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

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

+

+

-

-

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

Excitation in v3 distorts bending polyads

Steeves et. al., J. Mol. Spec., 256, 256, 2009.

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

Spectator Modes

½[E(v+1)+E(v)]-E(0) (cm-1)

E(v+

1)-E

(v)

(cm

-1)

What took so long?

Better experimental methodsAdvances in computation

New ideas embodied in Heff modelsThis is not your grandfather’s spectroscopy

Next Three Talks

TG05 Josh BarabanTG06 Bryan ChangalaTG07 Anthony Merer