Theoretical investigation on the ground state properties of the hexaamminecobalt(iii) and nitro–nitrito linkage isomerism in pentaamminecobalt(iii) in vacuo

Nitro–nitrito isomerization in Co(NH3)5NO22+ linkage isomers was investigated with a focus on the geometries, relative stabilities and chemical bonding using ωB97XD/6-31+G(d,p) to elucidate the photo-salient effect in [Co(NH3)5NO2]NO3Cl. Different techniques like atoms in molecules (AIM), electron localization function (ELF) and natural bonding orbital (NBO) were used to gain insight into the chemical bonds of the isomers and to identify the key factors influencing their relative stabilities. The study of the ground-state potential energy surface of [Co(NH3)5NO2]2+ reveals that the nitro/exo-nitrito isomerization reaction can proceed via the following two paths: (1) nitro → TS1 (38.16 kcal mol−1) → endo-nitrito → TS2 (9.68 kcal mol−1) → exo-nitrito and (2) nitro → TS3 (41.76 kcal mol−1) → exo-nitrito. Pathway (1) through endo-nitrito is the most likely isomerization mechanism because of a lower energy barrier than pathway (2). The intramolecular-resonance-assisted hydrogen bonds (N–H⋯O and N–H⋯N), the orientation of NO2, and the difference between Co–N and Co–O bond energies are identified as the key factors determining the relative stabilities of the linkage isomers. Co(NH3)63+ is less stable compared to Co(NH3)5NO22+ and undergoes a slight geometrical distortion from D3d to either D3 or S6 characterized by a stabilization energy of ∼750 cm−1 at CCSD(T)/6-31+G(d,p).


Introduction
Co complexes play various important roles in the chemistry of life processes and have been known for ages to impart blue color to ceramics. 1,2 Considerable research effort has been made to understand the properties of Co complexes, particularly those derived from cobaltammines. Sakiyama et al. 3 analyzed the electronic spectra of the hexaamminecobalt(III) complex cation in aqueous solution to obtain the spectral components attributed to the slight distortion from a regular octahedron around the central cobalt(III) ion and reported that the LC-BLYP/ 6-31G(d) optimized geometry of the complex in aqueous solution is a trigonally compressed octahedron under D 3d . The inuence of this reduction in the symmetry of [Co(NH 3 ) 6 ] 3+ on its vibrational spectrum was also examined in the solid state. 4 This trigonal deformation was reported to be sensitive to the environment of the complex. 3 A crystallographic study of the binding of oxo-anions with cationic cobaltammine carried out by Sharma et al. 5 revealed the presence of discrete [Co(NH 3 ) 6 ] 3+ ions and mixed anions (e.g. Cl À and ClO 3 À , Br À and ClO 3 À , Cl À and ClO 3 À ) which are stabilized by hydrogen bonding interactions and attractive electrostatic forces. The hexaamminecobalt(III) complex cation is a potential anion receptor 5,6 widely used in structural biology to characterize biomolecules like DNA, RNA, and proteins 7 and it is considered as a representative cationic Werner complex. It is worth mentioning that the works of Alfred Werner on cobaltammines led to a Nobel Prize in 1913, 8 which formed the basis of modern transition-metal coordination complex chemistry, especially the linkage of atoms in transition metal compounds.
Transition-metal linkage isomers have the same chemical composition, differing only in the nature of the metal-ligand connectivity. 9 For example, when one ammonia in hexaamminecobalt(III) is substituted by a nitrite anion, nitro, endonitrito, and exo-nitrito isomers are formed (Fig. 1). Nitrite anion is an ambident ligand with electronic density delocalized on both N-O bonds, and both N and O atoms acting as alternative reactive sites. It can bind to the metal through N as well as through O, leading to linkage isomerism. The ambident reactivity of the nitrite ion was studied in detail by Tishkov et al. 10 For instance, the cationic cobalt complex of formula [Co(NH 3 ) 5 NO 2 ]Cl 2 exists as either the yellow-colored nitro isomer ([Co(NH 3 ) 5 NO 2 ]Cl 2 ), where the nitro ligand is bound to Co through nitrogen, or the red-colored nitrito isomer ([Co(NH 3 ) 5 ONO]Cl 2 ), where the nitrito is bound to Co through one of the oxygen atoms [11][12][13][14][15][16] Several research groups have focused their studies on metal linkage compounds due to their potential applications in medicinal therapy, photo-responsive materials, tunable optical materials, and molecular devices. [11][12][13][17][18][19][20][21][22][23][24][25][26] The transformation of the N-bonded nitro isomer to the less stable O-bonded nitrito isomer has already been extensively studied experimentally and the conversion was demonstrated to occur intramolecularly. [13][14][15][16] The nitrito isomers of [Co(NH 3 ) 5 -ONO](NO 3 ) 2 and [Co(NH 3 ) 5 ONO](NO 3 )Cl convert slowly to the respective nitro isomers [Co(NH 3 ) 5 NO 2 ](NO 3 ) 2 and [Co(NH 3 ) 5 -NO 2 ](NO 3 )Cl when placed in a dark room. 19 The base dependence of this linkage isomerization and the transformation of the nitrito in nitrito was also observed overnight by Jackson et al. 27 in [Co(NH 3 ) 5 ONO](ClO 4 ) in solution using H 1 NMR and UV-vis techniques. The reaction of the transformation of [Co(NH 3 ) 5 ONO] 2+ in [Co(NH 3 ) 5 NO 2 ] 2+ in solution and in solid state was found to be accelerated by light. [27][28][29] More detailed information related to the experiments describing the synthesis of [Co(NH 3 ) 5 NO 2 ] 2+ and [Co(NH 3 ) 5 ONO] 2+ and the application of spectroscopic techniques to detect the nitrite bonding mode are provided elsewhere. 27,[29][30][31][32] Here we only recall that this transformation may pass through an intermediate endo-[Co(NH 3 ) 5 ONO] 2+ . According to Cioni, 33 experimental data do not provide a better understanding of the nitro/nitrito transformation mechanism, and theoretical methods can help in the elucidation of this reaction mechanism. This solid-state intramolecular reaction changes the conguration of the [Co(NH 3 ) 5 NO 2 ] 2+ complex cation alone at its site in the lattice, leaving the rest of the lattice unchanged 9 and was reported to be autocatalytic or auto-inhibitory. 24 In contrast to the dark condition, Naumov et al. 22,23 reported that the [Co(NH 3 ) 5 -NO 2 ](NO 3 )Cl crystal exhibits a forceful jump when exposed to UV light (referred to as the photo-salient effect). During this photo-isomerization process, [Co(NH 3 ) 5 ONO] 2+ was thought to serve as a local source of strains. 24,25 The discovery of photo-induced leaping in [Co(NH 3 ) 5 -ONO](NO 3 )Cl crystals stimulated extensive research into its structural and photo-rearrangement properties. 22,23,34,35 The design of dynamic molecular crystals with properties that can be controlled by applying an external stimulus is an important challenge in molecular materials science. Herein we investigate in detail the geometry, relative stability, and chemical bonding in the ground state of the hexaamminecobalt(III) cation and the nitro-/nitrito-pentaamminecobalt(III) linkage isomers (denoted as Co-NO 2 and Co-ONO) in vacuo using uB97XD/6-31+G(d,p). Knowledge of the structural and electronic properties of the nitro-/nitrito-pentaamminecobalt(III) linkage isomers is critical in the research of novel linked isomers with switchable optical properties. The main purpose of this study is the prediction of the pathway of the nitro-/nitrito-pentaamminecobalt(III) isomerization because the latter is the probable cause of the photosalient effect in [Co(NH 3 ) 5   (2) Secondly, MP2, CCSD, B3LYP, B3LYP-D3, M062X, LC-BLYP, and uB97XD methods are compared with CCSD(T). The uB97XD and LC-BLYP methods gave good results approaching CCSD(T). Therefore, the subsequent analysis is performed using uB97XD.
(4) Lastly, the nature of chemical bonding in the nitro-and nitrito linkage isomers is examined briey to understand how atoms are held together and to identify key factors to justify their order of stabilities. Hydrogen bonds, orientation of atoms in ONO group, and difference in natural bonding orbital (NBO) energy between Co-N and Co-O bonds are identied as the key factors to explain the relative stabilities of linkage isomers.
We conrmed through this analysis that the reaction path (1) through endo-nitrito is the most likely isomerization mechanism causing photo-salient effect, because it is the lowest energy reaction path. Fig. 1 shows the initial geometric structures used herein for geometry optimization. The [Co(NH 3 ) 5 NO 2 ] 2+ linkage isomers were constructed following the coordination modes proposed in literature. 36,37 Fig. 1c and d display two O-bonded nitrito isomers with different spatial orientation of the atoms of the ONO group, denoted as exo-Co-ONO and endo-Co-ONO. Only singlet states were considered in the present study because octahedral Co(III) prefers the low-spin state, contrary to the Co(II) state. [38][39][40] Comprehensive understanding of [Co(NH 3 ) 6 ] 3+ and [Co(NH 3 ) 5 NO 2 ] 2+ isomers requires state-of-the-art quantum chemical methods. All geometries were fully optimized and minima characterized by real vibrational modes at uB97XD/6-31+G(d,p). Transition states were located using QST3 and IRC methods, followed by vibrational frequency analysis. All the minima energy values reported here are zero-point energy (ZPE) corrected using the expression:

Computational details
where h and n i stand for Plank's constant and the vibrational frequency of mode Q i , respectively. CCSD(T) single-point calculations were performed based on CCSD optimized geometries to validate our methodology, and the structures and their relative energies were found to be similar to those obtained at uB97XD. The dynamic correlation in D 3d -Co(NH 3 Table  S1. † The HOMO and LUMO in D 3d -[Co(NH 3 ) 6 ] 3+ are on ammonia and belong respectively to e g and a 1g representation. Their energy difference computed is nearly 11.11 eV at uB97XD, 13.25 eV at LC-BLYP and 17.74 eV at MP2 (17.70 eV at CCSD(T)/ 6-31+G(d,p)). LC-BLYP, and uB97XD methods have tendency to underestimate the HOMO-LUMO gaps compare to MP2 method. LC-BLYP, uB97XD, and MP2 methods yield Co-N bonds distances of 1.97-2.01Å close to CCSD and BD(T) bond lengths calculated about 1.99-2.00Å in gas phase ( Table 1). The experimental value of the equilibrium Co-N bond length of Co(NH 3 ) 6 3+ is measured and found to be around 1.97Å; 58-60 this is not signicantly different from CCSD/6-31+G(d,p) calculated bond in the gas phase. This small difference between experiment and calculated bond distance is explained by different environment of [Co(NH 3 ) 6 ] 3+ in solid. It has been reported in solution that the neglect of solvent-solute charge transfer effect can yield too long Co-N bond lengths. 61 Our calculations show that D 3d in vacuo is unstable contrary to what was reported elsewhere, 3 in solid and aqueous media. Its optimized geometry is characterized by six imaginary modes of representations a 1u , a 2g , e g and e u at i167, i164, i101 and i90 cm À1 at uB97XD/6-31+G(d,p) (i154, i150, i74 and i45 cm À1 at CCSD/6-31G(d)), respectively. A distortion with the D 3 symmetry constraint yields a minimum energy characterized by the lowest vibrational mode of e symmetry located at 89 cm À1 at uB97XD/6-31+G(d,p) (79 cm À1 at CCSD/6-31G(d)). The energy difference between the HOMO and LUMO is slightly increased to 17.74 eV at CCSD(T)/6-31+G(d,p) for D 3 . A further optimization of D 3 and D 3d geometries using B3LYP/TZP method as implemented in TUR-BOMOLE gives an energy difference of 1.54 kcal mol À1 . The HOMO-LUMO gap in gas phase is 6.25 eV. The vibrational analysis is characterized by two imaginary frequency at i107.97 and i104.40 cm À1 of a 1u and a 2g representations, whereas a full optimization of the same geometry in D 3d at the SVWN/TZP including the scalar and spin-orbit ZORA as implemented in ADF program reproduces six imaginary frequencies estimated about i137.99 (a 1u ), i137.90 (a 2g ), i54.56 (e g ), i18.00 (e u ) cm À1 conrming that D 3d is not the true global minimum of [Co(NH 3 ) 6 ] 3+ .

Results and discussion
The structural change between D 3d and D 3 in [Co(NH 3 ) 6 ] 3+ is small (Fig. S2 †). The distortion vector responsible of this symmetry breaking can be expressed as: 62,63D where the coefficient in the expression is related to the weight of the imaginary modeQ G i j , and the subscript describes the irreducible representation of the vibrational mode.
Our calculations show a signicant contribution of the 1a 1u imaginary mode of nearly 98.89% in the distortion vector ( Fig. S3 †). A further distortion of D 3d along the imaginary vibrational mode a 2g will lead to S 6 . The distortion of D 3d -[Co(NH 3 ) 6 ] 3+ along 1a 1u vibrational mode acts essentially on H and destroys the center of symmetry. The full D 3d symmetry group is broken because by destroying the inversion point, 1a 1u will also remove the improper rotation axis (S 6 ) and the dihedral plane. However, the imaginary modes show a rotation of hydrogen atoms. The free rotation of NH 3 groups in octahedral symmetry observed in water solvent should not strictly be applicable to low symmetry complex. The decent in symmetry observed from D 3d to its subgroup D 3 can only arise from the Pseudo-Jahn-Teller (PJT) effect because the HOMO (e g ) 4 in D 3d is fully occupied and cannot trigger a pure Jahn-Teller distortion according to group theory. The computed PJT energy caused by this vibronic coupling is about 742 cm À1 at uB97XD/ 6-31+G(d,p) ($750 cm À1 at CCSD(T)/6-31+G(d,p)). The Pseudo-   (55) Jahn-Teller computed at CASSCF(2,2)-MRCAPF/SVP is about 154 cm À1 at SVP. Krisloff et al. 64 investigated the unphysical ground states of the multireference averaged coupled-pair functional and reported that CASSCF(2,2)-MRCAPF can provide unphysical solution in the avoided crossing or conical intersection and the instabilities can be removed by employing larger complete active spaces (CAS). Unfortunately, the latter is computationally more demanding. The molecular orbitals involved in this distortion mechanism require further investigation. The energy level of the valence molecular orbitals of the D 3d geometry is listed in Table S1 † and agree with the literature. 65 The HOMOs are localized on the metal and are nonbonding pure d orbitals. The LUMOs have high contribution on the metal and nitrogen and are antibonding orbitals (Fig. S1 †). The HOMO (e g ) and HOMO-1 (a 1g ) derived from the reduction of t 2g in O h . To validate the use of uB97XD, various DFT and MP2 methods were employed and compared with CCSD(T). The data obtained shown in Table 1 suggest uB97XD and LC-BLYP could perform quite well with respect to CCSD(T). Therefore, the uB97XD/6-31+G(d,p) method and the lowest D 3 geometry are considered for further analysis on nitro-/nitritopentaamminecobalt(III) linkage isomers.
We have extended this study to other hexammines complexes analogs of Ru(III), Cr(III) and Fe(II) which were reported to have either D 3d or D 3 symmetries. 3 6 ] 2+ ions can be considered as octahedral in which the d orbital of the transition metal splits in t 2g and e g . For comparison, the most popular functional for transition metal B3LYP was employed with LanL2DZ basis set for all atoms on the D 3d symmetry of the low-spin states [ 1 A 1g : (t 2g ) 6 (e g ) 0 ] and [ 2 T 2g : (t 2g ) 5 6 ] 2+ . The Pseudo-Jahn-Teller energies obtained at B3LYP/LanL2DZ for the symmetry breaking of D 3d towards either D 3 or S 6 are given in Table 2. D 3 and S 6 are higher ranking epikernels and are found as minima for all transition metal complexes studied in the present paper, whereas the lower ranking epikernel C 2h is found to be a saddle point [Tables 2 and 3]. The difference in metal-N bonds between D 3 and S 6 is negligible ($0.001 A). These ndings are in good agreement with the epikernel principle. 63 The Pseudo-Jahn-Teller distortion energies are considerably more important in Co-and Cr-complexes than Ru-and Fe-complexes. The M-N bonds distances listed in Table 2 67 using B3PW91 functional with the effective core potential/basis set combination SDB-cc-pVTZ. The authors found that the oscillator strengths of 1 A 1 / 1 T 1g is considerably larger than that of the 1 A 1g / 1 T 2g in both complexes and arises from H 3 N-M-NH 3 antisymmetric bending vibration. The metal ligand charge transfer (MLCT) was found larger in the Ru-complex than in its counterpart Cocomplex. Multicongurational self-consistent-eld (MCSCF)  Fig. 3 shows the geometries of the ground states of O-and N-linked isomers and transition states computed at uB97XD/6-31+G(d,p). A close inspection on the geometric structures shows that the substitution of ammonia by nitro or nitrito in [Co(NH 3 ) 6 ] 3+ to form [Co(NH 3 ) 5 NO 2 ] 2+ or [Co(NH 3 ) 5 ONO 2 ] 2+ gives rise to the shrinking of Co-N bonds formed by NH 3 positioned in the equatorial region with the concomitant elongation of the axial Co-NH 3 bond. The NH 3 ligands in the horizontal plane are apparently more strongly bound to Co than the axial NH 3 ligands. In Co-NO 2 (Fig. 3a), the bond length between Co and NO 2 is 1.924Å, which is 0.075 and 0.141Å shorter than those in the Co-N bonds formed by equatorial and axial NH 3 . The Co-O bond length in the exo-ONO complex (Fig. 3b) is $0.03Å shorter than that of the endo-ONO complex (Fig. 3c). The Co-NO 2 and exo-Co-ONO geometries were also studied by Cioni et al. 33 at B3LYP/LanL2DZ level in order to clarify the intrinsic and environmental effects on the kinetic and thermodynamics of linkage isomerizasion in nitropentaamminecobalt(III) complex. The geometrical parameters of our Co-NO 2 and Co-ONO complexes optimized at uB97XD/6-31+G(d,p) are compared in Table S4 † with B3LYP/ Lanl2dz geometries obtained by Cioni et al. 33 and the available X-ray data. 78,79 uB97XD/6-31+G(d,p) performs better than B3LYP/Lanl2dz and the small difference observed between X-ray and the optimized geometries can be attributed to crystal environment. 33 Boldyreva et al. 80  We have computed the IR spectra of nitro and nitrito complexes at B3LYP/6-31+G(d,p). Our calculations show a clear difference in vibrational frequencies between NO 2 and ONO isomers in the region between 700-1700 cm À1 (Fig. 4). The vibrational modes which characterize the NO 2 and ONO in Co-NO 2 and Co-ONO complexes are listed in Table 4 and shown in Fig. 5. The deformation NO 2 and ONO modes are well reproduced whereas our asymmetric N-O stretching modes are overestimated referring to Cioni ndings and experimental data. 33 Transition states. Co-NO 2 / endo-Co-ONO / exo-Co-ONO reaction mechanism describes the sequence of the elementary transformation of Co-NO 2 complex in exo-Co-ONO via the endo-Co-ONO complex. TS1 (i569 cm À1 computed at uB97XD/6-31+G(d,p)) and TS2 (i210 cm À1 uB97XD/6-31+G(d,p)) depicted in Fig. 3d and e are predicted sequential transition states in this reaction path by intrinsic reaction coordinate (IRC) method. TS1 has a NO 2 moiety detached from Co; the Co-N bond length is estimated to be about 2.27Å, but still binds to four NH 3 ligands through O/H-N hydrogen bonds ranging between 2.14 and 2.32Å at uB97XD/6-31+G(d,p). The TS1 geometry was reported as rst-order saddle point with one imaginary vibrational mode located at i385 cm À1 at B3LYP/LanL2DZ. 33 Its geometrical parameters geometry computed at uB97XD/6-31+G(d,p) and B3LYP/LanL2DZ are detailed in Table S4. † This transition state is difficult to detect experimentally. 15 The Fig. 4 Superimposed IR spectra of Co-NO 2 and Co-ONO complexes computed using a scaling factor of 0.9632 at B3LYP/6-31+G(d,p).  Origin of mechanical motion in solids. The electronic spatial extents 85 of [Co(NH 3 ) 5 ONO 2 ] 2+ and [Co(NH 3 ) 5 NO 2 ] 2+ were computed to gauge the increase in the size of those cations upon intramolecular conversion. The exo-Co-ONO has a larger electronic spatial extent than Co-NO 2 : these are estimated to be about 1556 and 1411 a.u., respectively (1451 for endo-Co-ONO). The effective size of the exo-Co-ONO isomer was evaluated to be 1.2 times greater than that of the NO 2 -Co. 16,17 According to Boldyreva, 24 the former is expected to play an important role in increasing the local pressure near the product in nitro and nitrito interconversion reaction in solids, and can be at the origin of the mechanical motion observed in crystals. Thus, it is important to rst understand this isomerization reaction as this constitutes the fundamental process that triggers the photosalient phenomenon in [Co(NH 3 ) 5 NO 2 ]NO 3 Cl.
3.2.2 Thermodynamic and kinetic stability Relative energy. Table 5 compares the relative energies of exo-Co-ONO and endo-Co-ONO complexes and their transitions states (TS1 and TS2) with respect to the Co-NO 2 isomer at uB97XD/6-31+G(d,p). According to the data listed in Table 5, the Co-NO 2 complex is 1.32 and 3.39 kcal mol À1 lower than endo-Co-ONO and exo-Co-ONO complexes, respectively (1.12 and 2.00 kcal mol À1 at CCSD(T)/6-31G(d)) on the potential energy surface (PES). Noted that the relative energy of the exo-Co-ONO computed by Cioni et al. 33 is about 3.9 kcal mol À1 at B3LYP/ LanL2DZ including ZPE corrections in gas phase. Thus, the nitro form is predicted to be the lowest isomer. The fact that the uB97XD/6-31+G(d,p) energy ordering of isomers is reconrmed by CCSD(T) (Table S5 †) shows that the uB97XD functional is an alternative method at an affordable cost for studying these linkage isomers. The dispersion energies in NO 2 -Co, endo-Co-ONO, and exo-Co-ONO isomers computed using dispersioncorrected B3LYP at 6-31+G(d,p) amount to À26.25, À25.43 and À24.95 kcal mol À1 , respectively. The zero-order regular approximation (ZORA), a two-component form of the fullyrelativistic Dirac equation used along with B3LYP at SVP, also indicates that Co-NO 2 is the most stable isomer, followed by endo-Co-ONO. The difference in relative energies obtained using non-relativistic and relativistic method is small, ranging from 0.13 to 0.5 kcal mol À1 .
Binding energy. The binding energies of NH 3 and NO 2 À to the metal in Co-complexes and the formation energy (FE) of complexes were obtained as electronic energy (E) difference between the most stable geometries of the products and reactants at uB97XD/6-31+G(d,p) from the following equations: (2) The heat of formation of Co(NH 3 ) 5 NO 2 2+ at 298 K calculated by means of the isodesmic reaction (eqn (5)) is À280.55 kcal mol À1 . The binding energies of NO 2 and NH 3 to the metal Co were found to be about À343.49 and À61.70 kcal mol À1 , showing that NO 2 binds more strongly to Co than NH 3 does. Thus, the Co(NH 3 ) 5 NO 2 2+ complex appears to be thermodynamically more stable than Co(NH 3 ) 6 3+ .
HOMO-LUMO & transition states. In conceptual DFT formalism, the HOMO-LUMO gap energy is related to the kinetic stability. The NO 2 -Co complex in Table 4 has the largest HOMO-LUMO gap of 8.68 eV, followed by endo-Co-ONO with a HOMO-LUMO gap energy of 7.92 eV. The HOMO-LUMO of exo-Co-ONO is 0.28 eV lower than that of endo-Co-ONO at uB97XD/6-31+G(d,p). Therefore, by considering the HOMO-LUMO gap energy, Co-NO 2 appears to be kinetically more stable than ONO-Co complexes. For this purpose, two trajectories involving TS1 and TS2 transitions states were investigated by exploring the ground state potential energy surface of [Co(NH 3 ) 5 NO 2 ] 2+ : the trajectory from the Co-NO 2 to endo-Co-ONO complex and that from the endo-Co-ONO to exo-Co-ONO complex. The mechanistic study of the intramolecular conversion reveals that the energy barrier for the intramolecular conversion of endo-Co-ONO in Co-NO 2 ($39 kcal mol À1 ) is 3.5 times larger than that of the interconversion between endo-Co-ONO and exo-Co-ONO. Our TS1 activation energy barrier carried out at uB97XD/6-31+G(d,p) is 9 kcal mol À1 above the activation energies computed at B3LYP/LanL2DZ (5 kcal mol À1 at B3LYP/ LanL2DZp) by Cioni et al. 33 Relative free energies. The relative free energies, enthalpies and entropies of the ground and transition states of the Co(NH 3 ) 5 NO 2 2+ isomers calculated at the uB97XD/6-31+G(d,p) theory level provided in Table 5 suggest that a direct transformation from nitro to exo-Co-ONO required more energy than that required for the transformation via the intermediate endo-Co-ONO. The energy difference between the activated complexes TS1 and TS3 is about 2.39 kcal mol À1 . endo-Co-ONO appears to be more structured (low relative entropy) than Co-NO 2 and exo-Co-ONO. The entropic energy differences can be associated with the strength of the hydrogen bonding in these systems. Overall, the entropy differences in these complexes are quite small ranging from 0.2 to 5 cal mol À1 and do not significantly affect the relative stabilities of Co-NO 2 and Co-ONO complexes and their transition states. Because of the large energy of the TS2 transition-state, the molecular conversion between nitro and endo-nitrito is predicted to be the slow step of the reaction and may determine the rate of the intramolecular The pathway (1) proceeds through the higher-energy transition state (TS1), but yields the lower-energy nitrito conformer (endo-Co-ONO) ( Fig. 6 and S5 †). The second pathway (2) leads through the lower-energy transition (TS2), but yields a relatively higher-energy nitrito conformer (exo-Co-ONO). Therefore, the pathways (1) and (2) of the interconversion of Co-NO 2 in exo-Co-ONO can be assumed to be respectively, the thermodynamically-favored and the kinetically-favored pathways (Fig. 6). TS4 and chelate structure (Fig. 1e) were also proposed as possible transition states. 11 Our calculations show that the former (TS4, i95 cm À1 ) requires $233 kcal mol À1 , while the chelate structure possesses several imaginary frequencies and relaxes towards TS2. However, the possibility of the reaction occurring via the TS4 state at standard conditions in gas phase is very low as the activation energy is too high. The reorientation of the NO 2 ligand slightly changes the magnitude of the dipole moments from 10D in Co-NO 2 to 11D in exo-Co-ONO (10D in endo-Co-ONO). With regards to the relative stabilities of linkage isomers, our results agree with previously reported experimental results, 17,18 and these can justify the reorientation of the NO 2 moiety in the [Co(NH 3 ) 5 NO 2 ]ClNO 3 isomer upon UV irradiation to form the exo-[Co(NH 3 ) 5 ONO]ClNO 3 isomer and the slow conversion of the less stable exo-[Co(NH 3 ) 5 ONO]ClNO 3 complex into [Co(NH 3 ) 5 NO 2 ]ClNO 3 in the dark. The fast conversion of endo-Co-ONO in the exo-Co-ONO conformer explains why the former has never been observed experimentally.
3.2.3 Chemical bonding analysis. In this section, we focus our analysis on the hydrogen bonding properties of the nitro and nitrito groups in Co-NO 2 and Co-ONO complexes, respectively, in an attempt to support their rank order of stabilities. Fig. 7 depicts the molecular graphs obtained from atoms in molecules (AIM) 86 analysis of Co-NO 2 and Co-ONO complexes. The molecular graphs of these complexes have bond critical points (bcps) between H and ONO that clearly show that nitro and nitrito are interconnected with ammonia through O/H-N and N/H-N intramolecular hydrogen bonds (IHBs), respectively. The electron densities and their Laplacians at different bcps in the three Co-complexes are given in Table 6   17.24 kcal mol À1 in exo-Co-ONO, Co-NO 2 , and endo-Co-ONO, respectively (Table 6); this indicates that intramolecular hydrogen bond strength increases in the following order: exonitrito < nitro < endo-nitro. The Co-O bond (NBO energy $ À1.00 kcal mol À1 ) is slightly more stable than the Co-N bond (NBO energy of À0.97 kcal mol À1 ). The stabilization energy E(2) associated with electron delocalization arising from the donor LPs of Co (d orbitals) to the acceptor Pi* of NO 2 is estimated about 7.01 kcal mol À1 while that arising from Co to Pi* ONO amount to be about 1 kcal mol À1 (0.93 kcal mol À1 in exo-Co-ONO and 0.68 in endo-Co-ONO) computed at B3LYP/6-31G(d). This result shows that NO 2 is a good pi* acceptor than ONO and is more favorable to pi*-back-bonding than the nitrito. Hence, the nitrito appears as a weaker pi electron acceptor than nitro. The latter can also explain the extra-stability of Co-NO 2 complex compare to Co-ONO complexes.
The difference in the electronic structure between Co-NO 2 , endo-Co-ONO and exo-Co-ONO is shown in Table S6. † The N-O Mayer bond order and electrons occupancies of Co-NO 2 and Co-ONO complexes are given in Table 7. The two N-O bonds in nitro have a 1.50 Mayer bond order, whereas in endo-Co-ONO, they are about 1.16 and 1.67 and are nearly 1.91 and 0.98 in exo-Co-ONO. These computed bond orders show that the electron density charge is delocalized over the two N-O bonds in Co-NO 2 giving both of them a partial double bond character, while the electron delocalization is diminishing in Co-ONO. The electronic density delocalization over N-O bonds diminishes the most when nitro is converted in exo-Co-ONO. These ndings suggest that the electron resonance in these complexes assists intramolecular hydrogen bonds and can justify the ranking relative stabilities of isomers. The electrostatic attraction between the Co and O atoms was proposed as driving force of the linkage isomerization due to the fact that the O atoms are rich in electrons than N in NO 2 ligand. 91,92 Fig. 8 shows the ELF   isosurfaces of nitro and nitrito complexes and their cut planes. The topologies of the molecular electron densities are similar, but a small difference can be noticed around ONO and NO 2 (Table S7 †). The N-H bond is of polar covalent type, while the bonds formed between Co and NH 3 are of dative type, as indicated by the orientation of the lone pairs of electrons located on N. The ELF and electron density Laplacian cut planes ( Fig. 8 and 9) clearly indicate the lone pair region of nitrogen and electron deciency in Co that enable the NH 3 donor ligand to form a dative bond.

Conclusion
The nitro-nitrito isomerization in Co(NH 3 ) 5 NO 2 2+ linkage isomers was investigated from a theoretical perspective using quantum chemical calculations at uB97XD/6-31+G(d,p), emphasizing on the structural, thermodynamic, and chemical bonding properties of the isomers. This isomerization is fundamental for a better understanding of the photo-salient effect in [(NH 3 ) 5 CoNO 2 ]ClNO 3 . The Bader theory based on the partitioning of electron density, the electron localization function, and natural bond orbitals were used for chemical bonding analysis. Our computational study led to the following conclusions: (a) The nitrito/exo-nitrito isomerization reaction is predicted to occur via the following reaction pathway:  (8) (b) The intramolecular conversion on the ground-state potential energy surface of Co-NO 2 between endo-Co-ONO and exo-Co-ONO complexes is kinetically controlled and that leading to the Co-NO 2 complex formation is thermodynamically controlled.
(c) O/H-N and N/H-N intramolecular hydrogen bonds, orientation of the atoms of the ONO group, and the difference in Co-N and Co-O bond energies are identied as key factors determining the relative stabilities of the Co-NO 2 and Co-ONO linkage isomers.
(d) Co(NH 3 ) 6 3+ is less stable compared to Co(NH 3 ) 5 NO 2 2+ and undergoes a slight geometry distortion from D 3d to D 3 characterized by a PJTE of 741 cm À1 at uB97XD/6-31+G(d,p) (750 cm À1 at CCSD(T)/6-31+G(d,p)). It is worth noting that the hydrogen can freely rotate to keep the high octahedral symmetry. The photo-isomerization of the [Co(NH 3 ) 5 NO 2 ] 2+ complex is currently under investigation in our lab to determine the role of conical intersection and excited states in the UV-initiated intramolecular conversion of [Co(NH 3 ) 5 NO 2 ]NO 3 Cl.

Conflicts of interest
The authors declare that they have no conict of interest.