Anharmonicity effects on thermally induced spin-crossover in tris(2-(aminomethyl)pyridine)iron(II)

Strong constraints can be placed on the origin of heterogeneity of seismic wave velocities and density if the observed ratios of various parameters are compared with mineral physics predictions. They include the shear to compressional wave velocity heterogeneity ratio,Rs/p≡ δ logVs/δ logVp, the bulk sound to shear wave velocity heterogeneity ratio,Rϕ/s≡ δ logVϕ/δ logVs, and the density to velocity heterogeneity ratio,Rρ/s,p≡ δ log ρ/δ logVs,p. Using mineral physics considerations, we calculate these ratios in the lower mantle corresponding to the thermal and chemical origin of velocity and density heterogeneity. Both anharmonic and anelastic effects are considered for thermal origin. Anharmonic effects are estimated from the theoretical calculations as well as from laboratory measurements which show a marked increase inRs/pwith pressure from ∼1.5 to ∼2.1 in the lower mantle. Such a trend is marginally consistent with seismological observations showing an increase inRs/pwith depth (from ∼1.7 to ∼3.2 in the lower mantle). However, anharmonic effect alone cannot explain inferred lowRρ/s(<0.2–0.4), and the values ofRs/ppredicted from anharmonic effects are systematically smaller than seismological observations. Anelastic effects must be included to account for these geophysical observations. A new formulation of anelastic effect is developed in which the role of nonlinear temperature dependence of anelasticity is included. When anharmonic and anelastic effects are combined, thermal effects on velocity and density can account for most of the geophysical observations in Earth's lower mantle. Effects other than temperature variations (such as chemical heterogeneity) are required only in the very deep portions of the mantle (deeper than ∼2000–2300 km). A puzzling observation is very large values ofRs/p(>2.7) and corresponding negative values ofRϕ/s(andRρ/s) in the deep lower mantle which cannot be accounted for by thermal or simple chemical heterogeneity such as the heterogeneity in the Fe/(Fe + Mg) and/or Mg/(Mg + Si) ratios. Possible causes of anomalies in this region are discussed, including the role of anisotropy and a combined effect of heterogeneity in Fe and Ca content.

Separate theoretical and experimental investigations of the effect of lattice anharmonicity on the ${A}_{1g}$ phonon dynamics in photoexcited bismuth are presented. First-principles density functional calculations show that the anharmonic contribution to the phonon period is negligible for an excitation of 1.25% or less of the valence electrons, corresponding to electronic frequency softening from $2.9\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}2.3\phantom{\rule{0.3em}{0ex}}\mathrm{THz}$. Experiments using optical double-pump-probe excitation of coherent phonon motion clearly separate the role of lattice anharmonicity from electron-hole plasma and other dynamics, confirming that the effect of anharmonicity on the phonon period is much smaller than the observed softening.

The structural and vibrational properties of the ethyl radical have been investigated by a series of finite temperature simulations that treat the nuclei as quantum particles. The potential energy surface of the electronic ground state has been described by a nonorthogonal tight-binding Hamiltonian that provides results in reasonable agreement with ab initio methods. The quantum nature of the nuclei has been described by path integral Monte Carlo simulations at temperatures between 25 and 1000 K. Special interest deserves the determination of anharmonic and tunneling effects in the zero-point vibrational structure. In particular, we have studied the influence of anharmonic effects both on the mean value and the quantum fluctuations of equilibrium bond lengths and bond angles. The local structure of the radical center is found to be planar as a result of the zero-point motion of the atomic nuclei, even though the minimum energy configuration exhibits a pyramidal structure for this center. Anharmonic effects in the fundamental vibrational modes of the molecule are studied by a nonperturbative approach based on the centroid density. This function is a path integral concept that provides information on the static response of the system to applied external forces. Our study reveals a softening of the stretching modes associated with the C–H bonds and a hardening of the out-of-plane rocking motion of the methylene group. Both effects are in good agreement with experimental and ab initio data. The softening of the C–C stretching mode predicted by our simulations suggests a revision of the currently accepted experimental assignment for two fundamental vibrations of the ethyl radical. The tunneling of an H atom between the methyl and methylene groups has been investigated. These simulations should contribute to the open question whether or not this process is responsible for the changes in the electron spin resonance spectrum at low temperatures.

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.

Anharmonic effects due to the shape of the molecular potential energy surface far from the equilibrium geometry are major responsible for the deviations of the actual frequencies of vibration from the harmonic estimates. However, anharmonic effects are not the solely responsible for this. Quantum nuclear effects also play a prominent role in theoretical vibrational spectroscopy as they contribute to drive away the molecular vibrational frequencies from their harmonic counterpart. The consequence of this is that anharmonicity and quantum effects may be difficult to separate spectroscopically and get often confused. In this work we show that anharmonicity can be detected by means of classical simulations, while quantum nuclear effects need to be identified by means of an approach originating from either the time independent or the time dependent Schroedinger equation of quantum mechanics. We show that classical methods are sensitive to the temperature or energy conditions under which they are undertaken. This leads to wrong frequency estimates, when dealing with few-Kelvin experiments, if one performs simulations simply matching the experimental temperature. Conversely, quantum approaches are not affected by this issue and they provide more and better information.

Infrared spectroscopy is a versatile technique for probing the structure and dynamics of condensed-phase systems. Simulating infrared absorption spectra with molecular dynamics (MD) offers a powerful means to establish a molecular-level interpretation of experimental results, as well as a basis for the parametrization of more accurate simulation force-fields. Two distinct methods for the calculation of infrared absorption line shapes of high-frequency (Planck's omega/k(B)T>>1) vibrational probes from MD simulations are examined: The classical dipole approximation (CDA) and the fluctuating frequency approximation (FFA). Although these two formalisms result in expressions for the infrared absorption line shape that appear very different, both approximations are shown to yield identical results for the infrared line shape of a harmonic system in the condensed-phase. The equivalence of the FFA and CDA is also demonstrated in the case where the transition dipole of the oscillator fluctuates in response to the environment (i.e., where the Condon approximation has been relaxed). Finally we examine the effects of solute anharmonicity and demonstrate that the CDA and FFA are not equivalent in general, and the magnitude of the deviations increases with anharmonicity. We conclude that the calculation of infrared absorption line shapes via the CDA is a promising alternative to the FFA approach in cases where it may be difficult or undesirable to employ the latter, particularly when the effects of anharmonicity are small.

The heat capacity of classical crystals is determined by the Dulong-Petit value CV ≃ D (where D is the spatial dimension) for softly interacting particles and has the gas-like value CV ≃ D/2 in the hard-sphere limit, while deviations are governed by the effects of anharmonicity. Soft- and hard-sphere interactions, which are associated with the enthalpy and entropy of crystals, are specifically anharmonic owing to violation of a linear relation between particle displacements and corresponding restoring forces. Here, we show that the interplay between these two types of anharmonicities unexpectedly induces two possible types of heat capacity anomalies. We studied thermodynamics, pair correlations, and collective excitations in 2D and 3D crystals of particles with a limited range of soft repulsions to prove the effect of interplay between the enthalpy and entropy types of anharmonicities. The observed anomalies are triggered by the density of the crystal, changing the interaction regime in the zero-temperature limit, and can provide about 10% excess of the heat capacity above the Dulong-Petit value. Our results facilitate understanding effects of complex anharmonicity in molecular and complex crystals and demonstrate the possibility of new effects due to the interplay between different types of anharmonicities.

Harmonic oscillators with time-dependent frequencies describe physics of the Paul trap of ions, radiation fields in media of time-varying dielectric constants, and so on. Their ground states are generically squeezed states. Here the effects of small anharmonicity on such nonclassical states are discussed. A perturbative calculation is performed, in which the unperturbed states are prepared in terms of the Hermitian invariant of the time-dependent harmonic oscillator. A quartic potential perturbation is investigated in detail. It is found that the correction term as well as the unperturbed term in the ground-state persistence probability can be expressed by the moments of a number operator alone. The oscillatory behavior is found in that correction term, which shows a competition of excitation and deexcitation due to the time dependence of the frequency and the nonlinear interaction. This may be observed experimentally as the temporal fluctuation of the quasienergy levels. Some formulas are also presented for the variances and correlations of the quadratures in the perturbed states.

A self-consistent thermodynamic model is constructed, which describes the effect of anharmonicity of crystal lattice on heat capacity, coefficient of thermal expansion, density, and bulk modulus of palladium. Fairly good agreement with experimental data is obtained within the model being developed, and the contribution to heat capacity associated with the effect of anharmonicity is identified. Significant increase is demonstrated of the effect made by lattice anharmonicity on the thermo-physical properties in the region of temperatures significantly exceeding the Debye temperature.

The dynamics of librational motion in N2-type crystals (α-N2, α-CO, N2O, CO2) is treated by taking into account both anharmonic and correlation effects. The method used is similar to Tyablikov's method in the theory of magnetism. The main thermodynamic characteristics of the librational subsystem are calculated: the order parameter, rms librational angle, librational mode frequencies and corresponding Gruneisen parameters, librational heat capacity, and internal and free energies. The librational isotope effects for α-14N2 and α-15N2 are considered. An explanation of the anomalous isotope effects in the heat capacity is proposed. A theory of the phase transition into the orientationally disordered state is developed.

For pt.II see ibid., vol.16, no.14, p.2705 (1983). The method and results of the two previous papers are extended to triplet and quartet electronic states in octahedral symmetry. Explicit expressions are given for all reduction factors to fourth order, including nonlinear, anharmonic and symmetric interactions. Sum rules for reduction factors, and the conditions under which they are broken, are discussed in detail for each system, in the general coupling case, in the case where one coupling symmetry only is assumed, and in the case of equal coupling. A general proof is given for all Jahn-Teller systems, including tetrahedral and icosahedral systems, that sum rules associated with time-reversal considerations at second order are also valid at fourth order to the case of coupling to isoenergetic modes. For triplet systems weak tau 2 coupling together with nonlinear and anharmonic effects may be expected to have disproportionately large effects by inducing violations of sum rules and by introducing resonant terms. For quartet systems many novel sum rules are discussed. By testing such rules or by measuring the temperature dependence of a reduction factor it is possible in principle to determine whether either coupling symmetry is dominant and whether any of nonlinear, anharmonic and symmetric coupling effects are significant in practice.

Superconductivity in compressed arises from the interplay between high‐frequency phonons and a pronounced van Hove singularity near the Fermi level. Using first‐principles calculations, we investigate the superconducting properties of and at 160 and 200 GPa, explicitly incorporating anharmonic lattice dynamics and first‐order vertex corrections to electron‐phonon (e‐ph) interactions, thereby going beyond the Migdal approximation underlying conventional Migdal‐Eliashberg theory. We find that both anharmonicity and nonadiabatic vertex corrections suppress the effective e‐ph coupling and reduce the superconducting critical temperature (). Calculations performed within the energy‐dependent full‐bandwidth Eliashberg formalism, including both anharmonic and vertex effects, yield values in close agreement with experimental measurements for at both pressures and for at 200 GPa.

The inclusion of anharmonic vibrational effects is critical for the interpretation of modern vibrational spectra and accurate thermodynamic quantities. Generalized techniques to computationally simulate anharmonicity include the vibrational self-consistent field (VSCF) method and correlated analogues thereof. The "n-mode representation" is a commonly used approximation for representing the vibrational potential in VSCF computations and includes pairwise (and higher) mode-coupling terms that dominate both the anharmonic effects and the computational cost. Localized vibrational coordinates are known to accelerate simulations involving pairwise couplings, but many systems require three- and four-mode couplings both for the convergence of the n-mode representation and to avoid spurious pathologies involving low-frequency modes. In this analysis, the convergence of this potential representation─and its distance dependence─is explored in the context of local modes. Convergence of the n-mode representation's impact on vibrational spectra is shown to be attainable in full vibrational dimensionality for water clusters and biomolecules. Furthermore, the requisite distance cutoffs are allowed to be successively more aggressive for three- and four-mode coupling terms, which further enhances the ensuing computational efficiency. For the Z-alanine molecule and (H2O)17 cluster, 290- and 590-fold computational accelerations, respectively, were observed, and these accelerations should increase for larger systems. This computational efficiency was achieved while retaining subwavenumber fidelity with the results of cutoff-free simulations.

Linear carbon chains (LCCs) are the ultimate one-dimensional molecular system, and they show unique mechanical, optical, and electronic properties that can be tuned by altering the number of carbon atoms, strain, encapsulation, and other external parameters. In this work we probe the effects of quantum anharmonicity, strain, and finite size on the structural and vibrational properties of these chains using high-level density-functional-theory calculations. We find strong anharmonicity effects for infinite chains, leading to ground-state nuclear wave functions that are barely localized at each of the dimerized geometries, i.e., strong tunneling occurs between the two minima of the potential energy surface. This effect is enhanced for compressive strains. In addition, vibrational C-band frequencies deviate substantially from experimental measurements in long chains encapsulated in carbon nanotubes. On the other hand, calculations for finite chains suggest that quantum anharmonicity effects are strongly suppressed in finite systems, even in the extrapolation to the infinite case. For finite systems, vibrational C-band frequencies agree well with experimental values at zero pressure. However, these frequencies increase under compressive strain, in contradiction with recent results. This contradiction is not resolved by adding explicitly the encapsulating carbon nanotubes to our calculations. Our results indicate that LCCs embody an intriguing 1D system in which the behavior of very large, finite systems do not reproduce or converge to the behavior of truly infinite ones.

Concurrent neutron Compton scattering (NCS) and neutron diffraction experiments at temperatures between 70 K and 300 K have been performed on proton-conducting hydrated BaZr0.7Ce0.2Y0.1O3−δ (BZCY72) fabricated by spark plasma sintering. A combined neutron data analysis, augmented with density functional theory modelling of lattice dynamics, has enabled, for the first time, a mass-selective appraisal of the combined thermal and nuclear quantum effect on nuclear dynamics and thermodynamic stability of this technologically important proton conducting perovskite oxide. The analysis suggests that the nuclear dynamics in hydrated BZCY72 is a result of a subtle interplay of harmonic, anharmonic and thermal effects, with the increased anharmonic character of the lattice dynamics above the orthorhombic to rhombohedral phase transition at 85 K. The anharmonic effect seems to be most pronounced in the case of oxygen and cerium. The analysis of the proton momentum distribution reveals that the concentration of the hydrogen in the BZCY72 lattice is constant across the orthorhombic to rhombohedral phase transition and further down to the room temperature. Moreover, the average hydrogen concentration obtained from our analysis of the mass-resolved neutron Compton scattering data seems to be commensurate with the total vacancy concentration in the BZCY72 framework. The calculation of the vibrational enthalpy of both phases allows obtaining the value of the enthalpy of the orthorhombic to the rhombohedral phase transition of −3.1 ± 1 kJ mol−1. Finally, our analysis of the nuclear kinetic energy of the proton obtained from NCS and the oxygen-oxygen distance distributions obtained from ND allows to conclude that BZCY72 in both the orthorhombic and rhombohedral phase at 70 K and 100 K respectively falls into the category of the KDP-type crystals where proton is probably under the influence of a double-well potential and forms hydrogen bonds of moderate strength. The obtained results have important ramifications for this technological important material.