The recently developed QETU algorithm (quantum eigenvalue transformation of matrices with real polynomials) allows the ground state preparation and energy estimation of a given Hamiltonian $H$ by queries to the corresponding controlled time evolution operator and one ancilla qubit. In the first part of this work, we provide a specific algorithm to find the rotation angles in the QETU circuit for any real polynomial that is bound by the interval [-1,1] and a formula to construct a polynomial approximation of the Heaviside function, which are essential components of the QETU algorithm. In the second part, we apply the QETU algorithm to estimate the ground state energy of atoms and molecules, which reveals the potential power of QETU (and, therefore, quantum computers) in quantum chemistry. Throughout this work, relevant time evolution operators are assumed to be given as a black box, and their decomposition into quantum circuits is not considered.