Anharmonic Theoretical Vibrational Spectroscopy of Polypeptides

Machine-learning to predict anharmonic frequencies: a study of models and transferability

With more and more accurate electronic structure methods at hand, the inclusion of anharmonic effects in the post-processing of such data towards thermochemical properties is the next step. In this context, the description of anharmonicity has been an important topic of physical chemistry and chemical physics for a long time. In this study, anharmonic frequencies of various hydrogen-halides and halogenated hydrocarbon molecular clusters are calculated using harmonic as well as explicitly anharmonic methods, i.e., normal mode analysis and vibrational self-consistent field. Simple harmonic model based descriptors were used to predict anharmonic frequencies via multilinear regression and gradient boosting regression. Gradient boosting regression is capable of predicting reliable anharmonic data and even the simple multilinear regression model yields reasonable predictions that can account for mode-to-mode couplings. Moreover, the transferability to unseen chemical systems is assessed and it is confirmed that the machine-learned models can be applied to larger, unseen molecules.

Photothermal Antibacterial and Osteoinductive Polypyrrole@Cu Implants for Biological Tissue Replacement

The treatment of bone defects caused by disease or accidents through the use of implants presents significant clinical challenges. After clinical implantation, these materials attract and accumulate bacteria and hinder the integration of the implant with bone tissue due to the lack of osteoinductive properties, both of which can cause postoperative infection and even lead to the eventual failure of the operation. This work successfully prepared a novel biomaterial coating with multiple antibacterial mechanisms for potent and durable and osteoinductive biological tissue replacement by pulsed PED (electrochemical deposition). By effectively regulating PPy (polypyrrole), the uniform composite coating achieved sound physiological stability. Furthermore, the photothermal analysis showcased exceptional potent photothermal antibacterial activity. The antibacterial assessments revealed a bacterial eradication rate of 100% for the PPy@Cu/PD composite coating following a 24 h incubation. Upon the introduction of NIR (near-infrared) irradiation, the combined effects of multiple antibacterial mechanisms led to bacterial reduction rates of 99% for E. coli and 98% for S. aureus after a 6 h incubation. Additionally, the successful promotion of osteoblast proliferation was confirmed through the application of the osteoinductive drug PD (pamidronate disodium) on the composite coating's surface. Therefore, the antimicrobial Ti-based coatings with osteoinductive properties and potent and durable antibacterial properties could serve as ideal bone implants.

The effect of machine learning predicted anharmonic frequencies on thermodynamic properties of fluid hydrogen fluoride

Anharmonic effects play a crucial role in determining thermochemical properties of liquids and gases. For such extended phases, the inclusion of anharmonicity in reliable electronic structure methods is computationally extremely demanding, and hence, anharmonic effects are often lacking in thermochemical calculations. In this study, we apply the quantum cluster equilibrium method to transfer density functional theory calculations at the cluster level to the macroscopic, liquid, and gaseous phase of hydrogen fluoride. This allows us to include anharmonicity, either via vibrational self-consistent field calculations for smaller clusters or using a regression model for larger clusters. We obtain the structural composition of the fluid phases in terms of the population of different clusters as well as isobaric heat capacities as an example for thermodynamic properties. We study the role of anharmonicities for these analyses and observe that, in particular, the dominating structural motifs are rather sensitive to the anharmonicity in vibrational frequencies. The regression model proves to be a promising way to get access to anharmonic features, and the extension to more sophisticated machine-learning models is promising.

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.

Efficient Prediction of Mole Fraction Related Vibrational Frequency Shifts

While so far it has been possible to calculate vibrational spectra of mixtures at a particular composition, we present here a novel cluster approach for a fast and robust calculation of mole fraction dependent infrared and vibrational circular dichroism spectra at the example of acetonitrile/(R)-butan-2-ol mixtures. By assigning weights to a limited number of quantum chemically calculated clusters, vibrational spectra can be obtained at any desired composition by a weighted average of the single cluster spectra. In this way, peak positions carrying information about intermolecular interactions can be predicted. We show that mole fraction dependent peak shifts can be accurately modeled and, that experimentally recorded infrared spectra can be reproduced with high accuracy over the entire mixing range. Because only a very limited number of clusters is required, the presented approach is a valuable and computationally efficient tool to access mole fraction dependent spectra of mixtures on a routine basis.

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.

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.

Electromagnetic bioeffects: a multiscale molecular simulation perspective

Electromagnetic bioeffects remain an enigma from both the experimental and theoretical perspectives despite the ubiquitous presence of related technologies in contemporary life. Multiscale computational modelling can provide valuable insights into biochemical systems and predict how they will be perturbed by external stimuli. At a microscopic level, it can be used to determine what (sub)molecular scale reactions various stimuli might induce; at a macroscopic level, it can be used to examine how these changes affect dynamic behaviour of essential molecules within the crowded biomolecular milieu in living tissues. In this review, we summarise and evaluate recent computational studies that examined the impact of externally applied electric and electromagnetic fields on biologically relevant molecular systems. First, we briefly outline the various methodological approaches that have been employed to study static and oscillating field effects across different time and length scales. The practical value of such modelling is then illustrated through representative case-studies that showcase the diverse effects of electric and electromagnetic field on the main physiological solvent - water, and the essential biomolecules - DNA, proteins, lipids, as well as some novel biomedically relevant nanomaterials. The implications and relevance of the theoretical multiscale modelling to practical applications in therapeutic medicine are also discussed. Finally, we summarise ongoing challenges and potential opportunities for theoretical modelling to advance the current understanding of electromagnetic bioeffects for their modulation and/or beneficial exploitation in biomedicine and industry.

Retinal Vibrations in Bacteriorhodopsin are Mechanically Harmonic but Electrically Anharmonic: Evidence From Overtone and Combination Bands

Fundamental vibrations of the chromophore in the membrane protein bacteriorhodopsin (BR), a protonated Schiff base retinal, have been studied for decades, both by resonance Raman and by infrared (IR) difference spectroscopy. Such studies started comparing vibrational changes between the initial BR state (all-trans retinal) and the K intermediate (13-cis retinal), being later extended to the rest of intermediates. They contributed to our understanding of the proton-pumping mechanism of BR by exploiting the sensitivity of fundamental vibrational transitions of the retinal to its conformation. Here, we report on new bands in the 2,500 to 1,800 cm⁻¹ region of the K-BR difference FT-IR spectrum. We show that the bands between 2,500 and 2,300 cm⁻¹ originate from overtone and combination transitions from C-C stretches of the retinal. We assigned bands below 2,300 cm⁻¹ to the combination of retinal C-C stretches with methyl rocks and with hydrogen-out-of-plane vibrations. Remarkably, experimental C-C overtone bands appeared at roughly twice the wavenumber of their fundamentals, with anharmonic mechanical constants ≤3.5 cm⁻¹, and in some cases of ∼1 cm⁻¹. Comparison of combination and fundamental bands indicates that most of the mechanical coupling constants are also very small. Despite the mechanical quasi-harmonicity of the C-C stretches, the area of their overtone bands was only ∼50 to ∼100 times smaller than of their fundamental bands. We concluded that electrical anharmonicity, the second mechanism giving intensity to overtone bands, must be particularly high for the retinal C-C stretches. We corroborated the assignments of negative bands in the K-BR difference FT-IR spectrum by ab initio anharmonic vibrational calculations of all-trans retinal in BR using a quantum-mechanics/molecular mechanics approach, reproducing reasonably well the small experimental anharmonic and coupling mechanical constants. Yet, and in spite accounting for both mechanical and electrical anharmonicities, the intensity of overtone C-C transitions was underestimated by a factor of 4–20, indicating room for improvement in state-of-the-art anharmonic vibrational calculations. The relatively intense overtone and combination bands of the retinal might open the possibility to detect retinal conformational changes too subtle to significantly affect fundamental transitions but leaving a footprint in overtone and combination transitions.

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.

Unravelling the structural complexity of glycolipids with cryogenic infrared spectroscopy

Glycolipids are complex glycoconjugates composed of a glycan headgroup and a lipid moiety. Their modular biosynthesis creates a vast amount of diverse and often isomeric structures, which fulfill highly specific biological functions. To date, no gold-standard analytical technique can provide a comprehensive structural elucidation of complex glycolipids, and insufficient tools for isomer distinction can lead to wrong assignments. Herein we use cryogenic gas-phase infrared spectroscopy to systematically investigate different kinds of isomerism in immunologically relevant glycolipids. We show that all structural features, including isomeric glycan headgroups, anomeric configurations and different lipid moieties, can be unambiguously resolved by diagnostic spectroscopic fingerprints in a narrow spectral range. The results allow for the characterization of isomeric glycolipid mixtures and biological applications.

Glycolipids are glycoconjugates with important biological functions, but techniques for their analysis are deficient. Here, the authors report the use of cryogenic gas-phase infrared spectroscopy to investigate isomerism in a set of immunologically relevant glycolipids, and show that their structural features can be accurately resolved based on a narrow spectral fingerprint region.

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.

Anharmonicity of Vibrational Modes in Hydrogen Chloride-Water Mixtures

A thorough analysis of molecular vibrations in the binary system hydrogen chloride/water is presented considering a set of small mixed and pure clusters. In addition to the conventional normal-mode analysis based on the diagonalization of the Hessian, anharmonic frequencies were obtained from the perturbative VPT2 and PT2-VSCF method using hybrid density functional theory. For all normal modes, potential energy curves were modeled by displacing the atoms from the minimum geometry along the normal mode vectors. Three model potentials, a harmonic potential, a Morse potential, and a fourth order polynomial, were applied to fit these curves. From these data, it was possible not only to characterize distinct vibrations as mainly harmonic, anharmonic, or involving higher order terms but also to extract force constants, k, and anharmonicity constants, x_e. By investigating all different types of intramolecular vibrations including covalent stretching or bending vibrations and intermolecular vibrations such as librations, we could demonstrate that while vibrational frequencies can be obtained applying scaling factors to harmonic results, useful anharmonicity constants cannot be predicted in such a way and the usage of more elaborate vibrational methods is necessary. For each particular type of molecular vibration, we could however determine a relationship between the wavenumber or wavenumber shift and the anharmonicity constant, which allows us to estimate mode dependent anharmonicity constants for larger clusters in the future.

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.

Quantitative Assessment of Tetrel Bonding Utilizing Vibrational Spectroscopy

A set of 35 representative neutral and charged tetrel complexes was investigated with the objective of finding the factors that influence the strength of tetrel bonding involving single bonded C, Si, and Ge donors and double bonded C or Si donors. For the first time, we introduced an intrinsic bond strength measure for tetrel bonding, derived from calculated vibrational spectroscopy data obtained at the CCSD(T)/aug-cc-pVTZ level of theory and used this measure to rationalize and order the tetrel bonds. Our study revealed that the strength of tetrel bonds is affected by several factors, such as the magnitude of the σ-hole in the tetrel atom, the negative electrostatic potential at the lone pair of the tetrel-acceptor, the positive charge at the peripheral hydrogen of the tetrel-donor, the exchange-repulsion between the lone pair orbitals of the peripheral atoms of the tetrel-donor and the heteroatom of the tetrel-acceptor, and the stabilization brought about by electron delocalization. Thus, focusing on just one or two of these factors, in particular, the σ-hole description can only lead to an incomplete picture. Tetrel bonding covers a range of -1.4 to -26 kcal/mol, which can be strengthened by substituting the peripheral ligands with electron-withdrawing substituents and by positively charged tetrel-donors or negatively charged tetrel-acceptors.

Intrinsic structure of pentapeptide Leu-enkephalin: geometry optimization and validation by comparison of VSCF-PT2 calculations with cold ion spectroscopy

The intrinsic structure of an opioid peptide [Ala2, Leu5]-leucine enkephalin (ALE) has been investigated using first-principles based vibrational self-consistent field (VSCF) theory and cold ion spectroscopy. IR-UV double resonance spectroscopy revealed the presence of only one highly abundant conformer of the singly protonated ALE, isolated and cryogenically cooled in the gas phase. High-level quantum mechanical calculations of electronic structures in conjunction with a systematic conformational search allowed for finding a few low-energy candidate structures. In order to identify the observed structure, we computed vibrational spectra of the candidate structures and employed the theory at the semi-empirically scaled harmonic level and at the first-principles based anharmonic VSCF levels. The best match between the calculated "anharmonic" and the measured spectra appeared, indeed, for the most stable candidate. An average of two spectra calculated with different quantum mechanical potentials is proposed for the best match with experiment. The match thus validates the calculated intrinsic structure of ALE and demonstrates the predictive power of first-principles theory for solving structures of such large molecules.

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.

Anharmonic vibrational spectra from double incremental potential energy and dipole surfaces

Using incremental approaches, size limitations for property surface generations are pushed significantly, enabling accurate large molecule anharmonic vibrational spectra calculations.

Electrical anharmonicity in hydrogen bonded systems: complete interpretation of the IR spectra of the Cl-H[combining right harpoon above] stretching band in the gaseous (CH3)2OHCl complex

Following the previous developments to simulate the fully infrared spectra of weak hydrogen bond systems within the linear response theory, an extension of the adiabatic model is presented here. A general formulation including the electrical anharmonicities in the calculation of the damped autocorrelation function of weak H-bonds is adopted to facilitate the support of the additional properties, and thus the IR spectra of the Cl-H[combining right harpoon above] stretching band in the gaseous (CH₃)₂OHCl complex. We have explored the origins of the broadening of the Cl-H[combining right harpoon above] stretching band. We found that the main features of the lineshape are attributed to electrical anharmonicity as a consequence of the large mixed second derivatives of the dipole moment with respect to the Cl-H[combining right harpoon above] bond and of the intermonomer elongations . In addition to providing more accurate theoretical band shapes, inclusion of the electrical anharmonicity in the present model paves the way for a more complete interpretation by generating three new Franck-Condon superposed distributions.