This chapter focuses on the concept of rotational motion. It explains that energy and angular momentum for a particle rotating in two- or three-dimensions are quantized and satisfied cyclic boundary conditions, which imply the quantization of angular momentum's magnitude and z-component. The electronic structure of atoms showcases rotational motion because electrons orbit around nuclei and spin on their axis. The chapter details the solutions for the Schrödinger equation and the vector model of angular momentum. It also discusses the concept of space quantization revolving around the quantum mechanical result of a rotating body that may not take up an arbitrary orientation concerning some specified axis.
We investigate the helium dimer in strong magnetic fields, focusing on the spectrum of low-lying electronic states and their dissociation curves, at the full configuration-interaction level of theory. To address the loss of cylindrical symmetry and angular momentum as a good quantum number for nontrivial angles between the bond axis and magnetic field, we introduce the almost quantized angular momentum (AQAM) and show that it provides useful information about states in arbitrary orientations. In general, strong magnetic fields dramatically rearrange the spectrum, with the orbital Zeeman effect bringing down states of higher angular momentum below the states with pure σ character as the field strength increases. In addition, the spin Zeeman effect pushes triplet states below the lowest singlet; in particular, a field of one atomic unit is strong enough to push a quintet state below the triplets. In general, the angle between the bond axis and the magnetic field also continuously modulates the degree of σ, π, and δ character of bonds and the previously identified perpendicular paramagnetic bonding mechanism is found to be common among excited states. Electronic states with preferred skew field orientations are identified and rationalized in terms of permanent and induced electronic currents.