On the definition of the atomic charge. Relationship between 13C NMR chemical shifts,dipole moments,and charges in saturated hydrocarbons

The problem of defining a reliable quantum mechanical charge by comparison with one-electron properties is analyzed, and it is stressed that properties involving the virtual space are not suited to that end. Particular attention is devoted to the relationship between charges and chemical shifts for the case of saturated hydrocarbons. A simple explanation of the Grant and Paul α effect is suggested, which can also account for the modified population analysis proposed by Fliszár. Moreover the vexata quaestio of the direction of the C H bond dipole moment has been reexamined. The awkward theoretical prediction (C⁺ H⁻) can be reconciled with the one based on experimental data and electronegativities (C⁻ H⁺) if one considers that the former is determined by an hydridization contribution to the dipole moment, which tend to cancel in a summation over all the bonds formed by each atom. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 68: 201–210, 1998     

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     

Correlation of the isosteric heat of adsorption of organic molecules over zeolites with equalized electronegativity and chemical hardness

Considering the direct correlation between charge transfer and heat of adsorption, we have equated the isosteric heat of adsorption (Q _st ) with Nalewajski’s charge transfer equation involving equalized electronegativities and chemical hardness given in the literature. The equation is then tested and compared with the experimental heat of adsorption values of organic molecules over zeolites given in the literature with the average percentage deviation of 15·9. Other similar types of equations of charge transfer affinity are also tested. Various semi-empirical equations based on Barrer’s approach of the determination ofQ _st and neural network method have been proposed, tested and compared for the first time     

Electric dipole moments in polar solvents. I. Audiofrequency measurement with slightly conducting solutions

Audiofrequency methods were used to measure dielectric constants of dilute solutions containing electrolytes up to free-ion concentrations of 10^–4 M. Using a calibrated transformer bridge, capacitance was measured with an accuracy of 0.03 pF at a conductance of 100 mho and within 0.3 pF at 800 mho. Evaluation of the double-layer capacitance from the frequency dependence of the data is discribed. The effect of the free ions on the dielectric constant is found to be relatively large and in reasonable agreement with the prediction of the Debye-Falkenhagen theory. The calculation of the electric dipole moment for polar solutes, including ion pairs, is discussed in terms of Kirkwood's theory. Experimental tests are described for finding out whether possible deviations of Kirk-wood's correlation factors from unity may be neglected. These tests involve changing the solvent and the temperature. The tests were satisfied for the ion pairs of tetraisoamylammonium nitrate and for nitrobenzene in chlorobenzene and acetic acid.     

Theoretical study with rovibrational and dipole moment calculation of sextet states of the CrCl molecule

The potential energy curves have been investigated for the 13 lowest sextet electronic states in the representation below 53,000 cm^?1 of the molecule CrCl via CASSCF and MRCI (single and double excitation with Davidson correction) calculations. The harmonic frequency ω_e, the internuclear distance r_e, the rotational constant B_e, the electronic energy with respect to the ground state T_e, and the permanent dipole moment μ have been calculated. By using the canonical functions approach, the eigenvalues E_v, the rotational constant B_v, and the abscissas of the turning points r_min and r_max have been calculated for the considered electronic states up to the vibrational level v = 16. Nine electronic states have been studied theoretically here for the first time. The comparison of these values with the theoretical and experimental results available in the literature shows a good agreement. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Exploring the conformation,charge density distribution and the electrostatic properties of galanthamine molecule in the active site of AChE using DFT and AIM theory

Quantum chemical calculations and charge density analysis were carried out to understand the geometry, charge density distribution and the electrostatic properties of isolated galanthamine molecule (form I) and for the same lifted out from the active site (form II) of AChE. The optimized geometry of isolated galanthamine was obtained from a hybrid density functional theory (B3LYP/6‐311G**) calculation. A docking analysis on galanthamine with AChE was performed, and the lowest docked energy structure was selected from the active site of AChE for the further study. A single point energy quantum chemical calculation (B3LYP/6‐311G**) was carried out for the lowest energy structure, which was lifted from the galanthamine–AChE complex from molecular docking analysis. The structural comparison between (I) and (II) helps to understand the conformational modification of the galanthamine molecule in the active site. When the molecule present in the active site, the molecular geometry is seen to be significantly altered, specifically, large changes were observed in the outer core of the molecule while the inner core geometry is intact. The bond topological and electrostatic properties of (I) and (II) were calculated. The dipole moment of the galanthamine molecule also increases from 2.09 to 2.67 D in the process. A large negative electrostatic potential region is found at the vicinity of oxygen and nitrogen atoms of the molecule, which predominantly involve strong hydrophobic and electrostatic interactions with the amino acid residues TRP84, PHE330, GLY118, TYR70, and SER122 present in the active site of AChE. © 2013 Wiley Periodicals, Inc.     

Studies of chemical hardness and Fukui function using the exact solution of the density functional theory

Neal's procedure has been applied to determine the electron density ρ(x) for the H₂ molecule. The chemical hardness has been calculated employing the ab initio and density functional theory methods and the values are found to be reasonably good. The principle of maximum hardness (PMH) was tested. Fukui functions and the distribution of electron density around the internuclear distance were studied employing the electron density of the H₂ molecule. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 4–10, 2001     

Ab Initio Diabatic energies and dipole moments of the electronic states of RbLi molecule

For all states dissociating below the ionic limit Li^? Rb⁺, we perform a diabatic study for ¹Σ⁺ electronic states dissociating into Rb (5s, 5p, 4d, 6s, 6p, 5d, 7s, 4f) + Li (2s, 2p, 3s). Furthermore, we present the diabatic results for the 1–11 ³σ, 1–8 ^1,3Π, and 1–4 ^1,3Δ states. The present calculations on the RbLi molecule are complementary to previous theoretical work on this system, including recently observed electronic states that had not been calculated previously. The calculations rely on ab‐initio pseudopotential, core polarization potential operators for the core‐valence correlation and full valence configuration interaction approaches, combined to an efficient diabatization procedure. For the low‐lying states, diabatic potentials and permanent dipole moments are analyzed, revealing the strong imprint of the ionic state in the ¹Σ⁺ adiabatic states. The transition dipole moment is used to evaluate the radiative lifetimes of the vibrational levels trapped in the 2 ¹Σ⁺ excited states for the first time. In addition to the bound–bound contribution, the bound–free term has been evaluated using the Franck–Condon approximation and also exactly added to the total radiative lifetime. © 2013 Wiley Periodicals, Inc.     

Theoretical study with vibration–rotation and dipole moment calculations of quartet states of the CrCl molecule

The potential energy curves have been investigated for the 10 lowest quartet electronic states in the ^2s+1Λ^± representation below 30,000 cm^?1 of the molecule CrCl via CASSCF and MRCI (singly and doubly excitation with Davidson correction) calculations. The harmonic frequency ω_e, the internuclear distance r_e, the rotational constant B_e, the electronic energy with respect to the ground state T_e, and the permanent dipole moment μ have been calculated. By using the canonical functions approach, the eigenvalues E_v, the rotational constant B_v, and the abscissas of the turning points r_min and r_max have been calculated for the considered electronic states up to the vibrational level v = 19. Seven electronic states have been studied here theoretically for the first time. The comparison of these values to the theoretical results available in the literature shows a good agreement. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

六烷氧基取代的苯并菲和六氮杂苯并菲盘状液晶中的电荷转移

用电子转移的半经典模型在量子化学B3LYP/6-31G(d)水平(对单体)和B3LYP/STO-3G水平(对二聚物)对六烷氧基取代的苯并菲和六烷氧基取代的六氮杂苯并菲组成的盘状晶体系的电荷转移性质进行了研究,发现在用量子化学方法研究电荷转移反应时,不能简单地用氢氧基代替长链烷氧取代基。由于在电荷转移反应中,要考虑参与反应的分子之间前线轨道的细微差别,所以将长链取代基用氢氧基取代,可能得不到定性正确的结果。     

The equilibrium structures, vibrational spectra, NLO and directional properties of transition dipole moments of diguanidinium arsenate monohydrate and diguanidinium phosphate monohydrate. The theoretical DFT calculations

For diguanidinium arsenate monohydrate and diguanidinium phosphate monohydrate the energies were minimized and the theoretical vibrational frequencies and potential energy distribution (PED) were calculated by density functional method. The 6-31++G(d,p) basis set was used. The assignment of the bands has been made on the basis of the calculated PED. For calculated equilibrium geometries two methods for determination of direction of transition dipole moments (TDM) were used. The oriented gas model was used for calculation of "static" TDM and from the other side the "dynamic" approximation of TDM by analysis of changes in internal coordination during characteristic vibrations was performed. The restricted Hartree-Fock (RHF) methods were used for calculation of the hyperpolarizability for both investigated molecules. The theoretical results are compared with experimental value of beta.     

Impedance of faradeic process with partial charge transfer

The electrochemical impedance of charge-transfer reaction involving the stages of adsorption and desorption of intermediate partially charged substance is analyzed theoretically in the frequency-potential plane in order to study the possibility for measuring the partial charge transfer. The simplest case of adsorption two-electron transfer, namely, the Langmuir adsorption with liner dependence of reaction rate on the coverage, is considered. It is assumed that the partial charge transfer is independent of the electrode potential.     

Mass transfer coupled with the relaxation of a polymeric matrix: A controlled release process

A solution to Fick's equation is presented which accurately predicts the transfer of mass out of a polymeric rod or sheet undergoing relaxation by a solvent permeating it by Case II transport. There is a critical length. Before the solvent permeates to this length the diffusible material can diffuse away from the moving boundary faster than it is becoming available at the boundary. Afterward the reverse is true. Five sets of experimental data from three different sources have been used to test the model. The agreement is excellent.     

Charge transfer in complexes of C60 and C70 in solutions and solid state

Electronic absorption spectra of complexes of C₆₀ and C₇₀ fullerenes with donors, tetrathiafulvalene and pyranylidene derivatives, were studied in solutions and in the solid state. Charge transfer bands were found in the 680–1300 nm range. The charge transfer energies (hv _ct) for the C₆₀ and C₇₀ complexes in solutions are close and almost independent of the solvent polarity. For the C₆₀ complexes in the solid state, the dependence ofhv _ct on the ionization potential (IP) of donors was found to behv _ct=0.82IP–3.93 eV. In the C₆₀ complexes in the solid state, thehv _ct values are 0.15–0.20 eV lower than those in the solution. The linear dependences ofhv _ct onIP of donors for the C₆₀ complexes lie 0.6–0.7 eV higher than those in the complexes with tetracyanoethylene (TCNE). This is associated with lower values of the electron affinity of C₆₀ and the energy of the electrostatic interaction in the fullerene complexes as compared to those of the TCNE complexes. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 478–483, March, 1999.     

A comprehensive study of the solvent effects on the cycloaddition reaction of diethyl azodicarboxylate and ethyl vinyl ether: Efficient implementation of QM and TD‐DFT study

In this work, quantum chemistry calculations performed to study the kinetics and thermodynamic parameters of [2+2] cycloaddition reaction of diethyl azodicarboxylate and ethyl vinyl ether in eighty‐three solvents and gas phase. The solvent effect on the reaction path and electron density of the C2? N6 critical bond as the reaction coordinate at the TS was investigated. Calculated rate constants in various solvents showed that increase in the activation dipole moment accelerates the reaction. Based on the time‐dependent studies, using a conductor like polarizable continuum model solvation model, the solvent effects on the excitation energies of the reactants and transition states (TSs) and the corresponding chemical shifts were analyzed. Finally, some correlations between the rate constant and quantum reactivity indices such as electrophilicity index, chemical hardness, and electronic chemical potential were investigated. © 2014 Wiley Periodicals, Inc.