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Fourier Transform Infrared Emission Spectra of MgF 2 Peter Bernath, Daniel Frohman Department of Chemistry and Biochemistry Old Dominion University, Norfolk, VA Jacek Koput Department of Chemistry, Adam Mickiewicz University, Poznań, Poland

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Alkaline Earth Dihalides Be and Mg dihalides are linear Ca and Sr dihalides may be either linear or bent Ba species are always bent VSEPR model predicts a linear structure; sd hybridization invoked 2 “The prediction, verification, and explanation of the unexpected bent structure of some alkaline earth dihalides and dihydrides pose extreme demands on experiment and theory and qualify among ‘the most intriguing problems of modern inorganic chemistry’. It must have come as a real surprise when Klemperer et al. showed that CaF 2, SrF 2, SrCl 2, and all barium halides display permanent dipoles in the gas phase and are therefore bent.” von Szentpaly, JPC A106, 11945 (2002)

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Alkaline Earth Difluorides Wavenumber (cm -1 ) BeF 2 ν 3 mode emission BeF 2 : linear, r e =1.373 Å, Frum et al. JCP 95, 1435 (1991), Yu et al. JCP 123, 134304 (2005) MgF 2 : linear; SrF 2 : bent; BaF 2 : bent

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Previous MgF 2 Studies 1964, Buchler, Stauffer, and Klemperer – no molecular beam deflection by inhomogeneous electric field: MgF 2 is linear 1966, Snelson - IR matrix isolation in Ne, Ar, and Kr - observed ν 2 (254 cm -1 ) & ν 3 (862 cm -1 ) in a neon matrix 1968,1969, Baikov – gas phase IR: observed ν 2 (160 cm -1 ) & ν 3 (825 cm -1 ) 1976, Lesiecki & Nibler – IR and Raman in matrices: ν 1 (550 cm -1 ), ν 2 (249 cm -1 ) & ν 3 (842 cm -1 ) in an argon matrix 1980, Kasparov et al. – gas phase electron diffraction study; recommend r g (Mg-F) = 1.77±0.01 Å, ν 1 (540±20 cm -1 ), ν 2 (165±10 cm -1 ) & ν 3 (825±20 cm -1 ) 2014, this work, ab initio calculation by J. Koput: r e (Mg-F) = 1.738 Å, ν 1 (569 cm -1 ), ν 2 (153 cm -1 ) & ν 3 (882 cm -1 ) 4 ν 1 (Σ g + ) ν 3 (Σ u + ) ν 2 (Π u ) doubly degenerate

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MgF 2 spectra recorded at University of Waterloo with Bruker IFS 120 HR Fourier transform spectrometer. Solid MgF 2 powder was heated in a tube furnace to 1675°C. Resolution was 0.01 cm -1 for 700-1300 cm -1 region.

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MgF 2 ν 3 Emission 6 001-000 head 011-010 head 021-020 head Series of band heads 1.6 cm -1 apart J max =68 Q vib =615(!)

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Ab Initio Calculations MOLPRO calculations similar to work on BeF 2 r e (Mg-F) = 1.7380(5) Å PES of r(MgF) = 1.4 to 2.4 Å and

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Ab initio Derived Constants (J=0-12) LevelG v -ZPEBDqqDqD η 000 Σ g + 00.14671122506(98)4.03992(79)E-08 100 Σ g + 569.118445119(39)0.1462626404(15)4.02693(98)E-08 02 0 0 Σ g + 305.096543045(39)0.1477537742(15)4.3833(10)E-08 0.0002254056(47) 001 Σ u + 878.712791791(52)0.1457896149(20)4.0225(13)E-08 02 0 1 Σ u + 1180.048336873(40)0.1468408264(15)4.3684(11)E-08 0.0002227591(48) 101 Σ u + 1441.918006802(52)0.1453459770(20)4.0076(13)E-08 01 1 0 Π u 153.11452066(12)0.1472334302(41)4.2125(26)E-08-0.0003176125(50)1.180(40)E-09 03 1 0 Π u 457.31934575(12)0.1482739583(41)7.5234(26)E-08-0.0006405951(50)3.938(40)E-09 11 1 0 Π u 724.85766566(12)0.1467745550(41)4.1980(26)E-08-0.0003191668(50)1.128(40)E-09 01 1 1 Π g 1029.93989514(10)0.1463161667(37)4.1963(24)E-08-0.0003139671(45)1.215(36)E-09 03 1 1 Π g 1330.40385937(10)0.1473654547(37)7.4561(24)E-08-0.0006329250(45)3.975(36)E-09 11 1 1 Π g 1595.76598081(10)0.1458624664(37)4.1803(24)E-08-0.0003152754(45)1.171(36)E-09 02 2 0 Δ g 306.419474886(39)0.1477552955(13)4.38822(82)E-08 0.0002254056(47) 02 2 1 Δ u 1181.363721335(40)0.1468425097(13)4.37342(84)E-08 0.0002227591(48) 03 3 0 Φ u 459.9154111(32)0.148276532(96)1.603(57)E-08 03 3 1 Φ g 1332.9848161(38)0.14736837(11)1.643(68)E-08 8

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Spectrum Overview 9

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Rotational and Vibrational Levels 10 l-type doubling via q and q D removes e/f parity degeneracy ν3ν3 ν3+ν2-ν2ν3+ν2-ν2 ν 3 +2ν 2 -2ν 2 ν 3 +3ν 2 -3ν 2

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ν 3, 001-000 (Σ u + – Σ g + ) A 3:1 intensity alternation due to nuclear spin statistics of equivalent fermions ( 19 F with I = ½) ν 3, antisymmetric stretch: 879.0060(24) cm -1 vs 878.7128 cm -1 (ab initio) Rotational constants: B 000 of 0.148591(20) cm -1 and B 001 of 0.147667(20) cm -1 vs ab initio values of 0.146711 cm -1 and 0.145790 cm -1, respectively 11

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ν 3 +ν 2 -ν 2, 01 1 1 – 01 1 0 (Π g – Π u ) 01 1 0 (Π u ) origin fixed to ab initio value 153.1145 cm -1 upper state term value 01 1 1 (Π g ) fit: 1030.2307(35) cm -1 and ab initio: 1029.9399 cm -1. Rotational constants: B 010 and B 011 fit: 0.149093(29) cm -1 and 0.148173(29) cm -1 vs ab initio: 0.147233 cm -1 and 0.146316 cm -1 l-type doubling observed for 01 1 0 (Π u ) and 01 1 1(Π g ) q fit: -3.130(73)E-4 cm -1 & - 3.096(72)E-4 cm -1 vs ab initio: -3.176E-04 cm -1 and -3.140E-04 cm -1 q D was held fixed as 1.180E-09 cm -1 and 1.215E-09 cm -1 12

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Rotational and Vibrational Levels 13 LevelG v -ZPEBDaDa qqDaqDa 000 Σ g + 00.148591(20)4.03992E-08 001 Σ u + 879.0060(24)0.147667(20)4.0225E-08 01 1 0 Π u 153.1145 a 0.149093(29)4.2125E-08-3.130(73)e-41.180E-09 01 1 1 Π g 1030.2307(35)0.148173(29)4.1963E-08-3.096(72)e-41.215E-09 BandOriginOrigin (calc)Bandhead Bandhead (calc) 001 Σ u + - 000 Σ g + 879.0060878.7128902.2059901.4221 01 1 1 Π g - 01 1 0 Π u 877.1162876.8254900.5687899.7727

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Equilibrium Rotational Constants 14 Re/ÅRe/ÅB e /cm -1 α 1 /cm -1 α 2 /cm -1 α 3 /cm -1 ab initio b 1.739490.146620.000449-0.000520.000922 semi- experimental1.726870.1487750.000449 a -0.00050.000924 a) This value fixed to ab initio value. b) The ab initio values are based on the CCSD(T)/aug-cc-pCV5Z; better ab initio value is 1.7380 Å. B v = B e – α 1 (v 1 + ½) – α 2 (v 2 + 1) – α 3 (v 3 + ½)

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Conclusion The first high resolution infrared emission spectra of MgF 2 were analyzed. Assignments were made for the ν 3 fundamental mode and one hot band with the help of high level ab initio calculations. Recording spectra with a higher signal-to-noise ratio might help, but the lines will remain overlapped, and assignments challenging. 15

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