Adiabatic similarity and dependence of the energy of molecular systems on the masses of particles

The dependence of the energy of three-particle molecules on their masses is examined. It is shown that such molecules with the same values of the rati o of the reduced masses for motion in a "fast" and "slow" Jacobi coordinate s have the property of adiabatic similarity: In the adiabatic approximation , their energies are proportional to the reduced masses. This allows inform ation on the energy of molecules symmetric in the masses of particles to be extended to asymmetric molecules adiabatically similar to the symmetric mo lecules. For molecules with arbitrary masses of the particles, an analytic expression for the adiabatic energy and a formula approximating the exact e nergy are constructed using the principle of adiabatic similarity. Along wi th the adiabatic energy, which is the lower bound of the exact energy, a si mple procedure is considered for determining the upper bound of the energy of asymmetric molecules from the energy of their symmetric counterparts. Ba sed on these results, values of the lower and upper energy bounds are calcu lated and an approximation of the exact energy is obtained for 43 three-par ticle molecular systems. (C) 2000 MAIK "Nauka/Interperiodica".