The keyword OPTGEOM opens the geometry optimization input.
The keyword must be inserted in the geometry input section (block 1) as the last keyword of the
section: the geometry must be completely defined before optimization.
Geometry optimization type
- By default, the relaxation of the atomic coordinates is performed.
- To fully optimized the periodic structure (i.e. cell parameters and atomic
positions) the keyword FULLOPTG must be specified.
- It is also possible to optimize the cell parameters at fixed atomic positions by specifying the keyword CELLONLY.
Symmetrized elastic distorsions are generated according to the space group symmetry. They do not usually
coincide with deformation of the crystallographic axes. To use crystallographic distorsions
the keyword CRYDEF must be specified.
Note that such an optimization type it is not possible when the redundant internal coordinate system is adopted.
- Another option exists (ITATOCEL) to perfom a full optimization through an iterative procedure. This
means that the optimization process starts with the relaxation of the cell parameters
at fixed atomic positions,
then the lattice constants are fixed and the atomic coordinates optimized. This two-step procedure
is repeated until both cell parameters and atomic positions no more change.
Input deck and output file
The basic CRYSTAL input and output of the geometry optimization of
alpha-Quartz
are reported and commented in the Quick tour of geometry optimization input/output.
Default values are supplied for all the parameters controlling the process. Note that the
tolerance for SCF convergence on total energy is set to 10-7 by
default.
Exercise: Repeat the optimization of alpha-Quartz with a STO-3G basis set
by using the default symmetrized fractional coordinates system, and analyze the output files.
Note that the final geometry is both printed in the CRYSTAL output and written in the fortran unit 34.
The keyword EXTERNAL (see "Geometry
Input") allows reading the geometry from the file fort.34. The script runcry06
saves the file fort.34 as inpfilename.gui at the end of optimization,
and recovers the data when the geometry is defined by the keyword EXTERNAL
in a subsequent run.
The file fort.33 contains the cartesian coordinates of the atoms in the unit cell
for each geometry optimization step in a simple xyz format.
This file is suitable to be read by molecular graphics programs (Molden, XMol, ...)
displaying the animation of the geometry optimization run.
Convergence criteria
The convergence of the optimization process is checked on the root-mean-square and
the absolute value of the largest component of both the gradients and
the estimated displacements. If these four conditions are satisfied
the optimization is considered complete.
In the current implementation the following defaults are used (in a.u.):
RMS GRADIENT
MAX GRADIENT |
0.000300
0.000450
|
TOLDEG
TOLDEG * 1.5 |
RMS DISPLAC.
MAX DISPLAC. |
0.001200
0.001800
|
TOLDEX
TOLDEX * 1.5 |
The RMS gradient and displacement can be modified in input by using
the keyword TOLDEG and TOLDEX. By default, the maximum gradient and
the maximum displacement thresholds are defined to be 1.5 times
TOLDEG and TOLDEX, respectively.
Additional convergence tests have been introduced to avoid wasting of time
when optimization shows odd behavior:
-
A combined test on gradient and energy has been adopted.
If the gradient criteria are satisfied and the energy difference
between two steps is below a given threshold, the optimizer
stops with a warning message.
-
Test on total energy change (flat surfaces). If the energy
does not change for four next steps, the optimizer stops with
a warning message.
The energy difference between next steps is checked with respect to a given
threshold (default: 2.0E-07). This threshold is controlled by the keywords TOLDEE.
Initial hessian and restart
When an equilibrium structure is determined by minimizing the energy in a quasi-Newton scheme, the number
of steps required depends critically on the choice of the initial Hessian.
By default, the initial Hessian is generated by means of a classical model as
proposed by Schlegel (keyword HESSMOD2). It adopts a simple valence force field. Empirical rules
are used to estimate the diagonal force constants for a set of redundant internal coordinates (stretches, bends and torsions).
Parameters are available from H to At.
Other options are available:
- HESSIDEN: The unit matrix is used. This was the old default but could be quite inefficient.
- HESSINP: The initial guess can be also read from an external fortran unit (fort.66).
During the optimization the hessian matrix is written in unit 66 at each step. Optimization
can restart from the hessian obtained in a previous run performed at
a lower level of calculation (e.g. a smaller basis set). The script runcry06
saves the file fort.66 as inpfilename.hessopt, and recover the data when
required.
- HESSNUM: An initial Hessian can be obtained by a numerical estimate.
This is done by calculating the second-derivatives
by a numerical differentiation of the gradients and is a very expensive procedure.
- HESSMOD1: The initial Hessian is generated by means of a classical model as
proposed by Lindht et al.. A simple function of the nuclear positions is adopted.
Parameters are available from H to Kr.
Exercise:
The use of a model Hessian significantly improves the optimization process. Compare the number of steps
required to optimize the molecular structure of urea with and without using the model Hessian.
In the latter case, use a unit matrix as initial guess. See the input below
Urea molecule
MOLECULE
15
5
6 0. 0. 0.
8 0. 0. 1.261401
7 0. 1.14824666034 -0.69979
1 0. 2.0265496501 -0.202817
1 0. 1.13408048308 -1.704975
|
|
Title
Dimensionality of the system
Point Group
Number of non equivalent atoms
Atomic number and cartesian coordinates
|
OPTGEOM
HESSIDEN
ENDOPT
|
|
Keyword to perform a geometry optimization
Unit matrix as initial hessian
End of the geometry optimisation input block
|
|
END |
|
End of the geometry input section |
Optimization restart
Restart is possible for a job
which is abruptly terminated (e.g. when the number of steps or the available cpu
time is exceeded). The optimization process restarts exactly from the last step of the previous run.
Information is read from fortran unit 68, saved at each step of the optimization
process. The script runcry03 saves fort.68 as inpfilename.allopt,
and recovers the data when required.
The keyword RESTART must be specified
in same input deck as for the initial geometry optimization. For
instance:
|
Initial geometry optimisation input
|
|
Restart input
|
Urea molecule
MOLECULE
15
5
6 0. 0. 0.
8 0. 0. 1.261401
7 0. 1.14824666034 -0.69979
1 0. 2.0265496501 -0.202817
1 0. 1.13408048308 -1.704975
|
|
Urea molecule
MOLECULE
15
5
6 0. 0. 0.
8 0. 0. 1.261401
7 0. 1.14824666034 -0.69979
1 0. 2.0265496501 -0.202817
1 0. 1.13408048308 -1.704975
|
OPTGEOM
ENDOPT
|
|
OPTGEOM
RESTART file fort.68 must exist
ENDOPT
|
|
END |
|
END |
Data saved in fortran file
Several fortran files related to the geometry optimisation are written in the temporary directory.
|
Fortran unit |
Description |
Status |
|
fort.33 |
coordinates of atoms in the unit cell (input for Xmol, Molden) |
F |
|
fort.34 |
geometry (in Å) and symmetry operators
of the system |
F |
|
SCFOUT.LOG |
secondary CRYSTAL output file - SCF and
gradients information |
F |
|
OPTHESS.DAT |
current hessian matrix |
F |
|
OPTINFO.DAT |
Information to restart
geometry optimization |
F |
|
fort.98 |
wave function information |
F |
F=formatted, U=unformatted
| Constrained geometry optimizations |
Constant volume optimization
Geometry optimization at constant volume can be carried out by specifing both FULLOPTG and
the keyword CVOLOPT in the geometry optimization input block. This option is very useful
to compute point-by-point E vs V curves by relaxing the periodic structure at different values of the cell volume.
Fixing atomic positions
Geometry optimization can be limited to an atomic fragment instead of the whole system.
The keyword FRAGMENT must be specified, in the geometry optimization input block.
The number and the label of the atoms free to move must then be inserted.
Symmetrized cartesian coordinates are generated according to the list of free atoms.
Symmetrized forces are computed by using the new set of symmetrized coordinates.
No advantage is taken in the gradient calculation which is still performed on the whole system.
Here the input deck for the optimization of the hydrogen positions only,
for the urea molecule is reported:
Urea molecule
MOLECULE
15
5
6 0. 0. 0.
8 0. 0. 1.261401
7 0. 1.14824666034 -0.69979
1 0. 2.0265496501 -0.202817
1 0. 1.13408048308 -1.704975
|
|
Title
Dimensionality of the system
Point Group
Number of non equivalent atoms
Atomic number and cartesian coordinates
|
OPTGEOM
FRAGMENT
4
5 6 7 8
ENDOPT
|
|
Keyword to perform a geometry optimization
Keyword to optimize a fragment of the structure
Number of atoms free to move
Labels of the atoms (as listed before opt ) free
End of the geometry optimization input block
|
|
END |
|
End of the geometry input section |
In the output file the following information are printed
*******************************************************************************
* PARTIAL OPTIMIZATION - FRAGMENT OF 4 ATOMS - INPUT LIST :
5( 1) 6( 1) 7( 1) 8( 1)
SYMMETRY MAY BE BROKEN
|
By default, the symmetry of the system may be broken. It can be preserved
either specifying the labels of all the atoms related by symmetry, as in the previuos example, or
automatically by specifying the keyword KEEPSYMM before the geometry
optimization input block.
In this case the output looks like
*******************************************************************************
* PARTIAL OPTIMIZATION - FRAGMENT OF 2 ATOMS - INPUT LIST :
5( 1) 7( 1)
SYMMETRY IS KEPT
ATOM 5 AND 6 ARE LINKED BY SYMMOP 2
ATOM 7 AND 8 ARE LINKED BY SYMMOP 2
|
FRAGMENT can also be used in a full optimization of the system (i.e. in
combination with the keyword FULLOPTG). This means that also lattice
constants are relaxed with constrained atomic positions.
| Geometry optimization in redundant internal coordinates |
Geometry optimization can also be performed in redundant internal coordinates by
specifying the keyword INTREDUN. Instead of adopting a symmetrized
fractionary coordinates system, a symmetrized set of internal coordinates (i.e.
bonds, angles and torsions) is defined that contains more coordinates than the
requisite internal degrees of freedom.
The adopted coordinate system can have a very large effect on the rate of
convergence of a geometry optimization. For molecular systems, it is now
well-established that redundant internal coordinates require fewer optimization
steps than Cartesian coordinates. However, this is not definitely demonstrated
for periodic systems.
Note that for a periodic systems the set of redundant internal coordinates naturally
includes the structural dependence on the lattice constants. Therefore, a full
geometry optimization of cell parameters and atomic positions is carried out
when redundant internal coordinates are used.
CRYSTAL input and output of a geometry optimization in redundant coordinates are
also described in the Quick tour of geometry optimization input/output.
Exercise: Repeat the optimization of a-Quartz with a STO-3G basis set
by using the redundant internal coordinates system, and analyze the output file.
A few useful options are discussed in the following.
-
Checking the consistency of the set of redundant internal coordinates
Before running a geometry optimization in redundant internal
coordinates, the set of coordinates generated automatically by
CRYSTAL should be checked for consistency. This can be done
by specifying the keyword TESTREDU.
Redundant internal coordinates are generated according to
a hierarchical scheme: bond lenghts are firstly identified
by using covalent radii. Then, angles are determined on the basis of the irreducible
set of distances and, finally, dihedral angles are defined
As an example, the set of redundant internal
coordinates defined for alpha-Quartz is reported below:
SYMMETRY IRREDUCIBLE INTERNAL COORDINATES
ATOMIC RADII (ANG) USED FOR BOND CAPTURE:
ELEMENT RADIUS
SI 1.230
O 0.780
N OF INTERNAL COORDINATES: 19
N OF ALLOWED DEGREES OF FREEDOM: 6
BOND LENGTHS (L), ANGLES (A) AND DIHEDRALS (D), THEIR VALUES (IN ANGS
AND DEGREES), MULTIPLICITIES AND WHETHER COORDINATE IS FROZEN(T) OR NOT(F).
NUM, ATOM LABELS AND CELL INDICES OF THE POINTS VALUE MUL FRZ
(L)
1 4 O 1 SI ( 0 0 0) 1.6046 6 F
2 5 O 1 SI (-1 0 0) 1.6137 6 F
(A)
3 4 O 1 SI ( 0 0 0) 7 O ( 0 0 0) 108.9557 3 F
4 4 O 1 SI ( 0 0 0) 5 O ( 1 0 0) 110.5188 6 F
5 1 SI 4 O ( 0 0 0) 3 SI ( 1 1 0) 143.7458 6 F
6 4 O 1 SI ( 0 0 0) 8 O ( 1 0 0) 108.8121 6 F
7 5 O 1 SI (-1 0 0) 8 O ( 0 0 0) 109.2201 3 F
(D)
8 7 O 1 SI ( 0 0 0) 4 O ( 0 0 0) 5 O ( 1 0 0) -119.5113 6 F
9 7 O 1 SI ( 0 0 0) 4 O ( 0 0 0) 3 SI ( 1 1 0) 151.5394 6 F
10 7 O 1 SI ( 0 0 0) 4 O ( 0 0 0) 8 O ( 1 0 0) 120.5661 6 F
11 5 O 1 SI (-1 0 0) 4 O (-1 0 0) 3 SI ( 0 1 0) -88.9493 6 F
12 4 O 1 SI ( 0 0 0) 5 O ( 1 0 0) 2 SI ( 1 0 0) 12.2650 6 F
13 5 O 1 SI (-1 0 0) 4 O (-1 0 0) 8 O ( 0 0 0) -119.9226 6 F
14 4 O 1 SI ( 0 0 0) 5 O ( 1 0 0) 7 O ( 0 0 0) -119.5979 6 F
15 4 O 1 SI ( 0 0 0) 5 O ( 1 0 0) 8 O ( 1 0 0) 119.6771 6 F
16 3 SI 4 O (-1-1 0) 1 SI (-1-1 0) 8 O ( 0-1 0) 30.9733 6 F
17 1 SI 4 O ( 0 0 0) 3 SI ( 1 1 0) 8 O ( 1 1 0) 131.8630 6 F
18 1 SI 4 O ( 0 0 0) 3 SI ( 1 1 0) 9 O ( 0 0 1) -107.4120 6 F
19 4 O 1 SI ( 0 0 0) 8 O ( 1 0 0) 5 O ( 1 0 0) -120.7250 6 F
|
Internal coordinates are specified in terms of the label of the atoms. The first atom is always in the zero-th cell while
the other ones are identified by their cell indices.
The value of the internal coordinate is printed along with its symmetry multiplicity.
It could be either frozen [T] (optimization with constrains) or not [F]
For alpha-Quartz, there are 19 redundant internal coordinates with respect to 6 allowed degrees of freedom.
Note that the number of internal coordinates depends on the value of the atomic covalent radii.
When the atomic covalent radius is too large (e.g. for alkali metal ions) too
many bonds are defined and the number of internal coordinates increases too much
leading to an overestimation of the redundant space.
The
Atomic covalent radii can be modified by using the RAYCOV option (see the CRYSTAL User's Manual
for further details).
-
Managing with almost linear angles
Linear or almost linear angles (i.e. close to 180o) can lead to numerical instability of the optimization algorithm.
To avoid this problem a common practice is to split the angle in two smaller ones.
The threshold value beyond which the almost linear angle is splitted, it is controlled by the
keyword ANGTODOUBLE. The default value is set to 165o. That means that all angles larger than 165o
are automatically splitted into two.
Hint: when optimizing zeolitic structures where siloxane bridges could
change a lot during the geometry minimization, it is better to reduce the default value to 150o.
-
Adding internal coordinates
If some relevant internal coordinates are missing (e.g. intermolecular bonds) they can be added by means of two keywords: DEFLNGS and DEFANGLS.
The number of new internal coordinates must be specified and then, to define the bond or the angle, the labels of the atoms along with the indices of the cell
where they are located have to be indicated. Here, is shown as an example
OPTGEOM
INTREDUN
DEFLNGS
1
1 8 1 0 0
ENDOPT
|
|
Keyword to perform a geometry optimization
Keyword to run the optimization in redundant coordinates
Keyword to define a new bond
Number of new bonds to be added
Label of the first atom and label of the second one with cell indices
End of the geometry optimisation input block
|
|
END |
|
End of the geometry input section |
Note that when a new bond is added all the related angles and dihedrals are automatically generated.
In the output file, the new bond is found on top of the list of internal coordinates
SYMMETRY IRREDUCIBLE INTERNAL COORDINATES
ATOMIC RADII (ANG) USED FOR BOND CAPTURE:
ELEMENT RADIUS
SI 1.230
O 0.780
N OF INTERNAL COORDINATES: 19
N OF ALLOWED DEGREES OF FREEDOM: 6
BOND LENGTHS (L), ANGLES (A) AND DIHEDRALS (D), THEIR VALUES (IN ANGS
AND DEGREES), MULTIPLICITIES AND WHETHER COORDINATE IS FROZEN(T) OR NOT(F).
NUM, ATOM LABELS AND CELL INDICES OF THE POINTS VALUE MUL FRZ
(L)
1 8 O 1 SI (-1 0 0) 1.6137 6 F
2 4 O 1 SI ( 0 0 0) 1.6046 6 F
(A)
3 8 O 1 SI (-1 0 0) 5 O ( 0 0 0) 109.2201 3 F
4 8 O 1 SI (-1 0 0) 4 O (-1 0 0) 108.8121 6 F
5 8 O 1 SI (-1 0 0) 7 O (-1 0 0) 110.5188 6 F
6 1 SI 8 O ( 1 0 0) 3 SI ( 1 0 0) 143.7458 6 F
7 4 O 1 SI ( 0 0 0) 7 O ( 0 0 0) 108.9557 3 F
(D)
8 5 O 1 SI (-1 0 0) 8 O ( 0 0 0) 4 O (-1 0 0) 120.7250 6 F
9 5 O 1 SI (-1 0 0) 8 O ( 0 0 0) 7 O (-1 0 0) -119.6771 6 F
10 5 O 1 SI (-1 0 0) 8 O ( 0 0 0) 3 SI ( 0 0 0) -107.4120 6 F
11 4 O 1 SI ( 0 0 0) 8 O ( 1 0 0) 7 O ( 0 0 0) 119.5979 6 F
12 8 O 1 SI (-1 0 0) 4 O (-1 0 0) 5 O ( 0 0 0) 119.9226 6 F
13 4 O 1 SI ( 0 0 0) 8 O ( 1 0 0) 3 SI ( 1 0 0) 131.8630 6 F
14 8 O 1 SI (-1 0 0) 4 O (-1 0 0) 3 SI ( 0 1 0) 30.9733 6 F
15 8 O 1 SI (-1 0 0) 4 O (-1 0 0) 7 O (-1 0 0) -120.5661 6 F
16 7 O 1 SI ( 0 0 0) 8 O ( 1 0 0) 3 SI ( 1 0 0) 12.2650 6 F
17 8 O 1 SI (-1 0 0) 7 O (-1 0 0) 2 SI (-1-1 0) -88.9493 6 F
18 8 O 1 SI (-1 0 0) 7 O (-1 0 0) 4 O (-1 0 0) 119.5113 6 F
19 1 SI 8 O ( 1 0 0) 3 SI ( 1 0 0) 6 O ( 1 0 0) 151.5394 6 F
|
-
Optimizing atomic positions only
To use the redundant internal coordinate system to optimize solely the atomic positions, the keyword
FIXCELL must be specified. Cell parameters are then fixed at their initial value.
Technical notes
Input decks and some output files for the proposed examples and exercises are listed
below.
Hint: Save the fort.33 in your directory and then read it with Molden
(the script runcry06 saves fort.33 as inpfilename.xyz).
The animation of the geometry optimization can be visualized.
Example 1:
Urea molecule and crystal
(
urea)
Complete the geometry input deck below to be a HF/STO-3G calculation
Urea molecule
MOLECULE
15
5
6 0. 0. 0.
8 0. 0. 1.261401
7 0. 1.14824666034 -0.69979
1 0. 2.0265496501 -0.202817
1 0. 1.13408048308 -1.704975
OPTCOORD
ENDOPT
END
|
Run CRYSTAL and compare the optimized structure
with the results from a geometry optimization performed in same conditions
with a molecular ab-initio code.
Here are the urea molecule optimized structures with both CRYSTAL
and Gaussian98 (referred to the centre of masses). The final total energy and the number of cycles taken
to converge are also reported. Note that the same initial conditions
have been used: cartesian coordinates, initial Hessian = identity matrix.
|
CRYSTAL optimized structure |
E = -221.016716 Hartree (14 cycles) |
|
Referred to the center of masses |
From output file
|
6 .000000 .000000 .169075
8 .000000 .000000 1.391191
7 .000000 1.174680 -.613688
7 .000000 -1.174680 -.613688
1 .000000 2.075250 -.150156
1 .000000 -2.075250 -.150156
1 .000000 1.155020 -1.626014
1 .000000 -1.155020 -1.626014 |
6 0.000000000000E+00 0.000000000000E+00 7.728541788412E-02
8 0.000000000000E+00 0.000000000000E+00 1.299402127671E+00
7 0.000000000000E+00 1.174680477800E+00 -7.054771776099E-01
7 0.000000000000E+00 -1.174680477800E+00 -7.054771776099E-01
1 0.000000000000E+00 2.075250728444E+00 -2.419446571055E-01
1 0.000000000000E+00 -2.075250728444E+00 -2.419446571055E-01
1 0.000000000000E+00 1.155020093098E+00 -1.717803438062E+00
1 0.000000000000E+00 -1.155020093098E+00 -1.717803438062E+00 |
| |
|
Gaussian98
optimized structure |
E = -221.016714 Hartree (20 cycles) |
6 .000000 .000000 .169024
8 .000000 .000000 1.391020
7 .000000 1.175371 -.613548
7 .000000 -1.175371 -.613548
1 .000000 2.076442 -.150416
1 .000000 -2.076442 -.150416
1 .000000 1.155881 -1.625897
1 .000000 -1.155881 -1.625897 |
Exercise: Repeat the optimization for urea molecule by relaxing
the hydrogen positions only.
Exercise: Repeat the optimization for urea molecule by using
a unit matrix as initial Hessian. Compare the required number of steps in the
two optimization runs.
Exercise: Run the full optimization of the urea molecular crystal.
Compare the computed total energy with the constrained optimization of: (i)
atomic positions only, (ii) the cell parameters at fixed atomic coordinates, and
(iii) at constant volume.
Exercise: Run the full optimization of the urea molecular crystal in
symmetrized fractional coordinates and redundant internal coordinates, and
compare the results.
Exercise: Modify the urea crystal input deck to perform a partial geometry
optimization (hydrogen positions).
Exercise 1:
Water - molecule, polymer and crystal
(
ice)
Perform a HF/STO-3G geometry optimization of the water molecule, of an infinite chain of water molecules and finally
of the Ice XI structure.
How does the water structure change?
Extension: Compute the cohesive energy of the infinite chain and of the
molecular crystal. Estimate the BSSE by using the keyword MOLEBSSE.
Exercise 2:
a-Alumina
crystal and surface relaxation
(alumina)
Perform a full optimization of the
a
-Al2O3
bulk structure at HF/STO-3G level. Define then a slab model (6 atomic layers)
parallel to the (0001) face of the optimized bulk structure and relax the slab
geometry.
Compare the unrelaxed and the relaxed slab model structures.
List of the available input decks
Here a list of the available input decks is reported.
The corresponding output files are also available. The xyz output file can be used
to visualize the animation of the geometry optimisation.
Summary of the CRYSTAL geometry optimization input keywords
The optional keywords must be inserted in separate records between OPTGEOM
and ENDOPT.
The available optional keywords follow:
|
SCF initial guess (default: Fock
matrix from the previous energy point) |
|
|
NOGUESS |
Superposition of atomic densities for all energy
points |
|
| |
|
|
|
Hessian control |
|
|
HESSIDEN |
Identity matrix as initial Hessian |
|
|
HESSMOD1 |
Initial model Hessian as proposed by Lindh et al. |
|
|
HESSMOD2 |
Initial model Hessian as proposed by Schlegel |
default |
|
HESSNUM |
Initial Hessian from a numerical estimate |
|
|
HESSINP |
Initial guess of the Hessian from external file |
|
| |
|
|
|
Printing options |
|
|
PRINTFORCES |
printing atomic gradients |
|
|
PRINTHESS |
Printing Hessian information |
|
|
PRINTOPT |
Prints information on optimization process |
|
|
PRINT |
Verbose printing |
|
| |
|
|
|
Convergence criteria |
|
|
TOLDEG |
Threshold on the RMS of the gradient [0.0003] |
Input |
|
TOLDEX |
Threshold on the RMS of the displacement [0.0012] |
Input |
|
TOLDEE |
Threshold on the energy change [7] |
Input |
| |
|
|
|
Optimization type |
|
|
FULLOPTG |
Full optimization of cell parameters and atomic positions |
|
|
CELLONLY |
Optimization of cell parameters at fixed atomic positions |
|
|
ITATOCELL |
Independent optimization of cell parameters and atomic positions by means of an iterative procedure |
|
|
CVOLOPT |
Structure optimization at constant cell volume |
|
| |
|
|
|
Optimization control |
|
|
MAXCYCLE |
Maximum number of optimisation steps [100] |
Input |
|
FRAGMENT |
Partial geometry optimisation |
Input |
|
RESTART |
Restart geometry optimisation from a previous run |
|
References
General papers on geometry optimisation methods in computational chemistry
H.B. Schlegel, Adv. Chem. Phys. 687 (1987) 249
H.B. Schlegel, "Geometry Optimisation: 1", in "Encyclopedia of Computational Chemistry",
Wiley, NY, 1998
Implementation of Hartree-Fock gradients in CRYSTAL
K. Doll, N.M. Harrison and V.R. Saunders, Int. J. Quantum. Chem. 82 (2001) 1
K. Doll, Comp. Phys. Comm., 137 (2001) 74
Implementation of DFT gradients in CRYSTAL
R. Orlando, V.R. Saunders, R. Dovesi et al., unpublished
Berny algorithm
H.B. Schlegel, J. Comp. Chem. 3 (1982) 214
Geometry optimisation of periodic systems with the CRYSTAL code
B. Civalleri, Ph. D'Arco, R. Orlando, V.R. Saunders, R. Dovesi, Chem. Phys. Lett. 348, 131-138 (2001)
Initial approximate Hessians
H.B. Schlegel, Theoret. Chim. Acta 66 (1984) 333
J.M. Wittbrodt and H.B. Schlegel, J. Mol. Struct. (Theochem) 398-399 (1997) 55
R. Lindh, A. Bernhardsson, G. Karlstrom and P.-A. Malmqvist, Chem. Phys. Lett. 241 (1996) 423
