A simple geometrical path towards hybrid orbitals

Nacbar, Denis Rafael; Ribeiro, Allan Victor; Bruno-Alfonso, Alexys

doi:10.1590/1516-1439.291014

Cited by 2 publications

(6 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…a and , one may notice that the GWFs of the

s - p_{x}

bands are similar to hybrid sp atomic orbitals. This is expressed by

{\overset{w}{true}}_{1} false(x, y, z false) \approx ϕ_{sp} false(x, y, z false),

where ()

ϕ_{sp} false(x, y, z false) = \frac{ϕ_{1} false(x, y, z false) - ϕ_{2} false(x, y, z false)}{\sqrt{2}}

is a hybrid sp orbital. This may be understood as if the transformation from single‐band WFs to the two‐band GWFs splits the bonding and anti‐bonding molecular orbitals into two hybrid atomic orbitals.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…The present study sheds further light on the chemical meaning of the generalized Wannier functions associated to the s and

p_{x}

atomic orbitals. In cumulene, these functions involve Bloch states both below and above the Fermi level and resemble hybrid sp orbitals (). In turn, the chemical bond is determined by the occupied bands.…”

Section: Discussionmentioning

confidence: 99%

“…Moreover, in order to find the coefficients in Eqs. (46) and (48), we have partially fitted the DFT bands reported by Tongay et al [38]. We have taken into account interactions up to the third nearest neighbors.…”

Section: Generalized Wannier Functionsmentioning

confidence: 99%

“…7a and 8, one may notice that the GWFs of the s−p x bands are similar to hybrid sp atomic orbitals. This is expressed bỹ where [46] ϕ sp (x, y, z) = ϕ 1 (x, y, z) − ϕ 2 (x, y, z) √ 2 (54)…”

Section: Generalized Wannier Functionsmentioning

confidence: 99%

See 3 more Smart Citations

Wannier functions of cumulene: A tight‐binding approach

Ribeiro

Nacbar

Bruno-Alfonso

2015

Physica Status Solidi (b)

Self Cite

View full text Add to dashboard Cite

Exponentially localized Wannier functions of cumulene are calculated from the Bloch functions obtained through a tight‐binding approach. Numerical results and discussions are given for the π and σ bands. In the latter case, the single‐band Wannier functions are similar to the orbitals of a diatomic molecule, while the two‐band Wannier functions resemble hybrid atomic orbitals. Contour plot of an sp‐like Wannier function of cumulene.

show abstract

“…a and , one may notice that the GWFs of the

s - p_{x}

bands are similar to hybrid sp atomic orbitals. This is expressed by

{\overset{w}{true}}_{1} false(x, y, z false) \approx ϕ_{sp} false(x, y, z false),

where ()

ϕ_{sp} false(x, y, z false) = \frac{ϕ_{1} false(x, y, z false) - ϕ_{2} false(x, y, z false)}{\sqrt{2}}

Section: Numerical Resultsmentioning

confidence: 99%

“…The present study sheds further light on the chemical meaning of the generalized Wannier functions associated to the s and

p_{x}

Section: Discussionmentioning

confidence: 99%

Section: Generalized Wannier Functionsmentioning

confidence: 99%

Section: Generalized Wannier Functionsmentioning

confidence: 99%

See 2 more Smart Citations

Wannier functions of cumulene: A tight‐binding approach

Ribeiro

Nacbar

Bruno-Alfonso

2015

Physica Status Solidi (b)

Self Cite

View full text Add to dashboard Cite

show abstract

“…This agreement confirms the identity of the resultant orbitals as the hybrid orbitals and numerically establishes the connection between maximal localization and hybridization. Such a connection between sp 3 hybridization and minimization of the total quadratic spread of s and the three p orbitals has been analytically proven . In this work, however, we do not use GTOs further and rather resort to KS states of isolated atoms.…”

Section: Methodological Detailsmentioning

confidence: 91%

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

Hossain

Bhattacharjee

2021

J. Phys. Chem. A

View full text Add to dashboard Cite

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.

show abstract

A simple geometrical path towards hybrid orbitals

Cited by 2 publications

References 16 publications

Wannier functions of cumulene: A tight‐binding approach

Wannier functions of cumulene: A tight‐binding approach

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

Contact Info

Product

Resources

About