TRANSITION STATE OPTIMIZATION MANUAL


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Manual for the transition state searching, based on Yury Abashkin and Nino Russo constrained search algorithm. The implementation of the original routine from deMon-KS1p2 into deMon-KS3p5 was done by Steeve Chrétien.

  1. Y. Abashkin and N. Russo, J. Chem. Phys., 100(6), p. 4477-4483 (1994)
  2. Y. Abashkin, N. Russo and M. Toscano, Int. J. Quantum Chem., 52, p. 695-704 (1994)

Note that reading ref. [1] is an essential prerequisite to this manual.

This manual is prepared by Steeve Chrétien.

First version : 98-03-04 Steeve Chrétien
Modified: 98-04-05 Steeve Chrétien

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The deMon-KS keyword for the transition state search is RUNTYPE TRANSITION. In addition, deMon-KS needs another input file, TRANSINP, to be copied in the deMon-KS temporary directory when you execute a transition state search. In the UdM version, the TRANSINP file has the same name as the usual deMon-KS input file but, the extension ".inp" is replaced by ".tra". During a transition state search another file (SUM) is created which contains a summary of the search. Don't forget to copy this file back to your home directory when the calculation is done.

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INDEX

  1. Basic concept
  2. Keywords
  3. Example
  4. Bugs

BASIC CONCEPT:

From ref. [1]:

"The purpose of this paper is to describe a new algorithm that is based on the constrained optimization approach, which implies the energy minimization on a hypersphere in the coordinate space. Starting from equilibrium geometry (zero value of the hypersphere radius R) and giving increment of R, a step-by-step walking uphill process along the MEP [minimum energy path] is carried out. Accounting for the constraints in a straightforward manner allows us to calculate gradients on a hypersphere and to use an efficient quasi-Newton-type algorithm for energy minimization at the given R. In a saddle point vicinity the refining procedure of TS [transition state] parameters is performed."

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KEYWORDS:

  1. TITLE - specify the title of the transition state search
  2. ROUGH - specify if rough procedure is wanted
  3. ROUNUMBER - number of point for the rough procedure
  4. ROUSTEP - value of the increment of the hypersphere radius
  5. ROUCONVERGENCE - convergence criteria for the rough procedure
  6. ROUMAXIMUM - maximum number of geometries by point for the rough procedure
  7. REFINING - specify if refining procedure is wanted
  8. REFNUMBER - maximum number of point for the refining procedure
  9. REFCONVERGENCE - convergence criteria for the refining procedure
  10. SIGN - direction of the search
  11. CENHYPERSPHERE - geometry of the hypersphere center
  12. VVECTOR - "V" vector
  13. HYPERSPHERE - which coordinates are fixed or allowed to move
  14. QNTRA - choosen coordinate for transition state search

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Description of Keywords:

TITLe

As in the usual deMon-KS input file, the user has to give a title to the transition state input file. This title should be smaller than 78 characters, and is entered on the first line following the keyword TITLE.

Return to keyword index.


ROUGh [ON,OFf]

When the keyword ROUGH is set to ON, this means that the rough procedure will be used to locate approximatively a minimum energy path. If this keyword is set to OFF or if it is omitted in the transition state input file, the ROUGH procedure will not be used.

Default value: OFF

Return to keyword index.


ROUNumber [NUMBER]

ROUNUMBER corresponds to the number of points (hyperspheres) that the user wants to optimized during the rough procedure. This keyword is not used by the program if ROUGH is set to OFF.

Allowed values: integer and positive numbers less than 40*
Default value: 2

*The user can change this limit by increasing the value of MAXTRALIM in the routine DECOTRA.

Return to keyword index.


ROUStep [NUMBER]

ROUSTEP is the value of the increment of the hypersphere radius between each points. Since it is the value of the hypersphere radius, which determines the optimized structure, the step size can be varied in an arbitrary range. However, the user has to keep in mind that a huge step may lead into another region of the potential energy surface. This keyword is not used by the program if ROUGH is set to OFF.

Allowed values: real numbers
Default value: 0.01

Return to keyword index.


ROUConvergence [NUMBER]

ROUCONVERGENCE is the convergence criterion for each constrained optimization (optimization with the constraint that the hypersphere radius is keeped constant). This number corresponds to the norm of the gradient of the N-1 degrees of freedom (see eq. 4-5 in ref. [1]). This keyword is not used by the program if ROUGH is set to OFF.

Allowed values: positive and real numbers smaller than 1
Default value: 0.0003

Return to keyword index.


ROUMaximum [NUMBER]

Maximum number of geometries during the optimization of a single point (hypersphere). This keyword is not used by the program if ROUGH is set to OFF.

Allowed values: integer and positive numbers
Default value: No default

Return to keyword index.


REFIning [ON,OFf]

When the keyword REFINING is set to ON, this means that the user wants to used the refining procedure to locate approximatively a minimum, a transition state or a saddle point. If this keyword is set to OFF or if it is omitted in the transition state input file, the program will not use the REFINING procedure.

Default value: OFF

Return to keyword index.


REFNumber [NUMBER]

REFNUMBER is the maximum number of SCF calculations during the refining search. This keyword is ignored if REFINING is set to OFF.

Allowed values: integer numbers
Default value: 2

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REFConvergence [NUMBER]

REFCONVERGENCE is the convergence criteria for the refining procedure. When the norm of the gradient of the N-1 degrees of freedom (dE'/dqi ) and the derivative of the potential energy function (dE'/dR) are smaller than REFCONVERGENCE, the program assumes that the desired structure has been found and stop (see eq. 4-6 in ref. [1]). This keyword is ignored if REFINING is set to OFF

Allowed values: real numbers
Default value: 0.001

Return to keyword index.


SIGN [POSitive,NEGative]

SIGN is the sign in eqs. (2-3,6) (see ref. [1]) This keyword specifies the part of the hypersphere that we want to search. The user chooses the option NEGATIVE if he wants to decrease the value of the choosen coordinate, qn, and POSITIVE if he wants to increase it.

Warning: if this keyword is not used, the program will stop.

Default value: POSitive

From ref. [1]:

"If the internal coordinate qn has a nonzero projection on the reaction coordinate, two values of qn ( in equation [2] ) satisfy the constraint, so that by choosing the sign we can manage the direction of walking. In other words, the definition of the sign is equivalent to applying the constrained optimization procedure on the "left" or the "right" half of the hypersphere."

Return to keyword index.


CENHypersphere [CARTesian,ZMATrix], [BOHr,ANGstrom]

Geometry of the center of the hyperspheres. The first option specifies the coordinate system used, CARTESIAN or ZMATRIX (internal coodinates). The second specifies the units used, ANGSTROM or BOHR. The CENHYPERSPHERE keyword entries begin with CENHYPERSPHERE and are terminated by "END" statement. In the CENHYPERSPHERE block, the atom labels should not appear. In the example below, we take the cis-N2H2 structure as the center of hypersphere. It may be necessary to slightly enlarge or reduce the value of the choosen coordinate in the hypersphere center geometry in order to avoid taking the square root of a negative number, a problem which occurs when the difference between an and qn is small (see eq 2 ref. [1]).

Warning: if this keyword is not used, the program will stop.

EXAMPLE 11.1 : Hypersphere center for the isomerization of cis-N2H2 to trans-N2H2.

CENHYPERSPHERE CARTESIAN BOHR
  1.184   0.000   0.000
 -1.184   0.000   0.000
  1.971   0.000   1.834
 -1.971   0.000   1.834
END

N.B. The ZMATRIX option is not available right now !

Return to keyword index.


VVECtor [CARTesian,ZMATrix] [BOHr,ANGstrom]

This keyword specifies the "V" vector in eq. 7 (see ref. [1]). The "V" vector corresponds to the derivative of a coordinate with respect to the hypersphere radius (dqi / dR). This vector is used for interpolate the next point. A guest is needed at the beginning because the program calculates this vector only after having first calculated two geometries. As with the keyword CENHYPERSPHERE, the VVECTOR entries begin with VVECTOR and are terminated by "END" statement. In the VVECTOR block, the atom labels should not appear.

Warning: if this keyword is not used, the program will stop.

EXAMPLE 12.1 : "V" vector for the isomerization of cis-N2H2 to trans-N2H2.

VVECTOR CARTESIAN BOHR
  -0.0512584   0.0000000   0.0000000
   0.0000000   0.0000000   0.0000000
  -0.0733405   0.0000000   0.0525574
  -0.8845824   0.0000000  -0.4776126
END

In this example, the second hydrogen rotates around the "y" axis.

N.B. The ZMATRIX option is not available right now !

Return to keyword index.


HYPEsphere [FIX,FREe] [NUMBERS]

The user has to specify which coordinates are fixed (FIX) or freed (FREE) to move during the search. It is recommanded to fix some degrees of freedom corresponding to translation and rotation if cartesian coordinates are used, in order to keep the search in the right direction. The HYPERSPHERE keyword works in the same way as CONSTRAIN keyword in deMon-KS. The integers (number1, number2, ...) following the word FIX or FREE correspond to the position of the degrees of freedom in the coordinate system (see the numbering system described below).

Warning: if this keyword is not used, the program will stop.

The system used for numbering the degrees of freedom is as follows:

A. Cartesian (x,y,z) coordinates:

        X  Y  Z
ATOM1   1  2  3
ATOM2   4  5  6
ATOM3   7  8  9
...

B. Internal coordinates (Z-matrix):

         R THETA PHI
ATOM1
ATOM2    1
ATOM3    2   3
ATOM4    4   5    6
...

EXAMPLE 13.1:cis-N2H2 in cartesian coordinates:

CENHYPERSPHERE CARTESIAN BOHR
  1.184   0.000   0.000
 -1.184   0.000   0.000
  1.971   0.000   1.834
 -1.971   0.000   1.834
END
To avoid rotation and translation of the N2H2 molecule during the search, use:

HYPERSPHERE FIX 1 2 3 5 6 8

which is equivalent to

HYPERSPHERE FREE 4 7 9 10 11 12

N.B. The ZMATRIX option is not available right now !

Return to keyword index.


QNTRa [NUMBER]

This keyword specifies which coordinate will be recalculated from the others one (see eq. 2 ref. [1]) during the search. Mathematically, the choice of the coordinate is arbitrary, but, for numerical stability reasons (i.e. avoiding the square root of a negative number), it is recommended to choose the coordinate which has the biggest and most regular change during the search. The number following QNTRA keyword corresponds to the position number of the choosen coordinate. The numerotation of the coordinates is the same as defined in HYPERSPHERE. For example, for the isomerization of cis-N2H2 to trans-N2H2, we can choose the "x" or the "z" coordinate of the second hydrogen (QNTRA 10 or QNTRA 12).

Warning: if this keyword is not used, the program will stop.

Allowed value: integer and positive number smaller than 3*N (where N is the number of atoms).
Default value: No default

Return to keyword index.


EXAMPLE:

Isomerization of the cis-N2H2 to trans-N2H2.

In the usual deMon-KS input file, we have to choose the option TRANSITION of the RUNTYPE keyword. In this example, we begin the search by the rough procedure to locate the transition state region. Here are the input file used, and the summary file, which is created by the program. Then, we use the refining procedure to get closer to the transition state. We begin the search with the optimized geometry #6 of the rough procedure (this structure has to be put into the usual deMon-KS input file). Here are the input and the summary file for the refining procedure. The following file contains all the optimized structure (in Ångstrom) by the rough procedure. Save this file and animate it with Xmol.

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Bugs:

  1. Z-matrix option unavailable
  2. Dummy atoms do not work

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