Mathematisches Institut

• Reaktionswege und deren Approximationen; minimum energie path; streambed
• Reaktionswegverzweigungen; Valley-Ridge-Inflection (VRI) Punkte; singuläre Punkte; Bifurkationen
• Suche von stationären Punkten; transition states
• Numerische Umsetzung in inneren Koordinaten; Metrik
• Predictor-Corrector Methode
historisch:
• Vibrations-Rotationslinien linearer und quasilinearer Moleküle

• gradient extremal
• "following a reduced gradient" (RGF); kontinuierliches Newtonverfahren; Branin-Methode
  Download: modular version of RGF
• "TAngent Search Concept" (TASC); a generalisation of RGF to follow a valley floor gradient extremal
  Download: modular version of TASC
• Steepest decent; intrinsic reaction coordinate (IRC)
• "String Method" - or chain method ; another way to find RGF or gradient extremal pathways
  Download: paper and fortran program here
• "Growing String Method" ; an effective way to find RGF pathways, application to alanine dipeptide, 22-atomic test molecule
  Download: paper and fortran programs here

162-atomic test molecule: Alanine_15-helix
Download: paper and fortran programs here
"Growing String Method" by a second order method
Download: paper and fortran programs here
• 
  "SkewVRIs" to determine valley-ridge inflection points by singular Newton trajectory
  Download: fortran programs here

• Quapp W, Hirsch M, Imig O, Heidrich D (1998) J. Comput. Chem. 19:1087-1100
  Searching for saddle points of potential energy surfaces by following a reduced gradient
  Artikel im Adobe-PDF Format: download
• Quapp W, Hirsch M, Heidrich D (1998) Theor Chem Acc 100:285-299
  Bifurcation of reaction path: the set of valley ridge inflection points of a simple three-dimensional potential energy surface
  Artikel im Adobe-PDF Format: download
• Hirsch M, Quapp W, Heidrich D (1999) Phys.Chemistry Chem.Physics 1, No23: 5291-5199
  The Set of Valley-Ridge-Inflection Points of the Potential Energy Surface of the Water Molecule
• Quapp W, Hirsch M, Heidrich D (2000) Theor.Chem.Acc. 105: 145-155, available on http://link.springer.de
  Following the Streambed Reaction on Potential Energy Surfaces: A New Robust Method
• M.Hirsch, W.Quapp: (2002) Journal of Computational Chemistry, 23: 887-894
  An Improved RGF Method to Find Saddle Points
  
• W.Quapp: J. Theor. Comput. Chem. 2, No 3, 385-417 (2003) -- Review --
  "REDUCED GRADIENT METHODS AND THEIR RELATION TO REACTION PATHS"
  (Reprints available)

some latest papers:

• W.Quapp:       J. Molec. Struct. 695-696 (2004) 95-101
  "How Does a Reaction Path Branching Take Place? A Classification of Bifurcation Events"
  Reprint im PDF Format: download
• W.Quapp, M.Hirsch, D.Heidrich:       Theor. Chem. Acc. 112,No.1 (2004) 40-51
  "An Approach to Reaction Path Branching using Valley-Ridge-Inflection Points of Potential Energy Surfaces "
• W.Quapp:       Journal Computat Chemistry 25 No.10 (2004) 1277-1285
  "Reaction Pathways and Projection Operators: Application to String Methods"
• M.Hirsch, W.Quapp:     J Math Chem 36 No 4 (2004) 307-340
  "Reaction Pathways and Convexity of the Potential Energy Surface: Application of Newton Trajectories"
• M.Hirsch, W.Quapp:   J.Mol.Struct. THEOCHEM 683 No.1-3 (2004) 1-13
  "Reaction Channels of the Potential Energy Surface: Application of Newton Trajectories"
• W.Quapp:   Theoret. Chem. Account, 121 No.5-6 (2008) 227-237
  "Chemical Reaction Paths and Calculus of Variations "
W.Quapp:   J.Theoret.Comput.Chem. 8, Iss.1 (2009) 101-117
"The growing string method for flows of Newton trajectories by a second order corrector"
• W.Quapp, A.Zech:   J.Comput.Chem. 31, Iss.3 (2010) 573-585
  "Transition State Theory with Tsallis Statistics"
• W.Quapp, B.Schmidt:   Theoret. Chem. Acc. 128, Iss.1 (2011) 47-61,
  "An empirical, variational Method of Approach to unsymmetric Valley-Ridge Inflection Points"

weitere Arbeiten:

• Pinaki Chaudhury, S.P. Bhattacharyya, W.Quapp (2000) Chem.Phys. 253: 295-303
  "A Genetic Algorithm based technique for locating first order saddle points using a gradient only recipe"
• Ruslan M. Minyaev, Ilya V. Getmanskii, W.Quapp: (2004) Russ. J. Phys. Chem. tom 78, No 8: 1-6 (in russian),
  english version (2004) vol. 78, No 9: 1494-1498
  "Ab initio Study of the NH_3...H_2 Complex -- First Saddle Point of Index Two on a Reaction Path"
• W.Quapp, E.Kraka, D.Cremer: (2007)   Journal of Physical Chemistry 111, No. 44: 11287-11293
  "Finding the transition state of quasi barrier-less reactions by a growing string method for Newton trajectories: applications to the dissociation of Methylenecyclopropene and Cyclopropane"