Anharmonic Effects Research Articles

The study of noncovalent interactions between sevoflurane and acetone in liquefied Xe by the method of IR spectroscopy

The IR spectra of sevoflurane + acetone mixtures in liquefied Xe were studied at T ~ 165-190 K. Complex formation stabilized by noncovalent interactions of weak H-bond type has been identified on the basis of changes found at selected bands of both components. Quantum-chemical calculations made on MP2/6-311++G(d,p) level, show that the spectrum in the region of stretching vibrations of CH and CH2 groups is formed due to anharmonic effects, specifically Fermi resonances. Keywords: cryospectroscopy, sevoflurane, acetone, complex, noncovalent interactions, quantum-mechanical calculations.

Theoretical insights into non-Arrhenius behaviors of thermal vacancies in anharmonic crystals.

Vacancies are prevalent point defects in crystals, but their thermal responses are elusive. Herein, we formulate a simple theoretical model to shed light on the vacancy evolution during heating. Vibrational excitations are thoroughly investigated via moment recurrence techniques in quantum statistical mechanics. On that basis, we carry out numerical analyses for Ag, Cu, and Ni with the Sutton-Chen many-body potential. Our results reveal that the well-known Arrhenius law is insufficient to describe the proliferation of vacancies. Specifically, anharmonic effects lead to a strong nonlinearity in the Gibbs energy of vacancy formation. Our physical picture is well supported by previous simulations and experiments.

Weak Anharmonicity Rationalizes the Temperature-Driven Acceleration of Nonradiative Dynamics in Cu2ZnSnS4 Photoabsorbers.

We report a time-domain ab initio investigation of the nonradiative electron-hole recombination in quaternary Cu2ZnSnS4 (CZTS) at different temperatures using a combination of time-dependent density functional theory and nonadiabatic molecular dynamics. Our results demonstrate that higher temperatures increase both inelastic and elastic electron-phonon interactions. Elevated temperatures moderately increase the lattice anharmonicity and cause stronger fluctuations of electronic energy levels, enhancing the electron-phonon coupling. The overall nuclear anharmonic effect is weak in CZTS, which can be ascribed to their stable bonding environment. Phonon-induced loss of electronic coherence accelerates with temperature, due to stronger elastic electron-phonon scattering. The enhanced inelastic electron-phonon scattering decreases charge carrier lifetimes at higher temperatures, deteriorating material performance in optoelectronic devices. The detailed atomistic investigation of the temperature-dependent charge carrier dynamics, with particular focus on anharmonic effects, guides the development of more efficient solar cells based on CZTS and related semiconductor photoabsorbers.

Ab initio thermodynamics of one-component plasma for astrophysics of white dwarfs and neutron stars

ABSTRACT Using path-integral Monte Carlo (PIMC) simulations, we have calculated energy of a crystal composed of atomic nuclei and uniform incompressible electron background in the temperature and density range, covering fully ionized layers of compact stellar objects, white dwarfs, and neutron stars, including the high-density regime, where ion quantization is important. We have approximated the results by convenient analytic formulae, which allowed us to integrate and differentiate the energy with respect to temperature and density to obtain various thermodynamic functions such as Helmholtz free energy, specific heat, pressure, entropy etc. In particular, we have demonstrated, that the total crystal specific heat can exceed the well-known harmonic lattice contribution by a factor of 1.5 due to anharmonic effects. By combining our results with the PIMC thermodynamics of a quantum Coulomb liquid, updated in the present work, we were able to determine density dependences of such melting parameters as the Coulomb coupling strength at melting, latent heat, and a specific heat jump. Our results are necessary for realistic modelling of thermal evolution of compact degenerate stars.

Lattice thermal conductivity including phonon frequency shifts and scattering rates induced by quartic anharmonicity in cubic oxide and fluoride perovskites

Lattice thermal conductivity ${\ensuremath{\kappa}}_{\mathrm{L}}$ is one of the key parameters involved in the design of microelectronics and energy-conversion devices. In determining the ${\ensuremath{\kappa}}_{\mathrm{L}}$, similar to the well-known cubic anharmonic effect, quartic anharmonicity is ubiquitous and also plays a crucial role in the final heat conduction of some compounds. In this paper, we use a high-throughput first-principles calculation method that combines self-consistent phonon (SCP) theory, compressive sensing techniques, and Boltzmann transport equation (BTE) to investigate the lattice thermal conductivity ${\ensuremath{\kappa}}_{\mathrm{L}}$ with the inclusion of cubic and quartic anharmonicity in 16 cubic oxide and fluoride perovskites. The BTE is solved on top of SCP theory for complete treatment of the quartic anharmonic effect that comprises four-phonon scattering and temperature-driven phonon frequency shift. In particular, only the ${\ensuremath{\kappa}}_{\mathrm{L}}$ within SCP theory is numerically valid for six of the 16 candidate perovskites, since the common calculation of BTE with harmonic phonons fails to estimate the ${\ensuremath{\kappa}}_{\mathrm{L}}$ due to the presence of imaginary frequencies in these materials. Our results exhibit that in addition to three-phonon scattering, the full inclusion of quartic anharmonicity is indispensable to capture a pertinent ${\ensuremath{\kappa}}_{\mathrm{L}}$ and rational temperature dependence of the ${\ensuremath{\kappa}}_{\mathrm{L}}$, while the consideration of only four-phonon scatterings (phonon frequency shifts) gives rise to a lower (higher) ${\ensuremath{\kappa}}_{\mathrm{L}}$ and stronger (weaker) temperature dependence. Meanwhile, we find a roughly linear relation between the ${\ensuremath{\kappa}}_{\mathrm{L}}$ and four-phonon scatterings in the 16 perovskites, which shows that the candidates with lower ${\ensuremath{\kappa}}_{\mathrm{L}}$ have stronger four-phonon scatterings. Moreover, very strong four-phonon scatterings are discovered in some cubic perovskites, especially in fluoride perovskites with imaginary harmonic phonons. The analyses of thermal conductivity spectrum ${\ensuremath{\kappa}}_{\mathrm{L}}(\ensuremath{\omega})$, scattering process, phase space, etc. reveal that the low-frequency four-phonon scattering rates in the structures with low ${\ensuremath{\kappa}}_{\mathrm{L}}$, e.g., $<1$ W/mK, are comparable to or even exceed those of three-phonon processes.

First-Principles Molecular Dynamics in Metal-Halide Perovskites: Contrasting Generalized Gradient Approximation and Hybrid Functionals.

First-principles molecular dynamics (FPMD) represents a valuable tool to probe dynamical properties of metal-halide perovskites (MHPs) which are key to their success in optoelectronic devices. Most FPMD studies rely on generalized gradient approximation (GGA) functionals for computational efficiency matters, while hybrid functionals, although computationally demanding, are usually needed to accurately describe structural and electronic properties of MHPs. This Letter reports FPMD simulations on CsPbI3 based on the hybrid PBE0 functional. Our results demonstrate that PBE0 leads to lattice parameters and phonon modes in excellent agreement with experimental data, while GGA results overestimate the lattice parameter and the electronic band gap and underestimate the phonon energies. Our FPMD results also shed light on anharmonic effects and double-well instabilities in the octahedral tilting, highlighting a lowered free energy barrier for PBE0 and farther separated potential wells. Our results suggest that hybrid functionals are required to accurately describe crystal structure, lattice dynamics, and anharmonicity in MHPs.

Intrinsic Planar Defects in Germanium and Their Contribution to the Excess Specific Heat at High Temperatures

Excessively high specific heat is usually observed in solids at comparatively high temperatures. It is believed to be associated with anharmonic effects. Using the simple case of elemental germanium with archetypical diamond structure, it is demonstrated that the anharmonicity effect can not fully describe the excess specific heat in germanium. Instead, two types of extended planar defects with a record low formation energy () are proposed, which can account for the discrepancy between theoretical and observed specific heat. These planar defects can be considered as finite distortion of crystal lattice produced by shear phonon modes accompanied by specific reconstruction of interatomic bonds on certain atomic planes. By comparison of experimental and theoretical specific heat, it is found that the germanium sample is subdivided into domains with intrinsic planar defects aligned along a single crystallographic direction.

Infrared Spectroscopy of Jet-cooled “GrandPAHs” in the 3–100 μm Region

Abstract Although large polycyclic aromatic hydrocarbons (PAHs) are likely to be responsible for IR emission of gaseous and dusty regions, their neutral experimental high-resolution gas-phase IR spectra—needed to construct accurate astronomical models—have so far remained out of reach because of their nonvolatility. Applying laser desorption to overcome this problem, we report here the first IR spectra of the jet-cooled large PAHs coronene (C24H12), peropyrene (C26H14), ovalene (C32H14), and hexa(peri)benzocoronene (C42H18) in the 3–100 μm region. Apart from providing experimental spectra that can be compared directly to astronomical data, such IR spectra are crucial for assessing the accuracy of theoretically predicted spectra used to interpret interstellar IR emission. Here we use the experimental spectra to evaluate the performance of conventional calculations using the harmonic approximation, as well as calculations with an anharmonic (GVPT2) treatment. The harmonic prediction agrees well with the experiment between 100 and 1000 cm−1 (100 and 10 μm) but shows significant shortcomings in the combination band (1600–2000 cm−1, 6.25–5 μm) and CH-stretch (2950–3150 cm−1, 3.4–3.17 μm) regions. Especially the CH-stretch region is known to be dominated by the effects of anharmonicity, and we find that large PAHs are no exception. However, for the CH out-of-plane region (667–1000 cm−1, 15–10 μm) the anharmonic treatment that significantly improves the predicted spectra for small PAHs leads to large and unrealistic frequency shifts, and intensity changes for large PAHs, thereby rendering the default results unreliable. A detailed analysis of the results of the anharmonic treatment suggests a possible route for improvement, although the underlying cause for the large deviations remains a challenge for theory.

A non-equilibrium dissociation and vibrational relaxation model for computational fluid dynamics simulations of flows with shock waves

Gasdynamic equations describing a vibrationally non-equilibrium flow of a chemically reacting binary mixture A2/A are derived within the previously proposed general approach of solving the Boltzmann equation. The obtained equations differ from the traditional ones in their expressions for the reaction and relaxation rates. Aiming to obtain analytical expressions for these rates, a cutoff harmonic oscillator model for the vibrational spectrum of A2 molecules and dissociation from the highest vibrational level are assumed. The equation for the dissociation rate describes two different dissociation regimes, determined by the dissociation rate constant at “low” temperatures and by the vibrational energy exchange rate constants at “high” temperatures, since it is limited by the vibrational energy delivery to the highest vibrational levels. A parameter for determining the appropriate regime is proposed. The derived expressions for the reaction and relaxation rates are used in computations of O2/O and N2/N mixture flows. A comparison of our results with the numerical and experimental data of other authors shows that the model used for the reaction and relaxation rates calculation should be refined, at least by considering anharmonicity effects.

Absence of Kondo effect in CeNiGe3 revealed by coherent phonon dynamics

Cerium-based intermetallic ${\mathrm{CeNiGe}}_{3}$ has been generally believed to be a heavy-fermion material with Kondo behavior at low temperatures. Using femtosecond-resolved coherent phonon spectroscopy, we present a temperature-dependent dynamic investigation of the bosonic quasiparticles in ${\mathrm{CeNiGe}}_{3}$. Our data do not agree with the heavy-fermion expectation and instead show that the phonon stiffening from room temperature down to 5 K can be well explained by the anharmonic effect in the absence of a Kondo mechanism. Furthermore, the coherent lattice vibration located at \ensuremath{\sim}7.9 THz exhibits a mode splitting at ${T}^{+}\ensuremath{\approx}105\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, which is close to the energy scale of the first excited crystal field splitting of the Ce $4f$ level. We argue that an orbital crossover may account for this intriguing observation.

Phase segregation in mixed-halide perovskites affects charge-carrier dynamics while preserving mobility

Mixed halide perovskites can provide optimal bandgaps for tandem solar cells which are key to improved cost-efficiencies, but can still suffer from detrimental illumination-induced phase segregation. Here we employ optical-pump terahertz-probe spectroscopy to investigate the impact of halide segregation on the charge-carrier dynamics and transport properties of mixed halide perovskite films. We reveal that, surprisingly, halide segregation results in negligible impact to the THz charge-carrier mobilities, and that charge carriers within the I-rich phase are not strongly localised. We further demonstrate enhanced lattice anharmonicity in the segregated I-rich domains, which is likely to support ionic migration. These phonon anharmonicity effects also serve as evidence of a remarkably fast, picosecond charge funnelling into the narrow-bandgap I-rich domains. Our analysis demonstrates how minimal structural transformations during phase segregation have a dramatic effect on the charge-carrier dynamics as a result of charge funnelling. We suggest that because such enhanced recombination is radiative, performance losses may be mitigated by deployment of careful light management strategies in solar cells.

Significant phonon anharmonicity drives phase transitions in CsPbI3

Due to its high chemical stability and high power conversion efficiency as a solar cell absorber, the inorganic halide perovskite, CsPbI3, is considered one of the most promising competitors to its hybrid organic-inorganic counterpart, CH3NH3PbI3. However, the phase transition from the photoactive black phase to the inactive yellow phase is a remarkable limitation that harms long-term phase stability. In particular, the phase transitions follow different pathways as the temperature increases and/or decreases, a phenomenon that is anomalous and remains poorly understood. In this study, we systematically calculated the temperature-dependent free energy of CsPbI3 in different crystal phases (α, β, γ, δ) by considering the phonon contribution to the Gibbs free energy. It is found that the free energy results from calculations that include harmonic phonons cannot reproduce experimental observations. Alternatively, we utilized the renormalized phonon quasiparticle approach to derive the free energies of different CsPbI3 phases at finite temperatures. Based on these calculated free energies, whose derivations included the anharmonic effect, we observed phase-transition processes consistent with experimental results. The analysis of the temperature effect on the phonon frequencies further demonstrated that anharmonic effects in the CsPbI3 had a significant influence on its phase transitions.

Theory and Calculation of Nontraditional Stable Isotope Fractionation

This paper conducts processing on isotope anharmonic effect with molecular dynamics method and Monte Carlo method based on path integration. It introduces the theoretical calculation method of pressure effect, and finally the nuclear volume effect and its theoretical calculation method, stressing that the nuclear volume effect is an important part of isotopic studies of heavy metals in the future. This paper makes an analysis on the equilibrium fractionation theory based on simple harmonic approximation.

Anharmonic effects on Vibrational circular dichroism and Raman optical activity spectra of medium‐size molecules: Alpha‐pinene and beta‐pinene

AbstractAn analysis of the vibrational circular dichoism (VCD) and Raman optical activity (ROA) of two medium‐sized molecules, alpha‐pinene and beta‐pinene, was performed using the second‐order perturbative PT2 method. We calculated the intensity (I in ) using the differential cross section. We reproduce mid‐IR spectra by generalized vibrational PT2 (GVPT2), where the GVPT2 approach has been applied to calculate both vibrational band wavenumbers and intensities to determine anharmonic effects on the spectral shape, adding combination bands to fundamental transition bands. Furthermore, the comparison with experimental spectra for both the band positions and the intensity pattern, our calculation, was evaluated.

Low-temperature photoluminescence study of GeV centres in HPHT diamond

The temperature (in the range of 20–180 K) and pressure (up to 6.9 GPa) effects on the photoluminescence of GeV centre ensembles in high-quality HPHT microcrystalline diamond are studied. The pressure coefficient obtained for a GeV centre dE/dp = 3.29(2) meV/GPa allows us to separate the total observed temperature shift of the zero-phonon line (ZPL) into two parts: the contribution of the lattice thermal expansion and the contribution of the electron–phonon coupling. The contribution of the electron–phonon coupling to the ZPL temperature shift is found to follow a cT2 – dT4 polynomial law rather than a T3 power law dependence reported for the total observed temperature shift of the ZPL. At the same time, the temperature dependence of the width of the ZPL is found to be in good agreement with a T3 power law. Thus, the found temperature dependences indicate the predominant role of the strong softening of elastic springs in the excited state in the temperature effect on the photoluminescence of GeV centres. The temperature effect on the quasi-local vibrational mode is investigated for the first time. The energy of the quasi-local vibrational mode is found to decrease with increasing temperature, which can be associated with the anharmonicity effect.

Raman spectra of hydrocarbons under extreme conditions of pressure and temperature: a first-principles study

Hydrocarbons are of great importance in carbon-bearing fluids in deep Earth and in ice giant planets at extreme pressure (P)–temperature (T) conditions. Raman spectroscopy is a powerful tool to study the chemical speciation of hydrocarbons. However, it is challenging interpreting Raman data at extreme conditions. Here, we performed ab initio molecular dynamics simulations coupled with the modern theory of polarization to calculate Raman spectra of methane, ethane and propane up to 48 GPa and 2000 K. Our method includes anharmonic temperature effects. We studied the pressure and temperature effects on the Raman bands and identified the characteristic Raman modes for the C–C and C–C–C bonds. To the best of our knowledge, this is the first time that the Raman spectra of hydrocarbons have been calculated at extreme P–T conditions. Our results may help with the interpretation of in situ Raman data of hydrocarbons at extreme P–T conditions, with important implications for studying hydrocarbon reactions in the deep carbon cycle inside Earth and the composition of ice giant planets.

Anharmonic Effects on the Thermodynamic Properties of Quartz from First Principles Calculations.

The simple chemistry and structure of quartz together with its abundance in nature and its piezoelectric properties make convenient its employment for several applications, from engineering to Earth sciences. For these purposes, the quartz equations of state, thermoelastic and thermodynamic properties have been studied since decades. Alpha quartz is stable up to 2.5 GPa at room temperature where it converts to coesite, and at ambient pressure up to 847 K where it transforms to the beta phase. In particular, the displacive phase transition at 847 K at ambient pressure is driven by intrinsic anharmonicity effects (soft-mode phase transition) and its precise mechanism is difficult to be investigated experimentally. Therefore, we studied these anharmonic effects by means of ab initio calculations in the framework of the statistical thermodynamics approach. We determined the principal thermodynamic quantities accounting for the intrinsic anharmonicity and compared them against experimental data. Our results up to 700 K show a very good agreement with experiments. The same procedures and algorithms illustrated here can also be applied to determine the thermodynamic properties of other crystalline phases possibly affected by intrinsic anharmonic effects, that could partially invalidate the standard quasi-harmonic approach.

Application of cell models to the melting and sublimation lines of the Lennard-Jones and related potential systems.

Harmonic cell models (HCMs) are shown to predict the melting line of the Lennard-Jones (LJ) but not the sublimation line. In addition, even for the melting line, the HCMs are found to be physically unrealistic for inverse power potential systems near the hard-sphere limit, and for the Weeks-Chandler-Andersen system at extremely low temperatures. Despite this, the HCM accurately predicts the LJ mean-square displacement (MSD) from molecular-dynamics (MD) simulations along both lines after simple scaling corrections, to include the effects of anharmonicity and correlated dynamics of the atoms, are applied. Single caged atom molecular dynamics and Monte Carlo simulations provide further quantitative characterization of these additional effects, which go beyond harmonicity. The melting indicator and a modification of the cell model in a similar form are shown to be approximately constant along the melting line, which indicates an isomorph. The less well studied LJ sublimation line is shown not to be an isomorph, yet it still can be represented analytically very accurately by the relationship k_{B}T=aρ^{4}+bρ^{2}, where a and b are constants (k_{B} is Boltzmann's constant, T is the temperature, and ρ is the number density). This relationship has been found previously for the melting line, but the two constants have opposite signs for the sublimation and melting lines. This simple formula is also predicted using a nonharmonic static lattice expression for the pressure. The probability distribution function of the melting factor indicates departures from harmonic or Gaussian behavior in the lower wing. Nevertheless, the mean melting factor is shown to follow a simple MSD Debye-Waller factor dependence along both the melting and sublimation lines. This work combining HCM and MD simulations provides a comparison of the melting and sublimation lines of the LJ system, which could provide the foundations for a more unified statistical mechanical description of these two solid boundary lines.

Anharmonicity of optical phonon modes in copper doped rutile TiO2 nanorod composed microflowers

Anharmonicity and impurities have a significant impact on the dynamic and optical properties of crystalline solids. In this report, we have performed temperature-dependent Raman spectroscopy in the range of 300–800 K for hydrothermally synthesized titanium dioxide (TiO2) nanorod composed microflowers doped with Cu. X-ray diffraction and high resolution transmission electron microscopy confirm the pure rutile phase of both pristine and Cu doped TiO2. The most intense Eg and A1g modes exhibit a frequency redshift, and the linewidth increases with temperature, which leads to Fano line shape type asymmetry. The anharmonicity induced phonon frequency shift as a function of temperature was well fitted using the Klemens model by combining three and four-phonon coupling processes. The Raman modes soften with the increasing concentration of Cu doping. The Cu dopant acts as an impurity, which manifests defect states to tune the bandgap and shorten the phonon lifetime and anharmonicity. Such an anharmonic effect can lead to applications in the sensing devices with suitable thermal and electrical conductivities.

Time-dependent density matrix renormalization group coupled with n-mode representation potentials for the excited state radiationless decay rate: Formalism and application to azulene

We propose a method for calculating the non-radiative decay rates for polyatomic molecules including anharmonic effects of the potential energy surface (PES) in the Franck-Condon region. The method combines the n-mode representation method to construct the ab initio PES and the nearly exact time-dependent density matrix renormalization group method (TD-DMRG) to simulate quantum dynamics. In addition, in the framework of TD-DMRG, we further develop an algorithm to calculate the final-state-resolved rate coefficient which is very useful to analyze the contribution from each vibrational mode to the transition process. We use this method to study the internal conversion (IC) process of azulene after taking into account the anharmonicity of the ground state PES. The results show that even for this semi-rigid molecule, the intramode anharmonicity enhances the IC rate significantly, and after considering the two-mode coupling effect, the rate increases even further. The reason is that the anharmonicity enables the C–H vibrations to receive electronic energy while C–H vibrations do not contribute on the harmonic PES as the Huang-Rhys factor is close to 0.