Exact and exclusive electron localization indices within QTAIM atomic basins

Lange, Jurgens Hendrik de; Cukrowski, Ignacy

doi:10.1002/jcc.25223

Cited by 9 publications

(21 citation statements)

References 42 publications

(48 reference statements)

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“…We recently introduced the FALDI ED decomposition scheme . FALDI uses concepts from the domain averaged Fermi hole (DAFH) approach to calculate pseudo‐second‐order contributions arising from electrons within QTAIM‐defined atomic basins.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…

L_{A} ((), r)

is known as a 1‐center localized ED ( loc –ED) distribution, and describes the ED that is localized exclusively within an atomic basin Ω A , as shown in eq. ,

L_{A} ((), r) = \sum_{i}^{N} {normaln}^{″}_{i}^{AA} {[φ_{i}^{AA} (boldr)]}^{2}

where N is the number of MOs,

φ_{i}^{AA} ((), r)

is a natural density function (NDF) obtained by diagonalizing the product of the atomic overlap matrices, S A S A , and

{normaln}^{″}_{i}^{AA}

is the occupation of the associated NDF; it is double‐primed to indicate that it is free of any localized–delocalized overlap, as previously described .

D_{normalA, normalB} ((), r)

is a 2‐center delocalized ED ( deloc –ED) distribution, and describes the ED that is delocalized between the atomic basins Ω A and Ω B :

D_{normalA, normalB} ((), r) = \sum_{j}^{N} {normaln}^{″}_{j}^{AB} {[φ_{j}^{AB} (boldr)]}^{2} + \sum_{j}^{N} \sum_{i}^{N} ({}, n^{″} ((), L_{A}^{i} \to D_{normalA, normalB}^{j}) {[φ_{i}^{AA} (boldr)]}^{2} + n^{″} ((), L_{B}^{i} \to D_{normalA, normalB}^{j}) {[φ_{i}^{BB} (boldr)]}^{2})

where

φ_{j}^{AB}

…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…]. Specifically, the degree of overlap the i th NDF of a loc –ED distribution (

L_{A}^{i}

) has with the j th NDF of a deloc –ED distribution (

D_{normalA, normalB}^{j}

) is calculated by the function

n^{″} ((), L_{A}^{i} \to D_{normalA, normalB}^{j})

, which relates the relative overlap between

L_{A}^{i}

and

D_{normalA, normalB}^{j}

to the total overlap of

L_{A}^{i}

with the remainder of the molecule's NDFs, as detailed in our previous work …”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…This approach is flawed, as it only measures the local , relative electron concentration rather than the absolute, and resultantly shows a large dependence on the local environment. Our own fragment, atom, localized, delocalized, and interatomic (FALDI) density decomposition scheme provides absolute measures of electron concentration for 1‐ and 2‐center ED distributions. Hence, FALDI provides a much more trustworthy measure with regards to a concentration (and its origin) of ED within an internuclear region.…”

Section: Introductionmentioning

confidence: 99%

“…In principle, this approach can be taken with a large number of established ED decompositions. However, we have chosen our recently developed FALDI density decomposition scheme, as FALDI is (i) inherently linked to QTAIM atomic basins and populations, and (ii) FALDI can provide visualization and quantify electron exchange‐correlation channels in real 3D space.…”

Section: Introductionmentioning

confidence: 99%

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FALDI‐based criterion for and the origin of an electron density bridge with an associated (3,–1) critical point on Bader's molecular graph

2018

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The total electron density (ED) along the λ 2 -eigenvector is decomposed into contributions which either facilitate or hinder the presence of an electron density bridge (DB, often called an atomic interaction line or a bond path). Our FALDI-based approach explains a DB presence as a result of a dominating rate of change of facilitating factors relative to the rate of change of hindering factors; a novel and universal criterion for a DB presence is, thus, proposed. Importantly, facilitating factors show, in absolute terms, a concentration of ED in the internuclear region as commonly observed for most chemical bonds, whereas hindering factors show a depletion of ED in the internuclear region. We test our approach on four intramolecular interactions, namely (i) an attractive classical H-bond, (ii) a repulsive OÁÁÁO interaction, (iii) an attractive ClÁÁÁCl interaction, and (iv) an attractive CHÁÁÁHC interaction. (Dis) appearance of a DB is (i) shown to be due to a "small" change in molecular environment and (ii) qualitatively and quantitatively linked with specific atoms and atom-pairs. The protocol described is equally applicable (a) to any internuclear region, (b) regardless of what kind of interaction (attractive/repulsive) atoms are involved in, (c) at any level of theory used to compute the molecular structure and corresponding wavefunction, and (d) equilibrium or nonequilibrium structures. Finally, we argue for a paradigm shift in the description of chemical interactions, from the ED perspective, in favor of a multicenter rather than diatomic approach in interpreting ED distributions in internuclear regions.

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Section: Theoretical Backgroundmentioning

confidence: 99%

“…

L_{A} ((), r)

is known as a 1‐center localized ED ( loc –ED) distribution, and describes the ED that is localized exclusively within an atomic basin Ω A , as shown in eq. ,

L_{A} ((), r) = \sum_{i}^{N} {normaln}^{″}_{i}^{AA} {[φ_{i}^{AA} (boldr)]}^{2}

where N is the number of MOs,

φ_{i}^{AA} ((), r)

is a natural density function (NDF) obtained by diagonalizing the product of the atomic overlap matrices, S A S A , and

{normaln}^{″}_{i}^{AA}

is the occupation of the associated NDF; it is double‐primed to indicate that it is free of any localized–delocalized overlap, as previously described .

D_{normalA, normalB} ((), r)

is a 2‐center delocalized ED ( deloc –ED) distribution, and describes the ED that is delocalized between the atomic basins Ω A and Ω B :

D_{normalA, normalB} ((), r) = \sum_{j}^{N} {normaln}^{″}_{j}^{AB} {[φ_{j}^{AB} (boldr)]}^{2} + \sum_{j}^{N} \sum_{i}^{N} ({}, n^{″} ((), L_{A}^{i} \to D_{normalA, normalB}^{j}) {[φ_{i}^{AA} (boldr)]}^{2} + n^{″} ((), L_{B}^{i} \to D_{normalA, normalB}^{j}) {[φ_{i}^{BB} (boldr)]}^{2})

where

φ_{j}^{AB}

…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…]. Specifically, the degree of overlap the i th NDF of a loc –ED distribution (

L_{A}^{i}

) has with the j th NDF of a deloc –ED distribution (

D_{normalA, normalB}^{j}

) is calculated by the function

n^{″} ((), L_{A}^{i} \to D_{normalA, normalB}^{j})

, which relates the relative overlap between

L_{A}^{i}

and

D_{normalA, normalB}^{j}

to the total overlap of

L_{A}^{i}

with the remainder of the molecule's NDFs, as detailed in our previous work …”

Section: Theoretical Backgroundmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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FALDI‐based criterion for and the origin of an electron density bridge with an associated (3,–1) critical point on Bader's molecular graph

2018

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Characterization of bonding modes in metal complexes through electron density cross‐sections

2020

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Qualitative inspection of molecular orbitals (MOs) remains one of the most popular analysis tools used to describe the electronic structure and bonding properties of transition metal complexes. In symmetric coordination complexes, the use of group theory and the symmetry-adapted linear combination (SALC) of fragment orbitals allows for a very accurate and informative interpretation of MOs, but the same procedure cannot be performed for asymmetric complexes, such as Schrock and Fischer carbenes. In this work, we present a straightforward approach for classifying and quantifying MO contributions to a particular metal-ligand interaction. Our approach utilizes the topology of MO density contributions to a cross-section of an internuclear region, and is computationally inexpensive and applicable to symmetric and asymmetric complexes alike. We also apply the same approach with similar decompositions using Natural Bond Orbitals (NBO) and the recently developed Fragment, Atomic, Localized, Delocalized and Interatomic (FALDI) density decomposition scheme. In particular, FALDI analysis provides additional insights regarding the multicentric nature of metal-carbene bonds without resorting to expensive multireference calculations.

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The CH···HC interaction in biphenyl is a delocalized, molecular‐wide and entirely non‐classical interaction: Results from FALDI analysis

2021

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In this study we aim to determine the origin of the electron density describing a CHÁÁÁHC interaction in planar and twisted conformers of biphenyl. In order to achieve this, the fragment, atomic, localized, delocalized, intra-and inter-atomic (FALDI) decomposition scheme was utilized to decompose the density in the inter-nuclear region between the ortho-hydrogens in both conformers. Importantly, the structural integrity, hence also topological properties, were fully preserved as no 'artificial' partitioning of molecules was implemented. FALDI-based qualitative and quantitative analysis revealed that the majority of electron density arises from two, non-classical and non-local effects: strong overlap of ortho C H σ-bonds, and long-range electron delocalization between the phenyl rings and ortho carbons and hydrogens. These effects resulted in a delocalized electron channel, that is, a density bridge or a bond path in a QTAIM terminology, linking the H-atoms in the planar conformer. The same effects and phenomena are present in both conformers of biphenyl. We show that the CHÁÁÁHC interaction is a molecular-wide event due to large and long-range electron delocalization, and caution against approaches that investigate CHÁÁÁHC interactions without fully taking into account the remainder of the molecule.

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Exact and exclusive electron localization indices within QTAIM atomic basins

Cited by 9 publications

References 42 publications

FALDI‐based criterion for and the origin of an electron density bridge with an associated (3,–1) critical point on Bader's molecular graph

FALDI‐based criterion for and the origin of an electron density bridge with an associated (3,–1) critical point on Bader's molecular graph

Characterization of bonding modes in metal complexes through electron density cross‐sections

The CH···HC interaction in biphenyl is a delocalized, molecular‐wide and entirely non‐classical interaction: Results from FALDI analysis

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