Pseudopotential plane wave

V. Milman, B. Winkler, J. A. White, C. J. Pickard, M. C. Payne, E. V. Akhmatskaya, and R. H. Nobes, Electronic Structure, Properties, and Phase Stability of Inorganic Crystals A Pseudopotential Plane-Wave Study, hit. 

Abstract The ab initio pseudopotential plane wave DPT simulation of the structure and properties of zeolite active sites and elementary catalytic reactions are discussed through the example of the protonation of water and the first step in the protolytic cracking mechanism of saturated hydrocarbons. 

Theoretical modeling of the structure and reactivity of zeolitic materials, with special emphasis on the mechanism of catalytic reactions, has been the subject of several exhaustive review articles in the past decade. Theoretical approaches that have been used to describe such systems range from empirical molecular mechanics calculations to various ab initio methods as well as different variants of the mixed quantum/classical (QM/MM) algorithms. In the present contribution we focus our attention mainly on those studies which were accomplished by ab initio pseudopotential plane wave density functional methods that are able to treat three-dimensional periodic models of the zeolite catalysts. Where appropriate, we attempt a critical comparison of with other theoretical approaches. 

The most obvious improvement of the model was to include the full zeolite structure in ab initio pseudopotential plane wave DPT calculations. However, the attempts to localize proton transferred HSAPO-34.H2O complexes have proved to be unsuccessful the water molecule remained physisorbed. A typical structure, selected from the numerous local minima, is shown in Pig. 6, illustrating that topologically distant framework oxygens participate also in the stabilization of such a complex. A correct account of this feature would neces-... 

The overwhelming majority of the theoretical studies were performed on cluster models of the catalytic site, hi spite of the fact that the role of space confinement and the secondary interactions with the framework atoms is well-known, there are only a few electronic structure calculations on lattice models involving hydrocarbons, using either periodic DFT calculations, or embedding methods. In this brief account of the subject we attempt to overview some of the recent computational results of the literature and present some new data obtained from ab initio DFT pseudopotential plane wave calculations on Cl - C4 alkanes in the chabazite framework. 

Ab initio DFT pseudopotential plane wave calculations were performed to study the transition structures and the corresponding activation energies for... 

The calculations were performed using the pseudopotential plane-wave formalism and the local-density ap-... 

In order to tackle large and complex structures, new methods have recently been developed for solving the eleetronie part of the problem. These are mostly applied to the pseudopotential plane wave method, because of the simplicity of the Hamiltonian matrix elements with plane wave basis functions and the ease with which the Hellmann-Feynman forces can he found. Conventional methods of matrix diagonalization for finding the energy eigenvalues and eigenfunctions of the Kohn-Sham Hamiltonian in (9) can tackle matrices only up to about 1000 x 1000. As a basis set of about 100 plane waves per atom is needed, this restricts the size of problem to... 

Beyond a certain system size, even DFT methods using conventional basis sets become computationally very intensive. In such situations, we have employed the pseudopotential plane wave or tight-binding methods to obtain the various physical properties [14,27]. 

We employed density functional calculations using the ultrasoft pseudopotential plane wave method to investigate the CHQ nanotubes and the encapsulated silver nanowires. The local density approximation (LDA) of Ceperley and Alder and Vanderbilt pseudopotential was employed and the cutoff energy of the plane wave basis set was 20 Ry [27,182-185]. Full-potential linearized augmented plane wave method calculations were also carried out on the isolated silver nanowire [195-197]. To check the reliability of our... 

More recently, other groups—primarily in Europe—have begun doing pseudopotential plane wave (often gradient-corrected) DFT supercell slab calculations (figure B3.2.12(D)) for chemisorption on metals. The groups of Norskov [156]. Scheffler [157]. Baerends [158. 159] and Hafher and Kresse [160. 161] have been the most active. Adsorbate-metal surface systems examined include alkalis and N2 on Ru [156]. NO on Pd... 

The disadvantage of the pseudopotential (plane-wave) approach can be summarized as follows. First, all information for the core-like wavefunctions and their associated electron density is lost, trivially so. Second, an essentially delocalized plane-wave basis set poses difficulties when it comes to questions of chemical interpretation in terms of atoms and bonds. In addition, there has always been some concern about the arbitrariness of pseudopotentials because there is certainly more than one pseudopotential (in fact, an infinite number) for a given atom. Recall that the partitioning of a quantum-mechanical system into subsystems is invalid because the electrons cannot be distinguished in principle, there are no "core" or "valence" electrons. Nonetheless, pseudopotential plane-wave calculations have established themselves as accurate and powerful tools for electronic-structure theory, both for molecules and, in... 

Let us now find out whether these classical enthalpies may be reproduced by electronic-structure calculations (VASP) on Sn/Zn supercells using ultra-soft pseudopotentials, plane-wave basis sets and the GGA. We therefore have to theoretically determine the total energies of all crystal structure types under consideration (a-Sn, j6-Sn, Zn) as a function of the composition SnxZni x by a variation of the available atomic sites in terms of Sn and Zn occupation, just as for the preceding oxynitrides (CoOi- N ). In the present case, supercells with a total of 16 atoms were generated, and nine different compositions per structure were numerically evaluated. Because this amounts to a significant computational task, the use of pseudopotentials is mandatory, and this also allows the rapid calculation of interatomic forces and stresses for structural... 

Metropohs N, Rosenbluth AW, Rosenbluth MN, TeUer AH, Teller E (1953) Eqrration of state calculations by fast computing machines. J Chem Phys 21 1087-1092 Milman V, Winkler B, White JA, Pickard CJ, Payne MC, Akhmatskaya EV, Nobes RH (2000) Electronic structirre, properties, and phase stability of inorganic crystals A pseudopotential plane-wave study. Int J Quantirm Chem 77 895-910... 

The advent of DFT-based Car-Parrinello (CP) molecular dynamics (MD) [8] marked an important step forward because it provided the possibility to explore the complex structural patterns of atomic clusters with the least biased procedures and to simulate their dynamics [9]. This eventually led to the discovery of new structures and thus to the understanding of some special features of the mass spectra. In particular, it became possible to investigate how the shape and the electronic structure of a cluster change with temperature, which is especially relevant for metal aggregates [10]. It also became clear that DFT pseudopotential-plane-wave methods allowed one to treat clusters of diverse elements in the periodic table as well as of much larger sizes than traditional calculations had done. Thus, they were particularly suitable for the study of size-evolution patterns. Soon a CP-like technique was also applied to the simulation of interesting dynamical processes, such as cluster fragmentation, with results that could be, at least in part, compared with experiment [11]. 

Density functional perturbation theory, as described in Ref. [92], has been applied to calculate phonon spectra of solids. It can easily be applied to clusters as well, the only limitation being that in the pseudopotential-plane-wave formalism, the computational cost is high, whereas the implementations within a localized basis formalism can be very involved. 

Pseudopotential Plane Wave (PPW) method We can manipulate the expression in Eq. (4.43) to obtain something more familiar. First notice that... 

We have performed ground state total-energy calculations using the pseudopotential plane-wave method based on density-functional theory in the local density approximation for exchange and correlationThe Vanderbilt ultrasoft pseudopotentials were used ... 

Meyer, B. (2006). The pseudopotential plane wave approach. In J. Grotendorst, S. Bliigel, 8c D. Marx (Eds.), Computational nanoscience Do it yourself jUlich NIC. http //www2.fz-juelich.de/ nic-series/volume31/meyerl.pdf. Accessed 02 July 2011. 

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