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     

电负性均衡

电负性是分子中一个原子把电子拉向它自身的能力,是化学理论的基本概念之一。继Pauling建立第一个电负性标度后,提出了众多的电负性标度。只是在密度泛函理论的基础上,电负性概念和电负性均衡原理,才被精密地论证。近二十多年来,电负性理论的重要发展是:应用电负性均衡模型或方法,可以快速地计算分子体系的电荷分布,从而确定分子的其他性质,甚至包括分子的结构和反应性指标。通常的电负性均衡方法只把分子划分到原子区域,虽然简单直观,但其精度和应用范围受到限制。原子与键电负性均衡方法,把分子划分到包括原子区域、化学键区域和孤对电子区域,能够较快速精密地计算分子的电荷分布和其他性质,并被应用到构建新一代可极化或浮动电荷力场的探索中,有广阔的应用前景。     

Valence state parameters of all transition metal atoms in metalloproteins—development of ABEEMσπ fluctuating charge force field

To promote accuracy of the atom‐bond electronegativity equalization method (ABEEMσπ) fluctuating charge polarizable force fields, and extend it to include all transition metal atoms, a new parameter, the reference charge is set up in the expression of the total energy potential function. We select over 700 model molecules most of which model metalloprotein molecules that come from Protein Data Bank. We set reference charges for different apparent valence states of transition metals and calibrate the parameters of reference charges, valence state electronegativities, and valence state hardnesses for ABEEMσπ through linear regression and least square method. These parameters can be used to calculate charge distributions of metalloproteins containing transition metal atoms (Sc‐Zn, Y‐Cd, and Lu‐Hg). Compared the results of ABEEMσπ charge distributions with those obtained by ab initio method, the quite good linear correlations of the two kinds of charge distributions are shown. The reason why the STO‐3G basis set in Mulliken population analysis for the parameter calibration is specially explained in detail. Furthermore, ABEEMσπ method can also quickly and quite accurately calculate dipole moments of molecules. Molecular dynamics optimizations of five metalloproteins as the examples show that their structures obtained by ABEEMσπ fluctuating charge polarizable force field are very close to the structures optimized by the ab initio MP2/6–311G method. This means that the ABEEMσπ/MM can now be applied to molecular dynamics simulations of systems that contain metalloproteins with good accuracy. © 2014 Wiley Periodicals, Inc.     

About the structure of phosphorus ylids: Electron distribution and geometry

Using ¹³C-chemical shifts as a probe for the electronic environment of carbon centers, triphenylphosphoniomethanide, the model case of a “reactive” phosphorus ylid, was found to have much more zwitterion than PC double bond character (resonance structure 1a being dominant). Triphenylphosphonio-propenide (“triphenylphosphonium-allylid”), a “moderated” ylid, accumulates electron excess mainly at the α-carbon atom (resonance structure 6a being dominant) whereas triphenylphosphonio-ethenoate (formyl-methylene-triphenylphosphorane) and other “stabilized” ylids carry roughly equal fractions of negative charge at the α-carbon and the oxygen atom (resonance formulas a and b being of comparable importance). The one-bond C,H coupling constant of triphenylphosphonio-methanide ( 1 ) argues against a perfectly planar ylid center. The three-bond P,C coupling constants permit the assignment of endo- or exo-configurations to ylids having an allyl-type side-chain.     

Semiempirical evaluation of the global hardness of the atoms of 103 elements of the periodic table using the most probable radii as their size descriptors

Relying upon the fact that the density functional computation of the global hardness of the atoms of the elements are still at large and there is some mathematical in congruency between the theory and operational formula of finite difference approximation, we have suggested a radial‐dependent ansatz for evaluating global hardness of atoms as: η=a(7.2/r)+b (in eV), where, “a” and “b” are the constants and r is the absolute radius of atoms in angstrom unit. The ansatz is invoked to evaluate the global hardness of atoms of 103 element of the periodic table. The evaluated new set of global hardness is found to satisfy the sine qua non of a reasonable scale of hardness by exhibiting perfect periodicity of periods and groups and correlating the gross physicochemical properties of elements. The inertness of Hg and extreme reactivity Cs atoms are nicely correlated. The chemical reactivity and its variation in small steps in the series of lanthanide elements are also nicely reproduced. The results of the present semiempirical calculation also have strong correlation with the result of some sophisticated DFT calculation for a set of atoms. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

吩噻嗪给体受体衍生物激发态的电荷转移

A series of N-bonded donor-acceptor derivatives of phenothiazine containing phenyl （PHPZ）, anisyl （ANPZ）, pyridyl （PYPZ）, naphthyl （NAPZ）, acetylphenyl （APPZ）, and cyanophenyl （CPPZ） as an electron acceptor have been synthesized. Their photophysical properties were investigated in solvents of different polarities by absorption and emission techniques. These studies clearly revealed the existence of an intramolecular charge transfer （ICT） excited state in the latter four compounds. The solvent dependent Stokes shift values were analyzed by the modified Lippert-Mataga equation to obtain the excited state dipole moment values. The large excited state dipole moment suggests that the full （or nearly full） electron transfer take place in the A-D systems. In the system of A-D phenothiazine derivatives, the transition dipole moments Mflu were determined mainly by direct interactions between the solvent-equilibrated fluorescence ^1CT state and ground state because of their lack of significant change with increase of the solvent polarity. The electron structure and molecular conformation of phenothiazine derivatives will be significantly changed with the increase of the electron affinity of the N-10 substituent.     

Charge sensitivities of the externally interacting open reactants

Effective chemical potential, hardness, softness, and Fukui function quantities of the simultaneously open reactants, e.g., adsorbates in catalytic systems, are examined. The derived reduced expressions in terms of the canonical chemical potentials and condensed hardness matrix elements of such molecular subsystems are compared with the corresponding analogs for the case of the closed complementary subsystem. Implications of the catalyst‐induced changes in the condensed hardness matrix of the reactive system consisting of a pair of donor/acceptor adsorbates, in the preferred complementary arrangement with the acidic/basic active sites of the surface, respectively, are discussed and interpreted as manifestations of the Le Châtelier–Braun principle. Only in such a complementary arrangement is the in‐phase, concerted, mutually enhancing pattern of the polarizational and charge transfer flows of electrons in a catalytic system obtained. The activating influence of the catalyst is identified through its softening, decoupling effect on the adsorbates. The catalyst‐induced chemical potential equalization creates electronic instability in the system of adsorbed species, thus increasing their reactivity. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 78: 168–178, 2000     

Stripped Charge of Ag Less than Deposited one Owing to Negative Capacitance Caused by Redox Reactions

Anodic stripping voltammetry was made in AgNO₃ solution, here Ag was deposited under long term potentiostatic conditions to evaluate the reduction charge, q_r, and then was stripped by linear sweep voltammetry to determine the oxidation charge, q_o. The charges were unbalanced, satisfying ca. q_o=0.7|q_r|, where other possible reduction charge such as by dioxygen and dichlorosilver were subtracted. The 30 % loss of the anodic charge can be ascribed to the negative capacitance by the potential sweep generation of Ag⁺. The generated Ag⁺ forms a dipole with a counter ion, of which orientation is the same as the direction of the externally applied electric field and opposite to the dipoles of solvent. The redox dipole decreases the conventional double layer capacitance caused by solvent dipoles, and high concentrations of Ag⁺ takes the capacitance to be negative values. The unbalanced charge, however, has no influence on quantitative determination of concentrations Ag⁺ by use of a calibration line.     

Studies of polarized ethylenes.: PART VII. experimental and theoretical dipole moments and electronic structures by CNDO/2 calculations

The dipole moments of a number of representative “push-pull” ethylenes have been calculated by the CNDO/2 method, and a comparison is made with experimental dipole moments, which are in general surprisingly well reproduced. An analysis of the calculated charge distributions shows that the π-electron displacements are in agreement with qualitative expectations, but no back-polarization of the σ-electrons can be observed. Instead, the distribution of the σ-electrons seems to be governed by atom electronegativities.The experimental dipole moments of some more or less flexible analogues are discussed in relation to conformations and expected charge distributions.     

An intramolecular induction correction model of the molecular dipole moment

A model for intramolecular polarization is presented. It is used to describe the changes in the molecular charge distribution occurring as a response to changes of dihedral angles in the molecule. The model is based on a multicenter multipole distribution of the molecular charge distribution. The electric field from this charge distribution induce dipole moments in the same molecule. The model contains atom type parameters to describe the damping of the electric field. A total of four atom types are used. The parameters are fitted to a calibration set with various functional groups, and tested against a validation set. The error obtained for the calibration set is reduced by 92% and by 88% for the validation set, if compared to an accurate state-of-the-art force field. It is shown that rotating the non-polarizable multicenter multipole distribution for the equilibrium geometry gives too large dipole moments for dihedral angles deviating from the equilibrium geometry. This will lead to too large long-range attractions in simulations. This problem is overcome by using the dipole polarizability correction suggested here, which gives dipole moments very close to the Hartree-Fock dipole moments obtained from reference calculations.     

异构现象与最大硬度原理

利用原子-键电负性均衡方法计算了700多个异构体的硬度, 通过与标准生成焓所确定的相对稳定性比较后发现, 多数异构体并不遵守最大硬度原理.     

Atranes

The dipole moments of the Si(OCH₂CH₂)₃N heterocyclic framework were calculated within the framework of an additive scheme by means of data from x-ray diffraction and conformational analysis of silatranes. The direction of the dipole moment of this fragment coincides with the “experimentally” determined value (from nitrogen to silicon), and its magnitude is ～3 D. The dipole moment of the Si ← N coordinate bond was estimated to be 2.2 D, which corresponds to charge transfer from the nitrogen atom to the silicon atom (to the extent of 0.2 e). These results refute the existing concepts of the exceptionally high polarity of the transannular Si ← N bond in silatranes.     

Density functional studies of LiN and LiN+ (N = 2–30) clusters: Structure,binding and charge distribution

Density functional calculations using B3LYP/6‐311G method have been carried out for small to medium‐sized lithium clusters (Li_N, N = 2–30). The optimized geometries of neutral and singly charged clusters, their binding energies, ionization potential, electron affinity, chemical potential, softness, hardness, highest occupied molecular orbital and lowest unoccupied molecular orbital (HOMO–LUMO) gap, and static dipole polarizability have been investigated systematically. In addition, we study the distribution of partial charges in detail using natural population analysis (NPA) in small‐sized clusters (Li_N, N = 2–10), both neutral and cationic, and demonstrate the correlation between symmetry and charge. Uniform distribution of charges in cationic clusters confirms them to be energetically more favorable than the neutral counterparts. Whenever possible, results have been compared with available data. An excellent agreement in every case supports new results as reliable predictions. A careful study of optimized geometries shows that Li₉ is derivable from bulk Li structure, i.e., body centered cubic cell, and higher clusters have optimized shapes derived from this. Further, the turnover form two to three dimensional structure occurs at cluster size N = 6. The quantity α^1/3 (α = polarizability) per atom is found to be broadly proportional to softness (per atom) as well as inverse ionization potential (per atom). The present work forms a sound basis for further study of large‐sized clusters as well as other atomic clusters. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Description of high‐spin restricted open‐shell molecules with the Piris natural orbital functional

The Piris natural orbital functional (PNOF) based on a new approach for the two‐electron cumulant is considered for the case of high‐spin restricted open‐shell systems. The theory is applied to the calculation of molecular energies, dipole moments, vertical ionization potentials (IP), and electron affinities (EA) of 10 open‐shell molecules. Vertical values of IP and EA were used to evaluate the hardness. It was observed that the results obtained using the PNOF method are comparable to the corresponding results obtained using CCSD(T) in the case of energies and dipole moments. Best agreement between theory and experiment is achieved by PNOF for EA and hardness values. The calculated PNOF values for the mentioned properties are in good agreement with the available experimental data, considering the basis sets used (6–31 ++G**). © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007