Entropy Term Research Articles

Bond-order bond energy model for alloys

We introduce a novel way to parameterize alloy energies in the form of a bond-order bond energy model. There, a bond order function models the transition between competing phases and switches their respective bond energies on and off. For the case of the Ni-Cr-Mo alloys investigated here, which assume face- or body-centered cubic structures, we propose a sigmoidal switching function fitted to the c/a ratio of “Bain-like” cells. With that, the model does an excellent job in describing the DFT-calculated alloy energies. We also show that the average atomic charge density can vary considerably as a function of composition, which can significantly modify alloy bond energies from simple expectation. The fitted bond energies can among others be used to determine phase diagrams, where we find excellent agreement with previous assessments in the solid range for Ni-Cr and Cr-Mo phase diagrams once the necessary entropy terms are added. They also allow quantitative, composition-dependent calculation of chemical potentials, which we use to determine vacancy formation energies in binary NiCr alloys for configurations that have been energy-minimized with Monte Carlo simulations. We show that the resulting regime of negative formation energies is a sign for thermodynamic instability of the underlying crystal and lies in the two-phase concentration range in the phase diagram, resulting in a holistic picture that unites defect and phase stability through the fully quantitative link between stoichiometry and chemical potentials enabled by the proposed bond energy model.

Transitions of lithium occupation in graphite: A physically informed model in the dilute lithium occupation limit supported by electrochemical and thermodynamic measurements

Understanding the role of the phase transitions during lithiation and delithiation of graphite remains a problem of fundamental importance, but also practical relevance owing to its widespread use as the anode material in most commercial lithium-ion cells. Previously performed density functional theory (DFT) calculations show a rapid change in the lithium-carbon interaction at low occupation, due to partial charge transfer from Li to C. We integrate this effect in our previously developed two level mean field model, which describes the Stage I – Stage II transition in graphite. The modified model additionally describes the most predominant transition that occurs at low Li content in graphite, which results in a previously unexplained feature in voltage and dQ/dV profiles, and thermodynamic measurements of partial molar enthalpy. In contrast with the Stage I-Stage II transition, this extra feature is not associated with observable features in the partial molar entropy and our model demonstrates why. There is a sharp change in the open circuit voltage at very low Li occupation, followed by a transition to a voltage plateau (peak in dQ/dV). The behaviour arises due to the contrasting effects of the partial molar entropy and enthalpy terms on the partial molar Gibbs energy and hence cell voltage. Hence the voltage profile and phase transitions can be approximated for all lithium occupations, potentially allowing a predictive capability in cell level models.

Water in protein hydration and ligand recognition.

This review describes selected basics of water in biomolecular recognition. We focus on a qualitative understanding of the most important physical aspects, how these change in magnitude between bulk water and protein environment, and how the roles that water plays for proteins arise from them. These roles include mechanical support, thermal coupling, dielectric screening, mass and charge transport, and the competition with a ligand for the occupation of a binding site. The presence or absence of water has ramifications that range from the thermodynamic binding signature of a single ligand up to cellular survival. The large inhomogeneity in water density, polarity and mobility around a solute is hard to assess in experiment. This is a source of many difficulties in the solvation of protein models and computational studies that attempt to elucidate or predict ligand recognition. The influence of water in a protein binding site on the experimental enthalpic and entropic signature of ligand binding is still a point of much debate. The strong water‐water interaction in enthalpic terms is counteracted by a water molecule's high mobility in entropic terms. The complete arrest of a water molecule's mobility sets a limit on the entropic contribution of a water displacement process, while the solvent environment sets limits on ligand reactivity.

A new activity model for Mg\u2013Al biotites determined through an integrated approach

A new activity model for Mg–Al biotites was formulated through an integrated approach combining various experimental results (calorimetry, line-broadening in infrared (IR) spectra, analysis of existing phase-equilibrium data) with density functional theory (DFT) calculations. The resulting model has a sound physical-experimental basis. It considers the three end-members phlogopite (Phl, KMg3[(OH)2AlSi3O10]), ordered eastonite (Eas, KMg2Al[(OH)2Al2Si2O10]), and disordered eastonite (dEas) and, thus, includes Mg–Al order–disorder. The DFT-derived disordering enthalpy, ΔHdis, associated with the disordering of Mg and Al on the M sites of Eas amounts to 34.5 ± 3 kJ/mol. Various biotite compositions along the Phl–Eas join were synthesised hydrothermally at 700 °C and 4 kbar. The most Al-rich biotite synthesized had the composition XEas = 0.77. The samples were characterised by X-ray diffraction (XRD), microprobe analysis and IR spectroscopy. The samples were studied further using relaxation calorimetry to measure their heat capacities (Cp) at temperatures from 2 to 300 K and by differential scanning calorimetry between 282 and 760 K. The calorimetric (vibrational) entropy of Phl at 298.15 K, determined from the low-T Cp measurements on a pure synthetic sample, is Scal = 319.4 ± 2.2 J/(mol K). The standard entropy, So, for Phl is 330.9 ± 2.2 J/(mol K), which is obtained by adding a configurational entropy term, Scfg, of 11.53 J/(mol K) due to tetrahedral Al-Si disorder. This value is ~1% larger than those in different data bases, which rely on older calorimetrical data measured on a natural near-Phl mica. Re-analysing phase-equilibrium data on Phl + quartz (Qz) stability with this new So, gives a standard enthalpy of formation of Phl, Delta H^{text{o}}_{text{f}} ,_{text{Phl}} = − 6209.83 ± 1.10 kJ/mol, which is 7–8 kJ/mol less negative than published values. The superambient Cp of Phl is given by the polynomial [J/(mol K)] as follows: C_{text{p}} = 667.37left( { pm 7} right) - 3914.50left( { pm 258} right) cdot T^{ - 0.5} - 1.52396left( { pm 0.15} right) times 10^{7} cdot T^{ - 2} + , 2.17269left( { pm 0.25} right) times 10^{9} cdot T^{ - 3}. Calorimetric entropies at 298.15 K vary linearly with composition along the Phl–Eas join, indicating ideal vibrational entropies of mixing in this binary. The linear extrapolation of these results to Eas composition gives So = 294.5 ± 3.0 J/(mol K) for this end-member. This value is in excellent agreement with its DFT-derived So, but ~ 8% smaller than values as appearing in thermodynamic data bases. The DFT-computed superambient Cp of Eas is given by the polynomial [in J/(mol K)] as follows: C_{text{p}} = 656.91left( { pm 14} right) - 3622.01left( { pm 503} right) cdot T^{ - 0.5} - 1.70983left( { pm 0.33} right) times 10^{7} cdot T^{ - 2} + , 2.31802left( { pm 0.59} right) times 10^{9} cdot T^{ - 3}. A maximum excess enthalpy of mixing, ΔHex, of ~6 kJ/mol was derived for the Phl–Eas binary using line-broadening from IR spectra (wavenumber region 400–600 cm−1), which is in accordance with ΔHex determined from published solution-calorimetry data. The mixing behaviour can be described by a symmetric interaction parameter W^{text{H}}_{{{text{Phl}},{text{Eas}}}} = 25.4 kJ/mol. Applying this value to published phase-equilibrium data that were undertaken to experimentally determine the Al-saturation level of biotite in the assemblage (Mg–Al)-biotite-sillimanite-sanidine-Qz, gives a Delta H^{text{o}}_{{{text{f}},{text{Eas}}}} = − 6358.5 ± 1.4 kJ/mol in good agreement with the independently DFT-derived value of {Delta H^{rm o}_{rm f,Eas}}^{rm DFT} = − 6360.5 kJ/mol. Application examples demonstrate the effect of the new activity model and thermodynamic standard state data, among others, on the stability of Mg–Al biotite + Qz.

The Learning of Fuzzy Cognitive Maps With Noisy Data: A Rapid and Robust Learning Method With Maximum Entropy.

Numerous learning methods for fuzzy cognitive maps (FCMs), such as the Hebbian-based and the population-based learning methods, have been developed for modeling and simulating dynamic systems. However, these methods are faced with several obvious limitations. Most of these models are extremely time consuming when learning the large-scale FCMs with hundreds of nodes. Furthermore, the FCMs learned by those algorithms lack robustness when the experimental data contain noise. In addition, reasonable distribution of the weights is rarely considered in these algorithms, which could result in the reduction of the performance of the resulting FCM. In this article, a straightforward, rapid, and robust learning method is proposed to learn FCMs from noisy data, especially, to learn large-scale FCMs. The crux of the proposed algorithm is to equivalently transform the learning problem of FCMs to a classic-constrained convex optimization problem in which the least-squares term ensures the robustness of the well-learned FCM and the maximum entropy term regularizes the distribution of the weights of the well-learned FCM. A series of experiments covering two frequently used activation functions (the sigmoid and hyperbolic tangent functions) are performed on both synthetic datasets with noise and real-world datasets. The experimental results show that the proposed method is rapid and robust against data containing noise and that the well-learned weights have better distribution. In addition, the FCMs learned by the proposed method also exhibit superior performance in comparison with the existing methods.

Maximum Entropy (Most Likely) Double Helical and Double Logarithmic Spiral Trajectories in Space-Time

The ubiquity of double helical and logarithmic spirals in nature is well observed, but no explanation is ever offered for their prevalence. DNA and the Milky Way galaxy are examples of such structures, whose geometric entropy we study using an information-theoretic (Shannon entropy) complex-vector analysis to calculate, respectively, the Gibbs free energy difference between B-DNA and P-DNA, and the galactic virial mass. Both of these analytic calculations (without any free parameters) are consistent with observation to within the experimental uncertainties. We define conjugate hyperbolic space and entropic momentum co-ordinates to describe these spiral structures in Minkowski space-time, enabling a consistent and holographic Hamiltonian-Lagrangian system that is completely isomorphic and complementary to that of conventional kinematics. Such double spirals therefore obey a maximum-entropy path-integral variational calculus (“the principle of least exertion”, entirely comparable to the principle of least action), thereby making them the most likely geometry (also with maximal structural stability) to be adopted by any such system in space-time. These simple analytical calculations are quantitative examples of the application of the Second Law of Thermodynamics as expressed in geometric entropy terms. They are underpinned by a comprehensive entropic action (“exertion”) principle based upon Boltzmann’s constant as the quantum of exertion.

A Note on the Entropy Force in Kinetic Theory and Black Holes.

The entropy force is the collective effect of inhomogeneity in disorder in a statistical many particle system. We demonstrate its presumable effect on one particular astrophysical object, the black hole. We then derive the kinetic equations of a large system of particles including the entropy force. It adds a collective therefore integral term to the Klimontovich equation for the evolution of the one-particle distribution function. Its integral character transforms the basic one particle kinetic equation into an integro-differential equation already on the elementary level, showing that not only the microscopic forces but the hole system reacts to its evolution of its probability distribution in a holistic way. It also causes a collisionless dissipative term which however is small in the inverse particle number and thus negligible. However it contributes an entropic collisional dissipation term. The latter is defined via the particle correlations but lacks any singularities and thus is large scale. It allows also for the derivation of a kinetic equation for the entropy density in phase space. This turns out to be of same structure as the equation for the phase space density. The entropy density determines itself holistically via the integral entropy force thus providing a self-controlled evolution of entropy in phase space.

Calculations of the relative populations of Lu@C82 isomers

Relative populations of five IPR (isolated-pentagon-rule) isomers of Lu@C82 are computed using the Gibbs energy based on characteristics from density functional theory calculations (B3LYP/6-31GSDD entropy term, B2PLYPD/6-31GSDD energetics). In agreement with observations, the major isomer has the cage.

On the Information Content of Coarse Data with Respect to the Particle Size Distribution of Complex Granular Media: Rationale Approach and Testing

The particle size distribution (PSD) of complex granular media is seen as a mathematical measure supported in the interval of grain sizes. A physical property characterizing granular products used in the Andreasen and Andersen model of 1930 is re-interpreted in Information Entropy terms leading to a differential information equation as a conceptual approach for the PSD. Under this approach, measured data which give a coarse description of the distribution may be seen as initial conditions for the proposed equation. A solution of the equation agrees with a selfsimilar measure directly postulated as a PSD model by Martín and Taguas almost 80 years later, thus both models appear to be linked. A variant of this last model, together with detailed soil PSD data of 70 soils are used to study the information content of limited experimental data formed by triplets and its ability in the PSD reconstruction. Results indicate that the information contained in certain soil triplets is sufficient to rebuild the whole PSD: for each soil sample tested there is always at least a triplet that contains enough information to simulate the whole distribution.

Erythromycin, Cethromycin and Solithromycin display similar binding affinities to the E. coli's ribosome: A molecular simulation study

Macrolide antibiotics bind to the exit tunnel of the ribosome and inhibit protein synthesis blocking its translocation. Thus, antibiotics including the known macrolide Erythromycin (ERY) are active against bacteria. However, at present, some bacteria show resistance to drugs, which requires the development of new powerful antibacterial agents. One possible way is to use the ERY structure, but change its side chains, while the size of the lactone ring can remain unchanged or change. In this work we consider Cethromycin (CET) and Solithromycin (SOL), which are ketolides with quinolylallyl group at C6 and aminophenyl at C11, respectively (both of them have the same lactone ring as ERY). Experiments have shown that these ketolides have improved efficacy against pathogens, but their binding affinity to the E. coli's ribosome is almost identical. To clarify this issue, we have studied in detail the binding mechanisms of ERY, CET and SOL using the docking and molecular dynamic simulations. In agreement with the experiments, we showed that these compounds have similar binding affinities. Desosamine and lactone ring groups play a critical role in the binding of ERY to the ribosome. In CET and SOL, the contribution of keto and alkylaryl groups is balanced by cyclic carbamate. We have demonstrated that increased fluctuations in the ribosomal residues at the binding site led to an increase in the entropic term in the free binding energy of ERY compared to SOL and CET. The alkyl-aryl arm of both ketolides strongly interacts with A752 and U2609. In addition, the presence of macrolides in the exit tunnel can alter the conformation of U2585, which is located in the peptidyl transferase center, through non-bonded interaction. Therefore, the side chain of ketolides affects not only the binding site but also other residues possibly leading to a strong effect on the protein synthesis process. We predict that to combat bacterial mutations, it is necessary either to design a bulk and charged group as a cladinose, or to use several groups with different signs of charges. This prediction can be used for the development of new efficient antibiotics.

Optimal reinsurance to minimize the discounted probability of ruin under ambiguity

We solve an optimal robust reinsurance problem for an ambiguity-averse insurer, who worries about ambiguity in the rate of claim occurrence and who develops an optimal robust reinsurance strategy to minimize the penalized discounted probability of ruin, in which we discount for the time of ruin. Specifically, we minimize the expectation of e−δτ1{τ<∞}, in which τ equals the time of ruin and δ measures the insurer’s time value. Moreover, we penalize this expectation with an entropic term that accounts for the insurer’s ambiguity concerning the claim rate.We suppose that the insurer is allowed to purchase per-claim reinsurance to transfer its risk exposure to a reinsurer. We derive the optimal robust reinsurance strategy and the corresponding value function by applying stochastic dynamic programming and by solving the corresponding boundary-value problem. We prove that, when the reinsurance premium is computed according to the mean–variance premium principle, the optimal robust reinsurance strategy is piecewise linear with respect to the claim size. Under the special case of the expected-value premium principle, excess-of-loss reinsurance is optimal, but under the special case of the variance premium principle, proportional reinsurance is not optimal due to the ambiguity. We also present and discuss two numerical examples to illustrate our results.

Thermodynamic study of aceclofenac solubility, distribution and sublimation

Equilibrium solubility of aceclofenac - a non-steroidal anti-inflammatory drug – has been measured using the shake-flask method between T = (293.15–313.15) K in four pharmaceutically important solvents: buffers (pH 2.0 and 7.4), 1-octanol and hexane. The activity coefficients at infinite dilution of the compound in each of the solvents and molar excess thermodynamic functions have been calculated. It has been established that the entropy term of the Gibbs energy makes the main contribution to the deviation from ideality in the studied drug – solvent systems. The saturated vapor pressures of aceclofenac have been measured in the temperature range T = (355.15–372.15) K, using the transpiration method and the sublimation enthalpy, at T = 298.15 K, has been found to be 102.7 kJ·mol−1. Based on the dissolution and sublimation data, the drug solvation enthalpies in the studied solvents have been obtained. The distribution coefficients of aceclofenac have been determined in the systems 1-octanol/buffer (pH 2.0 and 7.4) within the temperature range T = (293.15–313.15) K. The process of the drug distribution in the studied systems is characterized by favourable energy of transfer from the aqueous phase to the organic one and by positive values of transfer enthalpy and entropy. It has been found that the increase in the drug hydration in buffer solutions reduces the drug distribution coefficients.

All-atom molecular dynamics study on the non-solvent induced phase separation: Thermodynamics of adding water to poly(vinylidene fluoride)/N-methyl-2-pyrrolidone solution.

The change in the thermodynamics when adding water in poly(vinylidene fluoride) (PVDF)/N-methyl-2-pyrrolidone (NMP) solution is studied from all atom molecular dynamics (MD) simulations. This is done by estimating the free energy of mixing of PVDF/NMP solution with increasing volume fraction of water (ϕw) using an appropriately chosen thermodynamic cycle and the Bennett acceptance ratio method. The MD calculations predict the thermodynamic phase separation point of water/NMP/PVDF to be at ϕw = 0.08, in close agreement with the experimental cloud point measurement (ϕw = 0.05). Examining the enthalpic and entropic components of the free energy of mixing reveals that at low concentrations of water, the enthalpy term has the most significant contribution to the miscibility of the ternary system, whereas at higher concentrations of water, the entropy term dominates. Finally, the free energy of mixing was compared with the Flory-Huggins (FH) free energy of mixing by computing the concentration-dependent interaction parameters from MD simulations. The FH model inadequately predicted the miscibility of the PVDF solution, mainly due to its negligence of the excess entropy of mixing.

Combo loss: Handling input and output imbalance in multi-organ segmentation

Simultaneous segmentation of multiple organs from different medical imaging modalities is a crucial task as it can be utilized for computer-aided diagnosis, computer-assisted surgery, and therapy planning. Thanks to the recent advances in deep learning, several deep neural networks for medical image segmentation have been introduced successfully for this purpose. In this paper, we focus on learning a deep multi-organ segmentation network that labels voxels. In particular, we examine the critical choice of a loss function in order to handle the notorious imbalance problem that plagues both the input and output of a learning model. The input imbalance refers to the class-imbalance in the input training samples (i.e., small foreground objects embedded in an abundance of background voxels, as well as organs of varying sizes). The output imbalance refers to the imbalance between the false positives and false negatives of the inference model. In order to tackle both types of imbalance during training and inference, we introduce a new curriculum learning based loss function. Specifically, we leverage Dice similarity coefficient to deter model parameters from being held at bad local minima and at the same time gradually learn better model parameters by penalizing for false positives/negatives using a cross entropy term. We evaluated the proposed loss function on three datasets: whole body positron emission tomography (PET) scans with 5 target organs, magnetic resonance imaging (MRI) prostate scans, and ultrasound echocardigraphy images with a single target organ i.e., left ventricular. We show that a simple network architecture with the proposed integrative loss function can outperform state-of-the-art methods and results of the competing methods can be improved when our proposed loss is used.

Tikhonov-type regularization and the finite element method applied to point source estimation in the atmosphere

This work is concerned with the source identification problem in air pollution modeling. The forward problem is described by an advection-diffusion equation with physically realistic coefficients. It is solved by the combination of adaptive meshes and a stabilized finite element method. The source is estimated by Tikhonov-type regularization with a composite misfit function and an entropic penalty term. The composite misfit is given by the convex combination of ℓ1 and ℓ2 norms of the discrepancy between observed and predicted concentrations. Morozov's discrepancy principle is applied to simultaneously choose the regularization and the misfit combination parameters. Numerical experiments using Copenhagen field data is used to validate numerically the proposed methodology.

Interaction of aloe active compounds with calf thymus DNA.

Natural anthraquinone compounds have emerged as potent anticancer chemotherapeutic agents because of their promising DNA-binding properties. Aloe vera is among one of the very well-known medicinal plants, and the anthraquinone derivatives like aloe emodin (ALM), aloins (ALN), and aloe emodin-8-glucoside (ALMG) are known to have immense biological activities. Here, we have used biophysical methods to elucidate the comparative DNA-binding abilities of these three molecules. Steady-state fluorescence study indicated complexation between calf thymus DNA (ctDNA) and both the molecules ALM and ALMG whereas ALN showed very weak interaction with DNA. Displacement assays with ctDNA-bound intercalator (ethidium bromide) and a groove binder (Hoechst 33258) indicated preferential binding of both ALM and ALMG to minor groove of DNA. Isothermal titration calorimetric (ITC) data suggested spontaneous exothermic single binding mode of both the molecules: ALM and ALMG. Entropy is the most important factor which contributed to the standard molar Gibbs energy associated with relatively small favorable enthalpic contribution. The equilibrium constants of binding to ctDNA were (6.02±0.10)×104 M-1 and (4.90±0.11)×104 M-1 at 298.15K, for ALM and ALMG, respectively. The enthalpy vs temperature plot yielded negative standard molar heat capacity value, and a strong negative correlation between enthalpy and entropy terms was observed which indicates the enthalpy entropy compensation behavior in both systems. All these thermodynamic phenomena indicate that hydrophobic force is the key factor which is involved in the binding process. Moreover, the enhancement of thermal stability of DNA helix by ALM and ALMG fully agreed to the complexation of these molecules with DNA.

Engineering Order and Cooperativity in a Disordered Protein.

Structural disorder in proteins arises from a complex interplay between weak hydrophobicity and unfavorable electrostatic interactions. The extent to which the hydrophobic effect contributes to the unique and compact native state of proteins is, however, confounded by large compensation between multiple entropic and energetic terms. Here we show that protein structural order and cooperativity arise as emergent properties upon hydrophobic substitutions in a disordered system with non-intuitive effects on folding and function. Aided by sequence-structure analysis, equilibrium, and kinetic spectroscopic studies, we engineer two hydrophobic mutations in the disordered DNA-binding domain of CytR that act synergistically, but not in isolation, to promote structure, compactness, and stability. The double mutant, with properties of a fully ordered domain, exhibits weak cooperativity with a complex and rugged conformational landscape. The mutant, however, binds cognate DNA with an affinity only marginally higher than that of the wild type, though nontrivial differences are observed in the binding to noncognate DNA. Our work provides direct experimental evidence of the dominant role of non-additive hydrophobic effects in shaping the molecular evolution of order in disordered proteins and vice versa, which could be generalized to even folded proteins with implications for protein design and functional manipulation.

Calculated relative populations for the Eu@C82 isomers

Abstract Relative populations of four IPR (isolated-pentagon-rule) isomers of Eu@C82 are computed using the Gibbs energy based on characteristics from density functional theory calculations (M06-2X/6-31G∗∼SDD entropy term, M06-2X/6-31+G∗∼SDD or B2PLYPD/6-31G∗∼SDD energetics). Only the species observed by now also show significant calculated populations. A role of solubility in different solvents and/or composition of the arc electrodes could explain variability in the observed populations.

Application of trihexyltetradecylphosphonium dicyanamide ionic liquid for various types of separations problems: Activity coefficients at infinite dilution measurements utilizing GLC method

In this work, the ionic liquid trihexyltetradecylphosphonium dicyanamide [P 6 6 6 14] [DCA] was evaluated as a potential extraction solvent for organic compounds. The assessment was done based on the solute retention data obtained by gas liquid chromatography (GLC) for 33 solutes: (alkanes, alkenes, ketones, alcohols, alkynes, aromatic hydrocarbons, tetrahydrofuran, thiophene, acetonitrile and water). The experiment was conducted at a series of four temperatures (313.15–343.15) K at 10 K intervals. Experimental activity coefficients at infinite dilution data acquired over the investigated temperature range was then utilized to compute the thermodynamic functions at infinite dilution including partial molar excess enthalpy, ΔH1E,∞, Gibbs free energy, ΔG1E,∞ and entropy term, TrefΔS1E,∞. The selectivity and capacity values for some of the separation challenges (heptane/thiophene, water/butanol and heptane/benzene) were computed from the γ13∞ data and in contrast to the other phosphonium based ionic liquids in the literature. The selectivity and capacity data shows that the investigated ionic liquid can be utilized in the separation of heptane/thiophene or water/butan-1-ol mixtures.

Moving Molecules in Crystalline Solids: Gradual Structure Transition and Spin Transition/Crossover

Magnetic switches working in solid states are of recent interest for applications to sensor, memory, etc. The author and co-workers have developed various unconventional spin transition/crossover materials. The first example is a supramolecular chemistry consisting of genuine organic nitroxide biradicals with a triplet ground state. Each nitroxide group is located close to each other to form weak covalent bonds in an intermolecular fashion. Biradicals are polymerized/depolymerized stepwise. The second example belongs to 3d-2p heterospin systems where the nitroxide oxygen atom is directly bonded to a nickel(II) or copper(II) ion. The planar/nonplanar chelate structure changes, accompanied by high-/low-spin transition due to a 3d-2p exchange-coupling switch. A novel entropy-driven spin crossover scenario has been established. The third example is a 3d iron(II) spin crossover material carrying a stearyl (C18) group. An order-disorder-type structural transition appears with respect to the alkyl conformation. As these examples show, single-crystal-to-single-crystal structural transitions are often observed. It is because the spin entropy term regulates the atomic dislocation enthalpy, and the entropy change due to the spin multiplicity is basically small. These molecular motions clarified by means of detailed crystallography afford one of the most convincing evidence for the spin transition phenomenon.