A General Framework of Scanning Tunneling Microscopy Based on Bardeen’s Approximation for Isolated Molecules

[Image: see text] Scanning tunneling microscopy (STM) is one of the most popular techniques for precise characterization. Yet, its current theoretical implementation is often based on the periodic boundary condition with the Tersoff–Hamann approximation, which is inefficient to explore the tip states other than the s-wave and to treat properly the charged molecules that are ubiquitous in chemistry. In this work, we establish a general theoretical framework for STM image simulations, which is based on the Bardeen’s approximation and utilizes the boundary condition of the cluster model. We develop an analytic algorithm for the precise evaluation of the transfer Hamiltonian matrix, addressing correctly the asymptotic behaviors of the tip states. Numerical results demonstrate that the molecular images under different STM tip states and mapping modes can be quantitatively simulated in the present framework, which paves the avenue for the conclusive investigation of the ground state electronic structures for either neutral or charged molecules.