We report an easy computational procedure for qualitative prediction of hydrogen-deuterium exchange position in hydroxyindole derivatives. The efficiency of the procedure was confirmed with experimental results (Fig. 1). Hydrogen-deuterium exchange took place at the carbon atom having the big charge (Fig. 3), namely, that next to the hydroxy function. The predicted positions were in good agreement with the observations though there is an exception when steric hindrance should be considered to explain the results.Atomic charges in basic molecule skeleton obtained by using the molecular orbital calculation enable prediction for the position of hydrogen-deuterium exchange in hydroxy indole derivatives.

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We propose a simple computational algorithm to solve non-linear equations with multiple roots of two variables: F(x,y)=0. The algorithm is effective only where the relationship between two variables x and y is monotonous and continuous (for example, see Fig.s 1 and 3). The algorithm also gives a guideline of automatic adjustment of the notch width in the Euler method. The efficiency of the algorithm was demonstrated by analyzing two typical examples and an autocatalytic reaction in open systems.

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The number of structural isomers of alkanes was combinatorially enumerated by counting the different structures composed of several alkyl groups attached to the center of the molecule specifically defined. This algorithm is rather slow when compared with the conventional graph theoretical method. The correctness of the algorithm was checked by reproducing isomer numbers up to 40 carbon atoms.

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Enthalpies of benzene—monosubstituted benzene interactions were evaluated by semi-empirical MO calculations of heats of formation for (i) the benzene (PhH) dimer and (ii) benzene—monosubstituted benzene (PhX) pairs. Calculation methods, initial intermolecular distances (r_I), and so on were investigated for the benzene dimer. The interaction enthalpy and optimized geometry calculated with PM3 were consistent with the previous experimental and theoretical results. As initial arrangements of PhH—PhX systems, one parallel (P) and four vertical arrangements (V_r , V_p , V_m , and V_b) were chosen (Figure 1). In the case of V_p or V_m arrangement where the lowest H atom at the para or meta position to substituent X in PhX was located above the centroid of PhH, calculated enthalpies of the interactions (ΔΔH_f) between PhH and PhX had close correlation with experimental ones (ΔΔH^t) determined by gas-liquid partition chromatography (GLPC), with the correlation coefficient (ρ) as large as 0.94 (Figure 5); differences between the experimental ΔΔH^t values and the ΔΔH^t values calculated from the correlation equation were less than ca. 0.1 kcal mol^-1 . With the other arrangements except for V_p, no appreciable relationship was observed between the ΔΔH_f and ΔΔH^t (Figures 2, 3, and 4).

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