  Effects of rotation and valence nucleons in molecular-like linear
$\alpha$-chain nuclei are analyzed using a three-dimensional lattice cranking
model based on covariant density functional theory. The structure of $^{16}$C
and $^{16}$Ne is investigated as a function of rotational frequency. The
valence nucleons, with respect to the 3$\alpha$ linear chain core of $^{12}$C,
at low frequency occupy the $\pi$ molecular orbital. With increasing rotational
frequency these nucleons transition from the $\pi$ orbital to the $\sigma$
molecular orbital, thus stabilizing the 3$\alpha$ linear chain structure. It is
predicted that the valence protons in $^{16}$Ne change occupation from the
$\pi$ to the $\sigma$ molecular orbital at $\hbar\omega \approx 1.3$ MeV, a
lower rotational frequency compared to $\hbar\omega \approx 1.7$ MeV for the
valence neutrons in $^{16}$C. The same effects of valence protons are found in
$^{20}$Mg, compared to the four valence neutrons in $^{20}$O. The model is also
used to examine the effect of alignment of valence nucleons on the relative
positions and size of the three $\alpha$-clusters in $^{16}$C and $^{16}$Ne.

Nuclear Theory