A time averaged semiclassical approach to IR spectroscopy

We propose a new semiclassical approach to the calculation of molecular IR spectra. The method employs the time averaging technique of Kaledin and Miller upon symmetrization of the quantum dipole-dipole autocorrelation function. Spectra at high and low temperatures are investigated. In the first case, we are able to point out the possible presence of hot bands in the molecular absorption line shape. In the second case, we are able to reproduce accurate IR spectra as demonstrated by a calculation of the IR spectrum of the water molecule, which is within 4% of the exact intensity. Our time averaged IR spectra can be directly compared to time averaged semiclassical power spectra as shown in an application to the CO2 molecule, which points out the differences between IR and power spectra and demonstrates that our new approach can identify active IR transitions correctly. Overall, the method features excellent accuracy in calculating absorption intensities and provides estimates for the frequencies of vibrations in agreement with the corresponding power spectra. In perspective, this work opens up the possibility to interface the new method with the semiclassical techniques developed for power spectra, such as the divide-and-conquer one, to get accurate IR spectra of complex and high-dimensional molecular systems.

Modeling the dynamics of quantum systems coupled to large-dimensional baths using effective energy states

The quantum dynamics of a low-dimensional system in contact with a large but finite harmonic bath is theoretically investigated by coarse-graining the bath into a reduced set of effective energy states. In this model, the couplings between the system and the bath are obtained from statistically averaging over the discrete, degenerate effective states. Our model is aimed at intermediate bath sizes in which non-Markovian processes and energy transfer between the bath and the main system are important. The method is applied to a model system of a Morse oscillator coupled to 40 harmonic modes. The results are found to be in excellent agreement with the direct quantum dynamics simulations presented in the work of Bouakline et al. [J. Phys. Chem. A 116, 11118-11127 (2012)], but at a much lower computational cost. Extension to larger baths is discussed in comparison to the time-convolutionless method. We also extend this study to the case of a microcanonical bath with finite initial internal energies. The computational efficiency and convergence properties of the effective bath states model with respect to relevant parameters are also discussed.

Describing nuclear quantum effects in vibrational properties using molecular dynamics with Wigner sampling

In this work we discuss the generally applicable Wigner sampling and introduce a new, simplified Wigner sampling method, for computationally effective modeling of molecular properties containing nuclear quantum effects and vibrational anharmonicity. For various molecular systems test calculations of (a) vibrationally averaged rotational constants, (b) vibrational IR spectra and (c) photoelectron spectra have been performed. The performance of Wigner sampling has been assessed by comparing with experimental data and with results of other theoretical models, including harmonic and VPT2 approximations. The developed simplified Wigner sampling method shows advantages in application to large and flexible molecules.

How Crystal Symmetry Dictates Non-Local Vibrational Circular Dichroism in the Solid State

Solid-State Vibrational Circular Dichroism (VCD) can be used to determine the absolute structure of chiral crystals, but its interpretation remains a challenge in modern spectroscopy. In this work, we investigate the effect of a twofold screw axis on the solid-state VCD spectrum in a combined experimental and theoretical analysis of P2₁ crystals of (S)-(+)-1-indanol. Even though the space group is achiral, a single proper symmetry operation has an important impact on the VCD spectrum, which reflects the supramolecular chirality of the crystal. Distinguishing between contributions originating from molecular chirality and from chiral crystal packing, we find that while IR absorption hardly depends on the symmetry of the space group, the situation is different for VCD, where completely new non-local patterns emerge. Understanding the two underlying mechanisms, namely gauge transport and direct coupling, will help to use VCD to distinguish polymorphic forms.

Δ-Machine Learned Potential Energy Surfaces and Force Fields

There has been great progress in developing machine-learned potential energy surfaces (PESs) for molecules and clusters with more than 10 atoms. Unfortunately, this number of atoms generally limits the level of electronic structure theory to less than the "gold standard" CCSD(T) level. Indeed, for the well-known MD17 dataset for molecules with 9-20 atoms, all of the energies and forces were obtained with DFT calculations (PBE). This Perspective is focused on a Δ-machine learning method that we recently proposed and applied to bring DFT-based PESs to close to CCSD(T) accuracy. This is demonstrated for hydronium, N-methylacetamide, acetyl acetone, and ethanol. For 15-atom tropolone, it appears that special approaches (e.g., molecular tailoring, local CCSD(T)) are needed to obtain the CCSD(T) energies. A new aspect of this approach is the extension of Δ-machine learning to force fields. The approach is based on many-body corrections to polarizable force field potentials. This is examined in detail using the TTM2.1 water potential. The corrections make use of our recent CCSD(T) datasets for 2-b, 3-b, and 4-b interactions for water. These datasets were used to develop a new fully ab initio potential for water, termed q-AQUA.

High-dimensional neural network potentials for accurate vibrational frequencies: the formic acid dimer benchmark

In recent years, machine learning potentials (MLP) for atomistic simulations have attracted a lot of attention in chemistry and materials science. Many new approaches have been developed with the primary aim to transfer the accuracy of electronic structure calculations to large condensed systems containing thousands of atoms. In spite of these advances, the reliability of modern MLPs in reproducing the subtle details of the multi-dimensional potential-energy surface is still difficult to assess for such systems. On the other hand, moderately sized systems enabling the application of tools for thorough and systematic quality-control are nowadays rarely investigated. In this work we use benchmark-quality harmonic and anharmonic vibrational frequencies as a sensitive probe for the validation of high-dimensional neural network potentials. For the case of the formic acid dimer, a frequently studied model system for which stringent spectroscopic data became recently available, we show that high-quality frequencies can be obtained from state-of-the-art calculations in excellent agreement with coupled cluster theory and experimental data.

Evidence for Oxonium Ions in Ethereal "Hydrogen Chloride"

Although solutions of hydrogen chloride in ethereal solvents like diethyl ether or dioxane are commonly employed in the laboratory, the solution structure of these reagents has yet to be firmly established. Here, we analyze solutions of ethereal hydrogen chloride or deuterium chloride in toluene, in dichloromethane, or in the absence of a co-solvent by in situ infrared spectroscopy. The resulting spectra are inconsistent with free HCl or often-proposed 1:1 HCl-ether complexes but closely match the predicted spectra of oxonium ions generated via protonation of diethyl ether. Molecular dynamics simulation of the oxonium chloride complexes provides evidence for an outer-sphere contact ion pair. These results suggest new approaches for tuning the acidity of strong Brønsted acids in organic solvents and demonstrate the importance of conducting spectroscopic measurements under reaction-relevant conditions.

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.

The MD17 datasets from the perspective of datasets for gas-phase “small” molecule potentials

There has been great progress in developing methods for machine-learned potential energy surfaces. There have also been important assessments of these methods by comparing so-called learning curves on datasets of electronic energies and forces, notably the MD17 database. The dataset for each molecule in this database generally consists of tens of thousands of energies and forces obtained from DFT direct dynamics at 500 K. We contrast the datasets from this database for three “small” molecules, ethanol, malonaldehyde, and glycine, with datasets we have generated with specific targets for the potential energy surfaces (PESs) in mind: a rigorous calculation of the zero-point energy and wavefunction, the tunneling splitting in malonaldehyde, and, in the case of glycine, a description of all eight low-lying conformers. We found that the MD17 datasets are too limited for these targets. We also examine recent datasets for several PESs that describe small-molecule but complex chemical reactions. Finally, we introduce a new database, “QM-22,” which contains datasets of molecules ranging from 4 to 15 atoms that extend to high energies and a large span of configurations.

On the use of a volume constraint to account for thermal expansion effects on the low-frequency vibrations of molecular crystals

A volume-constraint method is presented as a means to capture the influence of thermal expansion on the low-frequency vibrations in molecular crystals. In particular, the room-temperature terahertz absorption spectra of L-tartaric acid, α-lactose monohydrate, and α-para-aminobenzoic acid (PABA) have been simulated using dispersion-corrected, solid-state density functional theory (DFT-D). By comparing the normal modes obtained with a unit cell optimised without constraints to those obtained with a unit cell optimised while constrained to keep its experimental volume, wholesale improvements to the resultant spectrum is achieved when using the constrained geometry by inhibiting cell contraction. These improvements are demonstrated over a range of popular density functionals and basis sets up to triple-zeta complexity. A correlation method is then presented as a means to quantitatively compare the vibrational pattern of normal modes obtained from both unit cells. This analysis reveals that thermal expansion can effect the character and relative frequency of normal modes, with the choice of geometry ultimately affecting the assignment of the experimental absorptions. The sensibility of using the experimental volume as an approximation is then discussed, where it is speculated that large basis sets or hybrid functionals are necessary to ensure that the thermal expansion effect is not overestimated. The low-frequency absorption spectrum of PABA is then fully characterised using the PBE-D3BJ/6-311G(2d,2p) method.

Potential energy barrier for proton transfer in compressed benzoic acid

Benzoic acid (BA) is a model system for studying proton transfer (PT) reactions. The properties of solid BA subject to high pressure (exceeding 1 kbar = 0.1 GPa) are of particular interest due to the possibility of compression-tuning of the PT barrier. Here we present simulations aimed at evaluating the value of this barrier in solid BA in the 1 atm - 15 GPa pressure range. We find that pressure-induced shortening of O⋯O contacts within the BA dimers leads to a decrease in the PT barrier, and subsequent symmetrization of the hydrogen bond. However, this effect is obtained only after taking into account zero-point energy (ZPE) differences between BA tautomers and the transition state. The obtained results shed light on previous experiments on compressed benzoic acid, and indicate that a common scaling behavior with respect to the O⋯O distance might be applicable for hydrogen-bond symmetrization in both organic and inorganic systems.

Slow monomer vibrations in formic acid dimer: Stepping up the ladder with FTIR and Raman jet spectroscopy

In an effort to extend the cold gas phase spectroscopic database of the cyclic formic acid dimer (FAD), we present and analyze the jet-cooled vibrational infrared and Raman spectrum of (HCOOH)₂ in the monomer fingerprint region between 600 and 1500 cm^-1. The present study bridges the gap between the intermolecular dimerization-induced and the carbonyl stretching fundamentals that have already been reexamined using jet-cooled or high-resolution spectroscopy. This completes the characterization of the jet-cooled vibrational (HCOOH)₂ spectrum below the complex OH (CH) stretching fundamentals, and we report resonance-induced FAD combination/overtone transitions that will serve as a valuable reference for a theoretical modeling of its vibrational dynamics. As a by-product, several new formic acid trimer fundamentals are identified in the jet spectra and assigned with the help of second-order vibrational perturbation theory (VPT2). The polar formic acid dimer still eludes detection in a supersonic jet, but we are able to estimate an experimental upper-bound of the polar dimer-to-trimer-to-cyclic dimer intensity ratio to about 1:10:100 under typical expansion conditions. Using VPT2 with resonance treatment (VPT2+K), we reinvestigate the notorious ν₂₂ resonance triad. Generally, we find that VPT2, which is, of course, inadequate for modeling the resonance-rich OH stretching spectrum of FAD, is performing very satisfactorily in predicting fundamental and two-quantum state term values for the slower modes below 1500 cm^-1. As these modes are the building blocks for the ultrafast energy dissipation in the OH stretching region, the present work opens the door for its quantitative understanding.

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.

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-νN 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-νN AC and the interatomic distance histograms, the high-frequency vibrational bands are discussed in detail.

CC-stretched formic acid: isomerisation, dimerisation, and carboxylic acid complexation

The cis-trans-isomerism of the propiolic acid monomer (HC[triple bond, length as m-dash]C-COOH) is examined with linear Raman jet spectroscopy, yielding the first environment-free vibrational band centres of a higher-energy cis-rotamer beyond formic acid (HCOOH) in addition to all fundamentals and a large number of hot and combination/overtone bands of the trans-conformer. Two near-isoenergetic trans-fundamentals of different symmetry (CC[double bond, length as m-dash]O bend and OH torsion) prove to be a sensitive benchmarking target, as their energetic order is susceptible to the choice of electronic structure method, basis set size, and inclusion of vibrational anharmonicity. For the infrared- and Raman-active C[double bond, length as m-dash]O stretching fundamentals of the cyclic (C_2h) trans-propiolic acid dimer, resonance couplings are found that in part extend to the C_s-symmetric heterodimer of trans-propiolic and trans-formic acid. Exploratory vibrational perturbation theory (VPT2) calculations show that all perturbing states involve displacements of the OH moieties located on the doubly hydrogen bonded ring. The comparison of the infrared spectra of the propiolic acid dimer and its heterodimer with formic acid to that of several other carboxylic acid dimers from the literature reveals a notable similarity regarding a non-fundamental dimer band around 1800 cm^-1, which in most cases is so far unassigned. VPT2 calculations and a simple harmonic model suggest an assignment to a combination vibration of the symmetric and antisymmetric OH torsion.

Evolution of the linker in microhydrated hydrogen dinitrate anions: From H+ to H5 O2. J Comput Chem 2021;42:1514-1525. [PMID: 33990989 DOI: 10.1002/jcc.26560] [Citation(s) in RCA: 0] [Impact Index Per Article: 0]

Hydrogen dinitrate anion, HNO₃ (NO₃ ^- ), is a proton-bound dimer with a very strong hydrogen bond. By employing ab initio molecular dynamics (AIMD) method, we studied the effects of the proton transfer and the rotation of the nitrates on the vibrational profiles of HNO₃ (NO₃ ^- )(H₂ O)_n (n = 0-2). The AIMD results indicate that the structure of the n = 0 cluster is very flexible, even though its hydrogen bond is quite strong. Significant rotations around the hydrogen bond and frequent transfers of proton from HNO₃ to NO₃ ^- are observed in AIMD simulations. Dynamic changes are therefore an important factor in understanding the broadening of vibrational features. For n = 1, the extent of structural fluctuation increases further, as H₂ O could move around the anion while the HNO₃ (NO₃ ^- ) core also goes through structural changes. Its vibrational spectrum can be understood as a mixture of many isomers visited during AIMD simulations. By n = 2, the structure is stabilized around one isomer, with the linker between the two nitrates being H₅ O₂ ⁺ , rather than H⁺ . Due to strong hydrogen bonds between nitrates and water molecules, this H₅ O₂ ⁺ takes the extraordinary structure with the H⁺ localized on one H₂ O, rather than being shared. While this novel structure is stable during AIMD simulations, the dynamic fluctuations in hydrogen bond distances still produce significant broadening in its vibrational profile.

Transfer Learning to CCSD(T): Accurate Anharmonic Frequencies from Machine Learning Models

The calculation of the anharmonic modes of small- to medium-sized molecules for assigning experimentally measured frequencies to the corresponding type of molecular motions is computationally challenging at sufficiently high levels of quantum chemical theory. Here, a practical and affordable way to calculate coupled-cluster quality anharmonic frequencies using second-order vibrational perturbation theory (VPT2) from machine-learned models is presented. The approach, referenced as "NN + VPT2", uses a high-dimensional neural network (PhysNet) to learn potential energy surfaces (PESs) at different levels of theory from which harmonic and VPT2 frequencies can be efficiently determined. The NN + VPT2 approach is applied to eight small- to medium-sized molecules (H₂CO, trans-HONO, HCOOH, CH₃OH, CH₃CHO, CH₃NO₂, CH₃COOH, and CH₃CONH₂) and frequencies are reported from NN-learned models at the MP2/aug-cc-pVTZ, CCSD(T)/aug-cc-pVTZ, and CCSD(T)-F12/aug-cc-pVTZ-F12 levels of theory. For the largest molecules and at the highest levels of theory, transfer learning (TL) is used to determine the necessary full-dimensional, near-equilibrium PESs. Overall, NN + VPT2 yields anharmonic frequencies to within 20 cm^-1 of experimentally determined frequencies for close to 90% of the modes for the highest quality PES available and to within 10 cm^-1 for more than 60% of the modes. For the MP2 PESs only ∼60% of the NN + VPT2 frequencies were within 20 cm^-1 of the experiment, with outliers up to ∼150 cm^-1, compared to the experiment. It is also demonstrated that the approach allows to provide correct assignments for strongly interacting modes such as the OH bending and the OH torsional modes in formic acid monomer and the CO-stretch and OH-bend mode in acetic acid.

Fingerprint region of the formic acid dimer: variational vibrational computations in curvilinear coordinates

Curvilinear kinetic energy models are developed for variational nuclear motion computations including the inter- and the low-frequency intra-molecular degrees of freedom of the formic acid dimer. The coupling of the inter- and intra-molecular modes is studied by solving the vibrational Schrödinger equation for a series of vibrational models, from two up to ten active vibrational degrees of freedom by selecting various combinations of active modes and constrained coordinate values. Vibrational states, nodal assignment, and infrared vibrational intensity information is computed using the full-dimensional potential energy surface (PES) and electric dipole moment surface developed by Qu and Bowman [Phys. Chem. Chem. Phys., 2016, 18, 24835; J. Chem. Phys., 2018, 148, 241713]. Good results are obtained for several fundamental and combination bands in comparison with jet-cooled vibrational spectroscopy experiments, but the description of the ν₈ and ν₉ fundamental vibrations, which are close in energy and have the same symmetry, appears to be problematic. For further progress in comparison with experiment, the potential energy surface, and in particular, its multi-dimensional couplings representation, requires further improvement.

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

The aqueous proton is a common and long-studied species in chemistry, yet there is currently intense interest devoted to understanding its hydration structure and transport dynamics. Typically described in terms of two limiting structures observed in gas-phase clusters, the Zundel H₅O₂ ⁺ and Eigen H₉O₄ ⁺ ions, the aqueous structure is less clear due to the heterogeneity of hydrogen bonding environments and room-temperature structural fluctuations in water. The linear infrared (IR) spectrum, which reports on structural configurations, is challenging to interpret because it appears as a continuum of absorption, and the underlying vibrational modes are strongly anharmonically coupled to each other. Recent two-dimensional IR (2D IR) experiments presented strong evidence for asymmetric Zundel-like motifs in solution, but true structure-spectrum correlations are missing and complicated by the anharmonicity of the system. In this study, we employ high-level vibrational self-consistent field/virtual state configuration interaction calculations to demonstrate that the 2D IR spectrum reports on a broad distribution of geometric configurations of the aqueous proton. We find that the diagonal 2D IR spectrum around 1200 cm^-1 is dominated by the proton stretch vibrations of Zundel-like and intermediate geometries, broadened by the heterogeneity of aqueous configurations. There is a wide distribution of multidimensional potential shapes for the proton stretching vibration with varying degrees of potential asymmetry and confinement. Finally, we find specific cross peak patterns due to aqueous Zundel-like species. These studies provide clarity on highly debated spectral assignments and stringent spectroscopic benchmarks for future simulations.

A general automatic method for optimal construction of matrix product operators using bipartite graph theory

Constructing matrix product operators (MPOs) is at the core of the modern density matrix renormalization group (DMRG) and its time dependent formulation. For the DMRG to be conveniently used in different problems described by different Hamiltonians, in this work, we propose a new generic algorithm to construct the MPO of an arbitrary operator with a sum-of-products form based on the bipartite graph theory. We show that the method has the following advantages: (i) it is automatic in that only the definition of the operator is required; (ii) it is symbolic thus free of any numerical error; (iii) the complementary operator technique can be fully employed so that the resulting MPO is globally optimal for any given order of degrees of freedom; and (iv) the symmetry of the system could be fully employed to reduce the dimension of MPO. To demonstrate the effectiveness of the new algorithm, the MPOs of Hamiltonians ranging from the prototypical spin-boson model and the Holstein model to the more complicated ab initio electronic Hamiltonian and the anharmonic vibrational Hamiltonian with the sextic force field are constructed. It is found that for the former three cases, our automatic algorithm can reproduce exactly the same MPOs as the optimally hand-crafted ones already known in the literature.

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.

The Methyl Torsion in Unsaturated Compounds

How the methyl torsion transition energy in unsaturated systems is affected by its environment is investigated. It is strongly influenced by both its immediate neighborhood, (the number of methyl groups present in the molecule) and the intermolecular interactions. It is clear that the intermolecular interactions have a major influence on the torsion transition energy, as demonstrated unambiguously previously for mesitylene and also seen here for other systems. In part, this may be caused by the fact that the methyl torsion is rarely a pure mode (unless enforced by symmetry). Where the crystal structure is available, the assignments have been supported by CASTEP calculations of the unit cell. The agreement between the observed and calculated spectra is generally good, although not perfect, toluene being a case in point, and highlights just how demanding it is to obtain accurate transition energies for low energy modes. The disagreement between observed and calculated inelastic neutron scattering spectra for meta-xylene and 9,10 dimethylanthracene is so severe that it would suggest that there are additional phases to those presently known. Comparison between the full periodic calculations and those for the isolated molecule shows that intermolecular interactions raise the methyl torsion transition energy by at least 8% and in some cases by more than 50%. The presence of more than one methyl group in the molecule generally raises the average torsion energy from the <100 cm^-1 seen for single methyl groups to 150-200 cm^-1.

Shifting formic acid dimers into perspective: vibrational scrutiny in helium nanodroplets

A metastable dimer of formic acid has been prepared inside superfluid helium nanodroplets and examined using IR spectroscopy and quantum chemical calculations.

Concerted Pair Motion Due to Double Hydrogen Bonding: The Formic Acid Dimer Case

Formic acid dimer as the prototypical doubly hydrogen-bonded gas-phase species is discussed from the perspective of the three translational and the three rotational degrees of freedom which are lost when two formic acid molecules form a stable complex. The experimental characterisation of these strongly hindered translations and rotations is reviewed, as are attempts to describe the associated fundamental vibrations, their combinations, and their thermal shifts by different electronic structure calculations and vibrational models. A remarkable match is confirmed for the combination of a CCSD(T)-level harmonic treatment and an MP2-level anharmonic VPT2 correction. Qualitatively correct thermal shifts of the vibrational spectra can be obtained from classical molecular dynamics in CCSD(T)-quality force fields. A detailed analysis suggests that this agreement between experiment and composite theoretical treatment is not strongly affected by fortuitous error cancellation but fully converged variational treatments of the six pair or intermolecular modes and their overtones and combinations in this model system would be welcome.

The smallest proton-bound dimer H5+: theoretical progress

The protonated hydrogen dimer, H5+, is the smallest system including proton transfer, and has been of long-standing interest since its first laboratory observation in 1962. H5+ and its isotopologues are the intermediate complexes in deuterium fractionation reactions, and are of central importance in molecular astrophysics. The recently recorded infrared spectra of both H5+ and D5+ reveal a rich vibrational dynamics of the cations, which presents a challenge for standard theoretical approaches. Although H5+ is a four-electron ion, which makes highly accurate electronic structure calculations tractable, the construction of ab initio-based potential energy and dipole moment surfaces has proved a hard task. In the same vein, the difficulties in treating the nuclear motion could also become cumbersome due to their high dimensionality, floppiness and/or symmetry. These systems are prototypical examples for studying large-amplitude motions, as they are highly delocalized, interconverting between equivalent minima through internal rotation and proton transfer motions requiring state-of-the-art treatments. Recent advances in the computational vibrational spectroscopy of the H5+ cation and its isotopologues are reported from full quantum spectral simulations, providing important information in a rigorous manner, and open perspectives for further future investigations. This article is part of a discussion meeting issue 'Advances in hydrogen molecular ions: H3+, H5+ and beyond'.

Soft experimental constraints for soft interactions: a spectroscopic benchmark data set for weak and strong hydrogen bonds

An experimental benchmark data base on rotational constants, vibrational properties and energy differences for weakly and more strongly hydrogen-bonded complexes and their constituents from the spectroscopic literature is assembled. It is characterized in detail and finally contracted to a more compact, discriminatory set (ENCH-51, for Experimental Non-Covalent Harmonic with 51 entries). The meeting points between theory and experiment consist of equilibrium rotational constants and harmonic frequencies and energies, which are back-corrected from experimental observables and are very easily accessible by quantum chemical calculations. The relative performance of B3LYP-D3, PBE0-D3 and M06-2X density functional theory predictions with a quadruple-zeta basis set is used to illustrate systematic errors, error compensation and selective performance for structural, vibrational and energetical observables. The current focus is on perspectives and different benchmarking methodologies, rather than on a specific theoretical method or a specific class of compounds. Extension of the data base in chemical, observable and quantum chemical method space is encouraged.

The Case of Formic Acid on Anatase TiO2 (101): Where is the Acid Proton?

Carboxylic-acid adsorption on anatase TiO₂ is a relevant process in many technological applications. Yet, despite several decades of investigations, the acid-proton localization-either on the molecule or on the surface-is still an open issue. By modeling the adsorption of formic acid on top of anatase(101) surfaces, we highlight the formation of a short strong hydrogen bond. In the 0 K limit, the acid-proton behavior is ruled by quantum delocalization effects in a single potential well, while at ambient conditions, the proton undergoes a rapid classical shuttling in a shallow two-well free-energy profile. This picture, supported by agreement with available experiments, shows that the anatase surface acts like a protecting group for the carboxylic acid functionality. Such a new conceptual insight might help rationalize chemical processes involving carboxylic acids on oxide surfaces.

Chiral Inversion of Amino Acids in Antiparallel β-Sheets at Interfaces Probed by Vibrational Sum Frequency Generation Spectroscopy

A parallel study of protein variants with all (l-), all (d-), or mixed (l-)/(d-) amino acids can be used to assess how backbone architecture versus side chain identity determines protein structure. Here, we investigate the secondary structure and side chain orientation dynamics of the antiparallel β-sheet peptide LK7β (Ac-Leu-Lys-Leu-Lys-Leu-Lys-Leu-NH2) composed of all (l-), all (d-), or alternating (l-Leu)/(d-Lys) amino acids. Using interface-selective vibrational sum frequency generation spectroscopy (VSFG), we observe that the alternating (l-)/(d-) peptide lacks a resonant C-H stretching mode compared to the (l-) and (d-) variants and does not form antiparallel β-sheets. We rationalize our observations on the basis of density functional theory calculations and molecular dynamics (MD) simulations of LK7β at the air-water interface. Irrespective of the handedness of the amino acids, leucine side chains prefer to orient toward the hydrophobic air phase while lysine side chains prefer the hydrophilic water phase. These preferences dictate the backbone configuration of LK7β and thereby the folding of the peptide. Our MD simulations show that the preferred side chain orientations can force the backbone of a single strand of (l-) LK7β at the air-water interface to adopt β-sheet Ramachandran angles. However, denaturation of the β-sheets at pH = 2 results in a negligible chiral VSFG amide I response. The combined computational and experimental results lend critical support to the theory that a chiral VSFG response requires macroscopic chirality, such as in β-sheets. Our results can guide expectations about the VSFG optical responses of proteins and should improve understanding of how amino acid chirality modulates the structure and function of natural and de novo proteins at biological interfaces.

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.