A First-Principles Model of Fermi Resonance in the Alkyl CH Stretch Region: Application to

Hydronaphthalenes, Indanes, and Cyclohexane

Funded by NSF and DOE

Molecular Spectroscopy Symposium, June, 2014

Nathanael Kidwell, Tim Zwier, Danny Tabor, and Ned Sibert

DPE C2h

DPOE C2h

DPE C2

DPOE C2

Probing molecular structure with CH chromophoreswith the Zwier Group at Purdue

Our goal is to develop theoretical models that will enable us to use the CH stretch as a probe of environment. Initial work focuses on developing Hamiltonians that allow us to predicting spectra of the molecules based on input from electronic structure theory and couplings that are scaled to the DPE C2h spectrum.

so/ss so

so/ssso/ss

ss/so as

asas

ss/so

ss as

asss/so

Background

CH2 Scissor CH Sym Stretch CH Asym Stretch 1450 cm-1 2960 cm-1 2980 cm-1

Images from Molecular Vibration; Wikipedia, the free encyclopedia

1500 3000

Wavenumber (cm-1)

A

/ /

ss asso

2900 3000

ss as

2900 3000

1) Calculate Ess, Eas, Eso and W with DFT.

2) Scale the results using a, b, and c.

3) For different X-CH2-Y species use the same a, b, and c.

The Strategy

The Hamiltonian

Stretch-Bend Fermi Coupling

An Aside

One can use either a symmetrized representation

Or one can use a localized representation

Complication No. 1 The spectra are extremely congested.

SolutionFind a good experimentalist.

Complication No. 2Normal modes are sensitive to small potential changes.

SolutionUse local modes.

Local modes are insensitive to small potential changes.Local modes potentials are transferrable.The local mode picture is approximate.

1476 cm-1

1479 cm-1

The CH2 Scissor Vibrations of TetralinNM picture hides interactions with scissor modes

1466 cm-1

The Scaled & Localized CH2 Scissor Vibrations of Tetralin

Enough with the preliminaries.

Onto the main event.

THNI2M

tetralin

A

C

AB

14DHN A

A

B

A

indane

A

B

A

indene 12DHN

B

A

B

A

A

Comparison to Normal Mode Results

Model HamiltonianStart with a zero order Hamiltonian and dipole

N

iii nH

1

)0( )2

1(

N

iiiq

1

)0(

Add some Fermi coupling terms

kjikjiikl chaaafH

,,

)1( .).(

Pick a basis, diagonalize the H matrix, and calculate the spectrum.

B3LYP/6-311+G(d,p)

12DHN Spectra

With anharmonic terms included.

12DHN Spectra

CH2 Decoupling Approximation

CH2 Decoupling Approximation

Calculate bilinear terms in dipole

14DHN Spectra

Comparison of Model Results to Experimental Results

CH2 Decoupling Approximation

Concluding Remarks

• Developed a model for CH2 stretches.• Hamiltonian has parameters that are fit to one

member of a group of similar species.• Working to extend to CH3 groups.• Working to better parameterize the

Hamiltonian.• Would like to add waters.

On to CH3 groups!

CH3-CD3 R1

F2

F1

R2

R3 F3