Non-adiabatic dynamics of ring opening in cyclohexa-1,3-diene described by an ensemble density-functional theory method

ABSTRACT

The dynamics of the ring opening in the $S_1$ state of cyclohexa-1,3-diene (CHD) is studied by a new direct mixed quantum-classical non-adiabatic dynamics approach which employs the decoherence-induced surface hopping based on the exact factorisation (DISH-XF) molecular dynamics method in connection with the state-interaction state-averaged spin-restricted ensemble-referenced Kohn–Sham (SI-SA-REKS, or SSR) electronic structure method. The critical species on the $S_0$ and $S_1$ PESs of CHD were studied using the SSR method and the minimum energy pathways (MEPs) were optimised. The obtained vertical excitation energies are in good agreement (within ca. 5–6 kcal/mol) with the experimental values. The optimised geometry of the $S_1$/$S_0$ minimum energy conical intersection (MECI) agrees well with the previously obtained MSPT2 geometry. The DISH-XF/SSR non-adiabatic molecular dynamics (NAMD) simulations of ring opening in CHD predict the $S_1$ exponential decay constant $\tau =234\pm 8$ fs in a reasonable agreement with an experimental estimate (230±30 fs). The calculated product branching ratio (CHD:HT = 64:36) is in agreement with the recent experimental measurement (70:30). The NAMD trajectories are analysed in terms of the vibrational normal modes and the obtained branching ratio is explained by persistent stretching of the fissile bond when the trajectories propagate on the $S_1$ PES.

GRAPHICAL ABSTRACT

KEYWORDS:

• Non-adiabatic molecular dynamics
• decoherence-induced surface hopping
• ensemble density-functional theory
• conical intersections
• photochemical ring opening

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. The PPS electronic configuration corresponds to a two-configurational wavefunction which combines two closed-shell determinants, a determinant with the first active orbital doubly occupied and a determinant with the second active orbital doubly occupied. The weighting factors before the closed-shell determinants are related to the fractional occupation numbers of the active orbitals; the latter are obtained by minimising the energy of the PPS configuration simultaneously with the orbitals. The OSS configuration corresponds to a two-configurational wavefunction combining two broken-symmetry determinants where the active orbitals are singly occupied by the α-spin and β-spin electrons. The two broken-symmetry determinants are coupled to a singlet state; their weighting factors are fixed by the spin-symmetry.

2. The oscillator strength is calculated by the usual formula $f_{01}=\frac{2}{3}(E_{S_1}-E_{S_0})|{\mu }_{01}{|}^2$; all quantities in a.u.

Additional information

Funding

This work was supported by Brain Pool Program [grant number 2018H1D3A2000493] and National Honor Scientist Program [grant number 2010-0020414] through the National Research Foundation of Korea (NRF) funded by the Ministry of Science and ICT. SKM acknowledges financial support by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIP) [grant number 2016R1C1B2015103].