Dear Harsha Haridas e S , Resonance Raman (RR) happens when the wavelength of the excitation laser matches some electronic transition of the molecule under study. So you would need some molecule that shows an absorption band at 532 or 785 nm.
Hope this helps. Thanks for asking and good luck with your research.
As Manuel Gómez has mentioned, you need the laser wavelength to excite an electronic transition of whatever analyte molecule you intend to use. Fluorescent molecules like conjugated dyes are good candidates for Resonance Raman, as they typically absorb in the UV-Visible region.
For a 532 nm laser, you could use molecules like Rhodamine-6G, Rhodamine-B etc. From the top of my head, I do not know of molecules suitable for 785 nm excitation, but you could search for the absorption-emission characteristics of different molecules and choose one which is close to 785 nm. For example : https://www.thermofisher.com/nl/en/home/references/molecular-probes-the-handbook/tables/spectral-characteristics-and-recommended-bandpass-filter-sets-for-molecular-probes-dyes.html
To answer your other question - a molecule whose absorption peak is between 500-520 nm may or may not be suitable for a 532 nm excitation - it solely depends on the absorption profile of the molecule. For instance, Rhodamine-6G in ethanol , with a peak absorbance at around 530 nm , is perfect for studying resonance Raman using a 532 nm laser. Even at around 510 nm - the absorption profile exhibits a significant shoulder, which can be used for studying those specific transitions with resonance Raman.
Another additional point is that just doing resonant Raman spectroscopy on molecules like R6G is not useful as you need some sort of fluorescence quencher like noble metal nanoparticles or even 2D materials. Otherwise your spectrum will be dominated by fluorescence. For example, if I tried measuring the spectrum of R6G dissolved in water even at concentrations as low as 50 nM, all you would see is a fluorescent response. The minute you use a Ag nano particle or graphene based sustrate and measure the adsorbed layer signal resonantly, you get a much more informative Raman spectrum of R6G.