Ab Initio Infrared Spectra and Electronic Response Calculations for the Insulating Phases of VO$_2$*

Previous studies have shown\footnote{J. H. Park et al., Nature {\bf 500}, 431 (2013).} that, under doping or tensile strain and upon heating, the well-known vanadium dioxide (VO$_2$) transition from an insulating monoclinic (M1) to a metallic rutile (R) phase progresses through a triclinic symmetry (T) phase and a magnetic monoclinic phase (M2), both of which are insulating. Structurally, this progression from M1 to R through T and M2 can be characterized by the progressive breaking of the V dimers. Investigation of the effect of these structural changes on the insulating phases of VO$_2$ may help resolve questions surrounding the long-debated issue of the respective roles of electronic correlation and Peierls mechanisms in driving the MIT. We investigated electronic and vibrational properties of the insulating phases of VO$_2$ in the framework of DFT+U. We will present {\em ab initio} calculations of infrared spectra and optical electronic responses for the insulating phases and compare these to available experimental measurements \footnote{T. J. Huffman et al., PRB {\bf 87}, 115121 (2013).}\footnote{A. S. Barker et al., PRL {\bf 17}, 1286 (1966).}\footnote{H. W. Verleur et al., PR {\bf 172}, 788 (1968).}\footnote{J. M. Tomczak and S. Biermann, PRB {\bf 80}, 085117 (2009).}.