Zero-point Energy Effects Research Articles

Extended benchmark set for lattice parameters of inorganic solids.

The development of novel methods in solid-state quantum chemistry necessitates reliable reference data sets for their assessment. The most fundamental solid-state property of interest is the crystal structure, quantified by the lattice parameters. In the last decade, several studies were conducted to assess theoretical approaches based on the agreement of calculated lattice parameters with respect to experiment as a measure. However, most of these studies used a limited number of reference systems with high symmetry. The present work offers a more comprehensive reference benchmark denoted as Sol337LC, which consists of 337 inorganic compounds with 553 symmetry-inequivalent lattice parameters, representing every element of the periodic table for atomic numbers between 1 and 86, except noble gases, the radioactive elements and lanthanoids. The reference values were taken from earlier benchmarks and from measurements at very low temperature or extrapolation to 0 K. The experimental low-temperature lattice parameters were then corrected for zero-point energy effects via the quasi-harmonic approximation for direct comparison with quantum-chemical optimized structures. A selection of standard density functional approximations was assessed for their deviations from the experimental reference data. The calculations were performed with the crystal orbital program CRYSTAL23, applying optimized atom-centered basis sets of triple-zeta plus polarization quality. The SCAN functional family and the global hybrid functional PW1PW, augmented with the D3 dispersion correction, were found to provide closest agreement with the Sol337LC reference data.

Pressure-induced novel phases with the high-Tc superconductivity in zirconium dihydride

The unprecedented structures in hydrides could be uncovered under high pressure, which probably possess unusual properties, such as high-Tc superconductivity. Here, the structural transition of ZrH2 at 0−500 GPa are comprehensively explored by using the evolutionary algorithm in the universal structure predictor combined with first-principles calculations. Three new phases are found: Pnma-ZrH2, P-3m1-ZrH2 and R-3m-ZrH2, with dynamic stability. Moreover, the sequence of phases of ZrH2 under pressure is I4/mmm → P4/nmm → Pnma → P-3m1 → R-3m with the zero-point energy effects. Structural feature, electronic properties, bonding characters and superconductivity of all the ZrH2 are analyzed in detail. More importantly, the superconducting critical temperature Tc values for P-3m1 at 440 GPa and R-3m at 500 GPa are 17.70–20.14 K and 26.68–30.03 K, respectively, which stems from the strong electron-phonon coupling.

Unraveling Water Solvation Effects with Quantum Mechanics/Molecular Mechanics Semiclassical Vibrational Spectroscopy: The Case of Thymidine.

We introduce a quantum mechanics/molecular mechanics semiclassical method for studying the solvation process of molecules in water at the nuclear quantum mechanical level with atomistic detail. We employ it in vibrational spectroscopy calculations because this is a tool that is very sensitive to the molecular environment. Specifically, we look at the vibrational spectroscopy of thymidine in liquid water. We find that the C═O frequency red shift and the C═C frequency blue shift, experienced by thymidyne upon solvation, are mainly due to reciprocal polarization effects, that the molecule and the water solvent exert on each other, and nuclear zero-point energy effects. In general, this work provides an accurate and practical tool to study quantum vibrational spectroscopy in solution and condensed phase, incorporating high-level and computationally affordable descriptions of both electronic and nuclear problems.

Zero-point energy effects on the stability of water clusters: Implications on the uptake of hydrogen isotope substituted water on ice and clathrate hydrate phases

To study the effect of hydrogen isotope substitution on the uptake of water during formation of clathrate hydrates, the harmonic intermolecular librational modes of selected water clusters (X2O)n with n = 2–6 and hydrogen isotopes X = H, D, and T are studied. The effects of the quantum mechanical zero-point energy (ZPE) in each cluster on the binding energies of the H2O, D2O, and T2O clusters are determined, with ZPE leading to the smallest binding energies in the H2O clusters and the largest binding energies in the T2O clusters. Corrections for anharmonicity of the librational modes are considered, and these bring the frequency ranges of the calculated intermolecular librational modes in the clusters to the experimental ranges of the librational modes in the infrared spectra of H2O and D2O solid ice and clathrate hydrate phases, and liquid H2O water. These calculations show the expected ranges of the binding energy of tritiated water onto a solid ice and clathrate hydrate surface and can help quantify the isotopic enrichment on a growing clathrate hydrate phase from the solution.

Nuclear-Electronic Orbital Quantum Dynamics of Plasmon-Driven H2 Photodissociation.

Leveraging localized surface plasmon resonances of metal nanoparticles to trigger chemical reactions is a promising approach for heterogeneous catalysis. First-principles modeling of such processes is challenging due to the large number of electrons and electronic excited states as well as the significance of nuclear quantum effects when hydrogen is involved. Herein, the nonadiabatic nuclear-electronic quantum dynamics of plasmon-induced H2 photodissociation near an Al13- cluster is simulated with real-time nuclear-electronic orbital time-dependent density functional theory (RT-NEO-TDDFT). This approach propagates the nonequilibrium quantum dynamics of both electrons and protons. The plasmonic oscillations are shown to inject hot electrons into the antibonding orbital of H2, thereby inducing H2 dissociation. The quantum mechanical treatment of the hydrogen nuclei leads to faster H2 photodissociation and slightly larger isotope effects. Analysis of the nonequilibrium electronic density suggests that these findings stem from enhanced excited-state electronic coupling between the plasmonic mode and the H2 antibonding orbital due to proton delocalization or zero-point energy effects. Given the low computational overhead for including nuclear quantum effects with the RT-NEO-TDDFT approach, this work paves the way for simulating nonadiabatic nuclear-electronic quantum dynamics in other plasmonic systems.

Atomistic Study of the Bandgap Engineering of Two-Dimensional Silicon Carbide by Hydrogenation.

This work studied hydrogen adsorption by a two-dimensional silicon carbide using a combined molecular dynamics and density functional theory approach. The geometrical properties of partially and fully hydrogenated structures were investigated, considering the effect of zero-point energy. The preferred hydrogen atom location is on top of silicon atoms. The hydrogen interaction energies were obtained for the first time as the attractive force. For fully hydrogenated 2D SiC, the chair-like conformer is the most stable configuration, and the next is the boat-like conformer, while the table-like structure is not stable. The coverage and arrangement of the adsorbed hydrogen atoms significantly influence the values of the direct/indirect bandgaps of the considered systems, increasing the bandgap to 4.07, 3.64, and 4.41 eV for chair-like, table-like, and boat-like, respectively. Their dynamical stability was investigated by phonon dispersion calculations. The obtained results can serve as a guide for the application of hydrogenated two-dimensional silicon carbide in optoelectronic applications in manufacturing innovation.

Nuclear-electronic orbital approach to quantization of protons in periodic electronic structure calculations.

The nuclear-electronic orbital (NEO) method is a well-established approach for treating nuclei quantum mechanically in molecular systems beyond the usual Born-Oppenheimer approximation. In this work, we present a strategy to implement the NEO method for periodic electronic structure calculations, particularly focused on multicomponent density functional theory (DFT). The NEO-DFT method is implemented in an all-electron electronic structure code, FHI-aims, using a combination of analytical and numerical integration techniques as well as a resolution of the identity scheme to enhance computational efficiency. After validating this implementation, proof-of-concept applications are presented to illustrate the effects of quantized protons on the physical properties of extended systems, such as two-dimensional materials and liquid-semiconductor interfaces. Specifically, periodic NEO-DFT calculations are performed for a trans-polyacetylene chain, a hydrogen boride sheet, and a titanium oxide-water interface. The zero-point energy effects of the protons as well as electron-proton correlation are shown to noticeably impact the density of states and band structures for these systems. These developments provide a foundation for the application of multicomponent DFT to a wide range of other extended condensed matter systems.

Simulation of Nuclear Quantum Effects in Condensed Matter Systems via Quantum Baths

This paper reviews methods that aim at simulating nuclear quantum effects (NQEs) using generalized thermal baths. Generalized (or quantum) baths simulate statistical quantum features, and in particular zero-point energy effects, through non-Markovian stochastic dynamics. They make use of generalized Langevin Equations (GLEs), in which the quantum Bose–Einstein energy distribution is enforced by tuning the random and friction forces, while the system degrees of freedom remain classical. Although these baths have been formally justified only for harmonic oscillators, they perform well for several systems, while keeping the cost of the simulations comparable to the classical ones. We review the formal properties and main characteristics of classical and quantum GLEs, in relation with the fluctuation–dissipation theorems. Then, we describe the quantum thermostat and quantum thermal bath, the two generalized baths currently most used, providing several examples of applications for condensed matter systems, including the calculation of vibrational spectra. The most important drawback of these methods, zero-point energy leakage, is discussed in detail with the help of model systems, and a recently proposed scheme to monitor and mitigate or eliminate it—the adaptive quantum thermal bath—is summarised. This approach considerably extends the domain of application of generalized baths, leading, for instance, to the successful simulation of liquid water, where a subtle interplay of NQEs is at play. The paper concludes by overviewing further development opportunities and open challenges of generalized baths.

Superconductivity on ScH3 and YH3 hydrides: Effects of applied pressure in combination with electron- and hole-doping on the electron–phonon coupling properties

The implementation of electron- and hole-doping, in conjunction with applied pressure, is analyzed as a mechanism to induce or enhance the superconducting state on fcc YH3 and ScH3. In particular, the evolution of their structural, electronic, and lattice dynamical properties, including the electron–phonon coupling and superconducting critical temperature (Tc) is presented and discussed, as a function of the electron- and hole-doping content as well as applied pressure. The study was performed within the density functional perturbation theory, taking into account the effects of zero-point energy through the quasi-harmonic approximation, while the doping was implemented by means of the construction of the Sc1−xMxH3 (M = Ca,Ti) and Y1−xMxH3 (M = Sr,Zr) solid solutions modeled with the virtual crystal approximation (VCA). We found that the ScH3 and YH3 hydrides showed a significant improvement of their electron–phonon coupling properties under hole-doping (M = Ca,Sr) and at pressure values close to dynamical instabilities. Instead, by electron-doping (M = Ti,Zr), the systems do not improve such properties, whatever value of applied pressure is considered. Then, as a result, Tc rapidly increases as a function of x on the hole-doping region, reaching its maximum value of 92.7(67.9) K and 84.5(60.2) K at x=0.3 for Sc1−xCaxH3 at 10.8GPa and Y1−xSrxH3 at 5.8GPa respectively, with μ∗=0(0.15), while for both, electron- and hole-doping, Tc decreases as a function of the applied pressure, mainly due to phonon hardening. By the thorough analysis of the electron–phonon properties as a function of doping and pressure, we can conclude that the tuning of the lattice dynamics is a promising path for improving superconductivity on both systems.

Molecular hydrogen isotope separation by a graphdiyne membrane: a quantum-mechanical study.

Graphdiyne (GDY) has emerged as a very promising two-dimensional (2D) membrane for gas separation technologies. One of the most challenging goals is the separation of deuterium (D2) and tritium (T2) from a mixture with the most abundant hydrogen isotope, H2, an achievement that would be of great value for a number of industrial and scientific applications. In this work we study the separation of hydrogen isotopes in their transport through a GDY membrane due to mass-dependent quantum effects that are enhanced by the confinement provided by its intrinsic sub-nanometric pores. A reliable improved Lennard-Jones force field, optimized on accurate ab initio calculations, has been built to describe the molecule-membrane interaction, where the molecule is treated as a pseudoatom. The quantum dynamics of the molecules impacting on the membrane along a complete set of incidence directions have been rigorously addressed by means of wave packet calculations in the 3D space, which have allowed us to obtain transmission probabilities and, in turn, permeances, as the thermal average of the molecular flux per unit pressure. The effect of the different incidence directions on the probabilities is analyzed in detail and it is concluded that restricting the simulations to a perpendicular incidence leads to reasonable results. Moreover, it is found that a simple 1D model-using a zero-point energy-corrected interaction potential-provides an excellent agreement with the 3D probailities for perpendicular incidence conditions. Finally, D2/H2 and T2/H2 selectivities are found to reach maximum values of about 6 and 21 at ≈50 and 45 K, respectively, a feature due to a balance between zero-point energy and tunneling effects in the transport dynamics. Permeances at these temperatures are below recommended values for practical applications, however, at slightly higher temperatures (77 K) they become acceptable while the selectivities preserve promising values, particularly for the separation of tritium.

Quantum versus classical unimolecular fragmentation rate constants and activation energies at finite temperature from direct dynamics simulations.

In the present work, we investigate how nuclear quantum effects modify the temperature dependent rate constants and, consequently, the activation energies in unimolecular reactions. In the reactions under study, nuclear quantum effects mainly stem from the presence of a large zero point energy. Thus, we investigate the behavior of methods compatible with direct dynamics simulations, the quantum thermal bath (QTB) and ring polymer molecular dynamics (RPMD). To this end, we first compare them with quantum reaction theory for a model Morse potential before extending this comparison to molecular models. Our results show that, in particular in the temperature range comparable with or lower than the zero point energy of the system, the RPMD method is able to correctly capture nuclear quantum effects on rate constants and activation energies. On the other hand, although the QTB provides a good description of equilibrium properties including zero-point energy effects, it largely overestimates the rate constants. The origin of the different behaviours is in the different distance distributions provided by the two methods and in particular how they differently describe the tails of such distributions. The comparison with transition state theory shows that RPMD can be used to study fragmentation of complex systems for which it may be difficult to determine the multiple reaction pathways and associated transition states.

Electron- and hole-doping on ScH2 and YH2: effects on superconductivity without applied pressure

We present the evolution of the structural, electronic, and lattice dynamical properties, as well as the electron–phonon (el–ph) coupling and superconducting critical temperature (T c) of ScH2 and YH2 metal hydrides solid solutions, as a function of the electron- and hole-doping content. The study was performed within the density functional perturbation theory, taking into account the effect of zero-point energy through the quasi-harmonic approximation, and the solid solutions Sc1−x M x H2 (M = Ca, Ti) and Y1−x M x H2 (M = Sr, Zr) were modeled by the virtual crystal approximation. We have found that, under hole-doping (M = Ca, Sr), the ScH2 and YH2 hydrides do not improve their el–ph coupling properties, sensed by λ(x). Instead, by electron-doping (M = Ti, Zr), the systems reach a critical content x ≈ 0.5 where the latent coupling is triggered, increasing λ as high as 70%, in comparison with its λ(x = 0) value. Our results show that T c quickly decreases as a function of x on the hole-doping region, from x = 0.2 to x = 0.9, collapsing at the end. Alternatively, for electron-doping, T c first decreases steadily until x = 0.5, reaching its minimum, but for x > 0.5 it increases rapidly, reaching its maximum value of the entire range at the Sc0.05Ti0.95H2 and Y0.2Zr0.8H2 solid solutions, demonstrating that electron-doping can improve the superconducting properties of pristine metal hydrides, in the absence of applied pressure.

High-Level ab Initio Predictions for the Ionization Energies, Bond Dissociation Energies, and Heats of Formation of Vanadium Methylidene, Vanadium Methyl Species, and Their Cations (VCH2/VCH2+, VCH3/VCH3+).

The ionization energies of VCH2 and VCH3, the various 0 K bond dissociation energies (D0s) in their neutrals and cations, and their respective heats of formation at 0 and 298 K are computed by the single-reference, wave function-based CCSDTQ/CBS procedure. The core of the composite method is the approximation to the complete basis set (CBS) limit at the coupled cluster (CC) level which includes up to full quadruple excitations. The zero-point vibrational energy, core-valence correlation, spin-orbit coupling, and scalar relativistic effects have their contributions incorporated in an additive manner. For the species in the current study, this protocol requires geometry optimizations and harmonic frequency calculations practically no higher than the CCSD(T)/aug-cc-pwCVTZ and CCSD(T)/aug-cc-pVTZ levels, respectively. The present calculations successfully predict D0(V+-CH3) = 2.126 eV and D0(V+-CH2) = 3.298 eV in remarkable agreement with the data recently measured by a spin-orbit state selected V+ + CH4 collision experiment (Phys. Chem. Chem. Phys. 2021, 23, 273-286). The good accord encourages the use of CCSDTQ/CBS protocol in thermochemical predictions of various feasible product channels identified in methane activation by transition metal species.

Thermal properties of energetic materials from quasi-harmonic first-principles calculations

The structure and properties at a finite temperature are critical to understand the temperature effects on energetic materials (EMs). Combining dispersion-corrected density functional theory with quasi-harmonic approximation, the thermodynamic properties for several representative EMs, including nitromethane, PETN, HMX, and TATB, are calculated. The inclusion of zero-point energy and temperature effect could significantly improve the accuracy of lattice parameters at ambient condition; the deviations of calculated cell volumes and experimental values at room temperature are within 0.62%. The calculated lattice parameters and thermal expansion coefficients with increasing temperature show strong anisotropy. In particular, the expansion rate (2.61%) of inter-layer direction of TATB is higher than intra-layer direction and other EMs. Furthermore, the calculated heat capacities could reproduce the experimental trends and enrich the thermodynamic data set at finite temperatures. The predicted isothermal and adiabatic bulk moduli could reflect the softening behavior of EMs. These results would fundamentally provide a deep understanding and serve as a reference for the experimental measurement of the thermodynamic parameters of EMs.

Temperature-Dependent Kinetic Isotope Effects in R67 Dihydrofolate Reductase from Path-Integral Simulations.

Calculation of temperature-dependent kinetic isotope effects (KIE) in enzymes presents a significant theoretical challenge. Additionally, it is not trivial to identify enzymes with available experimental accurate intrinsic KIEs in a range of temperatures. In the current work, we present a theoretical study of KIEs in the primitive R67 dihydrofolate reductase (DHFR) enzyme and compare with experimental work. The advantage of R67 DHFR is its significantly lower kinetic complexity compared to more evolved DHFR isoforms. We employ mass-perturbation-based path-integral simulations in conjunction with umbrella sampling and a hybrid quantum mechanics–molecular mechanics Hamiltonian. We obtain temperature-dependent KIEs in good agreement with experiments and ascribe the temperature-dependent KIEs primarily to zero-point energy effects. The active site in the primitive enzyme is found to be poorly preorganized, which allows excessive water access to the active site and results in loosely bound reacting ligands.

Tunneling Enhancement of the Gas-Phase CH + CO2 Reaction at Low Temperature.

The rates of numerous activated reactions between neutral species increase at low temperatures through quantum mechanical tunneling of light hydrogen atoms. Although tunneling processes involving molecules or heavy atoms are well known in the condensed phase, analogous gas-phase processes have never been demonstrated experimentally. Here, we studied the activated CH + CO2 → HCO + CO reaction in a supersonic flow reactor, measuring rate constants that increase rapidly below 100 K. Mechanistically, tunneling is shown to occur by CH insertion into the C-O bond, with rate calculations accurately reproducing the experimental values. To exclude the possibility of H-atom tunneling, CD was used in additional experiments and calculations. Surprisingly, the equivalent CD + CO2 reaction accelerates at low temperature as zero-point energy effects remove the barrier to product formation. In conclusion, heavy-particle tunneling effects might be responsible for the observed reactivity increase at lower temperatures for the CH + CO2 reaction, while the equivalent effect for the CD + CO2 reaction results instead from a submerged barrier with respect to reactants.

An improved path-integral method for golden-rule rates.

We present a simple method for the calculation of reaction rates in the Fermi golden-rule limit, which accurately captures the effects of tunneling and zero-point energy. The method is based on a modification of the recently proposed golden-rule quantum transition state theory (GR-QTST) of Thapa, Fang, and Richardson [J. Chem. Phys. 150, 104107 (2019)]. While GR-QTST is not size consistent, leading to the possibility of unbounded errors in the rate, our modified method has no such issue and so can be reliably applied to condensed phase systems. Both methods involve path-integral sampling in a constrained ensemble; the two methods differ, however, in the choice of constraint functional. We demonstrate numerically that our modified method is as accurate as GR-QTST for the one-dimensional model considered by Thapa and co-workers. We then study a multidimensional spin-boson model, for which our method accurately predicts the true quantum rate, while GR-QTST breaks down with an increasing number of boson modes in the discretization of the spectral density. Our method is able to accurately predict reaction rates in the Marcus inverted regime without the need for the analytic continuation required by Wolynes theory.

Structural localization in the classical and quantum Fermi-Pasta-Ulam model.

We study the statistics and short-time dynamics of the classical and the quantum Fermi-Pasta-Ulam chain in the thermal equilibrium. We analyze the distributions of single-particle configurations by integrating out the rest of the system. At low temperatures, we observe a systematic increase in the mobility of the chain when transitioning from classical to quantum mechanics due to zero-point energy effects. We analyze the consequences of quantum dispersion on the dynamics at short times of configurational correlation functions.

Three-dimensional docking of alcohols to ketones: an experimental benchmark based on acetophenone solvation energy balances.

The two hydrogen bond solvation sites exhibited by the carbonyl group in acetophenone are influenced by alkylation of the methyl group in both the acetophenone and in the prototype solvent methanol, largely due to London dispersion forces. Phenyl docking and alkyl docking preferences can be realized at will by appropriate substitution. In particular, cyclopropylation helps to stabilize the opposite phenyl docking site. In all cases, the energy gap is small enough to allow for a simultaneous detection even under low temperature conditions. This density functional prediction is checked experimentally by jet FTIR spectroscopy and largely confirmed. A spurious out-of-plane solvation preference predicted for cyclopropylphenylketone with tert-butyl alcohol by B3LYP-D3 calculations is not confirmed experimentally. It is unlikely that this discrepancy is due to zero-point energy effects. Instead, the second most stable alkyl-side solvation motif predicted with a more in-plane coordination is found in the jet expansion. Overall, the ability of carbonyl solvation balances to benchmark subtle electronic structure effects for non-covalent interactions without major nuclear motion corrections is supported.

Sampling the thermal Wigner density via a generalized Langevin dynamics.

The Wigner thermal density is a function of considerable interest in the area of approximate (linearized or semiclassical) quantum dynamics where it is employed to generate initial conditions for the propagation of appropriate sets of classical trajectories. In this paper, we propose an original approach to compute the Wigner density based on a generalized Langevin equation. The stochastic dynamics is nontrivial in that it contains a coordinate-dependent friction coefficient and a generalized force that couples momenta and coordinates. These quantities are, in general, not known analytically and have to be estimated via auxiliary calculations. The performance of the new sampling scheme is tested on standard model systems with highly nonclassical features such as relevant zero point energy effects, correlation between momenta and coordinates, and negative parts of the Wigner density. In its current brute force implementation, the algorithm, whose convergence can be systematically checked, is accurate and has only limited overhead compared to schemes with similar characteristics. We briefly discuss potential ways to further improve its numerical efficiency.