The Near-Sightedness of Many-Body Interactions in Anharmonic Vibrational Couplings.

Couplings between vibrational motions are driven by electronic interactions, and these couplings carry special significance in vibrational energy transfer, multidimensional spectroscopy experiments, and simulations of vibrational spectra. In this investigation, the many-body contributions to these couplings are analyzed computationally in the context of clathrate-like alkali metal cation hydrates, including Cs+(H2O)20, Rb+(H2O)20, and K+(H2O)20, using both analytic and quantum-chemistry potential energy surfaces. Although the harmonic spectra and one-dimensional anharmonic spectra depend strongly on these many-body interactions, the mode-pair couplings were, perhaps surprisingly, found to be dominated by one-body effects, even in cases of couplings to low-frequency modes that involved the motion of multiple water molecules. The origin of this effect was traced mainly to geometric distortion within water monomers and cancellation of many-body effects in differential couplings, and the effect was also shown to be agnostic to the identity of the ion. These outcomes provide new understanding of vibrational couplings and suggest the possibility of improved computational methods for the simulation of infrared and Raman spectra.

IR spectroscopic characterization of [M,C,2H]+ (M = Ru and Rh) products formed by reacting 4d transition metal cations with oxirane: Spectroscopic evidence for multireference character in RhCH2.

A combination of infrared multiple-photon dissociation (IRMPD) action spectroscopy and quantum chemical calculations was employed to investigate the [M,C,2H]+ (M = Ru and Rh) species. These ions were formed by reacting laser ablated M+ ions with oxirane (ethylene oxide, c-C2H4O) in a room-temperature ion trap. IRMPD spectra for the Ru species exhibit one major band and two side bands, whereas spectra for the Rh species contain more distinct bands. Comparison with density functional theory (DFT), coupled-cluster (CCSD), and equation-of-motion spin-flip CCSD (EOM-SF-CCSD) calculations allows assignment of the [M,C,2H]+ structures. For the spectrum of [Ru,C,2H]+, a combination of HRuCH+ and RuCH2+ structures reproduces the observed spectrum at all levels of theory. The well-resolved spectrum of [Rh,C,2H]+ could not be assigned unambiguously to any calculated structure using DFT approaches. The EOM-SF-CCSD calculations showed that the ground-state surface has multireference electronic character, and symmetric carbenes in both the 1A1 and 3A2 states are needed to reproduce the observed spectrum.

Pitfalls in the n-mode representation of vibrational potentials.

Simulations of anharmonic vibrational motion rely on computationally expedient representations of the governing potential energy surface. The n-mode representation (n-MR)-effectively a many-body expansion in the space of molecular vibrations-is a general and efficient approach that is often used for this purpose in vibrational self-consistent field (VSCF) calculations and correlated analogues thereof. In the present analysis, a lack of convergence in many VSCF calculations is shown to originate from negative and unbound potentials at truncated orders of the n-MR expansion. For cases of strong anharmonic coupling between modes, the n-MR can both dip below the true global minimum of the potential surface and lead to effective single-mode potentials in VSCF that do not correspond to bound vibrational problems, even for bound total potentials. The present analysis serves mainly as a pathology report of this issue. Furthermore, this insight into the origin of VSCF non-convergence provides a simple, albeit ad hoc, route to correct the problem by "painting in" the full representation of groups of modes that exhibit these negative potentials at little additional computational cost. Somewhat surprisingly, this approach also reasonably approximates the results of the next-higher n-MR order and identifies groups of modes with particularly strong coupling. The method is shown to identify and correct problematic triples of modes-and restore SCF convergence-in two-mode representations of challenging test systems, including the water dimer and trimer, as well as protonated tropine.

Accelerating and stabilizing the convergence of vibrational self-consistent field calculations via the direct inversion of the iterative subspace (vDIIS) algorithm.

The vibrational self-consistent field (VSCF) method yields anharmonic states and spectra for molecular vibrations, and it serves as the starting point for more sophisticated correlated-vibration methods. Convergence of the iterative, non-linear optimization in VSCF calculations can be erratic or altogether unsuccessful, particularly for chemical systems involving low-frequency motions. In this work, a vibrational formulation of the Direct Inversion of the Iterative Subspace method of Pulay is presented and investigated. This formulation accounts for distinct attributes of the vibrational and electronic cases, including the expansion of each single-mode vibrational wavefunction in its own basis set. The resulting Direct Inversion of the Iterative Subspace method is shown to substantially accelerate VSCF convergence in all convergent cases as well as rectify many cases where Roothaan-based methods fail. Performance across systems ranging from small, rigid molecules to weakly bound molecular clusters is investigated in this analysis.

Persistence of a Delocalized Radical in Larger Clusters of Hydrated Copper(II) Hydroxide, CuOH+(H2O)3-7.

The structures, vibrational spectra, and electronic properties of copper hydroxide hydrates CuOH+(H2O)3-7 were investigated with quantum chemistry computations. As a follow-up to a previous analysis of CuOH+(H2O)0-2, this investigation examined the progression as the square-planar metal coordination environment was filled and as solvation shells expanded. Four-, five-, and six-coordinate structures were found to be low-energy isomers. The delocalized radical character, which was discovered in the small clusters, was found to persist upon continued hydration, although the hydrogen-bonded water network in the larger clusters was found to play a more significant role in accommodating this spin. Partial charges indicated that the electronic structure includes more Cu2+···OH- character than was observed in smaller clusters, but this structure remains decidedly mixed with Cu+···OH· configurations and yields roughly half-oxidation of the water network in the absence of any electrochemical potential. Computed vibrational spectra for n = 3 showed congruence with spectra from recent predissociation spectroscopy experiments, provided that the role of the D2 tag was taken into account. Spectra for n = 4-7 were predicted to exhibit features that are reflective of both the mixed electronic character and proton-/hydrogen-shuttling motifs within the hydrogen-bonded water network.

Accelerating Anharmonic Spectroscopy Simulations via Local-Mode, Multilevel Methods.

Ab initio computer simulations of anharmonic vibrational spectra provide nuanced insight into the vibrational behavior of molecules and complexes. The computational bottleneck in such simulations, particularly for ab initio potentials, is often the generation of mode-coupling potentials. Focusing specifically on two-mode couplings in this analysis, the combination of a local-mode representation and multilevel methods is demonstrated to be particularly symbiotic. In this approach, a low-level quantum chemistry method is employed to predict the pairwise couplings that should be included at the target level of theory in vibrational self-consistent field (and similar) calculations. Pairs that are excluded by this approach are "recycled" at the low level of theory. Furthermore, because this low-level pre-screening will eventually become the computational bottleneck for sufficiently large chemical systems, distance-based truncation is applied to these low-level predictions without substantive loss of accuracy. This combination is demonstrated to yield sub-wavenumber fidelity with reference vibrational transitions when including only a small fraction of target-level couplings; the overhead of predicting these couplings, particularly when employing distance-based, local-mode cutoffs, is a trivial added cost. This combined approach is assessed on a series of test cases, including ethylene, hexatriene, and the alanine dipeptide. Vibrational self-consistent field (VSCF) spectra were obtained with an RI-MP2/cc-pVTZ potential for the dipeptide, at approximately a 5-fold reduction in computational cost. Considerable optimism for increased accelerations for larger systems and higher-order couplings is also justified, based on this investigation.

Structural, Thermodynamic, and Spectroscopic Evolution in the Hydration of Copper(II) Ions, Cu2+(H2O)2-8.

Gas-phase clusters of the hydrated Cu(II) cation with 2-8 water molecules were investigated using ab initio quantum chemistry. Isomer structures, energies, and vibrational spectra were computed across this size range, yielding a qualitative picture of this ion as an intact Cu2+ hydrate that also partially oxidizes the surrounding water network at equilibrium. At sufficient cluster sizes, these ion hydrates also become thermodynamically preferred over competitive Cu(II) hydroxide hydrates. Competitive coordination environments were found to exist at some cluster sizes, due to both hydrogen-bonding and d-orbital chemical effects, and the dominant coordination number was found in some cases to be temperature-dependent. Clear spectral signatures of the ion's coordination environment were computed to exist at each cluster size, which should make experimental verification of these computational predictions straightforward. Through comparison to recent studies of hydrated CuOH+, the effective charge on the metal center was shown to converge to approximately +1.5 in both cases, despite qualitatively different behavior of their radical spin densities. Therefore, nominally Cu(II) ions exhibit considerable electronic, chemical, and structural flexibility. The electronic origins of this flexibility─including key roles played by the water network itself─are investigated in this work and should provide a conceptual foundation for future studies of copper-based, water-oxidation catalysts.

Molecular Motion in the Interconverting σ-H2, Di-, and Tri-hydride Regimes: Mo(PH3)5H2.

The transition-metal complex Mo(PH3)5H2 is known to exist in three possible isomeric forms, including a nonclassical, σ-bound dihydrogen complex and two classical dihydride isomers. As such, it has served as a model complex for the energies of conversion between these limiting structural regimes. In the present study, ab initio molecular dynamics computer simulations, combined with enhanced sampling techniques, were utilized to directly assess the degree of motion and isomerization of the dihydrogen/dihydride moieties in this complex. Ligand rotations (for both the H2 unit and the phosphine units) were found to be dominant in the low-temperature (298 K) regime, and the classical thermodynamic distribution showed no probability of thermally accessing dihydride forms, although unrestrained molecular dynamics trajectories showed fleeting configurations outside of the σ-H2 configuration. Simulations at higher temperatures surprisingly revealed new tri-hydride isomers that are energetically competitive with the σ-H2 and cis-/trans-dihydride isomers. Low-energy pathways to hydrogen/hydride transfer and phosphine dissociation were readily accessible, which considerably expands the known isomeric flexibility of this complex.

Adiabatic Molecular Orbital Tracking in Ab Initio Molecular Dynamics.

The ab initio molecular dynamics (AIMD) method provides a computational route for the real-time simulation of reactive chemistry. An often-overlooked capability of this approach is the opportunity to examine the electronic evolution of a chemical system. For AIMD trajectories based on Hartree-Fock or density functional theory methods, the real-time evolution of single-particle molecular orbitals (MOs) can provide detailed insights into the time-dependent electronic structure of molecules. The evolving electronic Hamiltonians at each MD step pose problems for tracking and visualizing a given MO's character, ordering, and associated phase throughout an MD trajectory, however. This report presents and assesses a simple algorithm for correcting these deficiencies by exploiting similarity projections of the electronic structure between neighboring MD steps. Two aspects bring this analysis beyond a simple step-to-step projection scheme. First, the challenging case of coincidental orbital degeneracies is resolved via a quadrupole-field perturbation that nonetheless rigorously preserves energy conservation. Second, the resulting orbitals are shown to evolve adiabatically, in spite of the "preservation of character" concept that undergirds a projection of neighboring steps' MOs. The method is tested on water clusters, which exhibit considerable dynamic degeneracies, as well as a classic organic nucleophilic substitution reaction, in which the adiabatic evolution of the bonding orbitals clarifies textbook interpretations of the electronic structure during this reactive collision.

Electronic Structure and Vibrational Signatures of the Delocalized Radical in Hydrated Clusters of Copper("II") Hydroxide CuOH+(H2O)0-2.

The copper hydroxide ion, CuOH+, serves as the catalytic core in several recently developed water-splitting catalysts, and an understanding of its chemistry is critical to determining viable catalytic mechanisms. In spite of its importance, the electronic structure of this open-shell ion has remained ambiguous in the literature. In particular, computed values for both the thermodynamics of hydration and the vibrational signatures of the mono- and dihydrates have shown prohibitively large errors compared to values from recent experimental measurements. In this work, the source of this discrepancy is demonstrated to be the propensity of this ion to exist between traditional Cu(I) and Cu(II) oxidation-state limits. The spin density of the radical is accordingly shown to delocalize between the metal center and surrounding ligands, and increasing the hydration serves to exacerbate this behavior. Equation-of-motion coupled-cluster methods demonstrated the requisite accuracy to resolve the thermodynamic discrepancies. Such methods were also needed for spectral simulations, although the latter also required a direct simulation of the role of the deuterium "tag" molecules that are used in modern predissociation spectroscopy experiments. This nominally benign tag molecule underwent direct complexation with the open-valence metal ion, thereby forming a species akin to known metal-H2 complexes and strongly impacting the resulting spectrum. Thermal populations of this configuration and other more traditional noncovalently bound isomers led to a considerable broadening of the spectral lineshapes. Therefore, at least for the CuOH+(H2O)0-2 hydrates, these benchmark ions should be considered to be delocalized radical systems with some degree of multireference character at equilibrium. They also serve as a cautionary tale for the spectroscopy community, wherein the role of the D2 tag is far from benign.

Infrared signatures of isomer selectivity and symmetry breaking in the Cs+(H2O)3 complex using many-body potential energy functions.

A quantitative description of the interactions between ions and water is key to characterizing the role played by ions in mediating fundamental processes that take place in aqueous environments. At the molecular level, vibrational spectroscopy provides a unique means to probe the multidimensional potential energy surface of small ion-water clusters. In this study, we combine the MB-nrg potential energy functions recently developed for ion-water interactions with perturbative corrections to vibrational self-consistent field theory and the local-monomer approximation to disentangle many-body effects on the stability and vibrational structure of the Cs+(H2O)3 cluster. Since several low-energy, thermodynamically accessible isomers exist for Cs+(H2O)3, even small changes in the description of the underlying potential energy surface can result in large differences in the relative stability of the various isomers. Our analysis demonstrates that a quantitative account for three-body energies and explicit treatment of cross-monomer vibrational couplings are required to reproduce the experimental spectrum.

Stepwise Activation of Water by Open-Shell Interactions, Cl(H2O)n=4-8,17.

Chemical activation of water by a single chlorine atom was examined computationally for clusters of chlorine radicals and water in a size regime just prior to internal hydration of water/ions, Cl·(H2O)n=4-8,17. This investigation follows a recent analysis of this radical-molecule interaction [Christensen et al. J. Phys. Chem. A 2019, 123, 8657] for n = 1-4, which demonstrated that n = 4 marked a transition in which an oxidized-water structural motif became viable, albeit high in energy. Thousands of unique isomers were computed in the present analysis, which resulted in three structural classes of isomers, including intact hydrated chlorine, hydrogen-transferred (HCl)(OH·)(H2O)n-1, and charge-transferred (Cl-)(H3O+)(OH·)(H2O)n-2 configurations. The electronic structures of these classes were investigated, along with harmonic vibrational signatures that probed the degree of water-network perturbations and generated experimentally verifiable computational predictions. The main outcome of this analysis is that the charge-transferred isomers were stabilized considerably upon increased hydration-leading to an energetic crossover with the hydrogen-transferred forms-but the degree of hydration was surprisingly still not sufficient to achieve crossover between the intact chlorine-water complexes and these charge-separated configurations. Internal hydration of the ions appears to be necessary in order to achieve this separation, which will likely occur at larger cluster sizes.

Spectroscopic Signatures of Mode-Dependent Tunnel Splitting in the Iodide-Water Binary Complex.

The gas-phase vibrational spectrum of the isolated iodide-water cluster ion (I-·H2O), first reported in 1996, presents one of the most difficult, long-standing spectroscopic puzzles involving ion microhydration. Although the spectra of the smaller halides are well described in the context of an asymmetrical ground-state structure in which only one OH group is hydrogen-bonded to the ion, the I-·H2O spectrum displays multiplet structures with partially resolved rotational patterns that are additionally influenced by quantum nuclear spin statistics. In this study, this complex behavior is unraveled with a combination of experimental methods, including ion preparation in a temperature-controlled ion trap and spectral simplification through applications of tag-free, two-color IR-IR double-resonance spectroscopy. Analysis of the double-resonance spectra reveals a vibrational ground-state tunneling splitting of about 20 cm-1, which is on the same order as the spacing between the peaks that comprise the multiplet structure. These findings are further supported by the results obtained from a fully coupled, six-dimensional calculation of the vibrational spectrum. The underlying level structure can then be understood as a consequence of experimentally measurable, vibrational mode-dependent tunneling splittings (which, in the case of the ground vibrational state, is comparable to the rotational energy spacing between levels with Ka = 0 and 1), as well as Fermi resonance interactions. The latter include the hydrogen-bonded OH stretches and combination bands that involve the HOH bend overtones and soft-mode excitations of frustrated translation and rotation displacements of the water molecule relative to the ion. These anharmonic couplings yield closely spaced bands that are activated in the IR by borrowing intensity from the OH stretch fundamentals.

Probing the Partial Activation of Water by Open-Shell Interactions, Cl(H2O)1-4.

The partial chemical activation of water by reactive radicals was examined computationally for small clusters of chlorine and water, Cl•(H2O)n=1-4. Using an automated isomer-search procedure, dozens of unique, stable structures were computed. Among the resulting structural classes were intact, hydrated-chlorine isomers, as well as hydrogen-abstracted (HCl)(OH)(H2O)n-1 configurations. The latter showed increased stability as the degree of hydration increased, until n = 4, where a new class of structures was discovered with a chloride ion bound to an oxidized water network. The electronic structure of these three structural classes was investigated, and spectral signatures of this hydration-based evolution were connected to these electronic properties. An ancillary outcome of this detailed computational analysis, including coupled-cluster benchmarks, was the calibration of cost-effective quantum chemistry methods for future studies of these radical-water complexes.

Nuclear Motion in the Intramolecular Dihydrogen-Bound Regime of an Aminoborane Complex.

The 1,3-diaza-2,4-diborobutane (NBNB) molecule serves as the smallest model complex of an intramolecular "dihydrogen bond," which involves a nominally hydrogen-bonding interaction between amine and borane hydrogen atoms. In the present study, the role of this dihydrogen bond in influencing the inherent molecular dynamics of NBNB is investigated computationally with ab initio molecular dynamics and path integral molecular dynamics techniques, as well as vibrational spectra analysis and static quantum chemistry computations. These simulations indicate that the dihydrogen-bonding interaction impacts both the high- and low-frequency motions of the molecule, with the dominant motions involving low-frequency backbone isomerization and terminal amine rotation. Geometric isotope effects were found to be modest. The analysis also addresses the paradoxical fostering of amine rotation via a relatively strong dihydrogen bond interaction. Electrostatic and geometric factors most directly explain this effect, and although some orbital evidence was found for a small covalent component of this interaction, the dynamics and electronic structure suggest that electrostatic contributions are the controlling factors for molecular motion in NBNB.

Monitoring Water Clusters "Melt" Through Vibrational Spectroscopy.

Characterizing structural and phase transformations of water at the molecular level is key to understanding a variety of multiphase processes ranging from ice nucleation in the atmosphere to hydration of biomolecules and wetting of solid surfaces. In this study, state-of-the-art quantum simulations with a many-body water potential energy surface, which exhibits chemical and spectroscopic accuracy, are carried out to monitor the microscopic melting of the water hexamer through the analysis of vibrational spectra and appropriate structural order parameters as a function of temperature. The water hexamer is specifically chosen as a case study due to the central role of this cluster in the molecular-level understanding of hydrogen bonding in water. Besides being in agreement with the experimental data available for selected isomers at very low temperature, the present results provide quantitative insights into the interplay between energetic, entropic, and nuclear quantum effects on the evolution of water clusters from "solid-like" to "liquid-like" structures. This study thus demonstrates that computer simulations can now bridge the gap between measurements currently possible for individual isomers at very low temperature and observations of isomer mixtures at ambient conditions.

Signatures of Size-Dependent Structural Patterns in Hydrated Copper(I) Clusters, Cu+(H2O)n=1-10.

The isomers of a hydrated Cu(I) ion with n = 1-10 water molecules were investigated by using ab initio quantum chemistry and an automated isomer-search algorithm. The electronic structure and vibrational spectra of the hundreds of resulting isomers were used to analyze the source of the observed bonding patterns. A structural evolution from dominantly two-coordinate structures (n = 1-4) toward a mixture of two- and three-coordinate structures was observed at n = 5-6, where the stability provided by expanded hydrogen-bonding was competitive with the dominantly electrostatic interaction between the water ligand and remaining binding sites of the metal ion. Further hydration (n = 7-10) led to a mixture of three- and four-coordinate structures. The metal ion was found, through spectroscopic signatures, to appreciably perturb the O-H bonds of even third-shell water molecules, which highlighted the ability of this nominally simple ion to partially activate the surrounding water network.

Tuning vibrational mode localization with frequency windowing.

Local-mode coordinates have previously been shown to be an effective starting point for anharmonic vibrational spectroscopy calculations. This general approach borrows techniques from localized-orbital machinery in electronic structure theory and generates a new set of spatially localized vibrational modes. These modes exhibit a well-behaved spatial decay of anharmonic mode couplings, which, in turn, allows for a systematic, a priori truncation of couplings and increased computational efficiency. Fully localized modes, however, have been found to lead to unintuitive mixtures of characteristic motions, such as stretches and bends, and accordingly large bilinear couplings. In this work, a very simple, tunable localization frequency window is introduced, in order to realize the transition from normal modes to fully localized modes. Partial localization can be achieved by localizing only pairs of modes within this traveling frequency window, which allows for intuitive interpretation of modes. The optimal window size is suggested to be a few hundreds of wave numbers, based on small- to medium-sized test systems, including water clusters and polypeptides. The new sets of partially localized coordinates retain their spatial coupling decay behavior while providing a reduced number of potential energy evaluations for convergence of anharmonic spectra.