Zero-point Motion Research Articles

Preserving the symmetry of cis-1,2-difluoroethylene in the gas-phase heterodimer with hydrogen chloride: A microwave rotational study revealing a novel structure.

The microwave spectra of three isotopologues of the gas-phase heterodimer formed between cis-1,2-difluoroethylene and hydrogen chloride are obtained in the 5-21GHz region using Fourier transform microwave spectroscopy. The molecular structure, determined from the analysis of the spectra and supported by quantum chemistry calculations, has the hydrogen atom of the hydrogen chloride molecule interacting with both fluorine atoms of the fluoroethylene and no interaction between the chlorine atom and the olefin. Although the equilibrium structure has two inequivalent H⋯F interactions, zero-point motion averages over the two equivalent choices for these interactions, rendering the pairs of like atoms (C, H, and F) of the fluoroethylene equivalent, retaining the C2v symmetry of the olefin. This results in only one unique singly substituted 13C isotopologue and in the observed effects on transition intensities due to nuclear spin statistics. The heterodimer structure allows for a strong, linear hydrogen bond between the HCl donor and the fluoroethylene acceptor that is more important here than in the analogous acetylene containing complex, where the interaction between the π electrons of acetylene and an electrophilic hydrogen atom on the olefin compensates for the loss of linearity required for binding to a geminal F/H pair.

Electronic structure, absorption spectra and oxidation dynamics in polyynes and dicyanopolyynes.

The advent of femtosecond to attosecond experimental tools has made now possible to study such ultrafast carrier dynamics, e.g., the spatial and temporal charge density evolution, after an initial oxidation or reduction in molecules, candidates for atomic wires like polyynes and dicyanopolyynes. Here, we study the electronic structure and hole transfer in symmetric molecules containing carbon, nitrogen and hydrogen, the first members in the series of polyynic carbynes and dicyanopolyynes, using methods based on density functional theory (DFT): constrained DFT (CDFT), time-dependent DFT (TDDFT) and real-time TDDFT (RT-TDDFT), with Löwdin population analysis, comparing many levels of theory and obtaining convergence of the results. For the same purposes, we develop a tight binding (TB) variant using all valence orbitals of all atoms. This TB variant is applied here in linear molecules, but it is also adequate for electronic structure, charge transfer and charge transport of non-linear molecules and clusters of molecules. We calculate the electronic structure, the time-dependent dipole moment and the probabilities of finding the hole at each site, their mean over time values, the mean transfer rates from the oxidation site to other sites and the frequency content (using charge as well as dipole moment oscillations). We take into account zero-point motion. The initial conditions for RT-TDDFT are obtained by CDFT. For TB, we explore different initial conditions: we place the hole at a particular orbital or distribute it among a number of orbitals; it is also possible to include phase differences between orbitals. Finally, we compare with available experimental data.

Interpretation of molecular electron transport in ab initio many-electron framework incorporating zero-point nuclear motion effects.

A computational methodology, founded on chemical concepts, is presented for interpreting the role of nuclear motion in the electron transport through single-molecule junctions (SMJ) using many-electron ab initio quantum chemical calculations. Within this approach the many-electron states of the system, computed at the SOS-ADC(2) level, are followed along the individual normal modes of the encapsulated molecules. The inspection of the changes in the partial charge distribution of the many-electron states allows the quantification of the electron transport and the estimation of transmission probabilities. This analysis improves the understanding of the relationship between internal motions and electron transport. Two SMJ model systems are studied for validation purposes, constructed from a conductor (BDA, benzene-1,4-diamine) and an insulator molecule (DABCO, 1,4-diazabicyclo[2.2.2]octane). The trends of the resulting transmission probabilities are in agreement with the experimental observations, demonstrating the capability of the approach to distinguish between conductor and insulator type systems, thereby offering a straightforward and cost-effective tool for such classifications via quantum chemical calculations.

Direct observation of a magnetic-field-induced Wigner crystal.

Wigner predicted that when the Coulomb interactions between electrons become much stronger than their kinetic energy, electrons crystallize into a closely packed lattice1. A variety of two-dimensional systems have shown evidence for Wigner crystals2-11 (WCs). However, a spontaneously formed classical or quantum WC has never been directly visualized. Neither the identification of the WC symmetry nor direct investigation of its melting has been accomplished. Here we use high-resolution scanning tunnelling microscopy measurements to directly image a magnetic-field-induced electron WC in Bernal-stacked bilayer graphene and examine its structural properties as a function of electron density, magnetic field and temperature. At high fields and the lowest temperature, we observe a triangular lattice electron WC in the lowest Landau level. The WC possesses the expected lattice constant and is robust between filling factor ν ≈ 0.13 and ν ≈ 0.38 except near fillings where it competes with fractional quantum Hall states. Increasing the density or temperature results in the melting of the WC into a liquid phase that is isotropic but has a modulated structure characterized by the Bragg wavevector of the WC. At low magnetic fields, the WC unexpectedly transitions into an anisotropic stripe phase, which has been commonly anticipated to form in higher Landau levels. Analysis of individual lattice sites shows signatures that may be related to the quantum zero-point motion of electrons in the WC lattice.

A Many-Body Perspective of Nuclear Quantum Effects in Aqueous Clusters.

Nuclear quantum effects play an important role in the structure and thermodynamics of aqueous systems. By performing a many-body expansion with nuclear-electronic orbital (NEO) theory, we show that proton quantization can give rise to significant energetic contributions for many-body interactions spanning several molecules in single-point energy calculations of water clusters. Although zero-point motion produces a large increase in energy at the one-body level, nuclear quantum effects serve to stabilize higher-order molecular interactions. These results are significant because they demonstrate that nuclear quantum effects play a nontrivial role in many-body interactions of aqueous systems. Our approach also provides a pathway for incorporating nuclear quantum effects into water potential energy surfaces. The NEO approach is advantageous for many-body expansion analyses because it includes nuclear quantum effects directly in the energies.

Derivation of Miller’s rule for the nonlinear optical susceptibility of a quantum anharmonic oscillator

Miller’s rule is an empirical relation between the nonlinear and linear optical coefficients that applies to a large class of materials but has only been rigorously derived for the classical Lorentz model with a weak anharmonic perturbation. In this work, we extend the proof and present a detailed derivation of Miller’s rule for an equivalent quantum-mechanical anharmonic oscillator. For this purpose, the classical concept of velocity-dependent damping inherent to the Lorentz model is replaced by an adiabatic switch-on of the external electric field, which allows a unified treatment of the classical and quantum-mechanical systems using identical potentials and fields. Although the dynamics of the resulting charge oscillations, and hence the induced polarizations, deviate due to the finite zero-point motion in the quantum-mechanical framework, we find that Miller’s rule is nevertheless identical in both cases up to terms of first order in the anharmonicity. With a view to practical applications, especially in the context of ab initio calculations for the optical response where adiabatically switched-on fields are widely assumed, we demonstrate that a correct treatment of finite broadening parameters is essential to avoid spurious errors that may falsely suggest a violation of Miller’s rule, and we illustrate this point by means of a numerical example.

Effect of zero-point motion on properties of quantum particles adsorbed on a substrate

We qualitatively investigate the effect of zero-point motion (ZPM) on the structure and properties of a film composed of quantum particles adsorbed on a graphite substrate. The amplitude of ZPM is controlled by a change of the particle mass while keeping the interactions fixed. In that sense it is assumed that the interactions can be controlled by future doping methods. The worm-algorithm path integral Monte Carlo (WAPIMC) method is applied to simulate this system in the grand-canonical ensemble, where particles can be exchanged with the external particle reservoir. Another method, namely the multiconfigurational time-dependent Hartree method for bosons is additionally applied to verify some of the WAPIMC results and to provide further information on the entropy and the condensate fraction. Several important findings are reported. It is found that ZPM plays an important role in defining order and disorder in the crystalline structure of the adsorbed film. The total energy of the film drops with a reduction in the amplitude of ZPM, that is, it becomes more negative which is an indication to stronger adsorption. For a few particle numbers, a significant condensate fraction is detected that however drops sharply at critical values of the ZPM amplitude. Most importantly, a connection is established between chaos, in coordinate as well as momentum space, and the Heisenberg uncertainty principle. The importance of the present study lies in the fact that adsorbed two-dimensional films serve as an excellent experimental testbed for demonstrating low-dimensional quantum phenomena in the ground state. The present examination contributes also to a further understanding of the properties of heavy quantum particles adsorbed on substrates.

Spinel LiGa5O8 prospects as ultra-wideband-gap semiconductor: Band structure, optical properties, and doping

LiGa5O8 in the spinel type structure is investigated as a potential ultra-wideband-gap semiconductor. The band structure is determined using the quasiparticle self-consistent GW method, and the optical properties are calculated at the Bethe Salpeter Equation level including electron-hole interaction effects. The optical gap including exciton effects and an estimate of the zero-point motion electron phonon coupling renormalizations is estimated to be about 5.2±0.1 eV with an exciton binding energy of about 0.4 eV. Si doping as potential n-type dopant is investigated and found to be a promising shallow donor.

On: X-ray diffraction from the electron gas in monatomic metallic hydrogen

Solid hydrogen is expected to become a monatomic metal under sufficiently high compression. With hydrogen having only a single valence electron and no ion core, the nature of x-ray diffraction patterns from the electron gas of monatomic metallic hydrogen is uncertain, and it is unclear whether they may yield enough information for a crystal structure determination. With emphasis on the Cs-IV-type ( I41/amd ) structure predicted for hydrogen at ∼500 GPa, the electron density distributions, zero-point and thermal atomic motion, and x-ray diffraction intensities are determined from first-principles calculations for several candidate phases of metallic hydrogen. It is shown that the electron distribution is much more structured than might be expected from the commonly employed free-electron-gas picture, and in fact more modulated than what is obtained from the superposition of free-atom charge densities. We demonstrate that an identification of the crystal structure of monatomic metallic hydrogen from x-ray diffraction is fundamentally possible and discuss the possibility of single-crystal diffraction from metallic hydrogen. An atomic scattering factor for the hydrogen atom in monatomic metallic hydrogen is constructed to aid the quantitative analysis of diffraction intensities from future x-ray diffraction experiments.

Electron-vibrational renormalization in fullerenes through ab initio and machine learning methods.

The effect of nuclear vibrations on the electronic eigenvalues and the HOMO-LUMO gap is known for several kinds of carbon-based materials, like diamond, diamondoids, carbon nanoclusters, carbon nanotubes and others, like hydrogen-terminated oligoynes and polyyne. However, it has not been widely analysed in another remarkable kind which presents both theoretical and technological interest: fullerenes. In this article we present the study of the HOMO, LUMO and gap renormalizations due to zero-point motion of a relatively large number (163) of fullerenes and fullerene derivatives. We have calculated this renormalization using density-functional theory with the frozen-phonon method, finding that it is non-negligible (above 0.1 eV) for systems with relevant technological applications in photovoltaics and that the strength of the renormalization increases with the size of the gap. In addition, we have applied machine learning methods for classification and regression of the renormalizations, finding that they can be approximately predicted using the output of a computationally cheap ground state calculation. Our conclusions are supported by recent research in other systems.

Hydrogen bonding in duplex DNA probed by DNP enhanced solid-state NMR N-H bond length measurements.

Numerous biological processes and mechanisms depend on details of base pairing and hydrogen bonding in DNA. Hydrogen bonds are challenging to quantify by X-ray crystallography and cryo-EM due to difficulty of visualizing hydrogen atom locations but can be probed with site specificity by NMR spectroscopy in solution and the solid state with the latter particularly suited to large, slowly tumbling DNA complexes. Recently, we showed that low-temperature dynamic nuclear polarization (DNP) enhanced solid-state NMR is a valuable tool for distinguishing Hoogsteen base pairs (bps) from canonical Watson-Crick bps in various DNA systems under native-like conditions. Here, using a model 12-mer DNA duplex containing two central adenine-thymine (A-T) bps in either Watson-Crick or Hoogsteen confirmation, we demonstrate DNP solid-state NMR measurements of thymine N3-H3 bond lengths, which are sensitive to details of N-H···N hydrogen bonding and permit hydrogen bonds for the two bp conformers to be systematically compared within the same DNA sequence context. For this DNA duplex, effectively identical TN3-H3 bond lengths of 1.055 ± 0.011Å and 1.060 ± 0.011Å were found for Watson-Crick A-T and Hoogsteen A (syn)-T base pairs, respectively, relative to a reference amide bond length of 1.015 ± 0.010Å determined for N-acetyl-valine under comparable experimental conditions. Considering that prior quantum chemical calculations which account for zero-point motions predict a somewhat longer effective peptide N-H bond length of 1.041Å, in agreement with solution and solid-state NMR studies of peptides and proteins at ambient temperature, to facilitate direct comparisons with these earlier studies TN3-H3 bond lengths for the DNA samples can be readily scaled appropriately to yield 1.083Å and 1.087Å for Watson-Crick A-T and Hoogsteen A (syn)-T bps, respectively, relative to the 1.041Å reference peptide N-H bond length. Remarkably, in the context of the model DNA duplex, these results indicate that there are no significant differences in N-H···N A-T hydrogen bonds between Watson-Crick and Hoogsteen bp conformers. More generally, high precision measurements of N-H bond lengths by low-temperature DNP solid-state NMR based methods are expected to facilitate detailed comparative analysis of hydrogen bonding for a range of DNA complexes and base pairing environments.

Describing the scattering of keV protons through graphene.

Implementing two-dimensional materials in technological solutions requires fast, economic, and non-destructive tools to ensure efficient characterization. In this context, scattering of keV protons through free-standing graphene was proposed as an analytical tool. Here, we critically evaluate the predicted effects using classical simulations including a description of the lattice's thermal motion and the membrane corrugation via statistical averaging. Our study shows that the zero-point motion of the lattice atoms alone leads to considerable broadening of the signal that is not properly described by thermal averaging of the interaction potential. In combination with the non-negligible probability for introducing defects, it limits the prospect of proton scattering at 5keV as an analytic tool.

Frozen-phonon method for state anticrossing situations and its application to zero-point motion effects in diamondoids

Frozen-phonon method for state anticrossing situations and its application to zero-point motion effects in diamondoids

Momentum-independent magnetic excitation continuum in the honeycomb iridate H3LiIr2O6

Understanding the interplay between the inherent disorder and the correlated fluctuating-spin ground state is a key element in the search for quantum spin liquids. H3LiIr2O6 is considered to be a spin liquid that is proximate to the Kitaev-limit quantum spin liquid. Its ground state shows no magnetic order or spin freezing as expected for the spin liquid state. However, hydrogen zero-point motion and stacking faults are known to be present. The resulting bond disorder has been invoked to explain the existence of unexpected low-energy spin excitations, although data interpretation remains challenging. Here, we use resonant X-ray spectroscopies to map the collective excitations in H3LiIr2O6 and characterize its magnetic state. In the low-temperature correlated state, we reveal a broad bandwidth of magnetic excitations. The central energy and the high-energy tail of the continuum are consistent with expectations for dominant ferromagnetic Kitaev interactions between dynamically fluctuating spins. Furthermore, the absence of a momentum dependence to these excitations are consistent with disorder-induced broken translational invariance. Our low-energy data and the energy and width of the crystal field excitations support an interpretation of H3LiIr2O6 as a disordered topological spin liquid in close proximity to bond-disordered versions of the Kitaev quantum spin liquid.

H2 Chemical Bond in a High-Pressure Crystalline Environment.

We show that the hydrogen in metal superhydride compounds can adopt two distinct states-atomic and molecular. At low pressures, the maximum number of atomic hydrogens is typically equal to the valency of the cation; additional hydrogens pair to form molecules with electronic states far below the Fermi energy causing low-symmetry structures with large unit cells. At high pressures, molecules become unstable, and all hydrogens become atomic. This study uses density functional theory, adopting BaH4 as a reference compound, which is compared with other stoichiometries and other cations. Increased temperature and zero-point motion also favor high-symmetry atomic states, and picosecond-timescale breaking and remaking of the bond permutations via intermediate H3- units.

Many-body quantum muon effects and quadrupolar coupling in solids

Strong quantum zero-point motion (ZPM) of light nuclei and other particles is a crucial aspect of many state-of-the-art quantum materials. However, it has only recently begun to be explored from an ab initio perspective, through several competing approximations. Here we develop a unified description of muon and light nucleus ZPM and establish the regimes of anharmonicity and positional quantum entanglement where different approximation schemes apply. Via density functional theory and path-integral molecular dynamics simulations we demonstrate that in solid nitrogen, α–N2, muon ZPM is both strongly anharmonic and many-body in character, with the muon forming an extended electric-dipole polaron around a central, quantum-entangled [N2–μ–N2]+ complex. By combining this quantitative description of quantum muon ZPM with precision muon quadrupolar level-crossing resonance experiments, we independently determine the static 14N nuclear quadrupolar coupling constant of pristine α–N2 to be –5.36(2) MHz, a significant improvement in accuracy over the previously-accepted value of –5.39(5) MHz, and a validation of our unified description of light-particle ZPM.

Nonlinear nanomechanical resonators approaching the quantum ground state

It is an open question whether mechanical resonators can be made nonlinear with vibrations approaching the quantum ground state. This requires the engineering of a mechanical nonlinearity far beyond what has been realized so far. Here we discover a mechanism to boost the Duffing nonlinearity by coupling the vibrations of a nanotube resonator to single-electron tunnelling and by operating the system in the ultrastrong-coupling regime. We find that thermal vibrations become highly nonlinear when lowering the temperature. The average vibration amplitude at the lowest temperature is 13 times the zero-point motion, with approximately 42% of the thermal energy stored in the anharmonic part of the potential. Our work may enable the realization of mechanical Schrödinger cat states, mechanical qubits and quantum simulators emulating the electron–phonon coupling.

The electron-phonon renormalization in the electronic structure calculation: Fundamentals, current status, and challenges.

Electron-phonon (e-ph) interaction plays a crucial role in determining many physical properties of the materials, such as the superconducting transition temperature, the relaxation time and mean free path of hot carriers, the temperature dependence of the electronic structure, and the formation of the vibrational polaritons. In the past two decades, the calculations of e-ph properties from first-principles has become possible. In particular, the renormalization of electronic structures due to e-ph interaction can be evaluated, providing greater insight into the quantum zero-point motion effect and the temperature dependence behavior. In this perspective, we briefly overview the basic theory, outline the computational challenges, and describe the recent progress in this field, as well as future directions and opportunities of the e-ph coupling calculations.

Two-component density functional theory study of quantized muons in solids

The quantum effect of light nuclei in materials is usually considered as lattice vibration and zero-point motion from an ab initio perspective. Here we start from full-quantized particles and take the muon as an example, considering the two-body quantized system of the muon and the electrons within two-component density functional theory, which can calculate the related two-body wave functions directly and automatically taking into account the quantum effect of the muon. We first simulate the two-body correlation energy and the pair-correlation function by quantum Monte Carlo, then construct a two-body self-consistent loop to solve the two-body density and then the hyperfine couplings are estimated. This is an attempt to reveal the quantum effect of light nuclei in materials from a different perspective. We finally find this fundamental method agrees better with experiments and shows good potential for further such calculations.

Zero-point motion of liquid and solid hydrogen

We present an inelastic neutron scattering study of liquid and solid hydrogen carried out using the wide Angular Range Chopper Spectrometer at Oak Ridge National Laboratory. From the observed dynamic structure factor, we obtained empirical estimates of the molecular mean-squared displacement and average translational kinetic energy. We find that the former quantity increases with temperature, indicating that a combination of thermal and quantum effects is important near the liquid-solid phase transition, contrary to previous measurements. We also find that the kinetic energy drops dramatically on melting of the crystals, a consequence of the large increase in molar volume together with the Heisenberg indeterminacy principle. Our results are compared with quantum Monte Carlo simulations based on different model potentials. In general, there is good agreement between our findings and theoretical predictions based on the Silvera-Goldman and Buck potentials.