'Beautiful' study could dispel doubts over the validity of the Born-Oppenheimer approximation

Theoretical chemists can breathe a tentative sigh of relief after the publication of a ’beautiful’ study which shows that a cornerstone of their discipline seems to be intact [1] - despite earlier evidence to the contrary. 

At risk has been the ’Born-Oppenheimer approximation’, a key mathematical construct of theoretical chemistry which states that because electrons move so much faster than nuclei in atoms and molecules, the motion of each can be treated separately in quantum mechanical calculations and any ’coupling’ between the motions is generally insignificant. 

However, a few years ago a group of researchers in Taiwan provided startling evidence for a catastrophic failure of the Born-Oppenheimer approximation[2,3]. They were studying the reaction between chlorine and hydrogen, a reaction known to be ’non-adiabatic’ - it deviates slightly from Born-Oppenheimer. But the group showed that under certain circumstances a ’forbidden’ reaction could occur - a chlorine atom in its excited state would react preferentially with hydrogen rather than, as Born-Oppenheimer predicts, chlorine in its ground state. This finding caused a major headache among theoretical chemists. 

"If Born-Oppenheimer was shown not to work, it would have gone against a wide body of conventional wisdom and we would have to re-think everything we know about chemical dynamics" - David Manolopoulos

Now, Etienne Garand of the University of California, Berkeley, and colleagues have completed a seminal experimental and theoretical investigation that shows that the Born-Oppenheimer approximation holds good for the chlorine-hydrogen system[1]. 

The researchers reasoned that if they could interrogate with high precision the quantum states of a short-lived intermediate in the reaction between hydrogen and chlorine they would be able to test the validity of the approximation. 

The team slammed a pulse of laser light into the anion ClH2-, dislodging an electron to create the intermediate, ClH2. They measured the kinetic energy of the ejected electron using a technique called slow electron velocity-map imaging (SEVI) spectroscopy and so were able to deduce the quantum state of the complex from which the electron was emitted. 

’In this way we were able to obtain unprecedented information about the quantum states of the complex and the coupling between the nuclear and electronic motion,’ David Manolopoulos, a theoretical chemist at the University of Oxford who was on the team, told Chemistry World. ’We obtained experimental results beyond those described by the Born-Oppenheimer approximation and were therefore able to directly test the accuracy of the theoretical treatment.’ 

By applying the approximation to the system, the researchers obtained a reasonably accurate description of what they had observed experimentally. But when they took into account the known small coupling between the nuclear and electronic motion their results were far more precise. 

’We showed that, as Born-Oppenheimer suggests, coupling is very weak and that the theoretical implication is that the approximation remains good,’ Manolopoulos said. ’The implication is that chlorine in its excited state should not react significantly, in contrast with the earlier experimental results. Further chemical reaction dynamics experiments may be needed to resolve this issue.’ 

’If Born-Oppenheimer was shown not to work, it would have gone against a wide body of conventional wisdom and we would have to re-think everything we know about chemical dynamics,’ he added. 

Joel Bowman, a theoretical chemist at Emory University in Atlanta, US described the work as a ’beautiful joint theoretical-experimental study’. 

’This was a wonderful piece of work and to measure that spectrum was a tour de force,’ he told Chemistry World. ’The agreement between experiment and theory is outstanding. You can do the calculations with the approximation, but if you go beyond the approximation the experimental agreement improves. On that basis nothing seems to be amiss. It is significant because there were question marks over whether things were understood or not. It seems, tentatively at least, that we do have things right.’ 

Simon Hadlington