Examining Optimization Output

We ll now look at the output from the ethylene optimization. After some initial output from the setup portion of the optimization job, Gaussian displays a section like the following for each step (the items pointed to by dotted lines do not appear in terse output)  

Old and new values for-structure variables, in atomic units (bohrs and radians] 

The predicted energy change is displayed, but it is not one of the convergence criteria. 

The maximum displacement is the largest change in any coordinate in the molecular strucmre. The threshold column indicates the cutoff value for each criterion. The new structure generated at this step follows this ou ut. 

When all four values in the Converged column are YES, then the optimization is completed and has converged, presumably to a local minimum. For the ethylene optimization, convergence happens after 3 steps  

---

If an optimization tuns out of steps, do not blindly assume that increasing the number of steps will fix the problem. Examine the output and determine whether the optimization was making progress or not. For example this command will provide a quick summary of an optimization s progress on a UNIX system (blank lines ate added for readability) ... 

We can show the basic concepts and structure of optimization problems by a examining a least squares problem. The problem in this case is to determine the two coefficients (ao and af) such that the error between the measured output and model predicted output is minimized ... 

If the process is not known well, we need to evaluate the objective function on-line (while the process is operating) using the values of the controlled output. Then the adaptation mechanism will change the controller parameters in such a way as to optimize (maximize or minimize) the value of the objective function (criterion). In the following two examples we examine the logic of two special self-adaptive control systems model reference adaptive control (MRAC) and self-tuning regulators (STRs). 

Although methods of preparing several phosphor compositions have been explored, we have not yet examined methods of measuring phosphor properties. The need to measmre the "brightness" or light output under a controlled excitation source should be apparent if one is to optimize any... 

Conceptually, SIMS can be considered a straightforward and direct technique. In practice, there are many complexities introduced as a result of the various methodologies that can be applied, whether in the static or in the dynamic mode of SIMS. This exists because there are numerous conditions under which SIMS can be carried out. Each condition is optimized to deal with the analysis of a different elemental or molecular species, from different solid matrices. In addition, relating the output to the compositional variations that may occur on or within the sohd being examined can be problematic. This stems, in part, from the complexities surrounding secondary ion generation, or more precisely, the matrix effect. As the term suggests, the matrix effect describes the effect of the matrix on the population of ions emitted. Matrix effects and their associated transient effects are discussed in Section 3.3.3.1.2. 

Abstract. Heat and electric charge transfer through the thermoelectric (TE) module were analyzed numerically. The thermal heat can expand or shrink in the trapezoid shape in comparison with the conventional H type module, and the output and efficiency from the module with trapezoid TE elements was examined from the view of shape optimization. The temperature profile and some thermoelectric properties were calculated using the infinite volume method and the original code. The temperature profile in the module showed a complex distribution in the TE elements, however, the efficiency in power generation did not change from that of the rectangular TE module. 

As before, the Natural Atomic Orbitals (NAOs) serve as the optimal effective atom-like orbitals for describing the overall electron density distribution of the molecular wavefunction, so that finding the atomic electrons in NBO output is not more difficult than in Chapter 2. We shall first examine how the NAOs within the molecular environment differ from the free-space forms encountered in Chapter 2. We use the experience gained there to anticipate the breathing ... 

---