An orbital localization criterion based on the topological analysis of the electron localization function

This work proposes a new molecular orbital localization procedure. The approach is based on the decomposition of the overlap matrix in accordance with the partitioning of the three‐dimensional physical space into basins with clear chemical meaning arising from the topological analysis of the electron localization function. The procedure is computationally inexpensive, provides a straightforward interpretation of the resulting orbitals in terms of their localization indices and basin occupancies, and preserves the σ/π‐separability in planar N‐electron systems. The localization algorithm is tested on selected molecular systems. © 2012 Wiley Periodicals, Inc.     

An orbital localization criterion based on the topological analysis of the electron localization function at correlated level

This work describes a procedure for localizing orbitals based on the topological analysis of the electron localization function at correlated level. The decomposition of the overlap matrix according to the partitioning of the three dimensional physical space into basins provided by that function allows us to define a localization index to be maximized using isopycnic orbital transformations. The localization algorithm has been computationally implemented and its efficiency tested on selected molecular systems at equilibrium, stretched, and twisted geometries. We report results which allow to analyze the influence of the correlated and uncorrelated treatments on the orbital localization.     

Gaussian和Multiwfn软件在判断蒽和菲芳香性上的应用

利用Gaussian软件对蒽和菲分子进行几何优化,在Multiwfn软件中运用等化学屏蔽表面(ICSS)和电子定域化函数(ELF)方法对蒽和菲进行了芳香性分析,并使分析结果可视化。结果表明,Gaussian和Multiwfn软件结合可以直观地解释蒽和菲不同环的芳香性差异,将分析结果应用于课堂教学,可以使课堂教学更加直观可视化。     

NBO 6.0: Natural bond orbital analysis program

We describe principal features of the newly released version, NBO 6.0, of the natural bond orbital analysis program, that provides novel “link‐free” interactivity with host electronic structure systems, improved search algorithms and labeling conventions for a broader range of chemical species, and new analysis options that significantly extend the range of chemical applications. We sketch the motivation and implementation of program changes and describe newer analysis options with illustrative applications. © 2013 Wiley Periodicals, Inc.     

Principal component analysis of the effects of wavefunction modification on the electrostatic potential of indole

The molecular electrostatic potential (MEP) of the indole molecule was calculated in a three‐dimensional grid in which the molecule was centered at the origin. To evaluate the dependence of MEP on the type of calculation, semiempirical, ab initio, and density functional theory methods with different basis sets were employed. The data matrix generated by these calculations was analyzed by principal component analysis (PCA). The appearance of outliers and the effect of wavefunction modifications such as the introduction of electron correlations and diffuse functions were highlighted by the use of PCA. The spatial localization of such effects around the molecule was possible from the loadings values associated with the graphical analysis of the grid points. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

ORBKIT: A modular python toolbox for cross‐platform postprocessing of quantum chemical wavefunction data

ORBKIT is a toolbox for postprocessing electronic structure calculations based on a highly modular and portable Python architecture. The program allows computing a multitude of electronic properties of molecular systems on arbitrary spatial grids from the basis set representation of its electronic wavefunction, as well as several grid‐independent properties. The required data can be extracted directly from the standard output of a large number of quantum chemistry programs. ORBKIT can be used as a standalone program to determine standard quantities, for example, the electron density, molecular orbitals, and derivatives thereof. The cornerstone of ORBKIT is its modular structure. The existing basic functions can be arranged in an individual way and can be easily extended by user‐written modules to determine any other derived quantity. ORBKIT offers multiple output formats that can be processed by common visualization tools (VMD, Molden, etc.). Additionally, ORBKIT possesses routines to order molecular orbitals computed at different nuclear configurations according to their electronic character and to interpolate the wavefunction between these configurations. The program is open‐source under GNU‐LGPLv3 license and freely available at https://github.com/orbkit/orbkit/ . This article provides an overview of ORBKIT with particular focus on its capabilities and applicability, and includes several example calculations. © 2016 Wiley Periodicals, Inc.     

Theoretical study of 3d‐metal mononitrides using DFT method

3d‐Metal mononitrides are studied using the density functional theory method. The lowest spin state for these dimers is obtained using the B3LYP hybrid functional with the 6‐311+G* basis set. The equilibrium geometries, vibrational frequencies, binding energies, Mulliken, and natural orbital population analysis charges, natural orbital electronic configuration, electron affinity, and ionization potential are obtained. Mulliken as well as natural orbital population analysis charges indicate that for all dimers, in cations most of the positive charge localized on the transition metal atom where in anions most of the negative charge localized on nitrogen atom. The binding energies for 3d‐metal mononitrides are higher than those for monocarbides and monoxides. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Advancing beyond charge analysis using the electronic localization function: Chemically intuitive distribution of electrostatic moments

We propose here an evaluation of chemically intuitive distributed electrostatic moments using the topological analysis of the electron localization function (ELF). As this partition of the total charge density provides an accurate representation of the molecular dipole, the distributed electrostatic moments based on the ELF partition (DEMEP) allows computing of local moments located at non atomic centers such as lone pairs, sigma bonds and pi systems. As the local dipole contribution can be decomposed in polarization and charge transfer components, our results indicate that local dipolar polarization of the lone pairs and chemical reactivity are closely related whereas the charge transfer contribution is the key factor driving the local bond dipole. Results on relevant molecules show that local dipole contributions can be used to rationalize inductive polarization effects in alcohols derivatives and typical hydrogen bond interactions. Moreover, bond quadrupole polarization moments being related to a pi character enable to discuss bond multiplicities, and to sort families of molecules according to their bond order. That way, the nature of the C-O bond has been revisited for several typical systems by means of the DEMEP analysis which appears also helpful to discuss aromaticity. Special attention has been given to the carbon monoxide molecule, to the CuCO complex and to a weak intramolecular N|-CO interaction involved in several biological systems. In this latter case, it is confirmed that the bond formation is mainly linked to the CO bond polarization. Transferability tests show that the approach is suitable for the design of advanced force fields.     

Electronegativity estimator built on QTAIM‐based domains of the bond electron density

The electron localization function, natural localized molecular orbitals, and the quantum theory of atoms in molecules have been used all together to analyze the bond electron density (BED) distribution of different hydrogen‐containing compounds through the definition of atomic contributions to the bonding regions. A function, g_AH, obtained from those contributions is analyzed along the second and third periods of the periodic table. It exhibits periodic trends typically assigned to the electronegativity (χ), and it is also sensitive to hybridization variations. This function also shows an interesting S shape with different χ‐scales, Allred–Rochow's being the one exhibiting the best monotonical increase with regard to the BED taken by each atom of the bond. Therefore, we think this χ can be actually related to the BED distribution. © 2014 Wiley Periodicals, Inc.     

Determination of substitutional sites in heterocycles from the topological analysis of the electron localization function (ELF)

The topological analysis of the electron localization function ELF has been carried out on five‐membered (C₄H₄NH, C₄H₄PH, C₄H₄O, C₄H₄S) and six‐membered (C₅H₅N, C₅H₅P) heterocycles. The bonding in these molecules is discussed on the basis of the valence basin populations. It is shown that the values of the ELF function at the (3,−1) critical points between disynaptic basins related to a given center provide a criterion to determine substitutional sites. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 509–514, 2000     

Theoretical study of one‐electron bonds in a series of high‐spin lithium–beryllium–hydrogen clusters: “Valence shell single‐electron repulsion” rule and electron localization function analysis

A series of high‐spin clusters containing Li, H, and Be in which the valence shell molecular orbitals (MOs) are occupied by a single electron has been characterized using ab initio and density functional theory (DFT) calculations. A first type (⁵Li₂, ⁿ⁺¹LiH_n+ (n = 2–5), ⁸Li₂H) possesses only one electron pair in the lowest MO, with bond energies of ～3 kcal/mol. In a second type, all the MOs are singly occupied, which results in highly excited species that nevertheless constitute a marked minimum on their potential energy surface (PES). Thus, it is possible to design a larger panel of structures (⁸LiBe, ⁷Li₂, ⁸Li, ⁴LiH⁺, ⁶BeH, ⁿ⁺³LiH (n = 3, 4), ⁿ⁺²LiH (n = 4–6), ⁸Li₂H, ⁹Li₂H, ²²Li₃Be₃ and ²²Li₆H), single‐electron equivalent to doublet “classical” molecules ranging from CO to C₆H₆. The geometrical structure is studied in relation to the valence shell single‐electron repulsion (VSEPR) theory and the electron localization function (ELF) is analyzed, revealing a striking similarity with the corresponding structure having paired electrons. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Investigation of substituent effects in aerogen‐bonding interaction between ZO3 (Z=Kr,Xe) and nitrogen bases

The substituent effects in aerogen bond interactions between ZO₃ (Z = Kr, Xe) and different nitrogen bases are studied at the MP2/aug‐cc‐pVTZ level of theory. The nitrogen bases include the sp bases NCH, NCF, NCCl, NCBr, NCCN, NCOH, NCCH₃ and the sp³ bases NH₃, NH₂F, NH₂Cl, NH₂Br, NH₂CN, NH₂OH, and NH₂CH₃. The nature of aerogen bonds in these complexes is analyzed by means of molecular electrostatic potential, electron localization function, quantum theory atoms in molecules, noncovalent interaction index, and natural bond orbital analyses. The interaction energy (E_int) ranges from ?4.59 to ?9.65 kcal/mol in the O₃Z···NCX complexes and from ?5.30 to ?13.57 kcal/mol in the O₃Z···NH₂X ones. The dominant charge‐transfer interaction in these complexes occurs across the aerogen bond from the nitrogen lone‐pair (n_N) of the Lewis base to the σ*_Z‐O antibonding orbital of the ZO₃. Besides, the formation of aerogen bond tends to decrease the ⁸³Kr or ¹³¹Xe chemical shielding values in these complexes. © 2016 Wiley Periodicals, Inc.     

Photoionization cross sections of H2(+) and H2 with complex Gaussian-type basis functions optimized for the frequency-dependent polarizabilities

Within the framework of the complex basis function method, the photoionization cross sections of H(2)(+) and H(2) were calculated based on the variational principle for the frequency-dependent polarizabilities. In these calculations, complex orbital exponents of Gaussian-type basis functions for the final state continuum wavefunctions were fully optimized for each photon energy with the numerical Newton-Raphson method. In most cases, the use of only one or two complex Gaussian-type basis functions was enough to obtain excellent agreement with previous high precision calculations and available experimental results. However, there were a few cases, in which the use of complex basis functions having various angular momentum quantum numbers was crucial to obtain the accurate results. The behavior of the complex orbital exponents as a function of photon energy was discussed in relation to the scaling relation and the effective charge for photoelectron. The success of this method implies the effectiveness of the optimization of orbital exponents to reduce the number of basis functions and shows the possibility to calculate photoionization cross sections of general molecules using only Gaussian-type basis functions.     

Charge decomposition analysis of the electron localizability indicator: a bridge between the orbital and direct space representation of the chemical bond

The novel functional electron localizability indicator is a useful tool for investigating chemical bonding in molecules and solids. In contrast to the traditional electron localization function (ELF), the electron localizability indicator is shown to be exactly decomposable into partial orbital contributions even though it displays at the single-determinantal level of theory the same topology as the ELF. This approach is generally valid for molecules and crystals at either the single-determinantal or the explicitly correlated level of theory. The advantages of the new approach are illustrated for the argon atom, homonuclear dimers N2 and F2, unsaturated hydrocarbons C2H4 and C6H6, and the transition-metal-containing molecules Sc(2)2+ and TiF4.