Recenty, R.W.Zwanzig obtained an equation simian to the Chanarasekhar's equation for the Brownian motion.
His treatment is concerned with the diagonal elements only. If the off-diagonals were zero, however, the flow term in the phase-space would have to vanish.
We start from the equation obtained by I. Prigogee and M. Toda in which the off-diagonals are included. Without ambiguity we get the same result as Zwanzig's.
The relation to Chandrasekhar's equation is discussed also.

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Proton hyperfine splitting in aromatic radicals and aromatic negative ions are treated by MO method, and the semi-empirical equation, Q=a_Nρ is examined theoretically to be true. Here a_N is the splitting constant refer to proton N, ρ is the unpaired electron density at the carbon atom adjacent to proton N, and Q is the semi-empirical constant to be same for all CH bond, the value of which is about -22.5 gauss. The essential approximations in this treatment are that the siglettriplet exitation energies ΔE_jo in σ-orbitals are replaced by the average value ΔE_av of them, and all σ-orbitals containing CH bond are transformed into δ-orbitals which are strongly localized to each CH fragment. That is to say, δ-orbital is approximated to be CH bond orbital between Is hydrogen orbital and Sp₂ hybrid carbon orbital, and ΔE_av is to be the siglet-triplet exitation energy in this bond orbital. These approximations are explained briefly to be adequate in aromatic systems. Therefore it is obvious that the proton hyperfine splitting calculations in aromatic systems take place the same results in the hypothetical CH fragment treatment and in the general treatment containing the entire set of aromatic system.

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