Spin-phonon coupling and magnetic relaxation in single-molecule magnets.

Electron-phonon coupling is important in many physical phenomena, e.g. photosynthesis, catalysis and quantum information processing, but its impacts are difficult to grasp on the microscopic level. One area attracting wide interest is that of single-molecule magnets, which is motivated by searching for the ultimate limit in the miniaturisation of binary data storage media. The utility of a molecule to store magnetic information is quantified by the timescale of its magnetic reversal processes, also known as magnetic relaxation, which is limited by spin-phonon coupling. Several recent accomplishments of synthetic organometallic chemistry have led to the observation of molecular magnetic memory effects at temperatures above that of liquid nitrogen. These discoveries have highlighted how far chemical design strategies for maximising magnetic anisotropy have come, but have also highlighted the need to characterise the complex interplay between phonons and molecular spin states. The crucial step is to make a link between magnetic relaxation and chemical motifs, and so be able to produce design criteria to extend molecular magnetic memory. The basic physics associated with spin-phonon coupling and magnetic relaxation was outlined in the early 20th century using perturbation theory, and has more recently been recast in the form of a general open quantum systems formalism and tackled with different levels of approximations. It is the purpose of this Tutorial Review to introduce the topics of phonons, molecular spin-phonon coupling, and magnetic relaxation, and to outline the relevant theories in connection with both the traditional perturbative texts and the more modern open quantum systems methods.

Exploring Pyroelectricity, Thermal and Photochemical Switching in a Hybrid Organic-Inorganic Crystal by In Situ X-Ray Diffraction.

The switching behavior of the novel hybrid material (FA)Na[Fe(CN)5(NO)].H2O (1) in response to temperature (T), light irradiation and electric field (E) is studied using in situ X-ray diffraction (XRD). Crystals of 1 display piezoelectricity, pyroelectricity, second and third harmonic generation. XRD shows that the FA+ are disordered at room-temperature, but stepwise cooling from 273-100 K induces gradual ordering, while cooling under an applied field (E=+40 kVcm-1) induces a sudden phase change at 140 K. Structural-dynamics calculations suggest the field pushes the system into a region of the structural potential-energy surface that is otherwise inaccessible, demonstrating that application of T and E offers an effective route to manipulating the crystal chemistry of these materials. Photocrystallography also reveals photoinduced linkage isomerism, which coexists with but is not correlated to other switching behaviors. These experiments highlight a new approach to in situ studies of hybrid materials, providing insight into the structure-property relationships that underpin their functionality.

Structural Evolution of Paramagnetic Lanthanide Compounds in Solution Compared to Time- and Ensemble-Average Structures.

Anisotropy in the magnetic susceptibility strongly influences the paramagnetic shifts seen in nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI) experiments. A previous study on a series of C3-symmetric prototype MRI contrast agents showed that their magnetic anisotropy was highly sensitive to changes in molecular geometry and concluded that changes in the average angle between the lanthanide-oxygen (Ln-O) bonds and the molecular C3 axis due to solvent interactions had a significant impact on the magnetic anisotropy and, consequently, the paramagnetic shift. However, this study, like many others, was predicated on an idealized C3-symmetric structural model, which may not be representative of the dynamic structure in solution at the single-molecule level. Here, we address this by using ab initio molecular dynamics simulations to simulate how the molecular geometry, in particular the angles between the Ln-O bonds and the pseudo-C3 axis, evolves over time in the solution, mimicking typical experimental conditions. We observe large-amplitude oscillations in the O-Ln-C̃3 angles, and complete active space self-consistent field spin-orbit calculations show that this leads to similarly large oscillations in the pseudocontact (dipolar) paramagnetic NMR shifts. The time-averaged shifts show good agreement with experimental measurements, while the large fluctuations suggest that an idealized structure provides an incomplete description of the solution dynamics. Our observations have significant implications for modeling the electronic and nuclear relaxation times in this and other systems where the magnetic susceptibility is exquisitely sensitive to the molecular structure.

Accurate and Efficient Spin-Phonon Coupling and Spin Dynamics Calculations for Molecular Solids.

Molecular materials are poised to play a significant role in the development of future optoelectronic and quantum technologies. A crucial aspect of these areas is the role of spin-phonon coupling and how it facilitates energy transfer processes such as intersystem crossing, quantum decoherence, and magnetic relaxation. Thus, it is of significant interest to be able to accurately calculate the molecular spin-phonon coupling and spin dynamics in the condensed phase. Here, we demonstrate the maturity of ab initio methods for calculating spin-phonon coupling by performing a case study on a single-molecule magnet and showing quantitative agreement with the experiment, allowing us to explore the underlying origins of its spin dynamics. This feat is achieved by leveraging our recent developments in analytic spin-phonon coupling calculations in conjunction with a new method for including the infinite electrostatic potential in the calculations. Furthermore, we make the first ab initio determination of phonon lifetimes and line widths for a molecular magnet to prove that the commonplace Born-Markov assumption for the spin dynamics is valid, but such "exact" phonon line widths are not essential to obtain accurate magnetic relaxation rates. Calculations using this approach are facilitated by the open-source packages we have developed, enabling cost-effective and accurate spin-phonon coupling calculations on molecular solids.

Breathing Behaviour Modification of Gallium MIL-53 Metal-Organic Frameworks Induced by the Bridging Framework Inorganic Anion.

Controlling aspects of the µ2 -X- bridging anion in the metal-organic framework Ga-MIL-53 [GaX(bdc)] (X- =(OH)- or F- , bdc=1, 4-benzenedicarboxylate) is shown to direct the temperature at which thermally induced breathing transitions of this framework occur. In situ single crystal X-ray diffraction studies reveal that substituting 20 % of (OH)- in [Ga(OH)(bdc)] (1) for F- to produce [Ga(OH)0.8 F0.2 (bdc)] (2) stabilises the large pore (lp) form relative to the narrow pore (np) form, causing a well-defined decrease in the onset of the lp to np transition at higher temperatures, and the adsorption/desorption of nitrogen at lower temperatures through np to lp to intermediate (int) pore transitions. These in situ diffraction studies have also yielded a more plausible crystal structure of the int-[GaX(bdc)] ⋅ H2 O phases and shown that increasing the heating rate to a flash heating regime can enable the int-[GaX(bdc)] ⋅ H2 O to lp-[GaX(bdc)] transition to occur at a lower temperature than np-[GaX(bdc)] via an unreported pathway.

Location of Artinite (Mg2CO3(OH)2·3H2O) within the MgO-CO2-H2O system using ab initio thermodynamics.

The MgO-CO2-H2O system have a variety of important industrial applications including in catalysis, immobilisation of radionuclides and heavy metals, construction, and mineralisation and permanent storage of anthropogenic CO2. Here, we develop a computational approach to generate phase stability plots for the MgO-CO2-H2O system that do not rely on traditional experimental corrections for the solid phases. We compare the predictions made by several dispersion-corrected density-functional theory schemes, and we include the temperature-dependent Gibbs free energy through the quasi-harmonic approximation. We locate the Artinite phase (Mg2CO3(OH)2·3H2O) within the MgO-CO2-H2O phase stability plot, and we demonstrate that this widely-overlooked hydrated and carbonated phase is metastable and can be stabilised by inhibiting the formation of fully-carbonated stable phases. Similar considerations may apply more broadly to other lesser known phases. These findings provide new insight to explain conflicting results from experimental studies, and demonstrate how this phase can potentially be stabilised by optimising the synthesis conditions.

Construction of a Gaussian Process Regression Model of Formamide for Use in Molecular Simulations.

FFLUX, a novel force field based on quantum chemical topology, can perform molecular dynamics simulations with flexible multipole moments that change with geometry. This is enabled by Gaussian process regression machine learning models, which accurately predict atomic energies and multipole moments up to the hexadecapole. We have constructed a model of the formamide monomer at the B3LYP/aug-cc-pVTZ level of theory capable of sub-kJ mol-1 accuracy, with the maximum prediction error for the molecule being 0.8 kJ mol-1. This model was used in FFLUX simulations along with Lennard-Jones parameters to successfully optimize the geometry of formamide dimers with errors smaller than 0.1 Šcompared to those obtained with D3-corrected B3LYP/aug-cc-pVTZ. Comparisons were also made to a force field constructed with static multipole moments and Lennard-Jones parameters. FFLUX recovers the expected energy ranking of dimers compared to the literature, and changes in C═O and C-N bond lengths associated with hydrogen bonding were found to be consistent with density functional theory.

Quantum Confined High-Entropy Lanthanide Oxysulfide Colloidal Nanocrystals.

We have synthesized the first reported example of quantum confined high-entropy (HE) nanoparticles, using the lanthanide oxysulfide, Ln2SO2, system as the host phase for an equimolar mixture of Pr, Nd, Gd, Dy, and Er. A uniform HE phase was achieved via the simultaneous thermolysis of a mixture of lanthanide dithiocarbamate precursors in solution. This was confirmed by powder X-ray diffraction and high-resolution scanning transmission electron microscopy, with energy dispersive X-ray spectroscopic mapping confirming the uniform distribution of the lanthanides throughout the particles. The nanoparticle dispersion displayed a significant blue shift in the absorption and photoluminescence spectra relative to our previously reported bulk sample with the same composition, with an absorption edge at 330 nm and a λmax at 410 nm compared to the absorption edge at 500 nm and a λmax at 450 nm in the bulk, which is indicative of quantum confinement. We support this postulate with experimental and theoretical analysis of the bandgap energy as a function of strain and surface effects (ligand binding) as well as calculation of the exciton Bohr radiii of the end member compounds.

Towards an atomistic understanding of polymorphism in molecular solids.

Understanding and controlling polymorphism in molecular solids is a major unsolved problem in crystal engineering. While the ability to calculate accurate lattice energies with atomistic modelling provides valuable insight into the associated energy scales, existing methods cannot connect energy differences to the delicate balances of intra- and intermolecular forces that ultimately determine polymorph stability ordering. We report herein a protocol for applying Quantum Chemical Topology (QCT) to study the key intra- and intermolecular interactions in molecular solids, which we use to compare the three known polymorphs of succinic acid including the recently-discovered γ form. QCT provides a rigorous partitioning of the total energy into contributions associated with topological atoms, and a quantitative and chemically intuitive description of the intra- and intermolecular interactions. The newly-proposed Relative Energy Gradient (REG) method ranks atomistic energy terms (steric, electrostatic and exchange) by their importance in constructing the total energy profile for a chemical process. We find that the conformation of the succinic acid molecule is governed by a balance of large and opposing electrostatic interactions, while the H-bond dimerisation is governed by a combination of electrostatics and sterics. In the solids, an atomistic energy balance emerges that governs the contraction, towards the equilibrium geometry, of a molecular cluster representing the bulk crystal. The protocol we put forward is as general as the capabilities of the underlying quantum-mechanical model and it can provide novel perspectives on polymorphism in a wide range of chemical systems.

Structural Dynamics, Phonon Spectra and Thermal Transport in the Silicon Clathrates.

The potential of thermoelectric power to reduce energy waste and mitigate climate change has led to renewed interest in "phonon-glass electron-crystal" materials, of which the inorganic clathrates are an archetypal example. In this work we present a detailed first-principles modelling study of the structural dynamics and thermal transport in bulk diamond Si and five framework structures, including the reported Si Clathrate I and II structures and the recently-synthesised oC24 phase, with a view to understanding the relationship between the structure, lattice dynamics, energetic stability and thermal transport. We predict the IR and Raman spectra, including ab initio linewidths, and identify spectral signatures that could be used to confirm the presence of the different phases in material samples. Comparison of the energetics, including the contribution of the phonons to the finite-temperature Helmholtz free energy, shows that the framework structures are metastable, with the energy differences to bulk Si dominated by differences in the lattice energy. Thermal-conductivity calculations within the single-mode relaxation-time approximation show that the framework structures have significantly lower κlatt than bulk Si, which we attribute quantitatively to differences in the phonon group velocities and lifetimes. The lifetimes vary considerably between systems, which can be largely accounted for by differences in the three-phonon interaction strengths. Notably, we predict a very low κlatt for the Clathrate-II structure, in line with previous experiments but contrary to other recent modelling studies, which motivates further exploration of this system.

Two Is Better than One? Investigating the Effect of Incorporating Re(CO)3Cl Side Chains into Pt(II) Diynes and Polyynes.

Pt(II) diynes and polyynes incorporating 5,5'- and 6,6'-disubstituted 2,2'-bipyridines were prepared following conventional Sonogashira and Hagihara dehydrohalogenation reaction protocols. Using Pt(II) dimers and polymers as a rigid-rod backbone, four new heterobimetallic compounds incorporating Re(CO)3Cl as a pendant functionality in the 2,2'-bipyridine core were obtained. The new heterobimetallic Pt-Re compounds were characterized by analytical and spectroscopic techniques. The solid-state structures of a Re(I)-coordinated diterminal alkynyl ligand and a representative model compound were determined by single-crystal X-ray diffraction. Detailed photophysical characterization of the heterobimetallic Pt(II) diynes and polyynes was carried out. We find that the incorporation of the Re(CO)3Cl pendant functionality in the 2,2'-bipyridine-containing main-chain Pt(II) diynes and polyynes has a synergistic effect on the optical properties, red shifting the absorption profile and introducing strong long-wavelength absorptions. The Re(I) moiety also introduces strong emission into the monomeric Pt(II) diyne compounds, whereas this is suppressed in the polyynes. The extent of the synergy depends on the topology of the ligands. Computational modeling was performed to compare the energetic stabilities of the positional isomers and to understand the microscopic nature of the major optical transitions. We find that 5,5'-disubstituted 2,2'-bipyridine systems are better candidates in terms of yield, photophysical properties, and stability than their 6,6'-substituted counterparts. Overall, this work provides an additional synthetic route to control the photophysical properties of metallaynes for a variety of optoelectronic applications.

Phase stability of the tin monochalcogenides SnS and SnSe: a quasi-harmonic lattice-dynamics study.

The tin monochalcogenides SnS and SnSe adopt four different crystal structures, viz. orthorhombic Pnma and Cmcm and cubic rocksalt and π-cubic (P213) phases, each of which has optimal properties for a range of potential applications. This rich phase space makes it challenging to identify the conditions under which the different phases are obtained. We have performed first-principles quasi-harmonic lattice-dynamics calculations to assess the relative stabilities of the four phases of SnS and SnSe. We investigate dynamical stability through the presence or absence of imaginary modes in the phonon dispersion curves, and we compute Helmholtz and Gibbs free energies to evaluate the thermodynamic stability. We also consider applied pressures up to 15 GPa to obtain simulated temperature-pressure phase diagrams. Finally, the relationships between the orthorhombic crystal phases are investigated by explicitly mapping the potential-energy surfaces along the imaginary harmonic phonon modes in the Cmcm phase, and the relationships between the cubic phases are found by transition-state modelling using the climbing-image nudged elastic-band method.

Acoustic phonon lifetimes limit thermal transport in methylammonium lead iodide.

Hybrid organic-inorganic perovskites (HOIPs) have become an important class of semiconductors for solar cells and other optoelectronic applications. Electron-phonon coupling plays a critical role in all optoelectronic devices, and although the lattice dynamics and phonon frequencies of HOIPs have been well studied, little attention has been given to phonon lifetimes. We report high-precision momentum-resolved measurements of acoustic phonon lifetimes in the hybrid perovskite methylammonium lead iodide (MAPI), using inelastic neutron spectroscopy to provide high-energy resolution and fully deuterated single crystals to reduce incoherent scattering from hydrogen. Our measurements reveal extremely short lifetimes on the order of picoseconds, corresponding to nanometer mean free paths and demonstrating that acoustic phonons are unable to dissipate heat efficiently. Lattice-dynamics calculations using ab initio third-order perturbation theory indicate that the short lifetimes stem from strong three-phonon interactions and a high density of low-energy optical phonon modes related to the degrees of freedom of the organic cation. Such short lifetimes have significant implications for electron-phonon coupling in MAPI and other HOIPs, with direct impacts on optoelectronic devices both in the cooling of hot carriers and in the transport and recombination of band edge carriers. These findings illustrate a fundamental difference between HOIPs and conventional photovoltaic semiconductors and demonstrate the importance of understanding lattice dynamics in the effort to develop metal halide perovskite optoelectronic devices.

Photocrystallographic Studies on Transition Metal Nitrito Metastable Linkage Isomers: Manipulating the Metastable State.

The design of solid-state materials whose properties and functions can be manipulated in a controlled manner by the application of light is an important objective in modern materials chemistry. When the material changes property or function, it is helpful if a simple measurable response, such as a change in color, can be detected. Potential applications for such materials are wide ranging, from data storage to smart windows. With the growing emphasis on solid-state materials that have two or more accessible energy states and which exhibit bistability, attention has turned to transition metal complexes that contain ambidentate ligands that can switch between linkage isomeric forms when activated by light. Suitable ligands that show promise in this area include nitrosyls, nitro groups, and coordinated sulfur dioxide molecules, each of which can coordinate to a metal center in more than one bonding mode. A nitrosyl normally coordinates through its N atom (η1-NO) but when photoactivated can undergo isomerism and coordinate through its O atom (η1-ON). At a molecular level, converting between these two configurations can act as an "on/off" switch. The analysis of such materials has been aided by the development of photocrystallographic techniques, which allow the full three-dimensional structure of a single crystal of a complex, under photoactivation, to be determined, when it is in either a metastable or short-lived excited state. The technique effectively brings the dimension of "time" to the crystallographic experiment and brings us closer to being able to watch solid-state processes occur in real time. In this Account, we highlight the advances made in photocrystallography for studying solid-state, photoactivated linkage isomerism and describe the factors that favor the switching process and which allow complete switching between isomers. We demonstrate that control of temperature is key to achieving either a metastable state or an excited state with a specific lifetime. We draw our conclusions from published work on the formation of photoactivated metastable states for nitrosyl and sulfur dioxide complexes and from our own work on photoactivated switching between nitro and nitrito groups. We show that efficient switching between isomers is dependent on the wavelength of light used, on the temperature at which the experiment is carried out, on the flexibility of the crystal lattice, and on both the electronic and steric environment of the ambidentate ligand undergoing isomerism. We have designed and prepared a number of nitro/nitrito isomeric metal complexes that undergo reversible 100% conversion between the two forms at temperatures close to room temperature. Through our fine control over the generation of the metastable states, it should be possible to effectively "dial up" a suitable temperature to give a metastable or an excited state with a desired lifetime.

Assessment of dynamic structural instabilities across 24 cubic inorganic halide perovskites.

Metal halide perovskites are promising candidates for next-generation photovoltaic and optoelectronic applications. The flexible nature of the octahedral network introduces complexity when understanding their physical behavior. It has been shown that these materials are prone to decomposition and phase competition, and the local crystal structure often deviates from the average space group symmetry. To make stable phase-pure perovskites, understanding their structure-composition relations is of central importance. We demonstrate, from lattice dynamics calculations, that the 24 inorganic perovskites ABX3 (A = Cs, Rb; B = Ge, Sn, Pb; X = F, Cl, Br, I) exhibit instabilities in their cubic phase. These instabilities include cation displacements, octahedral tilting, and Jahn-Teller distortions. The magnitudes of the instabilities vary depending on the chemical identity and ionic radii of the composition. The tilting instabilities are energetically dominant and reduce as the tolerance factor increases, whereas cation displacements and Jahn-Teller type distortions depend on the interactions between the constituent ions. We further considered representative tetragonal, orthorhombic, and monoclinic perovskite phases to obtain phonon-stable structures for each composition. This work provides insights into the thermodynamic driving force of the instabilities and will help guide computer simulations and experimental synthesis in material screening.

Room Temperature Metallic Conductivity in a Metal-Organic Framework Induced by Oxidation.

Metal-organic frameworks (MOFs) containing redox active linkers have led to hybrid compounds exhibiting high electrical conductivity, which enables their use in applications in electronics and electrocatalysis. While many computational studies predict two-dimensional (2D) MOFs to be metallic, the majority of experiments show decreasing conductivity on cooling, indicative of a gap in the electronic band structure. To date, only a handful of MOFs have been reported that exhibit increased electrical conductivity upon cooling indicative of a metallic character, which highlights the need for a better understanding of the origin of the conductivity. A 2D MOF containing iron bis(dithiolene) motifs was recently reported to exhibit semiconducting behavior with record carrier mobility. Herein, we report that high crystallinity and the elimination of guest species results in an iron 2,3,6,7,10,11-tripheylenehexathiolate (THT) MOF, FeTHT, exhibiting a complex transition from semiconducting to metallic upon cooling, similar to what was shown for the analogous CoTHT. Remarkably, exposing the FeTHT to air significantly influences the semiconducting-to-metallic transition temperature (100 to 300 K) and ultimately results in a material showing metallic-like character at, and above, room temperature. This study indicates these materials can tolerate a substantial degree of doping that ultimately results in charge delocalization and metallic-like conductivity, an important step toward enabling their use in chemiresistive sensing and optoelectronics.

Intrinsic Flexibility of the EMT Zeolite Framework under Pressure.

The roles of organic additives in the assembly and crystallisation of zeolites are still not fully understood. This is important when attempting to prepare novel frameworks to produce new zeolites. We consider 18-crown-6 ether (18C6) as an additive, which has previously been shown to differentiate between the zeolite EMC-2 (EMT) and faujasite (FAU) frameworks. However, it is unclear whether this distinction is dictated by influences on the metastable free-energy landscape or geometric templating. Using high-pressure synchrotron X-ray diffraction, we have observed that the presence of 18C6 does not impact the EMT framework flexibility-agreeing with our previous geometric simulations and suggesting that 18C6 does not behave as a geometric template. This was further studied by computational modelling using solid-state density-functional theory and lattice dynamics calculations. It is shown that the lattice energy of FAU is lower than EMT, but is strongly impacted by the presence of solvent/guest molecules in the framework. Furthermore, the EMT topology possesses a greater vibrational entropy and is stabilised by free energy at a finite temperature. Overall, these findings demonstrate that the role of the 18C6 additive is to influence the free energy of crystallisation to assemble the EMT framework as opposed to FAU.

Monitoring photo-induced population dynamics in metastable linkage isomer crystals: a crystallographic kinetic study of [Pd(Bu4dien)NO2]BPh4.

We present a detailed kinetic study of photo-induced solid state linkage isomerism in the compound [Pd(Bu4dien)NO2]BPh4 (Bu4dien = N,N,N',N'-tetrabutyldiethylenetriamine) using in situ photocrystallographic techniques. We explore the key variables that influence the photoconversion and develop a detailed kinetic model for the excitation and decay processes and the temperature dependence of the conversion rates. We show that by varying the temperature the lifetime of the excited state can be varied over orders of magnitude, making these systems ideal test cases for the development of new time-resolved X-ray diffraction methods. The kinetic model is used to build a numerical-simulation tool, which we use to explore the practicalities of pump-probe single-crystal diffraction experiments with minute and second time-resolution.

Metallic Conductivity in a Two-Dimensional Cobalt Dithiolene Metal-Organic Framework.

Two-dimensional (2D) metal-organic frameworks (MOFs) have received a great deal of attention due to their relatively high charge carrier mobility and low resistivity. Here we report on the temperature-dependent charge transport properties of a 2D cobalt 2,3,6,7,10,11-triphenylenehexathiolate framework. Variable temperature resistivity studies reveal a transition from a semiconducting to a metallic phase with decreasing temperature, which is unprecedented in MOFs. We find this transition to be highly dependent on the film thickness and the amount of solvent trapped in the pores, with density functional theory calculations of the electronic-structure supporting the complex metallic conductivity of the material. These results identify the first experimentally observed MOF that exhibits band-like metallic conductivity.

Lattice dynamics of the tin sulphides SnS2, SnS and Sn2S3: vibrational spectra and thermal transport.

We present an in-depth first-principles study of the lattice dynamics of the tin sulphides SnS2, Pnma and π-cubic SnS and Sn2S3. An analysis of the harmonic phonon dispersion and vibrational density of states reveals phonon bandgaps between low- and high-frequency modes consisting of Sn and S motion, respectively, and evidences a bond-strength hierarchy in the low-dimensional SnS2, Pnma SnS and Sn2S3 crystals. We model and perform a complete characterisation of the infrared and Raman spectra, including temperature-dependent anharmonic linewidths calculated using many-body perturbation theory. We illustrate how vibrational spectroscopy could be used to identify and characterise phase impurities in tin sulphide samples. The spectral linewidths are used to model the thermal transport, and the calculations indicate that the low-dimensional Sn2S3 has a very low lattice thermal conductivity, potentially giving it superior performance to SnS as a candidate thermoelectric material.