Toward a semiempirical density functional theory of chemical binding

The new ideas ofbond electronegativity andbond hardness are introduced, and a semiempirical density functional approach to the theory of molecular electronic structure and chemical binding is outlined. There result effective electronegativity equalization procedures that permit calculation of binding energies as well as partial charges. By a modelling of the bond electronegativity and bond hardness, a density functional interpretation of earlier bond charge models is established. Some numerical results are given for diatomic molecules.Dedicated to Professor J. Koutecký on the occasion of his 65th birthday     

Electronegativity and chemical hardness of organoelement groups

The experimental approaches to estimation of comparative electronegativity and chemical hardness of organometallic groups have been proposed. Qualitative data on the electronegativity of L _nM groups were obtained from ¹⁹F NMR study of model systems 4‐FC₆H₄QML_n (Q = CC, N(R), O, C(O)O, S), (4‐FC₆H₄)₃ SnML _n and (4‐FC₆H₄)₃SnQML _n (Q = O, S), containing a great variety of different organometallic groups containing transition or heavy main‐group metals. The data on chemical hardness of L _nM groups were obtained from NMR study of distribution of different L _nM groups between hard and soft anions. The following basic results have been obtained. (1) The relative electronegativity and chemical hardness of L _nM groups can change in parallel or not with the electronegativity and hardness of the central metal atom. (2) The substituents in Ar can substantially modify electronegativity and hardness of Ar _nM groups; the influence of Ar groups has an inductive nature; the increase in electron‐donating ability of aryl ligands enhances the hardness of Ar _nM cations. (3) The relative electronegativity and hardness of L _nM groups in L _nMX are invariant and do not depend on X.     

Electronegativity and hardness in the chemical approximation

The chemical electronegativity of an atom (Mulliken definition) has been identified with the average value of χ, the electronegativity function given by the rigorous density functional theory. An appropriate definition of hardness is developed, and a scale of hardness for bonded atoms is proposed. The electrodynamical atom model is demonstrated to produce a simple relation between atomic hardness and size. Electronegativity has been calculated for bonded atoms in a variety of molecules and crystals, covalent and ionic, without any specific approximation for the energy function E(q). Expressions for the electronegativity of a molecule have been derived and critically discussed.     

Looking at self-consistent-charge density functional tight binding from a semiempirical perspective

The self-consistent-charge density functional tight binding (SCC-DFTB) method is compared with other semiempirical methods (MNDO, AM1, PM3, OM1, OM2, OM3). Despite the differences in the underlying philosophy and derivation, these methods share many common features. Systematic evaluations of their performance are reported for standard test sets that are in common use. The overall accuracy of SCC-DFTB and the other methods is in the same range, with the overall tendency AM1相似文献   

Numerical evaluation of the internal orbitally resolved chemical hardness tensor in density functional theory

The purpose of the present work was to develop a method allowing one to extract the information needed for the construction of the internal chemical hardness tensor at the molecular orbital level from standard density functional calculations. This method is based on the Janak theorem and on the extension of the Slater transition-state concept. A detailed discussion of the current ideas about the validity of the Janak theorem is presented as well as of the established relations of this subject with the ensemble V-representability problem. The internal chemical hardness tensor has been obtained for water molecule as an example system. Its structure is consistent with the criteria for the internal molecular stability. © 1997 John Wiley & Sons, 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     

Woodward-Hoffmann rules in density functional theory: initial hardness response

The Woodward-Hoffmann rules for pericyclic reactions, a fundamental set of reactivity rules in organic chemistry, are formulated in the language of conceptual density functional theory (DFT). DFT provides an elegant framework to introduce chemical concepts and principles in a quantitative manner, partly because it is formulated without explicit reference to a wave function, on whose symmetry properties the Woodward-Hoffmann [J. Am. Chem. Soc. 87, 395 (1965)] rules are based. We have studied the initial chemical hardness response using a model reaction profile for two prototypical pericyclic reactions, the Diels-Alder cycloaddition of 1,3-butadiene to ethylene and the addition of ethylene to ethylene, both in the singlet ground state and in the first triplet excited state. For the reaction that is thermally allowed but photochemically forbidden, the initial hardness response is positive along the singlet reaction profile. (By contrast, for the triplet reaction profile, a negative hardness response is observed.) For the photochemically allowed, thermally forbidden reaction, the behavior of the chemical hardness along the initial stages of the singlet and triplet reaction profiles is reversed. This constitutes a first step in showing that chemical concepts from DFT can be invoked to explain results that would otherwise require invoking the phase of the wave function.     

Application of semiempirical long-range dispersion corrections to periodic systems in density functional theory

Ewald summation is used to apply semiempirical long-range dispersion corrections (Grimme, J Comput Chem 2006, 27, 1787; 2004, 25, 1463) to periodic systems in density functional theory. Using the parameters determined before for molecules and the Perdew-Burke-Ernzerhof functional, structure parameters and binding energies for solid methane, graphite, and vanadium pentoxide are determined in close agreement with observed values. For methane, a lattice constant a of 580 pm and a sublimation energy of 11 kJ mol(-1) are calculated. For the layered solids graphite and vanadia, the interlayer distances are 320 pm and 450 pm, respectively, whereas the graphite interlayer energy is -5.5 kJ mol(-1) per carbon atom and layer. Only when adding the semiempirical dispersion corrections, realistic values are obtained for the energies of adsorption of C(4) alkenes in microporous silica (-66 to -73 kJ mol(-1)) and the adsorption and chemisorption (alkoxide formation) of isobutene on acidic sites in the micropores of zeolite ferrierite (-78 to -94 kJ mol(-1)). As expected, errors due to missing self-interaction correction as in the energy for the proton transfer from the acidic site to the alkene forming a carbenium ion are not affected by the dispersion term. The adsorption and reaction energies are compared with the results from M?ller-Plesset second-order perturbation theory with basis set extrapolation.     

Electronegativity and inductive and mesomeric parameters of atomic groups: A semiempirical quantum chemical estimation

The electronegativity, the inductive parameter, and the mesomeric dipole moments of substituents depend on the electronic structure characteristics of organic molecules calculated by the CNDO/2, INDO, MINDO, MINDO/3, MNDO, and AMI methods. It is shown that the electronegativity as well as the inductive and mesomeric characteristics of atomic groups may be estimated by semiempirical quantum chemical methods.     

The chemical Hamiltonian approach in density functional theory

The chemical Hamiltonian approach (CHA) for handling the basis set superposition error problem in intermolecular interactions has been implemented within density functional theory (DFT) using Gaussian atomic basis sets. As test examples, the potential curves of the water dimer were calculated using the Vosko-Wilk-Nusair, Becke-Perdew and Perdew exchange-correlation functionals. Comparisons with the counterpoise correction method show that CHA within DFT performs as well as previously for Hartree-Fock.     

Molecular binding energies from partition density functional theory

Approximate molecular calculations via standard Kohn-Sham density functional theory are exactly reproduced by performing self-consistent calculations on isolated fragments via partition density functional theory [P. Elliott, K. Burke, M. H. Cohen, and A. Wasserman, Phys. Rev. A 82, 024501 (2010)]. We illustrate this with the binding curves of small diatomic molecules. We find that partition energies are in all cases qualitatively similar and numerically close to actual binding energies. We discuss qualitative features of the associated partition potentials.     

Supramolecular binding thermodynamics by dispersion-corrected density functional theory

The equilibrium association free enthalpies ΔG(a) for typical supramolecular complexes in solution are calculated by ab initio quantum chemical methods. Ten neutral and three positively charged complexes with experimental ΔG(a) values in the range 0 to -21?kcal?mol(-1) (on average -6?kcal?mol(-1) ) are investigated. The theoretical approach employs a (nondynamic) single-structure model, but computes the various energy terms accurately without any special empirical adjustments. Dispersion corrected density functional theory (DFT-D3) with extended basis sets (triple-ζ and quadruple-ζ quality) is used to determine structures and gas-phase interaction energies (ΔE), the COSMO-RS continuum solvation model (based on DFT data) provides solvation free enthalpies and the remaining ro-vibrational enthalpic/entropic contributions are obtained from harmonic frequency calculations. Low-lying vibrational modes are treated by a free-rotor approximation. The accurate account of London dispersion interactions is mandatory with contributions in the range -5 to -60?kcal?mol(-1) (up to 200?% of ΔE). Inclusion of three-body dispersion effects improves the results considerably. A semilocal (TPSS) and a hybrid density functional (PW6B95) have been tested. Although the ΔG(a) values result as a sum of individually large terms with opposite sign (ΔE vs. solvation and entropy change), the approach provides unprecedented accuracy for ΔG(a) values with errors of only 2?kcal?mol(-1) on average. Relative affinities for different guests inside the same host are always obtained correctly. The procedure is suggested as a predictive tool in supramolecular chemistry and can be applied routinely to semirigid systems with 300-400 atoms. The various contributions to binding and enthalpy-entropy compensations are discussed.     

Magnetic effects of disulfide bridges: a density functional and semiempirical study

Density functional chemical shielding calculations are reported for methane and hydrogen disulfide dimers. The calculations show that the contributions of disulfide bridges to the chemical shielding of neighboring protons is sizable at distances that are frequently sampled in protein structures. A semiempirical model of the quantum chemical data is developed. It is shown that magnetic anisotropy effects of disulfide are poorly described by the McConnell equation, both qualitatively and quantitatively. In particular, the ratio of magnetic anisotropy contributions to shielding along and perpendicular to the magnetic anisotropy principal axis do not conform to the predictions of the McConnell equation, and magnetic anisotropy effects are not null along the magic angle axis. A sulfur-based model of the magnetic anisotropy of the disulfide is developed and shown to give much better agreement with the quantum chemical data.     

Energy surface, chemical potentials, Kohn-Sham energies in spin-polarized density functional theory

On the basis of the zero-temperature grand canonical ensemble generalization of the energy E[N,N(s),v,B] for fractional particle N and spin N(s) numbers, the energy surface over the (N,N(s)) plane is displayed and analyzed in the case of homogeneous external magnetic fields B(r). The (negative of the) left-/right-side derivatives of the energy with respect to N, N(↑), and N(↓) give the fixed-N(s), spin-up, and spin-down ionization potentials/electron affinities, respectively, while the derivative of E[N,N(s),v,B] with respect to N(s) gives the (signed) half excitation energy to the lowest-lying state with N(s) increased (or decreased) by 2. The highest occupied and lowest unoccupied Kohn-Sham spin-orbital energies are identified as the corresponding spin-up and spin-down ionization potentials and electron affinities. The excitation energies to the lowest-lying states with N(s)±2 can be obtained as the differences between the lowest unoccupied and the opposite-spin highest occupied spin-orbital energies, if the (N,N(s)) representation of the Kohn-Sham spin-potentials is used. The cases where the convexity condition on the energy does not hold are also discussed. Finally, the discontinuities of the energy derivatives and the Kohn-Sham potential are analyzed and related.     

Computation of the hardness and the problem of negative electron affinities in density functional theory

The absolute hardness in density functional theory (DFT) is discussed, emphasizing the charge-transfer excitation interpretation. Direct evaluation from the computed ionization potential and electron affinity is intrinsically problematic when the affinity is negative; the calculated affinity exhibits a strong basis set dependence, becoming near zero as diffuse functions are added. An alternative Koopmans-based approximation using local functional eigenvalues uniformly and significantly underestimates the hardness. A simple correction to the Koopmans expression is highlighted on the basis of a consideration of the integer discontinuity. The resulting hardness expression does not require the explicit computation of the affinity and has a straightforward interpretation in terms of the electronegativity. The correction eliminates the underestimation and gives hardness values that do not degrade as the electron affinity becomes more negative. For systems with large negative affinities, the values are an improvement over those from the other approaches. The success can be traced to an implicit, unconventional approximation for the electron affinity, which outperforms the standard approach when the affinity is significantly negative and which does not break down as the basis set becomes more diffuse.     

Two-component density functional theory of positron binding to negative ions

The problem of binding in positron-negative ion systems has been addressed via two-component density functional theory. Calculations have been performed within the local density approximation for electron exchange-correlation as well as for the electron-positron correlation potential using a self-interaction corrected version of the density functional equations. Our results indicate that a positron forms a stable bound state with the negative ions Li⁻,B⁻,C⁻,O⁻,F⁻ and Cl⁻ with respect to dissociation into a negative ion and a positron or a neutral atom and positronium. Inclusion of electron-positron correlation deepens the positron bound state and stabilizes the system compared to earlier exchange-only calculations.     

Structure, spectroscopy, and reactivity properties of porphyrin pincers: a conceptual density functional theory and time-dependent density functional theory study

Porphyrin and pincer complexes are both important categories of compounds in biological and catalytic systems. The idea to combine them is computationally investigated in this work. By employment of density functional theory (DFT), conceptual DFT, and time-dependent DFT approaches, structure, spectroscopy, and reactivity properties of porphyrin pincers are systematically studied for a selection of divalent metal ions. We found that the porphyrin pincers are structurally and spectroscopically different from their precursors and are more reactive in electrophilic and nucleophilic reactions. A few quantitative linear/exponential relationships have been discovered between bonding interactions, charge distributions, and DFT chemical reactivity indices. These results are implicative in chemical modification of hemoproteins and understanding chemical reactivity in heme-containing and other biologically important complexes and cofactors.     

Systematic formulations for electronegativity and hardness and their atomic scales within density functional softness theory

A unified Mulliken valence with Parr ground‐state electronegativity picture is presented. It provides a useful analytical tool on which the absolute hardness as well ionization potential and electron affinity functionals are based. For all these chemical reactivity indices, systematic approximate density functionals are formulated within density functional softness theory and are applied to atomic systems. For the absolute hardness, a special relationship with the new electronegativity ansatz and a particular atomic trend paralleling the absolute electron affinity are established that should complement and augment the earlier finite‐difference energetic approach. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006