Transcript Measurement and Computation of Molecular Potential Energy

Measurement and Computation of
Molecular Potential Energy Surfaces
Jennica Skoug, David Gorno, & Eli Scheele
Polik Research Group
Hope College
Department of Chemistry
Holland, MI 49423
Outline
• Potential Energy Surfaces
• Dispersed Fluorescence Spectroscopy
– Molecular Beam
– Lasers
– Monochromator
• Resonant Polyad Model
– Harmonic and Anharmonic Terms
– Vibrational State Mixing
• Computation of PES’s and Vibrational Levels
Potential Energy Surfaces
H
C
H
C
O
• A Potential Energy Surface (PES) describes how a
molecule’s energy depends on geometry
• Chemical structure, properties, and reactivity can be
calculated from the PES
Energy
Measuring PES’s & Vibrational States
Vibrational
Levels
Reactant
Products
Reaction Coordinate
• Measuring highly excited vibrational states allows
characterization of the PES away from the
equilibrium structure of the molecule
Energy
Molecular Beam for Sample Preparation
Reactant
Products
Reaction Coordinate
• A molecular beam cools the sample to 5K
• Molecules occupy the lowest quantum state and simplify
the resulting spectrum
Lasers for Electronic Excitation
Energy
Laser
excitation
Reactant
Products
Reaction Coordinate
• Laser provide an intense monochromatic light source
• Lasers motes molecules to an excited electronic state
Monochromator for Detection
Laser
excitation
Energy
Fluorescence
Reactant
Products
Reaction Coordinate
• A monchromator disperses molecular fluorescence
• Evibrational level = Elaser – Efluoresence
Dispersed Fluorescence Spectrum
Intensity
31 HFCO
0
5000
10000
15000
-1
Frequency (cm )
20000
Summary of Assignments
Molecule Previous # Current #
Energy
Range
(cm-1)
Year
H2CO
81
279
0 - 12,500
1996
D2CO
7
261
0 - 12,000
1998
HFCO
44
382
0 - 22,500
2002
H2COH2+CO dissociation barrier  28,000 cm-1
HFCOHF+CO dissociation barrier  17,000 cm-1
Harmonic and Anharmonic Models
E    i v i   x ij v i v j
i
Harmonic
Energy
i j
Anharmonic
Correction
• A harmonic oscillator predicts equally spaced
energy levels
• Anharmonic corrections shift vibrational energy
levels as the PES widens
Polyad Model
2 26 5
k26,5

 k44,66
2 24 26 3
 k44,66
k26,5

 k44,66
2 24 46 1
2 15 16 4
k26,5

2 14 25 16 2
5 26 3
 k44,66
k26,5

4 2 5 26 1
 k44,66
k26,5

2 14 45 1
• Groups of vibrational states interacting through
resonances are called polyads
• Resonances mix vibrational energy levels
• Energy levels are calculated from the Schrodinger Eqn
Matrix Form of Schrödinger Equation
H  E
 H11 H12
H
H
21
22

H31 H32
H13 

H23 
H33 
Diagonal Elements:
 i v i 
i
Harmonic
Energy
 x ijv iv j
i j
Anharmonic
Correction
c1
c1
c 2   E c 2 
 
 
c 3 
c 3 
Off-Diagonal Elements:
k


ij , k 


vi  1
2





1/ 2





vj  1
2





1/ 2
Resonant
Interactions






k



v
2
1/ 2
H2CO Anharmonic Polyad Model Fits
Parameter
Fit 1
Fit 2
Fit3
Fit 4
ω1°
2818.9
2812.3
2813.7
2817.4





ω6 °
1260.6
1254.8
1251.5
1251.9
x11
-40.1
-29.8
-30.7
-34.4





x66
-5.2
-2.8
-2.1
-2.2
k26,5
148.6
146.7
138.6
k36,5
129.3
129.6
135.1
k11,55
140.5
137.4
129.3
21.6
23.3
k44,66
k25,35
Std Dev
18.5
23.4
4.34
3.34
2.80
Model Fits to Experimental Data
Polyad Quantum Numbers
• H2CO
k36,5
k26,5
k11,55
Noop = v4 (destroyed by k44,66)
Nvib = v1+v4+v5+v6 (destroyed by k1,44 and k1,66)
Nres = 2v1+v2+v3+v4+2v5+v6 (remains good!)
• D2CO
k1,44
k44,66
k36,5
Nvib = v2+v3+v5 (ultimately destroyed)
NCO = v2 (remains good!)
Nres = 2v1+2v2+v3+v4+2v5+v6 (remains good!)
• HFCO
k2,66
others?
Npolyad = 2v2+v6
v1, v3, v4, v5 may remain good
Computation of PES’s
 E
E  E0   
i  q i

1   2E
 qi  
2! i , j  qi q j
0
1   3E

3! i , j ,k  qi q j qk

 qi q j 

0
4


1

E
 qi q j qk   

 q q q q
4
!
i
,
j
,
k
,
l
0
 i j k l

 qi q j qk ql  ...

0
• The Potential Energy E can be represented by a
Taylor series expansion of the geometry coordinates qi
• A quartic PES requires computation of many highorder force constants (partial derivatives)
• Force constants predict vibrational energy level shifts
and mixing
Parallel Computing
• Force constants are
computed as
numerical derivatives,
i.e., by calculating
energies of displaced
geometries
• PES calculation takes
hours instead of
weeks with parallel
computing
Computation of PES and Vibrations
Conclusions
• DF spectroscopy is a powerful technique for measuring
excited states (general, selective, sensitive)
• Resonances shift and mix vibrational states
• The anharmonic polyad model accounts for
resonances and assigns highly mixed spectra (, x, k)
• Polyad quantum numbers remain at high energy (Nres
always conserved)
• High level quartic PES calculations and polyad model
accurately predict excited vibrational states
Acknowledgements
• H2CO
Rychard Bouwens (UC Berkeley - Physics), Jon
Hammerschmidt (U Minn - Chemistry), Martha Grzeskowiak
(Mich St - Med School), Tineke Stegink (Netherlands Industry), Patrick Yorba (Med School)
• D2CO
Gregory Martin (Dow Chemical), Todd Chassee (U Mich Med School), Tyson Friday (Industry)
• HFCO
Katie Horsman (U Va - Chemistry), Karen Hahn (Med
School), Ron Heemstra (Pfizer - Industry), Ben Ellingson (U
Minn – Chemistry)
• Funding
NSF, Beckman Foundation, ACS-PRF, Research
Corporation, Wyckoff Chemical, Exxon, Warner-Lambert