Comment by JBits

The equations governing quarks admit negative energy solutions, which we interpret as antiquarks. Chemistry typically uses non-relativistic quantum mechanics which only have positive energy solutions (like classical mechanics).

The solutions in chemistry are wavefunctions. Wavefunctions give a complex number to each point in space so they may interfere constructively or destructively to give complex numbers of greater and smaller magnitude respectively. The Schrödinger equation can be solved for each atom independently to get one electron wavefunctions named atomic orbitals, and, in molecular orbital theory, these atomic combined to give molecular orbitals which are one electron wavefunctions for the molecule. When the atomic orbitals add up constructively to give a molecular orbital with a higher electron density between the atoms it's a bonding molecular orbital, otherwise it's anti-bonding.

Both quarks and anti-quarks can spin in two ways (even though this spin is not a conventional spin but something special to quantum). When a quark and an antiquark are produced, spin must be conserved, so in pair production each must have opposite spin so the total is zero.