Geometry optimization overview

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. 

The response to the second question is in terms of relative computation times for energy calculations, geometry optimizations and frequency evaluations on different size molecules. This is addressed in the final chapter of this section. Overview and Cost. 

Abstract This contribution focuses upon the application of evolutionary algorithms to the non-deterministic polynomial hard problem of global cluster geometry optimization. The first years of method development in this area are sketched briefly followed by a characterization of the current state of the art by an overview of recent application work. Strengths and weaknesses of this approach are highlighted by comparison with alternative methods. Last but not least, current method development trends and desirable future development directions are summarized. 

The remainder of this review is outlined as follows. The historical method development of EA use for global cluster geometry optimization is briefly recalled in Sect. 2. An overview of typical application work in recent years is provided in Sect. 3. In Sect. 4, we take a side glance at other methods to tackle the same and related problems, and briefly discuss advantages and disadvantages of some the prominent alternatives to EAs. Finally, in Sect. 5 recent method development work is summarized, and we try to give some (personal, biased) opinions on which open questions such developments should address in the future. 

Figrire 8 An overview of quantum chemical methods for excited states. Bold-italic entries indicate methods that are currently applicable to large molecules. Important abbreviations used Cl (configuration Interaction), TD (time-dependent), CC (coupled-cluster), HF (Hartree-Fock), CAS (complete active space), RAS (restricted active space), MP (Moller-Plesset perturbation theory), S (singles excitation), SD (singles and doubles excitation), MR (multireference). Geometry optimizations of excited states for larger molecules are now possible with CIS, CASSCF, CC2, and TDDFT methods. 

Figure 3. Overview of the three geometry-optimized structures of the cysteine thiyl radical, (a) 1st minimum, (b) 2nd minimum, and (c) 3rd minimum. The directions of the principal axes of the g-tensor z (brown, parallel to the synunetry axis of the 3p orbital in the SOMO) and the y (light-blue) principal axis of the g-tensor are indicated. The x axis is parallel to the Cp-Sy direction. Reproduced with pemussion from [128]. Copyright 2004, American Chemical Society.

In this chapter, we first present a brief overview of the experimental techniques that we and others have used to study torsional motion in S, and D0 (Section II). These are resonant two-photon ionization (R2PI) for S,-S0 spectroscopy and pulsed-field ionization (commonly known as ZEKE-PFI) for D0-S, spectroscopy. In Section HI, we summarize what is known about sixfold methyl rotor barriers in S0, S, and D0, including a brief description of how the absolute conformational preference can be inferred from spectral intensities. Section IV describes the threefold example of o-cholorotoluene in some detail and summarizes what is known about threefold barriers more generally. The sequence of molecules o-fluorotoluene, o-chlorotoluene, and 2-fluoro-6-chlorotoluene shows the effects of ort/io-fluoro and ortho-chloro substituents on the rotor potential. These are approximately additive in S0, S, and D0. Finally, in Section V, we present our ideas about the underlying causes of these diverse barrier heights and conformational preferences, based on analysis of the optimized geometries and electronic wavefunctions from ab initio calculations. 

This chapter gave an overview of how to simplify complex processes sufficiently to allow the use of analytical models for their analysis and optimization. These models are based on mass, momentum, energy and kinetic balance equations, with simplified constitutive models. At one point, as the complexity and the depth of these models increases by introducing more realistic geometries and conditions, the problems will no longer have an analytical solution, and in many cases become non-linear. This requires the use of numerical techniques which will be covered in the third part of this book, and for the student of polymer processing, perhaps in a more advanced course. 

---