Efficient anharmonic vibrational spectroscopy for large molecules using local-mode coordinates

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.

Monitoring water harvesting in metal-organic frameworks, one water molecule at a time

Metal-organic frameworks (MOFs) have gained prominence as potential materials for atmospheric water harvesting, a vital solution for arid regions and areas experiencing severe water shortages. However, the molecular factors influencing the performance of MOFs in capturing water from the air remain elusive. Among all MOFs, Ni2X2BTDD (X = F, Cl, Br) stands out as a promising water harvester due to its ability to adsorb substantial amounts of water at low relative humidity (RH). Here, we use advanced molecular dynamics simulations carried out with the state-of-the-art MB-pol data-driven many-body potential to monitor water adsorption in the three Ni2X2BTDD variants as a function of RH. Our simulations reveal that the type of halide atom in the three Ni2X2BTDD frameworks significantly influences the corresponding molecular mechanisms of water adsorption: while water molecules form strong hydrogen bonds with the fluoride atoms in Ni2F2BTDD, they tend to form hydrogen bonds with the nitrogen atoms of the triazolate linkers in Ni2Cl2BTDD and Ni2Br2BTDD. Importantly, the large size of the bromide atoms reduces the void volume in the Ni2Br2BTDD pores, which enable water molecules to initiate an extended hydrogen-bond network at lower RH. These findings not only underscore the prospect for precisely tuning structural and chemical modifications of the frameworks to optimize their interaction with water, but also highlight the predictive power of simulations with the MB-pol data-driven many-body potential. By providing a realistic description of water under different thermodynamic conditions and environments, these simulations yield unique, molecular-level insights that can guide the design and optimization of energy-efficient water harvesting materials.

Development of a universal method for vibrational analysis of the terminal alkyne C≡C stretch

The terminal alkyne C≡C stretch has a large Raman scattering cross section in the "silent" region for biomolecules. This has led to many Raman tag and probe studies using this moiety to study biomolecular systems. A computational investigation of these systems is vital to aid in the interpretation of these results. In this work, we develop a method for computing terminal alkyne vibrational frequencies and isotropic transition polarizabilities that can easily and accurately be applied to any terminal alkyne molecule. We apply the discrete variable representation method to a localized version of the C≡C stretch normal mode. The errors of (1) vibrational localization to the terminal alkyne moiety, (2) anharmonic normal mode isolation, and (3) discretization of the Born-Oppenheimer potential energy surface are quantified and found to be generally small and cancel each other. This results in a method with low error compared to other anharmonic vibrational methods like second-order vibrational perturbation theory and to experiments. Several density functionals are tested using the method, and TPSS-D3, an inexpensive nonempirical density functional with dispersion corrections, is found to perform surprisingly well. Diffuse basis functions are found to be important for the accuracy of computed frequencies. Finally, the computation of vibrational properties like isotropic transition polarizabilities and the universality of the localized normal mode for terminal alkynes are demonstrated.

Determining internal coordinate sets for optimal representation of molecular vibration

Arising from the harmonic approximation in solving the vibrational Schrödinger equation, normal modes dissect molecular vibrations into distinct degrees of freedom. Normal modes are widely used as they give rise to descriptive vibrational notations and are convenient for expanding anharmonic potential energy surfaces as an alternative to higher-order Taylor series representations. Usually, normal modes are expressed in Cartesian coordinates, which bears drawbacks that can be overcome by switching to internal coordinates. Considering vibrational notations, normal modes with delocalized characters are difficult to denote, but internal coordinates offer a route to clearer notations. Based on the Hessian, normal mode decomposition schemes for a given set of internal coordinates can describe a normal mode by its contributions from internal coordinates. However, choosing a set of internal coordinates is not straightforward. While the Hessian provides unique sets of normal modes, various internal coordinate sets are possible for a given system. In the present work, we employ a normal mode decomposition scheme to choose an optimal set. Therefore, we screen reasonable sets based on topology and symmetry considerations and rely on a metric that minimizes coupling between internal coordinates. Ultimately, the Nomodeco toolkit presented here generates internal coordinate sets to find an optimal set for representing molecular vibrations. The resulting contribution tables can be used to clarify vibrational notations. We test our scheme on small to mid-sized molecules, showing how the space of definable internal coordinate sets can significantly be reduced.

Flexible DMRG-Based Framework for Anharmonic Vibrational Calculations

We present a novel formulation of the vibrational density matrix renormalization group (vDMRG) algorithm tailored to strongly anharmonic molecules described by general, high-dimensional model representations of potential energy surfaces. For this purpose, we extend the vDMRG framework to support vibrational Hamiltonians expressed in the so-called n-mode second-quantization formalism. The resulting n-mode vDMRG method offers full flexibility with respect to both the functional form of the PES and the choice of the single-particle basis set. We leverage this framework to apply, for the first time, vDMRG based on an anharmonic modal basis set optimized with the vibrational self-consistent field algorithm on an on-the-fly constructed PES. We also extend the n-mode vDMRG framework to include excited-state-targeting algorithms in order to efficiently calculate anharmonic transition frequencies. We demonstrate the capabilities of our novel n-mode vDMRG framework for methyloxirane, a challenging molecule with 24 coupled vibrational modes.

A general expression for vibrational Hamiltonians expressed in oblique coordinates

We examine the properties of oblique coordinates. The coordinates, introduced by Zúñiga et al. [J. Phys. B: At., Mol. Opt. Phys. 52, 055101, (2019)], reduce vibrational mode-mixing and enhance the quality of vibrational assignments in quantum mechanical investigations of two-dimensional model Hamiltonians. Oblique coordinates are obtained by making non-orthogonal rotations of the original coordinates that convert the matrix representation of the quadratic Hamiltonian operator into a block-diagonal matrix where the blocks are distinguished by the total quanta of vibrational excitation. Using techniques for the polar decomposition of matrices, we present a scheme for finding these coordinates for systems of arbitrary dimensions. Several molecular examples are presented that highlight the advantages of these coordinates.

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 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.

Molecular Cage Reports on Its Contents: Spectroscopic Signatures of Cryo-Cooled K+- and Ba2+-Benzocryptand Complexes

UV photofragment spectroscopy and IR-UV double resonance methods are used to determine the structure and spectroscopic responses of a three-dimensional [2.2.2]-benzocryptand cage to the incorporation of a single K⁺ or Ba²⁺ imbedded inside it (labeled as K⁺-BzCrypt, Ba²⁺-BzCrypt). We studied the isolated ion-cryptand complex under cryo-cooled conditions, brought into the gas phase by nano-electrospray ionization. Incorporation of a phenyl ring in place of the central ethyl group in one of the three N-CH₂-CH₂-O-CH₂-CH₂-O-CH₂-CH₂-N chains provides a UV chromophore whose S₀-S₁ transition we probe. K⁺-BzCrypt and Ba²⁺-BzCrypt have their S₀-S₁ origin transitions at 35,925 and 36,446 cm^-1, respectively, blue-shifted by 174 and 695 cm^-1 from that of 1,2-dimethoxybenzene. These origins are used to excite a single conformation of each complex selectively and record their IR spectra using IR-UV dip spectroscopy. The alkyl CH stretch region (2800-3000 cm^-1) is surprisingly sensitive to the presence and nature of the encapsulated ion. We carried out an exhaustive conformational search of cage conformations for K⁺-BzCrypt and Ba²⁺-BzCrypt, identifying two conformations (A and B) that lie below all others in energy. We extend our local mode anharmonic model of the CH stretch region to these strongly bound ion-cage complexes to predict conformation-specific alkyl CH stretch spectra, obtaining quantitative agreement with experiment for conformer A, the gas-phase global minimum. The large electrostatic effect of the charge on the O- and N-lone pairs affects the local mode frequencies of the CH₂ groups adjacent to these atoms. The localized CH₂ scissors modes are pushed up in frequency by the adjacent O/N-atoms so that their overtones have little effect on the alkyl CH stretch region. However, the localized CH₂ wags are nearly degenerate and strongly coupled to one another, producing an array of delocalized wag normal modes, whose highest frequency members reach up above 1400 cm^-1. As such, their overtones mix significantly with the CH stretch modes, most notably involving the CH₂ symmetric stretch fundamentals of the central ethyl groups in the all-alkyl chains and the CH stretches adjacent to the N-atoms and antiperiplanar to the nitrogen lone pair.

Gaussian process regression adaptive density-guided approach: Toward calculations of potential energy surfaces for larger molecules

We present a new program implementation of the Gaussian process regression adaptive density-guided approach [Schmitz et al., J. Chem. Phys. 153, 064105 (2020)] for automatic and cost-efficient potential energy surface construction in the MidasCpp program. A number of technical and methodological improvements made allowed us to extend this approach toward calculations of larger molecular systems than those previously accessible and maintain the very high accuracy of constructed potential energy surfaces. On the methodological side, improvements were made by using a Δ-learning approach, predicting the difference against a fully harmonic potential, and employing a computationally more efficient hyperparameter optimization procedure. We demonstrate the performance of this method on a test set of molecules of growing size and show that up to 80% of single point calculations could be avoided, introducing a root mean square deviation in fundamental excitations of about 3 cm-1. A much higher accuracy with errors below 1 cm-1 could be achieved with tighter convergence thresholds still reducing the number of single point computations by up to 68%. We further support our findings with a detailed analysis of wall times measured while employing different electronic structure methods. Our results demonstrate that GPR-ADGA is an effective tool, which could be applied for cost-efficient calculations of potential energy surfaces suitable for highly accurate vibrational spectra simulations.

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.

Comparative Analysis of Uncoupled Mode Approximations for Molecular Thermochemistry and Kinetics

The accurate prediction of thermochemistry and kinetic parameters is an important task for reaction modeling. Unfortunately, the commonly used harmonic oscillator model is often not accurate enough due to the absence of anharmonic effects. In this work, we improve the representation of an anharmonic potential energy surface (PES) using uncoupled mode (UM) approximations, which model the full-dimensional PES as a sum of one-dimensional potentials of each mode. We systematically analyze different PES sampling schemes and coordinate systems for constructing the one-dimensional potentials, and benchmark the performance of UM methods on data sets of molecular thermochemistry and kinetic properties. The results show that the accuracy of the UM approach strongly depends on how the one-dimensional potentials are defined. If one-dimensional potentials are constructed by sampling along normal mode directions (UM-N) or along the directions that minimize intermode coupling (E- and E'-optimized), the accuracies of the predicted properties are not significantly improved compared to the harmonic oscillator model. However, significant improvements can be achieved by sampling the torsional modes separately from the vibrational modes (UM-T and UM-VT). In this work, three types of coordinate systems are examined, including redundant internal coordinates (RIC), hybrid internal coordinates (HIC), and translation-rotation-internal coordinates (TRIC). The HIC and TRIC coordinate systems can outperform RIC since transition state species may contain large-amplitude interfragmentary motions that regular internal coordinates can not describe adequately. Among all the methods we examined, the activation energies and pre-exponential factors calculated using UM-VT with either TRIC or HIC best agree with the reference values. Since UM-VT requires only a number of additional single point energy calculations for each independent mode, the scaling of computational costs of UM-VT is the same as that of the standard harmonic oscillator model, making UM-VT an appealing way of calculating the thermochemistry and kinetic properties for large-size systems.

Static Electron Correlation in Anharmonic Molecular Vibrations: A Hybrid TAO-DFT Study

Hybrid thermally-assisted-occupation density functional theory is used to examine the effects of static electron correlation on the prediction of a benchmark set of experimentally observed molecular vibrational frequencies. The B3LYP and B97-1 thermally-assisted-occupation measure of static electron correlation is important for describing the vibrations of many of the molecules that make up several popular test sets of experimental data. Shifts are seen for known multireference systems and for many molecules containing atoms from the second row of the periodic table of elements. Several molecules only show significant shifts in select vibrational modes, and significant improvements are seen for the prediction of hydrogen stretching frequencies throughout the test set.

A local mode study of ring puckering effects in the infrared spectra of cyclopentane

We report and interpret recently recorded high-resolution infrared spectra for the fundamentals of the CH2 scissors and CH stretches of gas phase cyclopentane at −26.1 and −50 °C, respectively. We extend previous theoretical studies of this molecule, which is known to undergo barrierless pseudorotation due to ring puckering, by constructing local mode Hamiltonians of the stretching and scissor vibrations for which the frequencies, couplings, and linear dipoles are calculated as functions of the pseudorotation angle using B3LYP/6-311++(d,p) and MP2/cc-pVTZ levels of theory. Symmetrization ( D5 h) of the vibrational basis sets leads to simple vibration/pseudorotation Hamiltonians whose solutions lead to good agreement with the experiment at medium resolution, but which miss interesting line fractionation when compared to the high-resolution spectra. In contrast to the scissor motion, pseudorotation leads to significant state mixing of the CH stretches, which themselves are Fermi coupled to the scissor overtones.

Matrix Product State Formulation of the MCTDH Theory in Local Mode Representations for Anharmonic Potentials

The matrix product state formulation of the multiconfiguration time-dependent Hartree theory, MPS-MCTDH, reported previously [Kurashige, J. Chem. Phys. 2018, 19, 194114] is extended to realistic anharmonic potentials with n-mode representations beyond the linear vibronic coupling model. For realistic vibrational potentials, the local mode representation should give a more compact representation of the potentials, i.e., lowering the dimensionality of the entanglements, than the normal coordinates, and the MPS-MCTDH formulation should work more efficiently and maintain the accuracy with a small bond dimension of the MPS ansatz. In fact, it was confirmed that the use of the local coordinates made the interaction matrices diagonal dominant and the number of terms in the n-body expansion of the potentials was significantly reduced. The method was applied to the IR spectrum of the CH₂O molecule, the zero-point energies, and the vibrational energy redistribution dynamics of polyenes C_2nH_2n+2. The results showed that the efficiency of the MPS-MCTDH method is significantly accelerated by the use of local coordinates even if the long-range interactions are included in the potential.

Infrared multiple photon dissociation action spectroscopy of protonated unsymmetrical dimethylhydrazine and proton-bound dimers of hydrazine and unsymmetrical dimethylhydrazine

The gas-phase structures of protonated unsymmetrical 1,1-dimethylhydrazine (UDMH) and the proton-bound dimers of UDMH and hydrazine are examined by infrared multiple photon dissociation (IRMPD) action spectroscopy utilizing light generated by a free electron laser and an optical parametric oscillator laser system. To identify the structures present in the experimental studies, the measured IRMPD spectra are compared to spectra calculated at the B3LYP-GD3BJ/6-311+G(d,p) level of theory. These comparisons show that protonated UDMH binds the proton at the methylated nitrogen atom (α) with two low-lying α conformers probably being populated. For (UDMH)₂H⁺, the proton is shared between the methylated nitrogen atoms with several low-lying α conformers likely to be populated. Higher-lying conformers of (UDMH)₂H⁺ in which the proton is shared between α and β (unmethylated) nitrogen atoms cannot be ruled out on the basis of the IRPMD spectrum. For (N₂H₄)₂H⁺, there are four low-lying conformers that all reproduce the IRMPD spectrum reasonably well. As hydrazine and UDMH see usage as fuels for rocket engines, such spectra are potentially useful as a means of remotely monitoring rocket launches, especially in cases of unsuccessful launches where environmental hazards need to be assessed.

Anharmonic Vibrational Calculations Based on Group-Localized Coordinates: Applications to Internal Water Molecules in Bacteriorhodopsin

An efficient anharmonic vibrational method is developed exploiting the locality of molecular vibration. Vibrational coordinates localized to a group of atoms are employed to divide the potential energy surface (PES) of a system into intra- and inter-group contributions. Then, the vibrational Schrödinger equation is solved based on a PES, in which the inter-group coupling is truncated at the harmonic level while accounting for the intra-group anharmonicity. The method is applied to a pentagonal hydrogen bond network (HBN) composed of internal water molecules and charged residues in a membrane protein, bacteriorhodopsin. The PES is calculated by the quantum mechanics/molecular mechanics (QM/MM) calculation at the level of B3LYP-D3/aug-cc-pVDZ. The infrared (IR) spectrum is computed using a set of coordinates localized to each water molecule and amino acid residue by second-order vibrational quasi-degenerate perturbation theory (VQDPT2). Benchmark calculations show that the proposed method yields the N-D/O-D stretching frequencies with an error of 7 cm-1 at the cost reduced by more than five times. In contrast, the harmonic approximation results in a severe error of 150 cm-1. Furthermore, the size of QM regions is carefully assessed to find that the QM regions should include not only the pentagonal HBN itself but also its HB partners. VQDPT2 calculations starting from transient structures obtained by molecular dynamics simulations have shown that the structural sampling has a significant impact on the calculated IR spectrum. The incorporation of anharmonicity, sufficiently large QM regions, and structural samplings are of essential importance to reproduce the experimental IR spectrum. The computational spectrum paves the way for decoding the IR signal of strong HBNs and helps elucidate their functional roles in biomolecules.

Reduced Two-Electron Interactions in Anharmonic Molecular Vibrational Calculations Involving Localized Normal Coordinates

Spatially localized vibrational normal mode coordinates are shown to reduce the importance of calculating the full set of two-electron terms in the molecular electronic Schrödinger equation. Electron correlation and dispersion interactions become less significant in (E,E)-1,3,5,7-octatetraene vibrational self-consistent field calculations when displacing remote atoms along multiple coordinates. Electron correlation interactions between spatially remote modes are also found to be less important compared to their corresponding uncorrelated interaction terms. Attenuation of the Coulomb operator indicates that the two-electron terms between remote electrons become less important for accurately describing the strongly contributing mode-coupling terms between sets of localized vibrational modes.

Development of an Electron-Atom Compton Scattering Apparatus Using a Picosecond Pulsed Electron Gun

An apparatus has been developed for electron-atom Compton scattering experiments that can employ a pulsed laser and a picosecond pulsed electron beam in a pump-and-probe scheme. The design and technical details of the apparatus are described. Furthermore, experimental results on the Xe atom in its ground state are presented to illustrate the performance of the pulsed electron gun and the detection and spectrometric capabilities for scattered electrons. The scope of future application is also discussed, involving real-time measurement of intramolecular force acting on each constituent atom with different mass numbers, in a transient, evolving system during a molecular reaction.

Neutral Peptides in the Gas Phase: Conformation and Aggregation Issues

Combined IR and UV laser spectroscopic techniques in molecular beams merged with theoretical approaches have proven to be an ideal tool to elucidate intrinsic structural properties on a molecular level. It offers the possibility to analyze structural changes, in a controlled molecular environment, when successively adding aggregation partners. By this, it further makes these techniques a valuable starting point for a bottom-up approach in understanding the forces shaping larger molecular systems. This bottom-up approach was successfully applied to neutral amino acids starting around the 1990s. Ever since, experimental and theoretical methods developed further, and investigations could be extended to larger peptide systems. Against this background, the review gives an introduction to secondary structures and experimental methods as well as a summary on theoretical approaches. Vibrational frequencies being characteristic probes of molecular structure and interactions are especially addressed. Archetypal biologically relevant secondary structures investigated by molecular beam spectroscopy are described, and the influences of specific peptide residues on conformational preferences as well as the competition between secondary structures are discussed. Important influences like microsolvation or aggregation behavior are presented. Beyond the linear α-peptides, the main results of structural analysis on cyclic systems as well as on β- and γ-peptides are summarized. Overall, this contribution addresses current aspects of molecular beam spectroscopy on peptides and related species and provides molecular level insights into manifold issues of chemical and biochemical relevance.

Anharmonic quantum nuclear densities from full dimensional vibrational eigenfunctions with application to protonated glycine

The interpretation of molecular vibrational spectroscopic signals in terms of atomic motion is essential to understand molecular mechanisms and for chemical characterization. The signals are usually assigned after harmonic normal mode analysis, even if molecular vibrations are known to be anharmonic. Here we obtain the quantum anharmonic vibrational eigenfunctions of the 11-atom protonated glycine molecule and we calculate the density distribution of its nuclei and its geometry parameters, for both the ground and the O-H stretch excited states, using our semiclassical method based on ab initio molecular dynamics trajectories. Our quantum mechanical results describe a molecule elongated and more flexible with respect to what previously thought. More importantly, our method is able to assign each spectral peak in vibrational spectroscopy by showing quantitatively how normal modes involving different functional groups cooperate to originate that spectroscopic signal. The method will possibly allow for a better rationalization of experimental spectroscopy.

Vibrational Spectroscopic Map, Vibrational Spectroscopy, and Intermolecular Interaction

Vibrational spectroscopy is an essential tool in chemical analyses, biological assays, and studies of functional materials. Over the past decade, various coherent nonlinear vibrational spectroscopic techniques have been developed and enabled researchers to study time-correlations of the fluctuating frequencies that are directly related to solute-solvent dynamics, dynamical changes in molecular conformations and local electrostatic environments, chemical and biochemical reactions, protein structural dynamics and functions, characteristic processes of functional materials, and so on. In order to gain incisive and quantitative information on the local electrostatic environment, molecular conformation, protein structure and interprotein contacts, ligand binding kinetics, and electric and optical properties of functional materials, a variety of vibrational probes have been developed and site-specifically incorporated into molecular, biological, and material systems for time-resolved vibrational spectroscopic investigation. However, still, an all-encompassing theory that describes the vibrational solvatochromism, electrochromism, and dynamic fluctuation of vibrational frequencies has not been completely established mainly due to the intrinsic complexity of intermolecular interactions in condensed phases. In particular, the amount of data obtained from the linear and nonlinear vibrational spectroscopic experiments has been rapidly increasing, but the lack of a quantitative method to interpret these measurements has been one major obstacle in broadening the applications of these methods. Among various theoretical models, one of the most successful approaches is a semiempirical model generally referred to as the vibrational spectroscopic map that is based on a rigorous theory of intermolecular interactions. Recently, genetic algorithm, neural network, and machine learning approaches have been applied to the development of vibrational solvatochromism theory. In this review, we provide comprehensive descriptions of the theoretical foundation and various examples showing its extraordinary successes in the interpretations of experimental observations. In addition, a brief introduction to a newly created repository Web site (http://frequencymap.org) for vibrational spectroscopic maps is presented. We anticipate that a combination of the vibrational frequency map approach and state-of-the-art multidimensional vibrational spectroscopy will be one of the most fruitful ways to study the structure and dynamics of chemical, biological, and functional molecular systems in the future.

Adaptive density-guided approach to double incremental potential energy surface construction

We present a combination of the recently developed double incremental expansion of potential energy surfaces with the well-established adaptive density-guided approach to grid construction. This unique methodology is based on the use of an incremental expansion for potential energy surfaces, known as n-mode expansion; an incremental many-body representation of the electronic energy; and an efficient vibrational density-guided approach to automated determination of grid dimensions and granularity. The reliability of the method is validated calculating potential energy surfaces and obtaining fundamental excitation energies for three moderate-size chain-like molecular systems. The use of our methodology leads to considerable computational savings for potential energy surface construction compared to standard approaches while maintaining a high level of accuracy in the resulting potential energy surfaces. Additional investigations indicate that our method can be applied to covalently bound and strongly interacting molecular systems, even though these cases are known to be very unfavorable for fragmentation schemes. We therefore conclude that the presented methodology is a robust and flexible approach to potential energy surface construction, which introduces considerable computational savings without compromising the accuracy of vibrational spectra calculations.

Specific Ion Effects on Hydrogen-Bond Rearrangements in the Halide-Dihydrate Complexes

Small aqueous ionic clusters represent ideal systems to investigate the microscopic hydrogen-bonding structure and dynamics in ion hydration shells. In this context, halide-dihydrate complexes are the smallest systems where the interplay between halide-water and water-water interactions can be studied simultaneously. Here, quantum molecular dynamics simulations unravel specific ion effects on the temperature-dependent structural transition in X^-(H₂O)₂ complexes (X = Cl, Br, and I), which is induced by the breaking of the water-water hydrogen bond. A systematic analysis of the hydrogen-bonding rearrangements at low temperature provides fundamental insights into the competition between halide-water and water-water interactions depending on the properties of the halide ion. While the halide-water hydrogen-bond strength decreases going from Cl^-(H₂O)₂ to I^-(H₂O)₂, the opposite trend in observed in the strength of the water-water hydrogen-bond, suggesting that nontrivial many-body effects may also be at play in the hydration shells of halide ions in solution, especially in frustrated systems (e.g., interfaces) where the water molecules can have dangling OH bonds.

On the choice of coordinates in anharmonic theoretical vibrational spectroscopy: Harmonic vs. anharmonic coupling in vibrational configuration interaction

By a suitable choice of coordinates, the computational effort required for calculations of anharmonic vibrational spectra can be reduced significantly. By using suitable localized-mode coordinates obtained from an orthogonal transformation of the conventionally used normal-mode coordinates, anharmonic couplings between modes can be significantly reduced. However, such a transformation introduces harmonic couplings between the localized modes. To elucidate the role of these harmonic couplings, we consider the vibrational self-consistent field (VSCF)/vibrational configuration interaction (VCI) calculations for both few-mode model systems and for ethene as a molecular test case. We show that large harmonic couplings can result in significant errors in localized-mode L-VSCF/L-VCI calculations and study the convergence with respect to the size of the VCI excitation space. To further elucidate the errors introduced by harmonic couplings, we discuss the connection between L-VSCF/L-VCI and vibrational exciton models. With the help of our results, we propose an algorithm for the localization of normal modes in suitable subsets that are chosen to strictly limit the errors introduced by the harmonic couplings while still leading to maximally localized modes.

Anharmonic Vibrational Analysis of Biomolecules and Solvated Molecules Using Hybrid QM/MM Computations

Quantum mechanics/molecular mechanics (QM/MM) calculations are applied for anharmonic vibrational analyses of biomolecules and solvated molecules. The QM/MM method is implemented into a molecular dynamics (MD) program, GENESIS, by interfacing with external electronic structure programs. Following the geometry optimization and the harmonic normal-mode analysis based on a partial Hessian, the anharmonic potential energy surface (PES) is generated from QM/MM energies and gradients calculated at grid points. The PES is used for vibrational self-consistent field (VSCF) and post-VSCF calculations to compute the vibrational spectrum. The method is first applied to a phosphate ion in solution. With both the ion and neighboring water molecules taken as a QM region, IR spectra of representative hydration structures are calculated by the second-order vibrational quasi-degenerate perturbation theory (VQDPT2) at the level of B3LYP/cc-pVTZ and TIP3P force field. A weight-average of IR spectra over the structures reproduces the experimental spectrum with a mean absolute deviation of 16 cm^–1. Then, the method is applied to an enzyme, P450 nitric oxide reductase (P450nor), with the NO molecule bound to a ferric (Fe^III) heme. Starting from snapshot structures obtained from MD simulations of P450nor in solution, QM/MM calculations have been carried out at the level of B3LYP-D3/def2-SVP(D). The spin state of Fe^III(NO) is likely a closed-shell singlet state based on a ratio of N–O and Fe–NO stretching frequencies (ν_N–O and ν_Fe–NO) calculated for closed- and open-shell singlet states. The calculated ν_N–O and ν_Fe–NO overestimate the experimental ones by 120 and 75 cm^–1, respectively. The electronic structure and solvation of Fe^III(NO) affect the structure around the heme of P450nor leading to an increase in ν_N–O and ν_Fe–NO.

Quantum approaches to vibrational dynamics and spectroscopy: is ease of interpretation sacrificed as rigor increases?

The subject of this Perspective is quantum approaches, beyond the harmonic approximation, to vibrational dynamics and IR spectroscopy.

Probing vibrational coupling via a grid-based quantum approach-an efficient strategy for accurate calculations of localized normal modes in solid-state systems

In this work an approach to investigate the properties of strongly localized vibrational modes of functional groups in bulk material and on solid‐state surfaces is presented. The associated normal mode vectors are approximated solely on the basis of structural information and obtained via diagonalization of a reduced Hessian. The grid‐based Numerov procedure in one and two dimensions is then applied to an adequate scan of the respective potential surface yielding the associated vibrational wave functions and energy eigenvalues. This not only provides a detailed description of anharmonic effects but also an accurate inclusion of the coupling between the investigated vibrational states on a quantum mechanical level. All results obtained for the constructed normal modes are benchmarked against their analytical counterparts obtained from the diagonalization of the total Hessian of the entire system. Three increasingly complex systems treated at quantum chemical level of theory have been considered, namely the symmetric and asymmetric stretch vibrations of an isolated water molecule, hydroxyl groups bound to the surface of GeO₂ (001), α‐quartz(001) and Rutil (001) as well as crystalline Li₂NH serving as an example for a bulk material. While the data obtained for the individual systems verify the applicability of the proposed methodology, comparison to experimental data demonstrates the accuracy of this methodology despite the restriction to limit this methodology to a few selected vibrational modes.

The possibility to investigate vibrational phenomena of localized normal modes without the requirement of executing costly harmonic frequency calculations of the entire system enables the application of this method to cases in which the determination of normal modes is prohibitively expensive or not available for a particular level of theory. © 2018 Wiley Periodicals, Inc.

Intra-cavity proton bonding and anharmonicity in the anionophore cyclen

Proton bonding drives the supramolecular chemistry of a broad range of materials with polar moieties. Proton delocalization and electronic charge redistribution have a profound impact on the structure of proton-bound molecular frameworks, and pose fundamental challenges to quantum chemical modelling. This study provides insights into the structural and spectral signatures of the intramolecular proton bond formed in a benchmark polyazamacrocycle anionophore (cyclen, 1,4,7,10-tetraazacyclododecane). Infrared action spectroscopy is employed to characterize the macrocycle, isolated in protonated form. In its most stable configuration, protonated cyclen adopts an open arrangement of Cs symmetry with a particularly strong NHδ+N bond across the cavity. The quantum chemical analysis of the infrared spectrum reveals intrinsic difficulties for the accurate description of the vibrational modes of the system. The reconciliation of the computational predictions with experiment demands a careful anharmonic treatment of the proton motion, which exposes the limitations of current methods. Best results are obtained with the incorporation of anharmonicity only to the fundamental modes directly related to motions of the proton. However, the full anharmonic treatment of the system fails to describe correctly the vibrations related to the macrocycle backbone. The results should serve as motivation for new developments in the modelling of proton bonded systems.

Reduced Basis Set Dependence in Anharmonic Frequency Calculations Involving Localized Coordinates

Localized normal coordinates are known to be effective in speeding up anharmonic frequency calculations by reducing the complexity of the nuclear Hamiltonian and wave function. Displacing atoms in localized coordinates can also cause relatively small changes in the electronic structure, which can be exploited for further computational efficiency improvements during ab initio electronic structure calculations of the potential energy surface by reducing the electronic basis set dependence. Three different schemes for reducing the basis set dependence have been investigated in this work. These include combining localized coordinate schemes with general mixed basis sets, distance based force-field reductions, and using coordinate specific basis sets. The importance of accurately describing electronic interactions is found to diminish both for multicoordinate terms involving the displacement of remote atoms and when describing the interactions between more remote atoms within specific coordinates.