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.

Theoretical justification has been provided to the method for monitoring the sequence of chemical bonds' rearrangement along a reaction path, by tracing the evolution of the diagonal elements of the Hessian matrix. Relations between the divergences of Hellman-Feynman forces and the energy and electron density derivatives have been demonstrated. By the proof presented on the grounds of the conceptual density functional theory formalism, the spectral amplitude observed on the atomic fragility spectra [L. Komorowski et al., Phys. Chem. Chem. Phys. 18, 32658 (2016)] reflects selectively the electron density modifications in bonds of an atom. In fact the spectral peaks for an atom reveal changes of the electron density occurring with bonds creation, breaking, or varying with the reaction progress.

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The amino group in adenine plays a key role in formation of hydrogen bonds in nucleic acids and in other molecular systems. Thus, the structure of this group is of fundamental importance in the molecular recognition phenomena. Ab initio MP2 and density functional B3LYP methods with various basis sets have been used to calculate the optimized structure and the infrared spectrum of adenine (the N9-H tautomer). Calculations at the MP2 level with larger basis sets tend to decrease the degree of pyramidalization of the C-NH2 group, whereas the B3LYP method consistently yields the planar or nearly planar structure of adenine. MP2 complete basis set (CBS) limit method with the aug-cc-pVTZ --> aug-cc-pVQZ (aTZ --> aQZ) extrapolation scheme has predicted very small planarization barrier of adenine, 0.015 kcal/mol, which is in very good agreement with the MP2-predicted planarization barrier of 0.020 kcal/mol, reported by S. Wang and H. F. Schaefer III, J. Chem. Phys. 2006, 124, 044303. Similar results were obtained in calculations by the coupled cluster CCSD(T) CBS method. Thus, it can be concluded that the amino group in adenine, in the gas phase, is very flexible with a small degree of nonplanarity. Extremely low planarization barrier implies that adenine requires very little energy to conform the structure of the amino group to formation of the complementary hydrogen bonds with other molecules. This fact is very important for base pairing in nucleic acids or other polymers containing adenine residues. The anharmonic frequencies of adenine have been calculated at the B3LYP/6-311++G(df,pd) level of theory. The theoretical results show excellent agreement with the available experimental data. The revised assignment of the infrared spectrum of adenine in Ar matrix has been made. The predicted anharmonic frequency of the NH2 inversion, 181 cm(-1), is supported by the experimental data. It is demonstrated that the vibrational frequencies and potential energy distribution (PED) obtained from the B3LYP calculations are more reliable than those obtained at the MP2 level.