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Input options

The real-space grid

The following parameters define the region of space where the Kohn-Sham equations will be solved, and the appropriate boundary conditions. In parallel environment, grid points are distributed among processors. Symmetry operations are used to reduce the sampled region to an irreducible wedge.

Periodic_System

(boolean), default value = false

This flag enables the use of periodic boundary conditions on all three directions. If set true, the input grid spacing may be increased so as to make it commensurable with the given size of periodic cell. Also, atomic coordinates are used as given, with no initial repositioning around the origin of real-space grid. If atoms are found to be outside the cell, they are replaced by their periodic image inside the cell.

Cell_Shape

(block), default value = no default

Length of periodic cell along the x, y, z coordinates. Relevant only in periodic systems.

Lattice_Vector_Scale

(real), default value = 1 , default unit = bohr (Bohr radii)

Constant that multiplies the length of all three unit lattice vectors. This is useful for volumetric expansions or contractions in periodic systems. Relevant only in periodic systems.

Boundary_Sphere_Radius

(real), default value = no default , default unit = bohr (Bohr radii)

Radius of enclosing spherical shell. Boundary conditions in non-periodic systems are such that all wave-functions vanish beyond a spherical shell centered in the origin and with given radius. The Hartree potential is also set to vanish on the shell (internally, this is done by solving Poisson's equation with a compensating charge outside the shell). Calculation stops if any atom is found outside the shell. The amount of extra space that should be given between the shell and any inner atom is strongly system-dependent and should be carefully tested for convergence.

Grid_Spacing

(real), default value = no default , default unit = bohr (Bohr radii)

Distance between neighbor points in the real-space grid. This is a critical parameter in the calculation and it should be carefully tested for convergence. The grid is assumed to be regular and orthogonal.

Expansion_Order

(integer), default value = 12

Order used in the finite-difference expansion of gradients and Laplacians. It corresponds to twice the number of neighbor points used on each side and for each direction. It must be an even number.

Olddat_Style

(boolean), default value = false

Compatibility flag. Removes the grid shift and ignores symmetry operations, so that the resulting grid is equal to the one used in older versions of this code. Output wave-functions and density are written to file old.dat instead of wfn.dat. Notice that these two files have different format!

Diagonalization parameters

Many DFT codes solve the Kohn-Sham equations by minimizing the total energy functional. Parsec uses a different approach: it performs direct diagonalization of the Kohn-Sham equations. Expressed in real space, the Hamiltonian is a sparse matrix, and efficient algorithms can be used to obtain the low-energy eigenstates with minimal memory usage and parallel communication.

Eigensolver

(word), default value = arpack

Implemented eigensolvers are: arpack (implicitly restarted Lanczos/Arnoldi) and diagla (block preconditioned Lanczos). The last solver uses significantly less memory, but it occasionally fails to converge in periodic systems.

Diag_Tolerance

(real), default value = 1.d-4

Tolerance in the residual norm of eigen-pairs.

Initial_Diag_Tolerance

(real), default value = 100.0

Tolerance in the residual norm used for the trial diagonalization. This can be a fairly large number, since the trial diagonalization does not need to be very accurate.

Subspace_Buffer_Size

(integer), default value = 1

Number of additional eigenvalues to be computed for each representation. Must be some positive value, so that the full set of eigenvalues can be reconstructed from the sum of representations without missing levels.

Self-consistency and mixing parameters

Max_Iter

(integer), default value = 50

Maximum number of iterations in the self-consistent loop.

Convergence_Criterion

(real), default value = 2.d-4 , default unit = Ry (rydbergs)

The density function is considered converged when the self-consistent residual error (SRE) falls below this value. The SRE is an integral of the square of the difference between the last two self-consistent potentials, weighted by electron density and taken squared root. This parameter should not be chosen less than the typical diagonalization accuracy.

Mixing_Method

(word), default value = Anderson

Defines the scheme used in the mixing of old an new potentials. Implemented schemes are Broyden and Anderson (which were proved to be equivalent by V. Eyert, 1996). In practice, there is no significant difference between these two schemes. Broyden mixing uses disk for input/output of internal data.

Mixing_Param

(real), default value = 0.30

Choice for the diagonal Jacobian used in the mixing of potentials. Small values reduce the amount of mixing and result in slower but more controlled convergence. For improved performance, the user may try reducing this parameter in cases where the energy landscape is too corrugated (e.g.: magnetic systems, or systems with many degrees of freedom).

Memory_Param

(integer), default value = 2

Number of previous SCF steps used in mixing. Ideal values range from 4 to 6. Larger values may actually worsen convergence because it includes steps far from the real solution.

Global atom and pseudopotential parameters

Atom_Types_Num

(integer), default value = no default

Number of different chemical elements present in the system.

Coordinate_Unit

(word), default value = Cartesian_Bohr

By default, positions of atoms are given in cartesian coordinates and units of Bohr radius. Other implemented options are:

• Cartesian_Ang atomic coordinates given in angstroms, cartesian.

• Lattice_Vectors atomic coordinates given in units of lattice vectors. Available only with periodic boundary conditions.

Old_Pseudopotential_Format

(boolean), default value = false

By default, pseudopotential files have atomic parameters (cut-off radii, etc. ) included. For back-compatibility, this flag enables the reading of old-format files, which do not have atomic parameters included. Notice that the naming convention of old-format files is *_POTR.DAT instead of *_POTRE.DAT. The use of mixed formats is not allowed: parsec reads all files in new format or all files in old format.

Old_Interpolation_Format

(boolean), default value = false

This is a compatibility flag. Normally, the local component of pseudopotentials V at some arbitrary point r is evaluated by linear interpolation of the function r*V. Due to the Coulomb-like behavior of V far away from the atom, this interpolation is exact beyond the cut-off radius. This flag reverts to the old method: linear interpolation of V itself. It should be used for debugging purposes only.

Parameters specific to each chemical element

These parameters should be given in sequence in parsec.in, and they refer to a particular chemical element in the system.

Atom_Type

(word), default value = no default

Chemical symbol of the current element. THIS IS CASE SENSITIVE!

Potential_Num

(integer), default value = no default

Number of available angular components. Relevant only if old-format pseudopotentials are used.

Core_Cutoff_Radius

(real), default value = no default , default unit = bohr (Bohr radii)

Maximum cut-off radius used in the generation of pseudopotential. Relevant only if old-format pseudopotentials are used.

Electron_Per_Orbital

(block), default value = no default

Number of electrons per atomic orbital used in the generation of pseudopotential. Relevant only if old-format pseudopotentials are used.

Local_Component

(integer), default value = no default

Choice of angular component to be considered local in the Kleinman-Bylander transformation. No ghost-state check is done in parsec. Therefore, check if the chosen component does not have ghost states.

Move_Flag

(integer), default value = 0

Type of movement to be applied to atoms. Relevant only if structural relaxation is performed. Value 0 makes all atoms movable in all directions. Value n positive makes the first n atoms movable. A negative value makes selected atoms movable (the selection is made inside block Atom_Coord).

Atom_Coord

(block), default value = no default

Coordinates of atoms belonging to the current chemical species. See Coordinate_Unit. If structural relaxation is done with selected atoms (Move_Flag < 0), each triplet of coordinates must be followed by an integer: 0 if this atom is fixed, 1 if it is movable.

Alpha_Filter

(real), default value = 0.0

Cut-off parameter in Fourier filtering of pseudopotentials, in reciprocal space. If value is non-positive, pseudopotentials are not filtered. Fourier filtering is implemented according to Briggs et al. Phys. Rev. B 54, 14362 (1996), but no second filtering in real space has been implemented so far.

Beta1_Filter

(real), default value = 0.0

Cut-off parameter in Fourier filtering of pseudopotentials, in reciprocal space. Referenced only if alpha_filter is positive.

Core_Filter

(real), default value = equal to Alpha_Filter

Cut-off parameter in Fourier filtering of non-linear core density. If non-positive, then core density is not filtered.

Electronic parameters

Restart_Run

(boolean), default value = false

By default, the initial charge density in a parsec run is built from the superposition of atomic charge densities. If you want instead to start from a previous run, choose value true. For confined systems, having restart_run = true prevents the initial centering of atoms. If this flag is used but an adequate file wfn.dat is not found, the calculation is interrupted.

States_Num

(integer), default value = no default

Number of energy eigenvalues to be computed. In spin-polarized calculations, this is the number of eigenvalues per spin orientation.

Net_Charges

(real), default value = 0.0 , default unit = e (electron charge)

Net electric charge in the system, in units of electron charge. It can also be used in periodic systems. In that case, a background charge is used and the divergent component of the Hartree potential is ignored.

Fermi_Temp

(real), default value = 80.0 , default unit = K (kelvins)

Fermi temperature used to smear out the Fermi energy. If a negative value is given, then the occupancy of Kohn-Sham orbitals is read from file occup.in and kept fixed throughout the calculation.

Correlation_Type

(word), default value = CA

Choice of exchange-Correlation functional to be used. Available choices and their variants are:

• CA, PZ : Ceperley-Alder (LDA), with spin-polarized option. D.M. Ceperley and B.J. Alder, Phys. Rev. Lett. 45, 566 (1980); J.P. Perdew and A. Zunger, Phys. Rev. B 23, 5048 (1981).

• XA: Slater's x-alpha (LDA). J.C. Slater, Phys. Rev. 81 385 (1951).

• WI: Wigner's interpolation (LDA). E. Wigner, Phys. Rev. 46, 1002 (1934).

• HL: Hedin-Lundqvist (LDA). L. Hedin and B.I. Lundqvist, J. Phys. C 4, 2064 (1971).

• LB: Ceperley-Alder with Leeuwen-Baerends correction (asymptotically corrected). R. van Leeuwen and E. J. Baerends, Phys. Rev. A 49, 2421 (1994).

• CS: Ceperley-Alder with Casida-Salahub correction (asymptotically corrected). M.E. Casida and D.R. Salahub, J. Chem. Phys. 113, 8918 (2000).

• PW, PW91: Perdew-Wang (GGA), with spin-polarized option. J.P. Perdew and Y. Wang, Phys. Rev. B 45, 13244 (1992).

• PB, PBE: Perdew-Burke-Ernzerhof (GGA), with spin-polarized option. J.P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996).

Ion_Energy_Diff

(real), default value = 0.0, default unit = Ry (rydbergs)

Energy difference used in the construction of the Casida-Salahub functional. Relevant only if that functional is used.

Spin_Polarization:

(boolean), default value = false

Enables spin-polarized densities and functional.

Structural relaxation

Minimization

(word), default value = none

Choice of method for structural relaxation. Available options are: none (no relaxation), simple (steepest-descent algorithm), BFGS (Broyden-Fletcher-Goldfarb-Shanno, the best), and manual (manual movement). Steepest-descent should be used as last resort. With manual movement, the sequence of atomic coordinates must be provided by the user in file manual.dat and it is used "as is". The last choice is useful for debugging. Symmetry operations are ignored if manual movement is performed

Movement_Num

(integer), default value = 500

Maximum number of iterations during structural relaxation.

Force_Min

(real), default value = 1.5d-3 , default unit = Ry/bohr (rydbergs/Bohr radii)

Maximum magnitude of the force on any atom in the relaxed structure. This should not be set less than about 0.01 Ry/a.u., which is the usual accuracy in the calculation of forces.

Max_Step

(real), default value = 0.05 (steepest descent), -1 (BFGS), default unit = bohr (Bohr radii)

If steepest-descent minimization is performed, this parameter sets the maximum displacement of atoms between two steps in relaxation. With BFGS, this defines the maximum displacement of atoms along each Cartesian component from their original position (if negative, no constraint in the movement of atoms is imposed). Ignored in all other circumstances.

Min_Step

(real), default value = 1.d-4 , default unit = bohr (Bohr radii)

Minimum displacement of atoms between two steps in steepest-descent relaxation. Relevant only if steepest descent is performed.

BFGS_Number_Corr

(integer), default value = 7

Number of variable metric corrections used to defined the limited-memory matrix. Relevant only if BFGS relaxation is performed.

Relax_Restart

(boolean), default value = false

Flag for the restart of a relaxation run. If true, the user must provide information about previous run in file relax_restart.dat. No need to input file wfn.dat. If this option is used, the atomic coordinates in parsec.in are replaced with the ones in relax_restart.dat. Appropriate warnings are written to output. If the restart file is not found, this flag is ignored and no information from previous relaxations is used.

Molecular dynamics

Molecular_Dynamics

(boolean), default value = false

Enables molecular dynamics. This feature can be used both for simulated annealing and for direct simulation of hot systems. Both canonical and micro-canonical ensembles are implemented. Symmetry operations are ignored if molecular dynamics is being performed.

Cooling_Method

(word), default value = stair

Type of cooling (i.e.: change of ensemble temperature) used during molecular dynamics. Possible choices are: stair (stair-case), log (logarithmic cooling), and linear (linear cooling). As the molecular dynamics simulation proceeds, the ensemble temperature changes according to the cooling method and to the choices of initial and final temperatures. At each step, the actual temperature is calculated from equipartition theorem and the kinetic energy (difference between the total energy and potential energy). In the first steps, the actual and ensemble temperatures may be very different, particularly if there are few atoms, when thermal fluctuations are enormous.

Tinit

(real), default value = 500.0 , default unit = K (kelvins)

Initial ensemble temperature in the system.

T_final

(real), default value = 500.0 , default unit = K (kelvins)

Final ensemble temperature.

T_Step

(real), default value = 150.0 , default unit = K (kelvins)

Step temperature used in the cooling.

Time_Step

(real), default value = 150.0 , default unit = ps ($10^{-12}$ seconds)

Time interval between two steps in molecular dynamics. The dynamical equations of motion are numerically integrated using a modified Verlet algorithm.

Friction_Coefficient

(real), default value = 0.0

Viscosity parameter in molecular dynamics, in atomic units (inverse time). If less than 1.d-6 a.u., then a micro-canonical ensemble is used: total energy is assumed constant, and the atoms start moving with a velocity distribution consistent with the initial temperature. If more, then a canonical ensemble is used and true Langevin molecular dynamics is performed.

Step_num

(integer), default value = 250

Number of steps in molecular dynamics. A successful simulation ends only after reaching the requested number of steps.

Restart_mode

(boolean), default value = false

Enables the restart of an aborted molecular dynamics simulation. With this feature, the last two sets of positions, velocities and accelerations stored in input file mdinit.dat are used. The number of steps in that file is included in the current run as well.

Polarizability

Polarizability

(boolean), default value = false

Enables calculation of polarizability using a finite-field method. Available only with non-periodic boundary conditions. An uniform electric field is applied successively along the +x,-x,+y,-y,+z,-z directions, and dipole moments are calculated and collected and printed in output file polar.dat. From dipole moments, the diagonal part of polarizability tensor is obtained. Symmetry operations are ignored if this flag is used.

Electric_Field

(real), default value = 0.001, default unit = ry/bohr/e (rydbergs/Bohr radii/electron charge)

Magnitude of external electric field to be applied.

Flags for additional input/output

Skip_force

(boolean), default value = false

Suppresses calculation of forces. Since forces are easily obtained, this flag is useless.

Output_All_States

(boolean), default value = false

Forces output of all wave-functions up to requested number of states to file wfn.dat, instead of only the occupied ones (default).

Save_Intermediate_Charge_Density

(boolean), default value = false

Causes wave-functions to be written to output after each self-consistent iteration, instead of only after self-consistency is reached. Previous wave-functions are over-written. This is useful for debugging purposes or if diagonalization is too demanding.

Output_Eigenvalues

(boolean), default value = false

Saves eigenvalues to file eigen.dat after self-consistency in density function is achieved. This is useful for debugging purposes.

Save_Intermediate_Eigenvalues

(boolean), default value = false

Saves eigenvalues after each SCF iteration, instead of after the last one. Useful for debugging purposes.

Output_Level

(integer), default value = 0

Output flag for additional info in parsec.out. With default value, only the basic output is written. Positive values cause additional information to be printed out:

> 0 : print out local/non-local components of force
> 1 : print out all symmetry data and additional arpack output
> 2 : print out more BFGS output
> 3 : print out all BFGS output
> 4 : print out all g-stars (warning: _lots_ of data)
> 5 : print out local potentials (warning: _lots_ of data)