Structural optimization

Figure 1.8 Optimization discards many structural features, leaving an optimized structure.

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. 

The heating phase is used to take a molecular system smoothly from lower temperatures, indicative of a static initial (possibly optimized) structure, to the temperature T at which it is desired to perform the molecular dynamics simulation. The run phase then constitutes a simulation at temperature T. If the heating has been done carefully, it may be possible to skip the equilibration phase... 

When using the heating and cooling features of HyperChem it should be remembered that it is accomplished through rescaling of the velocities, so if the velocities are zero no temperature can occur. This happens, for example, if you start with an exactly optimized structure and heat from a starting temperature Tj of zero, or use the restart option when velocities are all zero. 

To measure the goodness of fit, and to quantify the structural determination, a reliability (i -factor) comparison is used. In comparing the data and simulation of the experiment for many trial structures, a minimum R factor can be found corresponding to the optimal structure. In this way atomic positions can be determined in favorable cases to within a few hundredths of an A, comparable to the accuracy achieved in Low-Energy Electron Diffraction (LEED). 

Thermodynamic properties. A molecular-dynamics simulation method (using a steepest decent method) with Stillinger-Weber potential is employed to optimize structures and to obtain the cohesive en-... 

Fig. 7, Optimized structures of the tori shown by elongation to height pentagons and heptagons are shaded top views and side views are shown in each case.

In Gaussian, the molecule specification for a geometry optimization can be given in any format desired Cartesian coordinates, Z-matrix, mixed coordinates. The geometry optimization job will produce the optimized structure of the system as its output. 

The final optimized structure appears immediately after the final convergence tests ... 

Predicted bond lengths (R), bond angles (A and dihedral angles (D for the optimized structure. 

The Optimized Parameters are the predicted bond lengths (named Rn), bond angles (An) and dihedral angles (Dn) for the optimized structure. The applicable atom numbers are in parentheses. Atoms in the molecule are numbered according to their order in the molecule specification section. These center numbers also appear in the Cartesian coordinates for the optimized strucmre expressed in the standard orientation which follows the listing of the optimized parameters. 

The remainder of the optimization output file displays the population analysis, molecular orbitals (if requested with Pop=Reg) and atomic charges and dipole moment for the optimized structure. 

Here are the energies and dipole moments of the two optimized structures ... 

We are interested in the H-H bond length, so we specify the coordinate bonding those two atoms to the AddRedundant option so that its value will be included in the printout of the optimized structure (the Si-H bond lengths will be included by default). 

Because of the nature of the computations involved, firequency calculations are valid only at stationary points on the potential energy surface. Thus, frequency calculations must be performed on optimized structures. For this reason, it is necessary to run a geometry optimization prior to doing a frequency calculation. The most convenient way of ensuring this is to include both Opt and Freq in the route section of the job, which requests a geometry optimization followed immediately by a firequency calculation. Alternatively, you can give an optimized geometry as the molecule specification section for a stand-alone frequency job. 

Run frequenqf calculations on the two vinyl alcohol isomers we considered in the last chapter. Optimize the structures at the RHF level, using the 6-31G(d) basis set, and perform a frequency calculation on each optimized structure. Are both of the forms minima What effect does the change in structure (i.e., the position of hydrogen in the hydroxyl group) have on the frequencies ... 

So]ots ji A frequency job on the optimized structure for planar vinyl amine will produce one imaginary frequency. This indicates that it is a transition state, not a minimum... 

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. 

Diffuse functions have very little effect on the optimized structure of methanol but do significantly affect the bond angles in negatively charged methoxide anion. We can conclude that they are required to produce an accurate structure for the anion by comparing the two calculated geometries to that predicted by Hartree-Fock theory at a very large basis set (which should eliminate basis set effects). 

In contrast, the other two frequency calculations determine the corresponding optimized structure to be a minimum. 

Beginning with the final optimized structure from step 1, obtain the fii equilibrium geometry using the fuU MP2 method—requested with t MP2(Full keyword in the route section—which includes inner sh electrons. The 6-31G(d) basis set is again used. This geometry is used 1 all subsequent calculations. 

The results of the frequency calculation confirm that the optimized structure is a transition structure, producing one imaginary frequency. The predicted zero-point energy is 0.01774 (after scaling), yielding a total energy of-113.67578 hartrees. 

First, we perform an optimization of the transition structure for the reaction, yielding the planar structure at the left. A frequency calculation on the optimized structure confirms that it is a first-order saddle point and hence a transition structure, having a zero-point corrected energy of -113.67941 hartrees. The frequency calculation also prepares for the IRC computation to follow. 

A frequency calculation to verify the transition structure, compute its zero point energy, and prepare for the IRC (the optimized structure is given in the input file for this exercise). 

The first job step computes the energies of the three lowest excited states. The second job step uses its results to begin the optimization by including the Read option to the CIS keyword, Geom=Check, and Guess=Read (and of course the commands to name and save the checkpoint file). The Freq keyword computes the frequencies at the optimized structure. 

An SCRF frequency calculation at the two SCRF optimized structures. Note that frequency calculations must be run as a separate job step for SCRF calculations (Opt Freq does not do what might be expected). 

Perform frequency calculations on all three optimized structures, using the same SCRF method and model chemistry. 

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