Optimizing the Structures of Molecules

To calculate the properties of a molecule, you need to generate a well-defined structure. A calculation often requires a structure that represents a minimum on a potential energy surface. HyperChem contains several geometry optimizers to do this. You can then calculate single point properties of a molecule or use the optimized structure as a starting point for subsequent calculations, such as molecular dynamics simulations. 

---

In the previous chapters, you have learned how to use DFT calculations to optimize the structures of molecules, bulk solids, and surfaces. In many ways these calculations are very satisfying since they can predict the properties of a wide variety of interesting materials. But everything you have seen so far also substantiates a common criticism that is directed toward DFT calculations namely that it is a zero temperature approach. What is meant by this is that the calculations tell us about the properties of a material in which the atoms are localized at equilibrium or minimum energy positions. In classical mechanics, this corresponds to a description of a material at 0 K. The implication of this criticism is that it may be interesting to know about how materials would appear at 0 K, but real life happens at finite temperatures. 

Geometric Optimization. The structure of the molecule as built by CHEMLAB (or a input from other methods) can be optimized through either a full force field molecular mechanics calculation (MMII) or with the semi-empirical molecular orbital methods MINDO-3 and MNDO. 

As an example of why linear interpolation is not always a useful way to initialize an NEB calculation, consider the molecule HCN in the gas phase. This molecule can rearrange to form CNH. Optimize the structures of HCN and CNH, then use these states to examine the bond lengths in the structures that are defined by linear interpolation between these two structures. Why are the intermediate structures defined by this procedure not chemically reasonable Construct a series of initial images that are chemically reasonable and use them in an NEB calculation to estimate the activation energy for this molecular isomerization reaction. 

Although quantum pharmacology calculations are more rigorous and robust when applied to small molecules, such calculations may also be applied to macromolecules. There are few drug molecules that are macromolecules peptides, such as insulin, are the exception. Usually, it is the receptor that is the macromolecule. Although receptors are discussed in detail in chapter 2, the role of quantum pharmacology in optimizing the structure of macromolecules will be presented here. 

Barone et al studied the optical properties of solvated /7-benzoquinone, i.e., a benzene molecule in which two opposite C atoms have been replaced by oxygen cf. Fig. 15). They used time-dependent density-functional calculations in the determination of the optical properties of the solute and a polarizable-continuum approach for the solvent. By using a recent development that allows for optimizing the structure of the excited molecule in solution, they could determine both the ground-state structure and that of the excited state. Then, they could calculate both vertical... 

As the last example we shall study clusters of water molecules. Here, we have clusters formed by only weakly interacting units, but for which the units have an internal structure and, consequently, the interactions are directional. For water clusters the TIP potentials are very popular and have, therefore, been used in optimizing the structure of water clusters. One of the first studies in this direction is due to Tsai and Jordan8 who used their eigenmode method (see Section 2.4) in optimizing the structure for clusters with up to 5 units. Later... 

The cluster with the rotation axis C5 was used in our research of hy-droxyfullerene to simplify the calculation model. Figure 8.6(a) demonstrates the structure of molecule optimized by energy, and Figure 8.6(b) demonstrates the optimized structure of cluster eo[ ]io. All the... 

For small clusters of only one solvent molecule, Li (S) (S=EC, PC and VC), both the inner and the bulk solvent effect are fully optimized with density functional theory, using the B3PW91 method and the 6-31 l-i-HG(d,p) basis set, while the bulk solvent effect is accounted for using the CPCM method. The overall procedure is denoted as CPCM-B3PW91/6-311-H-HG(d,p). For the cases with more than one solvent molecules in the cluster models, B3PW91 with the basis set 6-31G(d) is employed to optimize the structure of Li (S) (n > 1) and... 

Another problem is to determine the optimal number of descriptors for the objects (patterns), such as for the structure of the molecule. A widespread observation is that one has to keep the number of descriptors as low as 20 % of the number of the objects in the dataset. However, this is correct only in case of ordinary Multilinear Regression Analysis. Some more advanced methods, such as Projection of Latent Structures (or. Partial Least Squares, PLS), use so-called latent variables to achieve both modeling and predictions. 

On the other hand, theoretical methods allow an insight into the structure of non-existent molecules like 2//-indazole (37) or the anion of indazole (38). INDO calculations have been performed by Palmer et al. on the anion of indazole (38) (75JCS(P1)1695). The optimized geometry obtained by them is shown in Figure 7. The N—N bond distance is longer in the... 

Our second example takes another member of the vinyl series, and considers the effect of replacing one of the hydrogens in ethylene with a fluorine. The fluoroethylene optimization converges at step 5. By looking at the optimized parameters for each job, we can compare the structures of the two molecules ... 

There is motion in the nitrogen atom and the hydrogens attached to it out of the plane of the molecule. This suggests that if we vary the structure of the NH2 group, we will be able to locate the minimum. It turns out that the nitrogen atom exhibits pyramidalization in the optimized structure. 

Optimize these three molecules at the Hartree-Fock level, using the LANL2DZ basis set, LANL2DZ is a double-zeta basis set containing effective core potential (ECP) representations of electrons near the nuclei for post-third row atoms. Compare the Cr(CO)5 results with those we obtained in Chapter 3. Then compare the structures of the three systems to one another, and characterize the effect of changing the central atom on the overall molecular structure. 

Chapter 3, Geometry Optimizations, describes how to locate equilibrium structures of molecules, or, more technically, stationary points on the potential energy surface. It includes an overview of the various commonly used optimization techniques and a consideration of optimizing transition strucmres as well as minimizations. 

---