Reply to the comment by Amano on “Linear and bent triatomic molecules are not qualitatively different!”

In Amano’s comment on Jensen’s paper, we notice two important misconceptions: (i) Amano overlooks the fact that all features special for a linear molecule originate in the double degeneracy in the bending motion (i.e., in the fact that for a linear triatomic molecule, the description of the bending motion must necessarily also involve the rotation about the axis of least moment of inertia, the a axis, which becomes the molecular axis at equilibrium), and (ii) the expectation value generated from the wavefunction gives an “average” value of the relevant observable (coordinate); the expectation value can, in principle, be obtained experimentally as the average of very many repeated measurements of the observable. In our previous papers on this subject, in particular the paper by Jensen discussed here, we have attempted to explain our results as coherently and “pedagogically” as we can, starting with the fundamental principles of quantum mechanics, and we encourage interested readers to refer to our previous works on the subject. Thus, we maintain our assertion that the vibrationally averaged structure of a linear molecule is observed as being bent, as we have demonstrated previously from both theoretical and experimental viewpoints.

Comment on “Linear and bent triatomic molecules are not qualitatively different!”

Jensen (Can. J. Phys. 98, 506 (2020). doi: 10.1139/cjp-2019-0395 ) presents theoretical justification for the claim that linear triatomic molecules are necessarily observed to be bent. The basis of the assertion is that the expectation value of the supplement of the bending angle, [Formula: see text] used in Jensen’s paper, is calculated to be positive. In this comment, we examine the interpretation of the expectation values of [Formula: see text] in stationary states, and indicate that Jensen’s claim contradicts a basic principle of quantum mechanics that the energy and geometrical variables cannot have definite values at the same time.

A Combined Experimental/Quantum-Chemical Study of Tetrel, Pnictogen, and Chalcogen Bonds of Linear Triatomic Molecules

Linear triatomic molecules (CO2, N2O, and OCS) are scrutinized for their propensity to form perpendicular tetrel (CO2 and OCS) or pnictogen (N2O) bonds with Lewis bases (dimethyl ether and trimethyl amine) as compared with their tendency to form end-on chalcogen bonds. Comparison of the IR spectra of the complexes with the corresponding monomers in cryogenic solutions in liquid argon enables to determine the stoichiometry and the nature of the complexes. In the present cases, perpendicular tetrel and pnictogen 1:1 complexes are identified mainly on the basis of the lifting of the degenerate ν 2 bending mode with the appearance of both a blue and a red shift. Van ′t Hoff plots of equilibrium constants as a function of temperature lead to complexation enthalpies that, when converted to complexation energies, form the first series of experimental complexation energies on sp1 tetrel bonds in the literature, directly comparable to quantum-chemically obtained values. Their order of magnitude corresponds with what can be expected on the basis of experimental work on halogen and chalcogen bonds and previous computational work on tetrel bonds. Both the order of magnitude and sequence are in fair agreement with both CCSD(T) and DFA calculations, certainly when taking into account the small differences in complexation energies of the different complexes (often not more than a few kJ mol−1) and the experimental error. It should, however, be noted that the OCS chalcogen complexes are not identified experimentally, most probably owing to entropic effects. For a given Lewis base, the stability sequence of the complexes is first successfully interpreted via a classical electrostatic quadrupole–dipole moment model, highlighting the importance of the magnitude and sign of the quadrupole moment of the Lewis acid. This approach is validated by a subsequent analysis of the molecular electrostatic potential, scrutinizing the σ and π holes, as well as the evolution in preference for chalcogen versus tetrel bonds when passing to “higher” chalcogens in agreement with the evolution of the quadrupole moment. The energy decomposition analysis gives further support to the importance/dominance of electrostatic effects, as it turns out to be the largest attractive term in all cases considered, followed by the orbital interaction and the dispersion term. The natural orbitals for chemical valence highlight the sequence of charge transfer in the orbital interaction term, which is dominated by an electron-donating effect of the N or O lone-pair(s) of the base to the central atom of the triatomics, with its value being lower than in the case of comparable halogen bonding situations. The effect is appreciably larger for TMA, in line with its much higher basicity than DME, explaining the comparable complexation energies for DME and TMA despite the much larger dipole moment for DME.