{"id":17498,"date":"2017-03-02T17:59:00","date_gmt":"2017-03-02T17:59:00","guid":{"rendered":"http:\/\/www.ch.imperial.ac.uk\/rzepa\/blog\/?p=17498"},"modified":"2025-08-21T13:52:57","modified_gmt":"2025-08-21T12:52:57","slug":"more-tetrahedral-fun-spherical-aromaticity-and-other-oddities-in-n4-and-c4-systems","status":"publish","type":"post","link":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=17498","title":{"rendered":"More tetrahedral fun. Spherical aromaticity (and other oddities) in N4 and C4 systems?"},"content":{"rendered":"
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The thread thus far. The post about Na2<\/sub>He<\/a> introduced the electride anionic counter-ion to Na+<\/sup> as corresponding topologically to a rare feature known as a non-nuclear attractor. This prompted speculation about other systems with such a feature, and the focus shifted to a tetrahedral arrangement of four hydrogen atoms<\/a> as a dication, sharing a total of two valence electrons. The story now continues here.<\/p>\n

What emerged during comments about\u00a0H4<\/sub>2+<\/sup>\u00a0was that a density functional (DFT) derived wavefunction seemed to predict it to be a stable minimum, but that wavefunctions derived from\u00a0coupled cluster or CASSCF methods predicted it to be a three-fold degenerate transition state instead. So I asked myself if perhaps other similar tetrahedral molecules\u00a0less susceptible to such method ambiguity might be found. Here I record some of the species I investigated.\u00a0<\/p>\n

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  1. N4<\/sub> in a tetrahedral allotropic arrangement of the element (\u03c9B97XD\/Def2-TZVPP DFT method:[1]<\/a><\/span>\u00a0and CCSD(T)\/Def2-TZVPP\u00a0[2]<\/a><\/span>). I found this intriguing, because each nitrogen has a lone pair of electrons\u00a0and such\u00a0an arrangement of eight electrons might\u00a0be spherically aromatic according to the rule: 2(n+1)2<\/sup><\/strong>, where n=1[3]<\/a><\/span>. N4\u00a0<\/sub>itself is indeed a true minimum (rN-N<\/sub>\u00a0\u00a01.460\u00c5) with all positive force constants at both the DFT (767, 1005\u00a0and 1443) and CCSD(T) (726, 940 and 1304 cm-1<\/sup>) levels, but with a free energy ~185 kcal\/mol higher than dinitrogen. The electronic topology is uneventfully classical, with six line (bond) critical points along each N-N axis (magenta), four ring critical points (green) and one cage point (inner blue sphere); there is no non-nuclear attractor present.\"\"The NICS value at the centre of the tetrahedron (coincident with the cage critical point) is -73 ppm, which does suggest aromaticity.<\/li>\n
  2. C<\/span>4<\/sub> in a tetrahedral allotropic arrangement of this element is also a minimum as closed shell singlet (rC-C\u00a0<\/sub>1.646\u00c5) again with positive force constants (\u03c9B97XD\/Def2-TZVPP DFT, 10.14469\/hpc\/2224<\/a>,\u00a0434, 715, 1052 cm-1<\/sup>) and the same electronic topology as\u00a0N4<\/sub>. \"\"
    \n The magnetic shielding at the ring centre is -1685 ppm, a value clearly perturbed by core ring currents or other factors; the molecule does not map to the\u00a02(n+1)2 <\/sup><\/strong>spherical aromaticity rule, which only allows values of 2,8,18, 32… electrons. I tried applying the ELF procedure using the computed WFN file (either direct or symmetrised, using both TopMod and MultiWFN) but the results did not have Td<\/sub> symmetry.\u2021<\/sup><\/li>\n
  3. C4<\/sub>2+<\/sup>\u00a0with two fewer electrons is also a minimum\u00a0as a closed shell singlet (rC-C<\/sub> 1.521\u00c5) tetrahedral species (\u03c9B97XD\/Def2-TZVPP:\u00a010.14469\/hpc\/2218<\/a>, 1132, 1136, 1448\u00a0cm-1<\/sup>;\u00a0CCSD(T)\/Def2-TZVPP\u00a010.14469\/hpc\/2225<\/a>\u00a0showing rather different normal mode energies of\u00a0~330, 592, 1126\u00a0cm-1 <\/sup>) which can be thought as mapping to the\u00a0spherical aromaticity formula\u00a02(n+1)2<\/sup>, where n=0. The electronic topology is slightly\u00a0different from C4<\/sub> itself, with four ring points (green) very close to the cage point in the centre.\"\"The ELF function now behaves itself in terms of symmetry, and produces a result in fact very similar to the\u00a0H4<\/sub>2+<\/sup>\u00a0molecule which started this topic rolling. There is an ELF basin with 0.14e located in the centroid and six equivalent basins (2.25e) spanning each pair of carbon atoms, although these C-C bonds are hugely banana shaped! That central electron basin closely resembles the one found in\u00a0H4<\/sub>2+<\/sup>\u00a0itself. The magnetic shielding at the centre of\u00a03349\u00a0ppm is not meaningful\u00a0in deciding if the molecule is indeed “aromatic”.
    \n \"\"<\/li>\n
  4. C4<\/sub>1-<\/sup>\u00a0 is again a\u00a0tetrahedral minimum, this time as a quartet 4<\/sup>A1<\/sub> state\u00a0(\u03c9B97XD\/Def2-TZVPP:\u00a010.14469\/hpc\/2219<\/a>, 918, 1024, 1377\u00a0cm-1<\/sup>; CCSD(T)\/Def2-TZVPP 10.14469\/hpc\/2237<\/a>, 824, 895, 1303 cm-1<\/sup>). The electronic topology is the same as before.\"\"Open shell spherical aromaticity[4]<\/a><\/span> is given by the 2N2<\/sup> + 2N + 1 (with S = N + \u00bd) rule. A quartet state has S=3\/2, hence N=1 and the formula stipulates\u00a05 delocalizable electrons for aromaticity, which this species has! The isotropic magnetic shielding is\u00a0695 ppm, which again is not immediately helpful.\"\"The ELF analysis ((above) shows just two types of basin, with four “lone pairs” at each carbon vertex (1.24e) and eight associated with the C-C “bent” bonds (1.95e).\u00a0<\/li>\n<\/ol>\n

    What did I learn?<\/p>\n