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Based on Bent’s rule and hybridization, which orbitals would be used to make the π-bond between carbon and sulfur, and in which plane would each of the atoms like?

To make solving the question easier (high school level), I have assumed that the $\mathrm{s},$ $\mathrm{p}_x,$ and $\mathrm{p}_y$ orbitals of the sulfur atom have been used to make the equatorial hybrid orbitals of the trigonal bipyramidal structure, and that the $\mathrm{p}_z$ and $\mathrm{d}_{z^2}$ orbitals of sulfur have been used to make the axial hybrid orbitals.

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Hybridization does not define the structure, the structure comes in first. The structure of $\ce{H2CSF4}$ has been determined using a multitude of methods. The single-crystal x-ray diffraction [1] showed that the molecular structure parameters of the solid also correspond to those of the liquid and gaseous phase determined using microwave, IR, 1H-, 13C-, and 19F-NMR spectroscopies as well as electron diffraction and ab initio calculations [2 and references therein]. There is an ylidic double bond of the spectroscopic order 1.8, and the bond is partially ionized (the charge at carbon atom is −0.6).

Bock et al. provide an insight based on the summary of the aforementioned experimental and theoretical methods [2, pp. 944–945]:

The methylene group is oriented in the plane of the axial fluorine atoms. This can be explained by the valence shell electron pair repulsion model Only in this configuration can the πCS-electron density easily be accommodated, and the equatorial fluorine atoms are brought closer together. The distance between the axial fluorine atoms and the hydrogen atoms is only $\pu{240 pm};$ however, no evidence of $\ce{H...F}$ bridges is apparent from the spectroscopic data.

The SCF geometrical optimization shows that the isomer with an equatorially oriented $\ce{CH2}$ group is unstable, and that a high torsional barrier exists, with an estimated value of $\pu{77 kcal/mol}.$

[…]

The polarity of the $\ce{C=S}$ bond is indicated by two further reactions: Lewis acids interact with the carbon atom, while Lewis bases attack the sulfur atom.

crystal structure of methylenesulfur tetrafluoride
Figure 1. Crystal structure of methylenesulfur tetrafluoride with selected distances (in Å), angles and dihedral angles (both in °). CSD ID: MESTFL10.

Simon et al. specifically state that there are a couple of qualitative arguments that could be used to explain the conformation of the molecule, although the result of the structural investigation could not be predicted with certainty using such arguments (adapted from [1, pp 13–14]):

  1. Applying the concept of electron pair repulsion, the space requirement of the bonding electrons of the $\ce{S=C}$ double bond should be better met in the plane of the recessed equatorial fluorine atoms and therefore the protons should be fixed in the plane of the axial fluorine atoms.

  2. A double bond can be loosely described as two bent single bonds — the "high-school concept" sometimes used to explain the planarity of ethylene resulting from the edge connection of two tetrahedrally coordinated carbon atoms. Analogously, $\ce{H2C=SF4}$ can be viewed as a linked tetrahedral carbon from ethylene and an octahedral sulfur from $\ce{SF6}$, also resulting in hydrogen atoms in the axial plane. An illustration from [2]:

    Structural possibilities of H2C=SF4
    Fig. 2. Structural possibilities of $\ce{H2C=SF4}$. According to the valence shell electron pair repulsion model the observed "axial" position of the protons is preferred. Qualitatively the observed structure (left) may be rationalized by linking a tetrahedron with an octahedron through two bent bonds.

  3. Axial hydrogen atoms also imply the torsion barrier of the methylene group with the same order of magnitude as in ethylene, which has been experimentally confirmed using NMR.

Reference

  1. Simon, A.; Peters, E. ‐M.; Lentz, D.; Seppelt, K. Die KristallStruktur von Methylenschwefeltetrafluorid. Z. Anorg. Allg. Chem. 1980, 468 (1), 7–14. DOI: 10.1002/zaac.19804680102. (in German)
  2. Bock, H.; Boggs, J. E.; Kleemann, G.; Lentz, D.; Oberhammer, H.; Peters, E. M.; Seppelt, K.; Simon, A.; Solouki, B. Structure and Reactions of Methylenesulfur Tetrafluoride. Angew. Chem. Int. Ed. Engl. 1979, 18 (12), 944–945. DOI: 10.1002/anie.197909441.
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