Ohio State (Current and recent): Laura Dzugan Jason FordSamantha Horvath Meng Huang Zhou LinMelanie Marlett Bernice Opoku-AgyemanAndrew PetitBethany Wellen Experimental Collaborators: Mark Johnson THE ROLE OF ELECTRICAL ANHARMONICITY IN DETERMINING INTENSITY IN THE 2100 cm −1 REGION OF THE WATER SPECTURM 69 th International Symposium on Molecular Spectroscopy, June 2014

OH Stretch librations HOH bend * Bertie, J. E.; Lan, Z. D. Appl. Spectrosc. 1996, 50, The spectrum of H 2 O(l) * HOH bend + librations Photon Energy, cm -1

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 Δ n = 1 Intensity of transition will depend on Symmetry How much the dipole moment is affected by vibration (specifically d μ /dr) (in H-bonded systems this leads to intense transitions associated with H- bonds) Such calculations of vibrational spectra can be (relatively) easily performed using widely available programs … but sometimes they fail to provide an complete physical picture

OH Stretch librations HOH bend * Bertie, J. E.; Lan, Z. D. Appl. Spectrosc. 1996, 50, The spectrum of H 2 O(l) * HOH bend + librations Photon Energy, cm -1

Predissociation Yield Photon Energy, cm -1 Cl - (H 2 O) Spectrum: Ben Elliot, Rob Roscioli and Mark Johnson, published in JCPA in 2010 Meng Huang Combination band Harmonic Measured

How can we move beyond the 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 two systems Manifestations of anharmonicity in the bend region of the chloride water spectrum Origin of the associate band in the spectrum of water and water clusters Ask how the explanation of the origin of anharmonic features depends on the coordinates used to express the model Hamiltonian.

How can we move beyond the 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 two systems Manifestations of anharmonicity in the bend region of the chloride water spectrum Origin of the associate band in the spectrum of water and water clusters Ask how the explanation of the origin of anharmonic features depends on the coordinates used to express the model Hamiltonian.

Types of anharmonicity: Potential (mechanical) Dipole (electrical) harmonic V=k 1 q k 2 q 2 2 μ =d 1 q 1 + d 2 q 2  

Effect of electrical anharmonicity: Potential (mechanical) Dipole (electrical) V=k 1 q k 2 q 2 2 μ =d 1 q 1 + d 2 q 2 V=k 1 q k 2 q 2 2 μ =d 1 q 1 + d 2 q 2 + D 12 q 1 q 2       

Predissociation Yield Photon Energy, cm -1 Cl - (H 2 O) Spectrum: Ben Elliot, Rob Roscioli and Mark Johnson, published in JCPA in 2010 Meng Huang Combination band

Making assignments/understanding intensities: Generate 1-d slices through the potential and dipole surfaces along the in-plane and out-of-plane bend [MP2/aug-cc- pVTZ] Calculate the frequencies and intensities of transitions for the fundamental; overtone and in combination with other modes Use this to interpret the origin of the intensity of these two “extra” bands in the low-frequency region

Assign the spectrum HOH + ip DOD + ip OH b + OX 2 oop H 2 oop D oop H OH f 2 HOH 2 DOD HOH DOD OD f OD b OH b OD b + OX A) Clˉ·H 2 O·Ar B) Clˉ·D 2 O·Ar Predissociation Yield Photon Energy, cm -1 HOH bend OOP bend

Look at the vibrational states: Value at equilibrium gives the intensity of the bend fundamental Slope gives the combination band intensity Why such a large slope ?

What is going on? Minimum HOH bend Frequency: 1670 cm -1 HOH fundamental Intensity: 100 km/mol Transition State HOH bend Frequency: 1650 cm -1 HOH fundamental Intensity: 310 km/mol Large change in the HOH bend intensity with in- plane rotation reflects difference in bend intensity depending on H-bonding environment! Origin of the intensity appears to be “electrical anharmonicity”

OH Stretch librations HOH bend * Bertie, J. E.; Lan, Z. D. Appl. Spectrosc. 1996, 50, Return to the spectrum of H 2 O(l) * HOH bend + librations Photon Energy, cm -1 Can we see this band in clusters?

Making assignments/understanding intensities: Perform harmonic calculations of the spectra of water clusters (up to six water molecules) Use finite difference approaches to obtain a quadratic expansion of the dipole and cubic expansion of the potential in normal modes* Evaluate the role of higher order terms in determining intensity in the combination band * Note we look at normal modes defined from both Cartesian and internal coordinates

Results for water dimer based on quadratic expansions of potential and dipole surfaces State Harmonic Frequency (cm -1 ) I (Cartesian) (km mol -1 ) I (Internals) (km mol -1 ) v free v free + v ip v free + v oop v H-bond v H-bond + v ip v H-bond + v oop Cartesian normal modes: v ip v oop Note: Intensity is captured only when internal coordinates are used…

OH Stretch librations HOH bend * Bertie, J. E.; Lan, Z. D. Appl. Spectrosc. 1996, 50, The spectrum of H 2 O(l) * HOH bend + librations Photon Energy, cm -1 Harmonic spectrum of the book structure of (HOH) 6 including quadratic terms in the dipole expansion Similar results are obtained for other water clusters

Results for several water hexamers Spectral feature of the association band reflects -Comes from electrical anharmonicity when potential and dipole are expanded in normal modes based on internal coordinates

Note: coordinates matter in this analysis! See ABMcCoy, JPCB, ASAP (DOI:

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) This picture will depend on the choice of coordinates used for the expansion While full-dimensional results will be independent of this choice, the internal coordinates provide the more rapidly converging expansion of the potential and dipole surfaces

Acknowledgements: Experiment Mark Johnson (Yale) Tim Guasco Chris Leavitt Chris Johnson and the rest of the Johnson Lab RECENT GRADUATES: Samantha Horvath Andrew Petit Funding:NSF Bernice Opoku- Agyeman Menanie Marlett Laura Dzugan Zhou Lin Meng HuangJason Ford