Towards an accurate description of anharmonic infrared spectra in solution within the polarizable continuum model: reaction field, cavity field and nonequilibrium effects

Reformulating Reactivity Design for Data-Efficient Machine Learning

Machine learning (ML) can deliver rapid and accurate reaction barrier predictions for use in rational reactivity design. However, model training requires large data sets of typically thousands or tens of thousands of barriers that are very expensive to obtain computationally or experimentally. Furthermore, bespoke data sets are required for each region of interest in reaction space as models typically struggle to generalize. We have therefore reformulated the ML barrier prediction problem toward a much more data-efficient process: finding a reaction from a prespecified set with a desired target value. Our reformulation enables the rapid selection of reactions with purpose-specific activation barriers, for example, in the design of reactivity and selectivity in synthesis, catalyst design, toxicology, and covalent drug discovery, requiring just tens of accurately measured barriers. Importantly, our reformulation does not require generalization beyond the domain of the data set at hand, and we show excellent results for the highly toxicologically and synthetically relevant data sets of aza-Michael addition and transition-metal-catalyzed dihydrogen activation, typically requiring less than 20 accurately measured density functional theory (DFT) barriers. Even for incomplete data sets of E2 and SN2 reactions, with high numbers of missing barriers (74% and 56% respectively), our chosen ML search method still requires significantly fewer data points than the hundreds or thousands needed for more conventional uses of ML to predict activation barriers. Finally, we include a case study in which we use our process to guide the optimization of the dihydrogen activation catalyst. Our approach was able to identify a reaction within 1 kcal mol-1 of the target barrier by only having to run 12 DFT reaction barrier calculations, which illustrates the usage and real-world applicability of this reformulation for systems of high synthetic importance.

Anharmonic Aspects in Vibrational Circular Dichroism Spectra from 900 to 9000 cm-1 for Methyloxirane and Methylthiirane

Vibrational circular dichroism (VCD) spectra and the corresponding IR spectra of the chiral isomers of methyloxirane and of methylthiirane have been reinvestigated, both experimentally and theoretically, with particular attention to accounting for anharmonic corrections, as calculated by the GVPT2 approach. De novo recorded VCD spectra in the near IR (NIR) range regarding CH-stretching overtone transitions, together with the corresponding NIR absorption spectra, were also considered and accounted for, both with the GVPT2 and with the local mode approaches. Comparison of the two methods has permitted us to better describe the nature of active “anharmonic” modes in the two molecules and the role of mechanical and electrical anharmonicity in determining the intensities of VCD and IR/NIR data. Finally, two nonstandard IR/NIR regions have been investigated: the first one about ≈2000 cm^–1, involving mostly two-quanta bending mode transitions, the second one between 7000 and 7500 cm^–1 involving three-quanta transitions containing CH-stretching overtones and HCC/HCH bending modes.

Vibrations of the guanine-cytosine pair in chloroform: an anharmonic computational study

We compute at the anharmonic level the vibrational spectra of the Watson-Crick dimer formed by guanosine (G) and cytidine (C) in chloroform, together with those of G, C and the most populated GG dimer. The spectra for deuterated and partially deuterated GC are also computed. We use DFT calculations, with B3LYP and CAM-B3LYP as reference functionals. Solvent effects from chloroform are included via the Polarizable Continuum Model (PCM), and by performing tests on models including up two chloroform molecules. Both B3LYP and CAM-B3LYP calculations reproduce the shape of the experimental spectra well in the fingerprint region (1500-1700 cm-1) and in the N-H stretching region (2800-3600 cm-1), with B3LYP providing better quantitative agreement with experiments. According to our calculations, the N-H amido streching mode of G falls at ∼2900 cm-1, while the N-H amino of G and C falls at ∼3100 cm-1 when hydrogen-bonded, or ∼3500 cm-1 when free. Overtone and combination bands strongly contribute to the absorption band at ∼3300 cm-1. Inclusion of bulk solvent effects significantly increases the accuracy of the computed spectra, while solute-solvent interactions have a smaller, though still noticeable, effect. Some key aspects of the anharmonic treatment of strongly vibrationally coupled supermolecular systems and the related methodological issues are also discussed.

Toward Fully Unsupervised Anharmonic Computations Complementing Experiment for Robust and Reliable Assignment and Interpretation of IR and VCD Spectra from Mid-IR to NIR: The Case of 2,3-Butanediol and trans-1,2-Cyclohexanediol

The infrared (IR) and vibrational circular dichroism (VCD) spectra of 2,3-butanediol and trans-1,2-cyclohexanediol from 900 to 7500 cm^–1 (including mid-IR, fundamental CH and OH stretchings, and near-infrared regions) have been investigated by a combined experimental and computational strategy. The computational approach is rooted in density functional theory (DFT) computations of harmonic and leading anharmonic mechanical, electrical, and magnetic contributions, followed by a generalized second-order perturbative (GVPT2) evaluation of frequencies and intensities for all the above regions without introducing any ad hoc scaling factor. After proper characterization of large-amplitude motions, all resonances plaguing frequencies and intensities are taken into proper account. Comparison of experimental and simulated spectra allows unbiased assignment and interpretation of the most interesting features. The reliability of the GVPT2 approach for OH stretching fundamentals and overtones is confirmed by the remarkable agreement with a local mode model purposely tailored for the latter two regions. Together with the specific interest of the studied molecules, our results confirm that an unbiased assignment and interpretation of vibrational spectra for flexible medium-size molecules can be achieved by means of a nearly unsupervised reliable, robust, and user-friendly DFT/GVPT2 model.

A combined experimental and theoretical study of optical rotatory dispersion for (R)-glycidyl methyl ether in aqueous solution

The dispersive optical activity for aqueous solutions of non-rigid (R)-glycidyl methyl ether (R-GME) has been explored synergistically from experimental and theoretical perspectives. Density functional theory analyses performed with the polarizable continuum model for implicit solvation identified nine low-lying stable conformers that are interconverted by rotation about two large-amplitude torsional coordinates. The antagonistic chiroptical signatures predicted for these structural isomers were averaged under a Boltzmann-weighting ansatz to estimate the behavior expected for a thermally equilibrated ensemble. This led to optical rotatory dispersion profiles that reproduced the overall shape of observations but failed to achieve uniform agreement with measured specific-rotation values even when anharmonic vibrational corrections were applied. A mixed QM/FQ paradigm, whereby quantum-mechanical (QM) calculations of optical activity were combined with classical molecular dynamics simulations of explicit solvation that included mutual-polarization effects by means of fluctuating charges (FQ), was enlisted to elucidate the microsolvation environment and gauge its impact upon conformer distributions and response properties. Although quantitative accord with experiments remained elusive, this approach revealed strong variations in the magnitude and sign of rotatory powers for R-GME as the configuration of surrounding water molecules evolved, thereby highlighting the inherently dynamical nature of the solvated chiroptical response, calling into question the validity of "static" descriptions based on the presumption of distinct energy minima, and giving insight into the inherent complexity posed by the modeling of such properties for solvated systems.

Effective computational route towards vibrational optical activity spectra of chiral molecules in aqueous solution

A polarizable QM/MM approach to accurately compute the Vibrational Optical Activity (VOA) spectra of chiral systems is proposed and applied to aqueous solutions of (l)-methyl lactate and (S)-glycidol.

Understanding the interplay between the solvent and nuclear rearrangements in the negative solvatochromism of a push–pull flexible quinolinium cation

The main effects (solvation, vibronic progression) affecting the band position and shape of a push–pull flexible quinolinium cation OPA are highlighted.

Effective Fully Polarizable QM/MM Approach To Model Vibrational Circular Dichroism Spectra of Systems in Aqueous Solution

We propose a methodology, based on the combination of classical Molecular Dynamics (MD) simulations with a fully polarizable Quantum Mechanical (QM)/Molecular Mechanics (MM)/Polarizable Continuum Model (PCM) Hamiltonian, to calculate Vibrational Circular Dichroism (VCD) spectra of chiral systems in aqueous solution. Polarization effects are included in the MM force field by exploiting an approach based on Fluctuating Charges (FQ). By performing the MD, the description of the solvating environment is enriched by taking into account the dynamical aspects of the solute-solvent interactions. On the other hand, the QM/FQ/PCM calculation of the VCD spectrum ensures an accurate description of the electronic density of the solute and a proper account for the specific interactions in solution. The application of our approach to (R)-methyloxirane and (l)-alanine in aqueous solution gives calculated spectra in remarkable agreement with their experimental counterparts and a substantial improvement with respect to the same spectra calculated with the PCM.

Local electric fields and molecular properties in heterogeneous environments through polarizable embedding

In spectroscopies, the local field experienced by a molecule embedded in an environment will be different from the externally applied electromagnetic field, and this difference may significantly alter the response and transition properties of the molecule. The polarizable embedding (PE) model has previously been developed to model the local field contribution stemming from the direct molecule-environment coupling of the electromagnetic response properties of molecules in solution as well as in heterogeneous environments, such as proteins. Here we present an extension of this approach to address the additional effective external field effect, i.e., the manifestations of the environment polarization induced by the external field, which allows for the calculation of properties defined in terms of the external field. Within a response framework, we report calculations of the one- and two-photon absorption (1PA and 2PA, respectively) properties of PRODAN-methanol clusters as well as the fluorescent protein DsRed. Our results demonstrate the necessity of accounting for both the dynamical reaction field and effective external field contributions to the local field in order to reproduce full quantum chemical reference calculations. For the lowest π→π* transition in DsRed, inclusion of effective external field effects gives rise to a 1.9- and 3.5-fold reduction in the 1PA and 2PA cross-sections, respectively. The effective external field is, however, strongly influenced by the heterogeneity of the protein matrix, and the resulting effect can lead to either screening or enhancement depending on the nature of the transition under consideration.

The cavity electromagnetic field within the polarizable continuum model of solvation

Cavity field effects can be defined as the consequences of the solvent polarization induced by the probing electromagnetic field upon spectroscopies of molecules in solution, and enter in the definitions of solute response properties. The polarizable continuum model of solvation (PCM) has been extended in the past years to address the cavity-field issue through the definition of an effective dipole moment that couples to the external electromagnetic field. We present here a rigorous derivation of such cavity-field treatment within the PCM starting from the general radiation-matter Hamiltonian within inhomogeneous dielectrics and recasting the interaction term to a dipolar form within the long wavelength approximation. To this aim we generalize the Göppert-Mayer and Power-Zienau-Woolley gauge transformations, usually applied in vacuo, to the case of a cavity vector potential. Our derivation also allows extending the cavity-field correction in the long-wavelength limit to the velocity gauge through the definition of an effective linear momentum operator. Furthermore, this work sets the basis for the general PCM treatment of the electromagnetic cavity field, capable to describe the radiation-matter interaction in dielectric media beyond the long-wavelength limit, providing also a tool to investigate spectroscopic properties of more complex systems such as molecules close to large nanoparticles.

The electronic circular dichroism of nicotine in aqueous solution: a test case for continuum and mixed explicit-continuum solvation approaches

In this paper, we extend an integrated QM/MM/polarizable continuum model (PCM) method, which combines a fluctuating charge (FQ) approach to the MM polarization with the PCM, to describe electronic circular dichroism (ECD) spectra of systems in aqueous solution. The main features of the approach are presented, and then applications to the UV and ECD spectra of neutral (S)-nicotine in aqueous solution are reported. The performance of the QM/FQ/PCM is compared with that of the PCM against newly measured UV ECD spectra, which are in agreement with previous findings. The inclusion of specific solvation effects via the QM/FQ/PCM method leads to an improvement in the calculated spectra compared to the experimental findings, though the pure PCM results are still qualitatively correct and are a useful tool for the characterization of the states.

Dispersion corrected DFT approaches for anharmonic vibrational frequency calculations: nucleobases and their dimers

Computational spectroscopy techniques have become in the last few years an effective means to analyze and assign infrared (IR) spectra of molecular systems of increasing dimensions and in different environments. However, transition from compilation of harmonic data to fully anharmonic simulations of spectra is still underway. The most promising results for large systems have been obtained, in our opinion, by perturbative vibrational approaches based on potential energy surfaces computed by hybrid (especially B3LYP) density functionals and medium size (e.g. SNSD) basis sets. In this framework, we are actively developing a comprehensive and robust computational protocol aimed at quantitative reproduction of the spectra of nucleic acid base complexes and their adsorption on solid supports (organic/inorganic). In this contribution we report the essential results of the first step devoted to isolated monomers and dimers. It is well known that in order to model the vibrational spectra of weakly bound molecular complexes dispersion interactions should be taken into proper account. In this work we have chosen two popular and inexpensive approaches to model dispersion interactions, namely the semi-empirical dispersion correction (D3) and pseudopotential based (DCP) methodologies both in conjunction with the B3LYP functional. These have been used for simulating fully anharmonic IR spectra of nucleobases and their dimers through generalized second order vibrational perturbation theory (GVPT2). We have studied, in particular, isolated adenine, hypoxanthine, uracil, thymine and cytosine, the hydrogen-bonded and stacked adenine and uracil dimers, and the stacked adenine-naphthalene heterodimer. Anharmonic frequencies are compared with standard B3LYP results and experimental findings, while the computed interaction energies and structures of complexes are compared to the best available theoretical estimates.

Stereo-electronic, vibrational, and environmental contributions to polarizabilities of large molecular systems: a feasible anharmonic protocol

Reliable computations of linear and non-linear optical properties of molecular systems in condensed phases require a proper account of stereo-electronic, vibrational, and environmental effects. In the framework of density functional theory, these effects can be accurately introduced using second-order vibrational perturbation theory in conjunction with polarizable continuum models. We illustrate the combination of an anharmonic description of the ground-state potential energy surface with solvation effects treated with the polarizable continuum model (PCM) in the calculation of the electronic, zero-point, and pure vibrational polarizabilities of selected systems. The description of the solvation environment is enriched by taking into account the dynamical aspects of the solute-solvent interactions through the inclusion of both electronic and vibrational non-equilbrium effects, as well as the direct effect of the solvent on the electric field that generates the molecular response (local field effect). This treatment yields accurate results which can be directly compared with experimental findings without the need of empirical corrections.

Fully anharmonic IR and Raman spectra of medium-size molecular systems: accuracy and interpretation

Computation of full infrared (IR) and Raman spectra (including absolute intensities and transition energies) for medium- and large-sized molecular systems beyond the harmonic approximation is one of the most interesting challenges of contemporary computational chemistry. Contrary to common beliefs, low-order perturbation theory is able to deliver results of high accuracy (actually often better than those issuing from current direct dynamics approaches) provided that anharmonic resonances are properly managed. This perspective sketches the recent developments in our research group toward the development of a robust and user-friendly virtual spectrometer rooted in second-order vibrational perturbation theory (VPT2) and usable also by non-specialists essentially as a black-box procedure. Several examples are explicitly worked out in order to illustrate the features of our computational tool together with the most important ongoing developments.

A robust and effective time-independent route to the calculation of Resonance Raman spectra of large molecules in condensed phases with the inclusion of Duschinsky, Herzberg-Teller, anharmonic, and environmental effects

We present an effective time-independent implementation to model vibrational resonance Raman (RR) spectra of medium-large molecular systems with the inclusion of Franck-Condon (FC) and Herzberg-Teller (HT) effects and a full account of the possible differences between the harmonic potential energy surfaces of the ground and resonant electronic states. Thanks to a number of algorithmic improvements and very effective parallelization, the full computations of fundamentals, overtones, and combination bands can be routinely performed for large systems possibly involving more than two electronic states. In order to improve the accuracy of the results, an effective inclusion of the leading anharmonic effects is also possible, together with environmental contributions under different solvation regimes. Reduced-dimensionality approaches can further enlarge the range of applications of this new tool. Applications to imidazole, pyrene, and chlorophyll a1 in solution are reported, as well as comparisons with available experimental data.

Development of a virtual spectrometer for chiroptical spectroscopies: the case of nicotine

The impressive advances of computational spectroscopy in most recent years are providing robust and user-friendly multifrequency virtual spectrometers, which can also be used by nonspecialists to complement experimental studies. At the heart of these developments there are latest-generation models based on Density Functional Theory for the proper treatment of stereo-electronic effects, coupled to the polarizable continuum model to deal with bulk solvent effects, and low-order perturbative treatments of anharmonic effects. Continuing our efforts to increase the range of application of virtual spectrometers, we report here about chiroptical spectroscopies with special reference to optical rotation and vibrational circular dichroism. The capabilities and possible limitations of our latest tool will be analyzed for the specific case of (S)-nicotine in vacuo and in different solvents.

In-solution conformational analysis of the XCYCH3 moiety for small esters and ethers with all combinations of X, Y = O, S

Favorable steric and electrostatic fit of a ligand to a receptor is of central interest in theoretical drug design. This paper considers the effects of non-protic solvents, in comparison with the gas phase, on the preferred conformation of the XCYCH3 moiety of simple aliphatic esters and heterocyclic methyl ethers with all combinations of the X and Y atoms as oxygen and sulfur. An IEF-PCM/B97D/aug-cc-pv(t+d)z continuum dielectric solvent study in chloroform and acetonitrile explores the through-space polarization effect of the environment on the conformational preference, not affected by possible solute-solvent hydrogen bond formation. The inherently favored structure for the present molecules is important, since the hypothetical oxygen and sulfur lone-pairs point approximately in opposite directions in the cis conformation of esters, whereas the trans and gauche conformations for the methyl group in ethers define nearly parallel or perpendicular directionality for the lone pairs of the ring heteroatoms and the O or S atoms connecting to the ring. These different preferences for the studied two families of compounds allow for designing formation of hydrogen bonds with a protein in fairly different regions of the latter still within the ligand-binding cavity. For a fine-tuning of these hydrogen bonds, a replacement of an oxygen atom of the ligand by a sulfur atom could be a straightforward possibility.

A gauge invariant multiscale approach to magnetic spectroscopies in condensed phase: general three-layer model, computational implementation and pilot applications

Analytical equations to calculate second order electric and magnetic properties of a molecular system embedded into a polarizable environment are presented. The treatment is limited to molecules described at the self consistent field level of theory, including Hartree-Fock theory as well as Kohn-Sham density functional theory and is extended to the Gauge-Including Atomic Orbital method. The polarizable embedding is described by means of our already implemented polarizable quantum mechanical/molecular mechanical (MM) methodology, where the polarization in the MM layer is handled by means of the fluctuating charge (FQ) model. A further layer of description, i.e, the polarizable continuum model, can also be included. The FQ(/polarizable continuum model) contributions to the properties are derived, with reference to the calculation of the magnetic susceptibility, the nuclear magnetic resonance shielding tensor, electron spin resonance g-tensors, and hyperfine couplings.

A second-order perturbation theory route to vibrational averages and transition properties of molecules: general formulation and application to infrared and vibrational circular dichroism spectroscopies

A general formulation to compute anharmonic vibrational averages and transition properties at the second-order of perturbation theory is derived from the Rayleigh-Schrödinger development. This approach is intended to be applicable to any property expanded as a Taylor series up to the third order with respect to normal coordinates or their associated momenta. The equations are straightforward to implement and can be easily adapted to various properties, as illustrated for the case of electric and magnetic dipole moments. From those, infrared and vibrational circular dichroism spectra can be readily obtained. This fully automatic procedure has been applied to several chiral molecules of small-to-medium sizes and compared to the standard double harmonic approximation and to experimental data.

Toward Ab Initio Anharmonic Vibrational Circular Dichroism Spectra in the Condensed Phase

The first implementation and calculation of anharmonic VCD rotational strengths for solvated systems is reported. Our approach, rooted in the polarizable continuum model (PCM) and in the second-order vibrational perturbation theory (VPT2), permits not only correction for anharmonicity in the signals associated with fundamental transitions but also calculation of rotational strengths of overtones and combination bands. This allows for a more physically consistent comparison between experiment and calculations together with the analysis of spectral regions dominated by anharmonic effects. The developed model is applied to a few test cases, and the computational outcomes are directly compared with experimental data.