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Scanning tunneling microscopy (STM) is a widely used experimental method in surface science to investigate and manipulate material surfaces at the atomic scale, employing the quantum tunneling of electrons. Advanced simulation tools of experimental STM are vital for the proper understanding of the physical and chemical processes involved in the imaging/manipulation. For this reason Chen’s derivative rule for electron tunneling has been revised  for the purpose of computationally efficient simulation of STM based on ab initio electronic structure calculations. New features include (i) the weighting of tunneling matrix elements of different tip-orbital characters by an arbitrary energy-independent choice or based on first-principles data, (ii) arbitrary tip geometrical orientations to mimick asymmetric tip-sample relations, and (iii) the possibility of quantitative analysis of tip-orbital interference contributions to the tunneling current. The simulation model has initially been applied to two functionalized surfaces where quantum interference effects play an important role in the STM imaging and the Tersoff-Hamann (spherical tip orbital) model fails to describe the correct STM contrast under certain conditions: N-doped graphene and a magnetic Mn2H complex on the Ag(111) surface . Recently, the revised Chen’s STM simulation method has been applied to diverse complex surface oxide [2,3,4] and iodide ultrathin films , where a better agreement with experiments has been achieved than obtained with the Tersoff-Hamann method. Other examples of our contributions to understand recent STM experiments will also be briefly listed. G. Mándi, K. Palotás, Phys. Rev. B 91, 165406 (2015). T. Lee, Y.-J. Lee, K. Palotás, G. Lee, C. Stampfl, A. Soon, Nanoscale 11, 6023 (2019). T. T. Ly, T. Lee, S. Kim, Y. J. Lee, G. Duvjir, K. Jang, K. Palotás, S. Y. Jeong, A. Soon, J. Kim, J. Phys. Chem. C 123, 12716 (2019). Y.-J. Lee, T. T. Ly, T. Lee, K. Palotás, S. Y. Jeong, J. Kim, A. Soon, Appl. Surf. Sci. 562, 150148 (2021). G. Lee, Y.-J. Lee, K. Palotás, T. Lee, A. Soon, J. Phys. Chem. C 124, 16362 (2020).