Subject: Geometry optimization

From: "Schiffer, Heinz, Dr., WIA / SC" <[email-masked]>
Date: Wed, 24 Jan 1996 11:34:49 +0100

Shridar Gadre wants to know the performance of various methods for geometry 
optimization of molecules. There are some good references in the literature 
about this subject, but it seems to me, that these are not well known in the 
computational chemistry community ( e.g. by looking through the list of 
questions in the CCL ). Therefore I give the list of my favourite references 
:

     For general optimization methods :
     
          R. Fletcher
          Practical Methods of Optimization
          Vol. 1 : Unconstrained Optimization
          Vol. 2 : Constrained Optimization
          Wiley, New York 1981

     Most algorithms of Fletcher's books can be found as FORTRAN programs in 
:

          William H. Press, Brian P. Flannery, Saul A. Teukolsky,
          William T. Vetterling
          Numerical Recipes. The Art of Scientific Computing
          Cambridge University Press 1986
          ( The FORTRAN routines are available on diskettes ! )

     For geometry optimization of molecules :

          P. Pulay
          Ab initio calculation of force constants and equilibrium 
geometries
          in polyatomic molecules. I. Theory
          Mol. Phys. 17 (1969) 197-204

          J. W. McIver Jr. and A. Komornicki
          Rapid Geometry Optimization for Semi-Empirical Molecular Orbital
          Methods
          Chem. Phys. Lett. 10 (1971) 303-306

          Dieter Poppinger
          Geometry Optimization in ab Initio Molecular Orbital Theory
          Chem. Phys. Lett. 34 (1975) 332-336

          Richard L. Hilderbrandt
          Application of Newton-Raphson Optimization Techniques in Molecular 

          Mechanics Calculations
          Computers & Chemistry 1 (1977) 179-186

          Peter Pulay, Geza Fogarasi, Frank Pang, and James E. Boggs
          Systematic ab Initio Gradient Calculation of Molecular Geometries,
          Force Constants, and Dipole Moment Derivatives
          J. Am. Chem. Soc. 101 (1979) 2550-2560

          M. B. Smirnov
          The Use of Internal Coordinates in the Variable Metric Method
          of Molecular Geometry Optimization
          J. Mol. Structure 65 (1980) 163-168

          Fernando Bernardi, Andrea Bottoni, Glaudo Tonachini
          A Comparative Analysis of Various Gradient Methods for Geometry
          Optimization at the ab Initio SCF-MO Level
          J. Mol. Structure 86 (1981) 123-129          

          H. Bernhard Schlegel
          Estimating the Hessian for gradient-type geometry optimizations
          Theoret. Chim. Acta 66 (1984) 333-340

          Pal Csaszar and Peter Pulay
          Geometry Optimization by Direct Inversion in the Iterative 
Subspace
          J. Mol. Structure 114 (1984) 31-34

          John D. Head and Michael C. Zerner
          A Broyden-Fletcher-Goldfarb-Shanno Optimization Procedure
          for Molecular Geometries
          Chem. Phys. Lett. 122 (1985) 264-270

          H. Bernhard Schlegel
          Optimization of Equilibrium Geometries and Transition Structures
          Adv. Chem. Phys. 67 (1987) 249-286

          John D. Head
          Partial Optimization of Large Molecules and Clusters
          J. Comput. Chem. 11 (1990) 67-75
          
          John F. Stanton, David E. Bernholdt
          An Empirically Adjusted Newton-Raphson Algorithm for Finding Local
          Minima on Molecular Potential Energy Surfaces
          J. Comput. Chem. 11 (1990) 58-63
          
          Da-hong Lu, Meishan Zhao, and Donald G. Truhlar
          Projection Operator Method for Geometry Optimization with 
Constraints
          J. Comput. Chem. 12 (1991) 376-384

          Peter Pulay, Geza Fogarasi, Xuefeng Zhou and Patterson W. Taylor
          Ab initio prediction of vibrational spectra : a database approach
          Vibrational Spectroscopy 1 (1990) 159-165

          Jon Baker and Warren J. Hehre
          Geometry Optimization in Cartesian Coordinates : The End of the
          Z-Matrix ?
          J. Comput. Chem. 12 (1991) 606-610
          
          Jon Baker
          Geometry Optimization in Cartesian Coordinates : Constrained
          Optimization
          J. Comput. Chem. 13 (1992) 240-253

          Geza Fogarasi, Xuefeng Zhou, Patterson W. Taylor, and Peter Pulay
          The Calculation of ab Initio Molecular Geometries : Efficient
          Optimization by Natural Internal Coordinates and Empirical 
Correction
          by Offset Forces
          J. Am. Chem. Soc. 114 (1992) 8191-8201

          P. Pulay and G. Fogarasi
          Geometry optimization in redundant internal coordinates
          J. Chem. Phys. 96 (1992) 2856-2860

          Thomas H. Fischer and Jan Almloef
          General Methods for Geometry and Wave Function Optimization
          J. Phys. Chem. 96 (1992) 9768-9774

          S. Vogel, T. H. Fischer, J. Hutter, and H. P. Luethi
          Third-Order Methods for Molecular Geometry Optimizations
          Int. J. Qunatum Chem. 45 (1993) 679-688

          Jon Baker
          Techniques for Geometry Optimization : A Comparison of Cartesian
          and Natural Internal Coordinates
          J. Comput. Chem. 14 (1993) 1085-1100

          Jon Baker and Doreen Bergeron
          Constrained Optimization in Cartesian Coordinates
          J. Comput. Chem. 14 (1993) 1339-1346

          Chunyang Peng, Philippe Y. Ayala, H. Bernhard Schlegel,
          Michael J. Frisch
          Using redundant Internal Coordinates to Optimize Equilibrium
          Geometries and Transition States
          J. Comput. Chem. 17 (1996) 49-56

          Roland Lindh, Anders Bernhardsson, Gunnar Karlstroem ,
          Per-Ake Malmqvist
          On the use of a Hessian model function in molecular geometry
          optimizations
          Chem. Phys. Lett. 241 (1995) 423-428

     Multiple Minima Problem :

          Martin Saunders, K. N. Houk, Yun-Dong Wu, W. Clark Still,
          Mark Lipton, George Chang and Wayne C. Guida
          Conformations of Cycloheptadecane. A Comparison of Methods for
          Conformational Searching
          J. Am. Chem. Soc. 112 (1990) 1419-1427

          Costas D. Maranas and Christodoulos A. Floudas
          A deterministic global optimization approach for molecular 
structure
          determination
          J. Chem. Phys. 100 (1994) 1247-1261

          Jordi Mestres and Gustavo E. Scuseria
          Genetic Algorithms : A Robust Scheme for Geometry Optimizations 
and
          Global Minimum Structure Problems
          J. Comput. Chem. 16 (1995) 729-742

          Djurdje Cvijovic and Jacek Klinowski
          Taboo Search : An Approach to the Multiple Minima Problem
          Science 267 (1995) 664-666

          Martin J. Field
          Global optimization using ab initio quantum mechanical potentials
          and simulated annealing of the classical Liouville equation
          J. Chem. Phys. 103 (1995) 3621-3628

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Dr. Heinz Schiffer            Phone     : ++49-69-305-2330
Hoechst AG                    Fax  : ++49-69-305-81162
Scientific Computing               Email     : 
[email-masked]
65926 Frankfurt am Main
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