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.
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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
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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
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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.
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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
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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.
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Kinetics how to locate transition states along the “minimum energy path”: Find stationary point (∂E/∂ = 0) with respect to all displacements.
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