  In this article, we present emerging fields of quantum chemistry at finite
temperature. We discuss its recent developments on both experimental and
theoretical fronts. First, we describe several experimental investigations
related to the temperature effects on the structures, electronic spectra, or
bond rupture forces for molecules. These include the analysis of the
temperature impact on the pathway shifts for the protein unfolding by atomic
force microscopy (AFM), the temperature dependence of the absorption spectra of
electrons in solvents, and the temperature influence over the intermolecular
forces measured by the AFM. On the theoretical side, we review advancements
made by the author in the coming fields of quantum chemistry at finite
temperature. Starting from the Bloch equation, we have derived the sets of
hierarchy equations for the reduced density operators in both canonical and
grand canonical ensembles. They provide a law according to which the reduced
density operators vary in temperature for the identical and interacting
many-body systems. By taking the independent particle approximation, we have
solved the equations in the case of a grand canonical ensemble, and obtained an
energy eigenequation for the molecular orbitals at finite temperature. The
explicit expression for the temperature-dependent Fock operator is also given.
They form a mathematical foundation for the examination of the molecular
electronic structures and their interplay with finite temperature. Moreover, we
clarify the physics concerning the temperature effects on the electronic
structures or processes of the molecules, which is crucial for both theoretical
understanding and computation. Finally, ....
