Hückel molecular orbital (HMO) energy diagrams can be constructed using linear combinations of orbitals for conjugated polyenes. Quantum chemistry packages have been used to model the molecules and moleculeorbitals via RHF/631G(d) or UB3LYP/631G(d). This Demonstration shows characteristics for a set of seven conjugated polyenes: the HMO energy diagram, a 3D view of the probability density (with boundary surface, phasecoloring included), and a ballandstick model for each example.
The simple Hückel method (SMO) is a rudimentary method for energies and orbitals of electron systems. Possible sets of corresponding LCAO molecular orbitals for cyclobutadiene and benzene are , , , , , , , , , . To visualize the different linear combinations of wavefunctions for electron systems of conjugated polyenes, a shaded version of the orbital is used . For example, the coefficients in the linear combinations for cyclobutadiene are all equal by size and differ only by sign. In benzene they can be ordered by size into three groups. In an HMO energy diagram for benzene, a combination of three different relative sizes of is used. The last column in the energy diagram shows no symbol or the symbols ↑ and ⥮ to indicate that the orbital is not occupied, singly occupied, or doubly occupied. ChemSpider [1] is the basis for the coordinates in the input files of the nonradical structures. The ChemSpider IDs for each structure are listed in the following table. molecule  chid  ethene  6085  butadiene  7557  1,3,5hexatriene  15830  cyclobutadiene  20626  benzene  236 
An input file for the allyl and 1,4pentadienylradical is created in Avogadro beginning with a sketch [6]. The nonradicals' optimizations are run in GAMESSUS with an RHF/631G(d) model via GamesQ [7]. For both radicals, an optimization with unrestricted Hartree–Fock is necessary. The model of choice is UB3LYP/631G(d). Here is a table for the final energy from the logfiles of the optimizations for each molecule. molecule  model  fin. energy [Hartree]  r.m.s. [Hartree]  ethene  RHF/631G(d)  78.03  0.0000219  allyl  UHFB3LYP/631G(d)  117.18  0.0000472  butadiene  RHF/631G(d)  154.92  0.0001377  pentadienyl  UHFB3LYP/631G(d)  194.54  0.0001311  hexatriene  RHF/631G(d)  231.81  0.0000598  cyclobutadiene  RHF/631G(d)  153.64  0.0000199  benzene  RHF/631G(d)  232.70  0.0000339 
From each logfile the last frame is exported as a molfile via MacMolPlt [8]. The Demonstration "Displaying Molecules with Multiple Bonds" by Bianca Eifert makes it possible to show the doublebonds of molecules in Mathematica [9]. Through slightly modifying her code, the modeled molecules can be imported as a molfile with doublebonds on. The corresponding moleculeorbitals for the molecules are created in Gabedit [10]. The results are copied to this Demonstration into the initalization code and named MOOrbitals and MOMolecules. [2] A. Rauk, Orbital Interaction Theory of Organic Chemistry, 2nd ed., New York: John Wiley & Sons, 2000. [3] E. Heilbronner and H. Bock, Das HMOModell und seine Anwendungen—Grundlagen und Handhabung, Weinheim: Verlag Chemie GmbH, 1970. [6] M. Hanwell, D. Curtis, D. Lonie, T. Vandermeersch, E. Zurek, and G. Hutchison, "Avogadro: An Advanced Semantic Chemical Editor, Visualization, and Analysis Platform," Journal of Chemoinformatics, 4(17), 2004 pp. 1758–2946. doi:10.1186/17582946417. [7] M. Schmidt, K. Baldridge, J. Boatz, S. Elbert, M. Gordon, J. Jensen, S. Koseki, N. Matsunaga, K. Nguyen, S. Su, T. Windus, M. Dupuis, and J. Montgomery, "General Atomic and Molecular Electronic Structure System," Journal of Computational Chemistry, 14, 1993 pp. 1347–1363. doi:10.1002/jcc.540141112. [8] B. Bode and M. Gordon, "MacMolPlt," Journal of Molecular Graphics and Modelling, 16, 1998 pp. 133–138. [10] A. Allouche, "Gabedit—A Graphical User Interface for Computational Chemistry Softwares," Journal of Computational Chemistry, 32, 2011 pp. 174–182. doi:10.1002/jcc.21600.
