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After gradients G^{k} have been calculated for coordinates q^{k} in
optimization cycle k, new coordinates (or basis set exponents)
q^{k+1} can be obtained from the quasiNewton update:
q^{k+1} = q^{k}  F^{k}G^{k} 

where F^{k} is the inverse of an approximate force constant matrix
H^{k}. This method would immediately converge to the equilibrium
geometry if F^{k} would be the inverse of the exact force constant matrix
and the force field would be quadratic. In real applications usually none
of these requirements is fulfilled. Often only a crude approximation
to the force constant matrix H^{k} is known. Sometimes a unit matrix
is employed (which means coordinate update along the negative gradient
with all coordinates treated on an equal footing).
The optimization of nuclear coordinates in the space of internal
coordinates is the default task performed by relax and does not need
to be enabled. Any other optimization task requires explicit
specifications in data group $optimize, which takes several
possible options:
$optimize options
 internal on/off
 Structure optimization
in internal coordinates.
 redundant on/off
 Structure optimization
in redundant coordinates.
 cartesian on/off
 Structure optimization
in cartesian coordinates.
 basis on/off
 Optimization of basis
set exponents, contraction coefficients, scaling factors.
 global on/off
 Optimization of global
scaling factor for all basis set exponents.
Note: All options except internal are switched off by default,
unless they have been activated explicitly by specifying on.
Some of the options may be used simultaneously, e.g.
internal
, basis
internal
, global
cartesian
, basis
Other options have to be used exclusively, e.g.
internal
, cartesian
basis
, global
The update of the coordinates may be controlled by special options
provided in data group $coordinateupdate which takes as
options:
 dqmax=real
 Maximum total coordinate change (default: 0.3).
 interpolate on/off
 Calculate
coordinate update by inter/extrapolation using coordinates and
gradients of the last two optimization cycles (default:
interpolate on) if possible.
 statistics integer/off
 Display
optimization statistics for the integer previous optimization
cycles. Without integer all available information will be
displayed. off suppresses optimization statistics.
The following data blocks are used by program relax:
 Input data from gradient programs grad, rdgrad, egrad, rimp2,
mpgrad, etc.:
 $grad
 cartesian atomic coordinates and their gradients.
 $egrad
 exponents and scale factors and their
gradients.
 $globgrad
 global scale factor and its
gradient.
 Input data from force constant program aoforce:
 $grad
 cartesian atomic coordinates and their
gradients.
 $globgrad
 global scale factor and its
gradient.
 $hessian
 the force constant matrix in the
space of cartesian coordinates.
 Output data from program relax:
 $coord
 cartesian atomic coordinates.
 $basis
 exponents and scale
factors.
 $global
 global scale factor.
For structure optimizations the use of (redundant) internal
coordinates is recommended, see Section 4.0.6. Normally
internal coordinates are not used for input or output by the
electronic structure programs (dscf, mpgrad, etc.). Instead the
coordinates, gradients, etc. are automatically converted to internal
coordinates by relax on input and the updated positions of the
nuclei are written in cartesians coordinates to the data group
$coord. Details are explained in the following sections.
Next: Force Constant Update Algorithms
Up: Program Relax
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