Can total internal reflection (TIR) occur in metals? Is it possible to get Total Internal Reflection (TIR) when a light beam hits a metallic surface of complex index $\tilde{n}=n_r+n_ii$? If not, is there a way where a light beam can hit a metallic surface in such a way that there's not transmitted light?
 A: Understand the concept of Total internal reflection (TIR) first. It is condition in which 100% of optical intensity is reflected when a light propogating through optically dense medium is incident on medium with lesser refractive index. It is usually used to understand behaviour of light at certain wavelength only in materials with extremely small or no extinction coefficient.
The atoms in opaque metals absorb some of the photons so light does not pass through them. The imaginary part represents absorption or attenuation. Near resonance of the atomic oscillators this absorption is strong. The imaginary part is usually denoted k. The metal obsorbs and scatters different wavelengths of light. This selective scattering and absorption also gives metal its color. So light can be reflected 100% and travel in metal (goals and condition of TIR)
Also Total internal reflection is concept from snell's law which ignore the behaviour of light at different wavelengths. e.g. The phase velocity of X-ray in plasmas can be faster than the speed of light in vacuum, and thereby give a refractive index below 1. Metals are transparent for UV rays.
Usually reported refractive indices values for materials are commonly reported using a single value for n, typically measured at 633 nm.
Nevertheless, refractive indices for materials are commonly reported using a single value for n, typically measured at 633 nm.
You can play with different values here
https://refractiveindex.info/?shelf=glass&book=NSG-multipurpose&page=Pilkington-Optiwhite
To conclude, the TIR in metals may be observed for wavelengths that are able to travel in metals and have optimal refractive index for partiular metal/wavlength. TIR is part of the ray model of light behaviour for particular applications. For metals, we use different model (quantum or electromagnetic) of light (wave) behaviour
