High-Temperature Atomic Diffusion and Specific Heat in Quasicrystals.

A quasicrystal is an ordered but nonperiodic structure understood as a projection from a higher-dimensional periodic structure. Some physical properties of quasicrystals are different from those of conventional solids. An anomalous increase in heat capacity at high temperatures has been discussed for over two decades as a manifestation of a hidden high dimensionality of quasicrystals. A plausible candidate for this origin has been the phason, which has excitation modes originating from the additional atomic rearrangements introduced by the quasiperiodic order, which can be understood in terms of shifting a higher-dimensional lattice. However, most theoretical studies of phasons have used toy models. A theoretical study of the heat capacity of realistic quasicrystals or their approximants has yet to be conducted because of the huge computational complexity. To bridge this gap between experiment and theory, we show experiments and molecular simulations on the same material, an Al-Pd-Ru quasicrystal, and its approximants. We show that at high temperatures, aluminum atoms diffuse with discontinuouslike jumps, and the diffusion paths of the aluminum can be understood in terms of jumps corresponding to hyperatomic-fluctuations-associated atomic rearrangements of the phason degrees of freedom. It is concluded that the anomaly in the heat capacity of quasicrystals arises from the hyperatomic fluctuations that play a role in diffusive Nambu-Goldstone modes.

Path integral Brownian chain molecular dynamics: A simple approximation of quantum vibrational dynamics.

An approximate approach to quantum vibrational dynamics, "Brownian chain molecular dynamics (BCMD)," is proposed to alleviate the chain resonance and curvature problems in the imaginary time-based path integral (PI) simulation. Here the non-centroid velocity is randomized at each step when solving the equation of motion of path integral molecular dynamics. This leads to a combination of the Newton equation and the overdamped Langevin equation for the centroid and non-centroid variables, respectively. BCMD shares the basic properties of other PI approaches such as centroid and ring polymer molecular dynamics: It gives the correct Kubo-transformed correlation function at short times, conserves the time symmetry, has the correct high-temperature/classical limits, gives exactly the position and velocity autocorrelations of harmonic oscillator systems, and does not have the zero-point leakage problem. Numerical tests were done on simple molecular models and liquid water. On-the-fly ab initio BCMD simulations were performed for the protonated water cluster, H 5 O 2 + , and its isotopologue, D 5 O 2 + .

Structures of liquid and aqueous water isotopologues at ambient temperature from ab initio path integral simulations.

The heavy hydrogen isotopes D and T are found in trace amounts in water, and when their concentration increases they can play an intricate role in modulating the physical properties of the liquid. We present an analysis of the microscopic structures of ambient light water (H2O(l)), heavy water (D2O(l)), T2O(l), HDO(aq) and HTO(aq) studied by ab initio path integral molecular dynamics (PIMD). Unlike previous ab initio PIMD investigations of H2O(l) and D2O(l) [Chen et al., Phys. Rev. Lett., 2003, 91, 215503] [Machida et al., J. Chem. Phys., 2017, 148, 102324] we find that D2O(l) is more structured than H2O(l), as is predicted by the experiment. The agreement between the experiment and our simulation for H2O(l) and D2O(l) allows us to accurately predict the intra- and intermolecular structures of T2O(l) HDO(aq) and HTO(aq). T2O(l) is found to have a similar intermolecular structure to that of D2O(l), while the intramolecular structure is more compact, giving rise to a smaller dipole moment than those of H2O(l) and D2O(l). For the mixed isotope species, HDO(aq) and HTO(aq), we find smaller dipole moments and fewer hydrogen bonds when compared with the pure species H2O and D2O. We can attribute this effect to the relative compactness of the mixed isotope species, which results in a lower dipole moment than that of the pure species.

X-ray absorption spectra of aqueous cellobiose: Experiment and theory.

The hydration structure of cellulose is very important for understanding the hydrolysis of cellulose at the molecular level. In this paper, we report a joint experimental and theoretical study on x-ray absorption spectroscopy (XAS) of aqueous cellobiose, a disaccharide unit of cellulose. In the experimental part, high resolution measurements of the carbon K-edge XAS spectra were taken. In the theoretical part, ab initio molecular dynamics simulations and ensemble calculations of electronic excited states were performed to obtain the continuous XAS spectra. The XAS spectra were found to have three characteristic peaks at 289.3, 290.7, and 293.6 eV, each representing the absorption by carbon atoms of the alcohol group, the hemiacetal group, and both of these functional groups. It was found that the peak heights in the spectrum change considerably over the temperature range of 25-60 °C, which is a reflection of the number of hydrogen bonds between cellobiose and water. We suggest that this spectral change could be useful information for identifying the hydration of cellulose in various environments.

Ab initio study of nuclear quantum effects on sub- and supercritical water.

The structures of water in the ambient, subcritical, and supercritical conditions at various densities were studied systematically by ab initio path integral molecular dynamics simulations. It was found that the nuclear quantum effects (NQEs) have a significant impact on the structure of hydrogen bonds in close contact, not only in the ambient condition but also in the sub- and supercritical conditions. The NQEs on the structure beyond the hydrogen bond contact are important in ambient water, but not much for water in the sub- and supercritical conditions. The NQEs are furthermore important for determining the number of hydrogen bonds in the ambient conditions, and this role is, however, diminished in the sub- and supercritical conditions. The NQEs do, nevertheless, show their importance in determining the intramolecular structure of water and the close contact structures of the hydrogen bonds, even at sub- and supercritical conditions. Using the RPBE-D3 functional, the computed radial distribution functions for ambient water are in excellent agreement with experimental data, upgrading our previous results using the BLYP-D2 functional [Machida et al., J. Chem. Phys. 148, 102324 (2018)]. The computed radial distribution functions for water in the sub- and supercritical conditions were carefully compared with experiment. In particular, we found that the first peak in hydrogen pair distribution functions matches only when the NQEs are taken into account.

Mean force based temperature accelerated sliced sampling: Efficient reconstruction of high dimensional free energy landscapes.

Temperature accelerated sliced sampling (TASS) is an efficient method to compute high dimensional free energy landscapes. The original TASS method employs the weighted histogram analysis method (WHAM) which is an iterative post-processing to reweight and stitch high dimensional probability distributions in sliced windows that are obtained in the presence of restraining biases. The WHAM necessitates that TASS windows lie close to each other for proper overlap of distributions and span the collective variable space of interest. On the other hand, increase in number of TASS windows implies more number of simulations, and thus it affects the efficiency of the method. To overcome this problem, we propose herein a new mean-force (MF) based reweighting scheme called TASS-MF, which enables accurate computation with a fewer number of windows devoid of the WHAM post-processing. Application of the technique is demonstrated for alanine di- and tripeptides in vacuo to compute their two- and four-dimensional free energy landscapes, the latter of which is formidable in conventional umbrella sampling and metadynamics. The landscapes are computed within a kcal mol-1 accuracy, ensuring a safe usage for broad applications in computational chemistry.

Self-learning hybrid Monte Carlo method for isothermal-isobaric ensemble: Application to liquid silica.

Self-learning hybrid Monte Carlo (SLHMC) is a first-principles simulation that allows for exact ensemble generation on potential energy surfaces based on density functional theory. The statistical sampling can be accelerated with the assistance of smart trial moves by machine learning potentials. In the first report [Nagai et al., Phys. Rev. B 102, 041124(R) (2020)], the SLHMC approach was introduced for the simplest case of canonical sampling. We herein extend this idea to isothermal-isobaric ensembles to enable general applications for soft materials and liquids with large volume fluctuation. As a demonstration, the isothermal-isobaric SLHMC method was used to study the vibrational structure of liquid silica at temperatures close to the melting point, whereby the slow diffusive motion is beyond the time scale of first-principles molecular dynamics. It was found that the static structure factor thus computed from first-principles agrees quite well with the high-energy x-ray data.

The mechanism of sorbitol dehydration in hot acidic solutions.

Sugar alcohol dehydration in hot water is an important reaction that allows for environmentally friendly biomass conversion without the use of organic solvents. Here, we report a free-energy analysis by metadynamics (MTD) simulations based on ab initio density functional theory and semiempirical density-functional tight-binding method to understand the mechanism of dehydration reactions of d-sorbitol (SBT) in hot acidic water. Comparing the results of ab initio and semiempirical MTD, it was found that the latter gives a reliable free energy surface of SBT dehydration reaction, although the results vary upon the inclusion of dispersion correction. It was found that the reaction proceeds consistently via an SN 2 mechanism, whereby the free energy of protonation of the hydroxyl group created as an intermediate is affected by the acidic species. This mechanism was further verified by real-time trajectories started from the transition state using ab initio molecular dynamics simulations. The free energy barriers of the reaction pathways leading to five-membered ether products are lower than those leading to six-membered ether products, in agreement with experiment. This outcome can be ascribed, in part, to our finding that the reaction barrier of the pathway is correlated to the stability of the SBT confined conformation at the initial stage of the reaction.

Nuclear quantum effects on autoionization of water isotopologs studied by ab initio path integral molecular dynamics.

In this study, we investigate the nuclear quantum effects (NQEs) on the acidity constant (pKA) of liquid water isotopologs under the ambient condition by path integral molecular dynamics (PIMD) simulations. We compared simulations using a fully explicit solvent model with a classical polarizable force field, density functional tight binding, and ab initio density functional theory, which correspond to empirical, semiempirical, and ab initio PIMD simulations, respectively. The centroid variable with respect to the proton coordination number of a water molecule was restrained to compute the gradient of the free energy, which measures the reversible work of the proton abstraction for the quantum mechanical system. The free energy curve obtained by thermodynamic integration was used to compute the pKA value based on probabilistic determination. This technique not only reproduces the pKA value of liquid D2O experimentally measured (14.86) but also allows for a theoretical prediction of the pKA values of liquid T2O and aqueous HDO and HTO, which are unknown due to their scarcity. It is also shown that the NQEs on the free energy curve can result in a downshift of 4.5 ± 0.9 pKA units in the case of liquid water, which indicates that the NQEs plays an indispensable role in the absolute determination of pKA. The results of this study can help inform further extensions into the calculation of the acidity constants of isotope substituted species with high accuracy.

Refined metadynamics through canonical sampling using time-invariant bias potential: A study of polyalcohol dehydration in hot acidic solutions.

We propose a canonical sampling method to refine metadynamics simulations a posteriori, where the hills obtained from metadynamics are used as a time-invariant bias potential. In this way, the statistical error in the computed reaction barriers is reduced by an efficient sampling of the collective variable space at the free energy level of interest. This simple approach could be useful particularly when two or more free energy barriers are to be compared among chemical reactions in different or competing conditions. The method was then applied to study the acid dependence of polyalcohol dehydration reactions in high-temperature aqueous solutions. It was found that the reaction proceeds consistently via an SN 2 mechanism, whereby the free energy of protonation of the hydroxyl group created as an intermediate is affected significantly by the acidic species. Although demonstration is shown for a specific problem, the computational method suggested herein could be generally used for simulations of complex reactions in the condensed phase.

Quantum-mechanical hydration plays critical role in the stability of firefly oxyluciferin isomers: State-of-the-art calculations of the excited states.

Stabilizing mechanisms of three possible isomers (phenolate-keto, phenolate-enol, and phenol-enolate) of the oxyluciferin anion hydrated with quantum explicit water molecules in the first singlet excited state were investigated using first-principles Born-Oppenheimer molecular dynamics simulations for up to 1.8 ns (or 3.7 × 106 MD steps), revealing that the surrounding water molecules were distributed to form clear single-layered structures for phenolate-keto and multi-layered structures for phenolate-enol and phenol-enolate isomers. The isomers employed different stabilizing mechanisms compared to the ground state. Only the phenolate-keto isomer became attracted to the water molecules in its excited state and was stabilized by increasing the number of hydrogen bonds with nearby water molecules. The most stable isomer in the excited state was the phenolate-keto, and the phenolate-enol and phenol-enolate isomers were higher in energy by ∼0.38 eV and 0.57 eV, respectively, than the phenolate-keto. This was in contrast to the case of ground state in which the phenolate-enol was the most stable isomer.

Photoabsorption Spectra of Aqueous Oxyluciferin Anions Elucidated by Explicit Quantum Solvent.

Experimental photoabsorption spectra of three possible isomers (phenolate-keto, phenolate-enol, and phenol-enolate) of oxyluciferin anions in aqueous solution were reproduced by first-principles time-dependent density functional theory simulations in which the entire system including the oxyluciferin anion and 64 water molecules were modeled by full quantum mechanics (full QM), unlike the conventional hybrid method, where the surrounding water molecules are modeled by molecular mechanics (MM) or a continuum solvent model. The full QM photoabsorption spectra were calculated from 1000 structures that had been obtained using the first-principles Born-Oppenheimer molecular dynamics simulations, which included the van der Waals correction, to take into account the effect of dynamical fluctuations of the hydration structure. The full QM calculation with CAM-B3LYP functional, which is the most elaborate one and is apparently the most consistent with experiment, is compared to others obtained with different levels of the functional and the solvent model. The amount of charge leakage from the oxyluciferin anions to the aqueous solution is found to differ significantly between the ground and excited states and is strongly dependent on the simulation method. The conventional solvent models do not take this into account, but the QM/MM can do it appropriately when including more than 10 water molecules into the QM region.

Understanding Competition of Polyalcohol Dehydration Reactions in Hot Water.

Dehydration of biomass-derived polyalcohols has recently drawn attention in green chemistry as a prototype of selective reactions controllable in hot water or hot carbonated water, without any use of organic solvents or metal catalysts. Here, we report a free-energy analysis based on first-principles metadynamics and blue-moon ensemble simulations to understand the mechanism of competing intramolecular dehydration reactions of 1,2,5-pentanetriol in hot acidic water. The simulations consistently predict that the most dominant mechanism is the proton-assisted SN2 process, where the protonation of the hydroxyl group by water and the C-O bond breaking and formation occur in a single step. However the free-energy barriers are different between the reaction paths: those leading to five-membered ether products, tetrahydrofurfuryl alcohol (THFA), are few kcal/mol lower than those leading to six-membered ether products, 3-hydroxytetrahydropyran (3-HTHP). A slight difference is seen in the timing of the protonation of the hydroxyl group of THFA and 3-HTHP on their reaction pathways. The detailed mechanism found from the simulations shows how the reaction paths are selective in hot water and why the reaction rates are accelerated in acidic environments, thus giving a clear explanation of experimental findings for a broad class of competing dehydration processes of polyalcohols.

Finding Free-Energy Landmarks of Chemical Reactions.

We propose a novel approach to search for free-energy landmarks, i.e., minima and the saddle points, of chemical reactions in an automated manner using a combination of steepest descent and gentlest ascent methods. A numerical approach is suggested to improve the sampling efficiency of the second derivatives of the free-energy surface, which is required in the gentlest ascent method. This technique opens a way to identify free-energy landmarks of bond-breaking/creating processes in which the underlying potential energy surface is described using on-the-fly electronic structure calculations. As demonstrations of the approach, we present applications to the ring-opening of cis-1,2-dimethylbenzocyclobutene using the semiempirical PM7 method, focusing on the temperature dependence of the paths and barrier of the reaction, and we study an SN2 reaction in aqueous solution using a semiempirical QM/MM approach combining PM7 with the TIP3P water model.

Nuclear quantum effects in the direct ionization process of pure helium clusters: path-integral and ring-polymer molecular dynamics simulations on the diatomics-in-molecule potential energy surfaces.

The direct photoionization of pure helium clusters, Hen (n = 100, 200 and 300), and its subsequent short-time process have been studied by path integral molecular dynamics (PIMD) and ring-polymer molecular dynamics (RPMD) simulations that can effectively describe the nuclear quantum effects in large systems. The modified diatomics-in-molecule (DIM) model [Calvo et al., J. Chem. Phys., 2011, 135, 124308] has been used to describe the electronic structures of Hen+ clusters. The PIMD simulations were able to reproduce the experimental ionization spectra having a broad and asymmetric nature, which can be ascribed to the inhomogeneity of the energy levels of He atoms in the inner and outer regions of the cluster. From the RPMD simulations, it is found that the ionized helium cluster in the higher excited state is followed by fast electronic state relaxation via nonadiabatic charge transfer including a small contribution of nuclear motions, and subsequently by slow relaxation of the cluster structure.

Quantum Simulation Verifies the Stability of an 18-Coordinated Actinium-Helium Complex.

Structures of a trivalent actinium cation in helium clusters (Ac3+ ⋅Hen ) have been studied by quantum path integral molecular dynamics simulations with different cluster sizes, n=18-200. The nuclear quantum effect of helium atoms plays an important role in the vibrational amplitude of the Ac3+ -He complex at low temperatures (1-3 K) at which the complex is stable. We found that the coordination number of helium atoms comprising the first solvation shell can be as high as eighteen. In this case, the helium atoms are arranged in D4d symmetry. The Ac3+ -He18 complex becomes more rigid as the cluster increases in size, which implies that it becomes more stable. The simulation results are based on an accurate description of the Ac3+ -He interaction using relativistic ab initio calculations.

Nuclear quantum effects of light and heavy water studied by all-electron first principles path integral simulations.

The isotopologs of liquid water, H2O, D2O, and T2O, are studied systematically by first principles PIMD simulations, in which the whole entity of the electrons and nuclei are treated quantum mechanically. The simulation results are in reasonable agreement with available experimental data on isotope effects, in particular, on the peak shift in the radial distributions of H2O and D2O and the shift in the evaporation energies. It is found that, due to differences in nuclear quantum effects, the H atoms in the OH bonds more easily access the dissociative region up to the hydrogen bond center than the D (T) atoms in the OD (OT) bonds. The accuracy and limitation in the use of the current density-functional-theory-based first principles PIMD simulations are also discussed. It is argued that the inclusion of the dispersion correction or relevant improvements in the density functionals are required for the quantitative estimation of isotope effects.

Photoexcited Ag ejection from a low-temperature He cluster: a simulation study by nonadiabatic Ehrenfest ring-polymer molecular dynamics.

Ring-polymer molecular dynamics (RPMD) simulations have been performed to understand the photoexcitation dynamics of an Ag atom embedded in a low-temperature cluster consisting of 500 helium atoms, after the electronic excitation 5p 2P1/2 ← 5p 2S1/2 and 5p 2P3/2 ← 5p 2S1/2 of the Ag atom. Along the RPMD trajectory the time evolution of electronic wavefunction within the spin-orbit 2P manifold is calculated, whereby the time-dependent Schrödinger equation and the RPMD equation of motion are coupled, using the à la Ehrenfest mean field approach. It is found from the simulations that the Ag atom is ejected from the helium cluster with the average time of 100 ps after photoexcitation with the average ejection velocity being 60-70 m s-1, which is roughly in line with experiment. Meanwhile it is also found that the present simulations do not agree with experiment as to the final state of the ejected Ag atom.

The effect of dynamical fluctuations of hydration structures on the absorption spectra of oxyluciferin anions in an aqueous solution.

In this study, the effect of hydration on the absorption spectra of oxyluciferin anion isomers in an aqueous solution is investigated for elucidating the influence of characteristic hydration structures. Using a canonical ensemble of hydration structures obtained from first-principles molecular dynamics simulations, the instantaneous absorption spectra of keto-, enol-, and enolate-type aqueous oxyluciferin anions at room temperature are computed from a collection of QM/MM calculations using an explicit solvent. It is demonstrated that the calculations reproduce experimental results concerning spectral shifts and broadening, for which traditional methods based on quantum chemistry and the Franck-Condon approximation fail because of the molecular vibrations of oxyluciferin anions and dynamical fluctuations of their hydration structures. Although the first absorption band associated with the lowest energy excitation corresponds to a π-π* transition for all oxyluciferin anion isomers, the changes in this band upon hydration are different among the isomers. In particular, the bands of enol- and enolate-type of oxyluciferin anions are significantly blue-shifted by hydration, whereas those of the keto-type oxylucifeion anion are shifted relatively less. Thus, the order of the first-peak positions in the aqueous solution changed relative to that in vacuo. We ascribe this to the nature of the oxyluciferin anion being more hydrophobic in the keto form as compared with the enol and enolate isomers.

The reaction mechanism of polyalcohol dehydration in hot pressurized water.

The use of high-temperature liquid water (HTW) as a reaction medium is a very promising technology in the field of green chemistry. In order to fully exploit this technology, it is crucial to unravel the reaction mechanisms of the processes carried out in HTW. In this work, the reaction mechanism of 2,5-hexanediol dehydration in HTW has been studied by means of three different ab initio simulations: the string method, metadynamics and molecular dynamics in real time. It is found that the whole reaction involving protonation, bond exchange and deprotonation occurs in a single step without a stable intermediate. The hydrogen bonded network of the surrounding water has a vital role in assisting an efficient proton relay at the beginning and at the end of the reaction. It is confirmed that the reaction is energetically most favorable in the SN2 pathway with an estimated barrier of 36 kcal mol-1, which explains the high stereoselectivity and the reaction rate observed in experiment. The mechanistic insights provided by our study are relevant for a prominent class of reactions in the context of sustainable biomass processing, namely dehydration reactions of polyalcohol molecules.