Roothaan

Roothaan - Self-Consistent Field Hartree Fock Theory...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Colby College Self-Consistent Field Hartree Fock Theory: Roothaan Equations LCAO approach: Ψ a = i=1 N c ia φ i Ψ a = one-electron molecular orbital φ i = atomic orbitals for N orbitals (Slater or Gaussian) c ia = orbital coefficients -- variational parameters Molecule wavefunctions are Slater determinants of one-electron MO’s Ψ = 1 / N! Ψ a (1) α (1) Ψ a (1) β (1) Ψ b (1) α (1) Ψ b (1) β (1) Ψ a (2) α (2) Ψ a (2) β (2) Ψ b (2) α (2) Ψ b (2) β (2) Ψ a (3) α (3) Ψ a (3) β (3) Ψ b (3) α (3) Ψ b (3) β (3) : : : : Spin wavefunction: σ (1) = α (1) or β (1) Variation Theorem: vary c ia ’s to find the lowest energy: Hartree-Fock Equations: f 1 Ψ a (1) σ (1) = ε a Ψ a (1) σ (1) ε a = one-electron orbital energy for MO a, b, c, … f 1 = h 1 + j=1 n/2 {2J j (1) - K j (1) } j = all the other filled orbitals for electron 1, 2, 3, … core Hamiltonian: h 1 = h 2 2m 2 1 - k=1 m Z k e 2 4 π ε o r k 1 k = all nuclei electron-electron repulsion: Coulomb operator: J j (1) Ψ a (1) =
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern