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Chemistry 6440 / 7440

Chemistry 6440 / 7440. SCF Convergence. Resources.

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Chemistry 6440 / 7440

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  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 H2

  6. 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)

  7. Roothaan-Hall Equations • basis set expansion leads to a matrix form of the Fock equations FCi = iSCi • F – Fock matrix • Ci – column vector of the molecular orbital coefficients • I – orbital energy • S – overlap matrix

  8. Fock matrix and Overlap matrix • Fock matrix • overlap matrix

  9. Solving the Roothaan-Hall Equations • choose a basis set • calculate all the one and two electron integrals • obtain an initial guess for all the molecular orbital coefficients Ci • use the current Ci to construct a new Fock matrix • solve FCi = iSCi for a new set of Ci • if the new Ci are different from the old Ci, go back to step 4.

  10. 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)

  11. 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)

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