Fast and Accurate Quantum Chemical Modeling of Infrared Spectra of Condensed-Phase Systems

Systematic improvement of redox potential calculation of Fe(III)/Fe(II) complexes using a three-layer micro-solvation model

Electrochemical transformations of metal ions in aqueous media are challenging to model accurately due to the dynamic solvation structure surrounding ions at different charge states. Predictive modeling at the atomistic scale is essential for understanding these solvation architectures but is often computationally prohibitive. In this contribution, we present a simple, fast, and accurate three-layer micro-solvation model to evaluate the redox potential of metal ions in aqueous solutions. Our model, developed and validated for Fe3+/Fe2+ redox potentials, combines the DFT-based geometry optimizations of the octahedral Fe complex with two layers of explicit water molecules to capture solute-solvent interactions and an implicit solvation model to account for bulk solvent effects. This approach yields accurate predictions for Fe3+/Fe2+ redox potentials in water, achieving errors of 0.02 V with ωB97X-V, 0.01 V with ωB97X-D3, 0.04 V with ωB97M-V, and 0.02 V with B3LYP-D3 functionals. We further demonstrate the generality of our model by applying it to additional metal complexes, including the challenging Fe(CN)63-/4- system, where our model successfully achieves close agreement with experimental values, with an error of 0.07 V and an average error of 0.21 V for all five systems. In summary, the presented simple solvation model has broad applicability and potential for enhancing computational efficiency in redox potential predictions across various chemical and industrial processes of metal ions.

Unlocking the Potential of Machine Learning in Enhancing Quantum Chemical Calculations for Infrared Spectral Prediction

Infrared (IR) spectroscopy is a fundamental tool for analyzing molecular structures and chemical interactions by identifying the vibrational modes of molecules. Traditional quantum mechanical methods, such as density functional theory, are highly accurate but computationally expensive and impractical for large-scale molecular systems. This project investigates the integration of machine learning (ML) techniques to predict IR spectra, offering a promising alternative that significantly reduces computational costs while maintaining high accuracy. Additionally, the project explores the utilization of IR spectra for molecular identification and classification into molecular families, enhancing the practical utility of spectral data in various scientific applications. Using TensorFlow-based ML frameworks, models were developed and trained on a data set derived from high-quality computational chemistry analyzers. These data sets, sourced from computationally optimized geometry and IR spectrum from the Gaussian 16 Program Suite, include extensive molecular geometry data, bond lengths, vibrational modes, and other quantum mechanical properties. The models aim to predict key IR spectral features, such as vibrational frequencies and intensities, while maintaining interpretability by linking chemical and quantum mechanical principles to predictions. The integration of ML with IR spectroscopy provides a scalable as well as accelerated solution for analyzing complex molecular systems. This approach holds potential in fields such as drug discovery, materials science, and chemical engineering, where rapid and accurate spectral predictions are critical. This perspective highlights the advancements achieved, the current challenges, and the future potential of ML in the context of IR spectroscopy, providing a solid foundation for further exploration at the intersection of chemistry and data science.

From Ab Initio to Instrumentation: A Field Guide to Characterizing Multivalent Liquid Electrolytes

In this field guide, we outline empirical and theory-based approaches to characterize the fundamental properties of liquid multivalent-ion battery electrolytes, including (i) structure and chemistry, (ii) transport, and (iii) electrochemical properties. When detailed molecular-scale understanding of the multivalent electrolyte behavior is insufficient we use examples from well-studied lithium-ion electrolytes. In recognition that coupling empirical and theory-based techniques is highly effective, but often nontrivial, we also highlight recent electrolyte characterization efforts that uncover a more comprehensive and nuanced understanding of the underlying structures, processes, and reactions that drive performance and system-level behavior. We hope the insights from these discussions will guide the design of future electrolyte studies, accelerate development of next-generation multivalent-ion batteries through coupling of modeling with experiments, and help to avoid pitfalls and ensure reproducibility of modeling results.

The Analysis of Vibrational Spectra: Past, Present and Future

Vibrational spectroscopy can be said to have started with the seminal work of Coblentz in the 1900s, who recorded the first recognisable infrared spectra. Today, vibrational spectroscopy is ubiquitous and there are many ways to measure a vibrational spectrum. But this is usually only the first step, almost always there is a need to assign the resulting spectra: "what property of the system results in a feature at this energy"? How this question has been answered has changed over the last century, as our understanding of the fundamental physics of matter has evolved. In this Perspective, I will present my view of how the analysis of vibrational spectra has evolved over time. The article is divided into three sections: past, present and future. The "past" section consists of a very brief history of vibrational spectroscopy. The "present" is centered around ab initio studies, particularly with density functional theory (DFT) and I will describe how this has become almost routine. For the "future", I will extrapolate current trends and also speculate as to what might come next.

Structure and intermolecular interactions in ionic liquid 1-ethyl-3-methylimidazolium bromide and its aqueous solutions investigated by vibrational spectroscopy and quantum chemical computations

The recently developed efficient protocol to explicit quantum mechanical modeling of structure and IR spectra of liquids and solutions (S. A. Katsyuba, S. Spicher, T. P. Gerasimova, S. Grimme, J. Phys. Chem. B 2020, 124, 6664) is applied to ionic liquid (IL) 1-ethyl-3-methylimidazolium bromide (EmimBr), its C2-deuterated analog [Emim-d]Br and its aqueous solutions. It is shown that the solvation strongly modifies frequencies and IR intensities of the CH/CD stretching vibrations (νCH/νCD) of the imidazolium ring. The main vibrational spectroscopic features of the neat IL are reproduced by the simulations for a cluster (EmimBr)9, in which all three imidazolium CH moieties of the solvated cation form short contacts with three Br- anions, and another two Br- anions are located on top and bottom of imidazolium ring. Cluster models of aqueous solutions reproduce the experimental vibrational frequencies of actual solutions, provided that the Br- anion of solvated contact ion pair (CIP) is situated on top of imidazolium ring, and CH/CD moieties of the latter participate in short contacts with surrounding water molecules. Both structural and spectroscopic analysis allow to interpret the short contacts CH/CD⋯Br- and CH/CD⋯OH2 as hydrogen bonds of approximately equal strength. Enthalpies of bonding of these liquid-state H-bonds, estimated with the use of empirical correlations, amount to ca. 1.4 kcal⋅mol-1, while the analogous estimates obtained for the gas-phase charged species [Emim]2Br+ increase to 5.6 kcal⋅mol-1. It is shown that formation of solvent-shared ion pair (SIP) in aqueous solution, where the counterions of IL are separated by two water molecules H-bonded to a Br- anion, produces frequency shifts ΔνCH/CD, strongly different from the case of CIP formation. This difference can be used for IR/Raman spectroscopic differentiation of the type of solvated ion pairs of EmimBr or other related ILs.

Computationally assisted vibrational spectroscopy of nucleic acid bases. 2. Thymine

As in the case of cytosine [Phys. Chem. Chem. Phys. 2023, 25, 24121-24128], Raman and infrared (IR) spectra of aqueous thymine and its N-deuterated derivative, thymine-d2 have been computationally reproduced and interpreted with the use of the recently developed efficient protocol to explicit quantum mechanical modeling of structure and IR spectra of liquids and solutions [J. Phys. Chem. B, 2020, 124, 6664-6670]. A cluster model of a solute surrounded by 30 water molecules is shown to be sufficient to reproduce experimental vibrational frequencies and relative Raman intensities with the use of B3LYP-D3/def2-TZVP or B3LYP-D3/aug-cc-pVDZ simulations. Analogous PBE-D3 computations provided a less good, but still reasonably accurate, modeling of Raman spectra. It is shown that strong changes of frequencies and relative intensities of the Raman bands of thymine, caused by its hydration, can be interpreted mainly as a result of hydrogen bonding with 6 nearest water molecules. Non-negligible improvement of the quality of simulations for larger clusters comprising water molecules that do not have direct contacts with the solute, suggests that spectroscopic effects of hydration should be ascribed to the joined action of solute-solvent and solvent-solvent interactions. Nevertheless, the moderate number of water molecules required for successful simulations of the Raman spectra of aqueous thymine, suggests that the vibrational modes and derivatives of the polarizability of the solute are mainly locally influenced, while the effect of bulk water is rather modest.

Infrared and vibrational circular dichroism spectra of methyl β-D-glucopyranose in water: The application of the quantum cluster growth and clusters-in-a-liquid solvation models

The infrared (IR) and vibrational circular dichroism (VCD) spectra of methyl β-D-glucopyranose in water were measured. Both implicit and explicit solvation models were utilized to explain the observed spectra. The vast body of existing experimental and theoretical data suggested that about eight explicit water molecules are needed to account for the solvent effects, supported by the current Quantum Cluster Growth (QCG) analysis. Extensive manual and systematic conformational searches of the molecular target and its water clusters were carried out by using a recently developed conformational searching tool, conformer-rotamer ensemble sampling tool (CREST), and the microsolvation model in the associated QCG code. The Boltzmann averaged IR and VCD spectra of the methyl β-D-glucopyranose-(water)n (n = 8) conformers in the PCM of water provide better agreement with the experimental ones than those with n = 0, 1, and 2. The explicit solvation with eight water molecules was shown to greatly modify the conformational preference of methyl β-D-glucopyranose from its monomeric form. Further analyses show that the result is consistent with the existence of long-lived methyl β-D-glucopyranose monohydrates with the additional explicit water effects being accounted for with the quantum mechanical treatment of the other seven close-by water molecules in the PCM of water.

Computational analysis of the vibrational spectra and structure of aqueous cytosine

The recently developed efficient protocol for the explicit quantum mechanical modeling of the structure and IR spectra of liquids and solutions [Katsyuba et al., J. Phys. Chem. B, 2020, 124, 6664-6670] is used to describe aqueous solutions of cytosine. The same cluster model of a solute surrounded by the first solvation shell of solvent molecules was shown to be sufficient to reproduce experimental vibrational frequencies and relative IR and Raman intensities. An equally good quality of Raman spectra was provided by B3LYP-D3/def2-TZVP and B3LYP-D3/aug-cc-pVDZ simulations. Computations using the PBE functional were sufficient for modeling of the IR spectra but failed in the simulations of Raman scattering. It is shown that strong changes of frequencies and relative intensities of Raman and IR bands of cytosine, caused by its hydration, cannot be completely assigned to the influence of hydrogen bonds (HBs) with 7 or 8 closest water molecules. They are rather ascribed to the combined effect of solute-solute and solute-solvent HBs with the participation of at least 30 water molecules separating cytosine from the bulk solvent. This suggests that the vibrational modes and derivatives of the polarizability and dipole moment of the solute are mainly locally influenced by its first hydration shell, while the influence of bulk water is rather modest.

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.

Best-Practice DFT Protocols for Basic Molecular Computational Chemistry

Nowadays, many chemical investigations are supported by routine calculations of molecular structures, reaction energies, barrier heights, and spectroscopic properties. The lion's share of these quantum-chemical calculations applies density functional theory (DFT) evaluated in atomic-orbital basis sets. This work provides best-practice guidance on the numerous methodological and technical aspects of DFT calculations in three parts: Firstly, we set the stage and introduce a step-by-step decision tree to choose a computational protocol that models the experiment as closely as possible. Secondly, we present a recommendation matrix to guide the choice of functional and basis set depending on the task at hand. A particular focus is on achieving an optimal balance between accuracy, robustness, and efficiency through multi-level approaches. Finally, we discuss selected representative examples to illustrate the recommended protocols and the effect of methodological choices.

Towards understanding solvation effects on the conformational entropy of non-rigid molecules

The absolute molecular entropy is a fundamental quantity for the accurate description of thermodynamic properties. For non-rigid molecules, a substantial part of the entropy can be attributed to a conformational contribution. Systems and properties where this is relevant, e.g., protein-ligand binding affinities or pK_a values refer usually to the liquid phase. In this work, the influence of solvation on the conformational entropy is investigated. A recently introduced state-of-the-art and automated computational protocol for the computation of conformational entropies [Pracht et al., Chem. Sci., 2021, 12, 6551-6568.] is applied in combination with fast and accurate semiempirical quantum-chemical methods and implicit solvation models for a set of 25 commercially available drug molecules and five transition metal compounds. Computed gas-phase conformational entropies are compared with values obtained in implicit n-hexane and water. It is found that implicit solvation can have a substantial effect of several cal mol^-1 K^-1 on the entropy as a result of large conformational changes in the different phases. We conclude that for flexible molecules chemical accuracy for free energies in solution can only be achieved if solvation effects on the conformational ensemble are considered.

Automated Molecular Cluster Growing for Explicit Solvation by Efficient Force Field and Tight Binding Methods

An automated and broadly applicable workflow for the description of solvation effects in an explicit manner is introduced. This method, termed quantum cluster growth (QCG), is based on the semiempirical GFN2-xTB/GFN-FF methods, enabling efficient geometry optimizations and MD simulations. Fast structure generation is provided using the intermolecular force field xTB-IFF. Additionally, the approach uses an efficient implicit solvation model for the electrostatic embedding of the growing clusters. The novel QCG procedure presents a robust cluster generation tool for subsequent application of higher-level (e.g., DFT) methods to study solvation effects on molecular geometries explicitly or to average spectroscopic properties over cluster ensembles. Furthermore, the computation of the solvation free energy with a supermolecular approach can be carried out with QCG. The underlying growing process is physically motivated by computing the leading-order solute-solvent interactions first and can account for conformational and chemical changes due to solvation for low-energy barrier processes. The conformational space is explored with the NCI-MTD algorithm as implemented in the CREST program, using a combination of metadynamics and MD simulations. QCG with GFN2-xTB yields realistic solution geometries and reasonable solvation free energies for various systems without introducing many empirical parameters. Computed IR spectra of some solutes with QCG show a better match to the experimental data compared to well-established implicit solvation models.

What quantum chemical simulations tell us about the infrared spectra, structure and interionic interactions of a bulk ionic liquid

The recently developed efficient protocol to explicit quantum mechanical modeling of the structure and IR spectra of liquids and solutions [Katsyuba et al., J. Phys. Chem. B, 2020, 124, 6664-6670] is applied to ionic liquid 1-ethyl-3-methyl-imidazolium tetrafluoroborate [Emim][BF₄], and its C2-deuterated analog [Emim-d][BF₄]. It is shown that the solvation strongly modifies the frequencies and IR intensities of both cationic and anionic components of the ionic liquids. The main features of the bulk spectra are reproduced by the simulations for cluster ([Emim][BF₄])₈, representing an ion pair solvated by the first solvation shell. The geometry of the cluster closely resembles the solid-state structure of the actual ionic liquid and is characterized by short contacts of all CH moieties of the imidazolium ring with [BF₄]^- anions. Both structural and spectroscopic analyses allow the contacts to be interpreted as hydrogen bonds of approximately equal strength. The enthalpies of these liquid-state H-bonds, estimated with the use of empirical correlations, amount to 1.2-1.5 kcal mol^-1, while the analogous estimates obtained for the gas-phase charged species [Emim][BF₄]₂^- and [Emim]₂[BF₄]⁺ increase to 3.6-3.9 kcal mol^-1.

Computer-aided simulation of infrared spectra of ethanol conformations in gas, liquid and in CCl4 solution

The recently developed efficient protocol combining implicit and explicit, accurate quantum-mechanical modeling of the condensed state (Katsyuba et al., J. Chem. Phys. 155, 024507 [2021]) is used to describe the IR spectra of liquid ethanol and its solutions in CCl₄ . The relative abundance of the anti and gauche conformers of ethanol is shown to increase from ~40:60 in the gas phase to ~55:45 in the liquid phase. In spite of a moderate impact of media effects on the conformational composition of the liquid, the solvent strongly influences vibrational frequencies, IR intensities, and normal modes of each conformer, producing qualitatively different spectra compared to the gas phase and CCl₄ solution. Further, these solvent effects affecting IR frequencies and intensities depend not only on the conformation of the solvated molecule but also on the solvating species. Nevertheless, vibrational frequencies of anti and gauche conformers of liquid ethanol and its several isotopomers practically coincide with each other. Convenient liquid-state conformational markers in the fingerprint region of IR spectra are revealed for the hydroxyl-deuterated species: CH₃ CH₂ OD, CH₃ CHDOD, CH₃ CD₂ OD, and CD₃ CD₂ OD.

Synthesis and Computationally Assisted Spectroscopic Study of Tautomerism in 3-(Phenyl(2-arylhydrazineylidene)methyl)quinoxalin-2(1H)-ones

The recently developed efficient protocol combining implicit and explicit, accurate quantum mechanical modeling of the condensed state [Katsyuba et al., J. Chem. Phys. 155, 024507 (2021)] is used to describe...

Integration of theory, simulation, artificial intelligence and virtual reality: a four-pillar approach for reconciling accuracy and interpretability in computational spectroscopy

The established pillars of computational spectroscopy are theory and computer based simulations. Recently, artificial intelligence and virtual reality are becoming the third and fourth pillars of an integrated strategy for the investigation of complex phenomena. The main goal of the present contribution is the description of some new perspectives for computational spectroscopy, in the framework of a strategy in which computational methodologies at the state of the art, high-performance computing, artificial intelligence and virtual reality tools are integrated with the aim of improving research throughput and achieving goals otherwise not possible. Some of the key tools (e.g., continuous molecular perception model and virtual multifrequency spectrometer) and theoretical developments (e.g., non-periodic boundaries, joint variational-perturbative models) are shortly sketched and their application illustrated by means of representative case studies taken from recent work by the authors. Some of the results presented are already well beyond the state of the art in the field of computational spectroscopy, thereby also providing a proof of concept for other research fields.

Revisiting conformations of methyl lactate in water and methanol

The recently developed efficient protocols to implicit [Grimme et al., J. Phys. Chem. A 125, 4039-4054 (2021)] and explicit quantum mechanical modeling of non-rigid molecules in solution [Katsyuba et al., J. Phys. Chem. B 124, 6664-6670 (2020)] are applied to methyl lactate (ML). Building upon this work, a new combination scheme is proposed to incorporate solvation effects for the computation of infrared (IR) absorption spectra. Herein, Boltzmann populations calculated for implicitly solvated single conformers are used to weight the IR spectra of explicitly solvated clusters with a size of typically ten solvent molecules, i.e., accounting for the first solvation shell. It is found that in water and methanol, the most abundant conformers of ML are structurally modified relative to the gas phase, where the major form is ML1, in which the syn conformation of the -OH moiety is stabilized by a OH⋯O=C intramolecular hydrogen bond (HB). In solution, this syn conformation transforms to the gauche form because the intramolecular HB is disrupted by explicit water molecules that form intermolecular HBs with the hydroxyl and carbonyl groups. Similar changes induced by the gas-solution transition are observed for the minor conformers, ML2 and/or ML3, characterized by OH⋯OCH₃ intramolecular HB in the gas phase. The relative abundance of ML1 is shown to decrease from ∼96% in gas to ∼51% in water and ∼92% in methanol. The solvent strongly influences frequencies, IR intensities, and normal modes, resulting in qualitatively different spectra compared to the gas phase. Some liquid-state conformational markers in the fingerprint region of IR spectra are revealed.

CH Mode Mixing Determines the Band Shape of the Carboxylate Symmetric Stretch in Apo-EDTA, Ca2+-EDTA, and Mg2+-EDTA

The infrared spectra of EDTA complexed with Ca²⁺ and Mg²⁺ contain, to date, unidentified vibrational bands. This study assigns the peaks in the linear and two-dimensional infrared spectra of EDTA, with and without either Ca²⁺ or Mg²⁺ ions. Two-dimensional infrared spectroscopy and DFT calculations reveal that, in both the presence and absence of ions, the carboxylate symmetric stretch and the terminal CH bending vibrations mix. We introduce a method to calculate participation coefficients that quantify the contribution of the carboxylate symmetric stretch, CH wag, CH twist, and CH scissor in the 1400-1550 cm^-1 region. With the help of participation coefficients, we assign the 1400-1430 cm^-1 region to the carboxylate symmetric stretch, which can mix with CH modes. We assign the 1000-1380 cm^-1 region to CH twist modes, the 1380-1430 cm^-1 region to wag modes, and the 1420-1650 cm^-1 region to scissor modes. The difference in binding geometry between the carboxylate-Ca²⁺ and carboxylate-Mg²⁺ complex manifests as new diagonal and cross-peaks between the mixed modes in the two complexes. The small Mg²⁺ ion binds EDTA tighter than the Ca²⁺ ion, which causes a redshift of the COO symmetric stretches of the sagittal carboxylates. Energy decomposition analysis further characterizes the importance of electrostatics and deformation energy in the bound complexes.

Predicting Infrared Spectra with Message Passing Neural Networks

Infrared (IR) spectroscopy remains an important tool for chemical characterization and identification. Chemprop-IR has been developed as a software package for the prediction of IR spectra through the use of machine learning. This work serves the dual purpose of providing a trained general-purpose model for the prediction of IR spectra with ease and providing the Chemprop-IR software framework for the training of new models. In Chemprop-IR, molecules are encoded using a directed message passing neural network, allowing for molecule latent representations to be learned and optimized for the task of spectral predictions. Model training incorporates spectra metrics and normalization techniques that offer better performance with spectral predictions than standard practice in regression models. The model makes use of pretraining using quantum chemistry calculations and ensembling of multiple submodels to improve generalizability and performance. The spectral predictions that result are of high quality, showing capability to capture the extreme diversity of spectral forms over chemical space and represent complex peak structures.

Comprehensive Assessment of GFN Tight-Binding and Composite Density Functional Theory Methods for Calculating Gas-Phase Infrared Spectra

Vibrational spectroscopy is a valuable and widely used analytical tool for the characterization of chemical substances. We investigate the performance of semiempirical quantum mechanical GFN tight-binding and force-field methods for the calculation of gas-phase infrared spectra in comparison to experiment and low-cost (B3LYP-3c) density functional theory. A data set of 7247 experimental references was used to evaluate method performance based on automatic spectra comparison. Various quantitative spectral similarity measures were employed for the comparison between theory and experiment and for determining empirical scaling factors. It is shown that the scaling of atomic masses provides an accurate yet simple alternative to standard global frequency scaling in density functional theory (DFT) and semiempirical calculations. Furthermore, the method performance for 58 exemplary transition metal complexes was investigated. The efficient DFT composite method B3LYP-3c, that was introduced in the course of this work, was found to be excellently suited for general IR spectra calculations. The GFN1- and GFN2-xTB tight-binding methods clearly outperformed the PMx competitors. Conformational changes were investigated for a subset of the data and are found to have a mediocre strong influence on the simulated spectra suggesting that the corresponding elaborate sampling steps may be neglected in automated compound identification workflows.