Density functional and molecular orbital study of physical process of inversion of nitrogen trifluoride (NF3) molecule

The physical process of the umbrella inversion of the nitrogen trifluoride molecule has been studied invoking the formalisms of the density functional theory, the frontier orbital theory, and the molecular orbital theory. An intuitive structure and dynamics of evolution of the transition state for the event of inversion is suggested. The physical process of dynamic evolution of the molecular conformations between the equilibrium (C_3v) shape and the planar (D_3h) transition state has been followed by a number of molecular orbital and density functional parameters like the total energy, the eigenvalues of the frontier orbitals, the highest occupied molecular orbital and lowest unoccupied molecular orbital, the (HOMO–LUMO) gap, the global hardness and softness, and the chemical potential. The molecular conformations are generated by deforming the ∠FNF angle through steps of 2° from its equilibrium value, and the cycle is continued till the planar transition state is reached, and the geometry of each conformation is optimized with respect to the length of the N? F bond. The geometry optimization demonstrates that the structural evolution entails an associated slow decrease in the length of the N? F bond. The dipole moment at the equilibrium form is small and that at the transition state is zero and shows a strange behavior with the evolution of conformations. As the molecular structure begins to distort from its equilibrium shape by opening of the ∠FNF angle, the dipole moment starts increasing very sharply, and the trend continues very near to the transition state but abruptly vanishes at the transition state. A rationale of the strange variation of dipole moment as a function of evolution of conformations could be obtained in terms of quantum mechanical hybridization of the lone pair on the N atom. The pattern of charge density reorganization as a function of geometry evolution is a continuous depletion of charge from the F center and piling up of charge on the N center. The continuous shortening of bond length and the pattern of variation of net charge densities on atomic sites with evolution of molecular conformations predicts that the bond moment would decrease continuously. The quantum mechanical hybridization of the lone pair of the central N atom shows that the percentage of s character of the lone‐pair hybrid on the N atom decreases at a very accelerated rate, and the lone pair at the transition state is accommodated in a pure p orbital. The result of the continued destruction of asymmetry of charge distribution in the lone pair on the central N atom due to the elimination of contribution of the s orbital with evolution of molecular conformations is the sharp decrease in lone‐pair moment. The decrease in bond moment is overcompensated by the sharp fall of its offsetting component, the lone‐pair moment, resulting in a net gain in dipole moment with the evolution of molecular geometry. Since the offsetting component decreases very sharply, the net effect is a sharp rise of dipole moment with the evolution of molecular conformations just before the transition state. The lone‐pair moment is zero by virtue of the symmetry of the pure p orbital, the lone pair of the central atom in the transition state, and the sum of the bond moments is zero by symmetry of the geometry. The barrier height is quite high at ～65.45 kcal/mol, which is close to values computed through more sophisticated methods. It is argued that an earlier suggestion regarding the development of high barrier value of NF₃ system seems to be misleading and confronting with the conclusions of the density functional theory. An analysis and a comparative study of the physical components of the one‐ and two‐center energy terms reveals that the pattern of the charge density reorganization has the principal role in deciding the origin and the magnitude of barrier of inversion of the molecule and the barrier originates not from a particular energetic effect localized in a particular region of the molecule, rather the barrier originates from a subtle interplay of one‐ and two‐center components of the total energy. The decomposed energy components show that the F?F nonbonded interaction and N? F bonded interaction favor the formation of transition state, while the one‐center energy terms prohibit the formation of the transition state. The barrier principally develops from the one‐center energy components. The profile of the HOMO is isomorphic and that of the LUMO is homomorphic with the potential energy curve for the physical process of the event of umbrella inversion of the molecule. The variation of the HOMO–LUMO gap, ?ε, the global hardness, η, and the softness, S, as a function of the reaction coordinates of angular deformation of NF₃ molecule are quite consistent with the predictions of the molecular orbital and the density functional theories in connection with the deformation of molecular geometry. The profiles of ?ε, η, and S, as a function of reaction coordinates, mimic the potential energy curve of the molecule. The eigenvalues of the frontier orbitals, and the ?ε, η, S parameters are found to be equally effective theoretical parameters, like the total energy, to monitor the physical process of the inversion of pyramidal molecules. The nature of the variation of the global hardness parameter between the equilibrium shape and the transition state form for the inversion is in accordance with the principle of maximum hardness (PMH). © 2002 John Wiley & Sons, Inc. Int J Quantum Chem, 2002     

Normal (decoupled) representation of electronegativity equalization equations in a molecule

The decoupled (normal) representation of the electronegativity (chemical potential) equalization equations, in which the hardness tensor {η_ij}={?μ_i/?N_j} becomes diagonal, is examined in the atoms-in-a-molecule (AIM ) approximation; μ_i=?E/?N_i is the chemical potential of the i-th AIM , N_i is its electron population, and E is the system energy. All relevant chemical potential, hardness, softness, and Fukui function quantities corresponding to the normal electron redistribution channels, Q_y, are discussed and expressed in terms of the canonical AIM parameters. The normal chemical potentials, μ _γ=?E/?Q_γ, provide a natural classification of the normal modes into three groups: (a) acceptor normal modes (μ _a < 0, positive mode Fukui function, hardness, and softness), (b) donor normal modes (μ _d > 0, negative mode Fukui function, hardness, and softness), and (c) polarization normal modes (μ _p=0, zero mode Fukui function, hardness, and softness). The implications of the normal mode analysis for the theory of chemical reactivity are briefly summarized.     

Alkaline Earth Metals Activate N2 and CO in Cubic Complexes Just Like Transition Metals: A Conceptual Density Functional Theory and Energy Decomposition Analysis Study

Following the recent discovery of stable octa-coordinated alkaline earth metals with N₂ and CO, the role of group II metals in the catalytic reduction of these ligands by means of density functional theory (DFT) calculations and conceptual DFT-based reactivity indices is investigated. Cubic group IV and octahedral group VI transition metal complexes as well as the free ligands are computed for reference. The outer and most accessible atoms of N₂ and CO become much more nucleophilic and electrophilic in all complexes, relevant for N₂ fixation, as probed by the Fukui function and local softness. Within one row of the periodic table, the alkaline earth complexes often show the strongest activation. On the contrary, the electrostatic character is found to be virtually unaffected by complexation. Trends in the soft frontier orbital and hard electrostatic character are in agreement with calculated proton affinities and energy decomposition analyses of the protonated structures, demonstrating the dominance of the soft (HOMO–LUMO) orbital interactions.     

Core ionization energies of atoms and ions calculated using the generalized Sturmian method

The physical event of the umbrella inversion of ammonia has been studied in detail by application of the formalisms of frontier orbital theory, the density functional theory, the localized molecular orbital method, and the energy partitioning analysis. An intuitive structure for the transition state and dynamics of the physical process of structural reorganization prior to inversion have been suggested. The computation starts with the CNDO/2 equilibrium geometry, and thereafter the cycle proceeds through all the conformations of ammonia obtained by varying the ∠HNH angle in steps of 2° from its equilibrium value up to the transition state. The geometry of each conformation is optimized with respect to the length of the N–H bond. The glimpses of the charge density reorganization during the movement of the molecule from equilibrium conformation toward the transition state is computed in terms of dipole moment and the quantum mechanical hybridizations of bond pair and lone pair of N atom through the localized molecular orbitals (LMOs) of all the conformations. Results demonstrate that as the geometry of the molecule begins to evolve through the reorganization of structure, the N–H bond length and the dipole moment begin to decrease, and the trend continues up to the transition state. The dipole moment of the molecule at the suggested transition state is zero. The computed nature of quantum mechanical hybridization of bond pair and lone pair of the N atom as a function of reaction coordinates of the ∠HNH angles reveals that the percentage of s character of the lone pair hybrid decreases and that of the bond pair hybrid forming the σ(N–H) bond increases during the process of geometry reorganization from the equilibrium shape to the transition state. The rationale of the zero dipole moment of the transition state for inversion is not straightforward from its point‐group symmetry, but is self‐evident from its electronic structure drawn in terms of LMOs. The electronic structure of the transition state, which may be drawn in terms of the LMOs, seems to closely reproduce its suggested intuitive structure. The pattern of variation of dipole moment and nature of the changes of the percentage of the s character in the lone pair hybrid creating dipole with the evolution of geometry during the physical process of structural reorganization for the inversion are found to be nicely correlated according to the suggestion of Coulson. The profiles of the increasing strength of the N–H bond and the increasing percentage of s character of the bond pair hybrid of N atom forming this bond as a function of reaction coordinates are also found to be correlated in accordance with the suggestion of Coulson. The profile of global hardness as a function of reaction coordinate seems to demonstrate that the dynamics of the evolution of the molecular structure from equilibrium shape to the transition state following the course of suggested mode of structural reorganization conforms to the principle of maximum hardness (PMH). The profiles of parameters like the energies of highest occupied and lowest unoccupied molecular orbital (HOMO and LUMO), the gap in energy between HOMO and LUMO, the global hardness, the global softness, and chemical potential as a function of reaction coodinates of a continuous structural evolution from equilibrium shape to the transition state mimic the potential energy diagram of the total energy. Both the frontier orbital parameters and the density functional quantities are found to be equally effective and reliable to monitor the process of necessary structural reorganization prior to the inversion of mofecules. An energy partitioning analysis demonstrates that the origin of barrier has no unique single source rather as many as four mutually exclusive but interacting one‐ and two‐center energy terms within the molecule entail the origin and the height of the barrier. From a close analysis of the results, it seems highly probable that the necessary structural reorganization prior to umbrella inversion of ammonia most realistically occurs following the course of normal modes of vibration of the molecule. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 80: 1–26, 2000     

Koopmans-like approximation in the Kohn-Sham method and the impact of the frozen core approximation on the computation of the reactivity parameters of the density functional theory

A Koopmans-like approximation is introduced in the spin-polarized version of the Kohn-Sham (KS) density functional theory to obtain a relation between KS orbital energies and vertical ionization potential and electron affinity. Expressions for reactivity indexes (like electronegativity, hardness, electrophilicity, and excitation energies) include KS frontier orbital energies and additional contributions associated with the self-interaction correction. Those reactivity parameters were computed with different exchange-correlation functionals to test the approach for a set of small molecules. The results show that the present approximation provides a better way to estimate hardness, electronegativity, and electrophilicity than just the use of frontier orbital energy values. However KS HOMO and LUMO energy gap gives a better agreement with excitation energies.     

Adsorption of the nitrosamine and thionitrosamine molecules as carcinogen compounds on the BN and B3Al N nanotubes: A DFT study

DFT calculations were performed to investigation of the influence of doping three atoms of aluminum on the electronic properties of the (4,0) zigzag boron nitride nanotube (BNNT). Also, adsorption properties of nitrosamine (NA) and thionitrosamine (TNA) molecules as carcinogen agents onto BN and B_Al3N nanotubes were studied. The results show that the B_3AlN nanotube is the most energetically favorable candidates for adsorption of these molecules. Also, B(B_3Al)NNT/TNA complexes are more stable than B(B_3Al)NNT/NA complexes. The HOMO–LUMO gap, electronic chemical potential (μ), hardness (?), softness (S), the maximum amount of electronic charge (ΔN_max) and electrophilicity index (ω) for monomers and complexes in the gas and polar solvent phases were calculated. The results show that the conductivity and reactivity of BNNT increase by doping Al atoms instead of B atoms. Also, the interaction of NA and TNA molecules with BN and B_Al3N nanotubes results in significant changes in the electronic properties of nanotubes. Based on the natural bond orbital (NBO) analysis, in all complexes charge transfer occurs from NA and TNA molecules to nanotubes. Theory of atoms in molecules (AIM) was applied to characterize the nature of interactions in nanotubes. It is predicted that, BN and B_3AlN nanotubes can be used to as sensor for detection of NA and TNA molecules.     

Interfacial Behavior of Cysteine between Mild Steel and Sulfuric Acid as Corrosion Inhibitor

Interfacial behavior of cysteine (Cys) between mild steel and sulfuric acid solution as a corrosion inhibitor has been studied with electrochemical AC (alternating current) and DC (direct current) techniques at (25.0±0.1) °C. The AC impedance results were evaluated using equivalent circuits in which a constant phase element (CPE) has been replaced with double layer capacitance (C_dl) to represent the frequency distribution of experimental data. Changes in impedance parameters (charge transfer resistance and double layer capacitance) indicated that cysteine molecules acted by accumulating at the metal/solution interface. The fractional coverage of the metal surface () was determined using AC impedance results and it was found that the adsorption of cysteine on the mild steel surface followed a Langmuir isotherm model with a standard free energy of adsorption (ΔG⁰_ads) of −35.1 kJ·mol⁻¹.To clarify the type of interaction between mild steel surface and cysteine molecules with a molecular orbital approach, electronic properties, such as, the highest occupied molecular orbital (HOMO) energy, the lowest unoccupied molecular orbital (LUMO) energy, and the frontier molecular orbital coefficients have been calculated. Energy gaps for the interaction of mild steel surface and cysteine molecules (E_{LUMO Fe}−E_{HOMO Cys} and E_{LUMO Cys}−E_{HOMO Fe}) were used to determine whether cysteine molecules acted as electron donors or electron acceptors when they interacted with the mild steel surface. The local reactivity was evaluated through the condensed Fukui indices. Theoretical calculations were carried out using the density functional theory (DFT) at B3LYP level with the 6-311++G(d,p) basis set for all atoms by Gaussian 03W program.     

The Analysis of Os≡C Bond and Electric Field Influence on the Properties in the Osmium Carbyne Complex OsCl3 (≡CCH2CMe3 )(PH3 )2: A Theoretical Insight

In this paper, we study the effect of electric field on the dipole moment, electronic structure, and frontier orbital energy in the osmium carbyne complex OsCl₃ (≡CCH₂CMe₃ )(PH₃ )₂ using MPW1PW91 quantum chemical computations. We demonstrate the nature of the chemical bond between the [OsCl₃ (PH₃ )₂]⁻ and [CCH₂CMe₃ ]⁺ fragments through energy and charge decomposition analyses. We also estimate the percentage composition in terms of the specified groups of frontier orbitals for this complex to investigate the feature in the metal–ligand bonds. Quantum theory of atoms in molecules (QTAIM ) is applied to elucidate the Os≡C bond in the complex. Also, the influence of external electric field on the energy, frontier orbital energies, and HOMO–LUMO gap values is analyzed.     

Facile Synthesis of 5-Aryl-N-(pyrazin-2-yl)thiophene-2-carboxamides via Suzuki Cross-Coupling Reactions,Their Electronic and Nonlinear Optical Properties through DFT Calculations

Synthesis of 5-aryl-N-(pyrazin-2-yl)thiophene-2-carboxamides (4a–4n) by a Suzuki cross-coupling reaction of 5-bromo-N-(pyrazin-2-yl)thiophene-2-carboxamide (3) with various aryl/heteroaryl boronic acids/pinacol esters was observed in this article. The intermediate compound 3 was prepared by condensation of pyrazin-2-amine (1) with 5-bromothiophene-2-carboxylic acid (2) mediated by TiCl₄. The target pyrazine analogs (4a–4n) were confirmed by NMR and mass spectrometry. In DFT calculation of target molecules, several reactivity parameters like FMOs (E_HOMO, E_LUMO), HOMO–LUMO energy gap, electron affinity (A), ionization energy (I), electrophilicity index (ω), chemical softness (σ) and chemical hardness (η) were considered and discussed. Effect of various substituents was observed on values of the HOMO–LUMO energy gap and hyperpolarizability. The p-electronic delocalization extended over pyrazine, benzene and thiophene was examined in studying the NLO behavior. The chemical shifts of ¹H NMR of all the synthesized compounds 4a–4n were calculated and compared with the experimental values.     

Dynamic behavior of chemical reactivity indices in density functional theory: A Bohn-Oppenheimer quantum molecular dynamics study

Dynamic behaviors of chemical concepts in density functional theory such as frontier orbitals (HOMO/LUMO), chemical potential, hardness, and electrophilicity index have been investigated in this work in the context of Bohn-Oppenheimer quantum molecular dynamics in association with molecular conformation changes. Exemplary molecular systems like CH ₅ ⁺ , Cl⁻ (H₂O)₃₀ and Ca²⁺ (H₂O)1₅ are studied at 300 K in the gas phase, demonstrating that HOMO is more dynamic than LUMO, chemical potential and hardness often fluctuate concurrently. It is argued that DFT concepts and indices may serve as a good framework to understand molecular conformation changes as well as other dynamic phenomena.     

Local and nonlocal density functional calculations of the molecular structure of isomeric thiadiazoles

The chemistry of thiadiazoles and their derivatives is of considerable interest in chemistry owing to their pharmacological and potential industrial applications. In this context, a detailed study of isomeric thiadiazole molecules has been done using local (SVWN; Slater, and Vosko, Wilk and Nusair) and nonlocal (BLYP; Becke, and Lee, Yang and Parr) density functionals and optimizing the molecular geometries by means of the gradient technique. A charge sensitivity analysis of the studied molecule has been performed by resorting to density functional theory, obtaining several sensitivity coefficients such as the molecular energy, net atomic charges, global and local hardness, global and local softness and Fukui functions. With these results and the analysis of the dipole moments, the molecular electrostatic potentials and the total electron density maps, several conclusions have been inferred about the preferred sites of chemical reaction of the studied compounds. The condensed Fukui functions are shown to be one of the best criteria for predicting chemical reactivity.     

Solvent effect on the stability and properties of platinum-substituted borirene and boryl isomers: The polarizable continuum model

The structure and properties of platinum borirene complex trans-[Cl(PMe₃)₂Pt{μ-BN(SiMe₃)₂C=C}Ph] and its isomer the platinum boryl complex trans–[Cl(PMe₃)₂PtBN(SiMe₃)₂C≡CPh] were investigated theoretically. The solvent effect on the stability, structural parameters, frontier orbital energies, HOMO–LUMO gaps, and hardness of isomers was investigated using the polarizable continuum model (PCM). It was found that borirene isomer is the most stable isomer in the gas phase and solvent. The calculated results show that the presence of solvent reduces the frontier orbital energy of the studied molecules. Geometries obtained from calculations were used to perform NBO analysis.     

Evaluation and comparison of global scalar properties for the simultaneous interaction of ionic liquids with thiophene and pyridine

Ab initio studies were carried out with mixtures containing ionic liquid with thiophene and pyridine for studying the simultaneous interaction. Global scalar properties such as HOMO/LUMO energies, HOMO–LUMO energy gap, chemical hardness, chemical potential, electronegativity, global hardness, global softness and electrophilicity index were determined for clusters containing ionic liquids with thiophene and pyridine. Ionic liquids containing: 1-butyl-3-methylpyrrolidinium [BUMPYR], 1-benzyl-3-methyimidazolioum [BeMIM] and 1-butyl-3-methylpyridinium [BUMPY] cations combined with inorganic anions containing fluorine ([BF₄] and [PF₆]) were studied in this work. [BeMIM][BF₄] (1-benzyl-3-methyimidazolioum tetrafluoroborate) with a HOMO–LUMO energy gap of 0.1882 Hartrees was found to be the most effective IL. Further a ranking based on all the mentioned scalar parameters also pointed out [BeMIM][BF₄] to be the most desirable IL. The overall ranking after taking into considerations all factors followed: [BeMIM][BF₄] > [BUMPYR][BF₄] > [BUMPY][PF₆] > [BUMPY][BF₄] > [BUMPYR][PF₆]. To validate the findings, infinite dilution activity coefficients were predicted using the quantum chemical based COSMO-RS methodology which gave the same trend as observed using scalar properties.     

Theoretical investigations on nonlinear optical and spectroscopic properties of 6-(3,3,4,4,4-pentafluoro-2-hydroxy-1-butenyl)-2,4-pyrimidinedione: An efficient NLO material

In this study, quantum chemical calculations of geometric parameters, conformational, natural bond orbital (NBO) and nonlinear optical (NLO) properties, vibrational frequencies, ¹H and ¹³C NMR chemical shifts of the title molecule [C₉H₇F₅N₂O₃] in the ground state have been calculated with the help of Density Functional Theory (DFT-B3LYP/6-311++G(d,p)) and Hartree-Fock (HF/6-311++G(d,p)) methods. The optimized geometric parameters, vibrational frequencies, ¹H and ¹³C NMR chemical shifts values are compared with experimental values of the investigated molecules. Comparison between experimental and theoretical results showed that B3LYP/6-311++G(d,p) method is able to provide more satisfactory results. In order to understand this phenomenon in the context of molecular orbital picture, we examined the molecular frontier orbital energies (HOMO, HOMO-1, LUMO, and LUMO + 1), the energy difference (ΔE) between E _HOMO and E _LUMO, electronegativity (χ), hardness (η), softness (S) calculated by HF/6-311++G(d,p) and B3LYP/6-311++G(d,p) levels. The molecular surfaces, Mulliken, NBO, and Atomic polar tensor (APT) charges of the investigated molecule have also been calculated by using the same methods.     

Effect of axial strain on structural and electronic properties of zig-zag type of boron nitride nanotube (BNNT): a quantum chemical study

The influence of strain on structural and electronic properties of zig-zag type of boron nitride nanotubes (BNNTs) has been studied by density functional theory calculations. The variations of HOMO–LUMO gaps, geometrical parameters, cohesive energy, radial buckling, isodensity surfaces of the HOMOs and LUMOs, electrophilicity index, chemical potential, and chemical hardness and softness have been investigated for BNNTs at different strains. Our results show that the effect of axial strain on the electronic and structural properties of zig-zag BNNTs depends on the diameter as well as the length of the nanotube.