Biomedical Engineering Reference
In-Depth Information
20.6 Custom and Hybrid Functionals
Hybrid functionals are those that contain mixtures of the HF exchange with DFT exchange-
correlation, whilst
ab Initio
codes usually give the user a choice of constructing their own
linear combination.
20.7 An Example
We worked through a typical HF-LCAO calculation on l-phenylanine using the 6-311G**
basis set in Chapter 16. The following output relates to a corresponding KS-LCAO single
point calculation. The first part of the .gjf is:
# b3lyp/6-311G** Pop=full
L-phenylanine single point
01
N
0.000 0.000
0.000
H
0.000 0.000
1.010
C
1.366 0.000
-0.483
...
Following current fashion, I chose the Becke three-parameter exchange and the Lee-
Yang-Parr correlation functionals (B3LYP). The usual iterative procedure is followed and
the output is all but identical to that shown in Chapters 16 and 17; a major difference from
HF-LCAO theory is that the numerical integration has to be done at the end of each cycle,
although this is not shown explicitly.
The electronic state of the initial guess is 1-A.
Warning! Cutoffs for single-point calculations used.
Requested convergence on RMS density matrix=1.00D-04 within 128 cycles.
Requested convergence on MAX density matrix=1.00D-02.
Requested convergence on energy=5.00D-05.
No special actions if energy rises.
SCF Done: E(RB+HF-LYP) = -554.845359196
A.U. after
8 cycles
Convg = 0.4690D-05
-V/T = 2.0027
S**2 = 0.0000
The energy reported is the equivalent of the usual HF-LCAO energy.
Next come the KS-LCAO orbital energies:
(A) (A) (A) (A) (A) (A) (A) (A) (A) (A)
The electronic state is 1-A.
Alpha occ. eigenvalues - -19.19197 -19.12622 -14.29542 -10.31653 -10.22146
Alpha occ. eigenvalues - -10.17833 -10.17422 -10.16835 -10.16719 -10.16615
Alpha occ. eigenvalues - -10.16444 -10.13667 -1.16057
-1.03817
-0.90705
Alpha occ. eigenvalues - -0.85012 -0.78882
-0.74037
-0.73113
-0.68902
Alpha occ. eigenvalues - -0.62748 -0.60433
-0.57744
-0.55764
-0.54022
Alpha occ. eigenvalues - -0.50460 -0.49534
-0.47506
-0.46924
-0.45013
