Atomic Natural Orbital Research Articles

Can Aromaticity Be Evaluated Using Atomic Partitions Based on the Hilbert-Space?

Aromaticity is a fundamental concept in chemistry that explains the stability and reactivity of many compounds by identifying atoms within a molecule that form an aromatic ring. Reliable aromaticity indices focus on electron delocalization and depend on atomic partitions, which give rise to the concept of an atom-in-the-molecule (AIM). Real-space atomic partitions present two important drawbacks: a high computational cost and numerical errors, limiting some aromaticity measures to medium-sized molecules with rings up to 12 atoms. This restriction hinders the study of large conjugated systems like porphyrins and nanorings. On the other hand, traditional Hilbert-space schemes are free of the latter limitations but can be unreliable for the large basis sets required in modern computational chemistry. This paper explores AIMs based on three robust Hilbert-space partitions - meta-Löwdin, Natural Atomic Orbitals (NAO), and Intrinsic Atomic Orbitals (IAO) - which combine the advantages of real-space partitions without their disadvantages. These partitions can effectively replace real-space AIMs for evaluating the aromatic character. For the first time, we report multicenter index (MCI) and Iring values for large rings and introduce ESIpy, an open-source Python code for aromaticity analysis in large conjugated rings.

Synthesis, characterization, DFT/M06 studies, NBO, QTAIM and RDG analyses of new copper (II) complexes with bis-phosphonamide obtained under microwave irradiation

We have devised a novel one-step approach for synthesizing bis-phosphonamides utilizing primary amines and phenylphosphonic dichloride (PPDC) under ultrasound irradiation. The bis-phosphonamides obtained were used as organophosphorus ligands for the synthesis of new copper (II) complexes with metal ions. The synthesis of these complexes was accomplished via a novel eco-friendly method employing microwave irradiation. The desired complex obtained, as a green powder in 65% yield, which were fully characterized by spectroscopic methods (FT-IR, UV–vis, XDR). To gain and further insights into structure and properties of studied complexes, several calculations such as Natural Atomic Orbitals (NAO), Natural Bond orbitals(NBO), Quantum Theory of Atoms in Molecules (QTAIM) analysis were performed at M06/6-311++g(d, p) level. Using the Reduced electron Density Gradient (RDG) approach, the non-covalent interactions were explored and visualized in two and three-dimensional spaces.

Novel Zn- and Cd-Schiff base complexes as the potent anticancer agents: Synthesis, spectral characterization and theoretical study

A novel unsymmetrical bidentate Schiff base ligand and its complexes, with the common formula of MLX2 (M(II) = Zn(II) and Cd(II); X− = Cl−, Br− and I−), using a reaction between 1,2-diaminobenzene and (E)-3-(4-(Dimethylamino) phenyl) acrylaldehyde were successfully synthesized. The structure of all the as-made compounds was identified by techniques including 1H NMR,13C NMR, ESI-mass, FT-IR, UV–Vis, melting point and molar conductivity. The analytical and spectral data confirmed the metal to ligand ratio of 1:1 in the Zn(II) and Cd(II) complexes. The anticancer activity of the compounds on cancer cells was investigated on HCT116 cell line, where the MTT method was used to screen cytotoxicity effects. The flow cytometry method also was used to determine the mechanism of cell death. Our data reveal that CdLCl2 can block the cell cycle and induction apoptosis. In addition, using Gaussian 16 program, the structure of the samples was optimized, and some important properties such as enthalpy change, entropy change and total energy were extracted. The molecular electrostatic potential, nonlinear optical properties, natural bond orbital and frontier molecular orbitals analysis were calculated for all compounds. Further, the electrophilic and nucleophilic sites, energy gap, ionization potential, electron affinity, natural population analysis and natural atomic orbitals were studied.

Novel copper (II) and zinc (II) complexes with enrofloxacin and oxolinic acid: synthesis, characterization, Hirshfeld surface and DFT/CAM-B3LYPD3BJ studies: NBO, QTAIM and RDG analysis

This study aimed to investigate the crystal structure of the synthesized complexes of Cu (II) and Zn (II) with enrofloxacin and oxolinic acid. The characterization of the complexes was carried out using single–crystal x-ray diffraction, Hirshfeld surface and 1H NMR spectroscopy. In addition, a DFT/6-31g(d) investigation was conducted to assess the performance of two exchange-correlation functionals CAM-B3LYP and CAM-B3LYPD3BJ to predict both covalent and non-covalent bonds lengths, and the vibrational frequencies of the metallic complexes.The main findings of this study indicate that the interaction between each metallic ion and the corresponding ligand leads to significant modifications in bond lengths, Mulliken charge distribution and electrostatic potential values in the complex molecules as compared to the ligands alone. To gain further insights into these complexes, several calculations were performed, such as Natural Atomic orbitals (NAO), Natural Bond orbitals (NBO), and Quantum Theory of Atoms in Molecules (QTAIM) analysis. The non-covalent interactions were explored and visualized in two and three-dimensional spaces with the help of the Reduced electron Density Gradient (RDG) approach.

Covalency in AnCl2 (An = Th-No).

A potential connection has previously been proposed between the emergence of unexpected covalent behaviour in various transcurium complexes and the increasing stability of the +2 oxidation state in the later members of the actinide series. We recently used computational methods to study AnCl3, finding evidence for energy degeneracy driven covalency in the later actinides, and here present a comparative study of AnCl2. The An-Cl bond lengths of the latter divide into two data sets; Th-Np, Cm, Bk and Pu, Am, Cf-No. On average the An-Cl bond length decreases for both sets but, with significant increases between Np and Pu, and between Bk and Cf, unlike the former group (Pu, Am, Cf-No)Cl2 have significantly larger lengths than the corresponding trichlorides. Using a range of Natural Bond Orbital (NBO), Natural Resonance Theory (NRT) and Quantum Theory of Atoms In Molecules (QTAIM) metrics, the covalency of the dichloride bonds is analysed. We find that the first group of dichlorides are similar to their trichloride counterparts and possess significantly more covalent bonds than (Pu, Am, Cf-No)Cl2. We believe this change in covalent behaviour across the series for the dichlorides is due to a decreased involvement of the 6d orbital in the later elements (as a result of the f-d excitation energy exceeding the d-stabilisation energy of the actinide ions in question). Moreover, we find that unlike the trichlorides, where the QTAIM delocalisation index indicates that covalency plateaus/moderately increases, An-Cl covalency decreases across the second half of the series for AnCl2. We attribute this difference in behaviour to a lack of significant energy degeneracy driven covalency for the dichlorides, with the energy difference between the dichlorides' β 5f and 3p Natural Atomic Orbitals being larger than for the trichlorides. Hence we find it is not the presence of a stable +2 oxidation state, but instead the extent of energy matching between the actinide 5f orbitals and the ligand 3p, that drives covalency in the transcurium chlorides.

Considering Density Functional Approaches for Actinide Species: The An66 Molecule Set.

The importance of spin-orbit effects on the predictions of energetic properties of actinide compounds has been considered for 18 different density functionals, comparing the spin-orbit and non-spin-orbit ("standard") forms of density functional theory (DFT). A set of enthalpies of formation for 66 small actinide (Th-Am) compounds-the An66 set, for which experimental data are available-have been investigated. The set includes actinide halides, oxides, and oxohalides in the general form AnOmXn, where n = 0-6, m = 0-3, and X = F, Cl, Br, or I. The impact of basis set choice was investigated, and to help account for the impact of relativity, the Stuttgart general and segmented contracted atomic natural orbital (ANO) basis sets paired with small core relativistic effective core potentials (RECP) as well as all-electron calculations utilizing the third-order Douglas-Kroll-Hess were considered.

Tuning Magnetic Relaxation in Square-Pyramidal Dysprosium Single-Molecule Magnets Using Apical Alkoxide Ligands

Tuning Magnetic Relaxation in Square-Pyramidal Dysprosium Single-Molecule Magnets Using Apical Alkoxide Ligands

Computational Exploration of 1-Amidino-O-(n-butyl) Urea (ABnUH) with Natural Atomic Orbitals, Natural Bond Orbital, Vibrational Analysis and Simulated UV-Visible Spectra

Theoretical treatment of 1-amidino-O-(n-butyl)urea (ABnUH) have been performed by DFT/B3LYP with 6-311++ G (d,p) basis set using Gaussian 09W. The compound has been analyzed on the basis of electronic structure, hybridization of the atoms, charge delocalization, hyper-conjugative interactions, vibrational modes, etc. NBO analysis was performed to figure out any charge transfer among the localized bond and lone pair of the proposed compound.

Solvent effect on the 195Pt NMR properties in pyridonate-bridged PtIII dinuclear complex derivatives investigated by ab initio molecular dynamics and localized orbital analysis.

An ab initio molecular dynamics investigation of the solvent effect (water) on the structural parameters, 195Pt NMR spin-spin coupling constants (SSCCs) and chemical shifts of a series of pyridonate-bridged PtIII dinuclear complexes is performed using Kohn-Sham (KS) Car-Parrinello molecular dynamics (CPMD) and relativistic hybrid KS NMR calculations. The indirect solvent effect (via structural changes) has a dramatic effect on the 1JPtPt SSCCs. The complexes exhibit a strong trans influence in solution, where the Pt-Pt bond lengthens with increasing axial ligand σ-donor strength. In the diaqua complex, where the solvent effect is more pronounced, the SSCCs averaged for CPMD configurations with explicit plus implicit solvation agree much better with the experimental data, while the calculations for static geometry and CPMD unsolvated configurations show large deviations with respect to experiment. The combination of CPMD with hybrid KS NMR calculations provides a much more realistic computational model that reproduces the large magnitudes of 1JPtPt and 195Pt chemical shifts. An analysis of 1JPtPt in terms of localized and canonical orbitals shows that the SSCCs are driven by changes in the s-character of the natural atomic orbitals of Pt atoms, which affect the 'Fermi contact' mechanism.

Electrostatic Potential Fitting Method Using Constrained Spatial Electron Density Expanded with Preorthogonal Natural Atomic Orbitals.

In this study, an electrostatic potential (ESP) fitting method using constrained spatial electron density (cSED) expanded with preorthogonal natural atomic orbitals (pNAOs) was proposed. In this method, the electron density of a molecule is divided into spherical atom-centered electron densities and the expansion coefficient is determined to reproduce the ESP around the molecule. Our method was then applied to two systems: (i) a hydration reaction of cis-platin and (ii) a variety of organic/inorganic molecules. By evaluating the atomic charges along the hydration reaction, our method showed good conformational transferability, which cannot be obtained using conventional ESP fitting methods. Moreover, we successfully obtained the hydration structure along the reaction by coupling our method with a reference interaction site model (RISM). Reasonable data were obtained not only for organic molecules but also for inorganic molecules. This success came from the introduction of pNAOs as auxiliary basis sets in the charge fitting.

Block deformation analysis: Density matrix blocks as intramolecular deformation density.

Block deformation analysis as deformation density of atomic orbitals is introduced to analyze intramolecular interactions. In this respect, density matrix blocks in terms of natural atomic orbitals are employed to find interacting and noninteracting multicenter subsystem and extract the corresponding deformation density. Eigenanalysis of this deformation density is performed to result eigenvalues and eigenorbitals as displaced charge due to the intramolecular interaction and orbital space responsible for charge reorganization, respectively, that possesses advantages of other methods, simultaneously. It is applied to several small molecules, different types of carbon allotropes including zero-, one-, and two-dimensional nanostructures, and challenging systems such as ortho-hydrogen atoms in planar biphenyl. Results highly correlate with delocalization and Wiberg bond indices and show that eigenvalues of block deformation analysis deserved to be considered as bonding index.

Chemical bonding in trimers of Ge2 with monovalent metals

AbstractChemical bonding of the monovalent metal‐doped germanium Ge2M (M belonging the groups IA and IB) clusters is investigated by using quantum chemical calculations combined with the analyses of natural atomic orbital (NAO), natural bond orbital (NBO) and natural resonance theory (NRT). All of the clusters have a ground state in isosceles triangle shape with two quasi‐degenerate electronic states (2A1, 2B1). The clusters doped with metals of the group IB are more stable than those doped with the alkali metals of the group IA due to the stronger Ge‐M bond of the former ones. Most clusters have the electron transfer from the dopant atoms to the dimer Ge2. This study reveals that the Ge‐M bonds is very weak and highly ionic with M being alkali metals, while they are stronger and possess both ionic and covalent nature with a larger contribution of the ionic character for M being IB elements. The participation of AO‐d in the Ge‐M bonds of the IB elements is the reason for their larger strength and covalent character.

Theoretical calculation of total electron-impact ionization cross section of C6F12O

C6F12O can be used in gas-insulated equipment due to its excellent insulation properties. The purpose of this paper is to calculate the total electron-impact ionization cross section to evaluate the dielectric strength of the molecule using the Deutsch–Märk formula. First, according to the calculation method of quantum chemistry, the structure of the molecule is optimized. Three different methods, such as Mulliken population analysis, C-squared population analysis, and natural atomic orbital (NAO), are used to calculate the molecular orbital components, and then the molecular collision cross section is obtained. The influence of different weighting factors on the calculation results is analyzed. The validity of the proposed method is verified by the calculation results of H2O, C3H6O, and C5F10O. The results show that the calculation value with the NAO method is closer to the experimental results, which provides a reference for the calculation and analysis of the collision cross section of C6F12O. The calculation results in this paper can provide basic data for further calculation of the dielectric strength of C6F12O.

Molecular Structural Properties of [n]-Annulene (n = 8, 10, 12, 14) and its Boron Nitride Derivatives: Analysis of NMR, NBO, ELF and PDI

Due to the importance of structural properties of annulene in physical and inorganic chemistry, the trajectory of the NBO to MO evolution can be written as natural atomic orbitals (NAO) → natural hybrid orbital (NHO) → natural bond orbital (NBO) → natural semi-localized MO (NLMO) → MO. The electron density distribution in this [n]-annulene series (both ions and molecules) (n = 8, 10, 12, 14) is investigated by NMR, NBO, ELF, FLU, and PDI analyses. The (4n+2)π and also 4nπ systems (Huckel’s rule) on variants of those compounds via the localized orbital localization (LOL) and electron localized function (ELF) are discussed, and a diatropic ring current (aromatic) is also distinguished for some other paratropic currents (anti-aromatic). The NHO direction and bond bending deviations from the line of nuclear centers are exhibited for understanding the situation of π and σ orbitals. In this work, for each NAO function, core, valence, or Rydberg, the orbital occupancy and the orbital energies are discussed. In addition, nucleus independent chemical shifts (NICSs) and statistical nucleus chemical shifts (S-NICSs) confirm the aromaticity and anti-aromaticity amounts in those rings.

Roby-Gould bond indices as a tool for understanding chemical bonding from a mathematical and quantum mechanical perspective

In this paper we elaborate and evaluate the Roby-Gould bond index method (RGBI) for classifying and interpreting the nature of chemical bonds [Gould et al., Theor. Chem. Acc., 2008, 119, 275]. We emphasize that the RGBI method defines atoms as subspaces of a Hilbert space, represented as projection operators, and in accord with basic mathematical requirements concerning the assignment of probabilities to such subspaces. The definition of the bond indices between such atoms follows from simple set theoretical ideas concerning the sharing of, and differences between, atomic electron populations; and from the geometric properties associated with these subspaces—properties which are closely aligned with older chemical notions, which are reviewed. We also introduce the Araki angle percentage ionicity of a bond, which is easily read off from a compact two-dimensional representation of the chemical bond, which we call the bond dial diagram. Additionally we explore the theory with defining atoms by the occupied natural atomic spinorbitals (NAOs) of Reed and coworkers, instead of the atomic natural orbitals (ANOs) previously used. Bond indices from these ANO- and NAO-based atoms are applied to a dataset of 353 molecules, including 27 first row molecules, 280 organic molecules, and 46 semiochemical molecules, comprising 33 A–H bonds, where A are first and second row elements, 1779 C–X, 3415 H–X bonds (X = C, N, O, S), and a few more other types of bonds. The bond indices from the ANO-based atoms are much more in accord with chemists' expectations as compared to those obtained from NAO-based atoms provided that the excited triplet state defines the ANOs for group 2 atoms.

Molecular structural properties of [n] annulene (n = 8, 10, 12 and 14) and its boron nitride derivatives: Analysis of NMR, NBO, ELF and PDI

Due to the importance of structural properties of annulene in physical and inorganic chemistry, the trajectory of the NBO to MO evolution can be written as natural atomic orbitals (NAO) → natural hybrid orbital (NHO) → natural bond orbital (NBO) → natural semi-localized MO (NLMO) → MO. The electron density distribution in this [n]-annulene series (both ions and molecules) (n = 8, 10, 12, 14) is investigated by NMR, NBO, ELF, FLU, and PDI analyses. The (4n+2)p and also 4np systems (Hückel's rule) on variants of those compounds via the localized orbital localization (LOL) and electron localized function (ELF) are discussed, and a diatropic ring current (aromatic) is also distinguished for some other paratropic currents (anti-aromatic). The NHO direction and bond bending deviations from the line of nuclear centers are exhibited for understanding the situation of p and s orbitals. In this work, for each NAO function, core, valence, or Rydberg, the orbital occupancy and the orbital energies are discussed. In addition, nucleus independent chemical shifts (NICSs) and statistical nucleus chemical shifts (S-NICSs) confirm the aromaticity and anti-aromaticity amounts in those rings.

İnce Cu2ZnSnS4 (CZTS) filmin RBS spektrumundan enerji kaybı analizi

The goal of this work is to offer an alternative method to the available literature on determining the energy loss of CZTS thin films. For this purpose, thin CZTS film structures were first produced by sol-gel method and then the RBS spectrum was received with RBS detector irradiating this structure with 3.034 MeV proton beams in a microbeam chamber. The energy calibration was implemented to this spectrum, where the it was fitted with SIMNRA program. In the RBS spectrum of the thin film generated, a method for the calculation of energy loss was used for the position and energy width analysis of the corresponding peaks and a polynomial fit was obtained from the stopping power of the CZTS thin film by making certain approaches. Also, the effective charge approach that we used in our previous studies for the stopping power was employed with atomic natural orbitals and it was founded that the results were close to each other at certain error rates. The data obtained from this study will inspire the future studies on the interaction of radiation with matter.

The ANO-R Basis Set.

In this work, the new ANO-R basis set for all elements of the first six periods is introduced. The ANO-R basis set is an all-electron basis set that was constructed including scalar-relativistic effects of the exact-two component (X2C) Hamiltonian and modeling the atomic nucleus by a Gaussian charge distribution, which makes the basis set suitable for calculations of both light and heavy elements. For high accuracy, it takes advantage of the general contraction scheme and was developed at the CASSCF/CASPT2 level of theory. The distinguishing feature of the ANO-R basis set is its compactness in terms of both primitive and contracted basis functions, thus containing no superfluous functions for a given quality. An optimum number of primitive basis functions was selected based on studying the convergence toward the complete basis set limit for each element individually. The primitive basis sets were then contracted using the density-averaged atomic-natural-orbital (ANO) scheme, and suitable contraction levels were determined solely based on the natural orbital occupation numbers that describe the contribution of each natural orbital to the one-particle density matrix. Rather than following the common "split-valence n-tuple zeta plus polarization functions" structure, the resulting basis sets ANO-R0 to ANO-R3 possess a unique composition for each element, ensuring that no unnecessary functions are included while the basis sets are still balanced across the first six periods (H-Rn).

A Comparison of Medium-Sized Basis Sets for the Prediction of Geometries, Vibrational Frequencies, Infrared Intensities and Raman Activities for Water

Optimized geometries, vibrational frequencies, as well as infrared intensities and Raman activities were calculated for water (H2O) utilizing popular quantum mechanical approaches. Here, density functional theory (DFT) calculations were performed using the B3LYP (Becke, three-parameter, Lee-Yang-Parr) functional, as well as ab initio calculations using second-order Møller-Plesset (MP2) perturbation theory and coupled-cluster with single, double and perturbative triple excitations [CCSD(T)] levels of theory were used. We assess and benchmark the performance of 69 different atomic orbital basis sets including various popular families of medium-sized basis sets typically of two to four zeta quality and differing levels of augmentation by polar and diffuse functions. The basis sets range from the commonly adopted Pople-style (6-31G & 6-311G), Dunning’s correlation consistent (cc-pV(n+d)Z & aug-cc-pV(n+d)Z, as well as Truhlar’s calendar variations, Jensen’s polarization consistent (pc-n & aug-pc-n), Ahlrichs (def2-…), Sapporo’s and Karlsruches as well as atomic natural orbitals (ANOs) such as NASA Ames (ANOn), Neese-style, and Roos-style. We also compare several basis sets specifically designed to calculate vibrational and electronic properties, including the Sadlej-pVTZ (and LPol-X families), as well as SNS families of Barone. The results are compared to experimental values where available, or calculations performed with 5 or 6 zeta-level (e.g., cc-pV6Z). The performance of each family of basis sets is discussed in terms of their accuracy (and pitfalls), as well as computational resource scaling and efficiency. The Def2 basis family performs very well overall, yielding more accurate results with lower runtimes than traditional basis sets. ‘May’ basis sets also provide accurate predictions of vibrational frequencies at significantly lower costs. Raman activities can be accurately calculated using MP2 under harmonic approximation with several ‘spectroscopic’ families performing well.

Density functional theory plus dynamical mean-field theory with natural atomic orbital projectors

We introduce natural atomic orbitals as the local projector to define the correlated subspace for DFT + DMFT (density functional theory plus dynamical mean-field theory) calculation. The natural atomic orbitals are found to be stably constructed against the number and the radius of basis orbitals. It can also be self-consistently updated inside the DFT+DMFT loop. The spatial localization, electron occupation and the degree of correlation are investigated and compared with other conventional techniques. As a `natural' choice to describe the electron numbers, adopting natural atomic orbitals has advantage in terms of electron number counting. We further explore the reduction of computation cost by separating correlated orbitals into two subgroups based on the orbital occupancy. Our new recipe can serve as a useful choice for DFT+DMFT and related methods.