complementary use of modern spectroscopy and theory in the study of rovibrational levels of bf 3...
TRANSCRIPT
Complementary Use of Modern Spectroscopy and Theory in the Study of
Rovibrational Levels of BF3
Robynne Kirkpatricka, Tony Masiellob, Alfons Weberc, and Joseph W. Niblera
aDepartment of Chemistry, Oregon State UniversitybPacific Northwest National Laboratory
cNational Institute of Standards and Technology, MD
Goals and Methods
• Push the limits of experiment to see how closely ab initio methods model experiment
• Use isotopic substitution to gain additional information about molecular potentials
How? Use modern, high resolution (0.0015 cm-1) spectroscopy to study “simple” molecules of high symmetry, such as BF3
Raman and IR active modes of group D3h
AX3 molecules 2
4
3
E (R, IR)
A2 (IR)
E (R, IR)
1
Exclusively Raman Active
A1
Consider SO3-- an intriguing molecule!
32S
16O 3
S16
O 3
1065.5 1066.5 1067.5
Raman Shift / cm-1
1065.5 1066.5 1067.5
34S16O3
32S16O3
1 CARS Q-Branch
32S
18O3
34S
18O3
1002.5 1003.5 1004.5 1005.5 1006.5 1007.5
Raman Shift / cm-1
1067.5
1002.5 1003.5 1004.5 1005.5 1006.5 1007.5
Raman Shift / cm-1
32S18O3
34S18O3
What causes this complex structure?
1 CARS Q-Branch
Q1 ≠ J(J+1)+(C1 - B1)K 2 + higher terms
Perturbations to 1 (SO3) deduced using the CARS Q-Branch
1
A1'
Fermi resonance
Coriolis
l-resonance
24 (l=0) A1 '
22 A1 '
24 (l=2) E '
2 + 4 E '
Let’s examine the CARS Q-Branches of 10BF3 and 11BF3
CARS Experiment
Vibrational energy, i
Anti-Stokes (AS) energy,
S
0
S A
Sample
Induced dipole in sample ↔ Non-Linear optical interaction
↔
E + 2 + E(0)E(0)E(S)
CARS Intensity
·Monitor CARS beam
·Scan Stokes beam
· Keep green beam at a constant frequency
◦ Long pulse → Very high spectral resolution (~0.001 cm-1)
Tunable Ring dye laser
Integrator
Nd:
YAG
PMT
Photodiode
I2 cell
Sample
Filter
Ar+ laser
Dye cell Dye cell Dye cell
Amplification of Stokes beam
Computer
Experimental Setup◦ Nd:YAG output locked to single frequency
CARS Q-Branch Spectra:
1 mode of 10BF3
884.7 885.1 885.5Raman Shift (cm-1)
Predict structure according to: Q1 = 1+B1 J(J+1)+(C1 - B1)K 2 + higher terms
With intensities I ~ C g(J,K) (2J+1) exp[-hF0(J,K)/kT])
Significant perturbations not evident for 10BF3
IR studies on BF3 (Masiello, Maki, Blake) give 1 parameters indirectly from various transitions:
GroundState
Energy 1
E'
2 ''
E '
Expt.
884.7 885.1 885.5Raman Shift (cm-1)
Calc.
1 Q-Branch of 10BF3
What do we predict for 11BF3?
10BF3 Expt.
11BF3 Expt.
884.5 884.9 885.3 885.7
Raman Shift (cm-1)
≈0.2 cm-1
Interesting Frequency Shift Observed with Isotopic Substitution at the Center of Mass!
Due to an unrecognized Fermi resonance?
Due to changes in anharmonicity constants?
1413121111 2
12 xxxx
1 Shift:
► IR data
► ab initio calculations
Answer these questions by
making use of
Ask: How well do Measured xij’s and isotopic shifts correspond to results of ab initio (Gaussian 03) calculations?
► Instruct Gaussian 03 to compute anharmonicities (and other ro-vibrational parameters) using the
anharm option and B3LYP/cc-pVTZ
Problem: anharm only works for asymmetric tops
Solution: Small distortion (0.0002 Å ) of one BF3 bond
Vibrational constants in cm -1 for 10BF3 and 11BF3
constant exp. theory exp. theory1 897.243 889.306 897.327 889.306
x 11 -1.158 -1.120 -1.169 -1.120
x 12 -3.374 -3.673 -3.318 -3.621
x 13 -4.479 -4.676 -3.607 -3.765
x 14 -3.115 -3.081 -3.879 -3.8181 885.645 877.473 885.843 877.673
1 -1 11.597 11.833 11.483 11.633
1(10BF3) - 1(
11BF3) -0.198 exp.-0.200 theory
10BF311BF3
1413121111 212 xxxx
(Hard to get)
(Easy to get)
What about other anharmonic shifts?
Anharmonic shifts (cm-1)
10BF3
constant Exp. B3LYP/ Exp.-calc % diff cc-pVTZ.
1-1 11.6 11.8 -0.2 -2.0
2-2 4.1 4.1 0.0 -1.0
3-3 25.2 25.6 -0.4 -1.5
4-4 2.9 2.8 0.1 3.1
Conclusion: theory gives excellent values for anharmonic shifts!
Vibration-rotation constants in cm-1 for 10BF3
Constant Exp. Theory
%DiffBe 0.346 0.342 1.2
1 103 0.685 0.676 1.2
2 103 -0.119 -0.138 -16.4
3 103 1.511 1.512 0.0
4 103 -0.509 -0.513 -0.7
Ce 0.173 0.171 1.2
1 103 0.343 0.338 1.4
2 103 -0.281 -0.291 -3.7
3 103 0.889 0.867 2.5
4 103 0.108 0.089 18.0
Coriolis constants
33z 0.777 0.812 -4.5
44z -0.806 -0.812 -0.7
Bv = Be – i i (vi+ di )+ higher terms KCKBCJJB ivvvv 2)()1(F 2v
Rotational distortion constants (cm-1) for ground state of 10BF3
Exp. Theory % diffDJ x 107 4.303 4.243 1.4DJK x 107 -7.593 -7.471 1.6DK x 107 3.570 3.482 2.5
HJ x 1012 1.332 1.335 -0.2HJK x 1012 -5.089 -5.154 -1.3HKJ x 1012 6.190 6.311 -1.9HK x 1012 -2.432 -2.490 -2.4
Since parameters are well-determined by theory, can we ab initio calcs. to accurately assess the potential surface?
We can be confident such higher order terms in the potential are well-defined by ab initio calculations.
10BF311BF3
mode kii kiii kiiii Kii kiii kiiii
1 889.3 -23.7 0.8 889.3 -23.7 0.8
2 711.4 --- 1.3 683.5 --- 1.2
3 1511.5 52.0 4.3 1457.9 49.2 4.1
4 476.9 4.2 0.4 475.0 4.3 0.4
...QkQkQkV 4iiiii
3iiii
2iiii
kii↔ikiii , kiiii↔xii
Symmetric BF stretch
V = 889.3 Q12 - 23.7 Q1
3 + 0.8 Q14
Cubic (100x)
Quartic (100x)
-400
-200
0
200
400
600
800
-1 -0.5 0 0.5 1
Q1
V/c
m-1
Out-of-plane bend
V = 711.4 Q22 + 0 Q2
3 + 1.3 Q24
Quartic (100x)
-400
-200
0
200
400
600
800
-1 -0.5 0 0.5 1
Q2
V/c
m-1
In-plane bend
V = 476.9 Q42 + 4.2 Q4
3 + 0.4 Q44
Cubic (100x)
Quartic (100x)
-400
-200
0
200
400
600
800
-1 -0.5 0 0.5 1
Q4
V/c
m-1
Anti-symmetric BF stretch
V = 1511.5 Q32 + 52.0 Q3
3 + 4.3 Q34
Cubic (100x)
Quartic (100x)
-400
-200
0
200
400
600
800
-1 -0.5 0 0.5 1
Q3
V/c
m-1
Conclusions
● CARS spectra of BF3 confirm validity of 1 parameters deduced indirectly from IR studies
● 1 - 101 shift reproduced by ab initio
calculations
● BF3 parameters (D’s, H’s, ’s, x’s, ’s, …) in excellent agreement with ab initio anharmonic
values
● Results indicate theory can give very useful estimates of higher-order parameters needed
for the analysis of complex ro-vibrational spectra.