Equations-of-motion method for the spin–orbit coupling of aromatic molecules: Application to the phosphorescence lifetime of benzene

Abstract

Articles you may be interested inEquation-of-motion coupled-cluster method for ionized states with spin-orbit coupling J. Chem. Phys. 136, 174102 (2012); 10.1063/1.4704894 Theoretical determination of the indirect nuclear spin-spin coupling tensors, nuclear screening tensors, and magnetic susceptibilities of multiply bonded systems via the equationsofmotion method J. Chem. Phys. 84, 3215 (1986); 10.1063/1.450252Application of the equationsofmotion method to the calculation of the indirect nuclear spin-spin coupling tensors A phosphorescence theory for aromatic molecules is formulated in terms of the equations-of-motion method. The theory is applied to the INDO/S calculations on the lowest triplet radiative lifetime of benzene. All the calculations are performed within the spin-same-orbit interaction approximation. The random-phase approximations are found to give better results than the Tamm-Dancoff approximation ͑or the singly excited CI͒. The importance of the spin-other-orbit interactions contributing to the phosphorescence lifetime is discussed from the formula derived in an Appendix.

Theory and Calculation of the Phosphorescence Phenomenon

“…These phenomena are rather complicated to analyze from the theoretical point of view because the spin prohibition of the S↔T transitions is complemented by orbital symmetry selection rules. Thus, we must apply not only electronic structure theory, like spin–orbit quadratic response theory but also take into account vibronic perturbations of the phosphorescence. ,,− Starting with benzene which is a milestone species of aromatic compounds and which exhibits a T 1 –S 0 transition that is a great challenge to theory because of the dual spin and orbital symmetry prohibition. However, at the same time the low-temperature phosphorescence spectrum of benzene has been successfully detected and characterized by the well-resolved rich vibronic structure .…”

“…However, at the same time the low-temperature phosphorescence spectrum of benzene has been successfully detected and characterized by the well-resolved rich vibronic structure . It is commonly established now that the first excited triplet state of benzene is of 3 B 1 u symmetry (in the framework of D 6 h symmetry point group). ,,− By this reason, the main problem for the benzene phosphorescence is that the 3 B 1u → X 1 A 1g transition is strongly forbidden both by spin and symmetry selection rules (actually the 0–0 transition is missing). Even accounting for “pure electronic” SOC effects the 3 B 1u → X 1 A 1g phosphorescence remains disallowed and is only allowed through the coupling of nuclear and electronic motions including SOC perturbation (so-called vibronically induced phosphorescence).…”

Car–Parrinello molecular dynamics on excited state surfaces

“…͑51͒ we obtain the so-called equation of motion method which was originally proposed by Rowe 14 and widely used in the studies of molecular excited states in quantum chemistry. [20][21][22] The same matrix RPA equation can be derived by several methods, e.g., by the Green function methods 13,23 and the linear response function method. 24,25 Each of these methods has the strong points in specific aspects but is deficient in other respects.…”

“…51 we obtain the so-called equation of motion method which was originally proposed by D.J. Rowe 14 and widely used in the studies of molecular excited states in quantum chemistry [20][21][22] . The same matrix RPA equation can be derived by several methods, e.g.…”