2.1 Chemistry

The synthesis of compound 1 was reported in references [10] and [11].

2.2 NMR

Solution NMR spectra were recorded on a Bruker DRX 400 (9.4 Tesla, 400.13 MHz for ¹H, 100.62 MHz for ¹³C, 161.96 for ³¹P) spectrometer with a 5-mm inverse-detection H–X probe equipped with a z-gradient coil, at 300 K. Chemical shifts (δ in ppm) are given from internal solvent, CDCl₃ 7.26 for ¹H and 77.0 for ¹³C; for ³¹P NMR 85% H₃PO₄ (0.0) was used as the external standard. Coupling constants (J in Hz) are accurate to ± 0.2 Hz for ¹H and ± 0.6 Hz for ¹³C and ³¹P, respectively.

Solid state ¹³C (100.73 MHz), ³¹P (162.16 MHz) and ¹⁵N (40.60 MHz) CPMAS NMR spectra have been obtained on a Bruker WB 400 spectrometer at 300 K using a 4 mm DVT probehead. Samples were carefully packed in a 4-mm diameter cylindrical zirconia rotor with Kel-F end-caps. Operating conditions involved 3.2 μs 90° ¹H pulses and decoupling field strength of 78.1 kHz by TPPM sequence. ¹³C spectra were originally referenced to a glycine sample and then, the chemical shifts were recalculated to the Me₄Si [for the carbonyl atom δ (glycine) = 176.1 ppm], ³¹P spectra to (NH₄)₂HPO₄ (AHP) and ¹⁵N spectra to ¹⁵NH₄Cl and then converted to nitromethane scale using the relationship: δ ¹⁵N (MeNO₂) = δ ¹⁵N(NH₄Cl) – 338.1 ppm. Typical acquisition parameters for ¹³C CPMAS were: spectral width, 40 kHz; recycle delay, 5 s; acquisition time, 30 ms; contact time, 2 ms; and spin rate, 12 kHz. In order to distinguish between protonated and unprotonated carbon atoms, the NQS (non-quaternary suppression) experiment by conventional cross-polarization was recorded; before the acquisition, the decoupler is switched off for a very short time of 25 μs [13,14]. Typical acquisition parameters for ³¹P CPMAS were: spectral width, 100 kHz; recycle delay, 5 s; acquisition time, 30 ms; contact time, 2 ms; and spin rate, 10 and 12 kHz. Typical acquisition parameters for ¹⁵N CPMAS were: spectral width, 40 kHz; recycle delay, 5 s; acquisition time, 35 ms; contact time, 6 ms; and spin rate, 6 kHz.

2.3 Computational details

The geometry of the systems has been optimized at the MP2 computational level [15] with the aug′-cc-pVTZ basis set [16]. This basis set is derived from the Dunning aug-cc-pVTZ basis set by removing diffuse functions from H atoms. The absolute chemical shielding and coupling constants of the systems have been calculated with the GIAO method [17] at the B3LYP/aug′-cc-pVTZ level [18]. The Gaussian-09 program has been used for these calculations [19].

The electronic properties of the system have been analyzed through molecular electrostatic potential (MEP), electron density [20], electron localization function (ELF) [21] and natural bond orbitals (NBO) [22] measurements. The MEP has been calculated with the Gaussian-09 program and has been represented on the 0.001 au electron density isosurface with the WFA program [23]. This program has been used to analyze the local minima and maxima of the MEP on the surface. The topological analysis of the electron density has been carried out with the AIMAll program [24]. The topological analysis of the electron density provides the critical points of this property. AIM permits to define the molecular graph of the investigated systems as the ensemble of maxima of the electron density, ρ, associated with the position of the nuclei, saddle points, in which ρ, has two negative and one positive curvatures, the so-called bond critical points (BCPs) and the zero gradient lines connecting them, or bond paths. The ELF function allows to detect those region where the electrons are more concentrated. Thus, information of the characteristics of the different types of bond and lone pair are easily obtained. The ELF function has been calculated with the Topmod program [25]. The natural bond orbital (NBO) method has been used to obtain atomic charges and to analyze the orbital charge transfer between the interactions molecules. The NBO-3 program has been used for these calculations [26].

3.1 NMR spectroscopy

In NMR, using CDCl₃ as solvent, monomer 1 is characterized by the data reported in Table 1.

Our attempts to add more data to Table 1 mostly failed: the ¹⁵N chemical shifts cannot be measured probably because the signal is a doublet (²J_PN) without near H atoms. Moreover, ²J_PN cannot be measured on the ¹⁵N satellites of the ³¹P signal because the coupling is buried inside the central peak. In our hands, the ³¹P NMR signal appears at –52.5 ppm instead of –54.7 ppm [10] (a concentration effect, calculated for the monomer –61.7 and for the dimer –60.3 ppm) and its ¹³C satellites corresponds to a ¹J_CP = |83.0| (Fig. 2). An isotope effect of 0.05 ppm (8.1 Hz) between ³¹P–¹²C and ³¹P–¹³C is also observed in Fig. 2. The ²J_NP coupling constant of 18.9 Hz (calculated, Table 2) is lost under the central peak. Since the ¹H decoupling was not complete, the lateral peaks due to ²J_HP = 42.0 Hz coupling were observed, where these peaks are split by the ⁴J_HP = 3.6 Hz (in principle, a septuplet, but only the three central lines were observed).

Then, we calculated theoretically the chemical shifts and coupling constants of 1 (Table 2). The calculations correspond to geometries optimized at the MP2/aug′-cc-pVTZ. On these optimized geometries, we carried out GIAO and SSCC calculations at the B3LYP/aug′-cc-pVTZ level [for references, see Section 2.3].

The calculations afford absolute shieldings (σ, ppm). To transform them into chemical shifts, we have used empirical equations established with many compounds of the largest diversity for GIAO/B3LYP/6-311++G(d,p) calculations. It is important to note that solvent effects are included in these equations since they have been obtained by comparing calculated values in the gas phase with experimental values in solution. Using data of nitriles and isonitriles [27], we have calculated the equation for the ¹⁵N chemical shifts of these compounds.

These equations are probably different for B3LYP/aug′-cc-pVTZ calculations but allow us to compare different calculations and, for some nuclei, are rather good. For instance, the experimental chemical shifts of compound 1 in CDCl₃ (Table 1) are well correlated with the calculated values of Table 2.

Comparing the values for 1 and 2, we note that the methyl groups at positions 3 and 4 exert a small influence on the coupling constants, the most affected being ¹J_CP (difference 10.8 Hz).

Both the chemical shifts and SSCC of 1 are acceptably calculated, the worse result concerns ¹J_CP is calculated to be –97.2 (experimental 83.0 Hz) and –8.4 Hz (experimental < |2| Hz). Thus, we have calculated the SSCC of the dimer (Table 3) to see if the value of ^1pJ_PP was experimentally attainable.

Using all the available data from the monomer and the dimer, the following equations are obtained:

δ_exp = (1.6 ± 1.2) + (0.977 ± 0.012) δ_{calc (minimum)}, n = 13, R² = 0.998, predicted, ¹⁵N (Table 1) –78.7

δ_exp = (1.1 ± 1.2) + (0.984 ± 0.012) δ_{calc (X-ray)}, n = 13, R² = 0.998, predicted ¹⁵N (Table 1) –79.7

Both equations are very similar even for the predictions for the missing value of the monomer in Table 1.

Concerning dimer 1₂, if we compare the calculations based on the minimum and on the X-ray geometry, only ^2pJ_CP (1.8 factor) and ^1pJ_PP (1.6 factor) are affected. Comparing 1 with 1₂ and 2 with 2₂ (X-ray P···P distance), the most affected SSCC is ¹J_CP of the CH that decrease to a half (from about –9 to about –4 Hz). The most important result of Table 4 is the sensitivity of the couplings through the pnictogen bond: ^2pJ_CP from +17.5 to +9.7 Hz and ^1pJ_PP from +163.2 to +101.8 Hz.

The ¹³C experimental results are shown in Fig. 3 (normal) and Fig. 4 (NQS), while the ³¹P CPMAS spectrum is depicted in Fig. 5.

For determining the ^1pJ_PP in the solid state of the dimer of 3,4-dimethyl-1-cyanophosphole (1), two situations are possible:

• • the symmetry is lifted in the solid state, in spite of the high symmetry obtained by X-ray crystallography (C_2h). In this case, the ³¹P CPMAS spectrum contains two signals. If J_P···P is larger than the line width, then one could see an AX or AB spin system and hence, J_P···P. That being the easiest case;
• • the symmetry is not lifted in the solid state.

Methods used to measure J_P···P:

• • the ³¹P spectrum shows only a single signal (Fig. 5). Under MAS conditions, it is difficult to measure J_P···P. However, by single crystal ³¹P NMR it would be possible [31] because due to the chemical shift anisotropy, the two ³¹P will not be chemically equivalent for many different orientations. Unfortunately, single crystals of 1 of suitable size for NMR studies [31] cannot be prepared;
• • another possibility is to try the use of the ¹³C satellites in ³¹P NMR. ³¹P near ¹²C and ¹³C have different chemical shifts, but the difference might be small;
• • a better approach would be to analyze the ¹³C signal of the cyano group, and proceed in a similar way as some of us do previously, using ¹⁵N labeled samples [32].

We tried the second method but as it can be seen in Fig. 5, no ¹³C satellites were observed. Taking into account that the full width at half maximum (WHM) is about 140 Hz and that the calculated values for ^1pJ_PP are ∼102 Hz (X-ray geometry) and ∼163 Hz (minimum geometry), it is not surprising that this approach failed. Then, we tried the third method. In Fig. 4, three signals were observed near 120 ppm: 120.1 ppm corresponds to a residual of the C2, C5 CHs (120.25 ppm in Fig. 3) and 119.1 and 117.4 ppm corresponding to the CN (118.25 ppm in Fig. 3, note that they are apparent in the spinning-side band near 0 ppm). The signal at 119.1 ppm is more intense than that at 117.4 ppm, but this may be due to overlapping with the 120.1 ppm signal; these signals are separated by 169.5 Hz. This cannot be due to the ¹J_CP because for the monomer its values are 83.0 (experimental, Table 1) and –97.2 Hz (calculated, Table 2) and for the dimer they are –96.0 (calculated, Table 4, minimum geometry) and –94.4 Hz (calculated, Table 4, X-ray geometry). Therefore, this “apparent” doublet is the X part of an AA′X system (A ³¹P–¹²C, A′ ³¹P–¹³C and X ¹³C). The difference between A and A′ can be estimated to be Δν ∼ 8 Hz (from the monomer), J_A′X = –80/–85 Hz, J_AX = 10/20 Hz and J_AA′ = 100/160 Hz. But lacking the small transitions of the X part of an AA′X system, it was not possible to carry out an analysis of the spin system to ascertain the values of these couplings.

3.2 Theoretical results

3.2.1 Monomers

It has been shown in the literature that in most weak interactions complexes, the electrostatic term is the most important one [33]. In the case of the pnictogen interactions, the presence of an electronegative group bonded to the P atom generates a region of positive charge, named in the literature as σ-hole [34]. This σ-hole interacts with an electron-rich region, such as a lone pair. In the case of symmetrical P···P interactions, two simultaneous σ-hole:lone pair interactions can be found.

In the systems studied in this paper, the cyano group generates a σ-hole with a value of 0.017 and 0.022 au, for 1 and 2, respectively (Fig. 6).

3.2.2 Dimers

Two minima, A and B, have been found in the optimization of 1₂ and 2₂ dimers in gas phase. In the case of 1, the most stable one B corresponds to two P···π pnictogen bond (E_i = –46.4 kJ mol⁻¹). This value of Ei is considerably higher that the stronger Ei reported in the introduction (–35 kJ mol⁻¹). The disposition of the monomers within the dimers studied could favor some extra stabilization similar to the π–π stacking found between aromatic rings.

The second minima (E_i = –37.1 kJ mol⁻¹) is analogous to the one found in the crystal structure and present a P···P pnictogen bond. In the case of 2, the relative stability of the two dimers is reversed and the one with a P···P interaction shows a stabilization energy of –29.8 kJ mol⁻¹ while the one with P···π contacts corresponds to –27.2 kJ mol⁻¹.

The intermolecular P···P distances in 1₂ and 2₂ are 3.21 and 3.19 Å, which is approximately 0.2 Å shorter than the distance found in the solid phase. Fixing the intermolecular distance to that in the solid phase, the interaction energies of the dimers obtained are only 1.4 and 1.1 kJ mol⁻¹ less stable, respectively, than the dimers without restrictions.

The topological analysis of the electron density (Fig. 7) shows a P···P bond for the dimers analogous to the one found in the solid phase and two P···π for the alternative dimer and interactions between the heterocyclic rings. In the case of 1₂, some additional interactions between the methyl groups and the P atoms are also found.

The NBO analysis shows two degenerate orbital interactions between the lone pair of the P atom of one molecule and the σ* P-C of the other one in the A dimers (12.0 and 14.1 kJ mol⁻¹ for 1₂ and 2₂, respectively) while in the B dimers, the charge transfer between intermolecular orbitals are very small (less than 2.5 kJ mol⁻¹).

The representation of the ELF (Fig. 8) shows that the lone pair of the P atoms of one molecule is located in the extension of the NC-P bond of the other molecule, where the σ-hole generated by the NC-P bond should be located.

For the B dimers, the σ-hole points toward the centre of the C3–C4 bond of the phosphole.