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Patterns of Broken Patterns
RWF, Barratt Park, Bryan Changala, Josh Baraban, John Stanton, and
Anthony Merer
I have always loved perturbations• Isolated State Patterns
– Need to see the small stuff: reduced term value plot
• Broken Pattern: Isolated Perturbation– Level crossing– Failure of second-order perturbation theory
• Patterns of Broken Patterns– Diatomic molecule: multiple (e,v) ~ (e’,v’) level crossings– Polyads: matrix element and membership scaling rules– S1 acetylene
• Broken Pattern of Broken Patterns– Proximity to isomerization path: S1 in-plane trans-cis– Polyad scaling violation and K-staggering
• Pattern of Broken Patterns of Broken Patterns• Advances in Laser and Computational Technology
BIG STUFF
0 300
1000
Term Value Plot
J(J+1)
EJ /
cm-1
SMALL STUFF
0 300
0.03
Reduced Term Value Plot
J(J+1)
[EJ -
Bes
t J(J
+1)]
/cm
-1
0.03
0
Patterns of Broken Patterns
•Diatomic Molecule: Multiple Level Crossings•Polyads: Membership and Scaling
trans conformer of S1 C2H2
+
+
-
-
Near-prolate top:
- Franck-Condon active from S0
- Totally symmetric
- Non-totally symmetric bends - Darling-Dennison resonance and Coriolis
coupling form bending polyads:
transbend
torsion
cis
bend
Bryan Changala
B2 Polyads
• Consists of (v4,v6) = (2,0), (1,1), and (0,2) vibrational levels
• Add some quanta in trans-bend (mode 3)– 3nB2
– Polyad pattern should be independent of n– Surprise!
• Broken pattern of broken patterns
New Patterns Emerge
both approach zero at trans-cis saddle point.
Modes 3 and 6 must both be excited.Mode 4 is a “spectator” mode.
ω 3eff ,ω6
eff{ }
Fitting the Barrier Height
½[E(v+1)+E(v)]-E(0) (cm-1)
E(v+
1)-E
(v)
(cm
-1)
ETS= 4695 ± 36 cm-1
ETS= 4852 ± 5 cm-1
ETS= 4592 ± 2 cm-1
Fits to Experimental 3n62 T0 data
What took so long?
Better experimental methodsAdvances in computation
New ideas embodied in Heff modelsThis is not your grandfather’s spectroscopy