Lattice Energy and Free Energy Minimization Techniques

Watson, GW; Tschaufeser, Petra; Wall, A.; Jackson, R. A.; Parker, Stephen C.

doi:10.1016/b978-012164135-1/50004-6

Cited by 15 publications

(4 citation statements)

References 37 publications

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“…In the latter simulation the net charge was neutralized by a uniform background charge . In addition, the energy was corrected for the polaron-polaron Coulombic interactions due to the periodic boundary conditions using the approach described by Watson et al and implemented in the computer code PARAPOCS . The polaron formation energy was calculated for both rutile ( E f R ) and anatase ( E f A ), and the difference between the rutile and anatase polaron formation energies (Δ E f = E f R − E f A ) was compared with that obtained from the DFT calculations for both the electron and hole polarons (Table ).…”

Section: Resultsmentioning

confidence: 99%

A Shell Model for Atomistic Simulation of Charge Transfer in Titania

et al. 2008

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The derivation of atomistic potential parameters, based on electronic structure calculations, for modeling electron and hole polarons in titania polymorphs is presented. The potential model is a polarizable version of the Matsui and Akaogi model (Matsui, M.; Akaogi, M. Mol. Simul. 1991, 6, 239) that makes use of a shell model to account for the polarizability of oxygen ions. The −1 and +1 formal charges of the electron and hole polarons, respectively, are modeled by delocalizing the polaron’s charge over a titanium or oxygen ion, respectively, and its first nearest-neighbors. The charge distributions and the oxygen polarizability were fitted to the reorganization energies of a series of electron and hole polaron transfers in rutile and anatase obtained from electronic structure calculations at zero Kelvin and validated against lattice deformation due to both types of polaron. Good agreement was achieved for both properties. In addition, the potential model yields an accurate representation of a range of bulk properties of several TiO2 polymorphs as well as Ti2O3. The model thus derived enables us to consider systems large enough to investigate how the charge transfer properties at titania surfaces and interfaces differ from those in the bulk. For example, reorganization energies and free energies of charge transfer were computed as a function of depth below vacuum-terminated rutile (110) and anatase (001) surfaces using a mapping approach first introduced by Warshel (Warshel, A. J. Phys. Chem. 1982, 86, 2218). These calculations indicate that deviations from bulk values at the surface are substantial but limited to the first couple of surface atomic layers and that polarons are generally repelled from the surface. Moreover, attractive subsurface sites may be found as is predicted for hole polarons at the rutile (110) surface. Finally, several charge transfers from under-coordinated surface sites were found to be in the so-called Marcus inverted-region.

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Section: Resultsmentioning

confidence: 99%

A Shell Model for Atomistic Simulation of Charge Transfer in Titania

et al. 2008

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“…Atomistic scale simulations used in the current study employ the Born model, where the ionic interactions are divided into long-range Coulombic forces and short-range forces representing electron–electron repulsion and van der Waals interactions . Short range interactions were modeled using a two body Buckingham potential.…”

Section: Methodsmentioning

confidence: 99%

Synthesis, Structure, and Na-Ion Migration in Na₄NiP₂O₇F₂: A Prospective High Voltage Positive Electrode Material for the Na-Ion Battery

et al. 2015

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In the recent hunt for novel Na-ion cathode hosts, a variety of sodium analogues of classic Li-ion structures have been thoroughly explored. However, Na-ion analogues generally possess modified structures and dissimilar Na-ion energetics compared to their Li-ion analogues due to the large size of Na + (102 pm) vs Li + (76 pm), often resulting in sluggish Na + kinetics. Materials development targeted toward new and different specific host structures possessing optimum properties for Na-ion migration is crucial. Here, we report the first sodium metal fluoropyrophosphate Na-ion host with a three-dimensional frameworkNa 4 NiP 2 O 7 F 2 which is predicted to have a high voltage (∼5 V) based on its Ni 2+/3+/4+ redox couple and composition. Structure solution from single crystal diffraction data combined with atomistic simulation computation suggests the presence of low activation energy Na-ion migration pathways (<0.6 eV) in all three dimensions. The particularly low barrier of 0.36 eV calculated for migration along the [010] direction is in full accord with temperature dependent ionic conductivity measurements that yield an experimental value of 0.32 eV. Spacious Na-ion pathways endow the material with good ionic conductivity as determined by ac impedance spectroscopy, and facile exchange of three Na + ions for Li + is observed at slightly elevated temperatures. Furthermore, the polycrystalline material exhibits excellent thermal stability under ambient atmosphere up to 600 °C, crucial for the safe operation of a Na-ion battery.

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“…Madelung constants provide a measure for the lattice energy of inorganic crystalline solids, and they play a central role in their description . The electrostatic interactions of extended lattice structures also are becoming more fully understood, and this knowledge is now being exploited in the design of inorganic films .…”

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confidence: 99%

Crystal Potential Formula for the Calculation of Crystal Lattice Sums

1998

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A new formula is derived for the determination of the potential energy of the central unit cell of a finite crystal; this formula is called the crystal potential formula. The crystal potential formula is based on a twocenter Cartesian multipole expansion. The key feature of the crystal potential formula is that it achieves a separation of the lattice geometry and multipole moments. This feature allows one to compute in a highly effective way the crystal energies as a function of the molecules contained in the unit cell. Numerical implementation is discussed, and a numerical example is given. The example mimics an organic crystal composed of dipolar molecules. It is found that the crystal environment may create local minima and that the effects of the environment might be well-approximated by consideration of the proximate unit cells only. Both of these effects have important implications for the crystal engineering of molecular organic materials.

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Lattice Energy and Free Energy Minimization Techniques

Cited by 15 publications

References 37 publications

A Shell Model for Atomistic Simulation of Charge Transfer in Titania

A Shell Model for Atomistic Simulation of Charge Transfer in Titania

Synthesis, Structure, and Na-Ion Migration in Na₄NiP₂O₇F₂: A Prospective High Voltage Positive Electrode Material for the Na-Ion Battery

Crystal Potential Formula for the Calculation of Crystal Lattice Sums

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Lattice Energy and Free Energy Minimization Techniques

Cited by 15 publications

References 37 publications

A Shell Model for Atomistic Simulation of Charge Transfer in Titania

A Shell Model for Atomistic Simulation of Charge Transfer in Titania

Synthesis, Structure, and Na-Ion Migration in Na4NiP2O7F2: A Prospective High Voltage Positive Electrode Material for the Na-Ion Battery

Crystal Potential Formula for the Calculation of Crystal Lattice Sums

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Synthesis, Structure, and Na-Ion Migration in Na₄NiP₂O₇F₂: A Prospective High Voltage Positive Electrode Material for the Na-Ion Battery