Ab initio theory of interband transitions

This chapter reviews the principles behind the theory and computation of interband transitions at surfaces. Particular emphasis is given to state-of-the-art ab-initio methodologies, and their application is illustrated through numerous practical examples in realistic surface systems. Following a simple introduction, we outline a general theoretical framework of surface spectroscopy, obtaining an expression for the surface response function that is appropriate for computation with ab-initio methods and for simulating various experimental spectroscopic techniques. We then revise the key ab-initio approaches, namely, density functional theory, Green's function-based many-body theory, and time-dependent density functional theory. The rest of the chapter presents examples of calculations at different levels of theory for various clean and modified surfaces of current interest, illustrating in each case the interplay between the surface geometry, electronic band structure, and interband excitations. Advanced concepts such as local field and excitonic effects at surfaces are highlighted. The chapter concludes with an outlook on challenges in the field and perspectives for future development.