“Divide-and-conquer” semiclassical molecular dynamics: An application to water clusters

CO2 electroreduction on single atom catalysts: the role of the DFT functional

One key process involving single atom catalysts (SACs) is the electroreduction of CO2 to fuels. The chemistry of SACs differs largely from that of extended catalytic surfaces, presenting an opportunity to improve the ability to activate very stable molecules, such as CO2. In this work, we performed a density functional theory (DFT) study of CO2 activation on a series of SACs, focusing on the role played by the adopted functional in activity predictions. The role of the exchange-correlation functional has been widely investigated in heterogenous catalysts, but it is less explored in SACs. We tested the widely used PBE and the PBE+U corrected functionals against the more robust hybrid PBE0 functional. The results show that PBE is reliable if one is interested in qualitative predictions, but it leads to some inaccuracies in other cases. A possible way to attenuate this effect is by adopting the PBE+U framework, as it gives results that are very similar to PBE0 at an acceptable computational cost. The results of this study further underline the importance of the computational framework adopted in predicting the activity of SACs. The work suggests that one needs to go beyond PBE for quantitative estimates, an important consideration when performing screening and high-throughput calculations.

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.

Modeling Single-Atom Catalysis

Electronic structure calculations represent an essential complement of experiments to characterize single-atom catalysts (SACs), consisting of isolated metal atoms stabilized on a support, but also to predict new catalysts. However, simulating SACs with quantum chemistry approaches is not as simple as often assumed. In this work, the essential factors that characterize a reliable simulation of SACs activity are examined. The Perspective focuses on the importance of precise atomistic characterization of the active site, since even small changes in the metal atom's surroundings can result in large changes in reactivity. The dynamical behavior and stability of SACs under working conditions, as well as the importance of adopting appropriate methods to solve the Schrödinger equation for a quantitative evaluation of reaction energies are addressed. The Perspective also focuses on the relevance of the model adopted. For electrocatalysis this must include the effects of the solvent, the presence of electrolytes, the pH, and the external potential. Finally, it is discussed how the similarities between SACs and coordination compounds may result in reaction intermediates that usually are not observed on metal electrodes. When these aspects are not adequately considered, the predictive power of electronic structure calculations is quite limited.

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.

A Semiclassical Framework for Mixed Quantum Classical Dynamics

Semiclassical (SC) approximations for quantum dynamic simulations in complex chemical systems range from rigorously accurate methods that are computationally expensive to methods that exhibit near-classical scaling with system size but are limited in their ability to describe quantum effects. In practical studies of high-dimensional reactions, neither extreme is the best choice: frequently a high-level quantum mechanical description is only required for a handful of modes, while the majority of environment modes that do not play a key role in the reactive event of interest are well served with a lower level of theory. In this feature, we introduce modified Filinov filtration as a powerful tool to construct mixed quantum-classical SC theories where different subsystems can be quantized to different extents without introducing ad hoc intersubsystem interaction terms. We demonstrate that these Filinov-based SC methods can systematically tune between quantum and classical limit SC behavior, offering a practical way forward to accurate and computationally efficient simulations of high-dimensional quantum processes.

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.

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.

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.

How many water molecules are needed to solvate one?

Many efforts undertaken to study the solvation process have led to general theories that may describe mean properties, but are unable to provide a detailed understanding at the molecular level. Remarkably, the basic question of how many solvent molecules are necessary to solvate one solute molecule is still open. By exploring several water aggregates of increasing complexity, in this contribution we employ semiclassical spectroscopy to determine on quantum dynamical grounds the minimal network of surrounding water molecules to make the central one display the same vibrational features of liquid water. We find out that double-acceptor double-donor tetrahedral coordination constituting the standard picture is necessary but not sufficient, and that particular care must be reserved for the quantum description of the combination band due to the coupling of the central monomer bending mode with network librations. It is actually our ability to investigate the combination band with a quantum-derived approach that allows us to answer the titular question. The minimal structure eventually responsible for proper solvation is made of a total of 21 water molecules and includes two complete solvation shells, of which the whole first one is tetrahedrally coordinated to the central molecule.

How quantum spectroscopic simulations can explain water solvation by comparison with experimental spectra.

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.

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.

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.

Reaction mechanism of synthetic thorium sulfides: theoretical calculation study

Actinide sulfides are especially significant in actinide chemistry because of their potentials that are used as nuclear fuel and the wide variety of their stoichiometries and physical properties. It is essential for studying the synthesis mechanism of actinide sulfides. In this study, the reactions of thorium cation Th²⁺ with the facile sulfur-atom donor OCS to produce thorium sulfides have been systematically explored by using density functional. The detailed insights of the primary reaction and secondary reaction paths are reported. We investigated that the multiple bonding characters and complexes involved in reaction exhibit significant covalent character. The reaction rate indicated that the tunneling effect is small compared with the effect of temperature on the rate. This study addresses some of the current limitation in understanding the detailed reaction information of Th²⁺+OCS.

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

The vibrational spectroscopy of adsorbates is becoming an important investigation tool for catalysis and material science. This paper presents a semiclassical molecular dynamics method able to reproduce the vibrational energy levels of systems composed by molecules adsorbed on solid surfaces. Specifically, we extend our divide-and-conquer semiclassical method for power spectra calculations to gas-surface systems and interface it with plane-wave electronic structure codes. The Born-Oppenheimer classical dynamics underlying the semiclassical calculation is full dimensional, and our method includes not only the motion of the adsorbate but also those of the surface and the bulk. The vibrational spectroscopic peaks related to the adsorbate are accounted together with the most coupled phonon modes to obtain spectra amenable to physical interpretations. We apply the method to the adsorption of CO, NO, and H₂O on the anatase-TiO₂ (101) surface. We compare our semiclassical results with the single-point harmonic estimates and the classical power spectra obtained from the same trajectory employed in the semiclassical calculation. We find that CO and NO anharmonic effects of fundamental vibrations are similarly reproduced by the classical and semiclassical dynamics and that H₂O adsorption is fully and properly described in its overtone and combination band relevant components only by the semiclassical approach.

Improved semiclassical dynamics through adiabatic switching trajectory sampling

We introduce an improved semiclassical dynamics approach to quantum vibrational spectroscopy. In this method, a harmonic-based phase space sampling is preliminarily driven toward non-harmonic quantization by slowly switching on the actual potential. The new coordinates and momenta serve as initial conditions for the semiclassical dynamics calculation, leading to a substantial decrease in the number of chaotic trajectories to deal with. Applications are presented for model and molecular systems of increasing dimensionality characterized by moderate or high chaoticity. They include a bidimensional Henon-Heiles potential, water, formaldehyde, and methane. The method improves accuracy and precision of semiclassical results and it can be easily interfaced with all pre-existing semiclassical theories.

Semiclassical dynamics in the mixed quantum-classical limit

The semiclassical double Herman-Kluk initial value representation is an accurate approach to computing quantum real time correlation functions, but its applications are limited by the need to evaluate an oscillatory integral. In previous work, we have shown that this "sign problem" can be mitigated using the modified Filinov filtration technique to control the extent to which individual modes of the system contribute to the overall phase of the integrand. Here, we follow this idea to a logical conclusion: we analytically derive a general expression for the mixed quantum-classical limit of the semiclassical correlation function-analytical mixed quantum-classical-initial value representation (AMQC-IVR), where the phase contributions from the "classical" modes of the system are filtered while the "quantum" modes are treated in the full semiclassical limit. We numerically demonstrate the accuracy and efficiency of the AMQC-IVR formulation in calculations of quantum correlation functions and reaction rates using three model systems with varied coupling strengths between the classical and quantum subsystems. We also introduce a separable prefactor approximation that further reduces computational cost but is only accurate in the limit of weak coupling between the quantum and classical subsystems.

Reduced rovibrational coupling Cartesian dynamics for semiclassical calculations: Application to the spectrum of the Zundel cation

We study the vibrational spectrum of the protonated water dimer, by means of a divide-and-conquer semiclassical initial value representation of the quantum propagator, as a first step in the study of larger protonated water clusters. We use the potential energy surface from the work of Huang et al. [J. Chem. Phys. 122, 044308 (2005)]. To tackle such an anharmonic and floppy molecule, we employ fully Cartesian dynamics and carefully reduce the coupling to global rotations in the definition of normal modes. We apply the time-averaging filter and obtain clean power spectra relative to suitable reference states that highlight the spectral peaks corresponding to the fundamental excitations of the system. Our trajectory-based approach allows for the physical interpretation of the very challenging proton transfer modes. We find that it is important, for such a floppy molecule, to selectively avoid initially exciting lower energy modes, in order to obtain cleaner spectra. The estimated vibrational energies display a mean absolute error (MAE) of ∼29 cm^-1 with respect to available multiconfiguration time-dependent Hartree calculations and MAE ∼ 14 cm^-1 when compared to the optically active experimental excitations of the Ne-tagged Zundel cation. The reasonable scaling in the number of trajectories for Monte Carlo convergence is promising for applications to higher dimensional protonated cluster systems.

Vibrational investigation of nucleobases by means of divide and conquer semiclassical dynamics

In this work, we report a computational study of the vibrational features of four different nucleobases employing the divide-and-conquer semiclassical initial value representation molecular dynamics method. Calculations are performed on uracil, cytosine, thymine, and adenine. Results show that the overall accuracy with respect to experiments is within 20 wavenumbers, regardless of the dimensionality of the nucleobase. Vibrational estimates are accurate even in the complex case of cytosine, where two relevant conformers are taken into account. These results are promising in the perspective of future studies on more complex systems, such as nucleotides or nucleobase pairs.

Semiclassical vibrational spectroscopy with Hessian databases

We report on a new approach to ease the computational overhead of ab initio "on-the-fly" semiclassical dynamics simulations for vibrational spectroscopy. The well known bottleneck of such computations lies in the necessity to estimate the Hessian matrix for propagating the semiclassical pre-exponential factor at each step along the dynamics. The procedure proposed here is based on the creation of a dynamical database of Hessians and associated molecular geometries able to speed up calculations while preserving the accuracy of results at a satisfactory level. This new approach can be interfaced to both analytical potential energy surfaces and on-the-fly dynamics, allowing one to study even large systems previously not achievable. We present results obtained for semiclassical vibrational power spectra of methane, glycine, and N-acetyl-L-phenylalaninyl-L-methionine-amide, a molecule of biological interest made of 46 atoms.

The formation mechanism of uranium and thorium hydride phosphorus: a systematically theoretical study

Activation of prototypical bonds by actinide atoms is an important aspect of material activity, and the results can be used for the study of nuclear material storage. In this study, the activation of the P–H bonds of the PH₃ molecule by U or Th to form uranium or thorium hydride phosphorus has been systematically explored using density functional theory. A detailed description of the reaction mechanism which includes the potential energy profiles and the properties of bond evolution is presented. There are two types of reaction channels, isomerization and dehydrogenation in U + PH₃ and Th + PH₃. The difference between the two reactions is the process of the first P–H bond dissociation. The evolution characteristics of the chemical bonds along reaction pathways is analyzed by using electron localization functions, quantum theory of atoms in molecules, Mayer bond orders and natural bond orbitals. The reaction rate constants are calculated at the variational transition state level, and rate-determining steps are predicted.

The reactions of U, Th with PH₃ to form the uranium and thorium hydride phosphorus have been systematically explored.

Protonated glycine supramolecular systems: the need for quantum dynamics

Quantum mechanical simulations unequivocally explain experimental IR spectra of protonated supramolecular systems.

IR spectroscopy is one of the most commonly employed techniques to study molecular vibrations and interactions. However, characterization of experimental IR spectra is not always straightforward. This is the case of protonated glycine supramolecular systems like Gly₂H⁺ and (GlyH + nH₂), whose IR spectra raise questions which have still to find definitive answers even after theoretical spectroscopy investigations. Specifically, the assignment of the conformer responsible for the spectrum of the protonated glycine dimer (Gly₂H⁺) has led to much controversy and it is still debated, while structural hypotheses formulated to explain the main experimental spectral features of (GlyH + nH₂) systems have not been theoretically confirmed. We demonstrate that simulations must account for quantum dynamical effects in order to resolve these open issues. This is achieved by means of our divide-and-conquer semiclassical initial value representation technique, which approximates the quantum dynamics of high dimensional systems with remarkable accuracy and outperforms not only the commonly employed but unfit scaled-harmonic approaches, but also pure classical dynamics simulations. Besides the specific insights concerning the two particular cases presented here, the general conclusion is that, due to the widespread presence of protonated systems in chemistry, quantum dynamics may play a prominent role and should not be totally overlooked even when dealing with large systems including biological structures.