Molecular hardness and softness parameters and their use in chemistry

Abstract

The semiempirical Atoms-in-a-Molecule (AIM) hardness matrix, 7 , is defined, using the usual finite difference formula, v,, = I, -A,, for the diagonal AIM hardness and the Ohno formula, r), = l / ( a 2 + R;)"*, for the off-diagonal AIM hardness. The Ohno formula is shown to exhibit the correct asymptotic behavior and satisfies the relevant stability criterion. The normal displacements in the AIM electron populations are examined for pyrmle and N-methyl pyrrole, and their relation to the polarization channels is briefly discussed. The new AIM hardness matrix is also tested by comparing the predicted global hardnesses with the corresponding experimental finite difference data for selected diatomics and triatomics. Finally implications of the hardness combination rules are examined and the corresponding softness combination rules are used to calculate the regional and global softnesses of selected molecules. We examine how the regional softnesses reflect known trends in selectivity of protonation of five membered heterocycles, and comment on the signs of the AIM fukui function and the Hard-Soft-Acids-and-Bases principle.

Rigid and Relaxed Diagonal Orbital Hardnesses of the Valence Shell of Transition Metal Ions from Xα Calculations

“…The molecular charge-sensitivity-analysis (CSA) [1][2][3][4][5][6][7][8][9][10][11][12][13][14], based upon the concepts of global and regional (rigid and relaxed) chemical potentials, hardnesses, softnesses, the Fukui function parameters, and the related energy derivatives, has recently been advocated as an attractive theoretical framework for applications in the theory of chemisorption and catalysis [11,13]. This approach has already been successfully applied both qualitatively and quantitatively to selected ules of chemistry [1, 2, 4, 5, 7, 9,] and trends in the chemical reactivity [4,7,[9][10][11][12][13][14][15][16][17].…”

“…This approach has already been successfully applied both qualitatively and quantitatively to selected ules of chemistry [1, 2, 4, 5, 7, 9,] and trends in the chemical reactivity [4,7,[9][10][11][12][13][14][15][16][17]. Most of the reporetd applications to large molecular systems adopt the atoms-in-molecules (AIM) resolution, although the orbitally resolved CSA has also been developed at various levels of sofistication [13,[18][19][20][21][22]. Future wider applications of this method would require the realistic AIM (global or orbital) data for alternative oxidation states and orbital configurations, sufficient to generate the canonical AIM chemical potentials and hardness tensor corresponding to the actual valence state of the AIM in the system under consideration, as revealed by the standard SCF MO calculations.…”

“…One possible source of such parameters, used in the semiempirical AIM CSA [7], are the experimental values of the electron a f f i n i t y a n d i o n i z a t i o n p o t e n t i a l d a t a [ 1 4 , 2 4 ] , b u t t h e y h a r d l y c o v e r t h e f u l l r a n g e o f the atomic valence states required for an adequate interpolation; alternatively such data can be calculated theoretically, e. g., using the Hartree-Fock (HF) or the SCF calculations [10- 13,17,19,21], the hyper-HF [20,25], Kohn-Sham [Local Density Approximation (LDA)] [14,15], and the Χα [20,22] theories. The latter method [26,27] is especially attractive for this purpose since the first derivatives of the energy, Ε = E(n), with respect to the canonical orbital occupation numbers, n = (n i , n2 , ...), both variational (orbitally relaxed) and partial (orbitally unrelaxed), give the repsective one-electron eigenvalues, e = (e l , e2 , ...):…”

Density Functional Theory and Materials Modeling at Atomistic Length Scales

“…The bond site chemical potential as well as the hardness parameters can be approximated [28] by suitable averaging [29] of the corresponding values for the neighbouring atoms. For the off-diagonal (i = j) elements of the hardness kernel η µν (i, j), one can essentially employ the atom-in-molecule hardness matrix concept of Nalewajski [30] generalised for the spin-dependence and model along similar lines [31] following basically an electrostatic analogy details of which have been discussed elsewhere [18]. For a nonbonded pair of sites (atom or bond), one considers a Coulomb potential η αβ (i, j) = 1/ R ij , with as the dielectric constant of the electron cloud medium.…”

“…For a nonbonded pair of sites (atom or bond), one considers a Coulomb potential η αβ (i, j) = 1/ R ij , with as the dielectric constant of the electron cloud medium. while for bonded sites, a better modeling [31] involves the Mataga-Nishimoto-Ohno formula as η αβ (i, j) = 1/(R ij + a (31)) for predicting the intra-as well as inter-molecular interaction energies.…”