Anharmonic calculations of vibrational spectra for molecular adsorbates: A divide-and-conquer semiclassical molecular dynamics approach

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

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

Molecular Hessian matrices from a machine learning random forest regression algorithm

In this article, we present a machine learning model to obtain fast and accurate estimates of the molecular Hessian matrix. In this model, based on a random forest, the second derivatives of the energy with respect to redundant internal coordinates are learned individually. The internal coordinates together with their specific representation guarantee rotational and translational invariance. The model is trained on a subset of the QM7 dataset but is shown to be applicable to larger molecules picked from the QM9 dataset. From the predicted Hessian, it is also possible to obtain reasonable estimates of the vibrational frequencies, normal modes, and zero point energies of the molecules.

Investigating the Spectroscopy of the Gas Phase Guanine-Cytosine Pair: Keto versus Enol Configurations

We report on a vibrational study of the guanine-cytosine dimer tautomers using state-of-the-art quasiclassical trajectory and semiclassical vibrational spectroscopy. The latter includes possible quantum mechanical effects. Through an accurate comparison to the experimental spectra, we are able to shine a light on the hydrogen bond network of one of the main subunits of DNA and put the experimental assignment on a solid footing. Our calculations corroborate the experimental conclusion that the global minimum Watson-and-Crick structure is not detected in the spectra, and there is no evidence of tunnel-effect-based double proton hopping. Our accurate assignment of the spectral features may also serve as a basis for the development of precise force fields to study the guanine-cytosine dimer.

Molecular Dynamics of Artificially Pair-Decoupled Systems: An Accurate Tool for Investigating the Importance of Intramolecular Couplings

We propose a numerical technique to accurately simulate the vibrations of organic molecules in the gas phase, when pairs of atoms (or, in general, groups of degrees of freedom) are artificially decoupled, so that their motion is instantaneously decorrelated. The numerical technique we have developed is a symplectic integration algorithm that never requires computation of the force but requires estimates of the Hessian matrix. The theory we present to support our technique postulates a pair-decoupling Hamiltonian function, which parametrically depends on a decoupling coefficient α ∈ [0, 1]. The closer α is to 0, the more decoupled the selected atoms. We test the correctness of our numerical method on small molecular systems, and we apply it to study the vibrational spectroscopic features of salicylic acid at the Density Functional Theory ab initio level on a fitted potential. Our pair-decoupled simulations of salicylic acid show that decoupling hydrogen-bonded atoms do not significantly influence the frequencies of stretching modes, but enhance enormously the out-of-plane wagging and twisting motions of the hydroxyl and carboxyl groups to the point that the carboxyl and hydroxyl groups may overcome high potential energy barriers and change the salicylic acid conformation after a short simulation time. In addition, we found that the acidity of salicylic acid is more influenced by the dynamical couplings of the proton of the carboxylic group with the carbon ring than with the hydroxyl group.

Vibrational spectroscopy simulation of solvation effects on a G-quadruplex

It is commonly believed that solvation effects on the vibrational properties of a solute are easily accounted for by simple rules of thumbs, that is, solvating a polar molecule in a polar medium has the only effect of red shifting all its spectroscopical features and, similarly, solvating a polar molecule in a nonpolar medium has the opposite effect. In this work, we use theoretical vibrational spectroscopy at quasi-classical and quantum approximate semiclassical level to gain atomistic insights about solvent-solute interactions for 2'-deoxyguanosine and the G-quadruplex. We employ the quasi-classical trajectory method to include full anharmonicity into our calculated spectra, and then introduce quantum nuclear effects by means of divide-and-conquer semiclassical spectroscopy calculations. Solvation is treated explicitly leading to a good reproducibility of the available experimental data and reliable predictions when an experimental reference is missing.Communicated by Ramaswamy H. Sarma.

Elucidating NO x Surface Chemistry at the Anatase (101) Surface in TiO2 Nanoparticles

Understanding NO _x chemistry at titania nanoparticle surfaces is important for photocatalytic environmental remediation processes. We focus on this problem and put forward an experimental-computational approach based on vibrational spectroscopy grounds. Temperature-dependent IR experiments of NO _x adsorption on shape-engineered nanoparticle (101) anatase surfaces are paired with power spectra obtained from Born-Oppenheimer trajectories. Then, the harmonic versus anharmonic vibrational frequencies of several adsorption scenarios are directly compared with the IR experiments. We conclude that molecules are adsorbed mainly by the N-end side and both the intermolecular interactions between adsorbed molecules and (NO)₂ dimer formation are responsible for the main NO adsorption spectroscopic features. We also investigate the spectroscopy and the mechanism of formation on defective anatase surfaces of the long-lived greenhouse gas N₂O.

Quantum Anharmonic Calculations of Vibrational Spectra for Water Adsorbed on Titania Anatase(101) Surface: Dissociative versus Molecular Adsorption

The interaction of water molecules and hydroxyl groups with titanium dioxide (TiO₂) surfaces is ubiquitous and very important in anatase nanoparticle photocatalytic processes. Infrared spectroscopy, assisted by ab initio calculations of vibrational frequencies, can be a powerful tool to elucidate the mechanisms behind water adsorption. However, a straightforward comparison between measurements and calculations remains a challenging task because of the complexity of the physical phenomena occurring on nanoparticle surfaces. Consequently, severe computational approximations, such as harmonic vibrational ones, are usually employed. In the present work we partially address this complexity issue by overcoming some of the standard approximations used in theoretical simulations and employ the Divide and Conquer Semiclassical Initial Value Representation (DC-SCIVR) molecular dynamics. This method allows to perform simulations of vibrational spectra of large dimensional systems accounting not only for anharmonicities, but also for nuclear quantum effects. We apply this computational method to water and deuterated water adsorbed on the ideal TiO₂ anatase(101) surface, contemplating both the molecular and the dissociated adsorption processes. The results highlight not only the presence of an anharmonic shift of the frequencies in agreement with the experiments, but also complex quantum mechanical spectral signatures induced by the coupling of molecular vibrational modes with the surface ones, which are different in the hydrogenated case from the deuterated one. These couplings are further analyzed by exploiting the mode subdivision performed during the divide and conquer procedure.

The complex vibrational spectrum of proline explained through the adiabatically switched semiclassical initial value representation

Proline, a 17-atom amino acid with a closed-ring side chain, has a complex potential energy surface characterized by several minima. Its IR experimental spectrum, reported in the literature, is of difficult and controversial assignment. In particular, the experimental signal at 3559 cm−1 associated with the OH stretch is interesting because it is inconsistent with the global minimum, trans-proline conformer. This suggests the possibility that multiple conformers may contribute to the IR spectrum. The same conclusion is obtained by investigating the splitting of the CO stretch at 1766 and 1789 cm−1 and other, more complex spectroscopic features involving CH stretches and COH/CNH bendings. In this work, we perform full-dimensional, on-the-fly adiabatically switched semiclassical initial value representation simulations employing the ab initio dft-d3-B3LYP level of theory with aug-cc-pVDZ basis set. We reconstruct the experimental spectrum of proline in its main features by studying the vibrational features of trans-proline and cis1-proline, and provide a new assignment for the OH stretch of trans-proline.

Quantum Vibrational Spectroscopy of Explicitly Solvated Thymidine in Semiclassical Approximation

In this paper, we demonstrate the possibility to perform spectroscopy simulations of solvated biological species taking into consideration quantum effects and explicit solvation. We achieve this goal by interfacing our recently developed divide-and-conquer approach for semiclassical initial value representation molecular dynamics with the polarizable AMOEBABIO18 force field. The method is applied to the study of solvation of the thymidine nucleoside in two different polar solvents, water and N,N-dimethylformamide. Such systems are made of up to 2476 atoms. Experimental evidence concerning the different behavior of thymidine in the two solvents is well reproduced by our study, even though quantitative estimates are hampered by the limited accuracy of the classical force field employed. Overall, this study shows that semiclassically approximate quantum dynamical studies of explicitly solvated biological systems are both computationally affordable and insightful.

On-the-fly adiabatically switched semiclassical initial value representation molecular dynamics for vibrational spectroscopy of biomolecules

Semiclassical (SC) vibrational spectroscopy is a technique capable of reproducing quantum effects (such as zero-point energies, quantum resonances, and anharmonic overtones) from classical dynamics runs even in the case of very large dimensional systems. In a previous study [Conte et al. J. Chem. Phys. 151, 214107 (2019)], a preliminary sampling based on adiabatic switching has been shown to be able to improve the precision and accuracy of semiclassical results for challenging model potentials and small molecular systems. In this paper, we investigate the possibility to extend the technique to larger (bio)molecular systems whose dynamics must be integrated by means of ab initio "on-the-fly" calculations. After some preliminary tests on small molecules, we obtain the vibrational frequencies of glycine improving on pre-existing SC calculations. Finally, the new approach is applied to 17-atom proline, an amino acid characterized by a strong intramolecular hydrogen bond.

Unsupervised Machine Learning Neural Gas Algorithm for Accurate Evaluations of the Hessian Matrix in Molecular Dynamics

The Hessian matrix of the potential energy of molecular systems is employed not only in geometry optimizations or high-order molecular dynamics integrators but also in many other molecular procedures, such as instantaneous normal mode analysis, force field construction, instanton calculations, and semiclassical initial value representation molecular dynamics, to name a few. Here, we present an algorithm for the calculation of the approximated Hessian in molecular dynamics. The algorithm belongs to the family of unsupervised machine learning methods, and it is based on the neural gas idea, where neurons are molecular configurations whose Hessians are adopted for groups of molecular dynamics configurations with similar geometries. The method is tested on several molecular systems of different dimensionalities both in terms of accuracy and computational time versus calculating the Hessian matrix at each time-step, that is, without any approximation, and other Hessian approximation schemes. Finally, the method is applied to the on-the-fly, full-dimensional simulation of a small synthetic peptide (the 46 atom N-acetyl-l-phenylalaninyl-l-methionine amide) at the level of DFT-B3LYP-D/6-31G* theory, from which the semiclassical vibrational power spectrum is calculated.

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

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

Caldeira-Leggett model vs ab initio potential: A vibrational spectroscopy test of water solvation

We present a semiclassically approximate quantum treatment of solvation with the purpose of investigating the accuracy of the Caldeira-Leggett model. We do that by simulating the vibrational features of water solvation by means of two different approaches. One is entirely based on the adoption of an accurate ab initio potential to describe water clusters of increasing dimensionality. The other one consists of a model made of a central water molecule coupled to a high-dimensional Caldeira-Leggett harmonic bath. We demonstrate the role of quantum effects in the detection of water solvation and show that the computationally cheap approach based on the Caldeira-Leggett bath is only partially effective. The main conclusion of the study is that quantum methods associated with high-level potential energy surfaces are necessary to correctly study solvation features, while simplified models, even if attractive owing to their reduced computational cost, can provide some useful insights but are not able to come up with a comprehensive description of the solvation phenomenon.

Representing molecular ground and excited vibrational eigenstates with nuclear densities obtained from semiclassical initial value representation molecular dynamics

We present in detail and validate an effective Monte Carlo approach for the calculation of the nuclear vibrational densities via integration of molecular eigenfunctions that we have preliminary employed to calculate the densities of the ground and the excited OH stretch vibrational states in the protonated glycine molecule [Aieta et al., Nat Commun 11, 4348 (2020)]. Here, we first validate and discuss in detail the features of the method on a benchmark water molecule. Then, we apply it to calculate on-the-fly the ab initio anharmonic nuclear densities in the correspondence of the fundamental transitions of NH and CH stretches in protonated glycine. We show how we can gain both qualitative and quantitative physical insight by inspection of different one-nucleus densities and assign a character to spectroscopic absorption peaks using the expansion of vibrational states in terms of harmonic basis functions. The visualization of the nuclear vibrations in a purely quantum picture allows us to observe and quantify the effects of anharmonicity on the molecular structure, also to exploit the effect of IR excitations on specific bonds or functional groups, beyond the harmonic approximation. We also calculate the quantum probability distribution of bond lengths, angles, and dihedrals of the molecule. Notably, we observe how in the case of one type of fundamental NH stretching, the typical harmonic nodal pattern is absent in the anharmonic distribution.

Morphology, Surface Structure and Water Adsorption Properties of TiO2 Nanoparticles: A Comparison of Different Commercial Samples

Water is a molecule always present in the reaction environment in photocatalytic and biomedical applications of TiO₂ and a better understanding of its interaction with the surface of TiO₂ nanoparticles is crucial to develop materials with improved performance. In this contribution, we first studied the nature and the surface structure of the exposed facets of three commercial TiO₂ samples (i.e., TiO₂ P25, SX001, and PC105) by electron microscopy and IR spectroscopy of adsorbed CO. The morphological information was then correlated with the water adsorption properties, investigated at the molecular level, moving from multilayers of adsorbed H₂O to the monolayer, combining medium- and near-IR spectroscopies. Finally, we assessed in a quantitative way the surface hydration state at different water equilibrium pressures by microgravimetric measurements.

Semiclassical Vibrational Spectroscopy of Biological Molecules Using Force Fields

Semiclassical spectroscopy is a practical way to get an accurately approximate quantum description of spectral features starting from ab initio molecular dynamics simulations. The computational bottleneck for the method is represented by the cost of ab initio potential, gradient, and Hessian matrix estimates. This drawback is particularly severe for biological systems due to their unique complexity and large dimensionality. The main goal of this manuscript is to demonstrate that quantum dynamics and spectroscopy, at the level of semiclassical approximation, are doable even for sizable biological systems. To this end, we investigate the possibility of performing semiclassical spectroscopy simulations when ab initio calculations are replaced by computationally cheaper force field evaluations. Both polarizable (AMOEBABIO18) and nonpolarizable (AMBER14SB) force fields are tested. Calculations of some particular vibrational frequencies of four nucleosides, i.e., uridine, thymidine, deoxyguanosine, and adenosine, show that ab initio simulations are accurate and widely applicable. Conversely, simulations based on AMBER14SB are limited to harmonic approximations, but those relying on AMOEBABIO18 yield acceptable semiclassical values if the investigated conformation has been included in the force field parametrization. The main conclusion is that AMOEBABIO18 may provide a viable route to assist semiclassical spectroscopy in the study of large biological molecules for which an ab initio approach is not computationally affordable.