•
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.

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- Spring '14
- Mole, Quantum Chemistry, Electrons, Atomic orbital, basis functions