The TD B3LYP/6-311G(d,p) method slightly overestimates the excitation energies of the first UV absorption band of the all-transoid conformers of SinMe2n + 2 (n = 2-8, 10), deduced from temperature-dependent measurements on conformer mixtures in hydrocarbon solvents, by a nearly constant amount (approximately 2000 cm-1). The TD B3LYP/6-31G(d) results are less satisfactory. The first band is calculated to be due to a sigma pi * excitation in Si2Me6 and to a superposition of overlapping sigma sigma * and sigma pi * excitations in the longer oligosilanes. The sigma pi * excitation is calculated to lie a little below the sigma sigma * excitation up to Si4Me10, the two transitions are nearly degenerate in Si5Me12, and the sigma sigma * excitation drops increasingly below the sigma pi * as the chain length is extended. The dipole strength of the sigma sigma * excitation grows by 4.8 D2 (D = debye) per added SiSi bond (more slowly up to n = 5) and the calculation overestimates it by a factor of about three. The sigma pi * excitation is computed to carry no or almost no oscillator strength, but as noted earlier by others, its presence is critical for the interpretation of the observed thermochromism. Upon cooling below room temperature, the first absorption maximum is blue-shifted in short chains and red-shifted in long chains. Unlike the prior investigators, we attribute the blue shift to the disappearance of hot bands built on the sigma pi * origin using intensity borrowing sigma-pi mixing vibrations (b1 in Si3Me8). As usual, the red shift is attributed to the disappearance of twisted conformers, which have higher calculated sigma sigma * excitation energies.