A first-principles relativistic orthogonalized-plane-wave calculation has been used to determine the energy eigenvalues of grey tin at seven key points of the reduced zone. An extended zone k→•p→ method has been used as an interpolation scheme to map out the band structure in the remainder of the zone. Optical constants and derivative optical constants have been calculated from the k→•p→ parameters. The calculated normal incidence reflectivity is compared to experiment. A detailed critical-point analysis of the calculated optical spectra is presented. Valence-band mass parameters, effective masses, and g factors at several points in the zone have been obtained and are compared to available experimental data. © 1970 The American Physical Society.