Stress Tensor Eigenvector Following with Next-Generation
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Heriot-Watt University Research Gateway Stress Tensor Eigenvector Following with Next-Generation Quantum Theory of Atoms in Molecules: Excited State Photochemical Reaction Path from Benzene to Benzvalene Citation for published version: Malcomson, T, Azizi, A, Momen, R, Xu, T, Kirk, SR, Paterson, MJ & Jenkins, S 2019, 'Stress Tensor Eigenvector Following with Next-Generation Quantum Theory of Atoms in Molecules: Excited State Photochemical Reaction Path from Benzene to Benzvalene', Journal of Physical Chemistry A, vol. 123, no. 38, pp. 8254-8264. https://doi.org/10.1021/acs.jpca.9b07519 Digital Object Identifier (DOI): 10.1021/acs.jpca.9b07519 Link: Link to publication record in Heriot-Watt Research Portal Document Version: Peer reviewed version Published In: Journal of Physical Chemistry A Publisher Rights Statement: This document is the Accepted Manuscript version of a Published Work that appeared in final form in The Journal of Physical Chemistry A, copyright © American Chemical Society after peer review and technical editing by the publisher. 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Sep. 2021 Stress Tensor Eigenvector Following with Next-Generation Quantum Theory of Atoms in Molecules: Excited State Photochemical Reaction Path from Benzene to Benzvalene Thomas Malcomson1, Alireza Azizi2, Roya Momen2, Tianlv Xu2, Steven R. Kirk*2, Martin J. Paterson1, Samantha Jenkins*2 1Institute of Chemical Sciences, School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, UK 2Key Laboratory of Chemical Biology and Traditional Chinese Medicine Research and Key Laboratory of Resource National and Local Joint Engineering Laboratory for New Petro-chemical Materials and Fine Utilization of Resources, College of Chemistry and Chemical Engineering, Hunan Normal University, Changsha, Hunan 410081, China email: [email protected] email: [email protected] In this investigation we considered both the scalar and 3-D vector-based measures of bonding using next generation quantum theory of atoms in molecules (QTAIM), constructed from the preferred direction of electronic charge density accumulation, to better understand the photo-chemical reaction associated with of the formation of benzvalene from benzene. The formation of benzvalene from benzene resulted in two additional C-C bonds forming compared with the benzene. The creation of the additional C-C bonds was explained in terms of an increasing the favorability of the reaction process by maximizing the bonding density. The topological instability of the benzvalene structure was determined using the scalar and vector-based measures to explain the short chemical half-life of benzvalene in terms of the competition between the formation of unstable new C-C bonding that also destabilizes nearest neighbor C-C bonds. The explosive character of benzvalene is indicated by the unusual tendency of the C-C bonds to rupture as easily as weak bonding. The topological instability of the short strong C-C bonds was explained by the existence of measures from conventional and next generation QTAIM that previously have only been observed in weak interactions such measures included twisted 3-D bonding descriptors. 1 Introduction While the 1971 synthesis of benzvalene, carried out by Katz,1 utilizing a ground state process by reacting cyclopentadiene with methyllithium and dichloromethane, this highly reactive olfin can also be produced in small quantities, alongside fulvene and Dewar benzene, through the excitation of benzene in the 245 nm range.2 Despite benzvalene possessing a chemical half-life of only 10 days3 before reverting back to benzene, benzvalene, along with fulvene and their associated excited state reactions are ideal to highlight the alterations in bonding structure induced through promotion of a molecule to an excited state4–6 The ability to understand this change in bonding, see Scheme 1, and the insights this provides about the potential energy surface surrounding the point of vertical excitation, could be a powerful tool throughout the chemical sciences. This understanding, however, is not easily discerned, even with modern advances in theoretical chemistry. S1 - vertical S - optimised 1 S1/S0 - conical intersection Benzvalene - S0 Benzene - S0 Scheme 1. The photochemical formulation of benzvalene from benzene. It is possible, however, to gleam some information on the interpretation of excited states through the manipulation of the CASSCF wavefunction to a VB like form, gaining local orbital occupancies (charge 7 densities) and spin-exchange coupling (Pij) values, see Table 1. For example, these electronic factors (successfully) predict that, upon optimisation in S1, the C-C bonds extend from the 1.40 Å (2.65 a.u), found in 7 S0, to 1.54 Å (2.91 a.u), see Scheme 2. The ability to analyze and visualize the continuous evolution of the chemical bonding can be highlighted in the excited state chemistry of calicene and sesquifulvalene, derivatives of fulvene, which has been previously studied.4–6 Despite the similarities of these compounds to fulvene, they each contain a significantly polarized central double bond, resulting in the most dominant resonance structure possessing a significantly polarized 2 bond. This highly polarized bond gives rise to significant charge transfer character in the lower excited state manifold8 that will have a strong effect on the excited state chemistry of these compounds, see the C4-C5 bond in Scheme 2. In this investigation therefore, we will present a new perspective of the chemical bonding of benzvalene using the 3-D, ‘next-generation’6 quantum theory of atoms in molecules (QTAIM) methodology.9,10 Next generation QTAIM has seen an increase in applications to excited states in recent years6 and is unique to theoretical chemistry due to being formulated as a directional 3-D vector based formulation as opposed to being comprised entirely of scalar measures that have recently been used for the prediction of stereoisomers.11 This three- stranded 3-D interpretation of the chemical bond is more complete than minimal definition of bonding (e3) the conventional QTAIM interpretation of a bond, provided by the bond-path (r) because it comprises all three of the {e1, e2, e3} eigenvectors. Within QTAIM the most preferred ‘easy’ direction e2 is determined on the basis of the ease of total electronic charge density ρ(rb) accumulation. Conversely, the least preferred directions were 12 found to be e1 for QTAIM and e2σ for the stress tensor. For the stress tensor, we have found that the e1σ eigenvector corresponds to the most preferred ‘easy’ direction on the basis of ease of compressibility. This finding was demonstrated using stress tensor trajectory formalism Tσ(s) in partnership with the potential energy surface to prove that the e2σ eigenvector was the least preferred direction of electronic charge density ρ(rb) accumulation and therefore that the e1σ eigenvector was the most preferred direction. Additional evidence for the most and least preferred directions for the stress tensor being defined by the e1σ and e2σ eigenvector was * * provided by the fact that the values for Hσ > Hσ and HσH > HσH consistent with previous findings from QTAIM that the preferred path has the longer associated eigenvector following path length. Previously, some of the current authors demonstrated that the stress tensor can be used within the QTAIM partitioning scheme by using next generation QTAIM.12 This analysis was undertaken using an adapted version of the recently introduced 3-D vector-based interpretation of the chemical bond B = {p,q,r} of the form Bσ = {ps,qs,r} to follow changes in the directional properties of the stress tensor that is robust to electronic excitations. We demonstrated that the construction of Bσ = {ps,qs,r} that used εσ ≤ 0 the most closely approximated the B = {p,q,r}. This is because the ‘easy’ direction for the stress tensor is determined by the most compressible λ1σ i.e. associated with the longer axis of the ellipse, whereas for QTAIM the ‘easy’ direction, (longer axis of the ellipse) is associated with the λ2 eigenvalue. 3 Scheme 2. The benzene S0, benzene S1vert and benzene S1opt (left), benzvalene S0/S1 ContInt (middle) and benzvalene S0 (right) molecular graphs, the bond-path (r) is indicated by the black lines with the undecorated green and red spheres representing the bond critical point (BCPs) and ring critical points (RCPs), respectively, with the white lines indicating the RCP-BCP paths. Recently,5 we provided a 3-D understanding of the bonding provided by using Lewis structures for the ground state S0 and first excited state S1 of fulvene. We discovered that the corresponding bond-path framework set B0,1 = {(p0,p1),(q0,q1),(r0,r1)}, was better approximated by the stress tensor formulation