Quantum Chemistry at Finite Temperature
  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, .... 
Liqiang Wei