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

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

… 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, 335 694 (2012).

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

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

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 134 184306 (2011)

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 134 184306 (2011) Electron Binding Energy (eV)

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

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 134 184306 (2011) Electron Binding Energy (eV)

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

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

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

Example of anharmonicity (formate.water complex) Helen Gerardi, Andrew DeBlase, X. Su, K. D. Jordan, ABM and M. A. Johnson (JPC-Lett, 2 2437 (2011).

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

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

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)

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, 2 2437 (2011).

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, 10138 (2003) IM rock

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.

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

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.

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)

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

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

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

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

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

Another example: The spectrum of H2O(l)

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.

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

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

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

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

Harmonic and anharomic spectrum predicitions my 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?

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

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

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

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

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.

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?

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

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)

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.

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.

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)

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, 3 6390 (2012).

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, 3 6390 (2012).

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

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