Optimized geometry

Schlegel H B 1995 Geometry optimization on potential energy surfaces Modern Electronic Structure Theory vo 2, ed D R Yarkony (Singapore World Scientific) pp 459-500... 

In this section, we will discuss general optimization methods. Our example is the geometry optimization problem, i.e., the minimization of (q). However, the results apply to electronic optimization as well. There are a number of usefiil monographs on the minimization of continuous, differentiable fimctions m many variables [6, 7]. 

For a very large number of variables, the question of storing the approximate Hessian or inverse Hessian F becomes important. Wavefunction optimization problems can have a very large number of variables, a million or more. Geometry optimization at the force field level can also have thousands of degrees of freedom. In these cases, the initial inverse Hessian is always taken to be diagonal or sparse, and it is best to store the... 

As noted above, the coordinate system is now recognized as being of fimdamental importance for efficient geometry optimization indeed, most of the major advances in this area in the last ten years or so have been due to a better choice of coordinates. This topic is seldom discussed in the mathematical literature, as it is in general not possible to choose simple and efficient new coordinates for an abstract optimization problem. A nonlmear molecule with N atoms and no... 

Table B3.5.1 Number of cycles to converge for geometry optimizations of some typical organic molecules usmg Cartesian, Z-matrix and delocalized internal coordinates. ...

Baker J 1987 An algorithm for geometry optimization without analytical gradients J. Comput. Chem. 8 563... 

Csaszar P and Pulay P 1984 Geometry optimization by direct inversion in the iterative subspace J. Moi. Struct. (Theochem) 114 31... 

Schlegel H B 1984 Estimating the Hessian for gradient-type geometry optimizations Theor. Chim. Acta 66 333... 

LIndh R, Bernhardsson A, Karlstrdm G and Malmqvist P-A 1995 On the use of a Hessian model function In molecular geometry optimizations Chem. Phys. Lett. 241 423... 

Baker J and Hehre W J 1991 Geometry optimization In Cartesian coordinates The end of the Z-matrIx J. Comput. Chem. 12 606... 

Palzs B, FogarasI G and Pulay P 1998 An efficient direct method for geometry optimization of large molecules J. Chem. Phys. 109 6571... 

Farkas O and Schlegel H B 1998 Methods for geometry optimization In large molecules. I. An O(N ) algorithm for solving systems of linear equations for the transformation of coordinates and forces J. Chem. Phys. 109 7100... 

Baker J, KInghorn D and Pulay P 1999 Geometry optimization In delocalized Internal coordinates An efficient quadratically scaling algorithm for large molecules J. Chem. Phys. 110 4986... 

Baker J 1993 Techniques for geometry optimization a comparison of Cartesian and natural Internal coordinates J. Comput. Chem. 14 1085... 

Eckert F, Pulay P and Werner H-J 1997 Ab initio geometry optimization for large molecules J. Comput. Chem. 18 1473... 

Pulay P and FogarasI G 1992 Geometry optimization In redundant Internal coordinates J. Chem. Phys. 96 2856... 

Baker J, KessI A and Delley B 1996 The generation and use of delocalized Internal coordinates In geometry optimization J. Chem. Phys. 105 192... 

Baker J 1992 Geometry optimization in Cartesian coordinates constrained optimization J. Comput. Chem. 13 240... 

Lu D-H, Zhao M and Truhlar D G 1991 Projection operator method for geometry optimization with... 

An excellent, up-to-date treatise on geometry optimization and reaction path algorithms for ab initio quantum chemical calculations, including practical aspects. 

The potential surfaces of the ground and excited states in the vicinity of the conical intersection were calculated point by point, along the trajectory leading from the antiaromatic transition state to the benzene and H2 products. In this calculation, the HH distance was varied, and all other coordinates were optimized to obtain the minimum energy of the system in the excited electronic state ( Ai). The energy of the ground state was calculated at the geometry optimized for the excited state. In the calculation of the conical intersection... 

A widely used 3D structure generator is CONCORD [131, 132] (for a more detailed description see Chapter II, Section 7.1 in the Handbook). CONCORD is also a rule- and data-based program system and uses a simplified force field for geometry optimization, CONCORD converts structures from 2D to 3D fairly fast... 

The additional integrated module, the ACD/3D Viewer, can visualize 2D structures as 3D models, after geometry optimization (see Section 2.12.3.1 and Figure 2-132, below). 

GAs or other methods from evolutionary computation are applied in various fields of chemistry Its tasks include the geometry optimization of conformations of small molecules, the elaboration of models for the prediction of properties or biological activities, the design of molecules de novo, the analysis of the interaction of proteins and their ligands, or the selection of descriptors [18]. The last application is explained briefly in Section 9.7.6. 

On e type of single point calculation, that of calculating vibration al properties, is distinguished as a vihmiions calculation in Ilyper-Chein. A lufcratilrui.s calculation predicts fun dam en tal vibrational frecinencies, m frared absorption in tensities, and norm al modes for a geometry optimized molecular structure. 

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