On the structure of the P-iodo-, bromo- and chloro-bis(imino)phosphoranes: A DFT study

2.1 Monomers

The principal aspects of bonding in (monomeric) bis(imino)phosphoranes of the type 1 and their related bis(methylene)phosphoranes were discussed some time ago [12], [13], [14]. The trigonal planar phosphorus system forms a π system with a concomitant weak tendency for pyramidalization at the central phosphorus atom [13]. For the amino derivative, 1, R=N(SiMe₃)₂, R′=SiMe₃, a Z/Z conformation for the substituents at the imino-nitrogen atoms has been experimentally found [15], [16]. A summary of the NMR data of bis(imino)phosphoranes was presented too, as skillfully compiled in the report of Gudat et al. [17]. The quantum chemical calculations predict [12], [13], [14] exclusively a Z/Z conformation, in agreement with experiment. It was attributed to the bulk of the amino substituents R′=(N(SiMe₃)₂), which exert steric hindrance with respect to the substituents R at the imino substituents.

The situation is different for the P-halogeno compounds 1 (R′=I, Br, Cl; R=alkyl, aryl). These compounds are highly unstable, in particular to Lewis bases; e.g. the bromo compound reacts readily with 4-dimethylaminopyridine (4-DMAP) to give a stable donor-acceptor complex which loses the halogen atom in the second stage of the reaction [18].

A priori a halogen atom (I, Br, Cl) at the trigonal phosphorus center is much smaller in size and could allow various possible conformations for 1. To reveal this aspect more closely we first performed density functional calculations (DFT) on a selected variety of differently substituted bis(imino)phosphoranes, with basis sets of triplet-ζ quality (RI-BP86/def2-TZVP-D3).

The analysis is started with a discussion of monomers 1 with R=alkyl, aryl and R′=I, Br, Cl. These were probed in all possible conformations, E/E, E/Z and Z/Z. The results of the DFT calculations for the iodo-compounds are collected in Table 1. We studied small substituents (R=H, CH₃, CF₃, phenyl) as well as sterically more demanding aryl substituents, R=2,6-dimethyl-C₆H₃ (Mes), 2,6-di-iso-propyl-C₆H₃ (Dip), 2,6-di-tert-butyl-C₆H₃ (Sume) and 2,6-diphenyl-C₆H₃ (Terph)) for the various conformations. The various substituents were solely placed at the 2- and 6-positions of the phenyl rings. In previous experiments [4], [5], however, alkyl substituents were located at the 4-position as well. In a later section of this report it will be shown that the bulky substituents at the 4-position play a decisive role for the stability of the resulting stack structures. A Terph substituent at bis(imino)phosphoranes and related bis(methylene)phosphoranes is hitherto unknown.

In contrast to P-amino substituted bis(imino)phosphoranes, the monomeric P-iodo compounds 1 (R′=I) are predicted to possess stable E/E as well as Z/Z conformations, at least for the small substituents at the nitrogen atoms (CH₃, CF₃, Ph, Mes). However, the energy differences between the various conformations are small, with the E/E conformations for these cases being the most stable (Table 1). The tendency for an E/E conformation becomes more attenuated if the substituents R increase in bulkiness (R=Mes<Dip<Sume<Terph). Finally, for the sterically more demanding substituents only an E/E conformation could be traced by the DFT calculations. Starting with a Z/Z conformation, rearrangement to the E/E conformer occurs without any energy barrier. In the cases where both conformations are stable (R=H, CH₃, CF₃, Ph, Mes), the I–P distances result slightly shorter in the Z/Z than in the E/E conformations.

Hitherto the results of the investigations were limited to the Iodo compound 1. For analogous structures with Br or Cl at the phosphorus atom the results are similar and are not further recorded here. The most relevant geometry parameters of the equilibrium geometries are collected in Table 1. For the derivatives with bulky substituents the equilibrium coordinates are given in the Supporting Information.

The low stability of the P-halogeno-bis(imino)phosphoranes is also witnessed by (relatively) small differences between the lowest energy adiabatic singlet (S) and triplet (T) states. The following S–T differences (in kcal mol⁻¹) emerge from the DFT calculations (RI-BP86/def2-TZVP-D3): (a) 1, R′=I, R=Sume, 23.1, (b) R′=Br, R=Sume, 22.6, (c) R′=Cl, R=Sume 23.0 kcal mol⁻¹, as compared with the amino-substituted (R′=NMe₂, R=TMS (trimethylsilyl) bis(imino)phosphorane with a S–T difference of 49.7 kcal mol⁻¹. The equilibrium geometries of the various structures for their singlet and triplet states are again collected in the Supporting Information.

2.2 One-dimensional stack formation

There is one aspect which makes up an electronic difference between P-amino and P-halogeno substituted bis(imino)phosphoranes. The iodo-bis(imino)phosphorane 1 (and the analogs with Br and Cl in the E/E conformation) possesses a set of nonbonding orbitals at iodine (Fig. 1). These are in (p_x and p_y) or orthogonal (p_z) with respect to the xy plane, as it is schematically sketched in Fig. 1a. The lone pairs at the imino nitrogen atoms (Fig. 1b) form a positive (n₊) or negative (n₋) combination of hybrid orbitals. Pendant to the latter are the antibonding orbitals (n+*) and (n−*). Thus, the bonding combination of orbitals refers to the hybrid orbitals at the nitrogen centers, while their antibonding counterparts point in the opposite direction.

Fig. 1:

Schematic mutual orbital interactions of two iodo-bis(imino)phosphoranes. (a) lone pair orbitals at I; (b) nonbonding and antibonding combinations of hybrid orbitals at the nitrogen atoms; (c) polarization of the nonbonding N···I bond in a dimer (I)···(II).

In contrast to the P-amino-substituted bis(imino)phosphoranes the P-halogeno compounds can mutually interact with a second entity, as it is schematically shown in (C). A mixing of the p orbitals at (I) with the hybrid orbitals at the nitrogen atoms can take place. The consequences emerge from one-electron second-order perturbation theory [19]: (a) The p_x orbital of one unit (I) (see Fig. 1c) interacts with the positive (n₊) lone pair combination of the other unit (II) forming a bonding (p_x+n₊) or antibonding (p_x–n₊) set of molecular orbitals. Similarly, the p_y orbital at unit (I) interacts with the negative (n₋) lone pair combination of unit (II). In both cases a doubly occupied orbital interacts with another doubly occupied orbital, which contributes no net energy to the overall bonding situation. In more detail, such a bonding situation may even be considered as slightly repulsive [20]. (b) An interaction of the p_x,y orbitals of (I) with the antibonding set of orbitals n+*,n−* of (II) is not feasible because there is no suitable overlap. (c) The situation changes when one considers the polarization of the more electropositive iodine (I) with the more electronegative nitrogen atoms. It originates from a concomitant mixing in of an antibonding n^* orbital into the bonding orbital (n) and causes rehydridization at the nitrogen atoms in (II). The overall p character of the orbitals at the nitrogen atoms in (II) is enhanced while that one at the iodine atoms in (I) is depleted. The effect is similar as the polarization of a π bond by donating substituents [20].

This analysis based one-electron perturbation theory has two consequences: (a) an electrostatic attraction between monomeric units (I) and (II), which should be weaker than a two-electron two-center bond. (b) The more, additional monomeric units can be added, following the same polarization mechanism and finally forming an infinite chain. The 1D-chain formation via a polarization mechanism may be contrasted to the formation of band structures in which continuous orbital overlap occurs [21].

All calculations, which are recorded in the following are in conformity with these considerations: (a) no bonding is traced between the nitrogen atoms and iodine, (b) p-electron density is transferred to the more electronegative nitrogen atoms.

How large then are the bond energies for stacking? A first answer to this question follows from an analysis of the stacking as a function of the size of the units. A linear stacking of monomers as functions of the numbers of parent iodo-bis(imino)phosphoranes was calculated upon optimization (C_2v imposed), assuming an E/E conformation of the substituents R.

The mean energy per bonded unit in the one-dimensional stack (E/n, n=number of monomeric units) is plotted in Fig. 2. It increases with increasing number of units and reaches an average of appr. –5 kcal mol⁻¹. In other words, further increase of the chain does not considerably alter the average bonding interaction. It constitutes a rather weak bonding interaction for the stack formation.

Fig. 2:

Average energy (ΔE=E/n) in kcal mol⁻¹ for a stacking array (RNP(I)NR)_n, R=H as function of increasing length of the chain, n=1 to 20, RI-BP86/SVP-D2 level.

The average attraction energy increases via mutual polarization of the units. As rationalized in the qualitative discussion before, it causes a depletion of p-electron density at iodine with concomitant shortening of the P–I bond, via an increase of the s character of the P–I bond. The bond shortening is largest in the center of the chain (≤10%) but becomes smaller in the peripheral regions.

Interestingly the simple rationale of the polarization mechanism for the iodine compound is based on one-electron considerations and should hold true also for analogous the Br and Cl compounds. Following the same methodology, the DFT calculations predict for n=20 an average bonding interaction energy of –2.6 (Br) and –1.8 (Cl) kcal mol⁻¹. It is in conformity with the fact that Br and even Cl are more electronegative and hence less polarizable than I.

For the present modeling of the chain we have chosen as substituent R=H, which yields information on the mere electronic effects, that govern the linear array formation.

2.3 Importance of van der Waals forces

Interactions among bulky substituents can be repulsive or attractive. A pertinent example for the latter is the dimerization equilibrium of the AlNacNac carbene analog to an Al–Al bonded dimer (Scheme 2).

Scheme 2:

Dimerization equilibrium of the AlNacNac compound.

DFT-D calculations predict association of two monomers to a bound Al–Al dimer [22]. For R=2,6-trimethyl-C₆H₄ an attraction of the substituents is calculated which stabilizes the weak Al–Al bond. Can such considerations hold true equally well in the present case?

A priori the bonding energy resulting in dimerization can be partitioned simply in an electronic energy part E_el plus the noncovalent intermolecular attraction E_disp of the substituents R, eq. (1).

The propagation energy for the growing process of the chain refers to eq. (2).

The contribution in eq. (1), E_el, refers in first-order to the electrostatic interaction of the monomeric units and can be evaluated by considering a chain with sterically “small” substituents (R=H, methyl for R, see Fig. 1). The contribution E_disp varies with the steric demand of the substituents R to exert repulsive or attractive forces among the substituents. A quantitative estimate is given by the overall bond energy for the formation of a dimer as a function of different substituents. Alternatively, eq. (2) yields an estimate for the propagation of the chain, i.e. the energy profit by adding a monomer to the already formed stack.

According to the electrostatic bonding interactions a linear geometrical arrangement of the P-halogeno (I, Br, Cl) units is expected, which is also in agreement with the linear stack formation observed in the experiment. Hence C₂ symmetry was adopted within further energy optimization of the structures. First, we probed the various substituent effects on dimerization. The energies [eq. (2), n=2] which were obtained (RI-BP86/def2-TZVP-D2[D3]) are listed in Table 2. Overall, the dimerization energies are exothermic.

As noted above the dimerization energies were calculated with post-density functional theory damped dispersion corrections (DFT-D). Two corrections were utilized, the D2-level and D3-level [11] [values in brackets]. Both correction procedures yield similar trends, albeit the obtained values are different in magnitude.

In agreement with the discussion above a methyl substituent does not appreciably affect the dimerization energy. It contributes almost to the same extent as R=Tbu and Ph. The effect changes for R=Mes and considerably for R=Mes*, Sume* and becomes even larger for the phenyl- instead of alkyl-substitution at the benzene ring, i.e. for R=Terph and Terph*. For convenience we have differentiated here between aryl substitution at 2,6-positions and at 2,4,6-positions. The latter types are marked with an asterisk (Mes*, Sume*, Terph*). The dimerization energies increase with the bulkiness of the substituents at the 4-positions of the phenyl rings.

Is it possible to give a simple rationale for these facts? An evaluation of dispersion interactions [23] by highly electron correlated ab initio calculations has been reported for a variety of cases, e.g. benzene-benzene interactions [24], benzene-hydrogen bonding [25], and interactions between alkane chains [26]. An important parameter for an estimation of the steric attraction is the distance between the substituents. For the case of 1 R=Ph, it is larger than 600 pm, while dispersion interactions require a H–H or H–benzene distance of 280–320 pm, as witnessed from accurate benchmark calculations [23], [24]. Consequently, contributions from steric attractions are small, in agreement with the values obtained from the calculations (Table 2). The situation changes when alkyl substituents (methyl<tert-butyl) are added to the 2.6-positions and even more so by addition to the 4-position (Mes*, Sume*, Terph*). The effect is even more pronounced for the phenyl-substituted cases Terph and Terph*, in accord with the (relatively) strong tendency for benzene dimerization [24].

The calculations (Table 2) also predict sizable dimerization energies for P-bromo- and P-chloro-bis(imino)phosphoranes. Hitherto, structures of these species have not been experimentally characterized, due to the high reactivity of these species. The bonding situation for R=Sume* is shown in Fig. 3. For the bromo and chloro compounds the bulky substituents come closer to each other, which finds a rationale in the enhanced attraction energy (Table 2). A pictorial representation of the bulky dimer (I)₂, R=Sume*, is shown in Fig. 3 for the iodo (left) and bromo derivative (right). The enforced closer proximity of the stacking units enhances the dispersions interactions for the latter case.

Fig. 3:

Relevant bond lengths (in pm) of dimers (I)₂, R=Sume*: I(Br)–P 248.8 (226.5) [exo], 244.9 (223.8) [endo], PP 623.3 (603.4), left iodo compound, right bromo compound. Top=representation with van der Waals size, low=representation with ball and stick models.

Finally, the understanding of the one-dimensional array is completed by a study of the growing process. It was performed up to n=5, relying on the results with a lower, less elaborate basis set (RI-BP86/SVP-D2). The results are shown schematically in Fig. 4.

Fig. 4:

Propagation energies according to eq. (2) (–ΔE, in kcal mol⁻¹) for the substituents R=Me, Mes and Sume*.

The investigations confirm the previous considerations about the dimerization energies. In more detail, the energies obtained for the chain propagation up to n=5 reveal almost constant energy progression. This indicates that the dispersion energies are to first-order pair-wise additive [24], i.e. the larger part of the dispersion interactions stems from the neighboring units rather than the units further apart. A pictorial representation of the optimized structures is given in the Supporting Information.