Magnetic Spin-Torsion Coupling in Methanol

Transcription

1 Magnetic pin-torsion Coupling in Methanol L. H. Coudert, 1 C. Gutle, 1 T. R. Huet, 2 and Jens-Uwe Grabow 3 1 Laboratoire Interuniveristaire des ystèmes Atmosphériques, UMR 7583 CNR - Universités Paris Est et Paris Diderot, Créteil, France 2 Laboratoire PhLAM, UMR 8523 CNR - Université de Lille 1, Villeneuve d Ascq, France 3 Institut für Physikalische Chemie und Elektrochemie, Gottfried-Wilhelm-Leibniz-Universität, Hannover, Germany June 24, 2015 Coudert et al. pin-torsion methanol 69 th IM 1 / 20

2 Overview Coudert et al. pin-torsion methanol 69 th IM 2 / 20

3 Overview 1 Magnetic hyperfine couplings in a non-rigid molecule Coudert et al. pin-torsion methanol 69 th IM 2 / 20

4 Overview 1 Magnetic hyperfine couplings in a non-rigid molecule 2 pin-torsion effects in methanol Coudert et al. pin-torsion methanol 69 th IM 2 / 20

5 Overview 1 Magnetic hyperfine couplings in a non-rigid molecule 2 pin-torsion effects in methanol 3 Analysis Coudert et al. pin-torsion methanol 69 th IM 2 / 20

6 Magnetic hyperfine coupling in 1 Σ molecules The spin-spin coupling 1 E = µ N 2 i g i j>i g j (I i I j ) 3(I i r ij )(I j r ij )/r ij 2 r ij 3 The spin-rotation coupling 1 E R = eµ N c g i I i i j i Z j r ji (v j γ i v i ) r ij 3 1 Gunther-Mohr, Townes, and van Vleck, Phys. Rev. 94 (1954) 1191 Coudert et al. pin-torsion methanol 69 th IM 3 / 20

7 Magnetic hyperfine coupling in 1 Σ molecules The two contributions to spin-rotation 1 v i = ω r }{{} i αλ σ }{{} i Rot. Torsion where σ i 0 if i top 1 Heuvel & Dymanus, J. Mol. pec. 45 (1973) 282 & J. Mol. pec. 47 (1973) 363 Coudert et al. pin-torsion methanol 69 th IM 4 / 20

8 Magnetic hyperfine coupling in 1 Σ molecules The two contributions to spin-rotation 1 v i = ω r }{{} i αλ σ }{{} i Rot. Torsion where σ i 0 if i top In methanol σ i = { rchi for i = 1 to 3 0 for i = 4 1 Heuvel & Dymanus, J. Mol. pec. 45 (1973) 282 & J. Mol. pec. 47 (1973) 363 Coudert et al. pin-torsion methanol 69 th IM 4 / 20

9 The 3 J = 0 magnetic coupling hyperfine operators pin-spin 1 H ss = pin-rotation 1 H sr = pin-torsion 2 H st = 4 F (I i, I j, J) ij (α) i<j 4 (I i J)E i (α) i=1 4 (I i J)G i (α) i=1 1 Thaddeus, Krisher, and Loubser, J. Chem. Phys. 40 (1964) Heuvel & Dymanus, J. Mol. pec. 45 (1973) 282 & J. Mol. pec. 47 (1973) 363 Coudert et al. pin-torsion methanol 69 th IM 5 / 20

10 The 3 rovibrational coupling operators Operator Expression Method ij (α) 1 E i (α) 1 G i (α) 2 2 βγ Rij βγ (α)j βj γ J(2J 1)(J + 1)(2J + 3) βγ Ci βγ (α)j βj γ J(J + 1) {ρj z + p α, β J βd i β (α)} 2J(J + 1) tructure Ab initio First order nuclear contribution only 1 Thaddeus, Krisher, and Loubser, J. Chem. Phys. 40 (1964) Heuvel & Dymanus, J. Mol. pec. 45 (1973) 282 & J. Mol. pec. 47 (1973) 363 Coudert et al. pin-torsion methanol 69 th IM 6 / 20

11 pin-rotation coupling tensor calculation Cβγ i (α), with 1 i 4, β, γ = x, y, z, and 0 α 360 with ACE2 2 at the CCD(T) 3 level with pvtz 4 basis set. 2 ACE2, tanton, Gauss, et al., Raghavachari, Trucks, Pople, & Head-Goreon, Chem. Phys. Lett. 157 (1989) Dunning, J. Chem. Phys. 90 (1989) 1007 Coudert et al. pin-torsion methanol 69 th IM 7 / 20

12 ymmetry considerations Using the G 6 symmetry group 1 Hyperfine operators H sr = H sr (A 1 ) O sr (A 1 ) + H h sr(a 1 ) O h sr(a 1 ) + H sr (E a ) O sr (E a ) + H sr (E b ) O sr (E b ) H sr (A 1 ) = (I 1 + I 2 + I 3 ) J, Hsr(A h 1 ) = I 4 J H sr (E a ) = 1 2 (2I 1 I 2 I 3 ) J, 3 H sr (E b ) = 2 (I 2 I 3 ) J Rovibrational operators O sr (A 1 ) = 1 3 (E1 + E 2 + E 3 ), O h sr(a 1 ) = E 4 O sr (E a ) = 1 3 (2E1 E 2 E 3 ), O sr (E b ) = 1 3 (E 2 E 3 ) 1 Hougen, Kleiner, & Godefroid, J. Mol. pec. 163 (1994) 559 Coudert et al. pin-torsion methanol 69 th IM 8 / 20

13 Accounting for the torsion For an n non-degenerate A 1 or A 2 level 1 3 O sr (A 1 ) and O h sr(a 1 ) This leads to the hyperfine spin-rotation coupling Hamiltonian H Hfs = C sr H sr (A 1 ) + C sr,h H h sr(a 1 ) where C sr = n O sr (A 1 ) n and C sr,h = n O h sr(a 1 ) n 1 Wolf, Williams, & Weatherly, J. Chem. Phys. 47 (1967) Coudert & López, J. Mol. pec. 239 (2006) Tudorie, Coudert, Huet, Jegouso, & edes, J. Chem. Phys. 134 (2011) Coudert et al. pin-torsion methanol 69 th IM 9 / 20

14 Accounting for the torsion For an n non-degenerate A 1 or A 2 level 1 3 imilar O sr (A results 1 ) and for Othe sr(a h 1 ) spin-torsion and spin-spin couplings. This leads to the hyperfine spin-rotation coupling Hamiltonian Doubly degenerate E-type H Hfs levels = Cshould sr H sr (Abe 1 ) treated + C sr,h Hinsr(A h 1 ) the same way. where C sr = n O sr (A 1 ) n and C sr,h = n Osr(A h 1 ) n 1 Wolf, Williams, & Weatherly, J. Chem. Phys. 47 (1967) Coudert & López, J. Mol. pec. 239 (2006) Tudorie, Coudert, Huet, Jegouso, & edes, J. Chem. Phys. 134 (2011) Coudert et al. pin-torsion methanol 69 th IM 9 / 20

15 ummary Level ymmetry pin-rotation pin-torsion pin-spin N A 1 /A 2 E C sr & C sr,h ame + C sr A Coupling constants C st & Cst,h ame + C st A C ss Hyperfine coupling operators & C ss,h ame + C ss A 6 & Css,h A 10 A 1 /A 2 H sr (A 1 ) & H h sr(a 1 ) H ss (A 1 ) & H h ss(a 1 ) 4 E ame + H sr (E a ) & H sr (E b ) ame + H ss (E a ), 10 H h ss(e a ), H ss (E b ), & H h ss(e b ) Coudert et al. pin-torsion methanol 69 th IM 10 / 20

16 Hyperfine coupling constants numerical evaluation ymmetry adapted operators for spin-torsion with O st (Γ) = {ρj z + p α, β J β Γ β (α)} 2J(J + 1) A1 β (α) = { s 0 β + s 3 β cos 3α for β = x, z sin 3α for β = y s 3 β Coudert et al. pin-torsion methanol 69 th IM 11 / 20

17 Hyperfine coupling constants numerical evaluation ymmetry adapted operators for spin-torsion with O st (Γ) = {ρj z + p α, β J β Γ β (α)} 2J(J + 1) A1 β (α) = { s 0 β + s 3 β cos 3α for β = x, z sin 3α for β = y s 3 β O st (A 1 ) O st (E a ) O h st(a 1 ) s 0 x s 1 x s 0,h x s 3 x s 2 x s 3,h x s 3 y s 1 y s 3,h y s 2 y s 0 z s 1 z s 0,h z s 3 z s 2 z s 3,h z Coudert et al. pin-torsion methanol 69 th IM 11 / 20

18 Hyperfine coupling constants numerical evaluation ymmetry adapted operators for spin-torsion with O st (Γ) = {ρj z + p α, β J β Γ β (α)} 2J(J + 1) A1 β (α) = { s 0 β + s 3 β cos 3α for β = x, z sin 3α for β = y s 3 β O st (A 1 ) O st (E a ) O h st(a 1 ) 92 constants arise s 0 x s 1 x s 0,h x s 3 x s 2 x s 3,h x s 3 y s 1 y s 3,h y s 2 y s 0 z s 1 z s 0,h z s 3 z s 2 z s 3,h z Coudert et al. pin-torsion methanol 69 th IM 11 / 20

19 Hyperfine coupling constants values Rotation-torsion energies and eigenvectors obtained from a fit of the high-resolution data 1 Level 1 01 A A A C sr C sr,h C ss C ss,h C st C st,h 2 02 A A A A A A Xu, Fisher, Lees, hi, Hougen, Pearson, Drouin, Blake, & Braakman, J. Mol. pec. 251 (2008) 305 Coudert et al. pin-torsion methanol 69 th IM 12 / 20

20 Hyperfine coupling constants values-continued C st for a J k E-type levels with J = 6 and 6 k 6. Coudert et al. pin-torsion methanol 69 th IM 13 / 20

21 Hyperfine coupling constants values-continued Calculated hyperfine pattern for the 1 01 A A 1 transition at MHz and the 1 0 E 0 0 E transition at MHz 1 1 Tudorie, Coudert, Huet, Jegouso, & edes, J. Chem. Phys. 134 (2011) Coudert et al. pin-torsion methanol 69 th IM 14 / 20

22 Hyperfine coupling constants values-continued Calculated hyperfine pattern for the 1 01 A A 1 transition at MHz and the 1 0 E 0 0 E transition at MHz 1 ymmetry adapted hyperfine functions are used so that the total nuclear spin-rotation-torsion function obeys the Pauli exclusion principle. 1 Tudorie, Coudert, Huet, Jegouso, & edes, J. Chem. Phys. 134 (2011) Coudert et al. pin-torsion methanol 69 th IM 14 / 20

23 Analysis: experimental data set Transition F pectrometer Hyp 2 11 A A Ref. 1 & Lille 3 12 A A Ref. 1 & Lille D 5 15 A A Hannover & Lille D 9 1 E 8 2 E Hannover & Lille 4 32 A A Lille 2 0 E 3 1 E Hannover & Lille D 6 15 A A Ref. 1 D 2 1 E 3 0 E Hannover 3 2 E 3 1 E Hannover D 4 2 E 4 1 E Hannover D 2 2 E 2 1 E Hannover 5 2 E 5 1 E Hannover D 6 2 E 6 1 E Hannover D 1 01 A A Ref. 1 M 1 Heuvel & Dymanus, J. Mol. pec. 45 (1973) 282 Coudert et al. pin-torsion methanol 69 th IM 15 / 20

24 Analysis results: observed & calculated hfs. patterns Coudert et al. pin-torsion methanol 69 th IM 16 / 20

25 Analysis results: observed & calculated hfs. patterns C sr Dominated by spin-spin coupling = 0.71 Csr,h = 1.80 C ss = 4.22 Css,h = 2.17 Coudert et al. pin-torsion methanol 69 th IM 16 / 20

26 Analysis results: observed & calculated hfs. patterns Coudert et al. pin-torsion methanol 69 th IM 17 / 20

27 Analysis results: observed & calculated hfs. patterns C sr Dominated by spin-rotation from the hydroxyl group = 1.69 Csr,h = 2.25 C ss = 0.35 Css,h = 0.18 C sr = 1.72 C sr,h = 3.24 C ss = 0.35 C ss,h = 0.19 Coudert et al. pin-torsion methanol 69 th IM 17 / 20

28 Analysis results: observed & calculated hfs. patterns Coudert et al. pin-torsion methanol 69 th IM 18 / 20

29 Analysis results: observed & calculated hfs. patterns Predicted spin-rotation splitting from the methyl group was too large Coudert et al. pin-torsion methanol 69 th IM 18 / 20

30 Analysis results: observed & calculated hfs. patterns Predicted spin-rotation splitting from the methyl group was too large Also dominated by spin-rotation from the hydroxyl group Coudert et al. pin-torsion methanol 69 th IM 18 / 20

31 Analysis results: observed & calculated hfs. patterns For lines displaying a doublet structure, it was assumed that spin-rotation from the hydroxyl group is dominant. Predicted spin-rotation splitting from the methyl group was too large Also dominated by spin-rotation from the hydroxyl group Coudert et al. pin-torsion methanol 69 th IM 18 / 20

32 Analysis results: parameters (khz) Parameter No fitting Fit I Fit II c 0 zz (974) 1.766(910) c 0,h zz (1060) (1055) s 0,h zz (12625) 12 center frequencies TD (unitless) Constrained value. Coudert et al. pin-torsion methanol 69 th IM 19 / 20

33 Thank you for your attention Coudert et al. pin-torsion methanol 69 th IM 20 / 20