Permutational symmetry, isotope effects, side crossing, and singlet-triplet splitting in anthracene⋅HeN (N=1, 2) clusters

Abstract

We present quantum-mechanical calculations for the vibrational states of anthracene⋅3HeN and anthracene⋅4HeN (N=1, 2) clusters in the ground (S0) and first excited singlet state (S1) of the anthracene molecule. The anthracene-He potential in the S0 state was described in terms of a sum of Lennard-Jones atom-atom potentials, while the potential in the S1 state also included changes in the dispersive energy and in the repulsive interactions. Variational calculations were carried out for anthracene⋅He1. For anthracene⋅He2, configuration interaction calculations were performed, accounting for the boson and fermion permutation symmetry. For both helium isotopes of the N=1 cluster, tunneling splitting is negligible (<0.01 cm−1), as an appreciable interaction of the densities was only found for highly excited states above the potential-energy barrier of side crossing (for energy eigenvalues ⩾−22 cm−1 below the dissociation limit). The two-boson anthracene⋅4He2 system assumes a singlet A11 ground state due to zero spin of the He4 isotope. Because of the dominance of the two-particle over the one-particle interactions, the two-fermion anthracene⋅3He2 system has a triplet (3B2) vibrational ground state. The singlet-triplet (13B2-11B2) splitting between the two lowest states of the same spatial symmetry of anthracene⋅3He2 was calculated to be 10.5 cm−1. Mass and permutation symmetry effects on the vibrational level structure of anthracene⋅He1 and anthracene⋅He2 were explored for anthracene⋅4He1, anthracene⋅3He1, the two-boson system anthracene⋅4He2, the two-fermion system anthracene⋅3He2 and for the hypothetical fermion system of mass 4. While the isotope effect on the zero-point energies ε0 in the S0 state is Δε0(1)/ε0(1)=[ε0(anthracene⋅3He1)−ε0(anthracene⋅4He1)]/ε0(anthracene⋅4He1)=12%, in accord with the mass effect in the harmonic approximation, the zero-point energy difference between the ground states of the two-fermion anthracene⋅3He2 and the two-boson anthracene⋅4He2 system is Δε0(2)/ε0(2)=[ε0(anthracene⋅3He2)−ε0(anthracene⋅4He2)]/ε0(anthracene⋅4He2)=10%, manifesting a cancellation of mass and permutation symmetry effects. The isotope effect on the red spectral shift δ of the electronic origin for the S0→S1 transition of anthracene⋅He1 is Δδ(1)=δ(anthracene⋅4He1)-δ(anthracene⋅3He1)=0.28 cm−1, while Δδ(2)=δ(anthracene⋅4He2)-δ(anthracene⋅3He2)=−0.50 cm−1, being of the opposite sign than Δδ(1). These features of the spectral shifts as well as the small isotope effects on the energetics and Franck-Condon factors for the S0→S1 vibronic spectra exhibit a delicate balance between differences in mass effects, He-He repulsion, and permutational symmetry of the boson and fermion systems.