Víctor Luaña

Gibbs2: A new version of the quasiharmonic model code. II. Models for solid-state thermodynamics, features and implementation ☆ ☆☆

Abstract In the second article of the series, we present the Gibbs 2 code, a Fortran90 reimplementation of the original Gibbs program [Comput. Phys. Commun. 158 (2004) 57] for the calculation of pressure–temperature dependent thermodynamic properties of solids under the quasiharmonic approximation. We have taken advantage of the detailed analysis carried out in the first paper to implement robust fitting techniques. In addition, new models to introduce temperature effects have been incorporated, from the simple Debye model contained in the original article to a full quasiharmonic model that requires the phonon density of states at each calculated volume. Other interesting novel features include the empirical energy corrections, that rectify systematic errors in the calculation of equilibrium volumes caused by the choice of the exchange-correlation functional, the electronic contributions to the free energy and the automatic computation of phase diagrams. Full documentation in the form of a userʼs guide and a complete set of tests and sample data are provided along with the source code. Program summary Program title: Gibbs 2 Catalogue identifier: AEJI_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEJI_v1_0.html Program obtainable from: CPC Program Library, Queenʼs University, Belfast, N. Ireland Licensing provisions: GNU General Public License, v3 No. of lines in distributed program, including test data, etc.: 936 087 No. of bytes in distributed program, including test data, etc.: 8 596 671 Distribution format: tar.gz Programming language: Fortran90 Computer: Any running Unix/Linux Operating system: Unix, GNU/Linux Classification: 7.8 External routines: Part of the minpack, pppack and slatec libraries (downloaded from www.netlib.org ) are distributed along with the program. Nature of problem: Given the static E ( V ) curve, and possibly vibrational information such as the phonon density of states, calculate the equilibrium volume and thermodynamic properties of a solid at arbitrary temperatures and pressures in the framework of the quasiharmonic approximation. Additional comments: A detailed analysis concerning the fitting of equations of state has been carried out in the first part of this article, and implemented in the code presented here. Running time: The tests provided only take a few seconds to run.

Critic : a new program for the topological analysis of solid-state electron densities

Abstract In this paper we introduce critic , a new program for the topological analysis of the electron densities of crystalline solids. Two different versions of the code are provided, one adapted to the LAPW (Linear Augmented Plane Wave) density calculated by the WIEN2k package and the other to the ab initio Perturbed Ion (aiPI) density calculated with the pi7 code. Using the converged ground state densities, critic can locate their critical points, determine atomic basins and integrate properties within them, and generate several graphical representations which include topological atomic basins and primary bundles, contour maps of ρ and ∇ 2 ρ , vector maps of ∇ ρ , chemical graphs, etc. Program summary Program title: CRITIC Catalogue identifier: AECB_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AECB_v1_0.html Program obtainable from: CPC Program Library, Queens University, Belfast, N. Ireland Licensing provisions: GPL, version 3 No. of lines in distributed program, including test data, etc.: 1 206 843 No. of bytes in distributed program, including test data, etc.: 12 648 065 Distribution format: tar.gz Programming language: FORTRAN 77 and 90 Computer: Any computer capable of compiling Fortran Operating system: Unix, GNU/Linux Classification: 7.3 Nature of problem: Topological analysis of the electron density in periodic solids. Solution method: The automatic localization of the electron density critical points is based on a recursive partitioning of the Wigner–Seitz cell into tetrahedra followed by a Newton search from significant points on each tetrahedra. Plotting of and integration on the atomic basins is currently based on a new implementation of Keiths promega algorithm. Running time: Variable, depending on the task. From seconds to a few minutes for the localization of critical points. Hours to days for the determination of the atomic basins shape and properties. Times correspond to a typical 2007 PC.

Gibbs2: A new version of the quasi-harmonic model code. I. Robust treatment of the static data

Abstract We describe in this article the techniques developed for the robust treatment of the static energy versus volume theoretical curve in the new version of the quasi-harmonic model code [Comput. Phys. Commun. 158 (2004) 57]. An average of strain polynomials is used to determine, as precisely as the input data allow it, the equilibrium properties and the derivatives of the static E ( V ) curve. The method provides a conservative estimation of the error bars associated to the fitting procedure. We have also developed the techniques required for detecting, and eventually removing, problematic data points and jumps in the E ( V ) curve. The fitting routines are offered as an independent octave package, called AsturFit , with an open source license. Program summary Program title: AsturFit Catalogue identifier: AEIY_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEIY_v1_0.html Program obtainable from: CPC Program Library, Queenʼs University, Belfast, N. Ireland Licensing provisions: GPL version 3 No. of lines in distributed program, including test data, etc.: 21 347 No. of bytes in distributed program, including test data, etc.: 620 496 Distribution format: tar.gz Programming language: GNU Octave Computer: Workstations Operating system: Unix, GNU/Linux Classification: 4.9 External routines: The GSL and OPTIM packages from the octaveforge site ( http://octave.sourceforge.net/ ). Nature of problem: Fit the total energy versus volume data of a solid to a continuous function and extract the equilibrium properties and the derivatives of the energy, with an estimation of the error introduced by the fitting procedure. Solution method: The use of averages of strain polynomials allows a robust and reliable representation of the energy curve and its derivatives, together with a statistical estimation of the goodness of the calculated properties. Additional comments: The techniques discussed have been implemented in Gibbs 2, to be included with the second part of this article. Included here is the OCTAVE implementation of the routines, useful for interactive work and also for the creation of independent scripts. Some representative examples are included as test cases with a collection of data sets, test scripts, and model outputs. Running time: Seconds at most in routine uses of the program. Special tasks like the bootstrap analysis may take up to some minutes.

Supramolecular architectures based on As(lone pair)⋯π(aryl) interactions

As(lone pair)···π interactions provide stability to their crystal structures often leading to supramolecular chains and prevailing over As···X secondary contacts. The interaction (ca 8 kJ mol(-1)) arises from polarisation induced in the aryl ring by the As-lone pair plus the weak sharing of these electrons with the ring-C atoms.

Effects of a quantum‐mechanical lattice on the electronic structure and d–d spectrum of the (MnF6)4− cluster in Mn2+ :KZnF3

The electronic structure of the Mn2+ :KZnF3 impurity system has been computed by means of a Hartree–Fock–Roothaan cluster model. First, the Mn2+ center has been simulated by the (MnF6 )4− unit in vacuo. Then, the effects of the KZnF3 lattice have been included in the cluster calculation using three different lattice models. The well‐known point–charge approximation has been compared with two rigorous quantum–lattice models derived from the ideas of the theory of electronic separability. In these two models the lattice ions are represented by an effective lattice potential and a lattice projection operator that enforces the cluster–lattice orthogonality. In the Coulomb or Hartree model the cluster–lattice exchange interactions are neglected. The ab initio model potential (MP) lattice model makes use of model potentials for representing the lattice ions and includes an accurate nonlocal exchange operator. According to the present results, the point–charge lattice model destroys the acceptable picture of the...

Non-nuclear maxima of the electron density on alkaline metals

The topological properties of the electron density of bcc alkaline metals (Li–Cs) is examined by means of Hartree–Fock and density functional calculations. Our best results indicate that lithium is the only alkaline metal showing non-nuclear maxima (NNM) at the room pressure and temperature experimental geometry. Sodium and potassium, but not rubidium and cesium, would also present NNM under an appropriate compression, even though the NNM in potassium would be residual at best and contain a negligible amount of electrons. Despite these differences, all five alkaline metals share a common tendency towards topological change that makes their behavior clearly distinct from what is typical in ionic, covalent and molecular crystals. When examined in a wide range of interatomic distances, the electron density of every metal follows a well defined topological sequence, with strong similarities across the five metals.

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

Abstract 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.

A fast and accurate algorithm for QTAIM integration in solids

A new algorithm is presented for the calculation of atomic properties, in the sense of the quantum theory of atoms in molecules. This new method, named QTREE, applies to solid‐state densities and allows the computation of the atomic properties of all the atoms in the crystal in seconds to minutes. The basis of the method is the recursive subdivision of a symmetry‐reduced wedge of the Wigner‐Seitz cell, which in turn is expressed as a union of tetrahedra, plus the use of β‐spheres to improve the performance. A considerable speedup is thus achieved compared with traditional quadrature‐based schemes, justified by the poor performance of the latter because of the particular features of atomic basins in solids. QTREE can use both analytical or interpolated densities, calculates all the atomic properties available, and converges to the correct values in the limit of infinite precision. Several gradient path tracing and integration techniques are tested. Basin volumes and charges for a selected set of 11 crystals are determined as a test of the new method.

Hirshfeld surfaces as approximations to interatomic surfaces

A simple algebraic model is used to show that Hirshfeld surfaces in condensed phases may be understood as approximations to the interatomic surfaces of the theory of atoms in molecules. The conditions under which this similarity is valid are explored, and both kinds of surfaces are calculated in the LiF and CS2 crystals to illustrate the main results. The link between Hirshfeld and interatomic surfaces provides a physical ground to understand the usage of the former to visualize intermolecular interactions.

Structural and chemical stability of halide perovskites

Abstract The ab initio Perturbed Ion ( ai PI) quantum mechanical method is used to study the solid state reaction: AX + MX 2 → AMX 3 from a thermodynamical point of view. The reaction energy is first determined by means of static calculations (i.e. at null absolute temperature) on the ideal cubic structures of the components. The very difficult problem of determining the most stable crystal structure of a compound is then undertaken by examining the differences in energy among many structures reported for AX , MX 2 and AMX 3 compounds. Finally, the reaction energy is again examined in the light of those corrections, and the results are used to analyze the experimental data available on the synthesis of perovskites.