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Analyzing Electron Properties Using Molecular Orbital Plots: Population and Dipole Moments

This article explores electron properties through molecular orbital plots, covering key aspects such as plotting the electron density, shading based on sign changes, and understanding orbital normalization in closed-shell molecules. We delve into population analysis to decompose total electron density into contributions from individual atoms or basis functions. Additionally, the dipole moment for Hartree-Fock wavefunctions is discussed, highlighting its calculation through expectation values, density matrices, and dipole integrals over basis functions, along with concepts of electron density and electrostatic potential.

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Analyzing Electron Properties Using Molecular Orbital Plots: Population and Dipole Moments

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Presentation Transcript

  1. Chemistry 6440 / 7440 One Electron Properties

  2. Molecular Orbital Plots • plot a surface where |i(r)|2 = c • i(r) can have positive and negative values • shade in different colors • only the change in sign matters, not the absolute sign

  3. Population Analysis • divide up the total electron density into contributions from the individual atoms or basis functions • each orbital is normalized • in a closed shell molecule, each occupied orbital contains 2 electrons (Ne is the total number of electrons)

  4. Population Analysis • each orbital is a linear combination of basis functions • plug into the expression for the total number of electrons and rearrange terms

  5. Population Analysis

  6. Dipole Moment • for Hartree-Fock wavefunctions, the dipole is the expectation value of the classical expression for the dipole • can be written in terms of the density matrix and a set of dipole integrals over the basis functions

  7. Electron Density • energy of a unit test charge placed at rC Electrostatic Potential

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