Ab Initio Perturbed Ion Method Research Articles

Compressibility of the high-pressure rocksalt phase of ZnO

We report the results of a combined experimental and theoretical investigation on the stability and the volume behavior under hydrostatic pressure of the rocksalt $(B1)$ phase of ZnO. Synchrotron-radiation x-ray powder-diffraction data are obtained from 0 to 30 GPa. Static simulations of the $\mathrm{ZnO} B1$ phase are performed using the ab initio perturbed ion method and the local and nonlocal approximations to the density-functional theory. After the pressure induced transition from the wurtzite phase, we have found that a large fraction of the $B1$ high-pressure phase is retained when pressure is released. The metastability of this ZnO polymorph is confirmed through the theoretical evaluation of the Hessian eigenvalues of a nine-parameter potential energy surface. This allows us to treat the experimental and theoretical pressure-volume data on an equal basis. In both cases, we have obtained values of the bulk modulus in the range of 160--194 GPa. For its zero-pressure first derivative, the experimental and theoretical data yield a value of $4.4\ifmmode\pm\else\textpm\fi{}1.0.$ Overall, our results show that the $\mathrm{ZnO} B1$ phase is slightly more compressible than previously reported.

Ab initio perturbed ion description of the equation of state and a high pressure phase transition of Al 2O 3

The electronic structure, equilibrium geometry, and equation of state of Al 2O 3 in the α — Al 2O 3 and Rh 2O 3(II) phases have been determined by means of the ab initio perturbed ion method augmented by a recently developed non-empirical Debye-like model for describing the vibrational thermal effects. A systematic multidimensional optimization of the structural parameters has been completed for the two phases from zero to 2200 K, and pressures up to 70 GPa for the α — Al 2O 3 phase, and 20 GPa for the high pressure phase. Our structural results are in good agreement with the experimental information available. Although the α — Al 2O 3 phase is more stable in the static ( p = T = 0) description, a pressure-induced phase transition is detected at room temperature near 4 GPa. The critical pressure p c increases very slightly with temperature, being about 5.5 GPa at 1000 K. This value is consistent with the phase transition found in Rh 2O 3 by Shannon and Prewitt [ Journal of Solid State Chemistry 2, (1970) 134] at p c 6.5 GPa. Furthermore, the α — Al 2O 3 phase shows a slight pressure-induced anisotropy, since the c a ratio decreases from 2.638, at zero pressure, to 2.474 at 70 GPa. Also, according to our calculations, the crystal maintains its symmetry and reduces moderately its compressibility in the high temperature regime. The present methodology gives detailed structural information on phase transitions of the type described in this work, as well as a meaningful description of the high pressure phase, a task rather difficult to undertake in the laboratory.

Theoretical study of lattice stability and selective doping effects of V 4+ and Tb 4+ in the ZrGeO 4 lattice

A theoretical study on lattice stability and local geometry distortions produced by the presence of V 4+ and Tb 4+ ions in a ZrGeO 4 lattice has been carried out by means of the ab initio perturbed ion method. Slater type orbitals for representing atomic centers and large clusters ranging from 122 to 135 atoms have been used. The energy required to substitute Zr 4+ or Ge 4+ for V 4+ is similar in spite of the negative defect reaction energy calculated for V 4+ entering into the dodecahedral site. The Tb 4+ doping into the eightfold coordinated site requires hafl the energy needed for Tb 4+ entering into the tetrahedral site. Positive defect reaction energies have been calculated for the substitution of Zr 4+ or Ge 4+ for Tb 4+. The doping process produces a decrease of force constant and vibrational frequency values associated with the approximate breathing normal vibrational mode for the two host sites.

Ionic structures as intercalation compound host lattices. An ab initio perturbed ion study on lattice stretching

The effect of lattice expansion along one axis on lattice energy has been analyzed from a theoretical viewpoint. Thirteen ionic structures (LiF, NaF, NaCl, MgO, CsF, CsCl, TiO 2, ZrO 2 (m), ZrO 2 (t), ZrO 2 (c), CaF 2, SrTiO 3 and KMgF 3) have been considered due to their role as potential host lattices for intercalation compounds of the CsF·Br 2 type. Their structural parameters have been optimized and lattice energies evaluated by means of the ab initio perturbed ion method. Results indicate that the most easily stretchable structures based on energy requirements and therefore the best suited as host lattices in this kind of intercalation compound, are those with a rock salt or perovskite type of structure, particularly those formed by low charge ions.

An ab initio perturbed ion study of bulk ceria

The ab initio perturbed ion method has been applied to CeO 2 in order to characterize the geometric, mechanical, thermodynamic and electronic properties of the ground state of this system. The lattice parameter is found to be 535.3 pm, the bulk modulus is 5977 MPa, the lattice energy is −9817.3 kJ mol −1 and the force constant associated with the breathing normal mode of the cerium hole is 46.2 kN m −1. The results are analyzed and compared with experimental data and previous theoretical results. The validity of the methodology is discussed.

Quantum mechanical cluster calculations of ionic materials: the ab initio perturbed ion (version 7) program

We describe the computational implementation of the ab initio perturbed ion method, a self-consistent calculation of the electronic structure and energy of a system under the assumption that the total wave function can be written as an antisymmetric product of local ionic (or atomic) wave functions. Large bases of Slater-type orbitals are supported on every center. Very large, realistic, models of ionic materials can be efficiently solved. The program is provided with an easy-to-use and easy-to-learn interface, with special orders for three-dimensional solids, either pure and defective, and for isolated clusters.

Ab initio cluster-in-the-lattice description of vanadium-doped zircon: analysis of the impurity centers in vanadium(4+)-doped zircon (ZrSiO4)

A theoretical description of crystal effects induced by the presence of impurity centers V 4+ entering the dodecahedral and tetrahedral sites of ZrSiO 4 is presented. The computation of the electronic structure and equilibrium geometry of the impurity center in the ionic crystal is carried out using an extension of the ab initio perturbed ion method. This theoretical model consists of a new type of cluster-in-the-lattice scheme that involves the rigorous quantum mechanical solution of clusters of varying size embedded in a quantum crystal lattice

Overlap, effective-potential, and projection-operator bicentric integrals over complex Slater-type orbitals.

The algorithm of Silverstone and Moats [Phys. Rev. A 16, 1731 (1977)] for the expansion of a function about a displaced center is used to derive analytical expressions for some bicentric integrals appearing in molecular and solid-state calculations. The 〈a\ensuremath{\Vert}b〉 (overlap), 〈a\ensuremath{\Vert}${\mathit{V}}_{\mathrm{eff}}$(b)\ensuremath{\Vert}a'〉 (effective-potential), and 〈a\ensuremath{\Vert}P(b)\ensuremath{\Vert}a'〉 (projection-operator) bicentric integrals over complex Slater-type orbitals (STO's) are explicitly considered. Simple and compact formulas for the spherically averaged integrals are obtained by straightforward summation over the angular-momentum subspecies of center A. fortran routines adapted to a vector computer have been implemented to compute the atom-lattice bicentric integrals of the abinitio perturbed ion method, a Hartree-Fock-Roothaan scheme recently developed by us for the study of ionic and van der Waals crystals. This algorithm is 4--40 times faster than one based on elliptic coordinates and the Mulliken orientation of the A-B diatomic molecule. Furthermore, its efficiency increases progressively with the principal and angular quantum numbers of the complex STO, showing the potentiality of this method in the study of closed-shell systems containing heavy atoms or ions.

Simulation of ionic crystals: The ab initio perturbed-ion method and application to alkali hydrides and halides.

A new theoretical scheme appropriate for studying the electronic structure of ionic crystals is presented and applied to nine AB-type cubic lattices (A=Li,Na,K; B=H,F,Cl). The scheme, called the ab initio perturbed-ion (PI) method, is based on the theory of electronic separability and the ab initio model-potential approach of Huzinaga. In the PI method, the self-consistent-field (SCF) equations for each different lattice ion are first solved in a lattice potential that contains nuclear attraction, Coulombic, and nonlocal exchange operators, and lattice projectors enforcing the required ion-lattice orthogonality. The ionic SCF solutions are then used to compute the lattice potential, and the process is repeated until ion-lattice consistency is achieved. The lattice energy and other equilibrium properties are immediately obtained from the PI wave functions. The most remarkable ideas suggested by this crystal simulation are the following: (a) The crystal potential produces a contraction of the free-ion valence radial density, large for the anions but very small for the cations, that works as a bonding mechanism able to describe accurately the stability and equilibrium elastic constants of simple ionic crystals; (b) the PI method explains well the variation of several crystal properties with hydrostatic pressure; (c) the crystal bonding can be clearly analyzed in terms of simple cationic and anionic contributions. Moreover, the PI code may be used as an efficient source of environment-consistent ionic wave functions and energies.