New method for calculating the moments of thermally averaged densities of distribution of internuclear distances in polyatomic molecules using the Bloch integral equation

A convenient method is suggested for calculating thermally averaged powers of the normal vibrational coordinates Q _i by iteratively solving the Bloch integral equation with an anharmonic function of potential energy using multidimensional Hermite polynomials. Analytical formulas of the first approximation regarding anharmonicity constant have been obtained for the following moments of thermally averaged density: 〈Q ₁〉, 〈 Q ₁ ² 〉, 〈Q ₁ Q ₂〉, 〈Q ₁ ³ 〉 〈Q ₁ ³ 〉, 〈Q ₁ Q ₂ Q ₃〉, 〈Q ₁ ⁴ 〉, 〈Q ₁ ² Q ₂ ² 〉, 〈Q ₁ Q _2/3〉, 〈Q ₁ Q ₂ Q ₃ ² 〉, 〈 Q 1 Q ₂ Q ₃ Q ₄〉.