Molecular mechanics Quantum mechanical calculations

Unlike quantum mechanics, molecular mechanics does not treat electrons explicitly. Molecular mechanics calculations cannot describe bond formation, bond breaking, or systems in which electron ic delocalization or m oleciilar orbital in teraction s play a m ajor role in determining geometry or properties. 

The generalised Born equation has been incorporated into both molecular mechan calculations (by Still and co-workers [Still et al. 1990 Qiu et al. 1997]) and semi-empiri quantum mechanics calculations (by Cramer and Truhlar, in an ongoing series of mod called SMI, SM2, SM3, etc. [Cramer and Truhlar 1992 Chambers et al. 1996]). In th( Ireafirients, the two terms in Equation (11.61) are combined into a single expression of 1 following form ... 

PW91 (Perdew, Wang 1991) a gradient corrected DFT method QCI (quadratic conhguration interaction) a correlated ah initio method QMC (quantum Monte Carlo) an explicitly correlated ah initio method QM/MM a technique in which orbital-based calculations and molecular mechanics calculations are combined into one calculation QSAR (quantitative structure-activity relationship) a technique for computing chemical properties, particularly as applied to biological activity QSPR (quantitative structure-property relationship) a technique for computing chemical properties... 

In addition to molecular mechanics calculations, HyperChem can perform various quantum mechanical calculations. These calculations are more universal than molecular mechanics, but are also more time consuming and less empirical. 

HyperChem quantum mechanical calculations are ab initio and semi-empirical. Ab initio calculations use parameters (contracted basis functions) associated with shells, such as an s shell, sp shell, etc., or atomic numbers (atoms). Semi-empirical calculations use parameters associated with specific atomic numbers. The concept of atom types is not used in the conventional quantum mechanics methods. Semi-empirical quantum mechanics methods use a rigorous quantum mechanical formulation combined with the use of empirical parameters obtained from comparison with experiment. If parameters are available for the atoms of a given molecule, the ab initio and semi-empirical calculations have an a priori aspect when compared with a molecular mechanics calculation, letting... 

The overall form of each of these equations is fairly simple, ie, energy = a constant times a displacement. In most cases the focus is on differences in energy, because these are the quantities which help discriminate reactivity among similar stmctures. The computational requirement for molecular mechanics calculations grows as where n is the number of atoms, not the number of electrons or basis functions. Immediately it can be seen that these calculations will be much faster than an equivalent quantum mechanical study. The size of the systems which can be studied can also substantially ecHpse those studied by quantum mechanics. 

The molecular mechanics calculations discussed so far have been concerned with predictions of the possible equilibrium geometries of molecules in vacuo and at OK. Because of the classical treatment, there is no zero-point energy (which is a pure quantum-mechanical effect), and so the molecules are completely at rest at 0 K. There are therefore two problems that I have carefully avoided. First of all, I have not treated dynamical processes. Neither have I mentioned the effect of temperature, and for that matter, how do molecules know the temperature Secondly, very few scientists are interested in isolated molecules in the gas phase. Chemical reactions usually take place in solution and so we should ask how to tackle the solvent. We will pick up these problems in future chapters. 

Zhang Y, Lin H (2008) Hexible-boundary quantum-mechanical/molecular-mechanical calculations partial charge transfer between the quantum-mechanical and molecular-mechanical subsystems. J Chem Theory Comput 4(3) 414—425... 

Molecular mechanics calculations have become a well established tool in the area of coordination chemistry, including the coordination chemistry of nickel375-379 where they are often applied for the analysis or the prediction of structures,380 the computation of isomer or conformer ratios and metal ion selectivities,381,382 and for simulating spectroscopic properties in combination with AOM calculations or by hybrid quantum mechanics/molecular mechanics (QMMM) methods.383,384 Details of the various approaches, e.g., the incorporation of d-electron stabilization energy... 

Density functional theory has been used to investigate the Diels-Alder reactions of triazolinedione with s-cis- and. y-fran -butadiene. " Combined quantum mechanics-molecular mechanics calculations have been used to investigate the asymmetric Diels-Alder reaction of cyclopentadiene with the complex dienophiles AICI3-methyl acrylate and methoxyaluminium dichloride-acrolein.Equilibrium constants have been determined for the molecular complexes formed from 1-alkyl-1-(2-naphthyl)ethenes and 1-vinylnaphthalene with TCNE in C1(CH2)2C1 at 27.1 °C ... 

The N,N -diphenylguanidinium (dpg+) has been foimd to adopt different conformations both in aqueous solutions [9] and in several salts that are being reviewed in this paper. The conformation of dpg+ is very sensitive to the counter-ion, and this effect has been the subject of ab-initio quantum mechanical and molecular mechanics calculations [10]. Stabilization of a particular conformation depends critically on intermolecular interactions with the solvent, since the energetic cost of rotation of the phenyl rings is much lower than typical solvation energies. 

The first three summations in equation 1 are over all bonds , all bond angles and all torsion angles , respectively. Thus, information about bonding is part of the input to a molecular mechanics calculation, in contrast to a quantum chemical calculation where it is part of the output . The last summation in equation 1 is over all pairs of atoms which are not bonded. 

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. Molecular mechanics is really the only viable alternative at present for molecules comprising more than a few hundred atoms. It is also likely to be the only practical alternative for conformational searching on molecules with more than a few degrees of freedom. 

Over the span of two decades, molecular modeling has emerged as a viable and powerful approach to chemistry. Molecular mechanics calculations coupled with computer graphics are now widely used in lieu of tactile models to visualize molecular shape and quantify steric demands. Quantum chemical calculations, once a mere novelty, continue to play an ever increasing role in chemical research and teaching. They offer the real promise of being able to complement experiment as a means to uncover and explore new chemistry. 

The expansion in the power of computers and theoretical methods has made it possible to investigate the mechanism of action of enzymes by combinations of quantum-mechanical and molecular-mechanical calculations. A study of two possible mechanisms for dihydrofolate reductase catalysis was consistent with indirect proton transfer from aspartate to N-5 of the pterin as has been suggested for many years by crystallographic evidence <2003PCB14036>. This conclusion is also consistent with the outcome of a study that directly measured the of the active site aspartate in the Lactobacillus casei enzyme <1999B8038>. Observations of chemical shifts of... 

Dynamic NMR gives information on the number and symmetries of conformations present in solution and on the energy barriers separating these conformations. This is particularly true for systems with barriers between about 25 and 90 kJ mol-1, a situation which often occurs in the medium ring. The interpretation of the NMR data can be carried out by the examination of molecular models, but this is a relatively crude and sometimes misleading method. Empirical force field (or molecular mechanics) calculations are much superior, even though the parametrization of heteroatoms may be open to question. Quantum mechanical calculations are not very suitable the semiempirical type, e.g. MINDO, do not reproduce conformational properties of even cyclohexane satisfactorily, and the ab initio... 

Ryde, U. 2003. Combined Quantum and Molecular Mechanics Calculations on Metalloproteins Curr. Opin. Chem. Biol., 7, 136. 

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