*3.1. Geometries of the B*··· *CO2, B*··· *N2O, and B*··· *CS2 Complexes*

Molecular diagrams showing the equilibrium geometry (drawn to scale) of each member of the B··· CO2 series, where B = CO, HCCH, H2S, HCN, H2O, PH3, and NH3, are shown in Figure 3. The calculated (equilibrium) intermolecular distances are recorded in Table 1, together with their experimental counterparts (where the latter are available). The experimental distances were determined from microwave or high-resolution infrared spectroscopy conducted on supersonically expanded gas mixtures composed of the two component molecules diluted in an inert gas. The molecular shapes and intermolecular distances are, in each case, in reasonable agreement with those from experiment. It should be noted that the experimental distances are, in most cases, of the *r*<sup>0</sup> type, but are corrected for the contributions of the angular oscillations of the two components to the zero-point motion. There is no correction for the intermolecular radial contribution, however, and this normally leads to *r*<sup>0</sup> distances that are greater than the calculated equilibrium values. For the very floppy molecules considered here, the *r*<sup>0</sup> values are greater by the order of 0.05 to 0.1 Å.


**Table 1.** Calculated and observed intermolecular distances in B··· CO2 complexes.

*<sup>a</sup>* See Figure <sup>3</sup> for the molecular diagrams (to scale) of the B··· CO2 complexes. *<sup>b</sup>* Reference [14]; *<sup>c</sup>* Reference [17]; *<sup>d</sup>* Reference [15,16]. *<sup>e</sup>* The distance reported here is the *<sup>r</sup>*<sup>s</sup> value from Reference [39]; *<sup>f</sup>* Reference [20]; *<sup>g</sup>* Reference [19]; *<sup>h</sup>* Reference [18].

**Complex Intermolecular Distance/Å (Obs.** *<sup>−</sup>* **Calc.)/Å Calculated Ab Initio** *<sup>a</sup>* **Observed** OC··· N2O *<sup>r</sup>*(C··· Ncenter) = 3.176 3.36(1) *<sup>b</sup>* 0.18 HCCH··· N2O *<sup>r</sup>*(πcenter··· Ncenter) = 3.201 3.296 *<sup>c</sup>* 0.095(1) HCN··· N2O (T-shaped) *r*(C··· Ncenter) = 3.002 ··· ··· HCN··· N2O (parallel) *<sup>r</sup>*(C··· Ncenter) = 3.271 3.392 *<sup>d</sup>* 0.121 H3N··· N2O *<sup>r</sup>*(N··· Ncenter) = 3.021 3.088 *<sup>e</sup>* 0.067 H2O··· N2O *<sup>r</sup>*(O··· Ncenter) = 2.855 2.97(2) *<sup>f</sup>* 0.11(2) H2S··· N2O *r*(S··· Ncenter) = 3.444 ··· ··· H3P··· N2O *r*(P··· Ncenter) = 3.479 ··· ···

**Table 2.** Calculated and observed intermolecular distances in B··· N2O complexes.

*<sup>a</sup>* See later for the molecular diagrams (to scale) of the B··· N2O complexes. *<sup>b</sup> <sup>r</sup>*<sup>s</sup> value estimated from data in Reference [24] is almost certainly an overestimate, as *<sup>b</sup>*<sup>N</sup> is very small, and therefore, severely underestimated. *<sup>c</sup>* References [26,27]; *<sup>d</sup>* Reference [25]; *<sup>e</sup>* Reference [29]; *<sup>f</sup>* Reference [28].

It is clear from Figure 3 that the intermolecular bond is a tetrel bond in the sense that it involves the electrophilic region around C (the blue band that surrounds the C atom in the MESP of CO2 shown in Figure 1) and either a non-bonding electron pair or a π-bonding electron pair as the nucleophilic site of the Lewis base B. In fact, the axis of the non-bonding electron pair coincides with the extension of the radius of the circle that defines the most electrophilic band around C in each of OC··· CO2, HCN··· CO2, H3N··· CO2, and H2S··· CO2, given that the n-pairs on S in H2S lie at ~±90◦ to the plane of the H2S nuclei, as established from earlier work on H2S··· HX and H2S··· XY (X and Y are halogen atoms) [9,40]. The fact that the ab-initio-derived configuration at O in H2O··· CO2 is planar is not inconsistent with this conclusion. It was found for all H2O··· HX and H2O··· XY [9,40] investigated through rotational spectroscopy and/or ab initio calculations that, although the equilibrium configuration at O is non-planar, the barrier to planarity is low and lies below the zero-point energy level in most cases. The configuration is, therefore, rapidly inverting in the zero-point state and the molecule is effectively planar. For an interaction as weak as that in H2O··· CO2, the barrier will probably be non-existent, as it is in H2O··· F2 [41], for example. Some rules put forward originally for hydrogen-bonded complexes B··· HX [9] and halogen-bonded complexes B··· XY [40] can be easily modified to allow the geometries of the tetrel-bonded complexes shown in Figure 3 to be predicted. Thus, the modified rules become:

**Figure 3.** Molecular models drawn to scale of the geometries of B··· CO2 complexes calculated at the CCSD(T)/aug-cc-pVTZ level of theory, where B = CO, HCCH, HCN, NH3, H2O, H2S, and PH3 (**a**–**g**, respectively). Not shown is the linear, hydrogen-bonded isomer CO2··· HCN, which is 1.5 kJ·mol−<sup>1</sup> higher in energy than the form in ©.

*The equilibrium geometry of tetrel-bonded* B··· CO2 *complexes can be predicted by assuming that a radius of the most electrophilic ring around the* C *atom of* CO2 *coincides with either (1) the axis of a non-bonding electron pair carried by* B*, or (2) the local symmetry axis of a π-bonding electron pair of* B.

That is, in the original rules, "hydrogen-bonded complexes B··· HX" is replaced by "tetrel-bonded complexes B··· CO2", and "the axis of HX" is replaced by "a radius of the most electrophilic ring around the C atom of CO2".

The case of H3P··· CO2 appears to be an exception to the rules, because the intermolecular bond does not lie exactly along the *C*<sup>3</sup> axis of phosphine. The reason for this becomes clear when the MESP of phosphine, shown in Figure 4, is examined. Approximately opposite the extension of each P–H bond is an electrophilic (blue) region which can interact with the nucleophilic (yellow-green) band around O of CO2 (see Figure 1). This secondary interaction is, in fact, a pnictogen bond, and it is responsible for the distortion found in Figure 3g.

**Figure 4.** Molecular electrostatic surface potentials (MESPs) for phosphine calculated for the 0.002 e/bohr3 iso-surface at the MP2/6-311++G\*\* level. The surface in the right-hand diagram is cut away to reveal both the electrophilic (blue) regions near P on approximately the extension of the H–P bonds, and the nucleophilic (red dot) region on the *C*<sup>3</sup> axis.

The molecular geometries calculated ab initio for the corresponding B··· N2O series are illustrated in Figure 5, and each has a similar, but not identical, shape to that of the corresponding member of the B··· CO2 series, with the central N atom of N2O acting as the primary electrophilic site. The lower symmetry of N2O compared with that of CO2 means, however, that the B··· N2O complexes necessarily have lower symmetry and that secondary interactions become more important. The geometries shown in Figure 5 can be understood in terms of the rule set out in the preceding paragraph, that is, with the primary interaction involving the electrophilic (blue) band on the central N atom of N2O with the n-pair or π-pair on the Lewis base B, but modified to allow a secondary interaction of the electrophilic region of B (i.e., C or H of HCN, H of HCCH, H of NH3, H of H2O, H of PH3, or H of H2S) with the nucleophilic region at O in N2O (see Figure 1, end-on view).The conclusions for B··· CO2 and B··· N2O are, therefore, consistent with the previously noted similarity of the MESPs of CO2 and N2O displayed in Figure 1. The molecular shapes shown in Figure 5 correspond closely to those that are available experimentally (see Reference [3] for a convenient collection of experimentally determined shapes). The ab initio and experimental (where available) intermolecular distances for each B··· N2O complex are included in Table 2.

Two geometries are given for HCN··· N2O in Figure 5. Both correspond to minima in the energy, but are separated in energy by only 0.03 kJ·mol−<sup>1</sup> at the CCSDT(T)/aug-cc-pVTZ level of theory and 0.45 kJ·mol−<sup>1</sup> at the CCSD(T)/CBS level, with the parallel form (Figure 5c) lower in energy than the nearly perpendicular form (Figure 5b) in both cases. It is of interest to note that Miller and co-workers [25] found two isomers of this complex in their investigation of the high-resolution infrared spectrum of (N2O, HCN) in a supersonically expanded gas mixture of the components diluted in helium. One was a parallel form (four such arrangements of N2O and HCN were consistent with their observed rotational constants, including that found here by ab initio calculation), while the other was a hydrogen-bonded, linear isomer N=N=O··· HCN; however, these authors did not observe the T-shaped isomer shown in Figure 5b. Our calculations at the CCSD(T)/CBS level find the linear, hydrogen-bonded form N=N=O··· HCN to be higher in energy than the parallel isomer by 1.5 kJ·mol<sup>−</sup>1. This observation suggests that, while the T-shaped isomer relaxes to the parallel form in

the supersonic expansion, the higher-energy, hydrogen-bonded, linear isomer does not. Both linear, hydrogen-bonded [39,42] and T-shaped, tetrel-bonded [15,16] isomers of (CO2, HCN) were observed experimentally. At the CCSD(T)/CBS level, O=C=O··· HCN is found to be 1.3 kJ·mol−<sup>1</sup> higher in energy than the T-shaped isomer, in agreement with the experimental conclusions.

We emphasized in the introduction that the MESP of carbon disulfide is different from those of CO2 and N2O in that the most electrophilic (blue) site of CS2 lies on the C<sup>∞</sup> axis at the surface of each S atom (see Figure 1). As is clear from Figure 6, which displays the geometries of seven B··· CS2 complexes calculated at the CCSD(T)/cc-aug-pVTZ level of theory, all complexes but H3P··· CS2 do indeed involve a chalcogen bond formed by the axial electrophilic region at one of the S atoms of CS2 with an n- or π-electron pair of the Lewis base B. The calculated intermolecular distances are collected in Table 3. To the best of our knowledge, only H2O··· CS2 was investigated by means of its rotational spectrum [30]. The resulting value of *r*(O··· S) is included in Table 3. The angular geometries of the B··· CS2 complexes displayed in Figure 6 can also be predicted by the rules set out elsewhere for hydrogen-bonded complexes B··· HX [9] or halogen-bonded complexes B··· XY [40], if they are modified by replacing, for example, "hydrogen-bonded complexes B··· HX" by "chalcogen-bonded complexes B··· CS2" and the "HX axis" by "C<sup>∞</sup> axis of CS2" in the wording (see earlier). We note that there is a planar configuration at O found theoretically (see Figure 6) and experimentally [30] for H2O··· CS2, rather than the pyramidal configuration predicted by the rules. The explanation for this difference is identical to that given earlier for H2O··· CO2. On the other hand, the configuration at S in H2S··· CS2 is strongly pyramidal, with the intermolecular bond making an angle of approximately 90◦ with the plane of the H2S nuclei, as found for almost all H2S··· HX and H2S··· XY complexes so far investigated [40]. However, there is a significant non-linearity of the S··· S=C nuclei. A possible reason for this non-linearity is that the intermolecular bond is very weak (*D*<sup>e</sup> = 5.28 kJ·mol−<sup>1</sup> , see Section 3.2) and the pair of equivalent electrophilic H atoms can undergo a secondary interaction with the weakly nucleophilic (yellow-green) region of CS2 (see the MESP of CS2 in Figure 1). The geometry of H3P··· CS2 involves a pnictogen bond and can be understood by reference to the MESP of phosphine in Figure 4. It seems that the primary interaction here involves one of the electrophilic (blue) regions near to P and approximately on the extension of each P–H bond (as seen in the cutaway version of the phosphine MESP in Figure 4) with the nucleophilic (yellow-green) region of CS2. Evidently, this interaction is stronger than that of the terminal electrophilic (blue) region at S with the n-electron pair of phosphine (the red spot in the cutaway version of the MESP in Figure 4), leading to a primary P pnictogen bond.


**Table 3.** Calculated and observed intermolecular distances in B··· CS2 complexes.

*<sup>a</sup>* See Figure <sup>6</sup> for the molecular diagrams (to scale) of the B··· CS2 complexes. *<sup>b</sup>* Reference [30].

**Figure 5.** Molecular models drawn to scale of the geometries of B··· N2O complexes calculated at the CCSD(T)/aug-cc-pVTZ level of theory, where B = CO, HCN, HCCH, NH3, H2O, PH3, and H2S (**a**–**h**, respectively; note that there are two models shown for HCN complexes). When B = HCN there are three low-energy conformers: the slipped parallel form at the global minimum, the T-shaped isomer higher in energy by only 0.03 kJ·mol<sup>−</sup>1, and a linear, hydrogen-bonded conformer N2O··· HCN (not shown) higher in energy by 1.3 kJ·mol−<sup>1</sup> (see text for discussion).

**Figure 6.** Molecular models drawn to scale of the geometries of B··· CS2 complexes calculated at the CCSD(T)/aug-cc-pVTZ level of theory, where B = CO, HCCH, HCN, NH3, H2O, PH3 and H2S (**a**–**g**, respectively).
