1. DECODING THE EFFECTS OF LARGE AMPLITUDE VIBRATIONAL MOTIONS IN SPECTRA
Ohio State (Current and recent):
Laura Dzugan Jason Ford Charlotte Hinkle
Samantha Horvath Meng Huang Zhou Lin
Bernice Opoku-Agyeman Andrew Petit Bethany Wellen
Experimental Collaborators:
Michael Duncan Mark Johnson Carl Lineberger
Marsha Lester Terry Miller Mitchio Okumura
68th MSS
June 17, 2013

2. How are we taught to treat vibrational contributions to spectra:
Vibrations are based on harmonic oscillators
Vibrational spectra:
selection rules (linear dipole/harmonic oscillator) are Δn = 1
Intensity of transition will depend on
Symmetry
How much the dipole moment is affected by vibration (specifically dμ/dr)
(in H-bonded systems this leads to intense transitions associated with H-bonds)
Electronic transitions (or electron photodetachment) Frank-Condon spectra based on normal modes give a good first “guess”
How much the structure of the molecule changes
Such calculations of vibrational spectra can be (relatively) easily performed using widely available programs

3. … but sometimes it fails to provide an complete physical picture
How well does this work?
Experiment:
Often the harmonic picture provides a good qualitative starting point for assigning spectra/identifying isomers that are present, etc…
Harmonic
Assumes:
… but sometimes it fails to provide an complete physical picture
E. Garand, M. Z. Kamrath, P. A. Jordan, A. B. Wolk, C. M. Leavitt, A. B. McCoy, S. J. Miller, M. A. Johnson, Science, (2012).

4. Cl-(H2O)
As we look more closely, often there are many more peaks in the spectrum than can be accounted for by 3N-6 normal modes. What are their presence and intensity telling us about the bonding in these systems?
1000
1500
2000
2500
3000
3500
Predissociation Yield
Photon Energy, cm-1
Spectrum: Ben Elliot, Rob Roscioli and
Mark Johnson, published in JCPA in 2010
More on these systems in RG13 – Meng Huang

5. Harmonic spectrum of H3O2-
For molecules with large amplitude motions harmonic treatments can fail badly…
E. Diken and M. A. Johnson

6. For many systems, this approximation works very well, but …
Harmonic descriptions of photoelectron spectra (Franck Condon approximation)
X + e-
Photoelectron Counts
(arb. units)
Electron Binding Energy (eV)
Simulation assume Franck-Condon approximation:
The intensity is determined by overlap of thermally populated states of the anion and neutral eigenstates
Add FC plot for simple case of HO’s X-
For many systems, this approximation works very well, but …
K. M. Vogelhuber, S. W. Wren, A. B. McCoy, K. M. Ervin and W. C. Lineberger, JCP (2011)

7. Harmonic descriptions of photoelectron spectra (Franck Condon approximation)
Photoelectron Counts (arb. units)
Large geometry change between anion and neutral coupled with large amplitude motion of neutral leads to break-down of harmonic FC treatment for CDCl2-
K. M. Vogelhuber, S. W. Wren, A. B. McCoy, K. M. Ervin, and W. C. Lineberger, JCP (2011)
Electron Binding Energy (eV)

8. Some cautionary tales of “deficiencies” in harmonic picture of molecular vibrations
How should we think about anharmonic effects in molecular spectra?
Electrical [non-linear terms in the dipole]
Mechanical [higher order terms in the potential]
Are there simple models we can employ to anticipate and/or understand these effects?
Focus on five systems (with a few more along the way)
Photoelectron spectrum of CHCl2-
Manifestations of anharmonicity in the formate.water complex
Investigating broad signatures of H-bonding
Solvated H3O+ and insights gained about the origins of the 2100 cm-1 band in the spectrum of H2O(l)
H5+ - exciting into the dissociation coordinate

9. Harmonic descriptions of photoelectron spectra (Franck Condon approximation)
Photoelectron Counts (arb. units)
Large geometry change between anion and neutral coupled with large amplitude motion of neutral leads to break-down of normal mode treatment for CDCl2-
K. M. Vogelhuber, S. W. Wren, A. B. McCoy, K. M. Ervin, and W. C. Lineberger, JCP (2011)
Electron Binding Energy (eV)

10. What’s going on? Large geometry change
Modes strongly coupled in the neutral
HCCl + HCCl’
Anion
Gnd State
FC active states of neutral
Out-of-plane bend

11. Lesson 2: Coordinates matter
What’s going on?
Large geometry change
Modes strongly coupled in the neutral
Lesson 1: large amplitude (out-of-plane) vibrations can challenge harmonic treatments, but often they can be treated with simplified reduced-dimensional approaches
Lesson 2: Coordinates matter
Anion
Gnd State
FC active states of neutral

12. Some cautionary tales of “deficiencies” in harmonic picture of molecular vibrations
How should we think about anharmonic effects in molecular spectra?
Electrical [non-linear terms in the dipole]
Mechanical [higher order terms in the potential]
Are there simple models we can employ to anticipate and/or understand these effects?
Focus on five systems (with a few more along the way)
Photoelectron spectrum of CHCl2-
Manifestations of anharmonicity in the formate.water complex
Investigating broad signatures of H-bonding
Solvated H3O+ and insights gained about the origins of the 2100 cm-1 band in the spectrum of H2O(l)
H5+ - exciting into the dissociation coordinate

13. Example of anharmonicity (formate.water complex)
Helen Gerardi, Andrew DeBlase, X. Su, K. D. Jordan, ABM and M. A. Johnson (JPC-Lett, (2011).

14. Types of anharmonicity:
V=k1 q12 + k2 q22
μ=d1 q1 + d2 q2
(mechanical)
Potential n2
Add specra
(electrical)
Dipole

15. Effect of mechanical anharmonicity:
anharmonic pot. n1
V=k1 q12 + k2 q22
μ=d1 q1 + d2 q2
(mechanical)
Potential n2
Add specra
(electrical)
Dipole
V=k1 q12 + k2 q22 + K12 q1q22
m=d1 q1 + d2 q2

16. Calculated spectrum of H2CO (presented at MSS – Jun 1991)
VPT2/
VPT4
based on a linear dipole moment
harmonic
ABM and ELSibert, JCP, 95, 3488 (1991)

17. Example of mechanical anharmonicity (intensity borrowing formate
Example of mechanical anharmonicity (intensity borrowing formate.water complex)
IM rock
Fermi resonance
(intensity borrowing)
Change in the potential
with vibration excitation
Helen Gerardi, Andrew DeBlase, X. Su, K. D. Jordan, ABM and M. A. Johnson (JPC-Lett, (2011).

18. Consider the OH stretch region
Approximate by a harmonic treatment of the rock and the two identical OH stretches, coupled to the rock by a cubic term (qOH2qrock) and analyze through an adiabatic approximations
The progression can be reproduced by applying a Franck-Condon approximation to these potential curves
Is this effect more general???
vOH=1; equilib.
geom. shifts
IM rock
vOH=0
Two equivalent OH stretches
E.L.Sibert, JCP 119, (2003)
IM rock

19. Broad bands are characteristic features of cyclic H-bond arrangements in polypeptides
Can we come up with a simple model to describe the origin of these bands?
C. M. Leavitt, A. F. DeBlase, C. J. Johnson, C. T. Wolke, and M. A. Johnson.

20. Theoretical treatment:
From formate-water – frequency of OH changes with low-frequency vibrations
Can we model the spectrum by sampling the OH stretch spectrum based on the zero-point motions of the other vibrations?
Start by carving out the
relevant subsystem…
vOH=1; equilib.
geom. shifts
Expt.
Harmonic
vOH=0
Two equivalent OH stretches

21. Results for oxalate-H+:
Results of model based sampling the OH stretch spectrum using the zero-point motions of the other vibrations?
Simple picture picks up the overall breadth of the spectral feature
Allows us to investigate coupling between modes by exploring correlation between geometry and calculated harmonic frequencies
More in talk WG04
[Laura Dzugan]
calc
expt
So far we’ve seen examples of mechanical anharmonicity, what about the dipole moment (e.g. electrical anharmonicity)
calc D
expt
C. M. Leavitt, L. D. Jacobson, A. F. DeBlase, C. J. Johnson, C. T. Wolke, A. B. McCoy and M. A. Johnson, to be submitted to JPC-A.

22. Abstract book from 46th MSS (1991)
“Lehmann and Smith1 have illustrated that the intensities of overtone transitions are sensitive to details of the inner wall of the potential”
K. K. Lehmann and A. M. Smith, J. Chem. Phys. 93, 6140 (1990)

23. Abstract book from 46th MSS (1991)
In that study, we focused on high XH stretch overtones and the results led us to focus on the role of the potential – here we will focus on stretch/bend combination bands and investigate contributions from the dipole surface

24. Some cautionary tales of “deficiencies” in harmonic picture of molecular vibrations
How should we think about anharmonic effects in molecular spectra?
Electrical [non-linear terms in the dipole]
Mechanical [higher order terms in the potential]
Are there simple models we can employ to anticipate and/or understand these effects?
Focus on five systems (with a few more along the way)
Photoelectron spectrum of CHCl2-
Manifestations of anharmonicity in the formate.water complex
Investigating broad signatures of H-bonding
Solvated H3O+ and insights gained about the origins of the 2100 cm-1 band in the spectrum of H2O(l)
H5+ - exciting into the dissociation coordinate

25. Types of anharmonicity:
V=k1 q12 + k2 q22
m=d1 q1 + d2 q2
(mechanical)
Potential n2
Add specra
(electrical)
Dipole

26. Effect of electrical anharmonicity:
V=k1 q12 + k2 q22
μ=d1 q1 + d2 q2
(mechanical)
Potential n2
Add specra n1
n1+n2
(electrical)
Dipole n2
V=k1 q12 + k2 q22
μ=d1 q1 + d2 q2 + D12 q1q2

27. Example of mechanical anharmonicity (intensity borrowing formate
Example of mechanical anharmonicity (intensity borrowing formate.HOH complex)
IM rock
Helen Gerardi, Andrew DeBlase
and M. Johnson

28. Another example: The spectrum of H2O(l)

29. The spectrum of H2O(l) * Can we see these bands in clusters?
OH Stretch
Work on ref…
HOH
bend
librations
HOH bend + librations
Can we see these bands in clusters?
1000
2000
3000
4000
Photon Energy, cm-1
* Bertie, J. E.; Lan, Z. D. Appl. Spectrosc. 1996, 50, 1047.

30. What do we think liquid water looks like?
Water bend frequency will depend on how tightly the OH bond is “tied” to the adjacent water molecule…
Solvated H3O+ provides a simpler model

31. Effects of solvation on the bend spectrum of solvated H3O+
ABM, T. Guasco, C. Leavitt, S. Olsen and MAJohnson, PCCP, (2012).

32. Effects of solvation on the bend spectrum of solvated H3O+
There is a band near 1900 cm-1 in all species
The band blueshifts with increased interaction strength
Its intensity also increases with interaction strength
Where does this intensity come from?
Tim Guasco, Solveig Olesen,,
Christopher Leavitt and M. A. Johnson

33. Potential and dipole surface for 3-Ar casemx my
COUPLING IS IN THE DIPOLE SURFACE
(ELECRICAL ANHARMONICITY)
fAr q1
POTENTIAL LOOKS SEPARABLE

34. Harmonic and anharomic spectrum predicitionsmy
α-band results from the electrical anharmonicity
(in the (q1+q2)fAr contribution to the x-component of the dipole moment)
Can this be anticipated by single point calculations?

35. Calculated bend intensities at stationary points
Number of Ar atoms
Minimum
Transition state w
(cm-1) I
(km mol-1)
3H2O
1646
0.01
1663
2.69
3CH4
1690
0.08
1629
3.38
3N2
1723
0.19
1617
3.28
3Ar
1688
0.22
1666
bare
1.00
N/A

36. Why does the intensity of the bend is going down with solvent strength?
charge
sloshing
Fixed charge
model + + +

37. Effects of solvation on the bend spectrum of solvated H3O+
There is a band near 1900 cm-1 in all species
The band blueshifts with increased interaction strength
Its intensity also increases with interaction strength
Where does this intensity come from?
Tim Guasco, Solveig Olesen,,
Christopher Leavitt and M. A. Johnson

38. What do we think liquid water looks like?
Water bend frequency will depend on how tightly the OH bond is “tied” to the adjacent water molecule…
Solvated H3O+ provides a simpler model

39. The spectrum of H2O(l) * Assignment is supported by cluster sizes
OH Stretch
Assignment is supported by cluster sizes
non-condon effects are clearly important
Work on ref…
HOH
bend
librations
HOH bend + librations
1000
2000
3000
4000
Photon Energy, cm-1
* Bertie, J. E.; Lan, Z. D. Appl. Spectrosc. 1996, 50, 1047.

40. So far we’ve considered combination bands, what about overtones?
NONE: The general expectation is that overtone intensities – decrease by ~ an order of magnitude with each quantum of vibration (by ~100 between 1 0 and 2  0).
Does this hold for “floppy systems”?
So far we’ve considered combination bands, what about overtones?

41. Example V. H5+ (more in RG02)
Zhou Lin

42. Reported spectra (multi-photon)
10
30
50
70
Calculations put the shared proton frequency at 369 cm-1
940
1399
Relative Intensity
379
1723
H5+  H3+ + H2
Is such a long progression in a single vibration reasonable ? Can it be anticipated by calculation? What is it telling us about H5+?
Note H5+ is another floppy molecule!
320
1952 *
1180
470
815 *
200
400
600
800
1000
1200
1400
1600
1800
2000
2200 cm -1
1767
1636
Relative Intensity
1357
D5+  D3+ + D2
1417
1299
1505
679
886
1059
600
800
1000
1200
1400
1600
1800
2000 cm -1
Duncan, Asmis and co-workers JPC-Letters (2012)

43. Short summary of calculations and results:*
Use Diffusion Monte Carlo to calculate the ground state and the v=1, 2 and 3 states in the shared proton stretch
The ground state is VERY
large amplitude
Excited state calculations
require a judicious choice
of coordinate**
H2 +H3+ R1 R2
H3+ +H2
**More on DMC/coordinates
A. S. Petit TG02
*Z. Lin and ABM, JPC-A, ASAP for Wittig issue.

44. Excited state wave functions for H5+
Excitation of the shared proton drives the system further into the H2 + H3+ dissociation channel
How do these numbers compare to the spectrum?
E0=7205 cm-1
369 cm-1
H2 +H3+
H2 +H3+
H3+ +H2
H3+ +H2
673 cm-1
983 cm-1
H2 +H3+
H2 +H3+
H3+ +H2 R1
H3+ +H2 R2
Z. Lin and ABM, JPC-A, ASAP for Wittig issue.

45. Reported spectra (multi-photon)
983
Calculations put the shared proton frequency at 369 cm-1
369
940
1399
Transitions reflect overtones in the shared proton stretch…
Is such a long progression reasonable?
Relative Intensity
379
1723
H5+  H3+ + H2
320
1952 *
1180
470
815 *
200
400
600
800
1000
1200
1400
1600
1800
2000
2200 cm -1
713
1767
1636
Relative Intensity
1357
D5+  D3+ + D2
1417
1299
1505
679
886
1059
600
800
1000
1200
1400
1600
1800
2000 cm -1
Duncan, Asmis and co-workers JPC-Letters (2012)

46. 2-d pseudo-linear triatomic calculation
v=1
I = 1.00
v=5
I = 0.02
G. S.
v=4
R1+R2
The next two states with correct symmetry carry comparable intensity to the v=5 state
The states that are being excited extend into the product channel for proton transfer between H3+ and H2
v=3
I = 0.06
v=6
v=2
R1+R2
R1-R2
R1-R2
R1-R2
R1-R2
Z. Lin and ABM, JPC-Letters, (2012).

47. 2-d pseudo-linear triatomic calculation
v=1
I = 1.00
v=5
I = 0.02
G. S.
v=4
R1+R2
v=3
I = 0.06
v=6
v=2
R1+R2
R1-R2
R1-R2
R1-R2
R1-R2
Z. Lin and ABM, JPC-Letters, (2012).

48. Outlooks and challenges
When we think about vibrational spectra of “floppy” systems we need to be aware of the prevalence of unexpected features that are not anticipated by harmonic pictures.
These can reflect both electrical and mechanical anharmonicity
Despite the large amplitude, often we can interpret the features through reduced dimensional pictures
The origins of the “association band” in the water spectrum are assigned to the electrical anharmonicity (non-condon effects)
For extremely large amplitude modes – high overtones may have unexpectedly large intensities
By identifying these transitions and understanding their origins we can gain insights into the nature of the bonding and vibrational dynamics of these important systems

49. Bernice Opoku-Agyeman
Acknowledgements:
Experiment
Mark Johnson (Yale)
Tim Guasco
Chris Leavitt
Chris Johnson
Helen Gerardi
Andrew DeBlase
(effects of cubic
coupling terms - MG14)
and the rest of the
Johnson Lab
Carl Lineberger (CU)
Kristen Vogelhuber
Scott Wrenn
Lineberger Lab
Michael Duncan (UGA)
RECENT GRADUATES:
Samantha Horvath
Charlotte Hinkle
Andrew Petit
(H3+;DMC
TG02)
Meng Huang
(X-.HOH
RG13)
Jason Ford
Bethany Wellen
(BS 2013)
Bernice Opoku-Agyeman
(Dynamics
of BrCN-
FE06)
Zhou Lin
(H5+ RG02)
Laura Dzugan
(Vib. Spectra
WG04)
A special thanks to Terry!
Funding: NSF