Efficient and reliable method for the simulation of scanning tunneling   images and spectra with local basis sets
  Based on Bardeen's perturbative approach to tunneling, we have found an expression for the current between tip and sample, which can be efficiently coded in order to perform fast ab initio simulations of STM images. Under the observation that the potential between the electrodes should be nearly flat at typical tunnel gaps, we have addressed the difficulty in the computation of the tunneling matrix elements by considering a vacuum region of constant potential delimited by two surfaces (each of them close to tip and sample respectively), then propagating tip and sample wave functions by means of the vacuum Green's function, to finally obtain a closed form in terms of convolutions. The current is then computed for every tip-sample relative position and for every bias voltage in one shot. The electronic structure of tip and sample is calculated at the same footing, within density functional theory, and independently. This allows us to carry out multiple simulations for a given surface with a database of different tips. We have applied this method to the Si(111)-(7x7) and Ge(111)-c(2x8) surfaces. Topographies and spectroscopic data, showing a very good agreement with experiments, are presented. 
Oscar Paz and Jose M. Soler