopologue. The feature appears with a diffuse band ∼380 cm-1 above it, which is assigned to a combination band involving the hydronium OH stretching vibration and the frustrated translation mode of the HD2O+ core and one of the solvating water molecules. These trends are analyzed with anharmonic calculations involving four-mode coupling on a realistic potential surface and interpreted in the context of vibrationally adiabatic potentials based on insights acquired from analysis of the ground state probability amplitudes obtained from diffusion Monte Carlo calculations.

Cobalt Schiff-base complexes for electrocatalytic hydrogen generation.

Two cobalt(iii) complexes containing inexpensive Schiff-base ligands have been found to be active for proton reduction at low overpotentials. The dinitro and tetranitro derivatized Schiff-base complexes show catalytic activity at -0.96 V and -1.1 V vs. Fc+/Fc, respectively, resulting in overpotentials of 120 mV and 280 mV. Foot-of-the-wave analysis is used to examine the kinetic properties of these complexes, yielding a theoretical TOFmax of up to 4100 s-1. Experimental TOFs of 7 s-1and 3 s-1 are observed. Catalytic Tafel plots are also presented in order to benchmark the relationship between turnover frequency and overpotential.

Iron Polypyridyl Complexes for Photocatalytic Hydrogen Generation.

A series of Fe(III) complexes were recently reported that are stable and active electrocatalysts for reducing protons into hydrogen gas. Herein, we report the incorporation of these electrocatalysts into a photocatalytic system for hydrogen production. Hydrogen evolution is observed when these catalysts are paired with fluorescein (chromophore) and triethylamine (sacrificial electron source) in a 1:1 ethanol:water mixture. The photocatalytic system is highly active and stable, achieving TONs > 2100 (with respect to catalyst) after 24 h. Catalysis proceeds through a reductive quenching pathway with a quantum yield of over 3%.