Lattice Dynamics Calculations Research Articles

Terahertz time-domain investigation of atacamite: Spectral analysis and theoretical insights for cultural heritage applications

Spectroscopic methods based on terahertz (THz) radiation can represent an innovative approach in the Cultural Heritage field. Specifically, contemporary and historical pigments can exhibit unique fingerprints. However, despite the high selectiveness of terahertz technique, the origin of spectral characteristics is not often known. In this work, the characteristic terahertz-time-domain spectroscopy spectrum of atacamite is reported in the spectral range 0.1–3.7 THz along with ab initio calculation of lattice dynamics to assess the nature of experimental features. The obtained results enable the acquisition of reliable new data in Heritage sciences, which is essential for developing accurate reference pigment databases.

Benchmark Investigation of SCC-DFTB Against Standard DFT to Model Phononic Properties in Two-Dimensional MOFs for Thermoelectric Applications.

Despite the importance of modeling lattice thermal conductivity in predicting thermoelectric (TE) properties, computational data on heat transport, especially from first-principles, in 2D metal-organic frameworks (MOFs) remain limited due to the high computational cost. To address this, we provide a benchmark of the performance of semiempirical self-consistent-charge density functional tight-binding (SCC-DFTB) methods against density functional theory (DFT) for monolayer, serrated, AA-stacked and/or AB-stacked Zn3C6O6, Cd3C6O6, Zn-NH-MOF, and Ni3(HITP)2 MOFs. Harmonic lattice dynamics calculations, including partial atomic contributions to phonon dispersions, are evaluated with both SCC-DFTB and DFT, whereas anharmonic transport (i.e., thermal conductivity) is evaluated with SCC-DFTB only. Our findings further suggest that unlike the other stacking geometries modeled, serrated Zn3C6O6, serrated Zn-NH-MOF, and wavy serrated Ni3(HITP)2 represent stable geometries. While Zn3C6O6 and Zn-NH-MOF exhibit a higher power factor than Ni3(HITP)2 (as found in our previous work), Zn-NH-MOF shows lower thermal conductivity, resulting in the highest thermoelectric figure of merit (ZT) among the studied MOFs.

Reactive scattering of H2 on Cu(111) at 925K: Effective Hartree potential vs sudden approximation.

We present new quantum dynamical results for the reactive scattering of hydrogen molecules from a Cu(111) surface at a surface temperature of 925K. Reaction, scattering, and diffraction probabilities are compared for results obtained using both an effective Hartree potential (EfHP) and a sudden approximation approach, implemented through the static corrugation model (SCM), to include surface temperature effects. Toward this goal, we show how the SRP48 DFT-functional and an embedded atom potential perform when used to calculate copper lattice constants and thermal expansion coefficients based on lattice dynamics calculations within the quasi-harmonic approximation. The so-calculated phonons are then used in the EfHP approach to replace the normal modes of a fictitious copper cluster used in earlier work. We find that both the EfHP and SCM approaches correctly predict the reaction probability curve broadening effect when the surface temperature is increased. Similarly, results for rovibrationally elastic scattering appear to be improved, predominantly for the SCM model. The behavior of the EfHP results appears to remain much closer to that of a Born-Oppenheimer static surface approach, which excludes any surface temperature effects. Finally, for the diffraction, we show very clear attenuation effects for the SCM approach, significantly decreasing specular diffraction probabilities at 925K surface temperature. These results demonstrate that state-of-the-art theoretical models are able to reproduce strictly quantum mechanical scattering effects with a sudden approximation model and open up interesting opportunities for further comparisons to experimental diffraction results.

Vibrational, optical, electronic and electrocatalytic properties of SrCuSi4O10 ceramic

This research reports the synthesis of powdered SrCuSi4O10 ceramic powder, obtained through a solid-state chemical reaction methodology. The sample was characterized using X-ray powder diffraction (XRPD), Raman and Fourier transform infrared (FT-IR) spectroscopy, scanning electron microscopy (SEM), reflectance (R), electron paramagnetic resonance spectrum (EPR), lattice dynamic calculations, electronic and electrocatalytic properties analyses. The X-ray analysis showed that crystalline structure of SrCuSi4O10 compound belongs to a tetragonal system with the P4/ncc space group, containing four formulas per unit cell (Z = 4). The SEM micrographs present a morphology of layered microplates with some irregularity in size and shapes. UV–vis diffuse reflectance spectra show three intense reflection regions. Regarding the vibrational properties, the theoretical calculation was performed using a rigid ion model in order to assign the experimental Raman and IR modes. Additionally, electronic properties calculations were carried out using Density Functional Theory (DFT). Finally, the hydrogen evolution reaction (HER) performance of the SrCuSi4O10 electrocatalyst was evaluated.

Lattice dynamics of Bi12GeO20 crystal: Polarized Raman scattering and first-principles analysis

Our paper presents a combined experimental and theoretical study of the lattice dynamics of Bi12GeO20 crystal. Polarized Raman spectra were measured in two x-ray oriented single crystals. In a crystal of cubic symmetry, phonon modes of A- and E-types are spectroscopically indistinguishable. Using a special experimental technique, we separated the phonon modes that transform according to A and E irreducible representations. Since the number of E-type lines observed in Raman scattering is higher than theoretically allowed by group theory, we performed a first-principles calculation of the Bi12GeO20 lattice dynamics to accurately identify the symmetry of phonon modes. All experimental lines observed in Raman scattering are classified according to irreducible representations of the cubic I23 group. Using samples of different thicknesses, 10 mm and 0.120 mm, we have demonstrated that the optical activity plays an insignificant role at Raman backscattering in Bi12GeO20 crystal.

Vibrational dynamics dictate heat transport in metal-organic frameworks with gas adsorbates

Understanding the thermal conductivity (κ) of metal-organic frameworks (MOFs) with adsorbates is critical for tailoring their heat dissipation in practical applications. However, a detailed description of how adsorbates influence the heat transport of MOFs is still lacking. In this work, we employ molecular dynamics simulations combined with lattice dynamics calculations to investigate the effect of gas adsorbates on κ of representative crystalline and glassy zeolitic imidazolate frameworks (ZIFs). We identify that the diffusive adsorbate motions in the crystalline ZIFs with large pores can enhance lattice anharmonicity, serving as a source of phonon scattering and significantly suppressing κ. Conversely, the adsorbates with restricted dynamics in limited space (i.e., in the dense ZIF crystals or glasses) behave more like a heat transfer medium and facilitate heat transport. Besides pore size, gas dynamics are also proved to vary upon gas-lattice interaction strength, and dictate if gas adsorbates serve as a heat conduction suppressor or promoter. We anticipate that this governing role of gas dynamics is applicable to a diverse range of MOF-adsorbate systems. As such, our work offers guidance for the practical thermal management of MOF porous materials to ensure their desired storage or separation performance.

Enhanced elastic stability of a topologically disordered crystalline metal–organic framework

By virtue of their open network structures and low densities, metal–organic frameworks (MOFs) are soft materials that exhibit elastic instabilities at low applied stresses. The conventional strategy for improving elastic stability is to increase the connectivity of the underlying MOF network, which necessarily increases the material density and reduces the porosity. Here we demonstrate an alternative paradigm, whereby elastic stability is enhanced in a MOF with an aperiodic network topology. We use a combination of variable-pressure single-crystal X-ray diffraction measurements and coarse-grained lattice-dynamical calculations to interrogate the high-pressure behaviour of the topologically aperiodic system TRUMOF-1, which we compare against that of its ordered congener MOF-5. We show that the topology of the former quenches the elastic instability responsible for pressure-induced framework collapse in the latter, much as irregularity in the shapes and sizes of stones acts to prevent cooperative mechanical failure in drystone walls. Our results establish aperiodicity as a counter-intuitive design motif in engineering the mechanical properties of framework structures that is relevant to MOFs and larger-scale architectures alike.

Phonon softening and atomic modulations in EuAl4

EuAl4 is a rare-earth intermetallic in which competing itinerant and/or indirect exchange mechanisms give rise to a complex magnetic phase diagram, including a centrosymmetric skyrmion lattice. These phenomena arise not in the tetragonal parent structure but in the presence of a charge-density wave (CDW), which lowers the crystal symmetry and renormalizes the electronic structure. Microscopic knowledge of the corresponding atomic modulations and their driving mechanism is a prerequisite for a deeper understanding of the resulting equilibrium of electronic correlations and how it might be manipulated. Here, we use synchrotron single-crystal x-ray diffraction, inelastic x-ray scattering, and lattice-dynamics calculations to clarify the origin of the CDW in EuAl4. We observe a broad softening of a transverse acoustic phonon mode that sets in well above room temperature and, at TCDW=142 K, freezes out in an atomic displacement mode described by the superspace group Immm(00γ)s00. In the context of previous work, our observation is a clear confirmation that the CDW in EuAl4 is driven by electron-phonon coupling. This result is relevant for a wider family of BaAl4 and ThCr2Si2-type rare-earth intermetallics known to combine CDW instabilities and complex magnetism. Published by the American Physical Society 2024

Evidences for local non-centrosymmetricity and strong phonon anomaly in EuCu2As2: a Raman spectroscopy and lattice dynamics study

Phonon modes and their association with the electronic states have been investigated for the metallic EuCu2As2 system. In this work, we present the Raman spectra of this pnictide system which clearly shows the presence of seven well defined peaks above 100 cm−1 that is consistent with the locally non-centrosymmetric P4/nmm crystal structure, contrary to that what is expected from the accepted symmorphic I4/mmm structure. Lattice dynamics calculations using the P4/nmm symmetry attest that there is a commendable agreement between the calculated phonon spectra at the Γ point and the observed Raman mode frequencies, with the most intense peak at ∼232 cm−1 being ascribed to the A 1g mode. Temperature dependent Raman measurements show that there is a significant deviation from the expected anharmonic behaviour around 165 K for the A 1g mode, with anomalies being observed for several other modes as well, although to a lesser extent. Attempts are made to rationalize the observed anomalous behavior related to the hardening of the phonon modes, with parallels being drawn from metal dichalcogenide and allied systems. Similarities in the evolution of the Raman peak frequencies with temperature seem to suggest a strong signature of a subtle electronic density wave instability below 165 K in this compound.

Stabilization of High-Pressure Phase of Face-Centered Cubic Lutetium Trihydride at Ambient Conditions.

Superconductivity at room temperature and near-ambient pressures is a highly sought-after phenomenon in physics and materials science. A recent study reported the presence of this phenomenon in N-doped lutetium hydride [Nature 615, 244 (2023)], however, subsequent experimental and theoretical investigations have yielded inconsistent results. This study undertakes a systematic examination of synthesis methods involving high temperatures and pressures, leading to insights into the impact of the reaction path on the products and the construction of a phase diagram for lutetium hydrides. Notably, the high-pressure phase of face-centered cubic LuH3 (fcc-LuH3) is maintained to ambient conditions through a high-temperature and high-pressure method. Based on temperature and anharmonic effects corrections, the lattice dynamic calculations demonstrate the stability of fcc-LuH3 at ambient conditions. However, no superconductivity is observed above 2K in resistance and magnetization measurements in fcc-LuH3 at ambientpressure. This work establishes a comprehensive synthesis approach for lutetium hydrides, thereby enhancing the understanding of the high-temperature and high-pressure method employed in hydrides with superconductivity deeply.

Can large lattice volume always facilitate ion diffusion in solids?

Large lattice volume is usually expected to expand the bottleneck size and enlarge free volume for fast Li ion transport in solids. But the universality of lattice expansion decreasing activation energy barrier for Li ion migration is still debatable. Herein, our molecular dynamics simulations and density functional theory calculations detect the unconventional phenomenon of lattice expansion increasing activation energy barrier for Li ion migration in β-Li3PS4, Li4SnS4 and Li4GeS4 sulfides with the hcp-type anion sublattice, and discover the underlying mechanism. On one hand, lattice expansion enlarges the relative energies between the octahedral and tetrahedral Li sites, and correspondingly increase activation energy barrier for tetrahedral Li ions migration along the Tet-Oct-Tet migration paths in β-Li3PS4, Li4SnS4 and Li4GeS4. On the other hand, the lattice dynamics calculations show Li energy landscapes of β-Li3PS4, Li4SnS4 and Li4GeS4 are anharmonic and enlarging lattice volume make the local minimum of Li potential energy surface flatter, simultaneously reduce the relative energy of Li occupation site, eventually resulting in the higher activation energy barrier for Li ion migration. Thus, understanding the effect of lattice volume on ion migration in solids should not only consider the factor of bottleneck size and free volume, but also combine the aspects of Li ion occupation type, Li ion migration path and anion sublattice type. These new understandings of the lattice expansion increasing activation energy barrier for ion migration would further promote the further optimization and rational design of superionic conductors by element doping or strain engineering.

Lattice dynamics and heat transport in zeolitic imidazolate framework glasses.

The glassy state of zeolitic imidazolate frameworks (ZIFs) has shown great potential for energy-related applications, including solid electrolytes. However, their thermal conductivity (κ), an essential parameter influencing thermal dissipation, remains largely unexplored. In this work, using a combination of experiments, atomistic simulations, and lattice dynamics calculations, we investigate κ and the underlying heat conduction mechanism in ZIF glasses with varying ratios of imidazolate (Im) to benzimidazolate (bIm) linkers. The substitution of bIm for Imtunes the node-linker couplings but exhibits only a minor impact on the average diffusivity of low-frequency lattice modes. On the other hand, the linker substitution induces significant volume expansion, which, in turn, suppresses the contributions from lattice vibrations to κ, leading to decreased total heat conduction. Furthermore, spatial localization of internal high-frequency linker vibrations is promoted upon substitution, reducing their mode diffusivities. This is ascribed to structural deformations of the bIm units in the glasses. Our work unveils the detailed influences of linker substitution on the dual heat conduction characteristics of ZIF glasses and guides the κ regulation of related hybrid materials in practical applications.

Towards the high-throughput prediction of finite-temperature properties using the quasi-harmonic approximation

Lattice dynamics calculations within the quasi-harmonic approximation (QHA) provide an infrastructure for modelling the finite-temperature properties of periodic solids at a modest computational cost. With the recent widespread interest in materials discovery by data mining, a database of computed finite-temperature properties would be highly desirable. In this work we provide a first step toward this goal with a comparative study of the accuracy of five exchange-correlation functionals, spanning the local density approximation (LDA), generalised-gradient approximation (GGA) and meta-GGA levels of theory, for predicting the properties of ten Group 1, 2 and 12 binary metal oxides. We find that the predictions are bounded by the LDA, which tends to underestimate lattice parameters and cell volumes relative to experiments, but yields the most accurate results for bulk moduli, expansion coefficients and Grüneisen parameters, and the PBE GGA, which shows the opposite behaviour. The PBEsol GGA gives the best overall predictions of the lattice parameters and volumes whilst also giving relatively reliable results for other properties. Our results demonstrate that, given a suitable choice of functional, a variety of finite-temperature properties can be predicted with useful accuracy, and hence that high-throughout QHA calculations are technically feasible.

Fast access of the lattice thermal conductivity and phonon quasiparticle spectra of Mo2TiC2T2 (T = -O and -F) and Janus Mo2TiC2OF MXenes from machine learning potentials.

The presence of strong anharmonic effects in surface functionalized MXenes greatly challenges the use of harmonic lattice dynamics calculations to predict their phonon spectra and lattice thermal conductivity at finite temperatures. Herein, we demonstrate the workflow for training and validating machine learning potentials in terms of moment tensor potential (MTP) for MXenes including Mo2TiC2, Mo2TiC2O2, Mo2TiC2F2 and Janus-Mo2TiC2OF monolayers. Then, the MTPs of MXenes are successfully combined with the harmonic lattice dynamics calculations to obtain the temperature renormalized phonon spectra, three-phonon scattering rates, phonon relaxation times and lattice thermal conductivity at finite temperatures. Furthermore, combining MTPs with classic molecular dynamics simulations at finite temperatures directly enables the calculation of phonon quasi-particle spectral energy density with a full inclusion of all anharmonic effects in MXenes. Our current results indicate that anharmonic effects are found to be relatively weak in Mo2TiC2 and Mo2TiC2O2 monolayers, whereas the phonon quasi-particle spectral energy densities largely resemble those of harmonic or renormalized lattice dynamics calculations. Significant broadening of spectral energy density at finite temperature is predicted for Mo2TiC2F2 and Janus-Mo2TiC2OF monolayers, implying strong anharmonic effects in those MXenes. Our work paves a new way for fast and reliable calculation of the phonon scattering process and lattice thermal conductivity of MXenes within MTPs trained from first-principles molecular dynamics simulations in the future.

Mechanism of Negative Thermal Expansion in Monoclinic Cu2P2O7 from First Principles.

Negative thermal expansion (NTE) materials generally have high-symmetry space groups, large average atomic volumes, and corner-sharing octahedral and tetrahedral coordination structures. By contrast, monoclinic α-Cu2P2O7, which has a small average atomic volume and edge-sharing structure, has been reported to exhibit NTE, the detailed mechanism of which is unclear. In this study, we investigate the A2B2O7 polymorphs and analyze the NTE behavior of α-Cu2P2O7 using first-principles lattice-dynamics calculations. From the polymorphism investigation in 20 A2B2O7 compounds using 6 representative crystal structures, small A and B cationic radii are found to stabilize the α-Cu2P2O7-type structure. We then analyze the NTE behavior of α-Cu2P2O7 using quasi-harmonic approximation. Our calculated thermal expansion coefficients and anisotropic atomic displacement parameters were in good agreement with those of the experimental reports at low temperatures. From the mode-Grüneisen parameter distribution plotted over the entire first-Brillouin zone, we found that the phonon contributing most significantly to NTE emerges not into the special points but between them. In this phonon mode, the O connecting two PO4 tetrahedra rotates, and the Cu and O vibrate perpendicular to the bottom of the CuO5 pyramidal unit, which folds the ac lattice plane. This vibration behavior can explain the experimentally reported anisotropic NTE behavior of α-Cu2P2O7. Our results demonstrate that the most negative mode-Grüneisen parameter contributing to NTE behavior is not always located on high-symmetry special points, indicating the importance of lattice vibration analyses for the entire first-Brillouin zone.

Application of the FFLUX Force Field to Molecular Crystals: A Study of Formamide.

In this work, we present the first application of the quantum chemical topology force field FFLUX to the solid state. FFLUX utilizes Gaussian process regression machine learning models trained on data from the interacting quantum atom partitioning scheme to predict atomic energies and flexible multipole moments that change with geometry. Here, the ambient (α) and high-pressure (β) polymorphs of formamide are used as test systems and optimized using FFLUX. Optimizing the structures with increasing multipolar ranks indicates that the lattice parameters of the α phase differ by less than 5% to the experimental structure when multipole moments up to the quadrupole are used. These differences are found to be in line with the dispersion-corrected density functional theory. Lattice dynamics calculations are also found to be possible using FFLUX, yielding harmonic phonon spectra comparable to dispersion-corrected DFT while enabling larger supercells to be considered than is typically possible with first-principles calculations. These promising results indicate that FFLUX can be used to accurately determine properties of molecular solids that are difficult to access using DFT, including the structural dynamics, free energies, and properties at finite temperature.

Primitive to conventional geometry projection for efficient phonon transport calculations

The primitive Wigner-Seitz cell and corresponding first Brillouin zone (FBZ) are typically used in calculations of lattice vibrational and transport properties as they contain the smallest number of degrees of freedom and thus have the cheapest computational cost. However, in complex materials, the FBZ can take on irregular shapes where lattice symmetries are not apparent. Thus, conventional cells (with more atoms and regular shapes) are often used to describe materials, though dynamical and transport calculations are more expensive. Here we discuss an efficient anharmonic lattice dynamic method that maps conventional cell dynamics to primitive cell dynamics based on translational symmetries. Such symmetries have not been utilized in typical lattice dynamical calculations. This leads to phase interference conditions that act like conserved quantum numbers and a conservation rule for phonon scattering that is hidden in conventional dynamics which significantly reduces the computational cost. We demonstrate this method for phonon transport in a variety of materials with inputs from first-principles calculations and attribute its efficiency to reduced scattering phase space and fewer summations in scattering matrix element calculations.

Phonon mixing in the charge density wave state of ScV6Sn6

Kagomé metals are widely recognized, versatile platforms for exploring topological properties, unconventional electronic correlations, magnetic frustration, and superconductivity. In the RV6Sn6 family of materials (R = Sc, Y, Lu), ScV6Sn6 hosts an unusual charge density wave ground state as well as structural similarities with the AV3Sb5 system (A = K, Cs, Rb). In this work, we combine Raman scattering spectroscopy with first-principles lattice dynamics calculations to reveal phonon mixing processes in the charge density wave state of ScV6Sn6. In the low temperature phase, we find at least four new peaks in the vicinity of the V-containing totally symmetric mode near 240 cm−1 suggesting that the density wave acts to mix modes of P6/mmm and Rbar{3}m symmetry - a result that we quantify by projecting phonons of the high symmetry state onto those of the lower symmetry structure. We also test the stability of the short-range ordered density wave state under compression and propose that both physical and chemical pressure quench the effect. We discuss these findings in terms of symmetry and the structure-property trends that can be unraveled in this system.

Infrared and Raman Diagnostic Modeling of Phosphate Adsorption on Ceria Nanoparticles.

Cerium dioxide (CeO2; ceria) nanoparticles (CeNPs) are promising nanozymes that show a variety of biological activity. Effective nanozymes need to retain their activity in the face of surface speciation in biological environments, and characterizing surface speciation is therefore critical to understanding and controlling the therapeutic capabilities of CeNPs. In particular, adsorbed phosphates can impact the enzymatic activity exploited to convert phosphate prodrugs into therapeutics in vivo and also define the early stages of the phosphate-scavenging processes that lead to the transformation of active CeO2 into inactive CePO4. In this work, we utilize ab initio lattice-dynamics calculations to study the interaction of phosphates with the three major surfaces of ceria and to predict the infrared (IR) and Raman spectral signatures of adsorbed phosphate species. We find that phosphates adsorb strongly to CeO2 surfaces in a range of stable binding configurations, of which 5-fold coordinated P species in a trigonal bipyramidal coordination may represent a stable intermediate in the early stages of phosphate scavenging. We find that the phosphate species show characteristic spectral fingerprints between 500 and 1500 cm-1, whereas the bare CeO2 surfaces show no active modes above 600 cm-1, and the 5-fold coordinated P species in particular show potential diagnostic P-O stretching modes between 650 and 700 cm-1 in both IR and Raman spectra. This comprehensive exploration of different binding modes for phosphates on CeO2 and the set of reference spectra provides an important step toward the experimental characterization of phosphate speciation and, ultimately, control of its impact on the performance of ceria nanozymes.

Identifying the Phonon Contributions to Li+ Hop in La0.5Li0.5TiO3 Solid Electrolyte

Ion diffusion is important in a variety of applications, yet fundamental understanding of the interaction of lattice vibrations (phonons and vibrational motifs) and the mobile species in solids is still missing. Particularly, for Li super ionic conductors (LISICONs), several studies have reported on the important role of the poly-anion octahedral rotations (rocking modes) in facilitating solid-state Li+ ion migration.[1], [2] However, direct calculation of the contribution of these rocking modes to the Li+ hop is missing, and the provided arguments in these reports are mostly based on establishing correlations between different properties of the rocking modes and the migration properties of the hopping Li+ ion without directly quantifying the contribution of the rocking modes to the Li+ hop. For instance, rocking modes have been argued to be able to (i) provide a softer lattice environment for Li+ ion vibration,[3] (ii) increase the bottleneck area of diffusion (4-O square area),[2] (iii) induce additional force on the carrier sublattice,[1] and (iv) maintain a relatively constant coordination number for Li+ ion during its hop[1] – all conducive to Li+ hop in the lattice. Although insightful, we still lack understanding of the exact vibrational frequencies (density of states) of the rocking modes, and, more importantly, the degree of their contribution to Li+ hop with respect to other phonon modes in the structure. In this work, using a combination of ab initio nudged elastic band (NEB) and lattice dynamics calculations based on the recently proposed formalism,[4] we identify the direct contributions of all phonons, including the rocking ones, to Li+ hop in the perovskite solid-state Li+ conductor Li0.5La0.5TiO3 (LLTO).We set up our NEB Li+ hop calculations considering (i) different orderings of the LLTO lattice,[5] and (ii) different Li+ hopping mechanisms (single and concerted (cooperative)) that can occur in the LLTO lattice.2 To sample such a high degree of complexity, we performed 22 independent NEB calculations of Li+ hop in three different LLTO structures with distinct Li|La orderings and based on two different ion hop mechanisms (single and concerted). Our calculations determined that the following two groups of vibrational modes dominate the contributions to the Li+ hop in the LLTO lattice: (i) rocking modes, and (ii) modes that induce large vibrational energies on the hopping Li+ along its hopping direction. Specifically, our results confirmed that the top 5% (10%) contributing modes to the Li+ hop in the LLTO lattice were responsible for 48% (61%) of the total contributions to the Li+ hop, and the two rocking and highly energetic modes comprised >95% (>85%) of these top 5% (10%) contributing modes. Notable from our calculations was that the rocking modes were only present in the < 5.5 THz frequency region, and in this < 5.5 THz frequency region, they comprised 33% of the vibrational modes and contributed 50% to all the possible contributions to the Li+ hop in this low frequency THz region. Moreover, through static modal excitement calculations, we determined that highly contributing rocking modes of vibration were important in solid-state Li+ ion migration because of their ability to (i) increase the O-4 square bottleneck area of conduction[6] and (ii) amplify the force on the hopping Li+ ion. In summary, our observations demonstrated the strong importance of the THz vibrational region to Li+ hop in the lattice, which can be accessible for further explorations using THz spectroscopy techniques to deepen our understanding of the relation between solid-state transport of Li+ and different vibrational motifs in the lattice.