Optimal Control
Name OCTCheckGradient
Section Calculation Modes::Optimal Control
Type float
Default 0.0
When doing QOCT with the conjugate-gradient optimization scheme, the gradient is
computed thanks to a forward-backwards propagation. For debugging purposes, this
gradient can be compared with the value obtained "numerically" (i.e. by doing
successive forward propagations with control fields separated by small finite
differences).
In order to activate this feature, set OCTCheckGradient to some non-zero value,
which will be the finite difference used to numerically compute the gradient.
Name OCTClassicalTarget
Section Calculation Modes::Optimal Control
Type block
If OCTTargetOperator = oct_tg_classical, the you must supply this block.
It should contain a string (e.g. "(q[1,1]-q[1,2])*p[2,1]") with a mathematical
expression in terms of two arrays, q and p, that represent the position and momenta
of the classical variables. The first index runs through the various classical particles,
and the second index runs through the spatial dimensions.
In principle, the block only contains one entry (string). However, if the expression is very long, you can split it into various lines (one column each) that will be concatenated.
The QOCT algorithm will attempt to maximize this expression, at the end of the propagation.
Name OCTControlFunctionOmegaMax
Section Calculation Modes::Optimal Control
Type float
Default -1.0
The Fourier series that can be used to represent the control functions must be truncated;
the truncation is given by a cut-off frequency which is determined by this variable.
Name OCTControlFunctionRepresentation
Section Calculation Modes::Optimal Control
Type integer
Default control_fourier_series_h
If OCTControlRepresentation = control_function_parametrized, one must
specify the kind of parameters that determine the control function.
If OCTControlRepresentation = control_function_real_time, then this variable
is ignored, and the control function is handled directly in real time.
Options:
- control_fourier_series_h:
The control function is expanded as a full Fourier series (although it must, of course, be a real function). Then, the total fluence is fixed, and a transformation to hyperspherical coordinates is done; the parameters to optimize are the hyperspherical angles.
- control_zero_fourier_series_h:
The control function is expanded as a Fourier series, but assuming (1) that the zero frequency component is zero, and (2) the control function, integrated in time, adds up to zero (this essentially means that the sum of all the cosine coefficients is zero). Then, the total fluence is fixed, and a transformation to hyperspherical coordinates is done; the parameters to optimize are the hyperspherical angles.
- control_fourier_series:
The control function is expanded as a full Fourier series (although it must, of course, be a real function). The control parameters are the coefficients of this basis-set expansion.
- control_zero_fourier_series:
The control function is expanded as a full Fourier series (although it must, of course, be a real function). The control parameters are the coefficients of this basis-set expansion. The difference with the option control_fourier_series is that (1) that the zero-frequency component is zero, and (2) the control function, integrated in time, adds up to zero (this essentially means that the sum of all the cosine coefficients is zero).
- control_rt:
(experimental)
Name OCTControlFunctionType
Section Calculation Modes::Optimal Control
Type integer
Default controlfunction_mode_epsilon
The control function may fully determine the time-dependent form of the
external field, or only the envelope function of this external field, or its phase.
Or, we may have two different control functions, one of them providing the phase
and the other one, the envelope.
Note that, if OCTControlRepresentation = control_function_real_time, then the control
function must always determine the full external field (THIS NEEDS TO BE FIXED).
Options:
- controlfunction_mode_epsilon:
In this case, the control function determines the full control function: namely, if we are considering the electric field of a laser, the time-dependent electric field.
- controlfunction_mode_f:
The optimization process attempts to find the best possible envelope. The full control field is this envelope times a cosine function with a "carrier" frequency. This carrier frequency is given by the carrier frequency of the TDExternalFields in the inp file.
Name OCTCurrentFunctional
Section Calculation Modes::Optimal Control
Type integer
Default oct_no_curr
(Experimental) The variable OCTCurrentFunctional describes which kind of
current target functional $J1_c[j]$ is to be used.
Options:
- oct_no_curr:
No current functional is used, no current calculated.
- oct_curr_square:
Calculates the square of current $j$: $J1_c[j] = {\tt OCTCurrentWeight} \int{\left| j(r) \right|^2 dr}$. For OCTCurrentWeight < 0, the current will be minimized (useful in combination with target density in order to obtain stable final target density), while for OCTCurrentWeight > 0, it will be maximized (useful in combination with a target density in order to obtain a high-velocity impact, for instance). It is a static target, to be reached at total time.
- oct_max_curr_ring:
Maximizes the current of a quantum ring in one direction. The functional maximizes the $z$ projection of the outer product between the position $\vec{r}$ and the current $\vec{j}$: $J1[j] = {\tt OCTCurrentWeight} \int{(\vec{r} \times \vec{j}) \cdot \hat{z} dr}$. For OCTCurrentWeight > 0, the current flows in counter-clockwise direction, while for OCTCurrentWeight < 0, the current is clockwise.
- oct_curr_square_td:
The time-dependent version of oct_curr_square. In fact, calculates the square of current in time interval [OCTStartTimeCurrTg, total time = TDMaximumIter * TDTimeStep]. Set TDPropagator = crank_nicolson.
Name OCTCurrentWeight
Section Calculation Modes::Optimal Control
Type float
Default 0.0
In the case of simultaneous optimization of density $n$ and current $j$, one can tune the importance
of the current functional $J1_c[j]$, as the respective functionals might not provide results on the
same scale of magnitude. $J1[n,j]= J1_d[n]+ {\tt OCTCurrentWeight}\ J1_c[j]$. Be aware that its
sign is crucial for the chosen OCTCurrentFunctional as explained there.
Name OCTDelta
Section Calculation Modes::Optimal Control
Type float
Default 0.0
If OCTScheme = oct_mt03, then you can supply the "eta" and "delta" parameters
described in [Y. Maday and G. Turinici, J. Chem. Phys. 118, 8191 (2003)], using the
OCTEta and OCTDelta variables.
Name OCTDirectStep
Section Calculation Modes::Optimal Control
Type float
Default 0.25
If you choose OCTScheme = oct_direct or OCTScheme = oct_nlopt_bobyqa,
the algorithms necessitate an initial "step" to perform the direct search for the
optimal value. The precise meaning of this "step" differs.
Name OCTDoubleCheck
Section Calculation Modes::Optimal Control
Type logical
Default true
In order to make sure that the optimized field indeed does its job, the code
may run a normal propagation after the optimization using the optimized field.
Name OCTDumpIntermediate
Section Calculation Modes::Optimal Control
Type logical
Default true
Writes to disk the laser pulse data during the OCT algorithm at intermediate steps.
These are files called opt_control/laser.xxxx, where xxxx is the iteration number.
Name OCTEps
Section Calculation Modes::Optimal Control
Type float
Default 1.0e-6
Define the convergence threshold. It computes the difference between the "input"
field in the iterative procedure, and the "output" field. If this difference is
less than OCTEps the iteration is stopped. This difference is defined as:
$ D[\varepsilon^{in},\varepsilon^{out}] = \int_0^T dt \left| \varepsilon^{in}(t)-\varepsilon^{out}(t)\right|^2 $
(If there are several control fields, this difference is defined as the sum over all the individual differences.)
Whenever this condition is satisfied, it means that we have reached a solution point
of the QOCT equations, i.e. a critical point of the QOCT functional (not
necessarily a maximum, and not necessarily the global maximum).
Name OCTEta
Section Calculation Modes::Optimal Control
Type float
Default 1.0
If OCTScheme = oct_mt03, then you can supply the "eta" and "delta" parameters
described in [Y. Maday and G. Turinici, J. Chem. Phys. 118, 8191 (2003)], using the
OCTEta and OCTDelta variables.
Name OCTExcludedStates
Section Calculation Modes::Optimal Control
Type string
If the target is the exclusion of several targets, ("OCTTargetOperator = oct_exclude_states")
then you must declare which states are to be excluded, by setting the OCTExcludedStates variable.
It must be a string in "list" format: "1-8", or "2,3,4-9", for example. Be careful to include
in this list only states that have been calculated in a previous "gs" or "unocc" calculation,
or otherwise the error will be silently ignored.
Name OCTFilter
Section Calculation Modes::Optimal Control
Type block
The block OCTFilter describes the type and shape of the filter function
that are applied to the optimized laser field in each iteration.
The filter forces the laser field to obtain the given form in frequency space.
Each line of the block describes a filter; this way you can actually have more
than one filter function (e.g. a filter in time and two in frequency space).
The filters are applied in the given order, i.e., first the filter specified
by the first line is applied, then second line.
The syntax of each line is, then:
%OCTFilter
domain | function
%
Possible arguments for domain are:
(i) frequency_filter: Specifies a spectral filter.
(ii) time_filter: DISABLED IN THIS VERSION.
Example:
%OCTFilter
time | "exp(-80*( w + 0.1567 )^2 ) + exp(-80*( w - 0.1567 )^2 )"
%
Be careful that also the negative-frequency component is filtered since the resulting field has to be real-valued.
Options:
- frequency_filter:
The filter is applied in the frequency domain.
Name OCTFixFluenceTo
Section Calculation Modes::Optimal Control
Type float
Default 0.0
The algorithm tries to obtain the specified fluence for the laser field.
This works only in conjunction with either the WG05 or the straight iteration scheme.
If this variable is not present in the input file, by default the code will not attempt a fixed-fluence QOCT run. The same holds if the value given to this variable is exactly zero.
If this variable is given a negative value, then the target fluence will be that of
the initial laser pulse given as guess in the input file. Note, however, that
first the code applies the envelope provided by the OCTLaserEnvelope input
option, and afterwards it calculates the fluence.
Name OCTFixInitialFluence
Section Calculation Modes::Optimal Control
Type logical
Default yes
By default, when asking for a fixed-fluence optimization (OCTFixFluenceTo = whatever),
the initial laser guess provided in the input file is scaled to match this
fluence. However, you can force the program to use that initial laser as the initial
guess, no matter the fluence, by setting OCTFixInitialFluence = no.
Name OCTHarmonicWeight
Section Calculation Modes::Optimal Control
Type string
Default “1”
(Experimental) If OCTTargetOperator = oct_tg_plateau, then the function to optimize is the integral of the
harmonic spectrum $H(\omega)$, weighted with a function $f(\omega)$
that is defined as a string here. For example, if
you set OCTHarmonicWeight = "step(w-1)", the function to optimize is
the integral of $step(\omega-1)*H(\omega)$, i.e.
$\int_1^{\infty} H \left( \omega \right) d\omega$.
In practice, it is better if you also set an upper limit, e.g.
$f(\omega) = step(\omega-1) step(2-\omega)$.
Name OCTInitialState
Section Calculation Modes::Optimal Control
Type integer
Default oct_is_groundstate
Describes the initial state of the quantum system.
Possible arguments are:
Options:
- oct_is_groundstate:
Start in the ground state.
- oct_is_excited:
Currently not in use.
- oct_is_gstransformation:
Start in a transformation of the ground-state orbitals, as defined in the block OCTInitialTransformStates.
- oct_is_userdefined:
Start in a user-defined state.
Name OCTInitialTransformStates
Section Calculation Modes::Optimal Control
Type block
If OCTInitialState = oct_is_gstransformation, you must specify an
OCTInitialTransformStates block, in order to specify which linear
combination of the states present in restart/gs is used to
create the initial state.
The syntax is the same as the TransformStates block.
Name OCTInitialUserdefined
Section Calculation Modes::Optimal Control
Type block
Define an initial state. Syntax follows the one of the UserDefinedStates block.
Example:
%OCTInitialUserdefined
1 | 1 | 1 | "exp(-r^2)exp(-i0.2*x)"
%
Name OCTLaserEnvelope
Section Calculation Modes::Optimal Control
Type block
Often a pre-defined time-dependent envelope on the control function is desired.
This can be achieved by making the penalty factor time-dependent.
Here, you may specify the required time-dependent envelope.
It is possible to choose different envelopes for different control functions.
There should be one line for each control function. Each line should
have only one element: a string with the name of a time-dependent function,
that should be correspondingly defined in a TDFunctions block.
Name OCTLocalTarget
Section Calculation Modes::Optimal Control
Type string
If OCTTargetOperator = oct_tg_local, then one must supply a function
that defines the target. This should be done by defining it through a string, using
the variable OCTLocalTarget.
Name OCTMaxIter
Section Calculation Modes::Optimal Control
Type integer
Default 10
The maximum number of iterations.
Typical values range from 10-100.
Name OCTMomentumDerivatives
Section Calculation Modes::Optimal Control
Type block
This block should contain the derivatives of the expression given in
OCTClassicalTarget with respect to the p array components.
Each line corresponds to a different classical particle, whereas the
columns correspond to each spatial dimension: the (i,j) block component
corresponds with the derivative wrt p[i,j].
Name OCTNumberCheckPoints
Section Calculation Modes::Optimal Control
Type integer
Default 0
During an OCT propagation, the code may write the wavefunctions at some time steps (the
"check points"). When the inverse backward or forward propagation
is performed in a following step, the wavefunction should reverse its path
(almost) exactly. This can be checked to make sure that it is the case – otherwise
one should try reducing the time-step, or altering in some other way the
variables that control the propagation.
If the backward (or forward) propagation is not retracing the steps of the previous
forward (or backward) propagation, the code will write a warning.
Name OCTOptimizeHarmonicSpectrum
Section Calculation Modes::Optimal Control
Type block
Default no
(Experimental)
If OCTTargetOperator = oct_tg_hhg, the target is the harmonic emission spectrum.
In that case, you must supply an OCTOptimizeHarmonicSpectrum block in the inp
file. The target is given, in general, by:
$J_1 = \int_0^\infty d\omega \alpha(\omega) H(\omega)$,
where $H(\omega)$ is the harmonic spectrum generated by the system, and $\alpha(\omega)$ is some function that determines what exactly we want to optimize. The role of the OCTOptimizeHarmonicSpectrum block is to determine this $\alpha(\omega)$ function. Currently, this function is defined as:
$\alpha(\omega) = \sum_{L=1}^{M} \frac{\alpha_L}{a_L} \sqcap( (\omega - L\omega_0)/a_L )$,
where $\omega_0$ is the carrier frequency. $M$ is the number of columns in the OCTOptimizeHarmonicSpectrum block. The values of L will be listed in the first row of this block; $\alpha_L$ in the second row, and $a_L$ in the third.
Example:
%OCTOptimizeHarmonicSpectrum
7 | 9 | 11
-1 | 1 | -1
0.01 | 0.01 | 0.01
%
Name OCTPenalty
Section Calculation Modes::Optimal Control
Type float
Default 1.0
The variable specifies the value of the penalty factor for the
integrated field strength (fluence). Large value = small fluence.
A transient shape can be specified using the block OCTLaserEnvelope.
In this case OCTPenalty is multiplied with time-dependent function.
The value depends on the coupling between the states. A good start might be a
value from 0.1 (strong fields) to 10 (weak fields).
Note that if there are several control functions, one can specify this variable as a one-line code, each column being the penalty factor for each of the control functions. Make sure that the number of columns is equal to the number of control functions. If it is not a block, all control functions will have the same penalty factor.
All penalty factors must be positive.
Name OCTPositionDerivatives
Section Calculation Modes::Optimal Control
Type block
This block should contain the derivatives of the expression given in
OCTClassicalTarget with respect to the q array components.
Each line corresponds to a different classical particle, whereas the
columns correspond to each spatial dimension: the (i,j) block component
corresponds with the derivative wrt q[i,j].
Name OCTRandomInitialGuess
Section Calculation Modes::Optimal Control
Type logical
Default false
The initial field to start the optimization search is usually given in the inp file,
through a TDExternalFields block. However, you can start from a random guess if you
set this variable to true.
Note, however, that this is only valid for the "direct" optimization schemes; moreover
you still need to provide a TDExternalFields block.
Name OCTScheme
Section Calculation Modes::Optimal Control
Type integer
Default oct_zbr98
Optimal Control Theory can be performed with Octopus with a variety of different
algorithms. Not all of them can be used with any choice of target or control function
representation. For example, some algorithms cannot be used if
OCTControlRepresentation = control_function_real_time
(OCTScheme > oct_straight_iteration), and others cannot be used
if OCTControlRepresentation = control_function_parametrized
(OCTScheme < oct_straight_iteration).
Options:
- oct_zbr98:
Backward-Forward-Backward scheme described in JCP 108, 1953 (1998). Only possible if target operator is a projection operator. Provides fast, stable and monotonic convergence.
- oct_zr98:
Forward-Backward-Forward scheme described in JCP 109, 385 (1998). Works for projection and more general target operators also. The convergence is stable but slower than ZBR98. Note that local operators show an extremely slow convergence. It ensures monotonic convergence.
- oct_wg05:
Forward-Backward scheme described in J. Opt. B. 7, 300 (2005). Works for all kinds of target operators, can be used with all kinds of filters, and allows a fixed fluence. The price is a rather unstable convergence. If the restrictions set by the filter and fluence are reasonable, a good overlap can be expected within 20 iterations. No monotonic convergence.
- oct_mt03:
Basically an improved and generalized scheme. Comparable to ZBR98/ZR98. See [Y. Maday and G. Turinici, J. Chem. Phys. 118, 8191 (2003)].
- oct_krotov:
The procedure reported in [D. Tannor, V. Kazakov and V. Orlov, in Time-Dependent Quantum Molecular Dynamics, edited by J. Broeckhove and L. Lathouweres (Plenum, New York, 1992), pp. 347-360].
- oct_straight_iteration:
Straight iteration: one forward and one backward propagation is performed at each iteration, both with the same control field. An output field is calculated with the resulting wavefunctions.
- oct_cg:
Conjugate-gradients, as implemented in the GNU GSL library. In particular, the Fletcher-Reeves version. The seed for the random number generator can be modified by setting GSL_RNG_SEED environment variable.
- oct_bfgs:
The methods use the vector Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm. Also, it calls the GNU GSL library version of the algorithm. It is a quasi-Newton method which builds up an approximation to the second derivatives of the function using the difference between successive gradient vectors. By combining the first and second derivatives the algorithm is able to take Newton-type steps towards the function minimum, assuming quadratic behavior in that region. We have chosen to implement the "bfgs2" version, as GSL calls it, which is supposed to be the most efficient version available, and a faithful implementation of the line minimization scheme described in "Practical Methods of Optimization", (Fletcher), Algorithms 2.6.2 and 2.6.4.
- oct_direct:
This is a "direct" optimization scheme. This means that we do not make use of the "usual" QOCT equations (backward-forward propagations, etc), but we use some gradient-free maximization algorithm for the function that we want to optimize. In this case, the maximization algorithm is the Nelder-Mead algorithm as implemented in the GSL. The function values are obtained by successive forward propagations. The seed for the random number generator can be modified by setting GSL_RNG_SEED environment variable.
- oct_nlopt_bobyqa:
The BOBYQA algorithm, as implemented in the NLOPT library -- therefore, octopus has to be compiled with it in order to be able to use this option. The seed for the random number generator can be modified by setting GSL_RNG_SEED environment variable.
- oct_nlopt_lbfgs:
The local BFGS, as implemented in the NLOPT library -- therefore, octopus has to be compiled with it in order to be able to use this option. The seed for the random number generator can be modified by setting GSL_RNG_SEED environment variable.
Name OCTSpatialCurrWeight
Section Calculation Modes::Optimal Control
Type block
Can be seen as a position-dependent OCTCurrentWeight. Consequently, it
weights contribution of current $j$ to its functional $J1_c[j]$ according to the position in space.
For example, oct_curr_square thus becomes
$J1_c[j] = {\tt OCTCurrentWeight} \int{\left| j(r) \right|^2 {\tt OCTSpatialCurrWeight}(r) dr}$.
It is defined as OCTSpatialCurrWeight$(r) = g(x) g(y) g(z)$, where $g(x) = \sum_{i} 1/(1+e^{-{\tt fact} (x-{\tt startpoint}_i)}) - 1/(1+e^{-{\tt fact} (x-{\tt endpoint}_i)})$. If not specified, $g(x) = 1$.
Each $g(x)$ is represented by one line of the block that has the following form
%OCTSpatialCurrWeight
dimension | fact | startpoint_1 | endpoint_1 | startpoint_2 | endpoint_2 |…
%
There are no restrictions on the number of lines, nor on the number of pairs of start- and endpoints.
Attention: startpoint and endpoint have to be supplied pairwise
with startpoint < endpoint. dimension > 0 is integer, fact is float.
Name OCTStartIterCurrTg
Section Calculation Modes::Optimal Control
Type integer
Default 0
Allows for a time-dependent target for the current without defining it for the total
time-interval of the simulation.
Thus it can be switched on at the iteration desired, OCTStartIterCurrTg >= 0
and OCTStartIterCurrTg < TDMaximumIter.
Tip: If you would like to specify a real time for switching
the functional on rather than the number of steps, just use something
like:
OCTStartIterCurrTg = 100.0 / TDTimeStep.
Name OCTTargetDensity
Section Calculation Modes::Optimal Control
Type string
If OCTTargetOperator = oct_tg_density, then one must supply the target density
that should be searched for. This one can do by supplying a string through
the variable OCTTargetDensity. Alternately, give the special string "OCTTargetDensityFromState"
to specify the expression via the block OCTTargetDensityFromState.
Name OCTTargetDensityFromState
Section Calculation Modes::Optimal Control
Type block
Default no
If OCTTargetOperator = oct_tg_density, and OCTTargetDensity = "OCTTargetDensityFromState",
you must specify a OCTTargetDensityState block, in order to specify which linear
combination of the states present in restart/gs is used to
create the target density.
The syntax is the same as the TransformStates block.
Name OCTTargetOperator
Section Calculation Modes::Optimal Control
Type integer
Default oct_tg_gstransformation
The variable OCTTargetOperator prescribes which kind of target functional is
to be used.
Options:
- oct_tg_groundstate:
The target operator is a projection operator on the ground state, i.e. the objective is to populate the ground state as much as possible.
- oct_tg_excited:
(Experimental) The target operator is an "excited state". This means that the target operator is a linear combination of Slater determinants, each one formed by replacing in the ground-state Slater determinant one occupied state with one excited state (i.e. "single excitations"). The description of which excitations are used, and with which weights, should be given in a file called oct-excited-state-target. See the documentation of subroutine excited_states_elec_init in the source code in order to use this feature.
- oct_tg_gstransformation:
The target operator is a projection operator on a transformation of the ground-state orbitals defined by the block OCTTargetTransformStates.
- oct_tg_userdefined:
(Experimental) Allows to define target state by using OCTTargetUserdefined.
- oct_tg_jdensity:
(Experimental)
- oct_tg_local:
(Experimental) The target operator is a local operator.
- oct_tg_td_local:
(Experimental) The target operator is a time-dependent local operator.
- oct_tg_exclude_state:
(Experimental) Target operator is the projection onto the complement of a given state, given by the block OCTTargetTransformStates. This means that the target operator is the unity operator minus the projector onto that state.
- oct_tg_hhg:
(Experimental) The target is the optimization of the HHG yield. You must supply the OCTOptimizeHarmonicSpectrum block, and it attempts to optimize the maximum of the spectrum around each harmonic peak. You may use only one of the gradient-less optimization schemes.
- oct_tg_velocity:
(Experimental) The target is a function of the velocities of the nuclei at the end of the influence of the external field, defined by OCTVelocityTarget
- oct_tg_hhgnew:
(Experimental) The target is the optimization of the HHG yield. You must supply the OCTHarmonicWeight string. It attempts to optimize the integral of the harmonic spectrum multiplied by some user-defined weight function.
- oct_tg_classical:
(Experimental)
- oct_tg_spin:
(Experimental)
Name OCTTargetSpin
Section Calculation Modes::Optimal Control
Type block
(Experimental) Specify the targeted spin as a 3-component vector. It will be normalized.
Name OCTTargetTransformStates
Section Calculation Modes::Optimal Control
Type block
Default no
If OCTTargetOperator = oct_tg_gstransformation, you must specify a
OCTTargetTransformStates block, in order to specify which linear
combination of the states present in restart/gs is used to
create the target state.
The syntax is the same as the TransformStates block.
Name OCTTargetUserdefined
Section Calculation Modes::Optimal Control
Type block
Define a target state. Syntax follows the one of the UserDefinedStates block.
Example:
%OCTTargetUserdefined
1 | 1 | 1 | "exp(-r^2)exp(-i0.2*x)"
%
Name OCTTdTarget
Section Calculation Modes::Optimal Control
Type block
(Experimental) If OCTTargetOperator = oct_tg_td_local, then you must supply
a OCTTdTarget block. The block should only contain one element, a string cotaining the
definition of the time-dependent local target, i.e. a function of x,y,z and t that
is to be maximized along the evolution.
Name OCTVelocityDerivatives
Section Calculation Modes::Optimal Control
Type block
If OCTTargetOperator = oct_tg_velocity, and
OCTScheme = oct_cg or OCTScheme = oct_bfgs
then you must supply the target in terms of the ionic velocities AND
the derivatives of the target with respect to the ionic velocity components.
The derivatives are supplied via strings through the block
OCTVelocityDerivatives.
Each velocity component is supplied by "v[n_atom,vec_comp]",
while n_atom is the atom number, corresponding to the
Coordinates block, and vec_comp is the corresponding
vector component of the velocity. The first line of the
OCTVelocityDerivatives block contains the derivatives
with respect to v[1,], the second with respect to v[2,] and so
on. The first column contains all derivatives with respect v[,1],
the second with respect to v[,2] and the third w.r.t. v[*,3].
As an example, we show the OCTVelocityDerivatives block
corresponding to the target shown in the OCTVelocityTarget
help section:
%OCTVelocityDerivatives
" 2*(v[1,1]-v[2,1])" | " 2*(v[1,2]-v[2,2])" | " 2*(v[1,3]-v[2,3])"
"-2*(v[1,1]-v[2,1])" | "-2*(v[1,2]-v[2,2])" | "-2*(v[1,3]-v[2,3])"
%
Name OCTVelocityTarget
Section Calculation Modes::Optimal Control
Type block
If OCTTargetOperator = oct_tg_velocity, then one must supply the
target to optimize in terms of the ionic velocities. This is done by
supplying a string through the block OCTVelocityTarget.
Each velocity component is supplied by "v[n_atom,vec_comp]",
where n_atom is the atom number, corresponding to the
Coordinates block, and vec_comp is the corresponding
vector component of the velocity. The target string can be
supplied by using several lines in this block.
As an example, the following target can be used to maximize the
velocity difference between atom 1 and 2 (in a 3D system):
%OCTVelocityTarget
"(v[1,1]-v[2,1])^2 + (v[1,2]-v[2,2])^2 + "
"(v[1,3]-v[2,3])^2"
%