**1. Introduction**

Investigation, both experimentally and theoretically, of non-covalent interactions among molecules is a topic of rapidly increasing interest. The hydrogen bond, known for almost a century, is of fundamental importance in chemistry and biology. The halogen bond is a weak interaction, in which interest within both disciplines grew rapidly in the last two decades. Modern definitions of the hydrogen bond [1] and the halogen bond [2], made under the auspices of the International Union of Pure and Applied Chemistry (IUPAC), arose naturally from the increased activity. Tetrel bonds, pnictogen bonds, and chalcogen bonds, close relatives of hydrogen and halogen bonds, were recognized as weak, non-covalent interactions in both the gas phase [3] and condensed phase [4] for several decades, but were named only in 2013 [5], 2011 [6], and 2009 [7], respectively. A task group set up by the IUPAC is currently working on the definitions of these three, newly named interactions (see: https://iupac.org/projects/project-details/?project\_nr=2016-001-2-300).

It is now widely accepted [2,3,8] that each of these non-covalent bonds arises mainly from the interaction of an electrophilic region associated with an atom of the element E (where E is hydrogen, a halogen, or an element of group 14, 15, or 16) with the nucleophilic region (e.g., a non-bonding or π-bonding electron pair) in another molecule or the same molecule. Electrophilic and nucleophilic regions can be identified via the electrostatic potential near to the appropriate regions of the molecules [9]. A convenient modern and readily available way of identifying such regions is the molecular electrostatic surface potential (MESP), which is the potential energy of a non-perturbing, unit-positive point charge at the iso-surface on which the electron density is constant [10], and it is usually expressed as 0.00*n* e/bohr3 (*n* = 2 here).

The closely related molecules CO2, N2O, and CS2 form a series of interest in the context of non-covalent bonding. Each provides an electrophilic site by means of which either tetrel, pnictogen, or chalcogen bonds, respectively, could be formed. Both CO2 and CS2 are non-dipolar; thus, the molecular electric quadrupole moment is the first non-zero term in the expansion of the electric charge distribution; however, this moment is of opposite sign in the two molecules [11,12]. For CO2, the sign corresponds to the partial charge description <sup>δ</sup>−O = <sup>2</sup><sup>δ</sup>+C=O<sup>δ</sup>−, while, for CS2, the reverse arrangement <sup>δ</sup>+S = <sup>2</sup>δ−C = Sδ<sup>+</sup> is implied. These charge distributions can be readily identified in the MESPs shown for each molecule (calculated at the 0.002 e/bohr3 iso-surface) in Figure 1, which shows side-on and end-on views of the MESPs of CO2, N2O, and CS2. Accordingly, we expect CO2 to form tetrel bonds perpendicular to its C<sup>∞</sup> axis, via the electrophilic (blue) region at the C atom, with, e.g., the n-pair of a Lewis base. Conversely, CS2 is likely to form chalcogen bonds via the electrophilic (blue) region that lies at each S atom and is centered on the C<sup>∞</sup> axis. Clearly, the charge distributions of CO2 and N2O, as represented by their MESPs in Figure 1, are very similar, as are the signs and magnitudes of their electric quadrupole moments [11,13]; however, N2O also has a small electric dipole moment. Nitrous oxide is, therefore, expected to form a complex with a given Lewis base of similar geometry to that of its carbon dioxide counterpart, but with small distortions resulting from the lower symmetry and the non-zero electric dipole moment in the case of N2O.

It this article, we present the geometries and interaction strengths of complexes of the type B··· CO2, B··· CS2, and B··· N2O for the series of Lewis bases, B = CO, HCCH, H2S, HCN, H2O, PH3, and NH3, as calculated ab initio at the CCSD(T)/aug-cc-pVTZ level of theory. The geometries so calculated can be compared with those established experimentally via gas-phase rotational or vibration–rotation spectra for some, but not all, of the complexes B··· CO2 [14–21] and B··· N2O [21–29]; however, data for B··· CS2 are sparse [30]. The interaction strength can be described in two possible ways. The first is the energy required for the reaction B··· CO2 = B + CO2, that is, the equilibrium dissociation energy *D*e. The second is the intermolecular quadratic stretching force constant *k*σ, which is proportional to the energy required for a unit infinitesimal displacement from equilibrium along the dissociation coordinate. It was shown elsewhere for hydrogen-bonded complexes B··· HX and halogen-bonded complexes B··· XY (X and Y are halogen atoms) that *D*<sup>e</sup> is directly proportional to *<sup>k</sup>*σ, with a constant of proportionality of 1.5(1) × <sup>10</sup>−<sup>3</sup> m2·mol<sup>−</sup>1, whether *<sup>k</sup>*<sup>σ</sup> is obtained experimentally [31] from centrifugal distortion effects in the rotational spectra of the complexes or calculated ab initio [32].

Given the definitions of hydrogen and halogen bonds in terms of the interaction of nucleophilic regions of Lewis bases B with electrophilic regions near the atoms H of HX and X of XY, the aim of the work presented here is to examine by means of ab initio calculations (1) whether the complexes B··· CO2, B··· N2O, and B··· CS2 involve tetrel, pnictogen, and chalcogen bonds, respectively, and (2) whether there is direct proportionality of *D*e and *k*σ for these complexes, and, if so, does the constant of proportionality found for hydrogen- and halogen-bonded complexes B··· HX and B··· XY also hold in these non-covalent bonds.

**Figure 1.** Molecular electrostatic surfaces potential (MESPs) for carbon dioxide, nitrous oxide, and carbon disulfide calculated for the 0.002 e/bohr3 iso-surface at the MP2/6-311++G\*\* level.

#### **2. Theoretical Methods**

We present here equilibrium geometries and values of *D*<sup>e</sup> and *k<sup>σ</sup>* (defined earlier) calculated ab initio for the members of three series of complexes, namely the series of B··· CO2, B··· N2O, and B··· CS2, where B is one of the simple Lewis bases, CO, HCCH, H2S, HCN, H2O, PH3, or NH3. The geometry optimizations and the calculations of *kσ* were conducted at the CCSD(T)/aug-cc-pVTZ level of theory [33,34]. To evaluate *kσ*, the energy *E*(*r*e) at the equilibrium geometry was first obtained, and the energy *E*(*r*) was then scanned for ±20 pm about the appropriate equilibrium intermolecular distance *r*<sup>e</sup> in increments (*r* − *r*e) = 5 pm with optimization in all internal coordinates but *r* at each point. The curve of *E* (*r* − *r*e) as a function of (*r* − *r*e) was fitted to a third-order polynomial in (*r* − *r*e), and the second derivative was evaluated at *r* = *r*<sup>e</sup> to yield the quadratic force constant *k<sup>σ</sup>* = *∂*2*E*(*r*) *∂r*<sup>2</sup> *r*=*r*<sup>e</sup> , which is the curvature at the minimum. All curves used in the evaluation of all *k<sup>σ</sup>* presented here are available as supplementary information, as are the optimized geometries. Figure 2 shows a plot of *E* (*r* − *r*e) versus (*r* − *r*e) for the complex H3N··· S=C=S, which is predicted by the ab initio calculations to possess *C*3v symmetry at equilibrium, with the linear CS2 molecule

lying along the *C*<sup>3</sup> axis of NH3, and therefore, with the inner S atom participating in a chalcogen bond to the n-electron pair of ammonia. Values of *D*<sup>e</sup> with better accuracy were obtained using the method of extrapolation to a complete basis set [35] (CCSD(T)/CBS energy). For this purpose, the HF/aug-cc-pV*n*Z//CCSD(T)/aug-cc-pVTZ energies, with *n* = D, T, and Q, for the HF contribution and the CCSD(T)/aug-cc-pV*n*'Z//CCSD(T)/aug-cc-pVTZ, with *n*' = T and Q, for the correlation part were obtained for each system [36]. Finally, *D*<sup>e</sup> was obtained as the difference of the CCSD(T)/CBS energy of the monomers and the complex. All the ab initio calculations were performed with the MOLPRO-2012 program [37]. The Z-matrices for optimized geometries are available as supplementary information. The molecular electrostatic surface potentials were generated using of the SPARTAN electronic structure package [38] at the MP2/6-311++G\*\* level for CO2, N2O, CS2, and PH3.

**Figure 2.** The variation in *E* (*r* − *r*e) with *r* − *r*e, used to calculate the intermolecular quadratic force *k*<sup>σ</sup> (the curvature at the minimum) for H3N··· S=C=S at the CCSD(T)/aug-cc-pVTZ level of theory. The curve is a third-order polynomial fit to the calculated points (*R*<sup>2</sup> of fit = 0.9998). The polynomial was differentiated twice to obtain *k*σ.

#### **3. Results**
