Infrared Spectroscopy of Fluxional Molecules from (ab Initio) Molecular Dynamics: Resolving Large-Amplitude Motion, Multiple Conformations, and Permutational Symmetries

Theoretical infrared spectroscopy of protonated methane isotopologues

The vibrational spectroscopy of protonated methane and its mixed hydrogen/deuterium isotopologues remains a challenge to both experimental and computational spectroscopy due to the iconic floppiness of CH5+. Here, we compute the finite-temperature broadband infrared spectra of CH5+ and all its isotopologues, i.e. CHnD5-n+ up to CD5+, from path integral molecular dynamics in conjunction with interactions and dipoles computed consistently at CCSD(T) coupled cluster accuracy. The potential energy and dipole moment surfaces have been accurately represented in full dimensionality in terms of high-dimensional neural networks. The resulting computational efficiency allows us to establish CCSD(T) accuracy at the level of converged path integral simulations. For all six isotopologues, the computed broadband spectra compare very favorably to the available experimental broadband spectra obtained from laser induced reactions action vibrational spectroscopy. The current approach is found to consistently and significantly improve on previous calculations of these broadband vibrational spectra and defines the new cutting-edge for what has been dubbed the "enfant terrible" of molecular spectroscopy in view of its pronounced large-amplitude motion that involves all intramolecular degrees of freedom.

A Perspective on the Investigation of Spectroscopy and Kinetics of Complex Molecular Systems with Semiclassical Approaches

In this Perspective we show that semiclassical methods provide a rigorous hierarchical way to study the vibrational spectroscopy and kinetics of complex molecular systems. The time averaged approach to spectroscopy and the semiclassical transition state theory for kinetics, which have been first adopted and then further developed in our group, provide accurate quantum results on rigorous physical grounds and can be applied even when dealing with a large number of degrees of freedom. In spectroscopy, the multiple coherent, divide-and-conquer, and adiabatically switched semiclassical approaches have practically permitted overcoming issues related to the convergence of results. In this Perspective we demonstrate the possibility of studying the semiclassical vibrational spectroscopy of a molecule adsorbed on an anatase (101) surface, a system made of 51 atoms. In kinetics, the semiclassical transition state theory is able to account for anharmonicity and the coupling between the reactive and bound modes. Our group has developed this technique for practical applications involving the study of phenomena like kinetic isotope effect, heavy atom tunneling, and elusive conformer lifetimes. Here, we show that our multidimensional anharmonic quantum approach is able to tackle on-the-fly the thermal kinetic rate constant of a 135 degree-of-freedom system. Overall, semiclassical methods open up the possibility to describe at the quantum mechanical level systems characterized by hundreds of degrees of freedom leading to the accurate spectroscopic and kinetic description of biomolecules and complex molecular systems.

Infrared Spectroscopy of Li+ Solvation in Diglyme: Ab Initio Molecular Dynamics and Experiment

Infrared (IR) spectra of solutions of the lithium salt LiBF4 in diglyme, CH3O(CH2CH2O)2CH3, are studied via IR spectroscopy and ab initio molecular dynamics (AIMD) simulations. Experiments show that the major effects of LiBF4, compared to neat diglyme, are the appearance of a new broad band in the 250-500 cm-1 frequency region and a broadening and intensity enhancement of the diglyme band in the 900-1150 cm-1 region accompanied by a red-shift. Computational analysis indicates that hindered translational motions of Li+ in its solvation cage are mainly responsible for the new far-IR band, while the changes in the mid-IR are due to Li+-coordination-dependent B-F stretching vibrations of BF4- anions coupled with diglyme vibrations. Molecular motions in these and lower frequency regions are generally correlated, revealing the collective nature of the vibrational dynamics, which involve multiple ions/molecules. Herein, a detailed analysis of these features via AIMD simulations of the spectrum and its components, combined with analysis of the generalized normal modes of the solution components, is presented. Other minor spectral changes as well as diglyme conformational changes induced by the lithium salt are also discussed.

Spectroscopic and Chemical Properties of Ionic Liquids: Computational Study

A brief account is given of highlights of our computational efforts - often in collaboration with experimental groups - to understand spectroscopic and chemical properties of ionic liquids (ILs). Molecular dynamics, including their inhomogeneous character, responsible for key spectral features observed in dielectric absorption, infra-red (IR) and fluorescence correlation spectroscopy (FCS) measurements are elucidated. Mechanisms of chemical processes involving imidazolium-based ILs are illustrated for CO2 capture and related reactions, transesterification of cellulose, and Au nanocluster-catalyzed Suzuki cross-coupling reaction with attention paid to differing roles of IL ions. A comparison with experiments is also made.

Vibrational Circular Dichroism from DFT Molecular Dynamics: The AWV Method

The paper illustrates the Activity Weighted Velocities (AWV) methodology to compute Vibrational Circular Dichroism (VCD) anharmonic spectra from Density Functional Theory (DFT) molecular dynamics. AWV calculates the spectra by the Fourier Transform of the time correlation functions of velocities, weighted by specific observables: the Atomic Polar Tensors (APTs) and the Atomic Axial Tensors (AATs). Indeed, AWV shows to correctly reproduce the experimental spectra for systems in the gas and liquid phases, both in the case of weakly and strongly interacting systems. The comparison with the experimental spectra is striking especially in the fingerprint region, as demonstrated by the three benchmark systems discussed: (1S)-Fenchone in the gas phase, (S)-(-)-Propylene oxide in the liquid phase, and (R)-(-)-2-butanol in the liquid phase. The time evolution of APTs and AATs can be adequately described by a linear combination of the tensors of a small set of appropriate reference structures, strongly reducing the computational cost without compromising accuracy. Additionally, AWV allows the partition of the spectral signal in its molecular components without any expensive postprocessing and any localization of the charge density or the wave function.

Some opinions on MD-based vibrational spectroscopy of gas phase molecules and their assembly: An overview of what has been achieved and where to go

We hereby review molecular dynamics simulations for anharmonic gas phase spectroscopy and provide some of our opinions of where the field is heading. With these new directions, the theoretical IR/Raman spectroscopy of large (bio)-molecular systems will be more easily achievable over longer time-scale MD trajectories for an increase in accuracy of the MD-IR and MD-Raman calculated spectra. With the new directions presented here, the high throughput 'decoding' of experimental IR/Raman spectra into 3D-structures should thus be possible, hence advancing e.g. the field of MS-IR for structural characterization by spectroscopy. We also review the assignment of vibrational spectra in terms of anharmonic molecular modes from the MD trajectories, and especially introduce our recent developments based on Graph Theory algorithms. Graph Theory algorithmic is also introduced in this review for the identification of the molecular 3D-structures sampled over MD trajectories.

Proton in the ring: spectroscopy and dynamics of proton bonding in macrocycle cavities

The proton bond is a paradigmatic quantum molecular interaction and a major driving force of supramolecular chemistry. The ring cavities of crown ethers provide an intriguing environment, promoting competitive proton sharing with multiple coordination anchors. This study shows that protons confined in crown ether cavities form dynamic bonds that migrate to varying pairs of coordinating atoms when allowed by the flexibility of the macrocycle backbone. Prototypic native crown ethers (12-crown-4, 15-crown-5 and 18-crown-6) and aza-crown ethers (cyclen, 1-aza-18-crown-6 and hexacyclen) are investigated. For each system, Infrared action spectroscopy experiments and ab initio Molecular Dynamics computations are employed to elucidate the structural effects associated with proton diffusion and its entanglement with the conformational and vibrational dynamics of the protonated host.

Chemically Accurate Vibrational Free Energies of Adsorption from Density Functional Theory Molecular Dynamics: Alkanes in Zeolites

We present a methodology to compute, at reduced computational cost, Gibbs free energies, enthalpies, and entropies of adsorption from molecular dynamics. We calculate vibrational partition functions from vibrational energies, which we obtain from the vibrational density of states by projection on the normal modes. The use of a set of well-chosen reference structures along the trajectories accounts for the anharmonicities of the modes. For the adsorption of methane, ethane, and propane in the H-CHA zeolite, we limit our treatment to a set of vibrational modes localized at the adsorption site (zeolitic OH group) and the alkane molecule interacting with it. Only two short trajectories (1–20 ps) are required to reach convergence (<1 kJ/mol) for the thermodynamic functions. The mean absolute deviations from the experimentally measured values are 2.6, 2.8, and 4.7 kJ/mol for the Gibbs free energy, the enthalpy, and the entropy term (−TΔS), respectively. In particular, the entropy terms show a major improvement compared to the harmonic approximation and almost reach the accuracy of the previous use of anharmonic frequencies obtained with curvilinear distortions of individual modes. The thermodynamic functions so obtained follow the trend of the experimental values for methane, ethane, and propane, and the Gibbs free energy of adsorption at experimental conditions is correctly predicted to change from positive for methane (5.9 kJ/mol) to negative for ethane (−4.8 kJ/mol) and propane (−7.1 kJ/mol).

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.

Gas-Phase Infrared Spectroscopy of Neutral Peptides: Insights from the Far-IR and THz Domain

Gas-phase, double resonance IR spectroscopy has proven to be an excellent approach to obtain structural information on peptides ranging from single amino acids to large peptides and peptide clusters. In this review, we discuss the state-of-the-art of infrared action spectroscopy of peptides in the far-IR and THz regime. An introduction to the field of far-IR spectroscopy is given, thereby highlighting the opportunities that are provided for gas-phase research on neutral peptides. Current experimental methods, including spectroscopic schemes, have been reviewed. Structural information from the experimental far-IR spectra can be obtained with the help of suitable theoretical approaches such as dynamical DFT techniques and the recently developed Graph Theory. The aim of this review is to underline how the synergy between far-IR spectroscopy and theory can provide an unprecedented picture of the structure of neutral biomolecules in the gas phase. The far-IR signatures of the discussed studies are summarized in a far-IR map, in order to gain insight into the origin of the far-IR localized and delocalized motions present in peptides and where they can be found in the electromagnetic spectrum.

Hydrogen molecular ions: H3+, H5+ and beyond

Three decades after the spectroscopic detection of H3+ in space, the inspiring developments in physics, chemistry and astronomy of Hn+ (n = 3, 5, 7) systems, which led to this Royal Society Discussion Meeting, are reviewed, the present state of the art as represented by the meeting surveyed and future lines of research considered. This article is part of a discussion meeting issue 'Advances in hydrogen molecular ions: H3+, H5+ and beyond'.

Vibrational investigation of nucleobases by means of divide and conquer semiclassical dynamics

In this work, we report a computational study of the vibrational features of four different nucleobases employing the divide-and-conquer semiclassical initial value representation molecular dynamics method. Calculations are performed on uracil, cytosine, thymine, and adenine. Results show that the overall accuracy with respect to experiments is within 20 wavenumbers, regardless of the dimensionality of the nucleobase. Vibrational estimates are accurate even in the complex case of cytosine, where two relevant conformers are taken into account. These results are promising in the perspective of future studies on more complex systems, such as nucleotides or nucleobase pairs.

Toward theoretical terahertz spectroscopy of glassy aqueous solutions: partially frozen solute-solvent couplings of glycine in water

The molecular-level understanding of THz spectra of aqueous solutions under ambient conditions has been greatly advanced in recent years. Here, we go beyond previous analyses by performing ab initio molecular dynamics simulations of glycine in water with artificially frozen solute or solvent molecules, respectively, while computing the total THz response as well as its decomposition into mode-specific resonances based on the "supermolecular solvation complex" technique. Clamping the water molecules and keeping glycine moving breaks the coupling of glycine to the structural dynamics of the solvent, however, the polarization and dielectric solvation effects in the static solvation cage are still at work since the full electronic structure of the quenched solvent is taken into account. The complementary approach of fixing glycine reveals both the dynamical and electronic response of the solvation cage at the level of its THz response. Moreover, to quantitatively account for the electronic contribution solely due to solvent embedding, the solute species is "vertically desolvated", thus preserving the fully coupled solute-solvent motion in terms of the solute's structural dynamics in solution, while its electronic structure is no longer subject to solute-solvent polarization and charge transfer effects. When referenced to the free simulation of Gly(aq), this three-fold approach allows us to decompose the THz spectral contributions due to the correlated solute-solvent dynamics into entirely structural and purely electronic effects. Beyond providing hitherto unknown insights, the observed systematic changes of THz spectra in terms of peak shifts and lineshape modulations due to conformational freezing and frozen solvation cages might be useful to investigate the solvation of molecules in highly viscous H-bonding solvents such as ionic liquids and even in cryogenic ices as relevant to polar stratospheric and dark interstellar clouds.

Conformational assignment of gas phase peptides and their H-bonded complexes using far-IR/THz: IR-UV ion dip experiment, DFT-MD spectroscopy, and graph theory for mode assignment

Graph theory based vibrational modes as new entities for vibrational THz spectroscopy.

Simulating structure and dynamics in small droplets of 1-ethyl-3-methylimidazolium acetate

To investigate the structure and dynamics of small ionic liquid droplets in gas phase, we performed a DFT-based ab initio molecular dynamics study of several 1-ethyl-3-methylimidazolium acetate clusters in vacuum as well as a bulk phase simulation. We introduce an unbiased criterion for average droplet diameter and density. By extrapolation of the droplet densities, we predict the experimental bulk phase density with a deviation of only a few percent. The hydrogen bond geometry between cations and anions is very similar in droplets and bulk, but the hydrogen bond dynamics is significantly slower in the droplets, becoming slower with increasing system size, with hydrogen bond lifetimes up to 2000 ps. From a normal mode analysis of the trajectories, we identify the modes of the ring proton C-H stretching, which are strongly affected by hydrogen bonding. From analyzing these, we find that the hydrogen bond becomes weaker with increasing system size. The cations possess an increased concentration inside the clusters, whereas the anions show an excess concentration on the outside. Almost all anions point towards the droplet center with their carboxylic groups. Ring stacking is found to be a very important structural motif in the droplets (as in the bulk), but side chain interactions are only of minor importance. By using Voronoi tessellation, we define the exposed droplet surface and find that it consists mainly of hydrogen atoms from the cation's and anion's methyl and ethyl groups. Polar atoms are rarely found on the surface, such that the droplets appear completely hydrophobic on the outside.

Protonated glycine supramolecular systems: the need for quantum dynamics

Quantum mechanical simulations unequivocally explain experimental IR spectra of protonated supramolecular systems.

IR spectroscopy is one of the most commonly employed techniques to study molecular vibrations and interactions. However, characterization of experimental IR spectra is not always straightforward. This is the case of protonated glycine supramolecular systems like Gly₂H⁺ and (GlyH + nH₂), whose IR spectra raise questions which have still to find definitive answers even after theoretical spectroscopy investigations. Specifically, the assignment of the conformer responsible for the spectrum of the protonated glycine dimer (Gly₂H⁺) has led to much controversy and it is still debated, while structural hypotheses formulated to explain the main experimental spectral features of (GlyH + nH₂) systems have not been theoretically confirmed. We demonstrate that simulations must account for quantum dynamical effects in order to resolve these open issues. This is achieved by means of our divide-and-conquer semiclassical initial value representation technique, which approximates the quantum dynamics of high dimensional systems with remarkable accuracy and outperforms not only the commonly employed but unfit scaled-harmonic approaches, but also pure classical dynamics simulations. Besides the specific insights concerning the two particular cases presented here, the general conclusion is that, due to the widespread presence of protonated systems in chemistry, quantum dynamics may play a prominent role and should not be totally overlooked even when dealing with large systems including biological structures.

"Divide and conquer" semiclassical molecular dynamics: A practical method for spectroscopic calculations of high dimensional molecular systems

We extensively describe our recently established "divide-and-conquer" semiclassical method [M. Ceotto, G. Di Liberto, and R. Conte, Phys. Rev. Lett. 119, 010401 (2017)] and propose a new implementation of it to increase the accuracy of results. The technique permits us to perform spectroscopic calculations of high-dimensional systems by dividing the full-dimensional problem into a set of smaller dimensional ones. The partition procedure, originally based on a dynamical analysis of the Hessian matrix, is here more rigorously achieved through a hierarchical subspace-separation criterion based on Liouville's theorem. Comparisons of calculated vibrational frequencies to exact quantum ones for a set of molecules including benzene show that the new implementation performs better than the original one and that, on average, the loss in accuracy with respect to full-dimensional semiclassical calculations is reduced to only 10 wavenumbers. Furthermore, by investigating the challenging Zundel cation, we also demonstrate that the "divide-and-conquer" approach allows us to deal with complex strongly anharmonic molecular systems. Overall the method very much helps the assignment and physical interpretation of experimental IR spectra by providing accurate vibrational fundamentals and overtones decomposed into reduced dimensionality spectra.

Tagging effects on the mid-infrared spectrum of microsolvated protonated methane

Although bare protonated methane is by now essentially understood at the level of intramolecular large-amplitude motion, scrambling dynamics and broadband vibrational spectra, the microsolvated species still offer plenty of challenges. One aspect is the effect of the attached solvent molecules on the infrared absorption spectra of microsolvated CH₅⁺ complexes compared to the bare parent molecule. In this study we analyze, based on ab initio molecular dynamics simulations, protonated methane molecules that have been microsolvated with up to three hydrogen molecules, i.e. CH₅⁺·(H₂) _n . In particular, upon introducing a novel multi-channel maximum entropy methodology described herein, we are able to decompose the infrared spectra of these weakly-bound complexes in the frequency window from 1000 to 4500 cm^-1 into additive single mode contributions. Detailed comparisons to the bare CH₅⁺ parent reveal that these perturbed modes encode distinct features that depend on the exact microsolvation pattern. Beyond the specific case, such understanding is relevant to assess tagging artifacts in vibrational spectra of parent molecules based on messenger predissociation action spectroscopy.

Mode specific THz spectra of solvated amino acids using the AMOEBA polarizable force field

We have used the AMOEBA model to simulate the THz spectra of two zwitterionic amino acids in aqueous solution, which is compared to the results on these same systems using ab initio molecular dynamics (AIMD) simulations. Overall we find that the polarizable force field shows promising agreement with AIMD data for both glycine and valine in water. This includes the THz spectral assignments and the mode-specific spectral decomposition into intramolecular solute motions as well as distinct solute-water cross-correlation modes some of which cannot be captured by non-polarizable force fields that rely on fixed partial charges. This bodes well for future studies for simulating and decomposing the THz spectra for larger solutes such as proteins or polymers for which AIMD studies are presently intractable. Furthermore, we believe that the current study on rather simple aqueous solutions offers a way to systematically investigate the importance of charge transfer, nuclear quantum effects, and the validity of computationally practical density functionals, all of which are needed to fully quantitatively capture complex dynamical motions in the condensed phase.

Spin-state dependence of the structural and vibrational properties of solvated iron(ii) polypyridyl complexes from AIMD simulations: aqueous [Fe(bpy)3]Cl2, a case study

LS and HS IR spectra of aqueous [Fe(bpy)₃]²⁺ and corresponding HS–LS difference IR spectrum as obtained from state-of-the-art ab initio molecular dynamics simulations applied to the determination of the structural and vibrational properties of the solvated complex.

Aqueous TMAO solutions as seen by theoretical THz spectroscopy: hydrophilic versus hydrophobic water

All THz resonances of aqueous TMAO solutions are computed and assigned based on ab initio molecular dynamics simulations.

Vibrational Spectroscopy of Ionic Liquids

Vibrational spectroscopy has continued use as a powerful tool to characterize ionic liquids since the literature on room temperature molten salts experienced the rapid increase in number of publications in the 1990's. In the past years, infrared (IR) and Raman spectroscopies have provided insights on ionic interactions and the resulting liquid structure in ionic liquids. A large body of information is now available concerning vibrational spectra of ionic liquids made of many different combinations of anions and cations, but reviews on this literature are scarce. This review is an attempt at filling this gap. Some basic care needed while recording IR or Raman spectra of ionic liquids is explained. We have reviewed the conceptual basis of theoretical frameworks which have been used to interpret vibrational spectra of ionic liquids, helping the reader to distinguish the scope of application of different methods of calculation. Vibrational frequencies observed in IR and Raman spectra of ionic liquids based on different anions and cations are discussed and eventual disagreements between different sources are critically reviewed. The aim is that the reader can use this information while assigning vibrational spectra of an ionic liquid containing another particular combination of anions and cations. Different applications of IR and Raman spectroscopies are given for both pure ionic liquids and solutions. Further issues addressed in this review are the intermolecular vibrations that are more directly probed by the low-frequency range of IR and Raman spectra and the applications of vibrational spectroscopy in studying phase transitions of ionic liquids.

A polarizable QM/MM approach to the molecular dynamics of amide groups solvated in water

The infrared (IR) spectra of polypeptides are dominated by the so-called amide bands. Because they originate from the strongly polar and polarizable amide groups (AGs) making up the backbone, their spectral positions sensitively depend on the local electric fields. Aiming at accurate computations of these IR spectra by molecular dynamics (MD) simulations, which derive atomic forces from a hybrid quantum and molecular mechanics (QM/MM) Hamiltonian, here we consider the effects of solvation in bulk liquid water on the amide bands of the AG model compound N-methyl-acetamide (NMA). As QM approach to NMA we choose grid-based density functional theory (DFT). For the surrounding MM water, we develop, largely based on computations, a polarizable molecular mechanics (PMM) model potential called GP6P, which features six Gaussian electrostatic sources (one induced dipole, five static partial charge distributions) and, therefore, avoids spurious distortions of the DFT electron density in hybrid DFT/PMM simulations. Bulk liquid GP6P is shown to have favorable properties at the thermodynamic conditions of the parameterization and beyond. Lennard-Jones (LJ) parameters of the DFT fragment NMA are optimized by comparing radial distribution functions in the surrounding GP6P liquid with reference data obtained from a "first-principles" DFT-MD simulation. Finally, IR spectra of NMA in GP6P water are calculated from extended DFT/PMM-MD trajectories, in which the NMA is treated by three different DFT functionals (BP, BLYP, B3LYP). Method-specific frequency scaling factors are derived from DFT-MD simulations of isolated NMA. The DFT/PMM-MD simulations with GP6P and with the optimized LJ parameters then excellently predict the effects of aqueous solvation and deuteration observed in the IR spectra of NMA. As a result, the methods required to accurately compute such spectra by DFT/PMM-MD also for larger peptides in aqueous solution are now at hand.

Simulating the vibrational spectra of ionic liquid systems: 1-ethyl-3-methylimidazolium acetate and its mixtures

The vibrational spectra of the ionic liquid 1-ethyl-3-methylimidazolium acetate and its mixtures with water and carbon dioxide are calculated using ab initio molecular dynamics simulations, and the results are compared to experimental data. The new implementation of a normal coordinate analysis in the trajectory analyzer TRAVIS is used to assign the experimentally observed bands to specific molecular vibrations. The applied computational approaches prove to be particularly suitable for the modeling of bulk phase effects on vibrational spectra, which are highly important for the discussion of the microscopic structure in systems with a strong dynamic network of intermolecular interactions, such as ionic liquids.

Exploring the vibrational fingerprint of the electronic excitation energy via molecular dynamics

A Fourier-based method is presented to relate changes of the molecular structure during a molecular dynamics simulation with fluctuations in the electronic excitation energy. The method implies sampling of the ground state potential energy surface. Subsequently, the power spectrum of the velocities is compared with the power spectrum of the excitation energy computed using time-dependent density functional theory. Peaks in both spectra are compared, and motions exhibiting a linear or quadratic behavior can be distinguished. The quadratically active motions are mainly responsible for the changes in the excitation energy and hence cause shifts between the dynamic and static values of the spectral property. Moreover, information about the potential energy surface of various excited states can be obtained. The procedure is illustrated with three case studies. The first electronic excitation is explored in detail and dominant vibrational motions responsible for changes in the excitation energy are identified for ethylene, biphenyl, and hexamethylbenzene. The proposed method is also extended to other low-energy excitations. Finally, the vibrational fingerprint of the excitation energy of a more complex molecule, in particular the azo dye ethyl orange in a water environment, is analyzed.