Without invoking the Markov approximation, we derive formulas for vibrational energy relaxation (VER) and dephasing for an anharmonic system oscillator using a time-dependent perturbation theory. The system-bath Hamiltonian contains more than the third order coupling terms since we take a normal mode picture as a zeroth order approximation. When we invoke the Markov approximation, our theory reduces to the Maradudin-Fein formula which is used to describe the VER properties of glass and proteins. When the system anharmonicity and the renormalization effect due to the environment vanishes, our formulas reduce to those derived by and Mikami and Okazaki [J. Chem. Phys. 121, 10052 (2004)] invoking the path-integral influence functional method with the second order cumulant expansion. We apply our formulas to VER of the amide I mode of a small amino-acid like molecule, N-methylacetamide, in heavy water.

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The solid solution formation criteria for the equi-atomic ratio alloys were discussed. It is found that higher entropy of mixing (Smix>1.61R), less atomic size difference (δ<4.6), and near zero of the absolute value of the enthalpy of mixing (-2.685δ-2.54<Hmix <-1.28δ+5.44 KJ/mol) facilitate the formation of solid solution for the multi-principle components equi-atomic alloys.

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