Are there any books/papers which correlates partial density of states and the corresponding HOMO-LUMO?
Yes, basically any textbook of quantum chemistry. Just select the one you prefer, I cannot advertise any one in particular for ethic reasons. Concerning papers, an interesting and understandable example is Figure 4 in Nature Vol.501,Pag. 399–402 (2013) DOI:doi:10.1038/nature12523 (http://www.nature.com/nature/journal/v501/n7467/full/nature12523.html) in which you can esaily realize that the top of the conduction band in your DOS/PDOS is the HOMO of your system and the bottom of the conduction band the LUMO (well, not surprising !).
Another clear example of practical application is reported in Beilstein J Nanotechnol. 2015;vol. 6, Pag. 1247–1259 (2015) doi: 10.3762/bjnano.6.128 (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4463971/) where the procedure for projecting the density of states (PDOS) onto molecular orbitals is detailed.
We have also several publications in which this is used (e.g. J. Phys. Chem. C vol. 118, Pag. 8331-8341 (2014) doi: 10.1021/jp410565e. http://pubs.acs.org/doi/abs/10.1021/jp410565e) if you feel this useful to you.
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