The ionic isomegethic rule and additivity relationships: estimation of ion volumes. A route to the energetics and entropics of new, traditional, hypothetical, and counterintuitive ionic materials

By virtue of our recently established relationships, knowledge of the formula unit volume, V(m), of a solid ionic material permits estimation of thermodynamic properties such as standard entropy, lattice potential energy, and, hence, enthalpy and Gibbs energy changes for reactions. Accordingly, development of an approach to obtain currently unavailable ion volumes can expose compounds containing these ions to thermodynamic scrutiny, such as predictions regarding stability and synthesis. The isomegethic rule, introduced in this paper, states that the formula unit volumes, V(m), of isomeric ionic salts are approximately the same; this rule then forms the basis for a powerful and successful means of predicting unknown ion volumes (as well as providing a means of validating existing volume and density data) and, thereby, providing solid state thermodynamic data. The rule is exploited to generate unknown ion and (by additivity) corresponding formula unit volumes.     

Internally consistent ion volumes and their application in volume-based thermodynamics

"Volume-based thermodynamics" (VBT) relates the thermodynamics of condensed-phase materials to their formula unit (or molecular) volumes, V(m). In order to secure the most accurate representation of these data, the volumes used are to be derived (in order of preference) from crystal structure data or from density or, in the absence of experimental data, estimated by ion-volume summation.     

New Atom/Functional Group Volume Additivity Data Bases for the Calculation of the Crystal Densities of C-, H-, N-, O-, F-, S-, P-, Cl-, and Br-Containing Compounds

The solid-state density of an energetic material is one of the most important parameters related to performance. With crystal structure data from the Cambridge Structural Database, four new additivity data bases have been determined to provide atom and functional group volumes or densities for the calculation of solid-state densities of organic compounds with the elements C, H, N, O, F, P, S, Cl, and Br. Volumes and densities for 96 atoms/groups were determined from approximately 26,000 crystal structure data. Sets of linear volumes (from observed unit cell volume per molecule data) and nonlinear volumes and linear densities (from observed crystal densities) were determined. The concept of an atom code was also introduced to allow the atoms and their connections to define the types of atoms present in a molecule. This approach lead to 1601 atom codes. With more than 2000 crystal structure data that were not used in the initial parameterizations, average percentage differences between the observed volumes/densities and calculated values ranged from 1.8–2.3%.     

The nature of interactions in the ionic crystal of 3-pentenenitrile, 2-nitro-5-oxo, ion(-1), sodium

The hybrid variation -- perturbation many-body interaction energy decomposition scheme has been applied to analyze the physical nature of interactions in the ionic 3-pentenenitrile, 2-nitro-5-oxo, ion(-1), sodium crystal, which can be regarded as a model for a large group of aromatic quaternary nitrogen salts. In the crystal structure the sodium ions and water molecules of adjacent unit cells form a positively charged "inorganic layer" with the sodium ions clustered together along the ab faces with the organic (negative) part in between. This puzzling crystal packing is due to a strong favorable interaction between the water molecule and the sodium ions and a substantial charge transfer from the carbanions that balances out the destabilizing sodium-sodium ion repulsion. Although the majority of cohesion energy of the crystal structure comes from the electrostatic interactions of ions, the resulting net stabilization also depends heavily on the nonadditive delocalization components, due to a counterbalance between the two-body delocalization and exchange effects. The estimated nonadditivity of interactions varies between 12% and 22%.     

Predictive thermodynamics for condensed phases

Thermodynamic information is central to assessment of the stability and reactivity of materials. However, because of both the demanding nature of experimental thermodynamics and the virtually unlimited number of conceivable compounds, experimental data is often unavailable or, for hypothetical materials, necessarily impossible to obtain. We describe simple procedures for thermodynamic prediction for condensed phases, both ionic and organic covalent, principally via formula unit volumes (or density); our volume-based approach (VBT) provides a new thermodynamic tool for such assessment. These methods, being independent of detailed knowledge of crystal structures, are applicable to liquids and amorphous materials as well as to crystalline solids. Examples of their use are provided.     

Thermodynamic clarification of the curious ferric/potassium ion exchange accompanying the electrochromic redox reactions of prussian blue, iron(III) hexacyanoferrate(II)

The recent Glasser-Jenkins method for lattice-energy prediction, applied to an examination of the solid-state thermodynamics of the cation exchanges that occur in electrochromic reactions of Prussian Blue, provides incisive thermodynamic clarification of an ill-understood ion exchange that accompanies particularly the early electrochromic cycles. A volume of 0.246 +/- 0.017 nm(3) formula unit(-1) for the ferrocyanide ion, Fe(II)[(CN)(6)],(4-) is first established and then used, together with other formula unit-volume data, to evaluate the changes of standard enthalpy, entropy, and Gibbs energy in those ion-exchange reactions. The results impressively show by how much the exchange of interstitial Fe(3+) ions by alkali metal ions, usually exemplified by K+, is thermodynamically favored.     

Measurement of the change in partial molar volume during electrode reaction by gravity electrode—II. Examination of the accuracy of the measurement

The reliability of the measurement of the change in partial molar volume between product and reactant ions measured by gravity electrode (GE) was examined by the thermodynamic measurement of pycnometer (PM). Since the PM method requires an experimental equation of the apparent molar volume to calculate the partial molar volumes of the individual ions, the most suitable experimental equation must be first determined. As a test reaction for the experiment, oxidation of ferrocyanide (FERO) ion to ferricyanide (FERI) ion was adopted. After fitting several experimental equations to the data of the apparent molar volumes by the PM method, the calculated changes in the partial molar volume were compared with the data of the GM method. Then, it is concluded that the polynomial with a degree of 3 of the logarithm of the molality of the FERO ion suggests the most suitable equation. As a result, the reliability of the GE method was also experimentally validated.     

Complex phosphorus thermochemistry. Volume-based thermodynamics and the estimation of standard enthalpies of formation of gas phase ions: Delta(f)H(o) (PCl4+, g) and Delta(f)H(o) (PCl6-, g)

Energy-resolved collision-induced dissociation in a flowing afterglow-guided ion beam tandem mass spectrometer has recently enabled the accurate determination of the standard enthalpy of formation of the gaseous phosphorus pentachloride cation, Delta(f)H(o) ([PCl4(+)], g), found to be 414 +/- 17 kJ mol(-1) (giving a value of 378 +/- 18 kJ mol(-1) at 0 K). Such experimental values for the standard enthalpy of formation of gas phase complex are now being incorporated into the NIST standard reference data program. Such results, can, inter alia, provide a benchmark by which to test earlier computationally based methods which were made to estimate such quantities in the absence of any experimental data. The establishment of this value experimentally also affords us with the opportunity to explore the likely success of newer, simpler approaches. Previous large-scale direct minimization computations to estimate this (and other) standard enthalpies of formation match very well these new experimental results. This paper raises the question as to whether the much simpler volume-based thermodynamics (VBT) approach could yield equally satisfactory results and so circumvent, completely, the need for detailed modeling of the lattices involved. The conclusion is that the VBT approach portrays the extremely complex thermodynamics quite adequately. Thus for the purposes of obtaining basic thermodynamic data, complex modeling of the underlying structures involved may no longer be necessary. At least this should be the case for highly symmetrical ions, like PCl4(+), where detailed packing with counterions is possibly less important than in other cases and where covalent interactions (less easily modeled) with neighboring ions is unlikely to be strongly featured. Other gaseous complex ion enthalpies of formation are also predicted here.     

Ni离子掺杂锐钛矿相TiO2体系的第一性原理研究

采用自旋密度泛函理论的第一性原理方法并结合晶体配位场理论,研究了Ni离子掺杂锐钛矿相TiO₂体系（Ni_xTi_1-xO₂;Ni_xTiO₂）的几何结构、缺陷形成能、电子结构以及磁性特征等问题。结果表明：实验上发现的有关Ni掺杂TiO₂体系的很多矛盾,如：晶粒体积的增减、掺杂Ni离子的不同价态、吸收光谱带边移动方向和体系磁性特征的差异等问题都可归因于Ni离子掺杂类型的不同（Ni_Ti;Ni_in）。分析表明,不同的Ni离子掺杂类型导致所成Ni-O键的键长和电荷布居不同,从而使Ni离子呈现不同的价态,这也是体系宏观电学和磁学性能差异的根本原因。形成能计算表明,通过控制Ni-TiO₂晶体生长过程中的氧环境,可以人为的控制Ni离子的掺杂类型。     

Electrostriction, ion solvation, and solvent release on ion pairing

The theoretical mean molar electrostriction volume of electrolytic solvents, DeltaVel(solvent), was calculated from their properties: the relative pressure derivatives of the density (the compressibility) and permittivity and their second pressure derivatives. The molar electrostriction caused by ions at infinite dilution was taken as the differences of their standard partial molar volumes in the solution and their intrinsic volumes: DeltaVel(ion) = Vinfinity(ion) - Vin(ion). The ratio ninfinity = DeltaVel(ion)/DeltaVel(solvent) then represents the solvation number of the ion in the solvent at infinite dilution. Similarly, from the molar volume change on ion pair formation, DeltaVip, the ratio Deltanip = DeltaVip/DeltaVel(solvent) represents the number of solvent molecules released thereby. These values were tabulated for those solvents, ions, and ion pairs for which the relevant information could be found, the extension to nonaqueous solvents not having been attempted previously.     

Ni离子掺杂锐钛矿相TiO_2体系的第一性原理研究

采用自旋密度泛函理论的第一性原理方法并结合晶体配位场理论,研究了Ni离子掺杂锐钛矿相TiO_2体系(NixTi1-xO2;NixTiO_2)的几何结构、缺陷形成能、电子结构以及磁性特征等问题。结果表明:实验上发现的有关Ni掺杂TiO_2体系的很多矛盾,如:晶粒体积的增减、掺杂Ni离子的不同价态、吸收光谱带边移动方向和体系磁性特征的差异等问题都可归因于Ni离子掺杂类型的不同(NiTi;Niin)。分析表明,不同的Ni离子掺杂类型导致所成Ni-O键的键长和电荷布居不同,从而使Ni离子呈现不同的价态,这也是体系宏观电学和磁学性能差异的根本原因。形成能计算表明,通过控制Ni-TiO_2晶体生长过程中的氧环境,可以人为的控制Ni离子的掺杂类型。     

Effect of dead volume on performance of simulated moving bed process

The volume of surrounding equipments (pipe transfer lines and valves) in the simulated moving bed (SMB) unit, which is called the dead volume, is modeled as bed-head, bed-tail and bed-line. Since the dead volume can be significant especially in industrial-scale SMB units, the consideration of dead volume has been required for high performance operation. In this study, a simple and unified approach based on the method of characteristics (MOC), called the extended node model, is established to solve fluid concentration dynamics within dead volumes. The computational efficiency of the approach is evaluated for three case studies of a standard four-zone SMB process with a linear adsorption equilibrium model. Insertion of one zone to flush the fluid trapped in extract bed-line into the standard four-zone SMB improves substantially purity, while recovery is kept constant.     

Volume-based thermodynamics: estimations for 2:2 salts

The lattice energy of an ionic crystal, U(POT), can be expressed as a linear function of the inverse cube root of its formula unit volume (i.e., Vm(-1/3)); thus, U(POT) approximately 2I(alpha/Vm(1/3) + beta), where alpha and beta are fitted constants and I is the readily calculated ionic strength factor of the lattice. The standard entropy, S, is a linear function of Vm itself: S approximately kVm + c, with fitted constants k and c. The constants alpha and beta have previously been evaluated for salts with charge ratios of 1:1, 1:2, and 2:1 and for the general case q:p, while values of k and c applicable to ionic solids generally have earlier been reported. In this paper, we obtain alpha and beta, k and c, specifically for 2:2 salts (by studying the ionic oxides, sulfates, and carbonates), finding that U(POT)[MX 2:2]/(kJ mol(-1)) approximately 8(119/Vm(1/3) + 60) and S degree [MX 2:2]/(J K(-1) mol(-1)) approximately 1382V(m) + 16.     

Accurate thermochemical properties for energetic materials applications. II. Heats of formation of imidazolium-, 1,2,4-triazolium-, and tetrazolium-based energetic salts from isodesmic and lattice energy calculations

A computational approach to the prediction of the heats of formation (DeltaH(f)degrees' s of solid-state energetic salts from electronic structure and volume-based thermodynamics (VBT) calculations is described. The method uses as its starting point reliable DeltaH(f)degrees' s for energetic precursor molecules and ions. The DeltaH(f)degrees' s of more complex energetics species such as substituted imidazole, 1,2,4-triazole, and tetrazole molecules and ions containing amino, azido, and nitro (including methyl) substituents are calculated using an isodesmic approach at the MP2/complete basis set level. On the basis of comparisons to experimental data for neutral analogues, this isodesmic approach is accurate to <3 kcal/mol for the predicted cation and anion DeltaH(f)degrees' s. The DeltaH(f)degrees' s of the energetic salts in the solid state are derived from lattice energy (U(L)) calculations using a VBT approach. Improved values for the alpha and beta parameters of 19.9 (kcal nm)/mol and 37.6 kcal/mol for the U(L) equation were obtained on the basis of comparisons to experimental U(L)' s for a series of 23 salts containing ammonium, alkylammonium, and hydrazinium cations. The total volumes are adjusted to account for differences between predicted and experimental total volumes due to different shapes of the ions (flat vs spherical). The predicted DeltaH(f)degrees' s of the energetic salts are estimated to have error bars of 6-7 kcal/mol, on the basis of comparisons to established experimental DeltaH(f)degrees' s of a subset of the salts studied. Energetic salts with the highest positive DeltaH(f)degrees' s are predicted for azido-containing cations, coupled with heterocyclic anions containing nitro substituents. The substitution of functional groups on carbon versus nitrogen atoms of the heterocyclic cations has interesting stabilization and destabilization effects, respectively.     

Conductance of a cobalt(II) terpyridine complex based molecular transistor: a computational analysis

A recent experiment, in which a molecular transistor based on the coordination chemistry of cobalt(II) and organic self-assembled monolayers is formed by means of self-aligned lithography,2 is analyzed with a computational approach. The calculations reveal that a complex involving two cobalt(II) ions bridged by acetate ions can effectively span the nanogap. This bridged complex is shown to be both more flexible and more conductive than the alternative structure involving a single cobalt(II) ion. The single cobalt(II) ion complex is the more stable structure in a nonconfined environment (i.e., in solution) but is found to be less effective at connecting the leads of the fabricated gap and is less likely to result in a conductive device.     

Quantum Mechanical/Molecular Mechanical Study of the HDV Ribozyme: Impact of the Catalytic Metal Ion on the Mechanism

A recent crystal structure of the precleaved HDV ribozyme along with biochemical data support a mechanism for phosphodiester bond self-cleavage in which C75 acts as a general acid and bound Mg(2+) ion acts as a Lewis acid. Herein this precleaved crystal structure is used as the basis for quantum mechanical/molecular mechanical calculations. These calculations indicate that the self-cleavage reaction is concerted with a phosphorane-like transition state when a divalent ion, Mg(2+) or Ca(2+), is bound at the catalytic site but is sequential with a phosphorane intermediate when a monovalent ion, such as Na(+), is at this site. Electrostatic potential calculations suggest that the divalent metal ion at the catalytic site lowers the pK(a) of C75, leading to the concerted mechanism in which the proton is partially transferred to the leaving group in the phosphorane-like transition state. These observations are consistent with experimental data, including pK(a) measurements, reaction kinetics, and proton inventories with divalent and monovalent ions.     

From synthetic montroseite VOOH to topochemical paramontroseite VO2 and their applications in aqueous lithium ion batteries

Synthetic montroseite VOOH has been successfully prepared via a simple template-free hydrothermal route on a large scale for the first time-after sixty years of delay. The as-obtained sample shows a hierarchical morphology of urchin-like nanoarchitecture with hollow interiors consisting of well-crystalline nanorods standing vertically on the shell surface. Time-dependent experiments illustrated that these hierarchical hollow nanourchins were formed through the hydrolysis-driven Kirkendall effect coupled with a new-phased vanadium oxyhydroxide V(10)O(14)(OH)(2) precursor templated approach. Meanwhile, the as-obtained VOOH hollow nanourchins could convert topochemically to paramontroseite VO(2) without altering the size and original appearance during the annealing process due to the extreme structural similarity revealed by crystal structure analysis. Furthermore, the improved electrochemical performance of both montroseite VOOH and paramontroseite VO(2) hierarchical hollow structures toward Li uptake and release verifies their potential applications as anode materials in aqueous lithium ion batteries. These improved electrochemical properties could be ascribed to the synergetic effect of the microscopic tunneled crystal structure and macroscopic hollow morphological features, which provide the easy infiltration of electrolyte, short diffusion lengths for lithium ions and electron transport as well as sufficient void space to buffer the volume change.     

Ion-water clusters, bulk medium effects, and ion hydration

Thermochemistry of gas-phase ion-water clusters together with estimates of the hydration free energy of the clusters and the water ligands are used to calculate the hydration free energy of the ion. Often the hydration calculations use a continuum model of the solvent. The primitive quasichemical approximation to the quasichemical theory provides a transparent framework to anchor such efforts. Here we evaluate the approximations inherent in the primitive quasichemical approach and elucidate the different roles of the bulk medium. We find that the bulk medium can stabilize configurations of the cluster that are usually not observed in the gas phase, while also simultaneously lowering the excess chemical potential of the ion. This effect is more pronounced for soft ions. Since the coordination number that minimizes the excess chemical potential of the ion is identified as the optimal or most probable coordination number, for such soft ions the optimum cluster size and the hydration thermodynamics obtained with and without account of the bulk medium on the ion-water clustering reaction can be different. The ideas presented in this work are expected to be relevant to experimental studies that translate thermochemistry of ion-water clusters to the thermodynamics of the hydrated ion and to evolving theoretical approaches that combine high-level calculations on clusters with coarse-grained models of the medium.