Selecting a Model

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, MP2 models, and the T1 thermochemical recipe) 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 and is available as a PDF file from our main help page.

A simple table summary
A discussion by Task
A discussion by Method
A Timing Comparison

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 may routinely be used for this purpose. At the very least, they can 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 nor (in most cases) the Hartree-Fock 3-21G model. Note, however, that Density Functional models and MP2 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 and PM6 Semi-Empirical models and Density Functional models provide perform well for these systems. 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, B3LYP, and ωB97X-D density functional models are more reliable. Given the large difference in cost between them, practical applications on any but the smallest systems are probably better handled using Density Functional models. Beginning with Spartan'18, multi-step recipes that utilize Molecular Mechanics, Hartree-Fock, and Density Functional models with large basis sets are available for conformational searching on typically sized systems (natural-products and drug-sized molecules).

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 a good 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 basis set) 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 models are not satisfactory for this purpose. Hartree-Fock models are satisfactory , however, in description of relative activation energies.

Hartree-Fock, Density Functional and MP2 models provide an excellent account of the energetics of isodesmic reactions.

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:

Equilibrium geometry determinations for large molecules, where the cost of Hartree-Fock and MP2 and density functional models may be prohibitive.
Transition-state geometry optimizations, where the cost of Hartree-Fock and MP2 and density functional models may be prohibitive.
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:

Calculations on reaction energies, including the energies of isodesmic processes.
Calculations of conformational energy differences.

Hartree-Fock models are particularly attractive for:

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.
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:

Calculation of reaction energies which involve net bond making or breaking and calculation of absolute activation energies.
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. Density Functional models also 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:

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.
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.
Thermochemical calculations, in particular, those which involve explicit bond making or breaking, and absolute activation energy calculations.

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

	camphor^a		morphine^b		triacetyldynemicin A^c
model	energy	geometry^d	energy	geometry^e	energy	geometry^f

MMFF			too small
PM3			to measure			0.1

HF/3-21G	1	5	1^g	12	1^h	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 fixed 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.