  Quantum chemistry calculations such as the prediction of molecular properties
and modeling of chemical reactions are a few of the critical areas where
near-term quantum computers can showcase quantum advantage. We present a method
to calculate energy derivatives for both ground state and excited state
energies with respect to the parameters of a chemical system based on the
framework of the variational quantum eigensolver (VQE). A low-depth
implementation of quantum circuits within the hybrid variational paradigm is
designed, and their computational costs are analyzed. We showcase the
effectiveness of our method by incorporating it in some key quantum chemistry
applications of energy derivatives, such as to perform minimum energy
configuration search and estimate molecular response properties estimation of
H$_2$ molecule, and also to find the transition state of H$_2$ + H
$\leftrightarrow$ H + H$_2$ reaction. The obtained results are shown to be in
complete agreement with their respective full configuration interaction (FCI)
values.
