Fourier Transform Infrared Emission Spectra of MgF2

Peter Bernath, Daniel FrohmanDepartment of Chemistry and Biochemistry

Old Dominion University, Norfolk, VA

Jacek KoputDepartment 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

“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 CaF2, SrF2, SrCl2, and all barium halides display permanent dipoles in the gas phase and are therefore bent.” von Szentpaly, JPC A106, 11945 (2002)

Alkaline Earth Difluorides

Wavenumber (cm-1)

BeF2 ν3 mode emission

BeF2: linear, re=1.373 Å, Frum et al. JCP 95, 1435 (1991), Yu et al. JCP 123, 134304 (2005)

MgF2: linear; SrF2: bent; BaF2: bent

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Previous MgF2 Studies• 1964, Buchler, Stauffer, and Klemperer – no molecular beam deflection by

inhomogeneous electric field: MgF2 is linear

• 1966, Snelson - IR matrix isolation in Ne, Ar, and Kr - observed ν2 (254 cm-1) & ν3 (862 cm-1) in a neon matrix

• 1968,1969, Baikov – gas phase IR: observed ν2 (160 cm-1) & ν3 (825 cm-1)

• 1976, Lesiecki & Nibler – IR and Raman in matrices: ν1 (550 cm-1), ν2 (249 cm-1) & ν3 (842 cm-1) in an argon matrix

• 1980, Kasparov et al. – gas phase electron diffraction study; recommend rg(Mg-F) = 1.77±0.01 Å, ν1 (540±20 cm-1), ν2 (165±10 cm-1) & ν3 (825±20 cm-1)

• 2014, this work, ab initio calculation by J. Koput: re(Mg-F) = 1.738 Å, ν1 (569 cm-1), ν2 (153 cm-1) & ν3 (882 cm-1)

ν1 (Σg+) ν3 (Σu

+)ν2 (Πu)doubly degenerate

MgF2 spectra recorded at University of Waterloo with Bruker IFS 120 HR Fourier transform spectrometer. Solid MgF2 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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MgF2 ν3 Emission

001-000 head

011-010 head021-020 head

Series of band heads 1.6 cm-1 apartJmax=68Qvib=615(!)

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Ab Initio Calculations• MOLPRO calculations similar to work on BeF2

• re(Mg-F) = 1.7380(5) Å• PES of r(MgF) = 1.4 to 2.4 Å and <FMgF = 80 to 180 °, calculated by

CCSD(T)/aug-cc-pCV5Z (Mg), auc-cc-pV5Z (F), with valence and Mg outer core correlation by CCSD(T)

• PES used to calculate vibration-rotation energy levels for 24MgF2

• fit the levels to obtain spectroscopic constants for PGOPHER

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Ab initio Derived Constants (J=0-12)

Level Gv -ZPE B D q qD η

000 Σg+ 0 0.14671122506(98) 4.03992(79)E-08

100 Σg+ 569.118445119(39) 0.1462626404(15) 4.02693(98)E-08

0200 Σg+ 305.096543045(39) 0.1477537742(15) 4.3833(10)E-08 0.0002254056(47)

001 Σu+ 878.712791791(52) 0.1457896149(20) 4.0225(13)E-08

0201 Σu+ 1180.048336873(40) 0.1468408264(15) 4.3684(11)E-08 0.0002227591(48)

101 Σu+ 1441.918006802(52) 0.1453459770(20) 4.0076(13)E-08

0110 Πu 153.11452066(12) 0.1472334302(41) 4.2125(26)E-08 -0.0003176125(50) 1.180(40)E-09

0310 Πu 457.31934575(12) 0.1482739583(41) 7.5234(26)E-08 -0.0006405951(50) 3.938(40)E-09

1110 Πu 724.85766566(12) 0.1467745550(41) 4.1980(26)E-08 -0.0003191668(50) 1.128(40)E-09

0111 Πg 1029.93989514(10) 0.1463161667(37) 4.1963(24)E-08 -0.0003139671(45) 1.215(36)E-09

0311 Πg 1330.40385937(10) 0.1473654547(37) 7.4561(24)E-08 -0.0006329250(45) 3.975(36)E-09

1111 Πg 1595.76598081(10) 0.1458624664(37) 4.1803(24)E-08 -0.0003152754(45) 1.171(36)E-09

0220 Δg 306.419474886(39) 0.1477552955(13) 4.38822(82)E-08 0.0002254056(47)

0221 Δu 1181.363721335(40) 0.1468425097(13) 4.37342(84)E-08 0.0002227591(48)

0330 Φu 459.9154111(32) 0.148276532(96) 1.603(57)E-08

0331 Φg 1332.9848161(38) 0.14736837(11) 1.643(68)E-08

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Spectrum Overview

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Rotational and Vibrational Levels

2222321 11

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111,, JJqJqJJDJJBJGJE D

l

l-type doubling via q and qD removes e/f parity degeneracy

ν3ν3+ν2-ν2

ν3+2ν2-2ν2

ν3+3ν2-3ν2

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ν3, 001-000 (Σu+ – Σg

+)

A 3:1 intensity alternation due to nuclear spin statistics of equivalent fermions (19F with I = ½)

ν3, antisymmetric stretch: 879.0060(24) cm-1 vs 878.7128 cm-1 (ab initio) Rotational constants: B000 of 0.148591(20) cm-1 and B001 of 0.147667(20) cm-

1 vs ab initio values of 0.146711 cm-1 and 0.145790 cm-1, respectively

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ν3+ν2-ν2, 0111 – 0110 (Πg – Πu) 0110 (Πu) origin fixed to ab initio value 153.1145 cm-1

upper state term value 0111 (Πg) fit: 1030.2307(35) cm-1 and ab initio: 1029.9399 cm-1.

Rotational constants: B010 and B011 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 0110 (Πu) and 0111(Πg) 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

• qD was held fixed as 1.180E-09 cm-1 and 1.215E-09 cm-1

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Rotational and Vibrational Levels

Level Gv -ZPE B Da q qDa

000 Σg+ 0 0.148591(20) 4.03992E-08

001 Σu+ 879.0060(24) 0.147667(20) 4.0225E-08

0110 Πu 153.1145a 0.149093(29) 4.2125E-08 -3.130(73)e-4 1.180E-09

0111 Πg 1030.2307(35) 0.148173(29) 4.1963E-08 -3.096(72)e-4 1.215E-09

Band Origin Origin (calc) BandheadBandhead

(calc)

001 Σu+ - 000 Σg

+ 879.0060 878.7128 902.2059 901.4221

0111 Πg - 0110 Πu 877.1162 876.8254 900.5687 899.7727

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Equilibrium Rotational Constants

Re/Å Be/cm-1 α1/cm-1 α2/cm-1 α3/cm-1

ab initiob 1.73949 0.14662 0.000449 -0.00052 0.000922semi-experimental 1.72687 0.148775 0.000449a -0.0005 0.000924

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.

Bv = Be – α1(v1 + ½) – α2(v2 + 1) – α3(v3 + ½)

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Conclusion The first high resolution infrared emission spectra of MgF2 were

analyzed. Assignments were made for the ν3 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.