"following a reduced gradient" (RGF) - modular version

''following a reduced gradient'' (RGF) is a method to examine potential-energy-surfaces (PES), espacially to search for stationary points. RGF is an second-order-method, that means it uses the Hessian of the PES, based on the continous newton method in it's algebraic form. The differential equation form is well known as Branin method. RGF is a predictor-corrector method which follows the path, that has the following property: at each point of it, the gradient points in the same direction. This direction -we call it search direction- is given as a parameter.

Up to now we have developed three main versions of the RGF method:

RGF ver. 1

RGF-path's can be followed in direction of any coordinate. The reduction is realized by deleting of one coordinate.
First analysed by us in: Quapp W, Hirsch M, Imig O, Heidrich D (1998) J. Comput. Chem. 19:1087-1100
Artikel im Adobe-PDF Format: download

no program release

RGF ver. 2

RGF-path's can be followed in any nonzero direction. The reduction is realized by projection.
First analysed by us in: Quapp W, Hirsch M, Heidrich D (1998) Theor Chem Acc 100:285-299
Artikel im Adobe-PDF Format: download

program is released in the web . Last revision 2, Jul 5, 2001

RGF ver. 3

Predictor- and Correctorstep are concentrated in one step. This should do better the pathfollowing and reduce the number of necessary (corrector-)steps.
Reference: Diener I, Schaback R, (1990) J. Opt. Theo. and Appl. 67:87-107
Applied by us: Hirsch M, Quapp W, (2002) J. Comput. Chem. 23, Issue 9, p.887-894

program release: in preparation

Th e program is to be called by a script which also calls the quantum chemical program. The RGF-program needs as input the first point, the gradient at every point, the hessian at least at first point, the Wilson B-matrix at every point. The hessian can be used updated or exact.

For a short Review of the RGF click here: Review

Download the program package RGF ver. 2, Jul 5, 2001 (including the manual)
Manual (Jul 2001) for modular RGF ver. 2,
Changed: Oct 2, 2001, M.Hirsch (E-Mail)

The applicability of RGF is shown:

-- W.Quapp, M.Hirsch, O.Imig, D.Heidrich:
J.Comput.Chem. 19(1998) 1087-1100
"Searching for Saddle Points of Potential Energy Surfaces by Following a Reduced Gradient"
Artikel im Adobe-PDF Format: download
In our first paper developing RGF, we have calculated the ring opening of 1H-Tetrazole, a 7-atomic molecule. Further applications: H$$₂CO PES with aproximately 50 stationary points, and the HCN-HNC isomerization using GAMESS_UK.
-- W.Quapp, D.Heidrich:
J.Mol.Struct.(THEOCHEM) 585, (2002) 105-117
"Exploring the Potential Energy Surface of the Ethyl Cation by New Procedures"
In this paper we give the example of C$$₂H$$₅$+$ using IRC, RGF, Branin-, and TASC pathways, to discuss the general definition of the reaction pathway.
In recent papers from the Bofill group there are given some still higher dimensional examples including up to 10-atomic molecules:
-- J.M.Anglada, E.Besalu, J.M.Bofill, R.Crehuet,
J.Comput.Chem. 22(2001) 387-406
gives a modification of RGF. Calculated is CH$$₃OOH, the ring opening of cyclopropyl radical, the hydroxymethylene radical, the oxydation of the methoxy radical, the Diels-Alder cycloaddition of butadiene plus ethylene, the rearrangement of cyclopropyl carbene to cyclobutane, the ring closure of vinylketene .

-- J.M.Bofill, J.M.Anglada, TCA 105 (2001) 463-472
"Finding transition states using reduced potential-energy surfaces"
applies a modified RGF to the isomerization reaction H$$₂CNH -- HCNH$$₂, the ring closure of vinylketene (10-atomic case) and the ring opening of cyclopropyl radical using MOPAC.

-- R.Crehuet, J.M.Bofill, J.M.Anglada, TCA 107 (2002) 130
"A new look at the reduced-gradient-following path"
deals with the ring opening of cyclopropyl radical (8-atomic case) using MOPAC.

-- J.Gonzalez, X.Gimenez, J.M.Bofill, JCP 116 (2002) 8713-8722
"A reaction path Hamiltonian defined on a Newton path"
applies the MHA-reaction path Hamiltonian to RGF paths and gives applications to isomerization reactions.
-- Michal Dallos, Hans Lischka, Elizete Ventura do Monte, M.Hirsch, W.Quapp:
Journal of Computational Chemistry, 23 (2002) 576-583
"Determination of Energy Minima and Saddle Points using Multireference Configuration Interaction Methods in Combination with Reduced Gradient Following:
the S$$₀ Surface of H$$₂CO and the T$$₁ and T$$₂ Surfaces of Acetylene"
In the paper of Dallos et al. are calculated RGF pathways on some higher electronic surfaces using the COLUMBUS program.
Here is a LINK to the Columbus web-page
Artikel im Adobe-PDF Format: download

-- Elizete Ventura, Michal Dallos and Hans Lischka:
Journal of Chemical Physics 118 No.24 (2003) pp.10963-10972
"Revisiting the stationary points on the potential energy surface of tetramethylene at the MR-AQCC level using analytic gradients"
Ventura, Dallos, and Lischka use the RGF for SPs of tetramethylene.
See LINK -- K.Schiele and R.Hemmecke have given in Z.Angew.Math.Mech. 81 (2001) 291-303 an application of RGF to the saddle point search for a driven multiple pendulum.
See LINK
-- R.Ahlrichs et al.:
Latest Improvements of TURBOMOLE V5.5 (January 2002)
New features: ...
--- transition states search algorithm using the reduced gradient following method
Here is a LINK to the TURBOMOLE web-page
-- The approach by W. Kliesch of an "activation and relaxation path" resembles to the RGF method:
J. Math. Chem. 28 (2000) 91-112.
A Mechanical String Model of Adiabatic Chemical Reactions, Lect. Notes Chem. 69, Springer, Berlin, 1999 .
J. Comput. Chem. 22 (2001) 1801. TASC method:
-- W.Quapp, M.Hirsch, D.Heidrich:
Theor. Chem. Acc 105 (2000) 145-155 [3]
"Following the Streambed Reaction on Potential Energy Surfaces: A New Robust Method" DOI 10.1007/s002140000192
Aritkel im Adobe-PDF Format: download
For the TASC method, this paper gives a 55-atomic Argon cluster to be up to date our highest dimensional example: in internal coordinates the cluster has 159 dimensions.


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