Accuracy of Localized Resolution of the Identity in Periodic Hybrid Functional Calculations with Numerical Atomic Orbitals

2020 ◽  
Vol 11 (8) ◽  
pp. 3082-3088 ◽  
Author(s):  
Peize Lin ◽  
Xinguo Ren ◽  
Lixin He
Author(s):  
Xudong Weng ◽  
O.F. Sankey ◽  
Peter Rez

Single electron band structure techniques have been applied successfully to the interpretation of the near edge structures of metals and other materials. Among various band theories, the linear combination of atomic orbital (LCAO) method is especially simple and interpretable. The commonly used empirical LCAO method is mainly an interpolation method, where the energies and wave functions of atomic orbitals are adjusted in order to fit experimental or more accurately determined electron states. To achieve better accuracy, the size of calculation has to be expanded, for example, to include excited states and more-distant-neighboring atoms. This tends to sacrifice the simplicity and interpretability of the method.In this paper. we adopt an ab initio scheme which incorporates the conceptual advantage of the LCAO method with the accuracy of ab initio pseudopotential calculations. The so called pscudo-atomic-orbitals (PAO's), computed from a free atom within the local-density approximation and the pseudopotential approximation, are used as the basis of expansion, replacing the usually very large set of plane waves in the conventional pseudopotential method. These PAO's however, do not consist of a rigorously complete set of orthonormal states.


Molecules ◽  
2021 ◽  
Vol 26 (13) ◽  
pp. 3978
Author(s):  
Rocco Peter Fornari ◽  
Piotr de Silva

Discovering new materials for energy storage requires reliable and efficient protocols for predicting key properties of unknown compounds. In the context of the search for new organic electrolytes for redox flow batteries, we present and validate a robust procedure to calculate the redox potentials of organic molecules at any pH value, using widely available quantum chemistry and cheminformatics methods. Using a consistent experimental data set for validation, we explore and compare a few different methods for calculating reaction free energies, the treatment of solvation, and the effect of pH on redox potentials. We find that the B3LYP hybrid functional with the COSMO solvation method, in conjunction with thermal contributions evaluated from BLYP gas-phase harmonic frequencies, yields a good prediction of pH = 0 redox potentials at a moderate computational cost. To predict how the potentials are affected by pH, we propose an improved version of the Alberty-Legendre transform that allows the construction of a more realistic Pourbaix diagram by taking into account how the protonation state changes with pH.


2021 ◽  
Vol 154 (6) ◽  
pp. 064102
Author(s):  
Juan Felipe Huan Lew-Yee ◽  
Mario Piris ◽  
Jorge M. del Campo

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Lei Wang ◽  
Yongpeng Shi ◽  
Mingfeng Liu ◽  
Ao Zhang ◽  
Yi-Lun Hong ◽  
...  

AbstractThe search for new two-dimensional monolayers with diverse electronic properties has attracted growing interest in recent years. Here, we present an approach to construct MA2Z4 monolayers with a septuple-atomic-layer structure, that is, intercalating a MoS2-type monolayer MZ2 into an InSe-type monolayer A2Z2. We illustrate this unique strategy by means of first-principles calculations, which not only reproduce the structures of MoSi2N4 and MnBi2Te4 that were already experimentally synthesized, but also predict 72 compounds that are thermodynamically and dynamically stable. Such an intercalated architecture significantly reconstructs the band structures of the constituents MZ2 and A2Z2, leading to diverse electronic properties for MA2Z4, which can be classified according to the total number of valence electrons. The systems with 32 and 34 valence electrons are mostly semiconductors. Whereas, those with 33 valence electrons can be nonmagnetic metals or ferromagnetic semiconductors. In particular, we find that, among the predicted compounds, (Ca,Sr)Ga2Te4 are topologically nontrivial by both the standard density functional theory and hybrid functional calculations. While VSi2P4 is a ferromagnetic semiconductor and TaSi2N4 is a type-I Ising superconductor. Moreover, WSi2P4 is a direct gap semiconductor with peculiar spin-valley properties, which are robust against interlayer interactions. Our study thus provides an effective way of designing septuple-atomic-layer MA2Z4 with unusual electronic properties to draw immediate experimental interest.


The construction of spin eigenfunctions and the evaluation of matrix elements between ,them are discussed generally in preparation for a development of the valence bond (VB) theory along the lines indicated in I. The customary approximation of considering explicitly only the electrons outside a ‘closed shell’ is shown to be defensible. The reformulation of the VB theory is now straightforward, but its final description of bonding is quite new. Atomic orbitals (AO’s) are replaced, whenever they appear, by orthogonalized atomic orbitals (AO’s); but when the assumptions of the conventional theory are rigorously validated in this way the ‘covalent’ structures (now ‘VB’ structures) are found, quite generally, to indicate only strong repulsion between the ‘bonded’ atoms, and formal descriptions of bonding and of bond orders, in terms of ‘spin-pairing’, become nonsensical. Bonding can be described only by admitting into the wave functions polar VB structures; a bond between two atoms demands the appearance (with considerable weight) of pairs of structures differing by a ‘charge hop’ between the atoms concerned. The conventional VB structures are found to be equivalent to certain groupings of VB structures (non-polar and polar) and do, indeed, predict bonds between spin-paired atoms and repulsion between the atoms of different pairs. It is then possible to make full use of chemical intuition, using a plausible combination of conventional structures as a starting approximation in the more rigorous theory. A numerical illustration is provided by a discussion of the Kekulé structures of benzene. Some important characteristics of energy calculations in the VB theory are pointed out. Quantities of intra - and inter -atomic origin are well separated, and the method is apparently well suited to development along either ab initio or empirical lines.


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