Vibronic coupling constant (VCC) and density (VCD) defined for a pure state, which have been successfully applied for reactions of fullerenes and nanographenes as reactivity indices, are extended for a mixed state. The extended VCC and VCD, thermodynamical vibronic coupling constant (ThVCC) and density (ThVCD), are formulated in the finite-temperature grand-canonical ensemble. ThVCD can be applied for charge transfer of a fractional number of electron. Based on the total differential of chemical potential, the relationship between chemical potential, absolute hardness, and vibronic coupling in a bimolecular reaction is discussed. (C) 2016 Elsevier B.V. All rights reserved.