Decoding the 2D IR spectrum of the aqueous proton with high-level VSCF/VCI calculations

Performant automatic differentiation of local coupled cluster theories: Response properties and ab initio molecular dynamics

In this work, we introduce a differentiable implementation of the local natural orbital coupled cluster (LNO-CC) method within the automatic differentiation framework of the PySCFAD package. The implementation is comprehensively tuned for enhanced performance, which enables the calculation of first-order static response properties on medium-sized molecular systems using coupled cluster theory with single, double, and perturbative triple excitations [CCSD(T)]. We evaluate the accuracy of our method by benchmarking it against the canonical CCSD(T) reference for nuclear gradients, dipole moments, and geometry optimizations. In addition, we demonstrate the possibility of property calculations for chemically interesting systems through the computation of bond orders and Mössbauer spectroscopy parameters for a [NiFe]-hydrogenase active site model, along with the simulation of infrared spectra via ab initio LNO-CC molecular dynamics for a protonated water hexamer.

Fully Quantum Simulation of Polaritonic Vibrational Spectra of Large Cavity-Molecule System

The formation of molecular vibrational polaritons, arising from the interplay between molecular vibrations and infrared cavity modes, is a quantum phenomenon necessitating accurate quantum dynamical simulations. Here, we introduce the cavity vibrational self-consistent field/virtual state configuration interaction method, enabling quantum simulation of the vibrational spectra of many-molecule systems within the optical cavity. Focusing on the representative (H2O)21 system, we showcase this parameter-free quantum approach's ability to capture both linear and nonlinear vibrational spectral features. Our findings highlight the growing prominence of molecular couplings among OH stretches and bending excited bands with increased light-matter interaction, revealing distinctive nonlinear spectral features induced by vibrational strong coupling.

Strong H-bonding from Zeolite Bro̷nsted Acid Site to Water: Origin of the Broad IR Doublet

Hydrogen bonding between water molecules and zeolite Bro̷nsted acid sites (BAS) has received much attention due to the significant influence of water on the adsorption and catalytic properties of these widely used porous materials. When a single water molecule is adsorbed at the BAS, the zeolite O-H stretch vibration decreases in frequency and splits into two extraordinarily broad bands peaked near 2500 and 2900 cm-1 in the infrared (IR) spectrum. This broad doublet feature is the predominant IR signature used to identify and interpret water-BAS H-bonding at low hydration levels, but the origin of the band splitting is not well understood. In this study, we used broadband two-dimensional infrared (2D IR) spectroscopy to investigate zeolite HZSM-5 prepared with a single water molecule per BAS. We find that the 2D IR spectrum is not explained by the most common interpretation of Fermi resonance coupling between the stretch and the bend of the BAS OH group, which predicts intense excited-state transitions that are absent from the experimental results. We present an alternative model of a double-well proton stretch potential, where the band splitting is caused by excited-state tunneling through the proton-transfer barrier. This one-dimensional model reproduces the basic experimental pattern of transition frequencies and amplitudes, suggesting that the doublet bands may originate from a highly anharmonic potential in which the excited state proton wave functions are delocalized over the H-bond between zeolite BAS and adsorbed H2O. Additional details about molecular orientation and coordination of the adsorbed water molecule are also resolved in the 2D IR spectroscopy.

Investigating Intramolecular H Atom Transfer Dynamics in β-Diketones with Ultrafast Infrared Spectroscopies and Theoretical Modeling

The vibrational signatures and ultrafast dynamics of the intramolecular H-bond in a series of β-diketones are investigated with 2D IR spectroscopy and computational modeling. The chosen β-diketones exhibit a range of H atom donor-acceptor distances and asymmetry along the H atom transfer coordinate that tunes the intramolecular H-bond strength. The species with the strongest H-bonds are calculated to have very soft H atom potentials, resulting in highly red-shifted OH stretch fundamental frequencies and dislocation of the H atom upon vibrational excitation. These soft potentials lead to significant coupling to the other normal mode coordinates and give rise to the very broad vibrational signatures observed experimentally. The 2D IR spectra in both the OH and OD stretch regions of the light and deuterated isotopologues reveal broadened and long-lived ground-state bleach signatures of the vibrationally hot molecules. Polarization-sensitive transient absorption measurements in the OH and OD stretch regions reveal notable isotopic differences in orientational dynamics. Orientational relaxation was measured to occur on ∼600 fs and ∼2 ps time scales for the light and deuterated isotopologues, respectively. The orientational dynamics are interpreted in terms of activated H/D atom transfer events driven by collective intramolecular structural rearrangements.

Thermal dependence of the hydrated proton and optimal proton transfer in the protonated water hexamer

Water is a key ingredient for life and plays a central role as solvent in many biochemical reactions. However, the intrinsically quantum nature of the hydrogen nucleus, revealing itself in a large variety of physical manifestations, including proton transfer, gives rise to unexpected phenomena whose description is still elusive. Here we study, by a combination of state-of-the-art quantum Monte Carlo methods and path-integral molecular dynamics, the structure and hydrogen-bond dynamics of the protonated water hexamer, the fundamental unit for the hydrated proton. We report a remarkably low thermal expansion of the hydrogen bond from zero temperature up to 300 K, owing to the presence of short-Zundel configurations, characterised by proton delocalisation and favoured by the synergy of nuclear quantum effects and thermal activation. The hydrogen bond strength progressively weakens above 300 K, when localised Eigen-like configurations become relevant. Our analysis, supported by the instanton statistics of shuttling protons, reveals that the near-room-temperature range from 250 K to 300 K is optimal for proton transfer in the protonated water hexamer.

Calculating Vibrational Excited State Absorptions with Excited State Constrained Minimized Energy Surfaces

The modeling and interpretation of vibrational spectra are crucial for studying reaction dynamics using vibrational spectroscopy. Most prior theoretical developments focused on describing fundamental vibrational transitions while fewer developments focused on vibrational excited state absorptions. In this study, we present a new method that uses excited state constrained minimized energy surfaces (CMESs) to describe vibrational excited state absorptions. The excited state CMESs are obtained similarly to the previous ground state CMES development in our group but with additional wave function orthogonality constraints. Using a series of model systems, including the harmonic oscillator, Morse potential, double-well potential, quartic potential, and two-dimensional anharmonic potential, we demonstrate that this new procedure provides good estimations of the transition frequencies for vibrational excited state absorptions. These results are significantly better than those obtained from harmonic approximations using conventional potential energy surfaces, demonstrating the promise of excited state CMES-based methods for calculating vibrational excited state absorptions in real systems.

Quantum-chemical calculation of two-dimensional infrared spectra using localized-mode VSCF/VCI

Computational protocols for the simulation of two-dimensional infrared (2D IR) spectroscopy usually rely on vibrational exciton models which require an empirical parameterization. Here, we present an efficient quantum-chemical protocol for predicting static 2D IR spectra that does not require any empirical parameters. For the calculation of anharmonic vibrational energy levels and transition dipole moments, we employ the localized-mode vibrational self-consistent field (L-VSCF)/vibrational configuration interaction (L-VCI) approach previously established for (linear) anharmonic theoretical vibrational spectroscopy [P. T. Panek and C. R. Jacob, ChemPhysChem 15, 3365-3377 (2014)]. We demonstrate that with an efficient expansion of the potential energy surface using anharmonic one-mode potentials and harmonic two-mode potentials, 2D IR spectra of metal carbonyl complexes and dipeptides can be predicted reliably. We further show how the close connection between L-VCI and vibrational exciton models can be exploited to extract the parameters of such models from those calculations. This provides a novel route to the fully quantum-chemical parameterization of vibrational exciton models for predicting 2D IR spectra.

Multidimensional Quantum Dynamical Simulation of Infrared Spectra under Polaritonic Vibrational Strong Coupling

Recent experimental and theoretical studies demonstrate that the chemical reactivity of molecules can be modified inside an optical cavity. Here, we provide a theoretical framework for conducting multidimensional quantum simulations of the infrared (IR) spectra for molecules interacting with cavity modes. A single water molecule under polaritonic vibrational strong coupling serves as an illustrative example. Combined with accurate potential energy and dipole moment surfaces, our cavity vibrational self-consistent field/virtual state configuration interaction (cav-VSCF/VCI) approach can predict the IR spectra when the molecule is inside or outside the cavity. The spectral signatures of Rabi splittings and shifts of certain bands are found to be strongly dependent on the frequency and polarization direction of the cavity modes. Analyses of the simulated spectra show that polaritonic vibrational strong coupling can induce unconventional couplings among the molecule's vibrational modes, suggesting that intramolecular vibrational energy transfer can be significantly accelerated by the cavity.

Proton-transfer spectroscopy beyond the normal-mode scenario

A stochastic theory is developed to predict the spectral signature of proton-transfer processes and is applied to infrared spectra computed from ab initio molecular-dynamics simulations of a single [Formula: see text] cation. By constraining the oxygen atoms to a fixed distance, this system serves as a tunable model for general proton-transfer processes with variable barrier height. Three spectral contributions at distinct frequencies are identified and analytically predicted: the quasi-harmonic motion around the most probable configuration, amenable to normal-mode analysis, the contribution due to transfer paths when the proton moves over the barrier, and a shoulder for low frequencies stemming from the stochastic transfer-waiting-time distribution; the latter two contributions are not captured by normal-mode analysis but exclusively reported on the proton-transfer kinetics. In accordance with reaction rate theory, the transfer-waiting-contribution frequency depends inversely exponentially on the barrier height, whereas the transfer-path-contribution frequency is rather insensitive to the barrier height.

In silico NIR spectroscopy - A review. Molecular fingerprint, interpretation of calibration models, understanding of matrix effects and instrumental difference

Quantum mechanical calculations are routinely used as a major support in mid-infrared (MIR) and Raman spectroscopy. In contrast, practical limitations for long time formed a barrier to developing a similar synergy between near-infrared (NIR) spectroscopy and computational chemistry. Recent advances in theoretical methods suitable for calculation of NIR spectra opened the pathway to modeling NIR spectra of various molecules. Accurate theoretical reproduction of NIR spectra of molecules reaching the size of long-chain fatty acids was accomplished so far. In silico NIR spectroscopy, where the spectra are calculated ab initio, provides substantial improvement in our understanding of the overtones and combination bands that overlap in staggering numbers and create complex lineshape typical for NIR spectra. This improves the comprehension of the spectral information enabling access to rich and detail molecular footprint, essential for fundamental research and useful in routine analysis by NIR spectroscopy and chemometrics. This review article summarizes the most recent accomplishments in the emerging field with examples of simulated NIR spectra of molecules reaching long-chain fatty acids and polymers. In addition to detailed NIR band assignments and new physical insights, simulated spectra enable innovative support in applications. Understanding of the difference in the performance observed between miniaturized NIR spectrometers and chemical interpretation of the chemometric models are noteworthy here. These new elements integrated into NIR spectroscopy framework enable a knowledge-based design of the analysis with comprehension of the processed chemical information.

State-resolved infrared spectrum of the protonated water dimer: revisiting the characteristic proton transfer doublet peak

The infrared (IR) spectra of protonated water clusters encode precise information on the dynamics and structure of the hydrated proton. However, the strong anharmonic coupling and quantum effects of these elusive species remain puzzling up to the present day. Here, we report unequivocal evidence that the interplay between the proton transfer and the water wagging motions in the protonated water dimer (Zundel ion) giving rise to the characteristic doublet peak is both more complex and more sensitive to subtle energetic changes than previously thought. In particular, hitherto overlooked low-intensity satellite peaks in the experimental spectrum are now unveiled and mechanistically assigned. Our findings rely on the comparison of IR spectra obtained using two highly accurate potential energy surfaces in conjunction with highly accurate state-resolved quantum simulations. We demonstrate that these high-accuracy simulations are important for providing definite assignments of the complex IR signals of fluxional molecules.

Spectral signatures of excess-proton waiting and transfer-path dynamics in aqueous hydrochloric acid solutions

The theoretical basis for linking spectral signatures of hydrated excess protons with microscopic proton-transfer mechanisms has so far relied on normal-mode analysis. We introduce trajectory-decomposition techniques to analyze the excess-proton dynamics in ab initio molecular-dynamics simulations of aqueous hydrochloric-acid solutions beyond the normal-mode scenario. We show that the actual proton transfer between two water molecules involves for relatively large water-water separations crossing of a free-energy barrier and thus is not a normal mode, rather it is characterized by two non-vibrational time scales: Firstly, the broadly distributed waiting time for transfer to occur with a mean value of 200–300 fs, which leads to a broad and weak shoulder in the absorption spectrum around 100 cm⁻¹, consistent with our experimental THz spectra. Secondly, the mean duration of a transfer event of about 14 fs, which produces a rather well-defined spectral contribution around 1200 cm⁻¹ and agrees in location and width with previous experimental mid-infrared spectra.

The spectroscopic signatures of excess protons in HCl solutions are studied by ab initio simulations and THz experiments. Two contributions beyond the normal-mode scenario are identified that reflect proton-waiting and proton-transfer processes.

Vibrational Dynamics of the Intramolecular H-Bond in Acetylacetone Investigated with Transient and 2D IR Spectroscopy

Acetylacetone (AcAc) has proven to be a fruitful but highly challenging model system for the experimental and computational interrogation of strong intramolecular hydrogen bonds. Key questions remain, however, regarding the identity of the minimum-energy structure of AcAc and the dynamics of intramolecular proton transfer. Here, we investigate the OH/OD stretch and bend regions of the enol tautomer of AcAc and its deuterated isotopologue with transient absorption and 2D IR spectroscopy. The OH bend region reveals a single dominant diagonal transition near 1625 cm^-1 with intense cross peaks to lower-frequency modes, demonstrating highly mixed fingerprint transitions that contain OH bend character. The anharmonic coupling of the OH bend results in a highly elongated OH bend excited-state absorption transition that indicates a large manifold of OH bend overtone/combination bands in the OH stretch region that leads to strong bend-stretch Fermi resonance interactions. The OH and OD stretch regions consist of broad ground-state bleach signals, but there is no clear evidence of ω₂₁ excited-state absorptions due to rapid population relaxation arising from strong intramolecular coupling to bending, fingerprint, and low-frequency H-bond modes. Orientational relaxation dynamics persist for timescales longer than the vibrational lifetimes, with polarization anisotropy components decaying within approximately 2 and 10 periods of the O-O oscillation for the OH and OD stretch, respectively. The significant isotopic dependence of the orientational dynamics is discussed in the context of intramolecular mode coupling, diffusional processes, and contributions from proton/deuteron transfer dynamics.

Resolving the Structural Debate for the Hydrated Excess Proton in Water

It has long been proposed that the hydrated excess proton in water (aka the solvated "hydronium" cation) likely has two limiting forms, that of the Eigen cation (H₉O₄⁺) and that of the Zundel cation (H₅O₂⁺). There has been debate over which of these two is the more dominant species and/or whether intermediate (or "distorted") structures between these two limits are the more realistic representation. Spectroscopy experiments have recently provided further results regarding the excess proton. These experiments show that the hydrated proton has an anisotropy reorientation time scale on the order of 1-2 ps. This time scale has been suggested to possibly contradict the picture of the more rapid "special pair dance" phenomenon for the hydrated excess proton, which is a signature of a distorted Eigen cation. The special pair dance was predicted from prior computational studies in which the hydrated central core hydronium structure continually switches (O-H···O)* special pair hydrogen-bond partners with the closest three water molecules, yielding on average a distorted Eigen cation with three equivalent and dynamically exchanging distortions. Through state-of-art simulations it is shown here that anisotropy reorientation time scales of the same magnitude are obtained that also include structural reorientations associated with the special pair dance, leading to a reinterpretation of the experimental results. These results and additional analyses point to a distorted and dynamic Eigen cation as the most prevalent hydrated proton species in aqueous acid solutions of dilute to moderate concentration, as opposed to a stabilized or a distorted (but not "dancing") Zundel cation.

Coupled Local-Mode Approach for the Calculation of Vibrational Spectra: Application to Protonated Water Clusters

Spectroscopic studies of protonated water clusters (PWCs) have yielded enormous insights into the fundamental nature of the hydrated proton. Here, we introduce a new coupled local-mode (CLM) approach to calculate PWC OH stretch vibrational spectra. The CLM method combines a sampling of representative configurations from density functional theory (DFT)-based ab initio molecular dynamics (AIMD) simulations with DFT calculations of local-mode vibrational frequencies and couplings. Calculations of inhomogeneous OH stretch vibrational spectra for H⁺(H₂O)₄ and H⁺(H₂O)₂₁ agree well with experiment and higher-level calculations, and decompositions of the calculated spectra in terms of the coupled modes aids in the interpretation of the spectra. This observation is consistent with the idea that capturing anharmonicity and coupling is as important to accuracy as the underlying level of electronic structure theory. The CLM calculations can easily discern the configuration that dominates the experimental measurement for H⁺(H₂O)₅, which can adopt several low-energy conformations.

Comparative studies of IR spectra of deprotonated serine with classical and thermostated ring polymer molecular dynamics simulations

Here we report the vibrational spectra of deprotonated serine calculated from the classical molecular dynamics (MD) simulations and thermostated ring-polymer molecular dynamics (TRPMD) simulation with third-order density-functional tight-binding. In our earlier study [Inakollu and Yu, "A systematic benchmarking of computational vibrational spectroscopy with DFTB3: Normal mode analysis and fast Fourier transform dipole autocorrelation function," J. Comput. Chem. 39, 2067 (2018)] of deprotonated serine, we observed a significant difference in the vibrational spectra with the classical MD simulations compared to the infrared multiple photon dissociation spectra. It was postulated that this is due to neglecting the nuclear quantum effects (NQEs). In this work, NQEs are considered in spectral calculation using the TRPMD simulations. With the help of potential of mean force calculations, the conformational space of deprotonated serine is analyzed and used to understand the difference in the spectra of classical MD and TRPMD simulations at 298.15 and 100 K. The high-frequency vibrational bands in the spectra are characterized using Fourier transform localized vibrational mode (FT-ν_N AC) and interatomic distance histograms. At room temperature, the quantum effects are less significant, and the free energy profiles in the classical MD and the TRPMD simulations are very similar. However, the hydrogen bond between the hydroxyl-carboxyl bond is slightly stronger in TRPMD simulations. At 100 K, the quantum effects are more prominent, especially in the 2600-3600 cm^-1, and the free energy profile slightly differs between the classical MD and TRPMD simulations. Using the FT-ν_N AC and the interatomic distance histograms, the high-frequency vibrational bands are discussed in detail.

Structural Characterization of Protonated Water Clusters Confined in HZSM-5 Zeolites

A molecular description of the structure and behavior of water confined in aluminosilicate zeolite pores is a crucial component for understanding zeolite acid chemistry under hydrous conditions. In this study, we use a combination of ultrafast two-dimensional infrared (2D IR) spectroscopy and ab initio molecular dynamics (AIMD) to study H₂O confined in the pores of highly hydrated zeolite HZSM-5 (∼13 and ∼6 equivalents of H₂O per Al atom). The 2D IR spectrum reveals correlations between the vibrations of both terminal and H-bonded O-H groups and the continuum absorption of the excess proton. These data are used to characterize the hydrogen-bonding network within the cluster by quantifying single-, double-, and non-hydrogen-bond donor water molecules. These results are found to be in good agreement with the statistics calculated from an AIMD simulation of an H⁺(H₂O)₈ cluster in HZSM-5. Furthermore, IR spectral assignments to local O-H environments are validated with DFT calculations on clusters drawn from AIMD simulations. The simulations reveal that the excess charge is detached from the zeolite and resides near the more highly coordinated water molecules in the cluster. When they are taken together, these results unambiguously assign the complex IR spectrum of highly hydrated HZSM-5, providing quantitative information on the molecular environments and hydrogen-bonding topology of protonated water clusters under extreme confinement.

Actual Symmetry of Symmetric Molecular Adducts in the Gas Phase, Solution and in the Solid State

This review discusses molecular adducts, whose composition allows a symmetric structure. Such adducts are popular model systems, as they are useful for analyzing the effect of structure on the property selected for study since they allow one to reduce the number of parameters. The main objectives of this discussion are to evaluate the influence of the surroundings on the symmetry of these adducts, steric hindrances within the adducts, competition between different noncovalent interactions responsible for stabilizing the adducts, and experimental methods that can be used to study the symmetry at different time scales. This review considers the following central binding units: hydrogen (proton), halogen (anion), metal (cation), water (hydrogen peroxide).