Insights into the Electronic Structure of Ozone and Sulfur Dioxide from Generalized Valence Bond Theory: Bonding in O₃ and SO₂

Abstract

There are many well-known differences in the physical and chemical properties of ozone (O3) and sulfur dioxide (SO2). O3 has longer and weaker bonds than O2, whereas SO2 has shorter and stronger bonds than SO. The O-O2 bond is dramatically weaker than the O-SO bond, and the singlet-triplet gap in SO2 is more than double that in O3. In addition, O3 is a very reactive species, while SO2 is far less so. These disparities have been attributed to variations in the amount of diradical character in the two molecules. In this work, we use generalized valence bond (GVB) theory to characterize the electronic structure of ozone and sulfur dioxide, showing O3 does indeed possess significant diradical character, whereas SO2 is effectively a closed shell molecule. The GVB results provide critical insights into the genesis of the observed difference in these two isoelectronic species. SO2 possesses a recoupled pair bond dyad in the a"(π) system, resulting in SO double bonds. The π system of O3, on the other hand, has a lone pair on the central oxygen atom plus a pair of electrons in orbitals on the terminal oxygen atoms that give rise to a relatively weak π interaction.

Combining rival π‐space descriptions of O3 and of SO2

“…It is clear from Table 1 that these total energies are little changed if instead of full optimization, we use frozen inactive r orbitals that are taken from fully optimized CAS (4,3) or CAS (4,5) calculations, in which we use either the intersection or the union, respectively, of the c and d active spaces. Similarly, we find that we may carry out a CAS d (4,4) calculation with frozen inactive orbitals that are taken from the fully optimized CAS c (4,4) description, and vice versa, without much energy penalty.…”

“…These observations were confirmed by Takeshita et al who also noted that the energy gap between the two types of solution for O 3 remains very small when the r bonding electrons are treated on an equal footing with the four p orbitals. [5] Two rival p-space solutions also exist in the case of SO 2 , but the corresponding difference in energy is very much larger. [5] The main purpose of the present work is to investigate what happens if the two competitive p-space SC solutions for O 3 are mixed, with or without orbital reoptimization, and thus to determine which (if either) description dominates a wave function that includes both of them.…”

“…[5] Two rival p-space solutions also exist in the case of SO 2 , but the corresponding difference in energy is very much larger. [5] The main purpose of the present work is to investigate what happens if the two competitive p-space SC solutions for O 3 are mixed, with or without orbital reoptimization, and thus to determine which (if either) description dominates a wave function that includes both of them. We perform similar analysis for the two rival p-space solutions in the case of SO 2 , even though they are now somewhat more separated in energy.…”

“…Takeshita et al have recently used full generalized valence bond (full-GVB) theory, also known as spin-coupled (SC) theory, to provide insights into the electronic structure of O 3 and SO 2 . [5] Whereas their full-GVB description of SO 2 featured two highly polar S@O double bonds, and could effectively be considered a closed-shell molecule, significant diradical character was found in the lowest full-GVB (or SC) solution for O 3 . [5] The natural orbitals of p symmetry for such descriptions of the two molecules do in fact span different active spaces, namely 2 3 B 1 1 2 3 A 2 for SO 2 as opposed to 3 3 B 1 1 1 3 A 2 for O 3 and, as was shown by Thorsteinsson et al, [6] a rival p-space SC (or full-GVB) solution for O 3 that is based instead on the 2 3 B 1 1 2 3 A 2 space is very close in energy to the lowest solution based on 3 3 B 1 1 1 3 A 2 .…”

“…[5] Whereas their full-GVB description of SO 2 featured two highly polar S@O double bonds, and could effectively be considered a closed-shell molecule, significant diradical character was found in the lowest full-GVB (or SC) solution for O 3 . [5] The natural orbitals of p symmetry for such descriptions of the two molecules do in fact span different active spaces, namely 2 3 B 1 1 2 3 A 2 for SO 2 as opposed to 3 3 B 1 1 1 3 A 2 for O 3 and, as was shown by Thorsteinsson et al, [6] a rival p-space SC (or full-GVB) solution for O 3 that is based instead on the 2 3 B 1 1 2 3 A 2 space is very close in energy to the lowest solution based on 3 3 B 1 1 1 3 A 2 . These observations were confirmed by Takeshita et al who also noted that the energy gap between the two types of solution for O 3 remains very small when the r bonding electrons are treated on an equal footing with the four p orbitals.…”