Anharmonic Effects Research Articles

Machine learning electronic structure methods based on the one-electron reduced density matrix

The theorems of density functional theory (DFT) establish bijective maps between the local external potential of a many-body system and its electron density, wavefunction and, therefore, one-particle reduced density matrix. Building on this foundation, we show that machine learning models based on the one-electron reduced density matrix can be used to generate surrogate electronic structure methods. We generate surrogates of local and hybrid DFT, Hartree-Fock and full configuration interaction theories for systems ranging from small molecules such as water to more complex compounds like benzene and propanol. The surrogate models use the one-electron reduced density matrix as the central quantity to be learned. From the predicted density matrices, we show that either standard quantum chemistry or a second machine-learning model can be used to compute molecular observables, energies, and atomic forces. The surrogate models can generate essentially anything that a standard electronic structure method can, ranging from band gaps and Kohn-Sham orbitals to energy-conserving ab-initio molecular dynamics simulations and infrared spectra, which account for anharmonicity and thermal effects, without the need to employ computationally expensive algorithms such as self-consistent field theory. The algorithms are packaged in an efficient and easy to use Python code, QMLearn, accessible on popular platforms.

Quantum bath augmented stochastic nonequilibrium atomistic simulations for molecular heat conduction.

Classical molecular dynamics (MD) has been shown to be effective in simulating heat conduction in certain molecular junctions since it inherently takes into account some essential methodological components which are lacking in the quantum Landauer-type transport model, such as many-body full force-field interactions, anharmonicity effects and nonlinear responses for large temperature biases. However, the classical MD reaches its limit in the environments where the quantum effects are significant (e.g. with low-temperatures substrates, presence of extremely high frequency molecular modes). Here, we present an atomistic simulation methodology for molecular heat conduction that incorporates the quantum Bose-Einstein statistics into an "effective temperature" in the form of a modified Langevin equation. We show that the results from such a quasi-classical effective temperature MD method deviates drastically when the baths temperature approaches zero from classical MD simulations and the results converge to the classical ones when the bath approaches the high-temperature limit, which makes the method suitable for full temperature range. In addition, we show that our quasi-classical thermal transport method can be used to model the conducting substrate layout and molecular composition (e.g. anharmonicities, high-frequency modes). Anharmonic models are explicitly simulated via the Morse potential and compared to pure harmonic interactions to show the effects of anharmonicities under quantum colored bath setups. Finally, the chain length dependence of heat conduction is examined for one-dimensional polymer chains placed in between quantum augmented baths.

Vibronic dynamics from real-time time-dependent density-functional theory coupled to the Ehrenfest scheme: the example of p-coumaric acid

We investigate the vibronic dynamics of a modified version of the p-coumaric acid using real-time time-dependent density-functional theory coupled with the Ehrenfest scheme in the adiabatic local density approximation. Due to the issues of this functional to yield a reliable starting point for the evolution of the electron-nuclear system triggered by a pulse, we start off the simulations constraining the electronic occupation of the molecule in two excited states corresponding to a bright, delocalized transition, and a dark, charge-transfer-like excitation. By monitoring the kinetic energy spectral density, we analyze the nature of the nuclear motion over a time window of 300 fs. Anharmonic effects appear at low frequencies, below 500 cm^{-1}, and are particularly pronounced in the charge-transfer excitation. In this case, after about 200 fs, the molecular backbone becomes largely distorted and the initially constrained occupations evolve toward a different electronic configuration. On the other hand, the dynamics initialized from the delocalized bright excitation are electronically and structurally stable, and the resulting nuclear motion is markedly harmonic. Our results provide indications to decipher the vibronic dynamics of this chromophore and related systems in view of more elaborated simulations embedding the molecules in a realistic environment.

Epiq: An open-source software for the calculation of electron-phonon interaction related properties

epiq (Electron-Phonon wannier Interpolation over k and q-points) is an open-source software for the calculation of electron-phonon interaction related properties from first principles. Acting as a post-processing tool for a density-functional perturbation theory code (Quantum ESPRESSO) and wannier90, epiq exploits the localization of the deformation potential in the Wannier function basis and the stationary properties of a force-constant functional with respect to the first-order perturbation of the electronic charge density to calculate many electron-phonon related properties with high accuracy and free from convergence issues related to Brillouin zone sampling. epiq features include: the adiabatic and non-adiabatic phonon dispersion, superconducting properties (including the superconducting band gap in the Migdal-Eliashberg formulation), double-resonant Raman spectra and lifetime of excited carriers. The possibility to customize most of its input makes epiq a versatile and interoperable tool. Particularly relevant is the interaction with the Stochastic Self-Consistent Harmonic Approximation (SSCHA) allowing anharmonic effects to be included in the calculation of electron-properties. The scalability offered by the Wannier representation combined with a straightforward workflow and easy-to-read input and output files make epiq accessible to the wide condensed matter and material science communities. Program summaryProgram Title:epiqCPC Library link to program files:https://doi.org/10.17632/f2syws66d7.1Developer's repository link:https://gitlab.com/the-epiq-team/epiqLicensing provisions: GPLv3Programming language: FORTRAN95External routines: BLAS (http://www/netlib.org/blas), LAPACK (http://www.netlib.org/lapack), Quantum ESPRESSO (https://www.quantum-espresso.org/), wannier90 (https://wannier.org/)Nature of problem: Direct first principles calculation of quantities obtained via linear response methods in solid-state systems, such as the deformation potential, can be computationally demanding, hindering proper convergence.Solution method: An interpolation scheme exploiting the localization of the deformation potential in the Wannier function basis and the stationary properties of a force-constant functional with respect to the first-order perturbation of the electronic charge density is implemented in epiq. Within this approach it is possible to calculate many electron-phonon related properties with high accuracy and a low computational effort.

Anharmonic effect on the vibrational properties of pristine and Co-doped β-FeSi2 semiconductors

The strength of the phonon anharmonic effect of the pristine FeSi2 and Co-doped Fe0.94Co0.06Si2 is investigated by a Raman scattering study on the vibrational properties of those materials in the temperature range of 300–1523 K. All the vibrational modes exhibit significant redshifts with increasing temperature, and their spectral widths increase simultaneously. The structure transition from the semiconducting β phase to the metallic α phase is evidenced by the sudden disappearance of the vibrational modes. The extended Klemens model is applied to study the anharmonic effect on the phonon frequency shift and damping constant, and the four-phonon decaying process is expected to be the dominant one after doping the metal Co. Such an enhancement is also suggested contributing to the reduction of the thermal conductivity in Fe0.94Co0.06Si2. In addition, the vibrational properties of the mode at 250 cm−1 are more sensitive to the anharmonicity effect than that of the mode at 195 cm−1. This work provides valuable insights for understanding the high-order anharmonic effects in thermoelectric materials, especially in chemically doped materials.

Equations of State and Phase Boundaries of SiO2 Polymorphs Under Lower Mantle Conditions

AbstractSiO2 is an important modally abundant component of terrestrial planets, while there are few studies that quantitatively determine the properties of silica under simultaneously high‐temperature and high‐pressure conditions. In this study, thermal properties of stishovite, CaCl2‐type SiO2 and seifertite have been obtained by using extensive first‐principles simulations. The quasi‐harmonic approximation and intrinsic anharmonic effects were considered, and a generalized rescaling method was adopted to eliminate systematic errors in the simulation results. Based on the simulation data, we have established new equations of state for the SiO2 polymorphs and determined their phase boundaries. Anharmonicity has been demonstrated to show noticeable effects on their thermal properties and phase boundaries. With the new results, we found that SiO2 polymorphs show increasing buoyancy in the subducted basaltic slabs at depths greater than ∼800–900 km. In the normal lower mantle, they are readily stable over a broad range of depths approximately from 1,500 km to 2,600 km. This implies that SiO2 polymorphs may contribute to the lateral heterogeneity in the deep lower mantle as observed by small‐scale seismic scatterers.

Vibrational-mechanical properties of the highly-mismatched Cd1−xBexTe semiconductor alloy: experiment and ab initio calculations

The emerging CdTe–BeTe semiconductor alloy that exhibits a dramatic mismatch in bond covalency and bond stiffness clarifying its vibrational-mechanical properties is used as a benchmark to test the limits of the percolation model (PM) worked out to explain the complex Raman spectra of the related but less contrasted Zn1−xBex-chalcogenides. The test is done by way of experiment (xle 0.11), combining Raman scattering with X-ray diffraction at high pressure, and ab initio calculations (x ~ 0–0.5; x~1). The (macroscopic) bulk modulus {B}_{0} drops below the CdTe value on minor Be incorporation, at variance with a linear {B}_{0} versus x increase predicted ab initio, thus hinting at large anharmonic effects in the real crystal. Yet, no anomaly occurs at the (microscopic) bond scale as the regular bimodal PM-type Raman signal predicted ab initio for Be–Te in minority (x~0, 0.5) is barely detected experimentally. At large Be content (x~1), the same bimodal signal relaxes all the way down to inversion, an unprecedented case. However, specific pressure dependencies of the regular (x~0, 0.5) and inverted (x~1) Be–Te Raman doublets are in line with the predictions of the PM. Hence, the PM applies as such to Cd1−xBexTe without further refinement, albeit in a “relaxed” form. This enhances the model’s validity as a generic descriptor of phonons in alloys.

Interplay between Anharmonic and Lattice Effects in MoS2 Nanoflowers: Probing through Temperature-Dependent Raman Spectroscopy

Interplay between Anharmonic and Lattice Effects in MoS₂ Nanoflowers: Probing through Temperature-Dependent Raman Spectroscopy

First-principles calculation of KH2PO4 anharmonic force constants phonon dispersion curves

The laser-induced damage threshold of potassium dihydrogen phosphate (KDP) crystal is far lower than the theoretical value. The damage mechanism of KDP crystal cannot be clearly determined by various experiments and first-principles density functional theory (DFT) calculation of electronic properties. We attempt to explore the impact of phonons on the damage process by studying lattice dynamics. The phonon dispersion curves of intrinsic KDP crystal with harmonic approximation and anharmonic effect are studied by using the first-principles DFT calculations. With harmonic approximation, there are three large imaginary frequencies in the PE phase, which are the O–H stretching soft modes leading to the FE-PE phase transition. For the large displacement vibration of H atoms in PE phase, the room-temperature phonon dispersion curves with anharmonic effect are calculated. The imaginary frequency caused by three O–H stretching soft modes disappears. Our results have important reference significance for understanding the damage mechanism of KDP crystal.

Equation of state predictions for ScF3 and CaZrF6 with neural network-driven molecular dynamics.

In silico property prediction based on density functional theory (DFT) is increasingly performed for crystalline materials. Whether quantitative agreement with experiment can be achieved with current methods is often an unresolved question, and may require detailed examination of physical effects such as electron correlation, reciprocal space sampling, phonon anharmonicity, and nuclear quantum effects (NQE), among others. In this work, we attempt first-principles equation of state prediction for the crystalline materials ScF3 and CaZrF6, which are known to exhibit negative thermal expansion (NTE) over a broad temperature range. We develop neural network (NN) potentials for both ScF3 and CaZrF6 trained to extensive DFT data, and conduct direct molecular dynamics prediction of the equation(s) of state over a broad temperature/pressure range. The NN potentials serve as surrogates of the DFT Hamiltonian with enhanced computational efficiency allowing for simulations with larger supercells and inclusion of NQE utilizing path integral approaches. The conclusion of the study is mixed: while some equation of state behavior is predicted in semiquantitative agreement with experiment, the pressure-induced softening phenomenon observed for ScF3 is not captured in our simulations. We show that NQE have a moderate effect on NTE at low temperature but does not significantly contribute to equation of state predictions at increasing temperature. Overall, while the NN potentials are valuable for property prediction of these NTE (and related) materials, we infer that a higher level of electron correlation, beyond the generalized gradient approximation density functional employed here, is necessary for achieving quantitative agreement with experiment.

Finite-temperature many-body perturbation theory for anharmonic vibrations: Recursions, algebraic reduction, second-quantized reduction, diagrammatic rules, linked-diagram theorem, finite-temperature self-consistent field, and general-order algorithm.

A unified theory is presented for finite-temperature many-body perturbation expansions of the anharmonic vibrational contributions to thermodynamic functions, i.e., the free energy, internal energy, and entropy. The theory is diagrammatically size-consistent at any order, as ensured by the linked-diagram theorem proved in this study, and, thus, applicable to molecular gases and solids on an equal footing. It is also a basis-set-free formalism, just like its underlying Bose-Einstein theory, capable of summing anharmonic effects over an infinite number of states analytically. It is formulated by the Rayleigh-Schrödinger-style recursions, generating sum-over-states formulas for the perturbation series, which unambiguously converges at the finite-temperature vibrational full-configuration-interaction limits. Two strategies are introduced to reduce these sum-over-states formulas into compact sum-over-modes analytical formulas. One is a purely algebraic method that factorizes each many-mode thermal average into a product of one-mode thermal averages, which are then evaluated by the thermal Born-Huang rules. Canonical forms of these rules are proposed, dramatically expediting the reduction process. The other is finite-temperature normal-ordered second quantization, which is fully developed in this study, including a proof of thermal Wick's theorem and the derivation of a normal-ordered vibrational Hamiltonian at finite temperature. The latter naturally defines a finite-temperature extension of size-extensive vibrational self-consistent field theory. These reduced formulas can be represented graphically as Feynman diagrams with resolvent lines, which include anomalous and renormalization diagrams. Two order-by-order and one general-order algorithms of computing these perturbation corrections are implemented and applied up to the eighth order. The results show no signs of Kohn-Luttinger-type nonconvergence.

Exploring anharmonic lattice dynamics and dielectric relations in niobate perovskites from first-principles self-consistent phonon calculations

Group I niobates (KNbO3 and NaNbO3) are promising lead-free alternatives for high-performance energy storage applications. Despite their potential, their complex phase transitions arising from temperature-dependent phonon softening and anharmonic effects on dielectric properties remain poorly explored. In this study, we employ density-functional theory (DFT) and self-consistent phonon (SCP) calculations to investigate finite-temperature phonons in cubic niobate perovskites. To include explicit anharmonic vibrational effects, SCP frequencies are shifted by the bubble self-energy correction within the quasiparticle (QP) approximation, providing precise descriptions of phonon softening in these strongly anharmonic solids. We further calculate the static dielectric constant of KNbO3 and NaNbO3 as a function of temperature using the Lyddane-Sachs-Teller (LST) relation and QP-corrected phonon dispersions. Our theoretical results align with experimental data, offering reliable temperature-dependent phonon dispersions while considering anharmonic self-energies and thermal expansion effects, enhancing our understanding of the complex relations between lattice vibrations and phase transitions in these anharmonic oxides.

Stress-dependent activation entropy in thermally activated cross-slip of dislocations

Cross-slip of screw dislocations in crystalline solids is a stress-driven thermally activated process essential to many phenomena during plastic deformation, including dislocation pattern formation, strain hardening, and dynamic recovery. Molecular dynamics (MD) simulation has played an important role in determining the microscopic mechanisms of cross-slip. However, due to its limited timescale, MD can only predict cross-slip rates in high-stress or high-temperature conditions. The transition state theory can predict the cross-slip rate over a broad range of stress and temperature conditions, but its predictions have been found to be several orders of magnitude too low in comparison to MD results. This discrepancy can be expressed as an anomalously large activation entropy whose physical origin remains unclear. Here, we resolve this discrepancy by showing that the large activation entropy results from anharmonic effects, including thermal softening, thermal expansion, and soft vibrational modes of the dislocation. We expect these anharmonic effects to be significant in a wide range of stress-driven thermally activated processes in solids.

Evaluating the Role of Anharmonic Vibrations in Zeolite β Materials.

The characterization of zeolitic materials is often facilitated by spectroscopic analysis of vibrations, which informs about the bonding character of the substrate and any adsorbents. Computational simulations aid the interpretation of the spectra but often ignore anharmonic effects that can affect the spectral characteristics significantly. Here, the impact of anharmonicity is demonstrated with a combination of dynamical and static simulations applied to the structures formed during the synthesis of Sn-BEA via solid-state incorporation (SSI): the initial siliceous BEA (Si-β), aluminosilicate BEA (H-β), dealuminated BEA (deAl-β), and Sn-BEA (Sn-β). Heteroatom and defect-containing BEA are shown to have strong anharmonic vibrational contributions, with atomic and elemental resolution highlighting particularly the prevalence for H atoms (H-β, deAl-β) as well as localization to heteroatoms at defect sites. We simulate the vibrational spectra of BEA accounting for anharmonic contributions and observe an improved agreement with experimental data compared to harmonic methods, particularly at wavenumbers below 1500 cm-1. The results demonstrate the importance of incorporating anharmonic effects in simulations of vibrational spectra, with consequences toward future characterization and application of zeolitic materials.

Kinetic study of hydrogen abstraction reactions from n-propyl/n-butylcyclohexane by hydrogen atom

Hydrogen abstraction reactions of alkylated cycloalkane by radicals play a fundamental role in combustion and atmospheric chemistry. In this work, we select two representative molecules in alkylated cycloalkane fuels, n-propylcyclohexane (nPCH) and n-butylcyclohexane (nBCH), to investigate the kinetics of their hydrogen abstraction reactions with hydrogen atom. The rate constants over a broad temperature range of 298–2000 K were calculated by using canonical transition state theory coupled with the multistructural torsional anharmonicity effect (TST/MS-T). We stress the particular importance of considering the MS-T anharmonicity for the investigated species involved in the H-abstraction pathways. Due to the approximate cancelation of the anharmonicity factor between the transition-state species and the reactant, the anharmonicity factors for reactions are spread over a narrower range of 0.7–3.3. The anharmonicity will slightly accelerate the H-abstraction for the nBCH system over the whole temperature range. The current results show that the multistructural torsional anharmonicity will influence the accurate estimation of competing relationships. We found that the total H-abstraction rate constants of the nBCH system by the TST/MS-T method are larger by factors of 1.2–1.3 than those for the nPCH system. The present data show that nPCH + H channels are less important by factors of 1.41–5.48 than currently estimated by the commonly used nPCH pyrolysis model. The H-abstraction ratios from the cyclic ring and side chain groups reveal that the rate rule for secondary carbon in chain alkanes does not represent the reactivity of all cycloalkanes well, e.g. the ratio between the cyclic ring and side chain group is high up to 2.8.

Effect of four-phonon scattering on the intrinsic thermal conductivity of penta-graphene

Penta-graphene (PG), as a novel and stable pentagonal structure, has attracted considerable attention due to its large band gap, ultrahigh strength, negative Poisson's ratio, which indicates promising potential in nanoelectronics and nanomechanics. Thermal conductivity is a key physical quantity for the potential applications of PG based nano-devices. However, previous studies focused on the thermal conductivity of PG dominated by the well-known cubic anharmonic effect, and the quartic anharmonicity, although probably significant, was still neglected. In this work, we study the effect of four-phonon scattering on the thermal transport in PG through using first-principles calculations and solving the Boltzmann transport equation (BTE). We find that the intrinsic lattice thermal conductivity of PG is 182.1 W/mK at room temperature after including four-phonon scattering, which is reduced by 73.5 % as compared to the obtained results with only three-phonon scattering. Meanwhile, the relative contribution of the flexural acoustic (ZA) branch is reduced from 60.5 % to 32.5 % when four-phonon scattering is included. Thus, the large reduction in thermal conductivity can be ascribed to the large four-phonon scattering rates, which are completely comparable with those of three-phonon processes in the acoustic phonon frequency range even at 300 K. It is well believed that this finding is not a special case but should exist in other 2D materials with similar phonon features. Furthermore, the validity of the sum of three- and four-phonon scattering rates has been verified by the results based on the MD simulations. Our finding provides critical revisit and valuable insight to the exact thermal conductivity value of PG.

Revisiting four-phonon scattering in WS2 monolayer with machine learning potential

Recently, the importance of the higher-order anharmonic effect on the thermal transport has been demonstrated in a few two-dimensional (2D) materials. As a member of 2D materials, the WS2 monolayer possesses excellent properties, but its higher-order phonon anharmonic effect is still unclear. As an emerging tool for atomistic simulations, the machine learning Gaussian approximation potential (GAP) has good computational speed and accuracy. In this work, the effect of the four-phonon scattering on the thermal transport properties of the WS2 monolayer is systematically investigated by combining a well-trained GAP with the Boltzmann transport equation. We find that the in-plane thermal conductivity of the WS2 monolayer decreases by 34.68% at 300 K compared to the results without considering the four-phonon scattering, which mainly originates from the strong low-frequency redistribution scattering process. The temperature-induced phonon renormalization in WS2 monolayer is investigated using the temperature-dependent effective potential method. The results show that phonon modes slightly soften with increasing temperature, and the temperature effect weakens the four-phonon scattering while hardly affect the three-phonon scattering. Our work reveals that previous studies considering only the three-phonon scattering and the temperature effect are insufficient, and the four-phonon interaction must be introduced to accurately describe the thermal transport properties of the WS2 monolayer.

Theoretical Study on the Influence of the Anharmonic Effect on the Ionic Conductivity and Thermal Stability of 8 mol% Yttria-Stabilized Zirconia Solid Electrolyte Material.

YSZ is a promising material for resistive memory devices due to its high concentration of oxygen vacancies, which provide the high anion migration rates crucial for the manifestation of resistance switching in metal oxides. Therefore, investigating the ionic conductivity of YSZ is an important issue. The ionic conductivity and thermal stability of 8 mol% YSZ were studied using the theories and methods of solid-state physics and physical chemistry. The impact of anomalous atomic vibrations on the material was also explored, and the variation in the ion vibration frequency, electrical conductivity, and thermal stability coefficient of electrical conductivity with temperature was obtained. The results show that the ion conductivity of an 8 mol% YSZ solid electrolyte increases nonlinearly with temperature, with a smaller increase at lower temperatures and a larger increase at higher temperatures. Considering the anharmonic effect of ion vibrations, the electrolyte conductivity is higher than the result of the harmonic approximation, and the anharmonic effect becomes more significant at higher temperatures. Our research fills the gap in the current literature regarding the theoretical non-harmonic exploration of the ion conductivity and thermal stability factor of YSZ solid electrolytes. These results provide valuable theoretical guidance for the development and application of high-performance YSZ resistive memory devices in high-temperature environments.

Correlating Stokes Shift with Huang‐Rhys Parameter for Diatomic Molecules: Effects of Finite Temperature, Anharmonicity and Breakdown of Franck‐Condon Approximation

AbstractIn order to compute optical absorption and fluorescence spectra, the harmonic oscillator model for molecular vibrations under Franck‐Condon approximation for optical transition at absolute zero temperature is often considered for ease of numerical simulation, which never truly reproduce the experimental spectra. In this article, we show how systematic introduction of realistic situation, i. e., anharmonicity of vibrations, thermalization and non‐adiabatic transition leading to failure of Franck‐Condon approximation plays a colossal role in determining the spectral shape of a model diatomic molecule. In particular, we investigate how the Huang‐Rhys parameter, describing the relative positioning of the ground and excited electronic surfaces, is correlated with the Stokes shift, considering both right‐ and left‐shifted potential wells, which is crucial to estimate changes in molecular length‐scale from experimentally determined quantities. Further, the result for iodine is shown to have excellent agreement with experimental absorption spectrum. These findings are promised to bring insights into origin of spectral shapes in complex polyatomic molecules.

Approaching the "Zundel" Limit: Tuning the Vibrational Coupling in N2H+Ng, Ng = {He, Ne, Ar, Kr, Xe, and Rn}.

The diazenylium ion (N2H+) is a ubiquitous ion in dense molecular clouds. This ion is often used as a dense gas tracer in outer space. Most of the previous works on diazenylium ion have focused on the shared-proton stretch band, νH+. In this work, we have performed reduced-dimensional calculations to investigate the vibrational structure of N2H+Ng, Ng = {He, Ne, Ar, Kr, Xe, and Rn}. We demonstrate a few interesting things about this system. First, the vibrational coupling in N2H+ can be tuned to switch on interesting anharmonic effects such as Fermi resonance or combination bands by tagging it with different noble gases. Second, a comparison of the vibrational spectrum from N2H+He to N2H+Rn shows that the νH+ can be swept from an "Eigen-like" to a "Zundel-like" limiting case. Anharmonic calculations were performed using a multilevel approach, which utilized the MP2 and CCSD(T) levels of theories. Binding energies for the elimination of Ng in N2H+Ng are also reported.