Topological analysis of the electron localisation function (ELF) applied to the electronic structure of oxaziridine: the nature of N-O bond

Topological analysis of the electron localisation function (ELF), natural bond orbital and Wiberg bond index calculations have been applied to study the electronic structure of the oxaziridine molecule with a special focus on the nitrogen-oxygen bond. The calculations have been performed at the DFT(B3LYP, CAM-B3LYP, ωB97XD, M06-L, M06-2X) and post-Hartree-Fock (CCSD(T) and CASSCF) computational levels with applied aug-cc-pVTZ basis set. Nature of N-O bonding has been characterised by two resonance forms, N+O− and N−O+, owing to a very small population (< 0.60e) of the bonding basin V(N,O), localised in the ELF field for the N-O region. The importance of electron correlation effects for the description of the N-O bonding has been observed in the CASSCF calculations. The orbital description (Wiberg, NBO) differs from topological characterisation, indicating a single N-O bond.


Introduction
Oxaziridine, H 2 CN(H)O, is an unstable molecule with triangular heterocycle, containing carbon, oxygen and nitrogen (see Fig. 1). Due to high electronegativity of oxygen and nitrogen, three-membered ring is relatively weak and therefore can break easily [1]. In nucleophilic substitution with small steric bulk, a nucleophile tends to attack nitrogen first, leading to ring opening. Otherwise, nucleophile attack takes place at the oxygen atom instead [2]. Most of the research was performed for oxaziridine intermediate or its derivatives due to its unstable nature [3,4]. First oxaziridine derivatives were reported by Emmons [5]. Weak N-O bond can lead to oxygen and nitrogen substitution in many chemical reactions, such as formation of stereospecific α-hydroxyketones [6][7][8]. Industrial production of hydrazine is also performed through imine oxidation with hydrogen peroxide to oxaziridine [9]. Chemical properties of oxaziridine are mostly related to the N-O bond; thus, understanding of its nature is crucial for studying physical properties of the molecule.
Analysis of the nitrogen-oxygen bond lengths carried out for 2802 cyclic molecules deposited in the Cambridge Structural Database, CSD [10], and presented at the histogram in Oxaziridine molecule has been previously investigated by Taghizadeh et al. [11], who applied Fukui functions [12] and studied the topography of molecular electrostatic potential, MEP, at the DFT(B3LYP)/6-311++G(d,p) level. Calculated Fukui functions show a carbon atom as possible site for electrophilic or nucleophilic attack. According to the MEP analysis, negative charges can be found on the O and N atoms and positive charges are present on the H atoms.
In our previous papers, the nature of formally single nitrogen-oxygen bond has been investigated using topological analysis of electron localisation function, η(r) (ELF), in small XONO (X = H, F, Cl, Br, I, OH, (CF 3 )N, Li, Na, K, Rb, CH 3 , C 2 H 5 ) molecules [13]. Our calculations showed that the population of formally single bond N-O differs essentially from 2e expected for a single N-O bond and its value lies between 0.24e and 0.57e. Furthermore, its electron density is highly delocalised. Thus, the nature of the bond is not based on an electron pair sharing by two atoms but stems from electron density fluctuation between the N and O atoms. Despite the large amount of knowledge about the N-O bonding, it must be emphasised that the nature of the N-O bond in a cycled molecule has not yet been studied using topological approach.
The main focus of this paper is a detailed analysisusing the DFT and post-Hartree-Fock methods, (CCSD(T), CASSCF)of the chemical bonding nature of oxaziridine, where the N-O bond is contained in the triatomic cycled molecule. Our methods of the choice are topological analysis of η(r), electron density, ρ(r), and natural bonding orbitals (NBO) theory. Overall, the study expands knowledge about non-typical covalent bonds.
Optimised CCSD(T) [27,28] structure has been taken as an initial geometry for the CASSCF(N,M) (complete active space self-consistent field) calculations: CASSCF(6,6), CASSCF (8,8) and CASSCF (10,10). First of all, the CASSCF calculations have been carried out with six electrons on the three occupied and three unoccupied orbitals (MOs), HOMO-2 to LUMO+2. Subsequently, the active space has been increased by adding one occupied molecular orbital and one virtual orbital, HOMO-3 to LUMO+3. Finally, the active space has been increased with 10 electrons on five occupied MOs, HOMO-4 to HOMO, and five unoccupied MOs, LUMO to LUMO+4.
Analysis of natural bond orbitals [29] has been carried out with the NBO 3.1 procedure available in the G09 programme.
Wave functions for topological analysis of ρ(r) and η(r) fields have been approximated using a set of MOs from single point energy calculations, performed using optimised structures (NoSymm keyword). For the CCSD(T)optimised structures, wave functions have been calculated at the CCSD level (CCSD/aug-cc-pVTZ//CCSD(T)/aug-cc-pVTZ) using the approximation proposed by Feixas et al. [30] with the natural orbitals and their occupancies only. Similar procedure has been applied for the CASSCF data.
Topological analysis of ρ(r) and η(r) has been performed using TopMod09 package [31] and DGrid 5.0 [32] programme. Electron localisation functions have been calculated with a cubical grid with step size of 0.05 bohr. Analysis of molecular orbital (MO) contribution to the ELF and electron localizability indicator (ELI-D) has been performed using DGrid 5.0.
Graphical representations of ELF and MO have been visualised in the Multiwfn [33] and Chimera [34] programmes.
Application of ab initio methods with explicit electron correlation (CCSD(T), CASSCF) yields the C-O, C-N and N-O bonds longer than those obtained using the DFT methods. The  Local geometry of the H-N, O-N and C-N bonds corresponds to pyramidal arrangement of the bonds, thus the lone electron pair is expected to be present in the vicinity of the N atom (sp 3 hybridised). Similarly, two lone pairs should be found in the vicinity of the O atom (sp 3 hybridised). The presence of lone pairs, as predicted by the Lewis formula (see Fig. 1a), should also be supported by topological analysis of ELF.

Analysis of bonding nature
Two modern methods for investigating electronic structure of molecules, free from arbitrary choice of molecular orbitals used in this study, are topological analysis of electron density by Bader (AIM) [35] and topological analysis of ELF [36] proposed by Silvi and Savin [37]. Both methods belong to the quantum chemical topology (QCT) [38]. An electronic structure of a molecule described by ELF is represented by maxima (attractors) and its localisation basin of η(r) field, which characterise covalent bonds, lone pairs, core regions, and valence shells in atoms. Calculated electron populations on chemical bonds, N, is related to integration electron density over localisation basins. Results represent average values with quantum uncertainty [39].
Firstly, the electronic structure of the H 2 CN(H)O molecule is investigated from the perspective of topological analysis of ρ(r) field. There are 13 critical points of ρ(r) field: six nuclear critical points (NCPs) (3,-3), six bond critical points (BCPs) (3,-1) and one ring critical point (RCP) (3,+1) in the C-N-O ring. For the N-O bond, the BCP exhibits high value of the electron density (0.233-0.266 e/au 3 ) and a small positive value of Laplacian of electron density, ∇ 2 ρ (3,-1) (r), (0.073-0.150 e/au 5 ). Interestingly, a typical topological signature for the covalent (shared-electron) bonding is not observed, since the positive sign of ∇ 2 ρ (3,-1) (r) suggests depletion rather than concentration of the electron density around BCP. Thus, the N-O bond, although formally single, has more complicated electronic structure than that expected using classical approach. The atomic charges calculated by the AIM method, q AIM , range between 0.70e and 0.80e for the carbon atom and are significantly larger than obtained for the nitrogen (−0.57e to −0.49e) and the oxygen (−0.71e to −0.66e) atoms.
In the second step, topographical analysis has been carried out for ELF. The 2D map of η(r) function for the molecular plane defined by the C, N and O atoms (CCSD//CCSD(T) data) is presented in Fig. 3. The core regions are characterised by circular localisation domains with high (≈ 1) values of electron localisation (red), whilst the chemical bonds C-N and C-O are described by irregular localisation domains (orange) with smaller values of electron localisation (0.8-0.9). Thus, both bonds have a covalent character and exhibit high electron localisation, typical for shared electron (covalent) bonding. For the N-O bonding, a quantitatively different topography is observed since a respective Table 1 The bond length, r, partial atom charges calculated by the AIM method, q AIM , delocalisation indices, DI, and properties of the bond critical point for the N-O bond The delocalisation index (see Table 1), DI, is a quantitative measure of the number of electron pairs, delocalised between two atomic basins and can be used as a topological bond order [40]. To get further insight into the electronic structure of the oxaziridine molecule, the gradient field analysis (topological analysis) has been performed for the ELF using the data obtained from the DFT and post-Hartree-Fock calculations. As a result, the core and valence attractors (local maxima), representing atomic cores, chemical bonds and lone pairs, have been found. The reader is encouraged to familiarise themselves with the publications of Silvi et al., where the principles of topological analysis of ELF are described [41][42][43][44].
Electron density of atomic cores is characterised by the C(C), C(N) and C(O) core attractors. Calculations performed using all the methods, with exception of DFT(M06-L) and DFT(B3LYP), show that the chemical bonds are represented by the V (H1,N), V(H2,C), V(H3,C), V(C,O), V(C,N) and V(N,O) attractors. Those attractors belong to the point, valence, disynaptic and bonding type, respectively. The concept of synapticity has been described by Silvi et al. in ref. [45].
The V(C,N) bonding attractor is localised approximately around the midpoint of the C-N bond, whilst the V(C,O) and V(N,O) attractors are found in the proximity of more electronegative oxygen atom. Such effect is especially visible for the N-O bond. Furthermore, the attractors are not found on an imaginary straight line linking the atomic nuclei. Such topology of ELF seems to be associated with the Pauli repulsion involved in three bonds forming a non-triangular structure. The different positions of the bonding attractors have been reported for some strained molecules (cyclopropane, cyclobutane, cyclopentane, cyclohexane, bicyclo[1.1.0]butane, spiropentane, tetrahedrane and cubane) by Chevreau and Sevin [46] and also for cyclobutane and perfluorinated cyclobutane molecules by one of us [47]. Thus, oxaziridine has more complicated structure than expected.  To aid the interpretation of bonding character in oxaziridine, the population analysis has been carried out for the localisation basins. The basin populations, N, calculated at all the computational levels, have been collected in Table 2.
Population for the N-O bond varies from 0.24e (CASSCF and CCSD) to 0.57e (M06-2X). It is worth emphasising that obtained N values are much smaller than 2e expected for the covalent single bond and even smaller than 1e. Thus, it is evident that the nature of the bonding between the N and O atoms differs quite significantly from a typical covalent bond with shared 2 electrons. In order to reflect such small basin populations, at least three resonance structures should be used,  [48]. However, the N-O bond classification as the CS bond is not straightforward, judging by topological analysis of electron density for heteronuclear bonds presented by Zhang et al. [49]. Positive values of ∇ 2 ρ (3,-1) (r) between 0.073 and 0.150 e/au 5 , and a large R BCP /R eq ratio of 0.47-0.48 are rather typical for covalent bonds, therefore do not fit the following criteria: large negative Laplacian, ∇ 2 ρ (3,-1) (r), and a small R BCP /R eq ratio or proximity of BCP to less electronegative atom. Thus, the N-O bond cannot be easily classed as CS type.
Analysis of covariance of ELF basin population (see Table 3) yields information about delocalisation of electron density between basins and helps in interpretation on electron density distribution in the oxaziridine [50]. For the V(N,O) basin, electron density is mainly delocalised with lone pairs, localised on oxygen, V i = 1,2 (O), and covariance value ranges between −0.10 to −0.14, and −0.09 to −0.13, respectively. The obtained results for lone pair of nitrogen, V(N), are similar to V i = 1,2 (O) and ranges between −0.08 and −0.12. It is worth noting that delocalisation Polarity of chemical bonds in the oxaziridine molecule has been calculated using the scheme proposed by Raub and Jansen [51], based on joined topological analysis of the ρ(r) and η(r) fields. The polarity index, p XY , ranges between 0 for homopolar bonds and 1 for idealised ionic bonds. Quantum atoms are defined through topological analysis of ρ(r) field. With exception of the CASSCF and CCSD calculations, all values of atomic contributions showed in Table 3 indicate slightly larger (50-55%) contribution of oxygen electron density to the V(N,O) basin. The N-O bond is slightly polarised towards the O atom with the value of the p ON index between 0  . Those values support our interpretation that the basin characterises mainly the non-bonding electron density of oxygen. The percentage contribution of electron density from the nitrogen is smaller than 8%. Nevertheless, the basin has common surface with two cores C(N) and C(O) and is of the disynaptic type.
Contributions of molecular orbitals (MO) to the ELF and ELI-D values [52,53] for the V(N,O) attractor have been calculated at DFT(M06-2X)/aug-cc-pVTZ level in order to find some correlation between orbital representation of the N-O bonding and topological description using real functions. Figure 6 shows DFT-MOs with the contribution above 5%. The N-O bond is characterised by V(N,O) attractor, η(r) = 0.755, associated with contribution of the seven occupied MOs (95%). Difference between contributions to ELF and ELI-D occurs only for the two DFT-MO, HOMO-5 and the HOMO-8. However, the difference is very small (HOMO-5, 2 percentage point; HOMO-8, 1 percentage point) and can be neglected. The largest contribution to V(N,O) is from the HOMO-8 (38% by ELI-D and 37% by ELF) and the HOMO-3 (18% ELI-D and ELF). The HOMO-8 MO is localised to σ C-O , σ C-N and σ N-O , and generated by atomic orbitals of N, C and O atoms. The nitrogen atom has significant orbital coefficient values of 2s and three p atomic orbitals. The carbon atom contributes 2s, 2p x , 2p y together with oxygen atom of 2s and 2p y atomic orbitals. The HOMO-3 also contributes significantly to the V(N,O) attractor and is formed by the sp 2 nitrogen hybrid and overlap with the sp hybrid of oxygen atom. The HOMO-2 with 14% contribution to V(N,O) basin is generated by sp 3 hybrid of nitrogen together with sp hybrid of oxygen atom.
Additional analysis of bonding has been performed using natural bonding orbitals theory [54]. The results obtained using the DFT data are collected in Table 4. There are negative natural charges, q NPA , on the nitrogen (−0.33e to −0.31e) and oxygen (−0.40e to −0.38e) atoms. However, the carbon atom has a slightly positive (0.07e -0.08e) q NPA values. Those results are in agreement with the q AIM charges calculated using topological analysis of ρ(r) field. The values of the Wiberg bond order [55] for the N-O bond are close to one (1.004-1.010), indicating a single bond. Such result differs essentially from the interpretation of small (< 0.60e, DFT) and fluctuating electron density for the V(N,O) basin, with an attractor localised in the bonding region. The covalent σ-natural bond orbital, characterising N-O interaction, is formed by nitrogen and oxygen natural  hybrid orbitals overlap with average of 9% s-orbital and 91% p-orbitals of both atoms. A larger contribution of the s-orbital can be noted for the NBOs, corresponding to the C-N and C-O bonds. The C-N has average of 21% s-orbital and 79% p-orbitals of carbon and nitrogen atoms, indicating the sp 3.73 hybrid on carbon, and also the sp 3.87 hybrid on nitrogen. Slightly smaller participation with only 2 percentage point of s-orbital in σ-bond has been found in the C-O bond, with average of 19% s-orbital and 81% p-orbitals. The electronic structure obtained by topology analysis of ρ(r) and η(r) fields indicate that the nature of the N-O bonding is far from being single N-O bond and its description depends on the computational method used.

Conclusions
The electronic structure of the oxaziridine molecule has been investigated using topological analysis of the ELF and electron density. The current research increases our knowledge about the nature of the nitrogen-oxygen bonding in molecular systems. Furthermore, the obtained results allow to explain the unstable nature of the oxaziridine through specific nature of the N-O bond. The