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Quantum-chemical calculations have been carried out of heterolytic dissociation energies of a series of tri(1H-indol-3-yl)methylium compounds with different counter-ions within the framework of density functional theory, using the functional B3LYP in the basis 6-31 + G(d). The results obtained have been compared with data calculated for unsubstituted triphenylmethane derivatives (triphenylmethylium chloride and methanesulfonate) and also for tri(4-dimethylaminophenyl)methylium chloride (crystal violet). Ionicity of tri(indol-3-yl)methylium salts is compared with that of crystal violet chloride and triphenylmethane derivatives.

The total energies of reactants, products, and transition states of nucleophilic substitution reactions in protonated tris(indol-3-yl)methane have been assessed with the semiempirical AM1 method and the theory of functional density B3LYP/6-31(d) method. The results of calculations indicated that the reactions proceed by an S N 1-like mechanism, since the activation barrier for it is significantly lower than in the case of the S N 2-like mechanism.

A series of 3-(indol-1-yl)maleimides has been synthesized, substituted at position 2 by residues of amines or various nitrogenous heterocycles. The possibility of obtaining new polycondensed heterocyclic structures from them has been studied. Experimental investigations confirmed theoretical predictions made on the basis of results of quantum-chemical calculations.

The geometric parameters, the charge distribution, and the energetics of N-methyl-2-(N-ethylanilino)-3-(indol-1-yl)-and N-methyl-2-(N-ethylanilino)-3-(indol-3-yl)maleimides and their conjugated acids were studied by density functional theory calculations at the B3LYP/6-31G(d) level. The mechanism of the tandem hydride transfer/cyclization sequence, which occurs after protonation of N-methyl-2-(N-ethylanilino)-3-(indol-1-yl)-and N-methyl-2-(N-ethylanilino)-3-(indol-3-yl)maleimides, was analyzed. The investigation of the potential energy surface for the tandem hydride transfer/cyclization of the iminium cation that formed upon protonation revealed that the hydride transfer followed by intramolecular cyclization at position 7 of the indole fragment in N-methyl-2-(N-ethylanilino)-3-(indol-1-yl)maleimide is the preferable process, unlike alternative intramolecular cyclization involving the cationic center at the C(2) atom of the indole fragment and the benzene ring of the N-ethylaniline fragment of the indoleninium cation in N-methyl-2-(N-ethylanilino)-3-(indol-3-yl)maleimide. A study of the key intermediates of the assumed reaction mechanism demonstrated that these intermediates are actually stationary points on the potential energy surface (minima and transition states).

Intramolecular cyclization reactions of 3,4-bis(indol-3-yl)maleimides 1, 3-(indol-1-yl)-4-(indol-3-yl)maleimides 2, and 3,4-bis(indol-1-yl)maleimides 3 under the action of protic acids were studied in order to estimate the parameters of the interaction between protonated and unprotonated indole moieties. Geometric parameters, charge distributions, energy characteristics, and information concerning the frontier orbitals of bisindolylmaleimides 1–3 were obtained from density functional B3LYP/6-31G(d) quantum chemical calculations. Alternative pathways of protonation of bisindolylmaleimides with differently bonded indole and maleimide moieties were studied and pathways of cyclization of corresponding conjugated acids leading to polyannelated compounds were analyzed. All the key intermediates of the cyclization reactions correspond to stationary points on the potential energy surfaces (minima and transition states). Analysis of the potential energy surfaces revealed almost linear dependences of the activation energies of the cyclization reactions under study on the distances between the reaction centers, on the angle of approach of intramolecular electrophile, and on the energy gap (energy difference between frontier orbitals). The key role in the cyclization reactions is played by structural similarity between the starting indoleninium cations and the activated complexes of the reactions under study.

The total energies of derivatives of N-hydroxyindole, indole, and phenol, and of their corresponding anions have been estimated with the aid of ab initio calculations on the 3-21G basis. The energies of proton removal were calculated from the difference in total energies of the appropriate anions and molecules. By comparing the calculated energies of proton removal with experimental values of pKa (acidity characteristic) a practically linear dependence was shown for the acidity characteristic on the energy of proton removal for the series of compounds investigated. An empirical formula has been proposed expressing the dependence of pKa on the energy of proton removal, which makes it possible to predict pKa in this series by carrying out calculations of the energy of proton removal (transfer).