Suppressing the geometric phase effect: Closely spaced seams of the conical intersection in Na3(2 2E′)

It is shown that for the Exε Jahn–Teller problem, the circulation, the line integral along a closed loop, of the actual, or an approximation to the, derivative coupling can be used to determine the number of closely spaced conical intersections in that closed loop. This approach has advantages over the use of the geometric phase theorem, which can only count conical intersections mod 2. The circulation is used to establish the locus of the seam of the conical intersection of the 2 2E′ state of Na3. It is found that in addition to the D3h seam of the conical intersection, three symmetry equivalent seams with C2v symmetry exist in close proximity to the D3h seam. The three C2v seams intersect the D3h seam. The net geometric phase effect is largely suppressed and this ostensibly Jahn–Teller pair of electronic states is more like a Renner–Teller pair.