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Complementary Use of Modern Spectroscopy and Theory in the Study of Rovibrational Levels of BF 3 Robynne Kirkpatrick a, Tony Masiello b, Alfons Weber c, and Joseph W. Nibler a a Department of Chemistry, Oregon State University b Pacific Northwest National Laboratory c National Institute of Standards and Technology, MD

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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 BF 3

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Raman and IR active modes of group D 3h AX 3 molecules 2 4 3 E (R, IR) A 2 (IR) E (R, IR) 1 Exclusively Raman Active A 1

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Consider SO 3 -- an intriguing molecule! 32 S 16 O 3 S O 3 1065.51066.51067.5 Raman Shift / cm -1 1065.51066.51067.5 34 S 16 O 3 32 S 16 O 3 1 CARS Q-Branch

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32 S 18 O 3 34 S 18 O 3 1002.51003.51004.51005.51006.51007.5 Raman Shift / cm 1067.5 1002.51003.51004.51005.51006.51007.5 Raman Shift / cm 32 S 18 O 3 34 S 18 O 3 What causes this complex structure? 1 CARS Q-Branch Q 1 ≠ J(J+1)+( C 1 - B 1 )K 2 + higher terms

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Perturbations to 1 (SO 3 ) deduced using the CARS Q-Branch 1 A 1 ' Fermi resonance Coriolis l-resonance 2 4 (l=0) A 1 ' 2 2 A 1 ' 2 4 (l=2) E ' 2 + 4 E ' Let’s examine the CARS Q-Branches of 10 BF 3 and 11 BF 3

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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

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◦ Long pulse → Very high spectral resolution (~0.001 cm -1 ) Tunable Ring dye laser Integrator Nd: YAG PMT Photodiode I 2 cell Sample Filter Ar + laser Dye cell Amplification of Stokes beam Computer Experimental Setup ◦ Nd:YAG output locked to single frequency

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Predict structure according to: Q 1 = 1 + B 1 J(J+1)+( C 1 - B 1 )K 2 + higher terms With intensities I ~ C g(J,K) (2J+1) exp[-hF 0 (J,K)/kT]) Significant perturbations not evident for 10 BF 3

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IR studies on BF 3 (Masiello, Maki, Blake) give 1 parameters indirectly from various transitions: Ground State Energy 1 E' 2 '' E'

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1 Q-Branch of 10 BF 3 What do we predict for 11 BF 3 ?

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≈0.2 cm -1 Interesting Frequency Shift Observed with Isotopic Substitution at the Center of Mass!

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Due to an unrecognized Fermi resonance? Due to changes in anharmonicity constants? 1413121111 2 1 2xxxx 1 Shift: ► IR data ► ab initio calculations Answer these questions by making use of

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Ask: How well do Measured x ij ’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 BF 3 bond

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Vibrational constants in cm for 10 BF 3 and 11 BF 3 constantexp.theoryexp.theory 1 897.243889.306897.327889.306 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 -3.115-3.081-3.879-3.818 1 885.645877.473885.843877.673 1 - 1 11.59711.83311.48311.633 1 ( 10 BF 3 ) - 1 ( 11 BF 3 )-0.198exp. -0.200theory 10 BF 3 11 BF 3 1413121111 2 1 2xxxx (Hard to get) (Easy to get) What about other anharmonic shifts?

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Anharmonic shifts (cm -1 ) 10 BF 3 constantExp.B3LYP/Exp.-calc % diff cc-pVTZ. 1 - 1 11.611.8 -0.2 -2.0 2 - 2 4.1 0.0 3 - 3 25.225.6 -0.4 -1.5 4 - 4 2.92.8 0.1 3.1 Conclusion: theory gives excellent values for anharmonic shifts!

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Vibration-rotation constants in cm -1 for 10 BF 3 Constant Exp.Theory %Diff BeBe 0.3460.3421.2 1 10 3 0.6850.6761.2 2 10 3 -0.119-0.138-16.4 3 10 3 1.5111.5120.0 4 10 3 -0.509-0.513-0.7 CeCe 0.1730.1711.2 1 10 3 0.3430.3381.4 2 10 3 -0.281-0.291-3.7 3 10 3 0.8890.8672.5 4 10 3 0.1080.08918.0 Coriolis constants 33 z 0.7770.812-4.5 44 z -0.806-0.812-0.7 B v = B e – i i (v i + d i )+ higher terms

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Rotational distortion constants (cm -1 ) for ground state of 10 BF 3 Exp.Theory % diff D J x 10 7 4.3034.243 1.4 D JK x 10 7 -7.593-7.471 1.6 D K x 10 7 3.5703.482 2.5 H J x 10 12 1.3321.335 -0.2 H JK x 10 12 -5.089-5.154 -1.3 H KJ x 10 12 6.1906.311 -1.9 H K x 10 12 -2.432-2.490 -2.4 Since parameters are well-determined by theory, can we ab initio calcs. to accurately assess the potential surface?

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We can be confident such higher order terms in the potential are well-defined by ab initio calculations. 10 BF 3 11 BF 3 modek ii k iii k iiii K ii k iii k iiii 1889.3-23.70.8889.3-23.70.8 2711.4---1.3683.5---1.2 31511.552.04.31457.949.24.1 4476.94.20.4 475.04.30.4...QkQkQkV 4 iiiii 3 iiii 2 iiii k ii ↔ i k iii, k iiii ↔ x ii

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Symmetric BF stretch Out-of-plane bend

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In-plane bend Anti-symmetric BF stretch

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Conclusions ● CARS spectra of BF 3 confirm validity of 1 parameters deduced indirectly from IR studies ● 1 - 10 1 shift reproduced by ab initio calculations ● BF 3 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.

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