Ohio State (Current and recent):Laura Dzugan Jason Ford Samantha Horvath Meng Huang Zhou Lin Melanie MarlettBernice 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

69th International Symposium on Molecular Spectroscopy, June 2014

OH Stretch

librations HOH bend

* Bertie, J. E.; Lan, Z. D. Appl. Spectrosc. 1996, 50, 1047.

The spectrum of H2O(l) *

HOH bend + librations

0 1000 2000 3000 4000

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 Δn = 1 Intensity of transition will depend on

SymmetryHow much the dipole moment is affected by vibration

(specifically dμ/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, 1047.

The spectrum of H2O(l) *

HOH bend + librations

0 1000 2000 3000 4000

Photon Energy, cm-1

cm-1

500 1000 1500 2000 2500 3000 3500 4000

calc

ula

ted s

ignal

(unscale

d h

arm

onic

)

0

1

2

3

4

5

6

1000 1500 2000 2500 3000 3500

Pre

disso

ciatio

n Yie

ld

Photon Energy, cm-1

Cl-(H2O)

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.

VHarmonic/μLinear

nq2

nq1

0.0 0.2 0.4 0.6 0.8 1.0

Energy (arb. units)

Types of anharmonicity:q 2

q1q1

q 2

Pote

nti

al

(mech

an

ical)

Dip

ole

(ele

ctri

cal)

harmonic

V=k1 q12 + k2 q2

2 μ=d1 q1 + d2 q2

n2

n1

q 2

q1q1

q 2VHarmonic/μLinear

nq2

nq1

0.0 0.2 0.4 0.6 0.8 1.0

Energy (arb. units)

Effect of electrical anharmonicity:

Pote

nti

al

(mech

an

ical)

Dip

ole

(ele

ctri

cal)

V=k1 q12 + k2 q2

2 μ=d1 q1 + d2 q2

q 2

q1q1

q 2

VHarmonic/μNonlinear

nq2nq1+q2

0.0 0.2 0.4 0.6 1.0

Energy (arb. units)

V=k1 q12 + k2 q2

2 μ=d1 q1 + d2 q2 + D12 q1q2

n1+n2

n2

n1

n1

n2

cm-1

500 1000 1500 2000 2500 3000 3500 4000

calc

ula

ted s

ignal

(unscale

d h

arm

onic

)

0

1

2

3

4

5

6

1000 1500 2000 2500 3000 3500

Pre

disso

ciatio

n Yie

ld

Photon Energy, cm-1

Cl-(H2O)

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

Look at the vibrational states:

ip (o)

-90 -60 -30 0 30 60 90

Cl– •H

2O V

(ip)

(cm

-1)

0

200

400

600

800

1000

1200

1400

1600

1800

2000

2200

2400

2600

2800

xhoh vs Col 2 xhoh vs Col 2

ip (o)

-90 -60 -30 0 30 60 90

tran

sitio

n m

omen

t (1<

--0)

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

Value at equilibrium gives the intensity of the bend fundamental

Slope gives the combination band

intensity

Why such a large slope?

ipHOHHOH 01 nn

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, 1047.

Return to the spectrum of H2O(l) *

HOH bend + librations

0 1000 2000 3000 4000

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

StateHarmoni

c Frequen

cy(cm-1)

I(Cartesi

an)(km mol-

1)

I(Interna

ls)(km

mol-1)

vfree 1624 86.0 86.0

vfree + vip 1982 0.7 0.4

vfree + voop 2262 0.0 5.6

vH-bond 1642 32.3 32.3

vH-bond + vip 2000 0.3 6.3

vH-bond + voop 2281 0.2 0.1Cartesian normal modes:

vip voop

Note: Intensity is captured only when internal coordinates are used…

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:ExperimentMark Johnson (Yale)

Tim GuascoChris LeavittChris Johnsonand the rest of the Johnson Lab

RECENT GRADUATES:Samantha HorvathAndrew Petit

Funding: NSF

Bernice Opoku-

Agyeman

Menanie Marlett

Laura Dzugan

Zhou Lin

Meng HuangJason Ford