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.
- Y. Abashkin and N. Russo, J. Chem. Phys., 100(6),
p. 4477-4483 (1994)
- 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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- Basic concept
- Keywords
- Example
- Bugs
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."
Return to INDEX.
- TITLE - specify the title of the transition state search
- ROUGH - specify if rough procedure is wanted
- ROUNUMBER - number of point for the rough procedure
- ROUSTEP - value of the increment of the hypersphere radius
- ROUCONVERGENCE - convergence criteria for the rough procedure
- ROUMAXIMUM - maximum number of geometries by point for the rough procedure
- REFINING - specify if refining procedure is wanted
- REFNUMBER - maximum number of point for the refining procedure
- REFCONVERGENCE - convergence criteria for the refining procedure
- SIGN - direction of the search
- CENHYPERSPHERE - geometry of the hypersphere center
- VVECTOR - "V" vector
- HYPERSPHERE - which coordinates are fixed or allowed to move
- QNTRA - choosen coordinate for transition state search
Return to INDEX.
Description of Keywords:
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.
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 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 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 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.
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.
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 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
Return to keyword index.
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.
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.
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.
Return to INDEX.
- Z-matrix option unavailable
- Dummy atoms do not work
Return to INDEX.