The Nambu-Goto model is investigated by using the canonical Monte Carlo simulations on fixed connectivity surfaces of spherical topology. Three distinct phases are found: crumpled, tubular, and smooth. The crumpled and the tubular phases are smoothly connected, and the tubular and the smooth phases are connected by a discontinuous transition. The surface in the tubular phase forms an oblong and one-dimensional object similar to a one-dimensional linear subspace in the Euclidean three-dimensional space R3 . This indicates that the rotational symmetry inherent in the model is spontaneously broken in the tubular phase, and it is restored in the smooth and the crumpled phases.
Rotationally resolved ultrahigh-resolution spectra of the S(1) (1)B(2u)<--S(0) (1)A(g) transition of anthracene-h(10) and anthracene-d(10) have been observed using a single-mode UV laser and a collimated supersonic jet. We have determined rotational constants of the zero-vibrational levels of the S(0) and S(1) states by analyzing the precisely calibrated transition wavenumbers of rotational lines. We measured Zeeman splitting of each rotational line in the external magnetic field, of which the magnitude was small and strongly dependent on the rotational quantum numbers. We have shown that the magnetic moment in the S(1) (1)B(2u) state arises from J-L coupling with the S(2) (1)B(3u) state and that mixing with the triplet state is negligibly small. We concluded that the main radiationless transition in the S(1) state of anthracene is not intersystem crossing to the triplet state but internal conversion to the ground state. We also examined methods of ab initio theoretical calculation to determine which method most closely yielded the same values of rotational constants as the experimentally obtained ones. Moller-Plesset second-order perturbation method with a 6-31G(d,p) basis set yielded approximately the same values for the S(0) (1)A(g) state with an error of less than 0.04%. Geometrical structure in the S(0) (1)A(g) state of the isolated anthracene molecule has been accurately determined by this calculation. However, configurational-interaction with single excitations, time-dependent Hartree-Fock, and time-dependent density-function-theory methods did not yield satisfactory results for the excitation energy of the S(1) (1)B(2u) state. Symmetry-adapted-cluster configuration-interaction calculation was sufficiently good for the excitation energy and rotational constants.
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