Electronic Transitions in 1,3-Butadiene
Copyright (c) RDMCHEM LLC 2020
Overview
Electronic Transitions
References
Electronic transitions of conjugated molecules are found in the ultraviolet region of the electromagnetic spectrum for short conjugated molecules and the optical region for longer conjugated molecules like chlorophyll. In this lesson we examine the electronic transitions in trans-1,3-butadiene with the Hartree-Fock method.
Figure 1: trans-1,3-butadiene from the PlotMolecule and MolecularGeometry commands
After loading the Quantum Chemistry package, we explore the electronic transitions of 1,3-butadiene.
Quantum Chemistry
We set the number of Digits to be used in computations to 15 and load the Quantum Chemistry package using Maple's with command.
Digits ≔ 15;
Digits≔15
withQuantumChemistry;
AOLabels,ActiveSpaceCI,ActiveSpaceSCF,AtomicData,BondAngles,BondDistances,Charges,ChargesPlot,CorrelationEnergy,CoupledCluster,DensityFunctional,DensityPlot3D,Dipole,DipolePlot,Energy,ExcitationEnergies,ExcitationSpectra,ExcitationSpectraPlot,ExcitedStateEnergies,ExcitedStateSpins,FullCI,GeometryOptimization,HartreeFock,Interactive,Isotopes,MOCoefficients,MODiagram,MOEnergies,MOIntegrals,MOOccupations,MOOccupationsPlot,MOSymmetries,MP2,MolecularData,MolecularGeometry,NuclearEnergy,NuclearGradient,OscillatorStrengths,Parametric2RDM,PlotMolecule,Populations,RDM1,RDM2,RTM1,ReadXYZ,Restore,Save,SaveXYZ,SearchBasisSets,SearchFunctionals,SkeletalStructure,Thermodynamics,TransitionDipolePlot,TransitionDipoles,TransitionOrbitalPlot,TransitionOrbitals,Variational2RDM,VibrationalModeAnimation,VibrationalModes,Video
1,3-Butadiene
With the MolecularGeometry command of the package we can obtain the following geometry of trans-1,3-butadiene from a molecular database
mol := [["C", -0.60220000, 0.39720000, 0], ["C", 0.60240000, -0.39750000, 0], ["C", -1.83150000, -0.13050000, 0], ["C", 1.83140000, 0.13080000, 0], ["H", -0.49750000, 1.47890000, 0.00010000], ["H", 0.49790000, -1.47920000, 0.00010000], ["H", -2.70350000, 0.51510000, 0], ["H", -1.99750000, -1.20270000, 0], ["H", 2.70360000, -0.51430000, 0], ["H", 1.99690000, 1.20300000, 0]];
mol≔C,−0.60220000,0.39720000,0,C,0.60240000,−0.39750000,0,C,−1.83150000,−0.13050000,0,C,1.83140000,0.13080000,0,H,−0.49750000,1.47890000,0.00010000,H,0.49790000,−1.47920000,0.00010000,H,−2.70350000,0.51510000,0,H,−1.99750000,−1.20270000,0,H,2.70360000,−0.51430000,0,H,1.99690000,1.20300000,0
Use Maple and the Quantum Chemistry package and the above geometry to answer the following questions:
(a) Compute and report the ground-state energy of trans-1,3-butadiene with the Hartree-Fock method in the cc-pVDZ basis set.
(b) Report the energies of the highest occupied (HOMO) and the lowest unoccupied (LUMO) molecular orbitals for trans-1,3-butadiene.
(c) Compute the wavelength of light (in nm) emitted when an electron moves from the LUMO to the HOMO orbital of trans-1,3-butadiene.
(d) According to Koopman's theorem what is the ionization energy for trans-1,3-butadiene?
(e) For trans-1,3-butadiene compute the distance between the first and fourth carbon atoms to produce a total length L.
(f) Using L within an electron-in-a-box model, compute the wavelength of light (in nm) emitted when an electron moves from the LUMO to the HOMO orbital of trans 1,3-butadiene.
(g) How does your result in (f) compare with the wavelength computed via the Hartree-Fock method in (c)?
(h) What minimum length within an electron-in-a-box model would be required for the the wavelength of emitted light (in nm) to lie in the visible region?
(u) How does this length compare to the length L of trans-1,3-butadiene?
D. J. Griffiths and D. F. Schroeter, Introduction to Quantum Mechanics 3rd Edition (Cambridge University Press, 2018).
F. Jensen, Introduction to Computational Chemistry 3rd Edition (John Wiley & Sons, New York, 2017).
I. N. Levine, Quantum Chemistry 7th Edition (Pearson, New York, 2017).
J. J. Sakurai and J. Napolitano, Modern Quantum Mechanics 2nd Edition (Cambridge University Press, Cambridge, 2017).
J. P. Lowe, Quantum Chemistry Illustrated Edition (Academic Press, New York, 2012).
P. W. Atkins and R. S. Friedman, Molecular Quantum Mechanics 5th Edition (Oxford University Press, Oxford, 2010).
C. Cramer, Essentials of Computational Chemistry: Theories and Models 2nd Edition (John Wiley & Sons, New York, 2007).
D. A. McQuarrie, Quantum Chemistry 2nd Edition (University Science, New York, 2007).
D. A. McQuarrie and J. D. Simon, Physical Chemistry: A Molecular Approach (University Science, New York, 1997).
A. Szabo and N. S. Ostlund, Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory (Dover Books, New York, 1996).
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