Zero-point Effects Research Articles

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 Probes of π-Delocalization in Prototypical Resonance-Stabilized Radicals: Hyperfine-Resolved Microwave Spectroscopy of Isotopic Propargyl and Cyanomethyl.

Delocalization of the unpaired electron in π-conjugated radicals has profound implications for their chemistry, but direct and quantitative characterization of this electronic structure in isolated molecules remains challenging. We apply hyperfine-resolved microwave rotational spectroscopy to rigorously probe π-delocalization in propargyl, CH2CCH, a prototypical resonance-stabilized radical and key reactive intermediate. Using the spectroscopic constants derived from the high-resolution cavity Fourier transform microwave measurements of an exhaustive set of 13C- and 2H-substituted isotopologues, together with high-level ab initio calculations of zero-point vibrational effects, we derive its precise semiexperimental equilibrium geometry and quantitatively characterize the spatial distribution of its unpaired electron. Our results highlight the importance of considering both spin-polarization and orbital-following contributions when interpreting the isotropic hyperfine coupling constants of π radicals. These physical insights are strengthened by a parallel analysis of the isoelectronic species cyanomethyl, CH2CN, using new 13C measurements also reported in this work. A detailed comparison of the structure and electronic properties of propargyl, cyanomethyl, and other closely related species allows us to correlate trends in their chemical bonding and electronic structure with critical changes in their reactivity and thermochemistry.

Nuclear quantum effects in gas-phase ethylene glycol.

Path integral molecular simulations are used to explore the nuclear quantum effects (NQEs) on the structure, dihedral landscape and infrared spectrum of ethylene glycol. The simulations are carried out on a new reaction surface Hamiltonian-based model potential energy surface, with special focus on the role of the OCCO and HOCC dihedrals. In contrast with classical simulations, we analyse how the intramolecular interactions between the OH groups change due to zero-point effects as well as temperature. These are found to be weak. The NQEs on the free energy profile along the OCCO dihedral are analysed, where notable effects are seen at low temperatures and found to be correlated with the radii of gyration of the atoms. Finally, the power spectrum of the molecule from path integral simulations is compared with the experimental infrared spectrum, yielding a good agreement of band positions.

Three-dimensional charged black holes in Gauss–Bonnet gravity

Using the zero-point length effect, we construct a new class of charged black hole solutions in the framework of three-dimensional Gauss–Bonnet (GB) gravity with Maxwell electrodynamics. The gravitational and electromagnetic potentials and the spacetime curvature are finite and regular everywhere; however, the computation of scalar curvature invariants suggests the presence of a singularity at the origin. We also explore the thermodynamics of the solutions obtained and reveal that the entropy of the black hole decreases due to the stringy effects. The thermodynamics and conserved quantities are computed, and the validity of the first law of thermodynamics on the black hole horizon is verified. Finally, the spinning black hole solution is reported.

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

A Quantum-Classical Model of Brain Dynamics.

The study of the human psyche has elucidated a bipartite structure of logic reflecting the quantum-classical nature of the world. Accordingly, we posited an approach toward studying the brain by means of the quantum-classical dynamics of a mixed Weyl symbol. The mixed Weyl symbol can be used to describe brain processes at the microscopic level and, when averaged over an appropriate ensemble, can provide a link to the results of measurements made at the meso and macro scale. Within this approach, quantum variables (such as, for example, nuclear and electron spins, dipole momenta of particles or molecules, tunneling degrees of freedom, and so on) can be represented by spinors, whereas the electromagnetic fields and phonon modes can be treated either classically or semi-classically in phase space by also considering quantum zero-point fluctuations. Quantum zero-point effects can be incorporated into numerical simulations by controlling the temperature of each field mode via coupling to a dedicated Nosé-Hoover chain thermostat. The temperature of each thermostat was chosen in order to reproduce quantum statistics in the canonical ensemble. In this first paper, we introduce a general quantum-classical Hamiltonian model that can be tailored to study physical processes at the interface between the quantum and the classical world in the brain. While the approach is discussed in detail, numerical calculations are not reported in the present paper, but they are planned for future work. Our theory of brain dynamics subsumes some compatible aspects of three well-known quantum approaches to brain dynamics, namely the electromagnetic field theory approach, the orchestrated objective reduction theory, and the dissipative quantum model of the brain. All three models are reviewed.

Adsorption of atomic and molecular monolayers on Pt-supported graphene

Adsorption energies of monolayers of noble gases (Ar, Kr, Xe) and small molecules (N2, O2, CO, CH4, C2H6, and C3H8) on graphene supported by Pt(111) surface were computed by DFT, corrected for temperature and zero-point effects, and, compared to the recent temperature-programmed desorption experiments (Smith et al., 2016). The results indicate that some of the considered DFT exchange–correlation functionals reasonably well describe molecule–graphene/Pt(111) noncovalent interactions. For selected models, fixed-node diffusion Monte Carlo computations were used for ultimate cross-validation of interaction energies between the molecule and free-standing graphene.

Zero-point lattice expansion and band gap renormalization: Grüneisen approach versus free energy minimization

The zero-point lattice expansion (ZPLE) is a small variation of the lattice parameters induced by the presence of phonons in a material compared to the static lattice picture. It contributes significantly to the zero-point renormalization (ZPR) of the band gap energy, but its consequences have not been investigated as thoroughly as those stemming from electron-phonon interactions. In the usual first-principles approach, one evaluates the ZPLE by minimizing the $T=0$ K Helmholtz free energy. In this work, we show that the formalism based on the Gr\"uneisen parameters, which commonly neglects zero-point effects, can be efficiently used to compute the ZPLE for both isotropic and anisotropic materials at a much lower computational cost. We systematically test this formalism on 22 cubic and wurtzite materials, and we obtain excellent agreement with free energy minimization results for both the ZPLE and the resulting band gap ZPR. We use our results to validate an empirical expression estimating the ZPLE-induced ZPR, and we unveil its sensitivity to the temperature range involved in estimating the ZPLE from experimental data. Our findings finally reveal that the ZPLE contribution to the band gap ZPR can reach from 20% to more than 80% of the electron-phonon interaction contribution for heavier or more ionic materials, including materials containing light atoms. Considering both contributions on an equal footing is thus essential should one attempt to compare theoretical ZPR results with experimental data.

Temperature-dependent band gaps in several semiconductors: from the role of electron–phonon renormalization

Temperature dependence of band gap is one of the most fundamental properties for semiconductors, and has strong influences on many applications. The renormalization of the band gap at finite temperatures is due to the lattice expansion and the phonon-induced atomic vibrations. In this work, we apply the recently-developed electron–phonon renormalization (EPR) method to study the temperature-dependent band gap in some classical covalent (diamond, Si, and SiC) and ionic semiconductors (MgO and NaCl). The contributions from both the lattice expansion and the phonon-induced atomic vibrations at finite temperatures are considered. The results show that the band gaps Eg all decrease as temperature T increases, consistent with the experiments and other theoretical studies (e.g., from 0 K to 1500 K, the reductions are ∼0.451 eV for diamond and ∼1.148 eV for MgO, respectively). The covalent compounds investigated show weaker temperature dependences of Egs than the ionic compounds, due to the much weaker lattice expansions and therefore low contributions from these. The zero-point motion effect has greater influence on the band gap in semiconductors with light atoms, such as diamond (reduction ∼0.437 eV), due to larger atomic displacements. By decomposing the EPR effect into respective phonon modes, it is found that the high-frequency optical phonon vibrations dominate the temperature-dependent band gap in both covalent and ionic compounds. Our work provides the fundamental understandings on the temperature-dependent band gaps caused by lattice dynamics.

Energy Gap Closure of Crystalline Molecular Hydrogen with Pressure.

We study the gap closure with pressure of crystalline molecular hydrogen. The gaps are obtained from grand-canonical quantum MonteCarlo methods properly extended to quantum and thermal crystals, simulated by coupled electron ion MonteCarlo methods. Nuclear zero point effects cause a large reduction in the gap (∼2 eV). Depending on the structure, the fundamental indirect gap closes between 380 and 530GPa for ideal crystals and 330-380GPa for quantum crystals. Beyond this pressure the system enters into a bad metal phase where the density of states at the Fermi level increases with pressure up to ∼450-500 GPa when the direct gap closes. Our work partially supports the interpretation of recent experiments in high pressure hydrogen.

Thermodynamic properties of graphene bilayers

Thermodynamic properties of graphene bilayers are studied by path-integral molecular dynamics (PIMD) simulations, considering quantization of vibrational modes and anharmonic effects. Bilayer graphene has been studied at temperatures between 12 and 1500 K for zero external stress, using the LCBOPII effective potential. We concentrate on the thermal expansion, in-plane and out-of-plane compressibility, and specific heat. Additional insight into the meaning of our results for bilayer graphene is obtained from a comparison with data obtained from PIMD simulations for monolayer graphene and graphite. They are also analyzed in view of experimental data for graphite. Zero-point and thermal effects on the in-plane and ``real'' area of bilayer graphene are studied. The thermal expansion coefficient ${\ensuremath{\alpha}}_{xy}$ of the in-plane area is negative at low temperatures and positive for $T\ensuremath{\gtrsim}800\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. The minimum ${\ensuremath{\alpha}}_{xy}$ is $\ensuremath{-}6.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}\phantom{\rule{4pt}{0ex}}{\mathrm{K}}^{\ensuremath{-}1}$ at $T\ensuremath{\approx}220\phantom{\rule{4pt}{0ex}}\mathrm{K}$. Both in-plane (${\ensuremath{\chi}}_{xy}$) and out-of-plane (${\ensuremath{\chi}}_{z}$) compressibilities of graphene bilayers are found to increase for rising temperature, and turn out to be lower than that corresponding to monolayer graphene and higher than those found for graphite. At 300 K, we find for the bilayer ${\ensuremath{\chi}}_{xy}=9.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}\phantom{\rule{4pt}{0ex}}{\AA{}}^{2}/\mathrm{eV}$ and ${\ensuremath{\chi}}_{z}=2.97\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}\phantom{\rule{4pt}{0ex}}{\mathrm{GPa}}^{\ensuremath{-}1}$. Results for the specific heat obtained from the simulations are compared with those given by a harmonic approximation for the vibrational modes. This approach is noticeably accurate at temperatures lower than 200 K.

Correcting HIRES/Keck radial velocities for small systematic errors

ABSTRACT The HIRES spectrograph, mounted on the 10-m Keck-I telescope, belongs to a small group of radial-velocity (RV) instruments that produce stellar RVs with long-term precision down to ∼1 m s−1. In 2017, the HIRES team published 64,480 RVs of 1699 stars, collected between 1996 and 2014. In this bank of RVs, we identify a sample of RV-quiet stars, whose RV scatter is <10 m s−1, and use them to reveal two small but significant nightly zero-point effects: a discontinuous jump, caused by major modifications of the instrument in August 2004, and a long-term drift. The size of the 2004 jump is 1.5 ± 0.1 m s−1, and the slow zero-point variations have a typical magnitude of ≲ 1 m s−1. In addition, we find a small but significant correlation between stellar RVs and the time relative to local midnight, indicative of an average intra-night drift of 0.051 ± 0.004 m s−1 h−1. We correct the 64 480 HIRES RVs for the systematic effects we find, and make the corrected RVs publicly available. Our findings demonstrate the importance of observing RV-quiet stars, even in the era of simultaneously-calibrated RV spectrographs. We hope that the corrected HIRES RVs will facilitate the search for new planet candidates around the observed stars.

Thermal control of graphene morphology: A signature of its intrinsic surface tension

The surface tension $\sigma$ of free-standing graphene is studied by path-integral simulations as a function of the temperature and the in-plane stress. Even if the applied stress vanishes, the membrane displays a finite surface tension $\sigma$ due to the coupling between the bending oscillations and the real area of the membrane. Zero-point effects for $\sigma$ are significant below 100 K. Thermal cooling drives the membrane from a planar to a wrinkled morphology. Upon heating the change is reversible and shows hysteresis, in agreement to recent experiments performed on supported graphene.

3D long-range magnetic ordering in (C2H5NH3)2CuCl4 compound revealed by internal magnetic field from muon spin rotation and first principal calculation

We report the results of muon spin rotation measurement that reveal a 3D long-range magnetic ordering in the inorganic CuCl4 layers separated by (C2H5NH3) organic ligands. The measured temperature dependent internal magnetic field down to 300 mK shows the 3D long-range magnetic ordering with magnetic transition at the Néel temperature of TN = 10.06 K and critical exponent of 0.31. The ground state internal dipole field is calculated by considering muon zero-point motion effect at the muon stop position determined by first principal DFT calculation, in combination with magnetization density calculated on the basis of a specific magnetic structure model. The calculated result is shown in good agreement with the measured value of internal field at the ground state temperature, thereby justifying the magnetic structure model adopted for this system and explaining the 3D nature of magnetic ordering. This model may therefore be applicable to the study of other magnetic materials.

Role of zero-point effects in stabilizing the ground state structure of bulk Fe2P

Structural stability of Fe2P is investigated in detail using first-principles calculations based on density functional theory. While the orthorhombic C23 phase is found to be energetically more stable, the experiments suggest it to be hexagonal C22 phase. In the present study, we show that in order to obtain the correct ground state structure of Fe2P from the first-principles based methods it is utmost necessary to consider the zero-point effects such as zero-point vibrations and spin fluctuations. This study demonstrates an exceptional case where a bulk material is stabilized by quantum effects, which are usually important in low-dimensional materials. Our results also indicate the possibility of magnetic field induced structural quantum phase transition in Fe2P, which should form the basis for further theoretical and experimental efforts.

From dimers to the solid-state: Distributed intermolecular force-fields for pyridine.

An anisotropic atom-atom force-field for pyridine, using distributed atomic multipoles, polarizabilities, and dispersion coefficients and an anisotropic atom-atom repulsion model derived from symmetry-adapted perturbation theory (density functional theory) dimer calculations, is used to model pyridine crystal structures. Here we show that this distributed intermolecular force-field (DIFF) models the experimental crystal structures as accurately as modelling all but the electrostatic term with an isotropic repulsion-dispersion potential that has been fitted to experimental crystal structures. In both cases, the differences are comparable to the changes in the crystal structure with temperature, pressure, or neglect of zero-point vibrational effects. A crystal structure prediction study has been carried out, and the observed polymorphs contrasted with hypothetical thermodynamically competitive crystal structures. The DIFF model was able to identify the structure of an unreported high pressure phase of pyridine, unlike the empirically fitted potential. The DIFF model approach therefore provides a model of the underlying pair potential energy surface that we have transferred to the crystalline phase with a considerable degree of success, though the treatment of the many-body terms needs improvement and the pair potential is slightly over-binding. Furthermore, this study of a system that exhibits isotopic polymorphism highlights that the use of an empirical potential has partially absorbed temperature and zero-point motion effects as well as the intermolecular forces not explicitly represented in the functional form. This study therefore highlights the complexity in modelling crystallization phenomena from a realistic pair potential energy surface.

Thermal properties of graphene from path-integral simulations.

Thermal properties of graphene monolayers are studied by path-integral molecular dynamics simulations, which take into account the quantization of vibrational modes in the crystalline membrane and allow one to consider anharmonic effects in these properties. This system was studied at temperatures in the range from 12 to 2000 K and zero external stress, by describing the interatomic interactions through the LCBOPII effective potential. We analyze the internal energy and specific heat and compare the results derived from the simulations with those yielded by a harmonic approximation for the vibrational modes. This approximation turns out to be rather precise up to temperatures of about 400 K. At higher temperatures, we observe an influence of the elastic energy due to the thermal expansion of the graphene sheet. Zero-point and thermal effects on the in-plane and "real" surface of graphene are discussed. The thermal expansion coefficient α of the real area is found to be positive at all temperatures, in contrast to the expansion coefficient αp of the in-plane area, which is negative at low temperatures and becomes positive for T ≳ 1000 K.

Static polarizabilities and C6 dispersion coefficients using the algebraic-diagrammatic construction scheme for the complex polarization propagator

An implementation of the damped linear response function, or complex polarization propagator, using the algebraic-diagrammatic construction (ADC) scheme has been developed and utilized for the calculation of electric-dipole polarizabilities and C6 dispersion coefficients. Four noble gases (He, Ne, Ar, and Kr), five n-alkanes (methane, ethane, propane, butane, and pentane), three carbonyls (formaldehyde, acetaldehyde, and acetone), and three unsaturated hydrocarbons (ethene, acetylene, and benzene) have been treated with the hierarchical set of models ADC(2), ADC(2)-x, and ADC(3/2), and comparison has been made to results obtained with damped linear response Hartree–Fock (HF) and coupled cluster singles and doubles (CCSD) theory as well as high-quality experimental estimates via the dipole oscillator strength distribution approach. This study marks the first ADC calculations of C6 dispersion coefficients and the first ADC(3/2) calculations of static polarizabilities. Results at CCSD and ADC(3/2) levels of theory are shown to be of similar quality, with electron correlation effects increasing the molecular property values for all calculations except CCSD considerations of ethene and acetylene (attributed to an overestimation of bond electron density at HF level of theory). The discrepancies between CCSD and ADC(3/2) are partially due to ADC overestimating anisotropies, and discrepancies with respect to experimental values are partially due to the lack of zero-point vibrational effects in the present study.

Accelerating ring-polymer molecular dynamics with parallel-replica dynamics.

Nuclear quantum effects are important for systems containing light elements, and the effects are more prominent in the low temperature regime where the dynamics also becomes sluggish. We show that parallel replica (ParRep) dynamics, an accelerated molecular dynamics approach for infrequent-event systems, can be effectively combined with ring-polymer molecular dynamics, a semiclassical trajectory approach that gives a good approximation to zero-point and tunneling effects in activated escape processes. The resulting RP-ParRep method is a powerful tool for reaching long time scales in complex infrequent-event systems where quantum dynamics are important. Two illustrative examples, symmetric Eckart barrier crossing and interstitial helium diffusion in Fe and Fe-Cr alloy, are presented to demonstrate the accuracy and long-time scale capability of this approach.

Zero-point term and quantum effects in the Johnson noise of resistors: a critical appraisal

There is a longstanding debate about the zero-point term in the Johnson noise voltage of a resistor. This term originates from a quantum-theoretical treatment of the fluctuation-dissipation theorem (FDT). Is the zero-point term really there, or is it only an experimental artifact, due to the uncertainty principle, for phase-sensitive amplifiers? Could it be removed by renormalization of theories? We discuss some historical measurement schemes that do not lead to the effect predicted by the FDT, and we analyse new features that emerge when the consequences of the zero-point term are measured via the mean energy and force in a capacitor shunting the resistor. If these measurements verify the existence of a zero-point term in the noise, then two types of perpetual motion machines can be constructed. Further investigation with the same approach shows that, in the quantum limit, the Johnson–Nyquist formula is also invalid under general conditions even though it is valid for a resistor-antenna system. Therefore we conclude that in a satisfactory quantum theory of the Johnson noise, the FDT must, as a minimum, include also the measurement system used to evaluate the observed quantities. Issues concerning the zero-point term may also have implications for phenomena in advanced nanotechnology.