QTAIM and stress tensor bond-path framework sets for the ground and excited states of fulvene

doi:10.1016/j.cplett.2018.10.029

Chemical Physics Letters

Volume 713, December 2018, Pages 125-131

https://doi.org/10.1016/j.cplett.2018.10.029 Get rights and content

Highlights

•
Present QTAIM and stress tensor 3-D bond-path framework sets B, B_σ and B_σH for fulvene.
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Provide a 3-D bonding morphology of the ground S₀ and first S₁ excited states of fulvene.
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Demonstrated variation of B, B_σ and B_σH with torsion and bond length alternation (BLA).
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Compare two versions of the stress tensor B_σ, B_σH and find best approximation to QTAIM B.
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Higher degree of asymmetry and lower ellipticity ε for the S₁ than S₀ electronic state.

Abstract

We present, for the ground and first excited states of fulvene, the complete 3-D bond-path framework set B = {(p₀,p₁), (q₀,q₁), (r₀,r₁)} from the quantum theory of atoms in molecules (QTAIM) and B_σH = {(p_σH0,p_σH1), (q_σH0,q_σH1), (r₀,r₁)} and B_σ = {(p_σ0,p_σ1), (q_σ0,q_σ1), (r₀,r₁)} from the stress tensor within the QTAIM partitioning. We find that both the QTAIM bond-path framework sets B = {(p₀,p₁), (q₀,q₁), (r₀,r₁)} and the stress tensor B_σ = {(p_σ0,p_σ1), (q_σ0,q_σ1), (r₀,r₁)} provide a quantitative 3-D rendering of the bonding that is consistent with understanding of the bonding provided by using Lewis structures.

Graphical abstract

Top: QTAIM bond-path frame-work set B corresponding to the C.I_planar configuration, where the (p₀,q₀)-paths (left panel) for S₀ and (p₁,q₁)-paths (middle panel) for the S₁ states are presented with (p₀,p₁)-paths (pale-blue) and (q₀,q₁)-paths (magenta) with a magnification factor of ×5. Variations of the ellipticity ε profiles (right panel) for the S₀ and S₁ states along the bond-path (r) associated with the torsional C2-C6 BCP.

Bottom: The corresponding stress tensor B_σ are presented also with a magnification factor of ×5 and the variations of the stress tensor ellipticity ε_σ profiles (right panel).

Section snippets

Acknowledgements

The National Natural Science Foundation of China is gratefully acknowledged, project approval number: 21673071. The One Hundred Talents Foundation of Hunan Province and the aid program for the Science and Technology Innovative Research Team in Higher Educational Institutions of Hunan Province are also gratefully acknowledged for the support of S.J. and S.R.K.

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Here we have determined the precessions K and K’ of the {p,p′} and {q,q′} path-packets for the excited state deactivation reaction of fulvene in terms of bond-flexing, bond-torsion and bond-anharmonicity that includes the tendencies towards bond-path-rigidity and bond-path-flexibility. An asymmetry is found for the S₁ state resulting in an unpredictable variation in the direction of the bond-path-rigidity as a function of the torsion coordinate. Uniquely, the S₁ state at torsion θ = 0.0° possesses the possible maximum bond-path-rigidity, along the entire bond-path but then drops lower than for the S₀ state at the conical intersection indicating photo-excitation facilitates the torsion.
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The current investigation on the differing reaction pathways in the first two excited states is undertaken using the next generation QTAIM, (NG-QTAIM) 3-D vector-based interpretation of the chemical bond, within the QTAIM[5] framework, referred to as the bond-path framework set B. The QTAIM bond-path framework sets B and the stress tensor Bσ were also found previously to provide a quantitative 3-D rendering of the bonding consistent with the chemical bonding insights provided by using Lewis structures of fulvene with double/single bond and resonance representations of S0 and S1 states for the values of torsion θ = 0.0° (FC) and 64.3° (CItorsion) along the excited state deactivation minimum energy path (MEP) [6]. The 64.3° CItorsion geometry represents the minimum energy conical intersection along a seam connecting all torsion angles [7] The new QTAIM B was used to demonstrate for fulvene that the ground state S0 and excited state S1 bonding existed on a continuous spectrum rather than as polar extremes, as presented on the Lewis structures.
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Research paperQTAIM and stress tensor bond-path framework sets for the ground and excited states of fulvene

Highlights

Abstract

Graphical abstract

Section snippets

Acknowledgements

Comput. Theor. Chem.

Chem. Phys. Lett.

The bond bundle in open systems

Int. J. Quantum Chem.

Quantum topology of molecular charge distributions. III. The mechanics of an atom in a molecule

J. Chem. Phys.

Atoms in Molecules: a Quantum Theory

Energieimpulssatz der Materiewellen

Ann. Phys.

Die allgemeinen prinzipien der wellenmechanik

Handb. Phys.

Coordinate invariance, the differential force law, and the divergence of the stress-energy tensor

J. Chem. Phys.

An electron-preceding perspective on the deformation of materials

J. Chem. Phys.

Dependence of the normal modes on the electronic structure of various phases of ice as calculated by ab initio methods

Can. J. Phys.

Identifying and Analyzing Intermolecular Bonding Interactions in van der Waals Molecules

J. Phys. Chem.

A bond path: a universal indicator of bonded Interactions

J. Phys. Chem. A

Bond paths are not chemical bonds

J. Phys. Chem. A

Research paper
QTAIM and stress tensor bond-path framework sets for the ground and excited states of fulvene