## Calculation Modes

CalculationMode
Section: Calculation Modes
Type: integer
Default: gs

Decides what kind of calculation is to be performed.
Options:

• gs: Calculation of the ground state.
• unocc: Calculation of unoccupied/virtual KS states. Can also be used for a non-self-consistent calculation of states at arbitrary k-points, if density.obf from gs is provided in the restart/gs directory.
• td: Time-dependent calculation (experimental for periodic systems).
• go: Optimization of the geometry.
• opt_control: Optimal control.
• em_resp: Calculation of the electromagnetic response: electric polarizabilities and hyperpolarizabilities and magnetic susceptibilities (experimental for periodic systems).
• casida: Excitations via Casida linear-response TDDFT; for finite systems only.
• vdw: Calculate van der Waals coefficients.
• vib_modes: Calculation of the vibrational modes.
• one_shot: Obsolete. Use gs with MaximumIter = 0 instead.
• kdotp: Calculation of effective masses by $$\vec{k} \cdot \vec{p}$$ perturbation theory (experimental).
• dummy: This calculation mode does nothing. Useful for debugging, testing and benchmarking.
• invert_ks: Invert the Kohn-Sham equations (experimental).
• recipe: Prints out a tasty recipe.

## Calculation Modes::Geometry Optimization

GOCenter
Section: Calculation Modes::Geometry Optimization
Type: logical
Default: no

(Experimental) If set to yes, Octopus centers the geometry at every optimization step. It also reduces the degrees of freedom of the optimization by using the translational invariance.

GOConstrains
Section: Calculation Modes::Geometry Optimization
Type: block

If XYZGOConstrains, PDBConstrains, and XSFGOConstrains are not present, Octopus will try to fetch the geometry optimization contrains from this block. If this block is not present, Octopus will not set any constrains. The format of this block can be illustrated by this example:

%GOConstrains
'C' | 1 | 0 | 0
'O' |  1 | 0 | 0
%

Coordinates with a constrain value of 0 will be optimized, while coordinates with a constrain different from zero will be kept fixed. So, in this example the x coordinates of both atoms will remain fixed and the distance between the two atoms along the x axis will be constant.

Note: It is important for the constrains to maintain the ordering in which the atoms were defined in the coordinates specifications. Moreover, constrains impose fixed absolute coordinates, therefore constrains are not compatible with GOCenter = yes

GOFireIntegrator
Section: Calculation Modes::Geometry Optimization
Type: integer
Default: verlet

The Fire algorithm (GOMethod = fire) uses a molecular dynamics integrator to compute new geometries and velocities. Currently, two integrator schemes can be selected
Options:

• euler: The Euler method.
• verlet: The Velocity Verlet algorithm.

GOFireMass
Section: Calculation Modes::Geometry Optimization
Type: float
Default: 1.0 amu

The Fire algorithm (GOMethod = fire) assumes that all degrees of freedom are comparable. All the velocities should be on the same scale, which for heteronuclear systems can be roughly achieved by setting all the atom masses equal, to the value specified by this variable. By default the mass of a proton is selected (1 amu). However, a selection of GOFireMass = 0.01 can, in manys systems, speed up the geometry optimization procedure. If GOFireMass <= 0, the masses of each species will be used.

GOLineTol
Section: Calculation Modes::Geometry Optimization
Type: float
Default: 0.1

Tolerance for line-minimization. Applies only to GSL methods that use the forces. WARNING: in some weird units.

GOMaxIter
Section: Calculation Modes::Geometry Optimization
Type: integer
Default: 200

Even if the convergence criterion is not satisfied, the minimization will stop after this number of iterations.

GOMethod
Section: Calculation Modes::Geometry Optimization
Type: integer
Default: fire

Method by which the minimization is performed. For more information see the GSL documentation.
Options:

• steep_native: (Experimental) Non-gsl implementation of steepest descent.
• steep: Simple steepest descent.
• cg_fr: Fletcher-Reeves conjugate-gradient algorithm. The conjugate-gradient algorithm proceeds as a succession of line minimizations. The sequence of search directions is used to build up an approximation to the curvature of the function in the neighborhood of the minimum.
• cg_bfgs: Vector Broyden-Fletcher-Goldfarb-Shanno (BFGS) conjugate-gradient algorithm. It is a quasi-Newton method which builds up an approximation to the second derivatives of the function f 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.
• cg_bfgs2: The bfgs2 version of this minimizer is the most efficient version available, and is a faithful implementation of the line minimization scheme described in Fletcher, Practical Methods of Optimization, Algorithms 2.6.2 and 2.6.4.
• simplex: This is experimental, and in fact, not recommended unless you just want to fool around. It is the Nead-Melder simplex algorithm, as implemented in the GNU Scientific Library (GSL). It does not make use of the gradients (i.e., the forces) which makes it less efficient than other schemes. It is included here for completeness, since it is free.
• fire: The FIRE algorithm. See also GOFireMass and GOFireIntegrator. Ref: E. Bitzek, P. Koskinen, F. Gahler, M. Moseler, and P. Gumbsch, Phys. Rev. Lett. 97, 170201 (2006).

GOMinimumMove
Section: Calculation Modes::Geometry Optimization
Type: float

Convergence criterion, for stopping the minimization. In units of length; minimization is stopped when the coordinates of all species change less than GOMinimumMove, or the GOTolerance criterion is satisfied. If GOMinimumMove < 0, this criterion is ignored. Default is -1, except 0.001 b with GOMethod = simplex. Note that if you use GOMethod = simplex, then you must supply a non-zero GOMinimumMove.

GOObjective
Section: Calculation Modes::Geometry Optimization
Type: integer
Default: minimize_energy

This rather esoteric option allows one to choose which objective function to minimize during a geometry minimization. The use of this variable may lead to inconsistencies, so please make sure you know what you are doing.
Options:

• minimize_energy: Use the total energy as objective function.
• minimize_forces: Use $$\sqrt{\sum_i \left| f_i \right|^2}$$ as objective function. Note that in this case one still uses the forces as the gradient of the objective function. This is, of course, inconsistent, and may lead to very strange behavior.

GOStep
Section: Calculation Modes::Geometry Optimization
Type: float

Initial step for the geometry optimizer. The default is 0.5. WARNING: in some weird units. For the FIRE minimizer, default value is 0.1 fs, and corresponds to the initial time-step for the MD.

GOTolerance
Section: Calculation Modes::Geometry Optimization
Type: float
Default: 0.001 H/b (0.051 eV/A)

Convergence criterion, for stopping the minimization. In units of force; minimization is stopped when all forces on ions are smaller than this criterion, or the GOMinimumMove is satisfied. If GOTolerance < 0, this criterion is ignored.

PDBGOConstrains
Section: Calculation Modes::Geometry Optimization
Type: string

Like XYZGOConstrains but in PDB format, as in PDBCoordinates.

XSFGOConstrains
Section: Calculation Modes::Geometry Optimization
Type: string

Like XYZGOConstrains but in XCrySDen format, as in XSFCoordinates.

XYZGOConstrains
Section: Calculation Modes::Geometry Optimization
Type: string

Octopus will try to read the coordinate-dependent constrains from the XYZ file specified by the variable XYZGOConstrains. Note: It is important for the contrains to maintain the ordering in which the atoms were defined in the coordinates specifications. Moreover, constrains impose fixed absolute coordinates, therefore constrains are not compatible with GOCenter = yes

## Calculation Modes::Invert KS

InvertKSConvAbsDens
Section: Calculation Modes::Invert KS
Type: float
Default: 1e-5

Absolute difference between the calculated and the target density in the KS inversion. Has to be larger than the convergence of the density in the SCF run.

InvertKSGodbyMu
Section: Calculation Modes::Invert KS
Type: float
Default: 1.0

prefactor for iterative KS inversion convergence scheme from Godby based on van Leeuwen scheme

InvertKSGodbyPower
Section: Calculation Modes::Invert KS
Type: float
Default: 0.05

power to which density is elevated for iterative KS inversion convergence scheme from Godby based on van Leeuwen scheme

InvertKSMaxIter
Section: Calculation Modes::Invert KS
Type: integer
Default: 200

Selects how many iterations of inversion will be done in the iterative scheme

InvertKSStellaAlpha
Section: Calculation Modes::Invert KS
Type: float
Default: 0.05

prefactor term in iterative scheme from L Stella

InvertKSStellaBeta
Section: Calculation Modes::Invert KS
Type: float
Default: 1.0

residual term in Stella iterative scheme to avoid 0 denominators

InvertKSTargetDensity
Section: Calculation Modes::Invert KS
Type: string
Default: target_density.dat

Name of the file that contains the density used as the target in the inversion of the KS equations.

InvertKSVerbosity
Section: Calculation Modes::Invert KS
Type: integer
Default: 0

Selects what is output during the calculation of the KS potential.
Options:

• 0: Only outputs the converged density and KS potential.
• 1: Same as 0 but outputs the maximum difference to the target density in each iteration in addition.
• 2: Same as 1 but outputs the density and the KS potential in each iteration in addition.

InvertKSmethod
Section: Calculation Modes::Invert KS
Type: integer
Default: iterative

Selects whether the exact two-particle method or the iterative scheme is used to invert the density to get the KS potential.
Options:

• two_particle: Exact two-particle scheme.
• iterative: Iterative scheme for $$v_s$$.
• iter_stella: Iterative scheme for $$v_s$$ using Stella and Verstraete method.
• iter_godby: Iterative scheme for $$v_s$$ using power method from Rex Godby.

KSInversionAsymptotics
Section: Calculation Modes::Invert KS
Type: integer
Default: xc_asymptotics_none

Asymptotic correction applied to $$v_{xc}$$.
Options:

• xc_asymptotics_none: Do not apply any correction in the asymptotic region.
• xc_asymptotics_sc: Applies the soft-Coulomb decay of $$-1/\sqrt{r^2+1}$$ to $$v_{xc}$$ in the asymptotic region.

KSInversionLevel
Section: Calculation Modes::Invert KS
Type: integer

At what level Octopus shall handle the KS inversion.
Options:

• ks_inversion_none: Do not compute KS inversion.
• ks_inversion_adiabatic: Compute exact adiabatic $$v_{xc}$$.

## Calculation Modes::Optimal Control

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.

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.

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.

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)

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.

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.

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.

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.

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.

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.

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.

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).

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.

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.

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.

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.

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.

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. $$f(\omega) = step(\omega-1) step(2-\omega)$$.

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.

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.

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(-i*0.2*x)"
%

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.

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.

OCTMaxIter
Section: Calculation Modes::Optimal Control
Type: integer
Default: 10

The maximum number of iterations. Typical values range from 10-100.

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].

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.

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
%

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.

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].

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.

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_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.
• 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 implemeted 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.

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.

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.

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.

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.

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_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)
• 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.

OCTTargetSpin
Section: Calculation Modes::Optimal Control
Type: block

(Experimental) Specify the targeted spin as a 3-component vector. It will be normalized.

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.

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(-i*0.2*x)"
%

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.

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])"
%

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"
%

## Calculation Modes::Test

InterpolationTestOrder
Section: Calculation Modes::Test
Type: integer
Default: 1

This variable controls the order of the grid interpolation used in the corresponding unit test.

TestBatchOps
Section: Calculation Modes::Test
Type: flag
Default: ops_axpy + ops_scal + ops_nrm2

Decides which part of the Hamiltonian is applied.
Options:

• ops_axpy: Tests batch_axpy operation
• ops_scal: Tests batch_scal operation
• ops_nrm2: Tests batch_nrm2 operation
• ops_dotp_matrix: Tests X(mesh_batch_dotp_matrix)
• ops_dotp_self: Tests X(mesh_batch_dotp_self)
• ops_dotp_vector: Tests X(mesh_batch_dotp_vector)

TestHamiltonianApply
Section: Calculation Modes::Test
Type: integer
Default: term_all

Decides which part of the Hamiltonian is applied.
Options:

• term_all: Apply the full Hamiltonian.
• term_kinetic: Apply only the kinetic operator
• term_local_potential: Apply only the local potential.
• term_non_local_potential: Apply only the non_local potential.

TestMaxBlockSize
Section: Calculation Modes::Test
Type: integer
Default: 128

Some tests can work with multiple blocksizes, in this case of range of blocksizes will be tested. This variable sets the lower bound of that range.

Currently this variable is only used by the derivatives test.

TestMinBlockSize
Section: Calculation Modes::Test
Type: integer
Default: 1

Some tests can work with multiple blocksizes, in this case of range of blocksizes will be tested. This variable sets the lower bound of that range.

Currently this variable is only used by the derivatives test.

TestMode
Section: Calculation Modes::Test
Type: integer
Default: hartree

Decides what kind of test should be performed.
Options:

• exp_apply: Tests the exponential of the Hamiltonian
• boundaries: Tests the boundaries conditions
• subspace_diag: Tests the subspace diagonalization
• batch_ops: Tests the batch operations
• clock: Tests for clock
• linear_solver: Tests the linear solvers
• hartree: Tests the Poisson solvers used to calculate the Hartree potential.
• cgal: Tests for cgal interface
• dense_eigensolver: Tests for dense eigensolvers (especially parallel ones)
• grid_interpolation: Tests for grid interpolation and multigrid methods.
• derivatives: Tests and benchmarks the implementation of the finite-difference operators, used to calculate derivatives.
• orthogonalization: Tests the implementation of the orthogonalization routines.
• interpolation: Test the interpolation routines.
• ion_interaction: Tests the ion-ion interaction routines.
• projector: Tests the code that applies the nonlocal part of the pseudopotentials in case of spin-orbit coupling
• dft_u: Tests the DFT+U part of the code for projections on the basis.
• hamiltonian_apply: Tests the application of the Hamiltonian, or a part of it
• density_calc: Calculation of the density.

TestRepetitions
Section: Calculation Modes::Test
Type: integer
Default: 1

This variable controls the behavior of oct-test for performance benchmarking purposes. It sets the number of times the computational kernel of a test will be executed, in order to provide more accurate timings.

Currently this variable is used by the hartree_test, derivatives, and projector tests.

TestType
Section: Calculation Modes::Test
Type: integer
Default: all

Decides on what type of values the test should be performed.
Options:

• real: Test for double-precision real functions.
• all: Tests for double-precision real and complex functions.

## Calculation Modes::Unoccupied States

UnoccShowOccStates
Section: Calculation Modes::Unoccupied States
Type: logical
Default: false

If true, the convergence for the occupied states will be shown too in the output. This is useful for testing, or if the occupied states fail to converge. It will be enabled automatically if only occupied states are being calculated.

UnoccUseTD
Section: Calculation Modes::Unoccupied States
Type: logical
Default: no

If true, Octopus will use the density and states from the restart/td folder to compute the bandstructure, instead of the restart/gs ones.