complementary use of modern spectroscopy and theory in the study of rovibrational levels of bf 3...

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.