A conceptually appealing and computationally economical course-grained molecular-orbital (MO) theory for extended quasi-linear molecular heterostructures is presented. The formalism, which is based on a straightforward adaptation, by including explicitly the vacuum, of the envelope-function approximation widely employed in solid-state physics, leads to a mapping of the three-dimensional single-particle eigenvalue equations into simple one-dimensional hole and electron Schrödinger-like equations with piecewise-constant effective potentials and masses. The eigenfunctions of these equations are envelope MO's in which the short-wavelength oscillations present in the full MO's, associated with the atomistic details of the molecular potential, are smoothed out automatically. The approach is illustrated by calculating the envelope MO's of high-lying occupied and low-lying virtual $π$ states in prototypical nanometric heterostructures constituted by oligomers of polyacetylene and polydiacetylene. Comparison with atomistic electronic-structure calculations reveals that the envelope-MO energies agree very well with the energies of the $π$ MO's and that the envelope MO's describe precisely the long-wavelength variations of the $π$ MO's. This envelope MO theory, which is generalizable to extended systems of any dimensionality, is seen to provide a useful tool for the qualitative interpretation and quantitative prediction of the single-particle quantum states in mesoscopic molecular structures and the design of nanometric molecular devices with tailored energy levels and wavefunctions.
Band Renormalization in a Metal-Organic Framework/Au(111) Triple-Lattice Heterostructure
Fudan University（复旦大学）；Westlake University（西湖大学）；Westlake Institute for Advanced Study（西湖高等研究院）；Songshan Lake Materials Laboratory（松山湖材料实验室）；Central South University（中南大学）；Shanghai Synchrotron Radiation Facility, Shanghai Advanced Research Institute, Chinese Academy of Sciences（中国科学院上海高等研究院上海同步辐射光源）
2D abrupt nano-junctions blending sp-sp2 bonds on atomically precise heterostructures
Politecnico di Milano（米兰理工大学）；Università degli Studi di Milano（米兰大学）；INFN Sezione di Milano（意大利国家核物理研究所米兰分部）；Università di Pavia（帕维亚大学）；Università Degli Studi Di Padova（帕多瓦大学）；Instituto de Nanociencia y Materiales de Aragon (INMA), CSIC-Universidad de Zaragoza（阿拉贡纳米科学与材料研究所（INMA），西班牙国家科学研究委员会-萨拉戈萨大学）
Nanopatterning process based on epitaxial masking for the fabrication of electronic and spintronic devices made of La0.67Sr0.33MnO3/LaAlO3/SrTiO3 heterostructures with in situ interfaces
