Electron localization function from density components

This work addresses the decomposition of the Electron Localization Function (ELF) into partial density contributions using an appealing split of kinetic energy densities. Regarding the degree of the electron localization, the relationship between ELF and its usual spin‐polarized formula is discussed. A new polarized ELF formula, built from any subsystems of the density, and a localization function, quantifying the measure of electron localization for only a subpart of the total system are introduced. The methodology appears tailored to describe the electron localization in bonding patterns of subsystems, such as the local nucleophilic character. Beyond these striking examples, this work opens up opportunities to describe any electronic properties that depend only on subparts of the density in atoms, molecules, or solids. © 2016 Wiley Periodicals, Inc.     

Electron localization function for transition-metal compounds

 The analysis of the electron localization function of molecules and solids needs to involve the atomic core regions as well to reveal a more detailed insight into the bonding situation. Received: 20 February 2002 /Accepted: 14 June 2002 /Published online: 19 August 2002     

Electron localization function at the correlated level

The electron localization function (ELF) has been proven so far a valuable tool to determine the location of electron pairs. Because of that, the ELF has been widely used to understand the nature of the chemical bonding and to discuss the mechanism of chemical reactions. Up to now, most applications of the ELF have been performed with monodeterminantal methods and only few attempts to calculate this function for correlated wave functions have been carried out. Here, a formulation of ELF valid for mono- and multiconfigurational wave functions is given and compared with previous recently reported approaches. The method described does not require the use of the homogeneous electron gas to define the ELF, at variance with the ELF definition given by Becke. The effect of the electron correlation in the ELF, introduced by means of configuration interaction with singles and doubles calculations, is discussed in the light of the results derived from a set of atomic and molecular systems.     

Electron localization function in full-potential representation for crystalline materials

The electron localization function (ELF) is implemented in the first-principles, all-electron, full-potential local orbital method. This full-potential implementation increases the accuracy with which the ELF can be computed for crystalline materials. Some representative results obtained are presented and compared with the results of other methods. Although for crystal structures with directed bonding only minor differences are found, in simple elemental metals, there are differences in the valence region, which give rise to different ELF topologies.     

Electron pair localization function: a practical tool to visualize electron localization in molecules from quantum Monte Carlo data

In this work we introduce an electron localization function describing the pairing of electrons in a molecular system. This function, called "electron pair localization function," is constructed to be particularly simple to evaluate within a quantum Monte Carlo framework. Two major advantages of this function are the following: (i) the simplicity and generality of its definition; and (ii) the possibility of calculating it with quantum Monte Carlo at various levels of accuracy (Hartree-Fock, multiconfigurational wave functions, valence bond, density functional theory, variational Monte Carlo with explicitly correlated trial wave functions, fixed-node diffusion Monte Carlo, etc). A number of applications of the electron pair localization function to simple atomic and molecular systems are presented and systematic comparisons with the more standard electron localization function of Becke and Edgecombe are done. Results illustrate that the electron pair localization function is a simple and practical tool for visualizing electronic localization in molecular systems.     

Electron localization function study on intramolecular electron transfer in the QTTFQ and DBTTFI radical anions

The unsymmetrical distribution of the unpaired electron in the ground state of the DBTTFI(?-) radical anion (bi(6-n-butyl-5,7-dioxo-6,7-dihydro-5H-[1,3]dithiolo[4,5-f]isoindole-2-ylidene) is theoretically predicted using the M06-2X/6-31+G(d,p) level of calculations. The results are additionally confirmed by single point calculations at B3LYP/aug-cc-pVTZ, LC-ωPBE/aug-cc-pVTZ, and M06-2X/aug-cc-pVTZ levels. DBTTFI, containing the TTF (tetrathiafulvalene) fragment, may be used in the construction of organic microelectronic devices, similarly to the radical anion of QTTFQ. The unsymmetrical distribution of spin density in (QTTFQ)(?-) has been confirmed using M06-2X/aug-cc-pVTZ calculations, with subsequent study using topological analysis of electron localization function (ELF). The reorganization of the chemical bonds during intramolecular electron transfer in (QTTFQ)(?-) and (DBTTFI)(?-) has been analyzed using bonding evolution theory (BET). The reaction path has been simulated by the IRC procedure, and the evolution of valence basins has been described using catastrophe theory. The simple mechanisms: (QTTFQ)(?-): η-1-3-CC(+)-0: (-?)(QTTFQ) and (DBTTFI)(?-): η-1-3-[F](4)[F(+)](4)-0: (-?)(DBTTFI), each consisting of three steps, have been observed. Two cusp or 4-fold catastrophes occur immediately after the TS. Our study shows that potential future microelectronic devices, constructed on the basis of the (QTTFQ)(?-) and (DBTTFI)(?-) systems, should exploit the properties of the C═C bond.     

Electron localization and delocalization in open-shell molecules

Localization and delocalization indices derived in the framework of the quantum Atoms in Molecules theory have recently been used to analyze the electron-pair structure of closed-shell molecules. Here we report calculations of localization and delocalization indices for open-shell molecules at the Hartree-Fock (HF) level. Several simple doublet and triplet radical molecules are studied. In general, interatomic delocalization between bonded atoms is heavily dependent on the order and polarity of the bond. Unpaired electrons also have a significant effect on the interatomic delocalization indices. Indeed, for many radicals, the analysis of the spin components reveals that the interatomic delocalization is very different for alpha and beta spin electrons in many cases. In general, at the HF level, the results can be rationalized in terms of orbital contributions. However, the definition of localization and delocalization indices is completely general, and they could be calculated at any level of theory, provided that the one- and two-electron densities are available.     

Electron localization in a finite one-dimensional chain

The localization characteristics of the electronic wave functions in a finite one-dimensional chain with the diagonal or the off-diagonal disorder of the potentials have been studied. It has been shown that the eigenfuction at the frontier level is relatively “strong” against the temptation to localize caused by the existence of the random potentials. It has also been pointed out that the spatial behavior of the total density reflects that of the diagonal random potentials, but that under the off-diagonal random potentials the total density is spatially uniform (completely extended).     

Electron localization and radiation chemistry of amides

Alkylamides (such as N,N'-dimethylformamide, N,N'-diethylformamide, and N,N'-dimethylacetamide) are aprotic solvents that are widely used in organic synthesis. These polar molecules have no electron affinity, and it is believed that irradiated liquid and solid amides stabilize excess electrons as cavity-type species analogous to hydrated and ammoniated electrons. In this study, we use isotope substitution and EPR spectroscopy to demonstrate that, in frozen amides, the suspected "cavity electron" is, in fact, a solvent-stabilized monomer anion. Our observations call into question other attributions of such features in the literature, both in low temperature solids and room temperature liquids. We also provide a general scheme describing amide radiolysis, as the related amides are used as metal ion extracting agents in nuclear separations.     

Electron localization and delocalization indices for solids

The electron localization and delocalization indices obtained by the integration of exchange‐correlation part of pair density over chemically meaningful regions of space, e.g., QTAIM atoms are valuable tools for the bonding analysis in molecular systems. However, among periodic systems only few simplest models were analyzed with this approach until now. This contribution reports implementation and evaluation of the localization and delocalization indices on the basis of solid state DFT calculations. A comparison with the results of simple analytical model of Ponec was made. In addition, a small set of compounds with ionic (NaCl), covalent (diamond, graphite), and metallic (Na, Cu) bonding interactions was characterized using this method. Typical features of different types of bonding were discussed using the delocalization indices. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

Electron mobility in supercritical pentanes as a function of density and temperature

The excess electron mobility in supercritical n-, iso- and neopentane was measured isothermally as a function of density. The density-normalized mobility μN in all three isomers goes through a minimum at a density below the respective critical densities, and the mobility is quite temperature-dependent in this region, then goes through a minimum. The μN behavior around the minimum in n-pentane is well accounted for by the Cohen-Lekner model with the structure factor S(K) estimated from the speed of sound, while that in iso- and neopentane is not.     

Electron localization function and electron localizability indicator applied to study the bonding in the peroxynitrous acid HOONO

The ground‐state electronic structure of peroxynitrous acid (HOONO) and its singlet biradicaloid form (HO ··· ONO) have been studied using topological analysis of the electron localization function (ELF), together with the electron localizability indicator (ELI‐D), at the DFT (B3LYP, M05, M052X, and M06), CCSD, and CASSCF levels. Three isomers of HOONO (cis‐cis, cis‐perp, and trans‐perp) have been considered. The results show that from all functionals applied, only B3LYP yields the correct geometrical structure. The ELF and ELI‐D‐topology of the O? O and central N? O bonds strongly depends on the wave function used for analysis. Calculations carried out at CAS (14,12)/aug‐cc‐pVTZ//CCSD(T)/aug‐cc‐pVTZ level reveal two bonds of the charge‐shift type: a protocovalent N? O bond with a basin population of 0.82–1.08e, and a more electron depleted O? O bond with a population of 0.66–0.71e. The most favorable dissociation channel (HOONO → HO + ONO) corresponds to breaking of the most electron‐deficient bond (O? O). In the case of cis‐ and trans‐HO ··· ONO, the ELF, ELI‐D, and electron density fields results demonstrate a closed‐shell O ··· O interaction. The α‐spin electrons are found mainly (0.64e) in the lone pairs of oxygen V_{i = 1,2} (O) from the OH group. The β‐spin electrons are delocalized over the ONO group, with the largest concentration (0.34e) on the lone pair of nitrogen V(N). © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

Electron transfer rates in DNA films as a function of tether length

A homologous series of DNA-modified electrodes has been investigated in which the molecular tether length varies. Using intercalated, covalently bound daunomycin as a redox probe, an exponential dependence of electron transfer rates on the number of intervening methylene groups in the sigma-bonded tether is observed. In contrast, variation in DM position within DNA yields no detectable change in rate. These data confirm that overall electron transfer rates in DNA films are limited by the tether, not the DNA.     

A quantitative measure of bond polarity from the electron localization function and the theory of atoms in molecules

 A quantitative measure of the polarity of a bond can be obtained through combining the two complementary topological partitionings of the electron density obtained from the atoms in molecules theory, on the one hand, and the electron localization function, on the other. This requires an integration of the electron density in the atomic subbasins of a common bond electron localization basin. We present the first numerical application of the resulting topological definition of bond polarity to a set of small linear systems consisting of the FCN, HF, HCl, HBr, and NaCl molecules and the NeAr van der Waals dimer. It is shown that the findings are essentially in line with common expectation for these simple molecules, thus confirming the potential value of the novel bond polarity index for the analysis of controversial bonding situations. Additional insight is provided through the detailed investigation of fluctuations in the basin populations. Received: 10 January 2001 / Accepted 12 February 2001 / Published online: 22 May 2001     

Electron pairing and chemical bonds. Electron fluctuation and pair localization in ELF domains

This article reports the numerical comparison of the quantities characterizing the extent of electron fluctuation and pair localization in the domains determined by the direct minimization of electron fluctuation with the domains resulting from the partitioning of the molecules based on the topological analysis of the so-called electron localization function (ELF). Such a comparison demonstrates that the ELF partitioning can be regarded as a feasible alternative to computationally much more demanding direct optimization of minimum fluctuation domains. This opened the possibility of the systematic scrutiny of the electron pair model of the chemical bond, and as it was demonstrated, the previous pessimistic claims about the applicability of this model are not completely justified.     

Electron localization functions and local measures of the covariance

The electron localization measure proposed by Becke and Edgecombe is shown to be related to the covariance of the electron pair distribution. Just as with the electron localization function, the local covariance does not seem to be, in and of itself, a useful quantity for elucidating shell structure. A function of the local covariance, however, is useful for this purpose. A different function, based on the hyperbolic tangent, is proposed to elucidate the shell structure encapsulated by the local covariance; this function also seems to work better for the electron localization measure of Becke and Edgecombe. In addition, we propose a different measure for the electron localization that incorporates both the electron localization measure of Becke and Edgecombe and the Laplacian of the electron density; preliminary indications are that this measure is especially good at elucidating the shell structure in valence regions. Methods for evaluating electron localization functions directly from the electron density, without recourse to the Kohn-Sham orbitals, are discussed.     

Thermodynamic functions of conformational changes. 2. Conformational entropy as a measure of information accumulation

Various folded molecular structures contain different amount of information. The relative amount of information may be related to relative entropy or entropy change. The conformational entropy change for n-butane has been computed as the function of rotation around the central C-C bond. It appears that the g+ or g- conformers contain about 16% more information than the anti-structure. Furthermore, the syn conformation with the two groups eclipsed contained about 42% more information than the fully staggered anti orientation. The conformational entropy function calculated from 3N - 7 internal degrees of freedom was found to be a continuous function.     

Shannon information entropy of fractional occupation probability as an electron correlation measure in atoms and molecules

A new method to determine electron correlation energy is presented for atoms and molecules. This method is based on Shannon information entropy that is obtained by fractional occupation probabilities of natural atomic orbitals. It is indicated that the Shannon entropy increases as the number of electrons increases and thus can be considered as a possible measure for the electron correlation in atomic and molecular systems. For neutral atoms and singly charged positive ions we proposed an expression for correlation energy with explicit dependence on the Shannon entropy and atomic number. The obtained correlation energies have been used to compute the first ionization potentials of the ground state of the main group elements from hydrogen through krypton. The calculated ionization potentials are in reasonably good agreement with their corresponding experimental values.We also developed the additivity scheme to find a connection between Shannon entropy and molecular correlation energy. The estimated molecular correlation energies show an excellent agreement with those obtained by elaborate G3 method with R² = 0.990.     

Electron pair density information measures in atomic systems

Shannon entropies of the pair density, conditional entropies, and mutual information are studied in position and in momentum space for ground state neutral atoms and selected excited states at the Hartree‐Fock level. We show that the mutual information, a measure of correlation, is larger in position space than in momentum space. This result also holds for a mutual information defined in terms of the exchange density; however, these quantities display much more structure than the corresponding ones based on the pair densities. The interpretation of this behavior is that exchange effects are smaller in momentum space than in position space in these systems. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011