The shapes an electron’s cloud can take around an atom. Electrons do not circle the nucleus like planets; each sits in an orbital, a region with a definite energy and shape – a sphere (s), a dumbbell (p) or a clover-like shape (d). When atoms bond, their orbitals overlap and can blend into new ones pointing at the neighbours, which is hybridisation: in graphene each carbon mixes one s and two p orbitals into three bonds in the plane (sp2), leaving one p orbital standing up out of the sheet. Which orbitals hold the outermost electrons decides much of what a material does. Electrons in an orbital still carry a kind of circling motion, angular momentum, and the magnetism that comes from it rather than from their is called orbital magnetism.
As the site uses it
The explanation on offer is exotic: loops of orbital current circulating on the tellurium edges of the manganese octahedra, which the field can switch on and off, making this crystal one of the few places where orbital currents are argued to control transport.
The two peaks above 2100 cm−1 come from the carbon–carbon triple bonds that link graphdiyne’s rings, and no sp2 carbon has them, so they show that graphdiyne is there; a map of the 2189.2 cm−1 peak shows where.
Orbitals are the shapes an electron’s cloud takes around an atom. In graphene each carbon mixes one s and two p orbitals into three bonds in the plane, and the remaining upright p orbitals join into the band that holds the Dirac cones. In the 2H dichalcogenides the filling of one split-off d band decides between metal and semiconductor.
Shapes and energies
An electron bound to an atom can occupy only certain states. Each has a fixed energy and a characteristic shape for the cloud of probability where the electron is likely to be found: s orbitals are spherical, p orbitals are dumbbells pointing along three directions, d orbitals have more complicated lobes, five in all. Each orbital holds at most two electrons, of opposite spin, and they fill from the lowest energy up – the order that builds the periodic table.
In a solid, orbitals on neighbouring atoms overlap, and their energies spread into bands. Which orbitals make up the bands near the is the first thing a calculation reports and the first choice a has to make: carbon’s p orbitals for graphene, the metal’s d orbitals mixed with the ’s p orbitals for a .
Hybrids and the shape of a sheet
Orbitals on one atom can mix. In diamond each carbon mixes its s orbital with all three p orbitals into four sp3 hybrids pointing to the corners of a . In graphene it mixes the s orbital with only two p orbitals: three sp2 hybrids at 120° in the plane form the strong σ bonds, 1.42 Å long, that hold the together, while the remaining p orbital stands perpendicular to the sheet. These upright orbitals join into the π band, half filled, and its crossing at the corners of the Brillouin zone is the .
Silicon and germanium do not settle into a flat sheet the same way. Calculations predicted that their honeycombs are stable only slightly buckled, yet still have π bands that cross linearly like graphene’s (Cahangirov and colleagues, 2009); grown on metals, silicene and germanene form corrugated, reconstructed layers rather than flat ones.
d orbitals in transition-metal compounds
In the transition-metal dichalcogenides the electrons that matter most sit in the metal’s d orbitals. The chalcogen atoms around each metal split the five d orbitals in energy, and in the structures a hybridisation gap separates one d band from the rest (Mattheiss, 1973). How many electrons it holds follows from the metal’s column of the periodic table: half filled for niobium and tantalum, so NbSe2 and TaS2 are metals; completely filled for molybdenum, so MoS2 is a . HfS2, whose d bands are empty, is a semiconductor too.
The same counting explains why a change of coordination can change everything: rearranging the chalcogens around molybdenum from trigonal prismatic to octahedral regroups the d levels and makes 1T-MoS2 a metal. In compounds of the 3d metals – chromium, manganese, iron, nickel – partly filled d orbitals carry the , and how they hybridise with the ligands sets the exchange between them.
For specialists
Single-electron states of an atom labelled by angular momentum – s, p, d, f – whose overlap between neighbours forms bonds and bands. Hybridisation mixes orbitals on one atom, as in graphene’s sp2 carbon, with three in-plane σ bonds 1.42 Å long and a half-filled π band from the out-of-plane p orbital, where the Dirac cones lie; or between atoms, as in the p–d hybridisation of transition-metal compounds. In 2H TMDCs a hybridisation gap splits a d band off from the rest, and whether it is half-filled or full separates NbSe2 and TaS2 from semiconducting MoS2. “Orbital” also names the electron’s motion: orbital magnetism comes from circulating electrons rather than from spin.
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