Geometries Calculated by MM

Errors are given as MMFF/MP2. In some cases (e.g. MeOH) errors for two bonds are given, on one line and on the line below. A minus sign means that the calculated value is less than the experimental. The numbers of positive, negative, and zero deviations from experiment are summarized at the bottom of each column. The averages at the bottom of each column ate arithmetic means of the absolute values of the errors. 

Lafferty, A. G. Makai, Molecular Structures of Gas-Phase Polyatomic Molecules Determined by Spectroscopic Methods, J. Phys. Chem. Ref. Data, 1979,8,619-721. 

4 and so was able to undergo Wolff rearrangement ring contraction to the ketene precursor of 4. 

A remarkable (and apparently still unconfirmed) prediction of MM is the claim that the perhydrofullerene C6oH60 should be stabler with some hydrogens inside the cage [29]. 

For common organic molecules the Merck Molecular Force Field is nearly as good as the ab initio MP2(fc)/6-31G method for calculating geometries. Both 

C-H Bond length errors, r-rexp (A) Bond angle errors, a-aexv  

MMFF dihedral angles are remarkably good, considering that torsional barriers are believed to arise from subtle quantum mechanical effects. The worst dihedral angle error is 10°, for HOOH, and the second worst, —5.0°, is for the analogous HSSH. The (granted, low-level) ab initio HF/3-21G (Chapter 5) and semiempirical PM3 (Chapter 6) methods also have trouble with HOOH, predicting a dihedral 

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Numerical calculations for the residual stresses in the anode-supported cells are carried out using ABAQUS. After modeling the geometry of the cell of the electro-lyte/anode bi-layer, the residual thermal stresses at room temperature are calculated. The cell model is divided into 10 by 10 meshes in the in-plane direction and 20 submeshes in the out-plane direction. In the calculation, it is assumed that both the electrolyte and anode are constrained each other below 1400°C and that the origin of the residual stresses in the cell is only due to the mismatch of TEC between the electrolyte and anode. The model geometry is 50 mm x 50 mm x 2 mm. The mechanical properties and cell size used for the stress calculation are listed in Table 10.5. 

A good strategy is to perform preliminary calculations by a relatively rapid (i.e., approximate) method. Recall, however, that MM methods are generally much, much faster than quantum mechanical ones, and for questions of ground state geometries can be just as accurate. For transition state... 

Is it surprising that the geometry and energy (compared to that of other isomers) of a molecule can often be accurately calculated by a ball-and springs model (MM) ... 

Ramos et al. [238] have also used the QM/MM LSCF method [312] to understand the reasons why the pancreatic trypsin inhibitor, PTI, behaves as an inhibitor of trypsin rather than as a substrate. In fact, PTI places a peptidic bond between a lysine and an alanine in the catalytic triad of trypsin with the side chain of the lysine in the binding pocket of the enzyme, exactly as a cleavable peptide would do, and this provokes no reaction between PTI and trypsin. The QM/MM calculations performed show that the geometry adopted by the active site of the enzyme in the complex is such that it prevents the nucleophilic attack of the hydroxyl oxygen on the peptide bond of PTI. 

In 1996 a force field model was proposed in which geometry-dependent charges are calculated by EEM. This model, called consistent implementation of the electronegativity equalization method (CIEEM), combines a force field representation for the PES (e.g., Eq. [19]) with the EEM equation for the electronic energy (Eq. [7]) in such a way that the atomic terms of Eq. [7] explicitly enter the expression for the potential energy. Thus, within the CIEEM, the expression for the steric energy in the MM force field model will read... 

The most sophisticated approach to locating a transition state with MM is to use an algorithm that optimizes the input structure to a true saddle point, that is to a geometry characterized by a Hessian with one and only one negative eigenvalue (chapter 2). To do this the MM program must be able not only to calculate second derivatives, but must also be parameterized for the partial bonds in transition states, which is a feature lacking in standard MM forcefields. 

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