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PSPW

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Pseudopotential plane-wave density functional theory (NWPW)

The NWChem plane-wave (NWPW) module uses pseudopotentials and plane-wave basis sets to perform Density Functional Theory calculations. This module complements the capabilities of the more traditional Gaussian function based approaches by having an accuracy at least as good for many applications, yet is still fast enough to treat systems containing hundreds of atoms. Another significant advantage is its ability to simulate dynamics on a ground state potential surface directly at run-time using the Car-Parrinello algorithm. This method's efficiency and accuracy make it a desirable first principles method of simulation in the study of complex molecular, liquid, and solid state systems. Applications for this first principles method include the calculation of free energies, search for global minima, explicit simulation of solvated molecules, and simulations of complex vibrational modes that cannot be described within the harmonic approximation.

The NWPW module is a collection of three modules.

  • PSPW - (PSeudopotential Plane-Wave) A gamma point code for calculating molecules, liquids, crystals, and surfaces.
  • Band - A band structure code for calculating crystals and surfaces with small band gaps (e.g. semi-conductors and metals).
  • PAW - a (gamma point) projector augmented plane-wave code for calculating molecules, crystals, and surfaces

The PSPW, Band, and PAW modules can be used to compute the energy and optimize the geometry. Both the PSPW and Band modules can also be used to find saddle points, and compute numerical second derivatives. In addition the PSPW module can also be used to perform Car-Parrinello molecular dynamics. Section PSPW Tasks describes the tasks contained within the PSPW module, section #Band Tasks describes the tasks contained within the Band module, section #PAW Tasks describes the tasks contained within the PAW module, and section #Pseudopotential and PAW basis Libraries describes the pseudopotential library included with NWChem. The datafiles used by the PSPW module are described in section #NWPW RTDB Entries and DataFiles. Car-Parrinello output data files are described in section #PSPW Car-Parrinello Output Datafiles, and the minimization and Car-Parrinello algorithms are described in section #Car-Parrinello Scheme for Ab Initio Molecular Dynamics. Examples of how to setup and run a PSPW geometry optimization, a Car-Parrinello simulation, a band structure minimization, and a PAW geometry optimization are presented at the end. Finally in section #NWPW Capabilities and Limitations the capabilities and limitations of the NWPW module are discussed.

If you are a first time user of this module it is recommended that you skip the next five sections and proceed directly to the tutorials.

PSPW Tasks

All input to the PSPW Tasks is contained within the compound PSPW block,

PSPW 
  ...
END

To perform an actual calculation a TASK PSPW directive is used (Section #Task).

TASK PSPW

In addition to the directives listed in #Task, i.e. TASK pspw energy TASK pspw gradient TASK pspw optimize TASK pspw saddle TASK pspw freqencies TASK pspw vib there are additional directives that are specific to the PSPW module, which are:

TASK PSPW [Car-Parrinello             || 
           pspw_dplot                 || 
           wannier                    || 
           psp_generator              || 
           steepest_descent           || 
           psp_formatter              || 
           wavefunction_initializer   || 
           v_wavefunction_initializer || 
           wavefunction_expander       ]

Once a user has specified a geometry, the PSPW module can be invoked with no input directives (defaults invoked throughout). However, the user will probably always specify the simulation cell used in the computation, since the default simulation cell is not well suited for most systems. There are sub-directives which allow for customized application; those currently provided as options for the PSPW module are:

PSPW 
 CELL_NAME <string cell_name default 'cell_default'> 
 INPUT_WAVEFUNCTION_FILENAME <string input_wavefunctions default input_movecs> 
 OUTPUT_WAVEFUNCTION_FILENAME <string output_wavefunctions default input_movecs> 
 FAKE_MASS <real fake_mass default 400000.0> 
 TIME_STEP <real time_step default 5.8> 
 LOOP <integer inner_iteration outer_iteration default 10 100> 
 TOLERANCES <real tole tolc default 1.0e-7 1.0e-7> 
 CUTOFF <real cutoff> 
 ENERGY_CUTOFF <real ecut default (see input description)> 
 WAVEFUNCTION_CUTOFF <real wcut default (see input description)> 
 EWALD_NCUT <integer ncut default 1> 
 EWALD_RCUT <real rcut default (see input description)> 
 XC (Vosko      || LDA          || PBE96         || revPBE       || HF            ||  
     LDA-SIC    || LDA-SIC/2    || LDA-0.4SIC    || LDA-SIC/4    || LDA-0.2SIC    || 
     PBE96-SIC  || PBE96-SIC/2  || PBE96-0.4SIC  || PBE96-SIC/4  || PBE96-0.2SIC  || 
     revPBE-SIC || revPBE-SIC/2 || revPBE-0.4SIC || revPBE-SIC/4 || revPBE-0.2SIC || 
     PBE0       || revPBE0      || default Vosko) 
 DFT||ODFT||RESTRICTED||UNRESTRICTED 
 MULT <integer mult default 1> 
 MULLIKEN 
 EFIELD 
 ALLOW_TRANSLATION 
 CG 
 LMBFGS 
 SCF [Anderson|| simple || Broyden] 
     [CG || RMM-DIIS] 
     [density || potential] 
     [ALPHA real alpha default 0.25] 
     [ITERATIONS integer inner_iterations default 5] 
     [OUTER_ITERATIONS integer outer_iterations default 0]
 SIMULATION_CELL            ... (see input description) END 
 DPLOT                      ... (see input description) END 
 WANNIER                    ... (see input description) END 
 CAR-PARRINELLO             ... (see input description) END 
 PSP_GENERATOR              ... (see input description) END 
 WAVEFUNCTION_INITIALIZER   ... (see input description) END 
 V_WAVEFUNCTION_INITIATIZER ... (see input description) END 
 WAVEFUNCTION_EXPANDER      ... (see input description) END 
 STEEPEST_DESCENT           ... (see input description) END
 MAPPING <integer mapping default 1>
 ROTATION (ON || OFF) TRANSLATION (ON || OFF)
END

The following list describes the keywords contained in the PSPW input block.

  • <cell_name> - name of the simulation_cell named <cell_name>. See section #Simulation Cell.
  • <input_wavefunctions> - name of the file containing one-electron orbitals
  • <output_wavefunctions> - name of the file that will contain the one-electron orbitals at the end of the run.
  • <fake_mass> - value for the electronic fake mass (0 Μ). This parameter is not presently used in a conjugate gradient simulation.
  • <time_step> - value for the time step (Δt). This parameter is not presently used in a conjugate gradient simulation.
  • <inner_iteration> - number of iterations between the printing out of energies and tolerances
  • <outer_iteration> - number of outer iterations
  • <tole> - value for the energy tolerance.
  • <tolc> - value for the one-electron orbital tolerance.
  • <cutoff> - value for the cutoff energy used to define the wavefunction. In addition using the CUTOFF keyword automatically sets the cutoff energy for the density to be twice the wavefunction cutoff.
  • <ecut> - value for the cutoff energy used to define the density. Default is set to be the maximum value that will fit within the simulation_cell <cell_name>.
  • <wcut> - value for the cutoff energy used to define the one-electron orbitals. Default is set to be the maximum value that will fit within the simulation_cell <cell_name>.
  • <ncut> - value for the number of unit cells to sum over (in each direction) for the real space part of the Ewald summation. Note Ewald summation is only used if the simulation_cell is periodic.
  • <rcut> - value for the cutoff radius used in the Ewald summation. Note Ewald summation is only used if the simulation_cell is periodic.
Default set to be \frac{MIN(\left| \vec{a_i} \right|)}{\pi}, i=1,2,3.
  • (Vosko || PBE96 || revPBE || ...) - Choose between Vosko et al's LDA parameterization or the orginal and revised Perdew, Burke, and Ernzerhof GGA functional. In addition, several hybrid options.
  • MULT - optional keyword which if specified allows the user to define the spin multiplicity of the system
  • MULLIKEN - optional keyword which if specified causes a Mulliken analysis to be performed at the end of the simulation.
  • ALLOW_TRANSLATION - By default the the center of mass forces are projected out of the computed forces. This optional keyword if specified allows the center of mass forces to not be zero.
  • CG - optional keyword which sets the minimizer to 1
  • LMBFGS - optional keyword which sets the minimizer to 2
  • SCF - optional keyword which sets the minimizer to be a band by band minimizer. Several options are available for setting the density or potential mixing, and the type of Kohn-Sham minimizer.
  • SIMULATION_CELL (see section #Simulation Cell)
  • DPLOT (see section #DPLOT)
  • WANNIER (see section #Wannier)
  • CAR-PARRINELLO(see section #Car-Parrinello)
  • PSP_GENERATOR (see section #PSP_GENERATOR)
  • WAVEFUNCTION_INITIALIZER (see section #WAVEFUNCTION_INITIALIZER)
  • V_WAVEFUNCTION_INITIALIZER (see section #V_WAVEFUNCTION_INITIALIZER)
  • WAVEFUNCTION_EXPANDER (see section #WAVEFUNCTION_EXPANDER).
  • STEEPEST_DESCENT (see section #STEEPEST_DESCENT)
  • <mapping> - for a value of 1 slab FFT is used, for a value of 2 a 2d-hilbert FFT is used.

A prototype limited memory BFGS (LMBFGS) minimizer can be used to minimize the energy. To use this new optimizer the following SET directive needs to be specified:

set nwpw:mimimizer 1 # Default - Grassman conjugate gradient minimizer is used to minimize the energy.
set nwpw:mimimizer 2 # Grassman LMBFGS minimimzer is used to minimize the energy.
set nwpw:minimizer 4 # Stiefel conjugate gradient minimizer is used to minimize the energy. 
set nwpw:minimizer 5 # Band-by-band minimizer is used to minimizethe energy.

Limited testing suggests that the Grassman LMBFGS minimizer is about twice as fast as the conjugate gradient minimizer. However, there are several known cases where this optimizer fails, so it is currently not a default option, and should be used with caution.

In addition the following SET directives can be specified:

set nwpw:lcao_skip .false. # Default - initial wavefunctions generated using an LCAO guess. 
set nwpw:lcao_skip .true. # Initial wavefunctions generated using a random plane-wave guess.
set nwpw:lcao_print .false. # Default - Output not produced during the generation of the LCAO guess. 
set nwpw:lcao_print .true. # Output produced during the generation of the LCAO guess.
set nwpw:lcao_iterations 2 #specifies the number of LCAO iterations.

Simulation Cell

The simulation cell parameters are entered by defining a simulation_cell sub-block within the PSPW block. Listed below is the format of a simulation_cell sub-block.

PSPW
... 
 SIMULATION_CELL CELL_NAME <string name default 'cell_default'> 
 BOUNDARY_CONDITIONS (periodic || aperiodic default periodic) 
 LATTICE_VECTORS 
   <real a1.x a1.y a1.z default 20.0 0.0 0.0> 
   <real a2.x a2.y a2.z default 0.0 20.0 0.0> 
   <real a3.x a3.y a3.z default 0.0 0.0 20.0> 
 NGRID <integer na1 na2 na3 default 32 32 32> END
...
END

Basically, the user needs to enter the dimensions, gridding and boundary conditions of the simulation cell. The following list describes the input in detail.

  • <name> - user-supplied name for the simulation block.
  • periodic - keyword specifying that the simulation cell has periodic boundary conditions.
  • aperiodic - keyword specifying that the simulation cell has free-space boundary conditions.
  • <a1.x a1.y a1.z> - user-supplied values for the first lattice vector
  • <a2.x a2.y a2.z> - user-supplied values for the second lattice vector
  • <a3.x a3.y a3.zh> - user-supplied values for the third lattice vector
  • <na1 na2 na3> - user-supplied values for discretization along lattice vector directions.

Alternatively, instead of explicitly entering lattice vectors, users can enter the unit cell using the standard cell parameters, a, b, c, α, β, and γ, by using the LATTICE block. The format for input is as follows:

PSPW
... 
 SIMULATION_CELL 
   ... 
   LATTICE 
     [lat_a <real a default 20.0>] 
     [lat_b <real b default 20.0>] 
     [lat_c <real c default 20.0>] 
     [alpha <real alpha default 90.0>] 
     [beta <real beta default 90.0>] 
     [gamma <real gamma default 90.0>] 
   END 
   ... 
 END
...
END

The user can also enter the lattice vectors of standard unit cells using the keywords SC, FCC, BCC, for simple cubic, face-centered cubic, and body-centered cubic respectively. Listed below is an example of the format of this type of input.

PSPW
... 
 SIMULATION_CELL SC 20.0 
   .... 
 END
...
END

Finally, the lattice vectors from the unit cell can also be defined using the fractional coordinate input in the GEOMETRY input (see section #GEOMETRY:LATTICE PARAMETERS). Listed below is an example of the format of this type of input for an 8 atom silicon carbide unit cell.

geometry units au 
 system crystal 
   lat_a 8.277d0 
   lat_b 8.277d0 
   lat_c 8.277d0 
   alpha 90.0d0 
   beta 90.0d0 
   gamma 90.0d0 
 end
 Si -0.50000d0 -0.50000d0 -0.50000d0
 Si 0.00000d0 0.00000d0 -0.50000d0
 Si 0.00000d0 -0.50000d0 0.00000d0
 Si -0.50000d0 0.00000d0 0.00000d0
 C -0.25000d0 -0.25000d0 -0.25000d0
 C 0.25000d0 0.25000d0 -0.25000d0
 C 0.25000d0 -0.25000d0 0.25000d0
 C -0.25000d0 0.25000d0 0.25000d0
end

Unit Cell Optimization

The PSPW module using the DRIVER geometry optimizer can optimize a crystal unit cell. Currently this type of optimization works only if the geometry is specified in fractional coordinates. The following SET directive is used to tell the DRIVER geometry optimizer to optimize the crystal unit cell in addition to the geometry.

set includestress .true.

DPLOT

The pspw dplot task is used to generate plots of various types of electron densities (or orbitals) of a molecule. The electron density is calculated on the specified set of grid points from a PSPW calculation. The output file generated is in the Gaussian Cube format. Input to the DPLOT task is contained within the DPLOT sub-block.

PSPW 
... 
 DPLOT 
   ... 
 END 
...
END

To run a DPLOT calculation the following directive is used:

TASK PSPW PSPW_DPLOT

Listed below is the format of a DPLOT sub-block.

PSPW
... 
 DPLOT 
   VECTORS <string input_wavefunctions default input_movecs> 
   DENSITY [total||difference||alpha||beta||laplacian||potential default total] <string density_name no default> 
   ELF [restricted|alpha|beta] <string elf_name no default> 
   ORBITAL <integer orbital_number no default> <string orbital_name no default>
   [LIMITXYZ [units <string Units default angstroms>] 
   <real X_From> <real X_To> <integer No_Of_Spacings_X> 
   <real Y_From> <real Y_To> <integer No_Of_Spacings_Y>
   <real Z_From> <real Z_To> <integer No_Of_Spacings_Z>]
 END
...
END

The following list describes the input for the DPLOT sub-block.

VECTORS <string input_wavefunctions default input_movecs>  

This sub-directive specifies the name of the molecular orbital file. If the second file is optionally given the density is computed as the difference between the corresponding electron densities. The vector files have to match.

DENSITY [total||difference||alpha||beta||laplacian||potential default total] <string density_name no default>

This sub-directive specifies, what kind of density is to be plotted. The known names for total, difference, alpha, beta, laplacian, and potential.

ELF [restricted|alpha|beta] <string elf_name no default>

This sub-directive specifies that an electron localization function (ELF) is to be plotted.

ORBITAL <integer orbital_number no default> <string orbital_name no default>

This sub-directive specifies the molecular orbital number that is to be plotted.

LIMITXYZ [units <string Units default angstroms>] 
<real X_From> <real X_To> <integer No_Of_Spacings_X> 
<real Y_From> <real Y_To> <integer No_Of_Spacings_Y>
<real Z_From> <real Z_To> <integer No_Of_Spacings_Z>

By default the grid spacing and the limits of the cell to be plotted are defined by the input wavefunctions. Alternatively the user can use the LIMITXYZ sub-directive to specify other limits. The grid is generated using No_Of_Spacings + 1 points along each direction. The known names for Units are angstroms, au and bohr.

Wannier

The pspw wannier task is generate maximally localized (Wannier) molecular orbitals. The algorithm proposed by Silvestrelli et al is use to generate the Wannier orbitals. The current version of this code works only for cubic cells.

Input to the Wannier task is contained within the Wannier sub-block.

PSPW 
... 
 Wannier 
   ... 
 END 
...
END

To run a Wannier calculation the following directive is used:

TASK PSPW Wannier

Listed below is the format of a Wannier sub-block.

PSPW
... 
 Wannier 
  OLD_WAVEFUNCTION_FILENAME <string input_wavefunctions default input_movecs> 
  NEW_WAVEFUNCTION_FILENAME <string output_wavefunctions default input_movecs> 
 END
...
END

The following list describes the input for the Wannier sub-block.

  • <input_wavefunctions> - name of pspw wavefunction file.
  • <output_wavefunctions> - name of pspw wavefunction file that will contain the Wannier orbitals.

Self-Interaction Corrections

The SET directive is used to specify the molecular orbitals contribute to the self-interaction-correction (SIC) term.

set pspw:SIC_orbitals <integer list_of_molecular_orbital_numbers>

This defines only the molecular orbitals in the list as SIC active. All other molecular orbitals will not contribute to the SIC term. For example the following directive specifies that the molecular orbitals numbered 1,5,6,7,8, and 15 are SIC active.

set pspw:SIC_orbitals 1 5:8 15

or equivalently

set pspw:SIC_orbitals 1 5 6 7 8 15

The following directive turns on self-consistent SIC.

set pspw:SIC_relax .false. # Default - Perturbative SIC calculation
set pspw:SIC_relax .true. # Self-consistent SIC calculation

Two types of solvers can be used and they are specified using the following SET directive

set pspw:SIC_solver_type 1 # Default - cutoff coulomb kernel
set pspw:SIC_solver_type 2 # Free-space boundary condition kernel

The parameters for the cutoff coulomb kernel are defined by the following SET directives:

set pspw:SIC_screening_radius <real rcut>
set pspw:SIC_screening_power <real rpower>

Point Charge Analysis

The MULLIKEN option can be used to generate derived atomic point charges from a plane-wave density. This analysis is based on a strategy suggested in the work of P.E. Blochl, J. Chem. Phys. vol. 103, page 7422 (1995). In this strategy the low-frequency components a plane-wave density are fit to a linear combination of atom centered Gaussian functions.

The following SET directives are used to define the fitting.

set pspw_APC:Gc <real Gc_cutoff> # specifies the maximum frequency component of the density to be used in the fitting in units of au.
set pspw_APC:nga <integer number_gauss> # specifies the the number of Gaussian functions per atom.
set pspw_APC:gamma <real gamma_list> # specifies the decay lengths of each atom centered Gaussian. 

We suggest using the following parameters.

set pspw_APC:Gc 2.5
set pspw_APC:nga 3
set pspw_APC:gamma 0.6 0.9 1.35 

Car-Parrinello

The Car-Parrinello task is used to perform ab initio molecular dynamics using the scheme developed by Car and Parrinello. In this unified ab initio molecular dynamics scheme the motion of the ion cores is coupled to a fictitious motion for the Kohn-Sham orbitals of density functional theory. Constant energy or constant temperature simulations can be performed. A detailed description of this method is described in section #Car-Parrinello Scheme for Ab Initio Molecular Dynamics.

Input to the Car-Parrinello simulation is contained within the Car-Parrinello sub-block.

PSPW 
... 
 Car-Parrinello 
   ... 
 END 
...
END

To run a Car-Parrinello calculation the following directive is used:

TASK PSPW Car-Parrinello 

The Car-Parrinello sub-block contains a great deal of input, including pointers to data, as well as parameter input. Listed below is the format of a Car-Parrinello sub-block.

PSPW
... 
 Car-Parrinello 
   CELL_NAME <string cell_name default 'cell_default'> 
   INPUT_WAVEFUNCTION_FILENAME <string input_wavefunctions default input_movecs> 
   OUTPUT_WAVEFUNCTION_FILENAME <string output_wavefunctions default input_movecs> 
   INPUT_V_WAVEFUNCTION_FILENAME <string input_v_wavefunctions default input_vmovecs> 
   OUTPUT_V_WAVEFUNCTION_FILENAME <string output_v_wavefunctions default input_vmovecs> 
   FAKE_MASS <real fake_mass default default 1000.0> 
   TIME_STEP <real time_step default 5.0> 
   LOOP <integer inner_iteration outer_iteration default 10 1> 
   SCALING <real scale_c scale_r default 1.0 1.0> 
   ENERGY_CUTOFF <real ecut default (see input description)> 
   WAVEFUNCTION_CUTOFF <real wcut default (see input description)> 
   EWALD_NCUT <integer ncut default 1> 
   EWALD_RCUT <real rcut default (see input description)> 
   XC (Vosko      || LDA          || PBE96         || revPBE       || HF            ||  
       LDA-SIC    || LDA-SIC/2    || LDA-0.4SIC    || LDA-SIC/4    || LDA-0.2SIC    || 
       PBE96-SIC  || PBE96-SIC/2  || PBE96-0.4SIC  || PBE96-SIC/4  || PBE96-0.2SIC  || 
       revPBE-SIC || revPBE-SIC/2 || revPBE-0.4SIC || revPBE-SIC/4 || revPBE-0.2SIC || 
       PBE0       || revPBE0      || default Vosko) 
   [Nose-Hoover <real Period_electron Temperature_electrion Period_ion Temperature_ion default 100.0 298.15 100.0 298.15>]  
   [SA_decay <real sa_scale_c sa_scale_r default 1.0 1.0>] XYZ_FILENAME <string xyz_filename default XYZ> 
   EMOTION_FILENAME <string emotion_filename default EMOTION> 
   HMOTION_FILENAME <string hmotion_filename default HMOTION> 
   OMOTION_FILENAME <string omotion_filename default OMOTION> 
   EIGMOTION_FILENAME <string eigmotion_filename default EIGMOTION>
   ION_MOTION_FILENAME <string ion_motion_filename default MOTION>
END ... END

The following list describes the input for the Car-Parrinello sub-block.

  • <cell_name> - name of the the simulation_cell named <cell_name>. See section #Simulation Cell.
  • <input_wavefunctions> - name of the file containing one-electron orbitals
  • <output_wavefunctions> - name of the file that will contain the one-electron orbitals at the end of the run.
  • <input_v_wavefunctions> - name of the file containing one-electron orbital velocities.
  • <output_v_wavefunctions> - name of the file that will contain the one-electron orbital velocities at the end of the run.
  • <fake_mass> - value for the electronic fake mass (μ).
  • <time_step> - value for the Verlet integration time step (Δt).
  • <inner_iteration> - number of iterations between the printing out of energies.
  • <outer_iteration> - number of outer iterations
  • <scale_c> - value for the initial velocity scaling of the one-electron orbital velocities.
  • <scale_r> - value for the initial velocity scaling of the ion velocities.
  • <ecut> - value for the cutoff energy used to define the density. Default is set to be the maximum value that will fit within the simulation_cell <cell_name>.
  • <wcut> - value for the cutoff energy used to define the one-electron orbitals. Default is set to be the maximum value that will fit within the simulation_cell <cell_name>.
  • <ncut> - value for the number of unit cells to sum over (in each direction) for the real space part of the Ewald summation. Note Ewald summation is only used if the simulation_cell is periodic.
  • <rcut> - value for the cutoff radius used in the Ewald summation. Note Ewald summation is only used if the simulation_cell is periodic.
 Default set to be \frac{MIN(\left| \vec{a_i} \right|)}{\pi}, i=1,2,3.
  • (Vosko || PBE96 || revPBE || ...) - Choose between Vosko et al's LDA parameterization or the orginal and revised Perdew, Burke, and Ernzerhof GGA functional. In addition, several hybrid options.
  • Nose-Hoover - optional subblock which if specified causes the simulation to perform Nose-Hoover dynamics. If this subblock is not specified the simulation performs constant energy dynamics. See section -sec:pspw_nose- for a description of the parameters.
    • <Period_electron> \equiv P_{electron} - estimated period for fictitious electron thermostat.
    • <Temperature_electron> \equiv T_{electron} - temperature for fictitious electron motion
    • <Period_ion> \equiv P_{ion} - estimated period for ionic thermostat
    • <Temperature_ion> \equiv T_{ion} - temperature for ion motion
  • SA_decay - optional subblock which if specified causes the simulation to run a simulated annealing simulation. For simulated annealing to work the Nose-Hoover subblock needs to be specified. The initial temperature are taken from the Nose-Hoover subblock. See section -sec:pspw_nose- for a description of the parameters.
    • <sa_scale_c> \equiv \tau_{electron} - decay rate in atomic units for electronic temperature.
    • <sa_scale_r> \equiv \tau_{ionic} - decay rate in atomic units for the ionic temperature.
  • <xyz_filename> - name of the XYZ motion file generated
  • <emotion_filename> - name of the emotion motion file. See section [[#EMOTION motion file] for a description of the datafile.
  • <hmotion_filenameh> - name of the hmotion motion file. See section [[#HMOTION motion file] for a description of the datafile.
  • <eigmotion_filename> - name of the eigmotion motion file. See section [[#EIGMOTION motion file] for a description of the datafile.
  • <ion_motion_filename> - name of the ion_motion motion file. See section [[#ION_MOTION motion file]- for a description of the datafile.
  • MULLIKEN - optional keyword which if specified causes an omotion motion file to be created.
  • <omotion_filename> - name of the omotion motion file. See section [[#OMOTION motion file] for a description of the datafile.

When a DPLOT sub-block is specified the following SET directive can be used to output dplot data during a Car-Parrinello simulation:

set pspw_dplot:iteration_list <integer list_of_iteration_numbers>

The Gaussian cube files specified in the DPLOT sub-block are appended with the specified iteration number.

For example, the following directive specifies that at the 3,10,11,12,13,14,15, and 50 iterations Gaussian cube files are to be produced.

set pspw_dplot:iteration_list 3,10:15,50

Adding Geometry Constraints To A Car-Parrinello Simulation

The Car-Parrinello module allows users to freeze the cartesian coordinates in a simulation (Note - the Car-Parrinello code recognizes Cartesian constraints, but it does not recognize internal coordinate constraints). The +SET+ directive (Section #GEOMETRIES:Applying constraints in geometry optimizations) is used to freeze atoms, by specifying a directive of the form:

set geometry:actlist <integer list_of_center_numbers>

This defines only the centers in the list as active. All other centers will have zero force assigned to them, and will remain frozen at their starting coordinates during a Car-Parrinello simulation.

For example, the following directive specifies that atoms numbered 1, 5, 6, 7, 8, and 15 are active and all other atoms are frozen:

set geometry:actlist 1 5:8 15

or equivalently,

set geometry:actlist 1 5 6 7 8 15

If this option is not specified by entering a +SET+ directive, the default behavior in the code is to treat all atoms as active. To revert to this default behavior after the option to define frozen atoms has been invoked, the +UNSET+ directive must be used (since the database is persistent, see Section #NWChem Architecture). The form of the +UNSET+ directive is as follows:

unset geometry:actlist

In addition, the Car-Parrinello module allows users to freeze bond lengths via a Shake algorithm. The following +SET+ directive shows how to do this.

set nwpw:shake_constraint "2 6 L 6.9334"

This input fixes the bond length between atoms 2 and 6 to be 6.9334 bohrs. Note that this input only recognizes bohrs.

When using constraints it is usually necessary to turn off center of mass shifting. This can be done by the following +SET+ directive.

set nwpw:com_shift .false.

QM/MM

A preliminary QM/MM capability that can run Car-Parrinello molecular dynamics has been integrated into the PSPW module. Currently, the input is not very robust but it is straightforward. The first step to run a QM/MM simulations is to define the MM atoms in the geometry block. The MM atoms must be at the end of the geometry and a carat, " ^ ", must be appended to the end of the atom name, e.g.

geometry units angstrom nocenter noautosym noautoz print xyz
 C -0.000283 0.000106 0.000047
 Cl -0.868403 1.549888 0.254229
 Cl 0.834043 -0.474413 1.517103
 Cl -1.175480 -1.275747 -0.460606
 Cl 1.209940 0.200235 -1.310743
 O^ 0.3226E+01 -0.4419E+01 -0.5952E+01 
 H^ 0.3193E+01 -0.4836E+01 -0.5043E+01 
 H^ 0.4167E+01 -0.4428E+01 -0.6289E+01
 O^ 0.5318E+01 -0.3334E+01 -0.1220E+01
 H^ 0.4978E+01 -0.3040E+01 -0.2113E+01
 H^ 0.5654E+01 -0.2540E+01 -0.7127E+00
end

Next the pseudopotentials have be defined for the every type of MM atom contained in the geometry blocks. The following local pseudopotential suggested by Laio, VandeVondele and Rothlisberger can be automatically generated.

\begin{matrix}V(\vec{r}) = -Z_{ion}\frac{{r_c}^{n_{\sigma}} - r^{n_{\sigma}}}{-sign(Z_{ion})*{r_c}^{n_{\sigma}+1}-r^{n_{\sigma}+1}}\end{matrix}

The following input To define this pseudopo the O^ MM atom using the following input

NWPW 
 QMMM 
   mm_psp O^ -0.8476 4 0.70 
 END
END

defines the local pseudopotential for the O^ MM atom , where Z{ion} = − 0.8476, nσ = 4, and rc = 0.7. The following input can be used to define the local pseudopotentials for all the MM atoms in the geometry block defined above

NWPW 
 QMMM 
   mm_psp O^ -0.8476 4 0.70 
   mm_psp H^ 0.4238 4 0.40 
 END
END

Next the Lenard-Jones potentials for the QM and MM atoms need to be defined. This is done as as follows

NWPW 
 QMMM 
   lj_ion_parameters C 3.41000000d0 0.10d0 
   lj_ion_parameters Cl 3.45000000d0 0.16d0 
   lj_ion_parameters O^ 3.16555789d0 0.15539425d0 
 END
END

Note that the Lenard-Jones potential is not defined for the MM H atoms in this example. The final step is to define the MM fragments in the simulation. MM fragments are a set of atoms in which bonds and angle harmonic potentials are defined, or alternatively shake constraints are defined. The following input defines the fragments for the two water molecules in the above geometry,

NWPW 
 QMMM 
   fragment spc 
     size 3                  #size of fragment 
     index_start 6:9:3       #atom index list that defines the start of 
                             # the fragments (start:final:stride)
     bond_spring 1 2 0.467307856 1.889726878   #bond i j Kspring r0 
     bond_spring 1 3 0.467307856 1.889726878   #bond i j Kspring r0 
     angle_spring 2 1 3 0.07293966 1.910611932 #angle i j k Kspring theta0 
   end 
 END
END

The fragments can be defined using shake constraints as

NWPW 
 QMMM 
   fragment spc 
     size 3                  #size of fragment 
     index_start 6:9:3       #atom index list that defines the start of 
                             # the fragments (start:final:stride)
     shake units angstroms 1 2 3 cyclic 1.0 1.632993125 1.0 
   end 
 END
END

Alternatively, each water could be defined independently as follows.

NWPW 
 QMMM 
   fragment spc1 
     size 3                  #size of fragment 
     index_start 6           #atom index list that defines the start of 
                             #the fragments 
     bond_spring 1 2 0.467307856 1.889726878 #bond i j Kspring r0 
     bond_spring 1 3 0.467307856 1.889726878 #bond i j Kspring r0 
     angle_spring 2 1 3 0.07293966 1.910611932 #angle i j k Kspring theta0 
   end 
   fragment spc2 
     size 3                  #size of fragment 
     index_start 9           #atom index list that defines the start of 
                             #the fragments 
     shake units angstroms 1 2 3 cyclic 1.0 1.632993125 1.0 
   end 
 END
END

PSP_GENERATOR

A one-dimensional pseudopotential code has been integrated into NWChem. This code allows the user to modify and develop pseudopotentials. Currently, only the Hamann and Troullier-Martins norm-conserving pseudopotentials can be generated. In future releases, the pseudopotential library (section #Pseudopotential and PAW basis Libraries) will be more complete, so that the user will not have explicitly generate pseudopotentials using this module.

Input to the PSP_GENERATOR task is contained within the PSP_GENERATOR sub-block.

PSPW 
... 
 PSP_GENERATOR 
   ... 
 END 
...
END

To run a PSP_GENERATOR calculation the following directive is used:

TASK PSPW PSP_GENERATOR

Listed below is the format of a PSP_GENERATOR sub-block.

PSPW
... 
 PSP_GENERATOR 
   PSEUDOPOTENTIAL_FILENAME: <string psp_name> 
   ELEMENT: <string element> 
   CHARGE: <real charge> 
   MASS_NUMBER: <real mass_number> 
   ATOMIC_FILLING: <integer ncore nvalence> ( (1||2||...) (s||p||d||f||...) <real filling>  ...)
   [CUTOFF: <integer lmax> ( (s||p||d||f||g) <real rcut> ...) ] 
   PSEUDOPOTENTIAL_TYPE: (TROULLIER-MARTINS || HAMANN default HAMANN) 
   SOLVER_TYPE: (PAULI || SCHRODINGER default PAULI) 
   EXCHANGE_TYPE: (dirac || PBE96 default DIRAC) 
   CORRELATION_TYPE: (VOSKO || PBE96 default VOSKO) 
   [SEMICORE_RADIUS: <real rcore>]
 END
... 
END

The following list describes the input for the PSP_GENERATOR sub-block.

  • <psp_name> - name that points to a.
  • <element> - Atomic symbol.
  • <charge> - charge of the atom
  • <mass> - mass number for the atom
  • <ncore> - number of core states
  • <nvalence> - number of valence states.
  • ATOMIC_FILLING:.....(see below)
  • <filling> - occupation of atomic state
  • CUTOFF:....(see below)
  • <rcore> - value for the semicore radius (see below)

ATOMIC_FILLING Block

This required block is used to define the reference atom which is used to define the pseudopotential. After the ATOMIC_FILLING: <ncore> <nvalence> line, the core states are listed (one per line), and then the valence states are listed (one per line). Each state contains two integer and a value. The first integer specifies the radial quantum number, n, the second integer specifies the angular momentum quantum number, l, and the third value specifies the occupation of the state.

For example to define a pseudopotential for the Neon atom in the 1s22s22p6 state could have the block

ATOMIC_FILLING: 1 2 
 1 s 2.0 #core state - 1s^2 
 2 s 2.0 #valence state - 2s^2 
 2 p 6.0 #valence state - 2p^6

for a pseudopotential with a 2s and 2p valence electrons or the block

ATOMIC_FILLING: 3 0 
 1 s 2.0 #core state 
 2 s 2.0 #core state 
 2 p 6.0 #core state

could be used for a pseudopotential with no valence electrons.

CUTOFF

This optional block specifies the cutoff distances used to match the all-electron atom to the pseudopotential atom. For Hamann pseudopotentials rcut(l) defines the distance where the all-electron potential is matched to the pseudopotential, and for Troullier-Martins pseudopotentials rcut(l) defines the distance where the all-electron orbital is matched to the pseudowavefunctions. Thus the definition of the radii depends on the type of pseudopotential. The cutoff radii used in Hamann pseudopotentials will be smaller than the cutoff radii used in Troullier-Martins pseudopotentials.

For example to define a softened Hamann pseudopotential for Carbon would be

ATOMIC_FILLING: 1 2 
 1 s 2.0 
 2 s 2.0 
 2 p 2.0
CUTOFF: 2
 s 0.8 
 p 0.85 
 d 0.85

while a similarly softened Troullier-Marting pseudopotential for Carbon would be

ATOMIC_FILLING: 1 2 
 1 s 2.0 
 2 s 2.0 
 2 p 2.0
CUTOFF: 2 
 s 1.200 
 p 1.275 
 d 1.275

SEMICORE_RADIUS

Specifying the SEMICORE_RADIUS option turns on the semicore correction approximation proposed by Louie et al (S.G. Louie, S. Froyen, and M.L. Cohen, Phys. Rev. B, 26(, 1738, (1982)). This approximation is known to dramatically improve results for systems containing alkali and transition metal atoms.

The implementation in the PSPW module defines the semi-core density, ρsemicore in terms of the core density, ρcore, by using the sixth-order polynomial

\rho_{semicore}(r) =
\begin{cases} 
\rho_{core} & \mbox{if } r \ge r_{semicore} \\
c_0 + c_3 r^3 + c_4 r^4 + c_5 r^5 + c_6 r^6 & \mbox{if } r < r_{semicore} 
\end{cases}

This expansion was suggested by Fuchs and Scheffler (M. Fuchs, and M. Scheffler, Comp. Phys. Comm.,119,67 (1999)), and is better behaved for taking derivatives (i.e. calculating ionic forces) than the expansion suggested by Louie et al.

WAVEFUNCTION_INITIALIZER

The functionality of this task is now performed automatically. For backward compatibility, we provide a description of the input to this task.

The wavefunction_initializer task is used to generate an initial wavefunction datafile. Input to the WAVEFUNCTION_INITIALIZER task is contained within the WAVEFUNCTION_INITIALIZER sub-block.

PSPW 
... 
 WAVEFUNCTION_INITIALIZER 
   ... 
 END 
...
END

To run a WAVEFUNCTION_INITIALIZER calculation the following directive is used:

TASK PSPW WAVEFUNCTION_INITIALIZER

Listed below is the format of a WAVEFUNCTION_INITIALIZER sub-block.

PSPW
... 
 WAVEFUNCTION_INITIALIZER 
   CELL_NAME: <string cell_name> 
   WAVEFUNCTION_FILENAME: <string wavefunction_name default input_movecs> 
   (RESTRICTED||UNRESTRICTED)
   if (RESTRICTED) 
     RESTRICTED_ELECTRONS: <integer restricted electrons> 
   if (UNRESTRICTED) 
     UP_ELECTRONS: <integer up_electrons> 
     DOWN_ELECTRONS: <integer down_electrons> 
 END
...
END

The following list describes the input for the WAVEFUNCTION_INITIALIZER sub-block.

  • <cell_name> - name of the simulation_cell named <cell_name>. See #Simulation Cell.
  • <wavefunction_name> - name that will point to a wavefunction file.
  • RESTRICTED - keyword specifying that the calculation is restricted.
  • UNRESTRICTED - keyword specifying that the calculation is unrestricted.
  • <restricted_electrons> - number of restricted electrons. Not used if an UNRESTRICTED calculation.
  • <up_electronsh> - number of spin-up electrons. Not used if a RESTRICTED calculation.
  • <down_electrons> - number of spin-down electrons. Not used if a RESTRICTED calculation.

Old Style Input (version 3.3) to WAVEFUNCTION_INITIALIZER

For backward compatibility, the input to the WAVEFUNCTION_INITIALIZER sub-block can also be of the form

PSPW
... 
 WAVEFUNCTION_INITIALIZER 
   CELL_NAME: <string cell_name> 
   WAVEFUNCTION_FILENAME: <string wavefunction_name default input_movecs> 
   (RESTRICTED||UNRESTRICTED)
   [UP_FILLING: <integer up_filling> [0 0 0 0] <integer kx ky kz> (-2||-1||1||2)] 
   [DOWN_FILLING: <integer down_filling> [0 0 0 0] <integer kx ky kz> (-2||-1||1||2)] 
 END
...
END

where

  • <cell_name> - name of the simulation_cell named <cell_name>. See #Simulation Cell.
  • <wavefunction_name> - name that will point to a wavefunction file.
  • RESTRICTED - keyword specifying that the calculation is restricted.
  • UNRESTRICTED - keyword specifying that the calculation is unrestricted.
  • <up_filling> - number of restricted molecular orbitals if RESTRICTED and number of spin-up molecular orbitals if UNRESTRICTED.
  • <down_filling> - number of spin-down molecular orbitals if UNRESTRICTED. Not used if a RESTRICTED calculation.
  • <kx ky kz> - specifies which planewave is to be filled.

The values for the planewave ( − 2 | | − 1 | | 1 | | 2) are used to represent whether the specified planewave is a cosine or a sine function, in addition random noise can be added to these base functions. That is + 1 represents a cosine function, and − 1 represents a sine function. The + 2 and − 2 values are used to represent a cosine function with random components added and a sine function with random components added respectively.

V_WAVEFUNCTION_INITIALIZER

The functionality of this task is now performed automatically. For backward compatibility, we provide a description of the input to this task.

The v_wavefunction_initializer task is used to generate an initial velocity wavefunction datafile. Input to the V_WAVEFUNCTION_INITIALIZER task is contained within the V_WAVEFUNCTION_INITIALIZER sub-block.

PSPW 
... 
 V_WAVEFUNCTION_INITIALIZER 
   ... 
 END 
...
END

To run a V_WAVEFUNCTION_INITIALIZER calculation the following directive is used:

TASK PSPW WAVEFUNCTION_INITIALIZER

Listed below is the format of a V_WAVEFUNCTION_INITIALIZER sub-block.

PSPW
... 
 V_WAVEFUNCTION_INITIALIZER 
   V_WAVEFUNCTION_FILENAME: <string v_wavefunction_name default input_vmovecs> 
   CELL_NAME: <string cell_name> 
   (RESTRICTED||UNRESTRICTED) 
   UP_FILLING: <integer up_filling> 
   DOWN_FILLING: <integer down_filling> 
 END
...
END

The following list describes the input for the V_WAVEFUNCTION_INITIALIZER sub-block.

  • <cell_name> - name of the simulation_cell named <cell_name>. See #Simulation Cell.
  • <wavefunction_name> - name that will point to a velocity wavefunction file.
  • RESTRICTED - keyword specifying that the calculation is restricted.
  • UNRESTRICTED - keyword specifying that the calculation is unrestricted.
  • <up_filling> - number of restricted velocity molecular orbitals if RESTRICTED and number of spin-up velocity molecular orbitals if
UNRESTRICTED.
  • <down_filling> - number of spin-down velocity molecular orbitals if UNRESTRICTED. Not used if a RESTRICTED calculation.

WAVEFUNCTION_EXPANDER

The functionality of this task is now performed automatically. For backward compatibility, we provide a description of the input to this task.

The wavefunction_expander task is used to convert a new wavefunction file that spans a larger grid space from an old wavefunction file. Input to the WAVEFUNCTION_EXPANDER task is contained within the WAVEFUNCTION_EXPANDER sub-block.

PSPW 
... 
 WAVEFUNCTION_EXPANDER 
   ... 
 END 
...
END

To run a WAVEFUNCTION_EXPANDER calculation the following directive is used:

TASK PSPW WAVEFUNCTION_EXPANDER

Listed below is the format of a WAVEFUNCTION_EXPANDER sub-block.

PSPW
... 
 WAVEFUNCTION_EXPANDER 
   OLD_WAVEFUNCTION_FILENAME: <string old_wavefunction_name default input_movecs> 
   NEW_WAVEFUNCTION_FILENAME: <string new_wavefunction_name default input_movecs> 
   NEW_NGRID: <integer na1 na2 na3>
 END
...
END

The following list describes the input for the WAVEFUNCTION_EXPANDER sub-block.

  • <old_wavefunction_name> - name of the wavefunction file.
  • <new_wavefunction_name> - name that will point to a wavefunction file.
  • <na1 na2 na3 - number of grid points in each dimension for the new wavefunction file.

STEEPEST_DESCENT

The functionality of this task is now performed automatically by the PSPW minimizer. For backward compatibility, we provide a description of the input to this task.

The steepest_descent task is used to optimize the one-electron orbitals with respect to the total energy. In addition it can also be used to optimize geometries. This method is meant to be used for coarse optimization of the one-electron orbitals.

Input to the steepest_descent simulation is contained within the steepest_descent sub-block.

PSPW 
... 
 STEEPEST_DESCENT 
   ... 
 END 
...
END

To run a steepest_descent calculation the following directive is used:

TASK PSPW steepest_descent 

The steepest_descent sub-block contains a great deal of input, including pointers to data, as well as parameter input. Listed below is the format of a STEEPEST_DESCENT sub-block.

PSPW
... 
 STEEPEST_DESCENT 
   CELL_NAME <string cell_name> 
   [GEOMETRY_OPTIMIZE] 
   INPUT_WAVEFUNCTION_FILENAME <string input_wavefunctions default input_movecs> 
   OUTPUT_WAVEFUNCTION_FILENAME <string output_wavefunctions default input_movecs> 
   FAKE_MASS <real fake_mass default 400000.0> 
   TIME_STEP <real time_step default 5.8> 
   LOOP <integer inner_iteration outer_iteration default 10 1> 
   TOLERANCES <real tole tolc tolr default 1.0d-9 1.0d-9 1.0d-4> 
   ENERGY_CUTOFF <real ecut default (see input desciption)> 
   WAVEFUNCTION_CUTOFF <real wcut default (see input description)> 
   EWALD_NCUT <integer ncut default 1> 
   EWALD_RCUT <real rcut default (see input description)> 
   XC (Vosko      || LDA          || PBE96         || revPBE       || HF            ||  
       LDA-SIC    || LDA-SIC/2    || LDA-0.4SIC    || LDA-SIC/4    || LDA-0.2SIC    || 
       PBE96-SIC  || PBE96-SIC/2  || PBE96-0.4SIC  || PBE96-SIC/4  || PBE96-0.2SIC  || 
       revPBE-SIC || revPBE-SIC/2 || revPBE-0.4SIC || revPBE-SIC/4 || revPBE-0.2SIC || 
       PBE0       || revPBE0      || default Vosko) 
   [MULLIKEN]
 END
...
END

The following list describes the input for the STEEPEST_DESCENT sub-block.

  • <cell_name> - name of the simulation_cell named <cell_name>. See #Simulation Cell.
  • GEOMETRY_OPTIMIZE - optional keyword which if specified turns on geometry optimization.
  • <input_wavefunctions> - name of the file containing one-electron orbitals
  • <output_wavefunctions> - name of the file tha will contain the one-electron orbitals at the end of the run.
  • <fake_mass> - value for the electronic fake mass (μ).
  • <time_step> - value for the time step (Δt).
  • <inner_iteration> - number of iterations between the printing out of energies and tolerances
  • <outer_iteration> - number of outer iterations
  • <tole> - value for the energy tolerance.
  • <tolc> - value for the one-electron orbital tolerance.
  • <tolr> - value for the ion position tolerance.
  • <ecut> - value for the cutoff energy used to define the density. Default is set to be the maximum value that will fit within the simulation_cell <cell_name>.
  • <wcut> - value for the cutoff energy used to define the one-electron orbitals. Default is set to be the maximum value that will fit within the simulation_cell <cell_name>.
  • <ncut> - value for the number of unit cells to sum over (in each direction) for the real space part of the Ewald summation. Note Ewald summation is only used if the simulation_cell is periodic.
  • <rcut> - value for the cutoff radius used in the Ewald summation. Note Ewald summation is only used if the simulation_cell is periodic.
 Default set to be \frac{MIN(\left| \vec{a_i} \right|)}{\pi}, i=1,2,3.
  • (Vosko || PBE96 || revPBE || ...) - Choose between Vosko et al's LDA parameterization or the orginal and revised Perdew, Burke, and Ernzerhof GGA functional. In addition, several hybrid options.
  • MULLIKEN - optional keyword which if specified causes a Mulliken analysis to be performed at the end of the simulation.

Band Tasks

All input to the Band Tasks is contained within the compound NWPW block,

NWPW 
 ...
END

To perform an actual calculation a TASK Band directive is used (Section #TASK).

TASK Band

Once a user has specified a geometry, the Band module can be invoked with no input directives (defaults invoked throughout). There are sub-directives which allow for customized application; those currently provided as options for the Band module are:

NWPW 
 CELL_NAME <string cell_name default 'cell_default'> 
 ZONE_NAME <string zone_name default 'zone_default'> 
 INPUT_WAVEFUNCTION_FILENAME <string input_wavefunctions default input_movecs> 
 OUTPUT_WAVEFUNCTION_FILENAME <string output_wavefunctions default input_movecs> 
 FAKE_MASS <real fake_mass default 400000.0> 
 TIME_STEP <real time_step default 5.8> 
 LOOP <integer inner_iteration outer_iteration default 10 100> 
 TOLERANCES <real tole tolc default 1.0e-7 1.0e-7> 
 CUTOFF <real cutoff> 
 ENERGY_CUTOFF <real ecut default (see input description)> 
 WAVEFUNCTION_CUTOFF <real wcut default (see input description)> 
 EWALD_NCUT <integer ncut default 1>] 
 EWALD_RCUT <real rcut default (see input description)> 
 XC (Vosko || PBE96 || revPBE default Vosko) 
 DFT||ODFT||RESTRICTED||UNRESTRICTED 
 MULT <integer mult default 1> 
 CG 
 LMBFGS 
 SCF [Anderson|| simple || Broyden] 
 [CG || RMM-DIIS] [density || potential] 
 [ALPHA real alpha default 0.25] 
 [ITERATIONS integer inner_iterations default 5] 
 [OUTER_ITERATIONS integer outer_iterations default 0]
 SIMULATION_CELL 
   ... (see input description) 
 END 
 BRILLOUIN_ZONE 
   ... (see input description) 
 END 
 MONKHORST-PACK <real n1 n2 n3 default 1 1 1>
 BAND_DPLOT 
   ... (see input description) 
 END
 MAPPING <integer mapping default 1> 
 SMEAR <sigma default 0.001> 
 [TEMPERATURE <temperature>] 
 [FERMI || GAUSSIAN default FERMI] 
 [ORBITALS <integer orbitals default 4>]
END 

The following list describes these keywords.

  • <cell_name> - name of the simulation_cell named <cell_name>. See #Simulation Cell.
  • <input_wavefunctions> - name of the file containing one-electron orbitals
  • <output_wavefunctions> - name that will point to file containing the one-electron orbitals at the end of the run.
  • <fake_mass> - value for the electronic fake mass (μ). This parameter is not presently used in a conjugate gradient simulation
  • <time_step> - value for the time step (Δt). This parameter is not presently used in a conjugate gradient simulation.
  • <inner_iteration> - number of iterations between the printing out of energies and tolerances
  • <outer_iteration> - number of outer iterations
  • <tole> - value for the energy tolerance.
  • <tolc> - value for the one-electron orbital tolerance.
  • <cutoff> - value for the cutoff energy used to define the wavefunction. In addition using the CUTOFF keyword automatically sets the cutoff energy for the density to be twice the wavefunction cutoff.
  • <ecut> - value for the cutoff energy used to define the density. Default is set to be the maximum value that will fit within the simulation_cell <cell_name>.
  • <wcut> - value for the cutoff energy used to define the one-electron orbitals. Default is set to be the maximum value that will fix within the simulation_cell <cell_name>.
  • <ncut> - value for the number of unit cells to sum over (in each direction) for the real space part of the Ewald summation. Note Ewald summation is only used if the simulation_cell is periodic.
  • <rcut> - value for the cutoff radius used in the Ewald summation. Note Ewald summation is only used if the simulation_cell is periodic.
 Default set to be \frac{MIN(\left| \vec{a_i} \right|)}{\pi}, i=1,2,3.
  • (Vosko || PBE96 || revPBE) - Choose between Vosko et al's LDA parameterization or the orginal and revised Perdew, Burke, and Ernzerhof GGA functional.
  • SIMULATION_CELL (see section -sec:pspw_cell-)
  • BRILLOUIN_ZONE (see section -sec:band_brillouin_zone-)
  • MONKHORST-PACK - Alternatively, the MONKHORST-PACK keyword can be used to enter a MONKHORST-PACK sampling of the Brillouin zone.
  • <smear> - value for smearing broadending
  • <temperature> - same as smear but in units of K.
  • CG - optional keyword which sets the minimizer to 1
  • LMBFGS - optional keyword which sets the minimizer to 2
  • SCF - optional keyword which sets the minimizer to be a band by band minimizer. Several options are available for setting the density or potential mixing, and the type of Kohn-Sham minimizer.

Brillouin Zone

To supply the special points of the Brillouin zone, the user defines a brillouin_zone sub-block within the NWPW block. Listed below is the format of a brillouin_zone sub-block.

NWPW
... 
 BRILLOUIN_ZONE 
   ZONE_NAME <string name default 'zone_default'> 
   (KVECTOR <real k1 k2 k3 no default> <real weight default (see input description)> 
    ...) 
 END
...
END

The user enters the special points and weights of the Brillouin zone. The following list describes the input in detail.

  • <name> - user-supplied name for the simulation block.
  • <k1 k2 k3> - user-supplied values for a special point in the Brillouin zone.
  • <weight<> - user-supplied weight. Default is to set the weight so that the sum of all the weights for the entered special points adds up to unity.

BAND_DPLOT

The BAND BAND_DPLOT task is used to generate plots of various types of electron densities (or orbitals) of a crystal. The electron density is calculated on the specified set of grid points from a Band calculation. The output file generated is in the Gaussian Cube format. Input to the BAND_DPLOT task is contained within the BAND_DPLOT sub-block.

NWPW 
... 
 BAND_DPLOT 
   ... 
 END 
...
END

To run a BAND_DPLOT calculation the following directive is used:

TASK BAND BAND_DPLOT

Listed below is the format of a BAND_DPLOT sub-block.

NWPW
... 
 BAND_DPLOT 
   VECTORS <string input_wavefunctions default input_movecs> 
   DENSITY [total||difference||alpha||beta||laplacian||potential default total] <string density_name no default> 
   ELF [restricted|alpha|beta] <string elf_name no default> 
   ORBITAL (density || real || complex default density) <integer orbital_number no default> <integer brillion_number default 1> <string orbital_name no default>
   [LIMITXYZ [units <string Units default angstroms>] 
   <real X_From> <real X_To> <integer No_Of_Spacings_X> 
   <real Y_From> <real Y_To> <integer No_Of_Spacings_Y>
   <real Z_From> <real Z_To> <integer No_Of_Spacings_Z>]
 END
...
END

The following list describes the input for the BAND_DPLOT sub-block.

VECTORS <string input_wavefunctions default input_movecs>

This sub-directive specifies the name of the molecular orbital file. If the second file is optionally given the density is computed as the difference between the corresponding electron densities. The vector files have to match.

DENSITY [total||difference||alpha||beta||laplacian||potential default total] <string density_name no default>

This sub-directive specifies, what kind of density is to be plotted. The known names for total, difference, alpha, beta, laplacian, and potential.

ELF [restricted|alpha|beta] <string elf_name no default>

This sub-directive specifies that an electron localization function (ELF) is to be plotted.

ORBITAL (density || real || complex default density) <integer orbital_number no default>  <integer brillion_number default 1> <string orbital_name no default>

This sub-directive specifies the molecular orbital number that is to be plotted.

LIMITXYZ [units <string Units default angstroms>] 
<real X_From> <real X_To> <integer No_Of_Spacings_X> 
<real Y_From> <real Y_To> <integer No_Of_Spacings_Y>
<real Z_From> <real Z_To> <integer No_Of_Spacings_Z>

By default the grid spacing and the limits of the cell to be plotted are defined by the input wavefunctions. Alternatively the user can use the LIMITXYZ sub-directive to specify other limits. The grid is generated using No_Of_Spacings + 1 points along each direction. The known names for Units are angstroms, au and bohr.

SMEAR - Fractional Occupation of the Molecular Orbitals

The smear keyword to turn on fractional occupation of the molecular orbitals

SMEAR <sigma default 0.001> [TEMPERATURE <temperature>] [FERMI || GAUSSIAN default FERMI] 
                            [ORBITALS <integer orbitals default 4>]

Both Fermi-Dirac (FERMI) and Gaussian broadening functions are available. The ORBITALS keyword is used to change the number of virtual orbitals to be used in the calculation. Note to use this option the user must currently use the SCF minimizer. The following SCF option is recommended for running fractional occupation

SCF Anderson

PAW Tasks

All input to the PAW Tasks is contained within the compound NWPW block,

NWPW 
 ...
END

To perform an actual calculation a TASK PAW directive is used (#TASK).

TASK PAW

In addition to the directives listed in #TASK, i.e.

TASK paw energy 
TASK paw gradient 
TASK paw optimize 
TASK paw saddle 
TASK paw freqencies 
TASK paw vib

there are additional directives that are specific to the PSPW module, which are:

TASK PAW [Car-Parrinello || steepest_descent ]

Once a user has specified a geometry, the PAW module can be invoked with no input directives (defaults invoked throughout). There are sub-directives which allow for customized application; those currently provided as options for the PAW module are:

NWPW 
 CELL_NAME <string cell_name default 'cell_default'> 
 [GEOMETRY_OPTIMIZE] 
 INPUT_WAVEFUNCTION_FILENAME <string input_wavefunctions default input_movecs> 
 OUTPUT_WAVEFUNCTION_FILENAME <string output_wavefunctions default input_movecs> 
 FAKE_MASS <real fake_mass default 400000.0> 
 TIME_STEP <real time_step default 5.8> 
 LOOP <integer inner_iteration outer_iteration default 10 100> 
 TOLERANCES <real tole tolc default 1.0e-7 1.0e-7> 
 CUTOFF <real cutoff> 
 ENERGY_CUTOFF <real ecut default (see input description)> 
 WAVEFUNCTION_CUTOFF <real wcut default (see input description)> 
 EWALD_NCUT <integer ncut default 1>] 
 EWALD_RCUT <real rcut default (see input description)> 
 XC (Vosko || PBE96 || revPBE default Vosko) 
 DFT||ODFT||RESTRICTED||UNRESTRICTED 
 MULT <integer mult default 1> 
 INTEGRATE_MULT_L <integer imult default 1>
 SIMULATION_CELL 
   ... (see input description) 
 END 
 CAR-PARRINELLO 
   ... (see input description) 
 END
 MAPPING <integer mapping default 1>
END 

The following list describes these keywords.

  • <cell_name> - name of the the simulation_cell named <cell_name>. The current version of PAW only accepts periodic unit cells. See #Simulation Cell.
  • GEOMETRY_OPTIMIZE - optional keyword which if specified turns on geometry optimization.
  • <input_wavefunctions> - name of the file containing one-electron orbitals
  • <output_wavefunctions> - name of the file that will contain the one-electron orbitals at the end of the run.
  • <fake_mass> - value for the electronic fake mass (μ). This parameter is not presently used in a conjugate gradient simulation
  • <time_step> - value for the time step (Δt). This parameter is not presently used in a conjugate gradient simulation.
  • <inner_iteration> - number of iterations between the printing out of energies and tolerances
  • <outer_iteration> - number of outer iterations
  • <tole> - value for the energy tolerance.
  • <tolc> - value for the one-electron orbital tolerance.
  • <cutoff> - value for the cutoff energy used to define the wavefunction. In addition using the CUTOFF keyword automatically sets the cutoff energy for the density to be twice the wavefunction cutoff.
  • <ecut> - value for the cutoff energy used to define the density. Default is set to be the maximum value that will fit within the simulation_cell <cell_name>.
  • <wcut> - value for the cutoff energy used to define the one-electron orbitals. Default is set to be the maximum value that will fix within the simulation_cell <cell_name>.
  • <ncuth> - value for the number of unit cells to sum over (in each direction) for the real space part of the smooth compensation summation.
  • <rcut> - value for the cutoff radius used in the smooth compensation summation.
 Default set to be \frac{MIN(\left| \vec{a_i} \right|)}{\pi}, i=1,2,3.
  • (Vosko || PBE96 || revPBE) - Choose between Vosko et al's LDA parameterization or the orginal and revised Perdew, Burke, and Ernzerhof GGA functional.
  • MULT - optional keyword which if specified allows the user to define the spin multiplicity of the system
  • INTEGRATE_MULT_L - optional keyword which if specified allows the user to define the angular XC integration of the augmented region
  • SIMULATION_CELL (see #Simulation Cell)
  • CAR-PARRINELLO(see #Car-Parrinello)
  • <mapping> - for a value of 1 slab FFT is used, for a value of 2 a 2d-hilbert FFT is used.

Pseudopotential and PAW basis Libraries

A library of pseudopotentials used by PSPW and BAND is currently available in the directory $NWCHEM_TOP/src/nwpw/libraryp/pspw_default

The elements listed in the following table are present:

 H                                                  He
-------                              ------------------
 Li Be                               B  C  N  O  F  Ne
-------                             -------------------
 Na Mg                               Al Si P  S  Cl Ar
-------------------------------------------------------
 K  Ca Sc Ti V  Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr         
-------------------------------------------------------
 Rb Sr Y  Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I  Xe
-------------------------------------------------------
 Cs Ba La Hf Ta W  Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn
-------------------------------------------------------
 Fr Ra . 
-----------------
         ------------------------------------------
          .  .  .  .  .  .  Gd .  .  .  .  .  .  .                      
         ------------------------------------------
          .  .  U  .  Pu .  .  .  .  .  .  .  .  .      
         ------------------------------------------

The pseudopotential libraries are continually being tested and added. Also, the PSPW program can read in pseudopotentials in CPI and TETER format generated with pseudopotential generation programs such as the OPIUM package of Rappe et al. The user can request additional pseudopotentials from Eric J. Bylaska at (Eric.Bylaska@pnl.gov).

Similarly, a library of PAW basis used by PAW is currently available in the directory $NWCHEM_TOP/src/nwpw/libraryp/paw_default

 H                                                  He
-------                              -----------------
 Li Be                               B  C  N  O  F  Ne
-------                             ------------------
 Na Mg                               Al Si P  S  Cl Ar
------------------------------------------------------
 K  Ca Sc Ti V  Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr         
------------------------------------------------------
 .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .
------------------------------------------------------
 .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .
------------------------------------------------------
 .  .  . 
-----------------         
         ------------------------------------------
          .  .  .  .  .  .  .  .  .  .  .  .  .  .                      
         ------------------------------------------
          .  .  .  .  .  .  .  .  .  .  .  .  .  .      
         ------------------------------------------

Currently there are not very many elements available for PAW. However, the user can request additional basis sets from Eric J. Bylaska at (Eric.Bylaska@pnl.gov).

A preliminary implementation of the HGH pseudopotentials (Hartwigsen, Goedecker, and Hutter) has been implemented into the PSPW module. To access the pseudopotentials the pseudopotentials input block is used. For example, to redirect the code to use HGH pseudopotentials for carbon and hydrogen, the following input would be used.

nwpw 
... 
 pseudopotentials 
  C library HGH_LDA 
  H library HGH_LDA 
 end 
...
end

The implementation of HGH pseudopotentials is rather limited in this release. HGH pseudopotentials cannot be used to optimize unit cells, and they do not work with the MULLIKEN option. They also have not yet been implemented into the BAND structure code.

To read in pseudopotentials in CPI format the following input would be used.

nwpw 
... 
 pseudopotentials 
  C CPI c.cpi 
  H CPI h.cpi 
 end 
...
end

In order for the program to recognize the CPI format the CPI files, e.g. c.cpi have to be prepended with the "<CPI>" keyword.

To read in pseudopotentials in TETER format the following input would be used.

nwpw 
... 
 pseudopotentials 
  C TETER c.teter 
  H TETER h.teter 
 end 
...
end

In order for the program to recognize the TETER format the TETER files, e.g. c.teter have to be prepended with the "<TETER>" keyword.

If you wish to redirect the code to a different directory other than the default one, you need to set the environmental variable NWCHEM_NWPW_LIBRARY to the new location of the libraryps directory.

NWPW RTDB Entries and DataFiles

Input to the PSPW and Band modules are contained in both the RTDB and datafiles. The RTDB is used to store input that the user will need to directly specify. Input of this kind includes ion positions, ion velocities, and simulation cell parameters. The datafiles are used to store input, such the one-electron orbitals, one-electron orbital velocities, formatted pseudopotentials, and one-dimensional pseudopotentials, that the user will in most cases run a program to generate.

Ion Positions

The positions of the ions are stored in the default geometry structure in the RTDB and must be specified using the GEOMETRY directive.

Ion Velocities

The velocities of the ions are stored in the default geometry structure in the RTDB, and must be specified using the GEOMETRY directive.

Wavefunction Datafile

The one-electron orbitals are stored in a wavefunction datafile. This is a binary file and cannot be directly edited. This datafile is used by steepest_descent and Car-Parrinello tasks and can be generated using the wavefunction_initializer or wavefunction_expander tasks.

Velocity Wavefunction Datafile

The one-electron orbital velocities are stored in a velocity wavefunction datafile. This is a binary file and cannot be directly edited. This datafile is used by the Car-Parrinello task and can be generated using the v_wavefunction_initializer task.

Formatted Pseudopotential Datafile

The pseudopotentials in Kleinman-Bylander form expanded on a simulation cell (3d grid) are stored in a formatted pseudopotential datafile. This is a binary file and cannot be directly edited. This datafile is used by steepest_descent and Car-Parrinello tasks and can be generated using the pseudopotential_formatter task.

One-Dimensional Pseudopotential Datafile

The one-dimensional pseudopotentials are stored in a one-dimensional pseudopotential file. This is an ASCII file and can be directly edited with a text editor. However, the user will usually use the psp_generator task to generate this datafile.

The data stored in the one-dimensional pseudopotential file is

character*2 element :: element name 
integer charge :: valence charge of ion 
real mass :: mass of ion 
integer lmax :: maximum angular component 
real rcut(lmax) :: cutoff radii used to define pseudopotentials 
integer nr :: number of points in the radial grid 
real dr :: linear spacing of the radial grid  
real r(nr):: one-dimensional radial grid 
real Vpsp(nr,lmax) :: one-dimensional pseudopotentials 
real psi(nr,lmax) :: one-dimensional pseudowavefunctions 
real r_semicore :: semicore radius 
real rho_semicore(nr) :: semicore density

and the format of it is:

[line 1: ] element [line 2: ] charge mass lmax
[line 3: ] (rcut(l), l=1,lmax)
[line 4: ] nr dr
[line 5: ] r(1) (Vpsp(1,l), l=1,lmax)
[line 6: ] ....
[line nr+4: ] r(nr) (Vpsp(nr,l), l=1,lmax)
[line nr+5: ] r(1) (psi(1,l), l=1,lmax) [line nr+6: ] ....
[line 2*nr+4:] r(nr) (psi(nr,l), l=1,lmax)
[line 2*nr+5:] r_semicore
if (r_semicore read) then
 [line 2*nr+6:] r(1) rho_semicore(1)
 [line 2*nr+7:] ....
 [line 3*nr+5:] r(nr) rho_semicore(nr)
end if

PSPW Car-Parrinello Output Datafiles

XYZ motion file

Data file that stores ion positions and velocities as a function of time in XYZ format.

[line 1: ] n_ion
[line 2: ] do ii=1,n_ion
[line 2+ii: ] atom_name(ii), x(ii),y(ii),z(ii),vx(ii),vy(ii),vz(ii)
end do
[line n_ion+3 ] n_nion
do ii=1,n_ion [line n_ion+3+ii: ] atom_name(ii), x(ii),y(ii),z(ii), vx(ii),vy(ii),vz(ii) end do [line 2*n_ion+4: ] ....

ION_MOTION motion file

Datafile that stores ion positions and velocities as a function of time

[line 1: ] it_out, n_ion, omega
[line 2: ] time
do ii=1,n_ion
[line 2+ii: ] x(ii),y(ii),z(ii), vx(ii),vy(ii),vz(ii)
end do
[line n_ion+3 ] time
do do ii=1,n_ion
[line n_ion+3+ii: ] x(ii),y(ii),z(ii), vx(ii),vy(ii),vz(ii)
end do
[line 2*n_ion+4: ] ....

EMOTION motion file

Datafile that store energies as a function of time.

[line 1: ] time, E1,E2,E3,E4,E5,E6,E7,E8, (E9,E10, if Nose-Hoover)
[line 2: ] ...

HMOTION motion file

Datafile that stores the rotation matrix as a function of time.

[line 1: ] time
[line 2: ] ms,ne(ms),ne(ms)
do i=1,ne(ms)
[line 2+i: ] (hml(i,j), j=1,ne(ms)
end do
[line 3+ne(ms): ] time
[line 4+ne(ms): ] ....

EIGMOTION motion file

Datafile that stores the eigenvalues for the one-electron orbitals as a function of time.

[line 1: ] time, (eig(i), i=1,number_orbitals)
[line 2: ] ...

OMOTION motion file

Datafile that stores a reduced representation of the one-electron orbitals. To be used with a molecular orbital viewer that will be ported to NWChem in the near future.

Car-Parrinello Scheme for Ab Initio Molecular Dynamics

Car and Parrinello developed a unified scheme for doing ab initio molecular dynamics by combining the motion of the ion cores and a fictitious motion for the Kohn-Sham orbitals of density-functional theory (R. Car and M. Parrinello, Phys. Rev. Lett. 55, 2471, (1985)). At the heart of this method they introduced a fictitious kinetic energy functional for the Kohn-Sham orbitals.

\begin{align}KE \left ( \left \{ \psi_{i,\sigma}(\vec{r}) \right \} \right ) &=& \sum_{i,\sigma}^{occ} \int d\vec{r}\ \mu \left | \dot{\psi}_{i,\sigma}(\vec{r}) \right | ^2\end{align}

Given this kinetic energy the constrained equations of motion are found by taking the first variation of the auxiliary Lagrangian.

\begin{align}
L & = \sum_{i,\sigma}^{occ} \int d\vec{r}\ \mu \left | \dot{\psi}_{i,\sigma}(\vec{r}) \right | ^2
     + \frac{1}{2} \sum_{I} M_I \left | \dot{\vec{R}}_{I} \right | ^2
- E \left [ \left \{ \psi_{i,\sigma}(\vec{r}) \right \} , \left \{ \vec{R}_I \right \} \right ] \\
& + \sum_{ij,\sigma} \Lambda_{ij,\sigma} \left ( \int d\vec{r}\ \psi_{i,\sigma}^{*}(\vec{r}) \psi_{j,\sigma}(\vec{r}) - \delta_{ij\sigma} \right )
\end{align}

Which generates a dynamics for the wavefunctions \psi_{i,\sigma}(\vec{r}) and atoms positions \vec{R}_I through the constrained equations of motion:

\begin{matrix}\mu \ddot{\psi}_{i,\sigma}(\vec{r},t) = -\frac{\delta E}{\delta \psi_{i,\sigma }^{*} \left( \vec{r},t \right) } + \sum\limits_j \Lambda_{ij,\sigma} \psi_{j,\sigma} \left( \vec{r},t \right) \end{matrix}

\begin{matrix}M_I \ddot{\vec{R}}_I = -\frac{\partial E}{\partial \vec{R}_I} \end{matrix}

where μ is the fictitious mass for the electronic degrees of freedom and MI are the ionic masses. The adjustable parameter μ is used to describe the relative rate at which the wavefunctions change with time. Λij are the Lagrangian multipliers for the orthonormalization of the single-particle orbitals \psi_{i,\sigma}(\vec{r}). They are defined by the orthonormalization constraint conditions and can be rigorously found. However, the equations of motion for the Lagrange multipliers depend on the specific algorithm used to integrate the Eqns. above.

For this method to give ionic motions that are physically meaningful the kinetic energy of the Kohn-Sham orbitals must be relatively small when compared to the kinetic energy of the ions. There are two ways where this criterion can fail. First, the numerical integrations for the Car-Parrinello equations of motion can often lead to large relative values of the kinetic energy of the Kohn-Sham orbitals relative to the kinetic energy of the ions. This kind of failure is easily fixed by requiring a more accurate numerical integration, i.e. use a smaller time step for the numerical integration. Second, during the motion of the system a the ions can be in locations where there is an Kohn-Sham orbital level crossing, i.e. the density-functional energy can have two states that are nearly degenerate. This kind of failure often occurs in the study of chemical reactions. This kind of failure is not easily fixed and requires the use of a more sophisticated density-functional energy that accounts for low-lying excited electronic states.

Verlet Algorithm for Integration

Integrating the Eqns. above using the Verlet algorithm results in

\begin{matrix}\psi_{i,\sigma}^{t+ \Delta t} \leftarrow 2 \psi_{i,\sigma}^{t} - \psi_{i,\sigma}^{t-\Delta t} + \frac{(\Delta t)^2}{\mu} \left[ \frac{\delta E}{\delta \psi_{i,\sigma}^{*}} + \sum_{j} \psi_{j,\sigma} \Lambda_{ji,\sigma} \right]_{t} \end{matrix}

\begin{matrix}\vec{R}_I^{t+\Delta t} \leftarrow 2 \vec{R}_I^{t} - \vec{R}_I^{t-\Delta t} + \frac{(\Delta t)^2}{M_I} \frac{\partial E}{\partial \vec{R}_I}\end{matrix}

In this molecular dynamic procedure we have to know variational derivative \begin{align}\frac{\delta E}{\delta \psi_{i,\sigma}^{*}}\end{align} and the matrix Λij. The variational derivative \begin{align}\frac{\delta E}{\delta \psi_{i,\sigma}^{*}}\end{align} can be analytically found and is

\begin{align}\frac{\delta E}{\delta \psi_{i,\sigma}^{*}} & = -\frac{1}{2} \nabla^2 \psi_{i,\sigma}(\vec{r}) \\ 
& + \int d\vec{r^{\prime}} W_{ext}(\vec{r},\vec{r^{\prime}}) \psi_{i,\sigma}(\vec{r^{\prime}}) \\ 
& + \int d\vec{r^{\prime}} \frac{n(\vec{r^{\prime}})}{|\vec{r}-\vec{r^{\prime}}|} \psi_{i,\sigma}(\vec{r})\\ 
& + \mu_{xc}^{\sigma}(\vec{r}) \psi_{i,\sigma}(\vec{r}) \\ 
& \equiv \hat{H} \psi_{i,\sigma} 
\end{align}

To find the matrix Λij we impose the orthonormality constraint on \psi_{i,\sigma}^{t+\Delta t} to obtain a matrix Riccatti equation, and then Riccatti equation is solved by an iterative solution.

Constant Temperature Simulations: Nose-Hoover Thermostats

Nose-Hoover Thermostats for the electrons and ions can also be added to the Car-Parrinello simulation. In this type of simulation thermostats variables xe and xR are added to the simulation by adding the auxiliary energy functionals to the total energy.

\begin{align}ION\_THERMOSTAT(x_R) & = \frac{1}{2} Q_R \dot{x_R} + E_{R0}x_R \\ ELECTRON\_THERMOSTAT(x_e) & = \frac{1}{2} Q_e \dot{x_e} + E_{e0}x_e \end{align}

In these equations, the average kinetic energy for the ions is

\begin{matrix}E_{R0} = \frac{1}{2} f k_B T \end{matrix}

where f is the number of atomic degrees of freedom, kB is Boltzmann's constant, and T is the desired t emperature. Defining the average fictitious kinetic energy of the electrons is not as straightforward. Blöchl and Parrinello (P.E. Blöchl and M. Parrinello, Phys. Rev. B, 45, 9413, (1992)) have suggested the following formula for determining the average fictitious kinetic energy

\begin{matrix}E_{e0} = 4 k_B T \frac{\mu}{M} \sum_{i} <\psi_i|-\frac{1}{2} \nabla^2 |\psi_{i}> \end{matrix}

where μ is the fictitious electronic mass, M is average mass of one atom, and \begin{matrix}\sum_{i} <\psi_i|-\frac{1}{2} \nabla^2 |\psi_{i}> \end{matrix} is the kinetic energy of the electrons.

Blöchl and Parrinello suggested that the choice of mass parameters, Qe, and QR should be made such that the period of oscillating thermostats should be chosen larger than the typical time scale for the dynamical events of interest but shorter than the simulation time.

\begin{align}P_{ion} & = 2\pi \sqrt{\frac{Q_R}{4E_{R0}}}\\P_{electron} & = 2\pi \sqrt{\frac{Q_e}{4E_{e0}}}
\end{align}

where P{ion} and P{electron} are the periods of oscillation for the ionic and fictitious electronic thermostats.

In simulated annealing simulations the electronic and ionic Temperatures are scaled according to an exponential cooling schedule,

\begin{align}T_e(t) & = T_e^0 \exp^{-\frac{t}{\tau_e}}\\T_{ionic}(t) & = T_{ionic}^0 \exp^{-\frac{t}{\tau_{ionic}}}
\end{align}

where T_e^0 and T_{ionic}^0 are the initial temperatures, and τe and τionic are the cooling rates in atomic units.

PSPW Tutorial 1: Minimizing the geometry for a C2 molecule

In this section we show how use the PSPW module to optimize the geometry for a C2 molecule at the PBE96 levels.

In the following example we show the input needed to optimize the geometry for a C2 molecule at the LDA level. In this example, default pseudopotentials from the pseudopotential library are used for C, the boundary condition is free-space, the exchange correlation functional is PBE96, The boundary condition is free-space, and the simulation cell cell is aperiodic and cubic with a side length of 10.0 Angstroms and has 40 grid points in each direction (cutoff energy is 44 Ry).

start c2_pspw_pbe96
title "C2 restricted singlet dimer optimization - PBE96/44Ry"
geometry 
  C -0.62 0.0 0.0
  C 0.62 0.0 0.0
end
pspw 
  simulation_cell units angstroms 
    boundary_conditions aperiodic 
    SC 10.0 ngrid 40 40 40 
  end 
  xc pbe96
end
set nwpw:minimizer 2
task pspw optimize

PSPW Tutorial 2: Running a Car-Parrinello Simulation

In this section we show how use the PSPW module to perform a Car-Parrinello molecular dynamic simulation for a C2 molecule at the LDA level. Before running a PSPW Car-Parrinello simulation the system should be on the Born-Oppenheimer surface, i.e. the one-electron orbitals should be minimized with respect to the total energy (i.e. task pspw energy). The input needed is basically the same as for optimizing the geometry of a C2 molecule at the LDA level, except that and additional Car-Parrinello sub-block is added.

In the following example we show the input needed to run a Car-Parrinello simulation for a C2 molecule at the LDA level. In this example, default pseudopotentials from the pseudopotential library are used for C, the boundary condition is free-space, the exchange correlation functional is LDA, The boundary condition is free-space, and the simulation cell cell is aperiodic and cubic with a side length of 10.0 Angstroms and has 40 grid points in each direction (cutoff energy is 44 Ry). The time step and fake mass for the Car-Parrinello run are specified to be 5.0 au and 600.0 au, respectively.

start c2_pspw_lda_md
title "C2 restricted singlet dimer, LDA/44Ry - constant energy Car-Parrinello simulation"
geometry 
  C -0.62 0.0 0.0
  C 0.62 0.0 0.0
end
pspw 
  simulation_cell units angstroms 
    boundary_conditions aperiodic 
    lattice 
      lat_a 10.00d0 
      lat_b 10.00d0 
      lat_c 10.00d0 
    end 
    ngrid 40 40 40 
  end 
  Car-Parrinello 
    fake_mass 600.0 
    time_step 5.0 
    loop 10 10 
  end
end
set nwpw:minimizer 2
task pspw energy
task pspw Car-Parrinello

PSPW Tutorial 3: optimizing a unit cell and geometry for Silicon-Carbide

The following example demonstrates how to uses the PSPW module to optimize the unit cell and geometry for a silicon-carbide crystal.

title "SiC 8 atom cubic cell - geometry and unit cell optimization"
start SiC
#**** Enter the geometry using fractional coordinates ****
geometry units au center noautosym noautoz print 
  system crystal 
    lat_a 8.277d0 
    lat_b 8.277d0 
    lat_c 8.277d0 
    alpha 90.0d0 
    beta 90.0d0 
    gamma 90.0d0 
  end
  Si -0.50000d0 -0.50000d0 -0.50000d0
  Si 0.00000d0 0.00000d0 -0.50000d0
  Si 0.00000d0 -0.50000d0 0.00000d0
  Si -0.50000d0 0.00000d0 0.00000d0
  C -0.25000d0 -0.25000d0 -0.25000d0
  C 0.25000d0 0.25000d0 -0.25000d0
  C 0.25000d0 -0.25000d0 0.25000d0
  C -0.25000d0 0.25000d0 0.25000d0
end
#***** setup the nwpw gamma point code ****
nwpw 
  simulation_cell 
    ngrid 16 16 16 
  end 
  ewald_ncut 8
end
set nwpw:minimizer 2
set nwpw:psi_nolattice .true. # turns of unit cell checking for wavefunctions
driver 
  clear 
  maxiter 40
end
set includestress .true. # this option tells driver to optimize the unit cell
task pspw optimize

PSPW Tutorial 4: QM/MM simulation for CCl4 + 64H2O

In this section we show how use the PSPW module to perform a Car-Parrinello QM/MM simulation for a CCl4 molecule in a box of 64 H2O. Before running a PSPW Car-Parrinello simulation the system should be on the Born-Oppenheimer surface, i.e. the one-electron orbitals should be minimized with respect to the total energy (i.e. task pspw energy).

In the following example we show the input needed to run a Car-Parrinello QM/MM simulation for a CCl4 molecule in a box of 64 H2O. In this example, default pseudopotentials from the pseudopotential library are used for C, Cl, O^ and H^, exchange correlation functional is PBE96, The boundary condition is periodic, and with a side length of 23.577 Bohrs and has a cutoff energy is 50 Ry). The time step and fake mass for the Car-Parrinello run are specified to be 5.0 au and 600.0 au, respectively.

title "CCl4 + water64 QM/MM simulation- 195 atom cell"
memory 1500 mb
start CCl4-water64
#scratch_dir ./perm
#permanent_dir ./perm
geometry nocenter noautoz noautosym
 C 0.7804E-02 -0.2897E-02 0.1420E-02 -0.2910E-07 -0.1055E-07 -0.2001E-07
 Cl -0.8603E+00 0.1547E+01 0.2556E+00 -0.2910E-07 -0.1055E-07 -0.2001E-07
 Cl 0.8421E+00 -0.4774E+00 0.1518E+01 -0.2910E-07 -0.1055E-07 -0.2001E-07
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-0.2685E+01 -0.1490E+01 -0.1628E-03 0.1207E-03 -0.5201E-04 H^ -0.4735E+01 -0.2235E+01 -0.2365E+01 -0.7933E-03 0.5578E-04 0.5343E-04 H^ -0.5002E+01 -0.2175E+01 -0.7554E+00 -0.7371E-03 -0.5704E-03 0.7546E-04 O^ 0.3475E+01 -0.4761E+01 -0.1158E+01 0.4877E-04 0.1059E-04 -0.5547E-04 H^ 0.3973E+01 -0.5628E+01 -0.1186E+01 0.4343E-03 0.2527E-03 -0.6376E-03 H^ 0.2590E+01 -0.4871E+01 -0.1610E+01 0.9492E-04 -0.8052E-04 -0.1260E-03 O^ 0.3854E+01 -0.3250E+01 -0.4023E+01 0.1560E-03 -0.1082E-03 0.5321E-04 H^ 0.3588E+01 -0.3599E+01 -0.4922E+01 0.9956E-03 -0.1719E-03 -0.1793E-03 H^ 0.4732E+01 -0.2777E+01 -0.4097E+01 0.5500E-03 -0.7001E-03 0.9756E-03 O^ 0.5345E+01 -0.2101E+01 0.4132E+01 -0.2089E-03 -0.2574E-03 0.1618E-04 H^ 0.6127E+01 -0.2332E+01 0.4711E+01 -0.9618E-03 -0.1658E-03 0.1067E-02 H^ 0.4498E+01 -0.2226E+01 0.4648E+01 -0.8397E-03 0.5189E-03 -0.8292E-03 O^ 0.1412E+00 -0.6149E+01 0.3138E+01 0.2892E-03 0.5036E-03 0.3292E-04 H^ -0.7153E+00 -0.6083E+01 0.2626E+01 0.1289E-03 0.4802E-03 0.3119E-03 H^ -0.2587E-01 -0.6612E+01 0.4008E+01 0.3628E-03 0.1494E-02 0.5832E-03 O^ -0.3946E+00 -0.1042E+01 0.4471E+01 -0.1576E-04 -0.2368E-03 0.1489E-03 H^ 0.9542E-03 -0.3942E+00 0.3820E+01 -0.3498E-03 0.1869E-03 0.3694E-03 H^ -0.1312E+01 -0.1300E+01 0.4169E+01 0.4445E-03 -0.1244E-02 -0.3945E-03 O^ 0.5287E+01 -0.5793E+01 0.1490E+01 -0.7884E-04 -0.1027E-03 -0.2446E-03 H^ 0.5544E+01 -0.5748E+01 0.2455E+01 0.2712E-03 -0.1871E-03 -0.3382E-03 H^ 0.4354E+01 -0.5449E+01 0.1377E+01 0.1098E-03 0.5129E-03 0.2576E-04 O^ -0.1759E+01 0.2460E+01 0.3320E+01 -0.7676E-04 -0.2161E-03 -0.1200E-03 H^ -0.2739E+01 0.2657E+01 0.3343E+01 -0.8392E-04 -0.2861E-03 -0.1401E-03 H^ -0.1350E+01 0.2896E+01 0.2518E+01 0.1772E-03 0.9790E-03 0.6584E-03 O^ -0.3269E+01 0.3863E+01 -0.6091E+01 -0.1391E-03 0.5335E-04 0.6947E-04 H^ -0.3641E+01 0.4123E+01 -0.6982E+01 -0.1000E-02 0.3166E-03 0.5059E-03 H^ -0.2735E+01 0.4622E+01 -0.5719E+01 -0.3032E-03 0.1718E-03 0.6328E-04 O^ -0.1995E+01 -0.3980E+01 0.5500E+01 -0.2062E-03 0.5484E-04 -0.1547E-03 H^ -0.1956E+01 -0.3408E+01 0.6320E+01 0.2765E-03 -0.4418E-03 0.1804E-03 H^ -0.2256E+01 -0.3419E+01 0.4714E+01 -0.9111E-03 0.4974E-03 0.3954E-03 O^ 0.4884E+01 0.6075E+01 -0.3080E+01 0.7152E-05 0.2327E-03 -0.1652E-05 H^ 0.5552E+01 0.5525E+01 -0.2578E+01 -0.1376E-04 -0.1713E-03 -0.4170E-03 H^ 0.5056E+01 0.7045E+01 -0.2906E+01 0.7043E-03 0.1266E-03 -0.1535E-03 O^ 0.2615E+01 -0.1474E+01 0.4779E+01 0.2480E-03 0.2773E-03 0.6476E-04 H^ 0.3294E+01 -0.7726E+00 0.4997E+01 0.6977E-03 -0.5022E-03 0.1176E-02 H^ 0.2248E+01 -0.1858E+01 0.5626E+01 -0.5883E-03 -0.2609E-03 -0.5399E-03 O^ -0.3116E+01 -0.1271E+01 0.5862E+01 0.4484E-04 -0.4921E-03 -0.2958E-03 H^ -0.3824E+01 -0.1292E+01 0.6568E+01 0.4160E-03 -0.1014E-02 0.6119E-04 H^ -0.3115E+01 -0.3749E+00 0.5417E+01 0.2101E-03 0.3728E-04 0.7720E-03 O^ -0.3732E+01 0.4587E+00 -0.1024E+01 0.1530E-04 0.1409E-03 0.2144E-03 H^ -0.3291E+01 0.6710E+00 -0.1521E+00 0.4425E-03 0.2528E-04 0.2437E-04 H^ -0.3039E+01 0.3972E+00 -0.1742E+01 -0.2884E-03 -0.8982E-04 -0.6985E-04 O^ -0.6022E+01 -0.2054E+01 0.9880E+00 0.1148E-03 0.2240E-04 -0.6860E-04 H^ -0.5613E+01 -0.2820E+01 0.1483E+01 -0.8247E-03 -0.3674E-03 0.1037E-03 H^ -0.6561E+01 -0.1498E+01 0.1621E+01 -0.9049E-03 -0.3507E-03 -0.6107E-03 O^ 0.5388E+01 -0.6596E-01 0.2375E+01 0.1300E-03 0.7636E-04 0.9649E-04 H^ 0.4393E+01 0.2216E-01 0.2323E+01 0.8852E-05 -0.9209E-03 0.5667E-03 H^ 0.5638E+01 -0.5050E+00 0.3238E+01 0.9431E-03 -0.1611E-03 -0.2704E-03 O^ -0.3777E+00 -0.3378E+01 0.1384E+01 -0.1187E-03 0.6597E-04 -0.9305E-04 H^ 0.3137E+00 -0.3344E+01 0.2106E+01 0.6941E-04 -0.1725E-03 -0.2510E-03 H^ -0.2333E+00 -0.2620E+01 0.7483E+00 -0.1763E-03 0.1878E-03 0.5338E-04 O^ -0.5167E+01 0.9137E-01 0.4518E+01 -0.7764E-04 -0.2549E-04 0.4651E-03 H^ -0.4490E+01 0.2494E+00 0.3799E+01 -0.5003E-03 -0.3149E-03 0.3790E-05 H^ -0.5695E+01 0.9276E+00 0.4669E+01 -0.8687E-03 -0.3647E-03 -0.4836E-03 end #set up the QM/MM simulation and cell NWPW SIMULATION_CELL SC 23.577 END QMMM lj_ion_parameters C 3.41000000d0 0.10000000d0 lj_ion_parameters Cl 3.45000000d0 0.16d0 lj_ion_parameters O^ 3.16555789d0 0.15539425d0 # new input format fragment spc size 3 index_start 6:195:3 shake units angstroms 1 2 3 cyclic 1.0 1.632993125 1.0 end END END #***** Setup conjugate gradient code **** nwpw cutoff 25.0 xc pbe96 lmbfgs ewald_ncut 1 end set nwpw:lcao_skip .true. task pspw energy #***** Setup Car-Parrinello code **** nwpw car-parrinello Nose-Hoover 1200.0 300.0 1200.0 300.0 time_step 5.00 fake_mass 750.0 loop 10 2000 xyz_filename ccl4.00.xyz ion_motion_filename ccl4.00.ion_motion emotion_filename ccl4.00.emotion end end task pspw car-parrinello

Band Tutorial 1: Minimizing the energy of a silicon-carbide crystal by running a PSPW and Band simulation in tandem

The following input deck performs a PSPW energy calculation followed by a Band energy calculation at the Γ-point for a cubic (8-atom) silicon-carbide crystal. Since the geometry is entered using fractional coordinates the unit cell parameters do not have to be re-specified in the simulation_cell nwpw sub-block. In this example, default pseudopotential from the pseudopotential library are used for C and Si. The advantage of running these calculations in tandem is that the Band code uses the wavefunctions generated from the faster PSPW calculation for its initial guess. The PSPW energy is -38.353570, and the Band energy is -38.353570.

start SiC_band
title "SiC 8 atom cubic cell"
#**** geometry entered using fractional coordinates ****
geometry units au center noautosym noautoz print 
  system crystal 
    lat_a 8.277d0
    lat_b 8.277d0
    lat_c 8.277d0
    alpha 90.0d0
    beta  90.0d0
    gamma 90.0d0
  end
Si    -0.50000d0  -0.50000d0  -0.50000d0
Si     0.00000d0   0.00000d0  -0.50000d0
Si     0.00000d0  -0.50000d0   0.00000d0
Si    -0.50000d0   0.00000d0   0.00000d0
C     -0.25000d0  -0.25000d0  -0.25000d0
C      0.25000d0   0.25000d0  -0.25000d0
C      0.25000d0  -0.25000d0   0.25000d0
C     -0.25000d0   0.25000d0   0.25000d0
end
#***** setup the nwpw gamma point code ****
nwpw
   simulation_cell
     ngrid 16 16 16
   end
   brillouin_zone
     kvector  0.0 0.0 0.0
   end
   ewald_ncut 8
end
set nwpw:minimizer 2
set nwpw:psi_brillioun_check .false.
task pspw energy
task band energy

BAND Tutorial 2: optimizing a unit cell and geometry for Silicon-Carbide

The following example demonstrates how to uses the BAND module to optimize the unit cell and geometry for a silicon-carbide crystal.

title "SiC 8 atom cubic cell - geometry and unit cell optimization"
start SiC
#**** Enter the geometry using fractional coordinates ****
geometry units au center noautosym noautoz print
  system crystal
    lat_a 8.277d0
    lat_b 8.277d0
    lat_c 8.277d0
    alpha 90.0d0
    beta  90.0d0
    gamma 90.0d0
  end
Si    -0.50000d0  -0.50000d0  -0.50000d0
Si     0.00000d0   0.00000d0  -0.50000d0
Si     0.00000d0  -0.50000d0   0.00000d0
Si    -0.50000d0   0.00000d0   0.00000d0
C     -0.25000d0  -0.25000d0  -0.25000d0
C      0.25000d0   0.25000d0  -0.25000d0
C      0.25000d0  -0.25000d0   0.25000d0
C     -0.25000d0   0.25000d0   0.25000d0
end
#***** setup the nwpw gamma point code ****
nwpw
   simulation_cell
     ngrid 16 16 16
   end
   ewald_ncut 8
   monkhorst-pack 2 2 2 
   lmbfgs
end
driver
  clear
  maxiter 40
end
set includestress .true.          # this option tells driver to optimize the unit cell
#set nwpw:stress_numerical .true.  #option to use numerical stresses 
task band optimize

BAND Tutorial 3: optimizing a unit cell and geometry for Aluminum with fractional occupation

The following example demonstrates how to uses the BAND module to optimize the unit cell and geometry for a Aluminum.

title "Aluminum optimization with fractional occupation"
start aluminumfrac
memory 900 mb
geometry noautoz
   system crystal
     lat_a 3.0
     lat_b 3.0
     lat_c 3.0
     alpha 90.0
     beta  90.0
     gamma 90.0
   end
Al  0.0 0.0 0.0
Al  0.0 0.5 0.5
Al  0.5 0.5 0.0
Al  0.5 0.0 0.5
end
set nwpw:cif_filename aluminum
nwpw
   scf anderson
   mult 1
   smear  temperature 3500.0 fermi
   cutoff 15.0
   monkhorst-pack 3 3 3
   ewald_ncut 8
   mapping 2
end
set nwpw:lcao_skip .true.
set includestress .true.
#set nwpw:stress_numerical .true.
driver
   clear
end
task band optimize ignore

PAW Tutorial

The following input deck performs for a water molecule a PSPW energy calculation followed by a PAW energy calculation and a PAW geometry optimization calculation. The default unit cell parameters are used (SC=20.0, ngrid 32 32 32). In this simulation, the first PAW run optimizes the wavefunction and the second PAW run optimizes the wavefunction and geometry in tandem.

title "paw steepest descent test"
start paw_test
charge 0
geometry units au nocenter noautoz noautosym
O      0.00000    0.00000    0.01390
H     -1.49490    0.00000   -1.18710
H      1.49490    0.00000   -1.18710
end
nwpw
  time_step 15.8
  ewald_rcut 1.50
  tolerances 1.0d-8 1.0d-8
end
set nwpw:lcao_iterations 1
set nwpw:minimizer 2
task pspw energy
task paw energy
nwpw
  time_step 5.8
  geometry_optimize
  ewald_rcut 1.50
  tolerances 1.0d-7 1.0d-7 1.0d-4
end
task paw steepest_descent
task paw optimize

PAW Tutorial 2: optimizing a unit cell and geometry for Silicon-Carbide

The following example demonstrates how to uses the PAW module to optimize the unit cell and geometry for a silicon-carbide crystal.

title "SiC 8 atom cubic cell - geometry and unit cell optimization"
start SiC
#**** Enter the geometry using fractional coordinates ****
geometry units au center noautosym noautoz print
 system crystal
   lat_a 8.277d0
   lat_b 8.277d0
   lat_c 8.277d0
   alpha 90.0d0
   beta  90.0d0
   gamma 90.0d0
 end
Si    -0.50000d0  -0.50000d0  -0.50000d0
Si     0.00000d0   0.00000d0  -0.50000d0
Si     0.00000d0  -0.50000d0   0.00000d0
Si    -0.50000d0   0.00000d0   0.00000d0
C     -0.25000d0  -0.25000d0  -0.25000d0
C      0.25000d0   0.25000d0  -0.25000d0
C      0.25000d0  -0.25000d0   0.25000d0
C     -0.25000d0   0.25000d0   0.25000d0
end
#***** setup the nwpw gamma point code ****
nwpw
  simulation_cell
    ngrid 16 16 16
  end
  ewald_ncut 8
end
set nwpw:minimizer 2
set nwpw:psi_nolattice .true.  # turns of unit cell checking for wavefunctions
driver
  clear
  maxiter 40
end
set includestress .true.         # this option tells driver to optimize the unit cell
set nwpw:stress_numerical .true. #currently only numerical stresses implemented in paw
task paw optimize

PAW Tutorial 2: Running a Car-Parrinello Simulation

In this section we show how use the PAW module to perform a Car-Parrinello molecular dynamic simulation for a C2 molecule at the LDA level. Before running a PAW Car-Parrinello simulation the system should be on the Born-Oppenheimer surface, i.e. the one-electron orbitals should be minimized with respect to the total energy (i.e. task pspw energy). The input needed is basically the same as for optimizing the geometry of a C2 molecule at the LDA level,except that and additional Car-Parrinello sub-block is added.

In the following example we show the input needed to run a Car-Parrinello simulation for a C2 molecule at the LDA level. In this example, default pseudopotentials from the pseudopotential library are used for C, the boundary condition is free-space, the exchange correlation functional is LDA, The boundary condition is free-space, and the simulation cell cell is aperiodic and cubic with a side length of 10.0 Angstroms and has 40 grid points in each direction (cutoff energy is 44 Ry). The time step and fake mass for the Car-Parrinello run are specified to be 5.0 au and 600.0 au, respectively.

start c2_paw_lda_md
title "C2 restricted singlet dimer, LDA/44Ry - constant energy Car-Parrinello simulation"
geometry  
 C    -0.62 0.0 0.0
 C     0.62 0.0 0.0
end
pspw
  simulation_cell units angstroms
     boundary_conditions aperiodic
     lattice
       lat_a 10.00d0
       lat_b 10.00d0
       lat_c 10.00d0
     end
     ngrid 40 40 40
  end
  Car-Parrinello
    fake_mass 600.0
    time_step 5.0
    loop 10 10
  end
end
set nwpw:minimizer 2
task paw energy
task paw Car-Parrinello

NWPW Capabilities and Limitations

  • Hybrid Functionals (e.g. PBE0, LDA-SIC) only work in PSPW.
  • Car-Parrinello QM/MM simulation only work with PSPW.
  • Fractional occupations only work for BAND simulations.

Questions and Difficulties

Questions and encountered problems should be reported to nwchem-users@emsl.pnl.gov or to Eric J. Bylaska, Eric.Bylaska@pnl.gov