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
Reduced Term Value Plot
Term Value Plot
0.03
1000
EJ /cm-1
[EJ - Best J(J+1)]/cm-1
0
0
0
0
J(J+1)
BIG STUFF
30
0
J(J+1)
SMALL STUFF
30
Perturbation-Free and Perturbed Bands of SiO
Patterns of Broken Patterns
•Diatomic Molecule: Multiple Level Crossings
•Polyads: Membership and Scaling
Proc. Phys. Soc. A 63, 1132 (1950)
Scaling: Hev,e’v’ = Hee’<v|v’>
Polyads
One low-P polyad generates all higher-P polyads!
Acetylene: S1 Electronic
State
trans conformer of S1 C2H2
- Franck-Condon active from S0
- Totally symmetric
trans
bend
torsion
cis
bend
Bryan Changala
-
+
+
-
- Non-totally symmetric bends
- Darling-Dennison resonance and Coriolis
coupling form bending polyads:
Near-prolate top:
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
Excitation in v3 distorts bending polyads
Steeves et. al., J. Mol. Spec., 256, 256, 2009.
New Patterns Emerge

eff
3
,
eff
6
both approach zero at
trans-cis saddle point.
Modes 3 and 6 must both be excited.
Mode 4 is a “spectator” mode.
Fitting the Barrier Height
1100
E(v+1)-E(v) (cm-1)
1000
ETS= 4592 ± 2 cm-1
900
800
700
600
Fits to Experimental 3n62 T0 data
500
ETS= 4695 ± 36 cm-1
400
ETS= 4852 ± 5 cm-1
300
0
1000
2000
3000
4000
½[E(v+1)+E(v)]-E(0) (cm-1)
5000
6000
Spectator Modes
1050
E(v+1)-E(v) (cm-1)
1000
950
900
850
800
750
700
650
0
500
1000
1500
2000
2500
3000
½[E(v+1)+E(v)]-E(0) (cm-1)
3500
4000
4500
5000
What took so long?
Better experimental methods
Advances in computation
New ideas embodied in Heff models
This is not your grandfather’s spectroscopy
Next Three Talks
TG05 Josh Baraban
TG06 Bryan Changala
TG07 Anthony Merer