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Selecting a Model

A brief overview of the performance of molecular mechanics and quantum chemical models (including semi-empirical models, Hartree-Fock models, density functional models and MP2 models) with regard to the calculation of equilibrium and transition-state geometries, conformations and reaction thermochemistry is provided below. This is based on an extensive series or comparisons presented in A Guide to Molecular Mechanics and Quantum Chemical Comparisons which accompanies Spartan'14 and is available as a PDF file from the Wavefunction Website.


For each task the methods are "graded" as follows
G good
C good with cautious application
P poor
task molecular
mechanics
semi-
empirical
Hartree-
Fock
density
functional
MP2 T1
geometry(organic)
C
G
G
G
G
G
geometry(metals)
-
G
P
G
P
-
transition-state geometry
-
C
G
G
G
-
conformation
G
P
G
G
G
G
thermochemistry (general)
-
P
C
G
G
G
thermochemistry (isodesmic)
-
P
G
C
G
G
cost low ------------------------------> high


In Terms of Task:

i)   Geometries:
All models provide a good account of molecular equilibrium geometries for organic molecules and, where they are applicable, of transition-state geometries. Molecular mechanics and semi-empirical molecular orbital models often provide very good equilibrium geometries, and only rarely yield very poor geometries. They should be used for this purpose wherever possible. At the very least, they should be employed to furnish "guess geometries" to start higher-level calculations.

Hartree-Fock models with basis sets larger than 6-31G* do not provide significantly improved descriptions of either equilibrium or transition-state geometries over the Hartree-Fock 6-31G* model and, in most cases, the 3-21G model. Note, however, that MP2 and density functional models require (at the very least) basis sets which incorporate polarization functions.

Hartree-Fock models do not provide a reliable account of the geometries of compounds incorporating transition metals, but the PM3 semi-empirical model and density functional models provide good accounts. MP2 models provide good geometries for some transition metal systems, but very poor geometries for others.

ii)  Conformational Energies
Hartree-Fock and MP2 models with 6-31G* and larger basis sets and density functional models all generally provide good descriptions of conformational energy differences in organic compounds. MP2 and B3LYP density functional models are the most reliable. Given the large difference in cost between them, practical applications on any but the smallest systems are probably better handled using B3LYP models.

Semi-empirical models may in some cases be suitable for identifying conformational minima, and for determining the geometries of these minima, but they are not suitable at providing accurate relative conformer energies.

The MMFF molecular mechanics model provides an excellent account of conformational energy differences in organic compounds. Note, however, that most of the data used in the assessment were also used to parameterize MMFF. Caution is needed in the application of MMFF outside the original range of its parameterization.

iii) Energetics
MP2 and density functional models are generally more reliable than Hartree-Fock models for describing the energetics of non-isodesmic reactions although, except for reactions which involve explicit bond making or breaking, the 6-31G* and larger-basis-set Hartree-Fock models (and to a lesser extent the 3-21G model) also yield acceptable results. Hartree-Fock models with basis sets larger than 6-31G* generally yield reaction energies which are nearly identical to those from the Hartree-Fock 6-31G* model.

MP2 and density functional models are needed to accurately account for the energetics of reactions where bonds are broken or formed and to properly describe absolute activation energies. Hartree-Fock and local density models are unsatisfactory. Hartree-Fock models are satisfactory in description of relative activation energies.

Hartree-Fock and MP2 models provide an excellent account of the energetics of isodesmic reactions. Density functional models are not reliable in all instances and should be applied only with caution.

Semi-empirical models are unsatisfactory in their description of the energetics of all types of reactions, isodesmic processes included.

In Terms of Method:

Molecular mechanics models are restricted to the description of molecular equilibrium geometry and conformation. They are perhaps the only practical techniques for searching conformation space for any but the simplest molecules or for systems with more than a few degrees of conformational freedom.

Semi-empirical models are particularly attractive for:
  1. Equilibrium geometry determinations for large molecules, where the cost of Hartree-Fock and MP2 and density functional models may be prohibitive.
  2. Transition-state geometry optimizations, where the cost of Hartree-Fock and MP2 and density functional models may be prohibitive.
  3. Equilibrium and transition-state geometry optimizations involving transition-metal inorganic and organometallic compounds, where Hartree-Fock models are known to produce poor results, and where the cost of MP2 and density functional models may be prohibitive.
Semi-empirical models are unsuitable for:
  1. Calculations on reaction energies, including the energies of isodesmic processes.
  2. Calculations of conformational energy differences.
Hartree-Fock models are particularly attractive for:
  1. Equilibrium and transition-state structure determinations of medium-size organic and main-group inorganic molecules, where increased accuracy over that available from semi-empirical models is required, and where the cost of MP2 and density functional models may be prohibitive.
  2. Calculations of reaction energies (except reactions involving explicit bond making or breaking), where semi-empirical models yield unacceptable results, and where the cost of MP2 and density functional models may be prohibitive.
Hartree-Fock models are unsuitable for:
  1. Calculation of reaction energies which involve net bond making or breaking and calculation of absolute activation energies.
  2. Equilibrium and transition-state structure determinations for transition-metal inorganic and organometallic molecules.

MP2 and density functional models are needed for accurate descriptions of the thermochemistry of reactions which involve explicit bond making or breaking, and for calculation of absolute activation energies. Local density models do not provide acceptable results, but the other density functional models provide good descriptions of reactions which involve net bond making or breaking. In practice, MP2 models may only be applied to relatively small molecules, whereas density functional models are comparable in cost to Hartree-Fock models for molecules of moderate size and less costly for large molecules.

Density functional models are particularly attractive for:
  1. Calculations on large molecules, where the cost of and MP2 models may be prohibitive, and where Hartree-Fock semi-empirical calculations may not be sufficiently accurate.
  2. li>Calculations on inorganic and organometallic systems where Hartree-Fock models may not be sufficiently accurate, and where the cost of MP2 models may be prohibitive.
  3. Thermochemical calculations, in particular, those which involve explicit bond making or breaking, and absolute activation energy calculations.


  4. 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

       

     

    PM3    
    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
    -
    -
    -
                 
    EDF2/6-31G*
    12
    57
    10
    140
    5
    160
    EDF2/6-311+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
    -
    -
    -
                 

    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 PM3 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.

    EDF2 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 and geometry optimizations. 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.


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    Last modified: Thu Jun 20 10:47:57 PDT 2013