They have fixed the owest unoccupied molecular orbital (LUMO) level of both donor materials to be equal to −4.0 eV, which is the optimum value for bulk-heterojunction composites with 1-(3-methoxycarbonyl) propyl-1-phenylC 61 (PC 60BM) as acceptor.
LUMO ORBITAL SERIES
(2008) have built a model assuming a series connection of two donor–acceptor solar cells stacked via an ideal intermediate layer. In order to quantify the highest efficiency realistically achievable with an organic tandem cell and the properties of the donor materials required for this goal, Dennler et al. Moreover, the electron affinity is estimated as EA = − ε L, which is minus the orbital energy of the lowest unoccupied orbital. Reiterating, Koopmans' theorem states: The ionization energy of an atom or molecule can be estimated as IE = − ε H, which is minus the orbital energy of the HOMO. In other words, there are two approximations in using Koopmans' theorem to estimate ionization energies, which limit the accuracy:ĭifferences in the “correlation energy” of the electrons in the ion and neutral atom are ignored.Įlectron “relaxation” of the remaining N − 1 electrons is neglected. The derivation of Koopmans' theorem assumes that the electronic wave function of multielectron atom or molecule can be described as the product, or Slater determinant, of a set of one-electron orbitals, and assumes that upon the addition or subtraction of a single electron to, or from, the system, the mean field of the electrons does not change. Electron affinities calculated via Koopmans' theorem are usually quite poor. Koopmans' theorem, named after Tjalling Koopmans, is an approximation that results from the Hartree or Hartree–Fock approximation, in which the ionization energy of an atom or molecule is equal to the energy of the highest occupied molecular orbital (often abbreviated HOMO), and the electron affinity is the negative of the energy of the lowest unoccupied (i.e., virtual) molecular orbital (LUMO). Yet, if before the reaction the ethylene molecules were excited to the triplet state ( π) 1 ( π *) 1, then at the end of the reaction they would correspond to the configuration: (SS) 2 (AS) 2, of very low energy, and the photochemical reaction proceeds. This is energetically unfavourable and such a thermic reaction does not proceed. The four electrons should occupy, therefore, the SS and AS type orbitals, whereas (according to the Woodward–Hoffmann rule) they still occupy SS and SA. (d)) have higher energy, but their order is different than before (b): AS, SA, AA. Once more, the lowest energy (b) corresponds to the SS symmetry orbital (d). The four electrons are no longer of the π type, we now call them the σ type, and they occupy the hybrid orbitals shown in the figure. (d) shows the situation after the reaction. Hence, the four electrons occupy SS and SA, (b). (c)) are of higher energies that increases in the following order: SA, AS, AA. The other three orbitals (not shown in Fig. At the beginning the lowest-energy molecular orbital of the total system (b, c) is of the SS type (i.e. We concentrate on four π electrons − the main actors in the drama. According to these rules we assume that the ethylene molecules preserve two planes of symmetry: P 1 and P 2 during all stages of the reaction. We obtain the same from the Woodward–Hoffmann rules (Fig. Two ethylene molecules, after excitation to the triplet state, dimerize forming cyclobutane (a), because everything is prepared for electron pairing and formation of the new bonds (see text). Two equivalent schemes for the cycloaddition reaction of ethylene.