Mechanics, molecular modelling

A final important area is the calculation of free energies with quantum mechanical models [72] or hybrid quanmm mechanics/molecular mechanics models (QM/MM) [9]. Such models are being used to simulate enzymatic reactions and calculate activation free energies, providing unique insights into the catalytic efficiency of enzymes. They are reviewed elsewhere in this volume (see Chapter 11). 

One great advantage of the molecular mechanics model is that it can be applied to large molecules on your average PC. Apart from single molecular structure... 

Deeth RJ (2001) The ligand field molecular mechanics model and the stereoelectronic effects of d and s electrons. Coord Chem Rev 212 11... 

Cieplak, P., Caldwell, J. W., Kollman, P. A., Molecular mechanical models for organic and biological systems going beyond the atom centered two body additive approximation aqueous solution free energies of methanol and IV-methyl acetamide, nucleic acid base, and amide hydrogen bonding and chloroform/water partition coefficients of the nucleic acid bases, J. Comput. Chem. 2001, 22, 1048-1057... 

One tool for working toward this objective is molecular mechanics. In this approach, the bonds in a molecule are treated as classical objects, with continuous interaction potentials (sometimes called force fields) that can be developed empirically or calculated by quantum theory. This is a powerful method that allows the application of predictive theory to much larger systems if sufficiently accurate and robust force fields can be developed. Predicting the structures of proteins and polymers is an important objective, but at present this often requires prohibitively large calculations. Molecular mechanics with classical interaction potentials has been the principal tool in the development of molecular models of polymer dynamics. The ability to model isolated polymer molecules (in dilute solution) is well developed, but fundamental molecular mechanics models of dense systems of entangled polymers remains an important goal. 

B. Waszkowycz, I. H. Hiller, N. Gensmantel, D. W. Payling, A Combined Quantum Mechanical/Molecular Mechanical Model of the Potential Energy Surface of Ester Hydrolysis by the Enzyme Phospholipase A2 ,. /. Chem. Soc., Perkin Trans. 2 1991, 225-231. 

Chemists seeking to use computational chemistry to support experimental efforts now have three generd theoretical tools available to them force field or molecular mechanics models, ab initio molecular orbital (MO) models and semiempirical MO models (1). Each of these tools have strengths and weaknesses which must be evaluated to determine which is most appropriate for a given applications. 

As pointed out in the preface, a wide variety of different procedures or models have been developed to calculate molecular structure and energetics. These have generally been broken down into two categories, quantum chemical models and molecular mechanics models. 

The opening chapter in this section outlines a number of different classes of Quantum Chemical Models and provides details for a few specific models. It anticipates issues relating to cosf and capability (to be addressed in detail in Section II). Similar treatment of Molecular Mechanics Models is provided in the second chapter in this section. 

This chapter describes the basis of molecular mechanics models and introduces the SYBYL and MMFF force fields. It also compares and contrasts molecular mechanics and quantum chemical models. 

Molecular mechanics models differ both in the number and specific nature of the terms which they incorporate, as well as in the details of their parameterization. Taken together, functional form and parameterization, constitute what is termed a force field. Very simple force fields such as SYBYL, developed by Tripos, Inc., may easily be extended to diverse systems but would not be expected to yield quantitatively accurate results. On the other hand, a more complex force field such as MMFF94 (or more simply MMFF), developed at Merck Pharmaceuticals, while limited in scope to common organic systems and biopolymers, is better able to provide quantitative accounts of molecular geometry and conformation. Both SYBYL and MMFF are incorporated into Spartan. 

The fact that molecular mechanics models are parameterized may also be seen as providing an advantage over quantum chemical models. It is possible, at least in principle, to construct molecular mechanics models which will accurately reproduce known experimental data, and hopefully will anticipate (unknown) data on closely-related systems. 

Finally, it needs to be noted that molecular mechanics is essentially an interpolation scheme, the success of which depends not only on good parameters, but also on systematics among related molecules. Molecular mechanics models would not be expected to be highly successful in describing the structures and conformations of new (unfamiliar) molecules outside the range of parameterization. 

As commented previously, molecular mechanics models are applicable only to investigation of equihbrium geometries and conformations. 

Calculated equilibrium geometries for hydrogen and main-group hydrides containing one and two heavy (non-hydrogen) atoms are provided in Appendix A5 (Tables A5-1 and A5-10 for molecular mechanics models, A5-2 and A5-11 for Hartree-Fock models, A5-3 and A5-12 for local density models, A5-4 to A5-7 and A5-13 to A5-16 for BP, BLYP, EDFl and B3LYP density functional models, A5-8 and A5-17 for MP2 models and A5-9 and A5-18 for MNDO, AMI and PM3 semi-empirical models). Mean absolute errors in bond lengths are provided in Tables 5-1 and 5-2 for one and two-heavy-atom systems, respectively. 

The MMFF molecular mechanics model provides an excellent account of C-N and C-0 bond distances. SYBYL also presents a credible account, although bond lengths for some systems are significantly in error. MMFF is clearly the better choice. 

Calculated heavy-atom bond distances in molecules with three or more first and/or second-row atoms are tabulated in Appendix A5 molecular mechanics models (Table A5-21), Hartree-Fock models (Table A5-22), local density models (Table A5-23), BP, BLYP, EDFl and B3LYP density functional models (Tables A5-24 to A5-27), MP2 models (Table A5-28), and MNDO, AMI and PM3 semi-empirical models (Table A5-29). Results for STO-3G, 3-21G, 6-31G and 6-311+G basis sets are provided for Hartree-Fock models, but as in previous comparisons, only 6-3IG and 6-311+G basis sets are employed for local density, density functional and MP2 models. 

Comparative data for heavy-atom bond lengths and skeletal bond angles for molecules incorporating one or more third or fourth-row, main-group elements are provided in Appendix A5 Table A5-39 for Hartree-Fock models with STO-3G, 3-2IG and 6-3IG basis sets. Table A5-40 for the local density model, BP, BLYP, EDFl andB3LYP density functional models and the MP2 model, all with the 6-3IG basis set, and in Table A5-41 for MNDO, AMI and PM3 semi-empirical models. 6-31G, local density, density functional and MP2 calculations have been restricted to molecules with third-row elements only. Also, molecular mechanics models have been excluded from the comparison. A summary of errors in bond distances is provided in Table 5-8. 

The present coverage is divided according to the class of intermediate carbocations, anions, carbenes (and related divalent compounds) and radicals. Within each class, the usual set of models is assessed, the exception being that molecular mechanics models have been excluded. These have not been explicitly parameterized for charged species or molecules with unpaired electrons, and cannot be expected to perform favorably. Note that in some, but not all cases, the quality of the experimental structural data is not up to the same standard as for other small molecules. This is particularly true for carbocations and anions, where differences among counterions may lead to large differences in structure. 

Representative examples are provided in Table 5-19. Only a single (intermolecular) distance is examined for each system, underlying the fact that the experimental structure data are incomplete. The usual quantum chemical models have been surveyed. Comparisons with molecular mechanics models have not been included even though force fields such as MMFF have been explicitly parameterized to reproduce known hydrogen-bond distances. 

---