NOVEL MODIFICATIONS OF ELEMENTAL NITROGEN AND THEIR MOLECULAR STRUCTURES – A QUANTUM- CHEMICAL CALCULATION

Using the quantum-chemical calculation methods QCISD and G3, the possibility of the existence of nitrogen molecules with the composition N4, N6, N8 and N10 has been discussed. On the basis of the data obtained, the conclusion about possibility of existence of three novel polymorphic modifications of elemental nitrogen with an even number of atoms in molecules, namely N4 with rectangular and regular tetrahedron shapes, and N6 in a form remotely resembling an "open book", has been made. The values of bond lengths, valence and torsion angles, and oscillations frequencies in each of the above-mentioned forms of elemental nitrogen have been presented.


INTRODUCTION
Molecule of elemental nitrogen is known to consist of two atoms with a triple bond between them. 1 The length of this bond is only 109.5 pm, and, owing to this, the N2 molecule (dinitrogen) is characterized by a very high dissociation energy (941.64 kJ mol -1 ) and by very less chemical activity.
Three crystalline modifications of N2 are known. In the temperature range 36.61-63.29 K, β-N2 phase having a hexagonal dense packing, a space P63 mmc -2 group, lattice parameters a = 3.93 Å and c = 6.50 Å, exists. At a temperature lower than 36.61 K, a stable α-N2 phase having cubic lattice, a space P213 group and a period of a = 5.660 Å, occurs. At a pressure of more than 3500 atmospheres and a temperature below 83.0 K, a hexagonal phase of dinitrogen, namely γ-N2, is formed.
There are some theoretical indications that other nitrogen oligomers and polymers may be possible. These nitrogen modifications may have potential applications as materials with a very high energy density and as powerful propellants or explosives. 1 For most neutral polynitrogens are not expected to have a large barrier towards decomposition, and that the few exceptions would be even more challenging to synthesize than the tetranitrogen N4 which is an analogue of tetrahedrane C4, and has potential as a high-performance energetic material. 2 Nevertheless, cationic and anionic polynitrogens, namely cations of triazenium (N3 + ), tetrazenium (N4 + ), pentazenium (N5 + ), and azide-anione (N3 − ), pentazolide-anione (cyclic aromatic N5 − ) have been characterized. 1,[3][4][5][6][7][8][9] However, all these nitrogen compounds have a positive or negative charge. Up to now, however, there is no information in the literature on the existence of other neutral simple substances consisting solely of nitrogen atoms. [10][11][12] In this connection, in the this article the possibility of the existence of polyatomic molecules of nitrogen with an even number of atoms, namely nitrogen molecules of N4, N6, N8 and N10 compositions will be discussed.

CALCULATION METHOD
The calculation of molecular structures of polyatomic nitrogen molecules of N4, N6, N8 and N10 compositions was carried out using the QCISD(T)/TZVP method, as described in detail earlier, 13 in combination with the Gaussian09 software package. 14 The initial structures of the N4, N6, N8 and N10 molecules for carrying out quantum-chemical calculations are shown in figure 1.

N4A
N4B N6A N6B N8 N10 The choice of these initial structures was determined by two factors. First, the valence possibilities of the nitrogen atom (which capable to bind with one, two or three neighboring atoms by means of three chemical bonds according to the exchange mechanism) and secondly, with the greatest typicality of these structures compared with other structures with a corresponding number of atoms. In this connection, the regular octahedron in the case of N6, the N N N N hexagonal bipyramid and the dodecahedron in the case of N8, the two-capped cube or the two-capped dodecahedron in the case of N10 were not included in the number of initial structures. The correspondence of the found stationary points to energy minima was proved in all cases by the calculation of the second derivatives of energy with respect to the atom coordinates All equilibrium structures corresponding to the minima on the potential energy surfaces has only positive frequencies. The values of the standard thermodynamic characteristics of the nitrogencontaining compounds under examination were calculated using the G3 method described in earlier in detail. 15 All quantum-chemical calculations were carried out in the Joint Supercomputer Center, Kazan Branch of RAS -Branch of Federal Scientific Center "Research Institute for System Studies of the Russian Academy of Sciences" (http://www.jscc.ru).

RESULTS AND DISCUSSION
According to the results of our calculations, only three of the six structures of polyatomic nitrogen molecules mentioned above are stable, namely the N4A structure in the form of a rectangle, N4B in the form of a regular tetrahedron, and the N6B structure in the form of an "open book". All these modifications have been shown in figure 2. The geometric parameters of these above-mentioned stable structures (bond lengths, valence and torsion angles) have been presented in the Table 1. As can be seen from these data, in the polyatomic nitrogen molecules under examination, the nitrogen-nitrogen bond lengths are much larger than those in the N2 molecule; it is quite natural, because the theoretically expected multiplicity of bonds in them should be lesser than one in a dinitrogen molecule. It should be noted in this connection that for the N2 molecule itself, according to the QCISD(T)/TZVP method, the bond length (N1N2) is 110.3 pm that is very close to the experimental value of (109.5-110.0) pm. 1 It is interesting that, according to our calculations, for a "planar" version of the tetranitrogen molecule N4A, not a square or orthorhombic structure is realized, as might be expected, but a rectangular structure, with rather considerably different "longitudinal" and "transverse" bond lengths (154.6 and 127.1 pm, respectively) ( Figure 2). At the same time, for the "tetrahedral" variant N4B, the structure of the regular tetrahedron, where all the lengths of nitrogennitrogen bonds are exactly the same and have an intermediate values between the nitrogen-nitrogen bond lengths in the structure of N4A.  The structure of N6B, as it should be expected, is noncoplanar. There are three different kinds of nitrogennitrogen bonds having different lengths in it. Two of them 80 are relatively short (125.8 pm) and correspond to the double N=N bond; the other five in own length correspond to a single N-N bond, but one of them forming sui generis "binding" of this "open book" itself, is noticeably longer than the other four, 153.0 and 147.7 pm, respectively. As a result of the above differences, both sides of the "cover" of this "open book" are in fact not rectangles, as might be expected at first glance, but are identical isosceles trapezoids. The sum of the valence angles (N3N6N1) + (N6N1N2) + (N1N2N3 ) + (N2N3N6) and (N4N3N2) + (N3N2N5) + (N2N5N4) + (N5N4N3) are the same and are equal to exactly 360.0°. What is remarkable, the values of the valence angles (N1N2N5) and (N4N3N6) are much closer to 90° than to 180°, so the degree of non-coplanarity of the molecular structure of N6B should be considered as very significant.
Oscillation frequencies of polynitrogen molecules N4A, N4B and N6B are depicted in Table 2. According to theoretical expectations, 6 oscillations must be active in the IR spectrum in the case of N4A and N4B, and 12, in the case of N6B. Our calculated values match the theoretical expectations.( Table 2). As may be seen from these data, the sets of vibrational frequencies in polynitrogen molecules are quite different among themselves. At the same time, what is interesting, in N4B, there are two pairs of oscillations of different nature with the almost identical in frequency, 695 and 915 cm -1 whereas in N4B and N6B, nothing like this occurs. The values of standard thermodynamic characteristics, namely ∆fH 0 (kJ mol -1 ), S 0 (J mol -1 К -1 ) and ∆fG 0 (kJ mol -1 ), of the formation of N4A, N4B and N6B were calculated with using of G3 method and are presented in the Table 3. As follows from the data given in it, they all have positive values. In this connection, this fact attracts its attention that the values of these standard parameters for compounds N4A and N4B despite the very significant difference in their molecular structures, are nevertheless extremely close to each other. It is easy may be shown with using of these data and well-known values of ∆fH 0 and S 0 for dinitrogen (0 kJ mol -1 and 191.6 J mol -1 К -1 , respectively, 16 they cannot be formed directly from N2 within the framework of the isobar process by general eqns. (1-3) 2N2 (gas) → N4B (gas) 3N2 (gas) → N6 (gas) (3) The point is that for each of these processes, the value of the standard enthalpy of the reaction (∆H 0 298) is positive, and, on the contrary, the standard entropy (S 0 298) is negative (Table 4), and in accordance with the classical Gibbs-Helmholtz equation ∆G 0 = ∆H 0 -T∆S 0 , their synthesis directly from the "ordinary" dinitrogen N2 is thermodynamically forbidden process. However, from the thermodynamic point of view, the formation of N4A, N4B and N6B from atomic nitrogen according to schemes (4-6) is perfectly permissible and, nevertheless, as can be shown using the values of ∆fH 0 and S 0 for atomic nitrogen (472.8 kJ mol -1 and 153.3 J mol -1 К -1 , respectively), 16 for each of reactions (4-6) ∆H 0 as well as ∆S 0 are negative (Table 5) so that in a certain temperature range each of them are thermodynamically resolved. It should be noted in this connection that according to our calculation using the G3 method, the standard enthalpy of the N2(gas) → 2N (gas) process, in fact, the energy of N≡N bond in the dinitrogen molecule is 936.60 kJ mol -1 , which is in very good agreement with the experimental value of 941.64 kJ mol -1 . How to synthesize these novel polymorphic modifications of nitrogen is another problem, the discussion of which is beyond the scope of this paper, and further researches are needed for it. 4N (gas) →N4(A) (gas) 4N (gas) → N4(B) (gas) 6N (gas) → N6 (gas) (6)

FUNDING INFORMATION
All quantum-chemical calculations were performed at the Kazan Department of Joint Supercomputer Center of Russian Academy of Sciences -Branch of Federal Scientific Center "Scientific Research Institute for System Analysis of the RAS". Contribution of author Chachkov D.V. was funded by the state assignment to the Federal State Institution "Scientific Research Institute for System Analysis of the Russian Academy of Sciences" for scientific research.