Relative Computation Times

Relative computation times for camphor (C10H16O), morphine (C17H19NO2) and triacetyldynemicin A (C36H25NO12) for a variety of models are provided below:


 
camphora
morphineb
triacetyldynemicin Ac
model
energy
geometryd
energy
geometrye
energy
geometryf

MMFF    

too small

   

 

AM1    
to measure
   
0.1
             
HF/3-21G
1
5
1g
12
1h
40
HF/6-31G*
7
30
8
110
7
360
HF/6-311+G**
42
180
-
-
-
             
EDF1/6-31G*
12
57
10
140
5
160
EDF1/6-311+G**
60
290
50
-
-
-
             
B3LYP/6-31G*
13
65
12
160
10
400
B3LYP/6-311+G**
85
370
76
-
-
-
             
MP2/6-31G*
27
270
80
2000
320
-
MP2/6-311+G**
260
-
650
-
-
-
             
LMP2/6-31G*
25
-
50
-
90
-
LMP2/6-311+G**
140
-
270
-
-
-

a) 131 basis functions for 3-21G, 197 basis functions for 6-31G* and 338 basis functions for 6-311+G**
b
) 227 basis functions for 3-21G, 353 basis functions for 6-31G* and 576 basis functions for 6-311+G**
c) 491 basis functions for 3-21G and 785 basis functions for 6-31G*
d) assumes 4 optimization steps
e) assumes 12 optimization steps
f) assumes 24 optimization steps
g) 4 relative to 3-21G energy calculation on camphor
h) 27 relative to 3-21G energy calculation on camphor


The estimates for geometry optimizations assume a fix number of steps (increasing with molecule size). The required number may vary by as much as a factor of two depending on the molecule and the "quality" of the guess. Transition state optimizations will typically require two to three times the number of optimization steps as equilibrium geometry optimizations.

Molecular mechanics calculations do not "show up" on the chart. They are at least an order of magnitude less costly than the simplest (semi-empirical) quantum chemical calculations, and the ratio between the two increases rapidly with increasing molecular size.

The cost of evaluating the energy using the Hartree-Fock 3-21G model is two orders of magnitude greater than that for obtaining an equilibrium geometry using the AM1 semi-empirical model. This ratio should maintain with increasing size, as both semi-empirical and Hartree-Fock models scale as the cube of number of basis functions. Geometry optimization using 3-21G is approximately an order of magnitude more costly than energy calculation. This ratio should increase with increasing molecule size, due to an increase in the number of geometrical variables and a corresponding increase in the number of steps required for optimization. The cost difference for both energy evaluation and geometry optimization between (Hartree-Fock) 3-21G and 6-31G* calculations is on the order of five or ten times.

EDF1 density functional calculations are only slightly more costly than Hartree-Fock calculations with the same basis set for small and medium size molecules, and actually less costly for large molecules. B3LYP calculations are roughly 50% more than Hartree-Fock calculations. This applies both to energy calculations. MP2 calculations are much more costly than comparable (same basis set) Hartree-Fock and density functional calculations. In practice, their application is much more limited than either Hartree-Fock or density functional models. Localized MP2 (LMP2) energy calculations are similar in cost to MP2 calculations for small molecules, but the cost differential rapidly increases with increasing size. Still they are close to an order of magnitude more costly than Hartree-Fock or density functional calculations.