sigma donation and pi back-donation
/ pi (pie), sigma (SIG-muh) /
A good handshake goes both ways: you offer your hand and the other person grips back, and the grip is firmer because of the mutual effort. The bond between certain ligands and a metal is exactly that kind of two-way handshake. One direction is sigma donation, the ligand offering a lone pair to the metal; the other is pi back-donation, the metal pushing electrons back into the ligand. Together they make a bond far stronger than either flow alone, and the whole idea is called synergic bonding.
Take carbon monoxide as the model. CO has a lone pair on carbon that points straight at the metal; this pair flows into an empty metal orbital along the bond axis, the sigma donation. But CO also has empty antibonding pi orbitals just above its filled levels, and a transition metal in a low oxidation state has filled d orbitals of the right shape and symmetry to overlap with them sideways. Electron density slides from those filled metal d orbitals into CO's empty pi orbitals, the back-donation. The two flows reinforce each other: donation makes the metal slightly electron-poor, which makes it pull harder, while back-donation makes the metal slightly electron-rich, which makes the ligand donate more eagerly. The same picture describes how alkenes, dinitrogen, and many other pi-acceptor ligands bind.
This synergy is the secret engine of a huge swathe of inorganic chemistry. It explains why low-valent metals love CO, why metal carbonyls are stable, and why infrared spectroscopy is such a powerful probe: back-donation populates orbitals that weaken the carbon-oxygen bond, so the C-O stretch drops in frequency by an amount you can measure and use to rank how strongly a metal back-donates. It is also worth being honest that this is a molecular-orbital description, a model of where the electrons go, and the relative weight of sigma versus pi can be argued; but as a working picture it predicts bond strengths, geometries, and spectra remarkably well.
Compare the cation [Mn(CO)6]+, neutral Cr(CO)6, and the anion [V(CO)6]-. As you add electron density to the metal, back-donation grows and the C-O stretching frequency falls steadily across the series, a clean demonstration that the metal really is pushing electrons into CO.
More electron density on the metal means more back-donation and a lower C-O stretch.
Back-donation is a model of electron flow, not a literally measurable current; what we measure is its consequence, such as the shifted C-O stretching frequency.