Hybrid Atomic Orbital Basis from First Principles: Bottom-Up Mapping of Self-Energy Correction to Large Covalent Systems

Abstract

Construction of hybrid atomic orbitals is proposed as the approximate common eigenstates of finite first moment matrices. Their hybridization and orientation can be a priori tuned as per their anticipated neighborhood. Their Wannier function counterparts constructed from the Kohn−Sham (KS) single particle states constitute an orthonormal multiorbital tight binding (TB) basis resembling hybrid atomic orbitals locked to their immediate atomic neighborhood, while spanning the subspace of KS states. The proposed basis thus renders predominantly single TB parameters from first principles for each nearest neighbor bond involving no more than two orbitals irrespective of their orientation and also facilitates an easy route for the transfer of such TB parameters across isostructural systems exclusively through mapping of neighborhoods and projection of orbital charge centers. With hybridized 2s, 2p and 3s, 3p valence electrons, the spatial extent of the self-energy correction (SEC) to TB parameters in the proposed basis is found to be localized mostly within the third nearest neighborhood, thus allowing effective transfer of self-energy-corrected TB parameters from smaller reference systems to much larger target systems, with nominal additional computational cost beyond that required for explicit computation of SEC in the reference systems. The proposed approach promises inexpensive estimation of the quasi-particle structures of large covalent systems with workable accuracy.

Maximally valent orbitals in systems with non-ideal bond-angles: atomic Wannier orbitals guided by the Mayer bond order

“…The construction of a template free variant of the maximally localized Wannier functions (MLWFs) 25,26 to describe bonding and non-bonding orbitals in isolated systems, is performed before the construction of HAOs, 27 in terms of the technique for spatial localization. The only difference is that the MLWFs are constructed exclusively within the subspace of the occupied KS states of a given system, while the HAOs are constructed within an extended sub-space beyond the occupied sub-space of an isolated atom.…”

“…The same has been used in this work, as well as for the construction of HAOs described in ref. 27, which may be referred to for relevant details of computation of the rotation matrices. Construction of CHAOs from HAOs involves two steps -(1) reconstruction of unhybridized atomic orbitals (UAOs) from degenerate HAOs, and (2) re-hybridization of UAOs to construct CHAOs.…”

“…The same has been used in this work, as well as for the construction of HAOs described in ref. 27, which may be referred to for relevant details of computation of the rotation matrices.…”

“…CHAOs represent generalization of degenerate HAOs constructed from KS states of isolated atoms as demonstrated in ref. 27. Wannierization of CHAOs on the basis of KS states of a given system results in custom hybridized atomic Wannier orbitals (CHAWOs), which constitute a set of orthonormal localized basis which incorporates effects of the local environment of a given atom in the system, and are notionally similar to the quasi-atomic orbitals.…”

Correct and Accurate Polymorphic Energy Ordering of Transition-Metal Monoxides Obtained from Semilocal and Onsite-Hybrid Exchange-Correlation Approximations

“…One may note that in addition to the aforementioned works, a very large number of other studies have investigated the ground-state or electronic properties of the rs -AF2 phase of MnO. A certain number of DFT and beyond DFT methods are used, and this includes many semilocal DFT methods (see refs and − for recent work), DFT+ U , , various types of hybrids, − the self-interaction corrected local density approximation, the optimized effective potential method, , model Hamiltonian approach, ,− the quasi-particle GW method, − and dynamical mean field theory (DMFT). − Nevertheless, it is important to mention that the most accurate of all these methods, namely, RPA, DMC, GW, and DMFT are computationally much more expensive than DFT-based methods.…”