For transition metals large number of electrons call for a large number of

# For transition metals large number of electrons call

This preview shows page 51 - 58 out of 83 pages.

For transition metals, large number of electrons call for a large number of basis functions to describe them. More electrons mean more energy associated with electron correlation too. SCF Convergence SCF oscillation: SCF energy bounces back and forth between the two discrete values associated with two different unconverged wave functions (P (a) and P (b) ), due to the diagonalization of the Fock matrix creating a density matrix P (b) that is indistinguishable from P (a) . Solutions: change optimizer Initial guess problem (first obtain a wave function from a minimal basis set, i.e., STO-3G, then use that as an initial guess. Molecular structures are too bad: optimize structure at lower level of theory first, visualization of the structure Restricted vs. Unrestricted RHF – Restricted Hartree-Fock Closed shell calculation All orbitals are doubly occupied Each orbital holds two electrons with opposite spins. UHF – Unrestricted Hartree-Fock Open shell system Species with odd number of electrons (ions, radicals, etc.) Excited states Bond dissociations Performance of Ab Initio HF Energetics HF theory ignores electron correlation (not good for making/breaking bonds) CO + HO· = CO2 + H· HF STO-3G 3-21G 6-31G(d,p) Exp Kcal/mol 34.1 3.1 -5.8 -23 Mean unsigned errors in 11 predicted glucose conformational energies HF STO-3G 3-21G 6-31G(d) cc-pVDZ cc-pVTZ cc-pVQZ 1.1 2.0 0.2 0.1 0.6 0.8 Conformation scanning Hm-X-Y-Hn, X, Y = {B, C, N, O, Si, S, P} HF/STO-3G 3-21G* 6-31G(d) 0.5 0.2 0.2 (unsigned errors) Geometry HF geometries are usually very good when using basis set of relatively modest size, cc-pVDZ or 6-31G* level & better. Properties Calculated Phase and reaction equilibria Bond and interaction energies Reaction kinetics Rate constants, products Transport properties Interaction energies, dipole: µ. Analytical information Spectroscopy: Frequencies, UV / Vis /IR absorptivity Mass spectrometric ionization potentials and cross-sections, fragmentation patterns NMR shifts Vibrational Frequencies Vibrational frequencies (at 0 K) are calculated using parabolic approximation at the well bottom. How many? Need 3 N atoms coordinates to define molecule. If we have free translational motion in 3 dimensions, then three translational degrees of freedom. Likewise for free rotation: 3 d.f. if nonlinear, 2 if linear. Thus, 3 N atoms -5 (linear) or 3 N atoms -6 (nonlinear) vibrations. For diatomic, ∂ 2 E /∂ r 2 = force constant k [for r dimensionless]. F (= ma = m 2 r /∂ t 2 ) = - kr is a harmonic oscillator in Newtonian mechanics (Hooke’s law). For polyatomic, analyze Hessian matrix [∂ 2 E /∂ r i r j ] instead. Kinetics how to locate transition states along the “minimum energy path”: Find stationary point (∂E/∂ = 0) with respect to all displacements.  #### You've reached the end of your free preview.

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