1. Chemistry 6440 / 7440 SCF Convergence

2. Resources Schlegel, H. B.; McDouall, J. J. W.; Do you have SCF Stability and convergence problems?. in "Computational Advances in Organic Chemistry, Ögretir, C.; Csizmadia, I. G.; eds., (Kluwer Academic, the Netherlands), NATO-ASI series C 330, 1991, pg 167-185. (HBS publication no. 126)

3. Types of Hartree-Fock Wavefunctions Closed shell, RHF –spin restricted Hartree-Fock –  and  spin electrons share the same spatial orbitals Open shell, UHF –spin unrestricted Hartree-Fock –  and  spin electrons have different spatial orbitals Open shell, ROHF –spin restricted open shell Hartree-Fock –most  and  spin electrons have the same spatial orbitals –singly occupied orbitals hold the remaining electrons

4. UHF and ROHF open shell Virtual Orbitals Occupied Orbitals

5. UHF orbitals for H 2

7. Fock Operator Coulomb operator (electron-electron repulsion) exchange operator (purely quantum mechanical -arises from the fact that the wavefunction must switch sign when you exchange to electrons)

8. Roothaan-Hall Equations basis set expansion leads to a matrix form of the Fock equations F C i =  i S C i F – Fock matrix C i – column vector of the molecular orbital coefficients  I – orbital energy S – overlap matrix

9. Fock matrix and Overlap matrix Fock matrix overlap matrix

10. Solving the Roothaan-Hall Equations 1.choose a basis set 2.calculate all the one and two electron integrals 3.obtain an initial guess for all the molecular orbital coefficients C i 4.use the current C i to construct a new Fock matrix 5.solve F C i =  i S C i for a new set of C i 6.if the new C i are different from the old C i, go back to step 4.

11. Initial Guess for SCF Semi-empirical calculation (default) Alter the orbital occupancy (GUESS=ALTER) Read in orbitals from a smaller basis set calculation (GUESS=CHECK) Read in orbitals from a nearby calculation (default for a geomtry optimization) Mix HOMO and LUMO (GUESS=MIX) Stability analysis (STABLE=OPT)

12. SCF Convergence Simple SCF iteration sometimes has convergence difficulties Damping and extrapolation of the iteration steps can help DIIS (direct inversion of iterative subspace) is very effective at getting the SCF to converge (default method) Level shift (VSHIFT=n) Quadraticly convergent SCF (SCF=QC)