ohio state (current and recent): laura dzugan jason fordsamantha horvath meng huang zhou linmelanie...
TRANSCRIPT
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