The complete and original calculation scheme beyond the finite difference approximation, for the atomic (and orbital) Fukui function (FF) indices is proposed. The method explores an expansion for derivatives of LCAO coefficients, ∂C/∂N=CU. The separation scheme for the U matrix has been elaborated at the ab initio level. Nucleophilic and electrophilic FF indices, as well as atomic softness, have been derived from the standard result of SCF HF ab initio calculations. The indices reproduce two effects; the change in orbital occupancy and the relaxation of the electronic system. The molecular hardness (softness) provided by this scheme explicitly includes these two effects.
In this paper, we verify the usefulness of the alchemical derivatives in the prediction of chemical properties. We concentrate on the stability of the transmutation products, where the term "transmutation" means the change of the nuclear charge at an atomic site at constant number of electrons. As illustrative transmutations showing the potential of the method in exploring chemical space, we present some examples of increasing complexity starting with the deprotonation, continuing with the transmutation of the nitrogen molecule, and ending with the substitution of isoelectronic B-N units for C-C units and N units for C-H units in carbocyclic systems. The basis set influence on the qualitative and quantitative accuracies of the alchemical predictions was investigated. The alchemical deprotonation energy (from the second order Taylor expansion) correlates well with the vertical deprotonation energy and can be used as a preliminary indicator for the experimental deprotonation energy. The results of calculations for the BN derivatives of benzene and pyrene show that this method has great potential for efficient and accurate scanning of chemical space.
We present an analytical approach to treat higher order derivatives of Hartree-Fock (HF) and Kohn-Sham (KS) density functional theory energy in the Born-Oppenheimer approximation with respect to the nuclear charge distribution (so-called alchemical derivatives). Modified coupled perturbed self-consistent field theory is used to calculate molecular systems response to the applied perturbation. Working equations for the second and the third derivatives of HF/KS energy are derived. Similarly, analytical forms of the first and second derivatives of orbital energies are reported. The second derivative of Kohn-Sham energy and up to the third derivative of Hartree-Fock energy with respect to the nuclear charge distribution were calculated. Some issues of practical calculations, in particular the dependence of the basis set and Becke weighting functions on the perturbation, are considered. For selected series of isoelectronic molecules values of available alchemical derivatives were computed and Taylor series expansion was used to predict energies of the "surrounding" molecules. Predicted values of energies are in unexpectedly good agreement with the ones computed using HF/KS methods. Presented method allows one to predict orbital energies with the error less than 1% or even smaller for valence orbitals.
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