Polar Beer

And now: the effects of blogging on Ultracold Polar Molecules

17 February 2006

Ground work

In times like these, there are very few reasons to stop and think before inflicting another blog on the net. My excuse must be a recent infatuation with molecules and their wonderfully complicated physics. Hopefully this space will get filled up with lots of ultracool quantum mechanics, horrifically bad puns and insights into the private lives of molecules and their innards. For those who prefer a little more entertainment, there are also vague plans to finally broadcast The Curse of the Vibrating Polar Bear - chronicling the adventures of a daring/dashing/very cool pirate crew as they attempt to win back Diatomic Molecules (and save the world) from the Dastardly Chemists.

For starters, a chain of thought: Is there an analogue of Hund's rules that one can mindlessly crank to figure out the ground state term of a molecule ? After a windy afternoon trying to cook up Hundish rules, here is a summary of some rather doggerel thoughts:

  • Too many molecules have 1Σ ground states. Is this some laziness-induced selection at work, or as Landau claims, is the ground state often the maximally symmetric state ?
  • Bonding/anti-bonding molecular orbitals are exactly the same as exchange-coupled spin anti-symmetric/symmetric electron pairs ! Molecules with anti-bonding HOMOs are in spin triplets, while the bonding HOMOs lead to spin singlets.
  • Details of the tensor-Stark shift determine whether a σ bonding orbital is lower in energy than a π orbital - which is another way of saying: sometimes the σ is lower than the π± and sometimes not ... so blame the Stark shift.
  • Hund-like filling rules for electrons into the molecular orbitals determine the Λ for the ground state term. The π± are degenerate and electrons fill them repulsively.
After doodling for a while, the ground state terms for a lot of Herzberg's list seem to make sense. The preponderance of 1Σ terms is likely because of the preponderance of filled bonding orbitals whose Λ 's (σ: Λ = 0, π±: Λ = ±1) add up to zero. O2 and He2 both have 3Σ ground terms, but the singly ionized molecular ground states show that the antibonding σ is lower than the antibonding π in He2, and so on ...