next up previous contents
Next: 12. Spin-Orbit DFT (SODFT) Up: user Previous: 10. Hartree-Fock or Self-consistent   Contents

Subsections

11. DFT for Molecules (DFT)

The NWChem density functional theory (DFT) module uses the Gaussian basis set approach to compute closed shell and open shell densities and Kohn-Sham orbitals in the:

The formal scaling of the DFT computation can be reduced by choosing to use auxiliary Gaussian basis sets to fit the charge density (CD) and/or fit the exchange-correlation (XC) potential.

DFT input is provided using the compound DFT directive 

  DFT
    ...
  END
The actual DFT calculation will be performed when the input module encounters the TASK directive (Section 5.10). 
  TASK DFT

Once a user has specified a geometry and a Kohn-Sham orbital basis set the DFT 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 DFT module are: 

  VECTORS [[input] (<string input_movecs default atomic>) || \
                   (project <string basisname> <string filename>)] \
           [swap [alpha||beta] <integer vec1 vec2> ...] \
           [output <string output_filename default input_movecs>] \
           [lock]


  XC [[acm] [b3lyp] [beckehandh] [pbe0]\
     [becke97]  [becke97-1] [becke98] [hcth] [h120] [h147]\
      [h402] [becke97gga1] \
      [HFexch <real prefactor default 1.0>] \
      [becke88 [nonlocal] <real prefactor default 1.0>] \
      [xperdew91 [nonlocal] <real prefactor default 1.0>] \
      [xpbe96 [nonlocal] <real prefactor default 1.0>] \
      [gill96 [nonlocal] <real prefactor default 1.0>] \
      [xhcth  <real prefactor default 1.0>] \
      [lyp <real prefactor default 1.0>] \
      [perdew81 <real prefactor default 1.0>] \
      [perdew86 [nonlocal] <real prefactor default 1.0>] \
      [perdew91 [nonlocal] <real prefactor default 1.0>] \
      [cpbe96 [nonlocal] <real prefactor default 1.0>] \
      [chcth  <real prefactor default 1.0>] \
      [pw91lda <real prefactor default 1.0>] \
      [slater <real prefactor default 1.0>] \
      [vwn_1 <real prefactor default 1.0>] \
      [vwn_2 <real prefactor default 1.0>] \
      [vwn_3 <real prefactor default 1.0>] \
      [vwn_4 <real prefactor default 1.0>] \
      [vwn_5 <real prefactor default 1.0>] \
      [vwn_1_rpa <real prefactor default 1.0>]]


  CONVERGENCE [[energy <real energy default 1e-7>] \
               [density <real density default 1e-5>] \
               [gradient <real gradient default 5e-4>] \
               [dampon <real dampon default 0.0>] \
               [dampoff <real dampoff default 0.0>] \
               [diison <real diison default 0.0>] \
               [diisoff <real diisoff default 0.0>] \
               [levlon <real levlon default 0.0>] \
               [levloff <real levloff default 0.0>] \
               [ncydp <integer ncydp default 2>] \
               [ncyds <integer ncyds default 30>] \
               [ncysh <integer ncysh default 30>] \
               [damp <integer ndamp default 70>] [nodamping] \
               [diis [nfock <integer nfock default 10>]] \
               [nodiis] [lshift <real lshift default 0.5>] \
               [nolevelshifting] \
               [hl_tol <real hl_tol default 0.1>]]


  GRID [(xcoarse||coarse||medium||fine||xfine) default medium] \
       [(gausleg||lebedev ) default lebedev ] \
       [(old||new) default new ] \
       [(becke||erf1||erf2||ssf) default erf1] \
       [(euler||mura||treutler||lindh) default mura] \
       [rm <real rm default 2.0>]
        

  TOLERANCES [[tight] [tol_rho <real tol_rho default 1e-10>] \
              [accCoul <integer accCoul default 10>] \
              [radius <real radius default 25.0>]]


  DECOMP
  DFT||ODFT
  DIRECT
  INCORE
  ITERATIONS <integer iterations default 30>
  MAX_OVL
  MULLIKEN
  MULT <integer mult default 1>
  NOIO
  PRINT||NOPRINT

The following sections describe these keywords and optional sub-directives that can be specified for a DFT calculation in NWChem.

11.1 Specification of Basis Sets for the DFT Module

The DFT module requires at a minimum the basis set for the Kohn-Sham molecular orbitals. This basis set must be in the default basis set named "ao basis", or it must be assigned to this default name using the SET directive (see Section 5.7).

In addition to the basis set for the Kohn-Sham orbitals, the charge density fitting basis set can also be specified in the input directives for the DFT module. This basis set is used for the evaluation of the Coulomb potential in the Dunlap scheme11.1. The charge density fitting basis set must have the name "cd basis". This can be the actual name of a basis set, or a basis set can be assigned this name using the SET directive, as described in Section 5.7. If this basis set is not defined by input, the $O(N^4)$y exact Coulomb contribution is computed.

The user also has the option of specifying a third basis set for the evaluation of the exchange-correlation potential. This basis set must have the name "xc basis". If this basis set is not specified by input, the exchange contribution (XC) is evaluated by numerical quadrature. In most applications, this approach is efficient enough, so the "xc basis" basis set is not generally required.

For the DFT module, the input options for defining the basis sets in a given calculation can be summarized as follows;

11.2 VECTORS and MAX_OVL -- KS-MO Vectors

The VECTORS directive is the same as that in the SCF module (Section 10.5). Currently, the LOCK keyword is not supported by the DFT module, however the directive 

  MAX_OVL
has the same effect.


11.3 XC and DECOMP -- Exchange-Correlation Potentials 

  XC [[acm] [b3lyp] [beckehandh] [pbe0]\
     [becke97]  [becke97-1] [becke98] [hcth] [h120] [h147] \
      [h402] [becke97gga1] \
      [HFexch <real prefactor default 1.0>] \
      [becke88 [nonlocal] <real prefactor default 1.0>] \
      [xperdew91 [nonlocal] <real prefactor default 1.0>] \
      [xpbe96 [nonlocal] <real prefactor default 1.0>] \
      [gill96 [nonlocal] <real prefactor default 1.0>] \
      [xhcth  <real prefactor default 1.0>] \
      [lyp <real prefactor default 1.0>] \
      [perdew81 <real prefactor default 1.0>] \
      [perdew86 [nonlocal] <real prefactor default 1.0>] \
      [perdew91 [nonlocal] <real prefactor default 1.0>] \
      [cpbe96 [nonlocal] <real prefactor default 1.0>] \
      [chcth  <real prefactor default 1.0>] \
      [pw91lda <real prefactor default 1.0>] \
      [slater <real prefactor default 1.0>] \
      [vwn_1 <real prefactor default 1.0>] \
      [vwn_2 <real prefactor default 1.0>] \
      [vwn_3 <real prefactor default 1.0>] \
      [vwn_4 <real prefactor default 1.0>] \
      [vwn_5 <real prefactor default 1.0>] \
      [vwn_1_rpa <real prefactor default 1.0>]]

The user has the option of specifying the exchange-correlation treatment in the DFT Module. The default exchange-correlation functional is defined as the local density approximation (LDA) for closed shell systems and its counterpart the local spin-density (LSD) approximation for open shell systems. Within this approximation the exchange functional is the Slater $\rho^{1/3}$ functional (from J.C. Slater, Quantum Theory of Molecules and Solids, Vol. 4: The Self-Consistent Field for Molecules and Solids (McGraw-Hill, New York, 1974)), and the correlation functional is the Vosko-Wilk-Nusair (VWN) functional (functional V) (S.J. Vosko, L. Wilk and M. Nusair, Can. J. Phys. 58, 1200 (1980)). The parameters used in this formula are obtained by fitting to the Ceperley and Alder11.2Quantum Monte-Carlo solution of the homogeneous electron gas.

These defaults can be invoked explicitly by specifying the following keywords within the DFT module input directive, 

  XC slater vwn_5

The DECOMP directive causes the components of the energy corresponding to each functional to be printed, rather than just the total exchange-correlation energy which is the default.

Many alternative exchange and correlation functionals are available to the user. The following sections describe these options.

11.3.1 Optional Exchange Functionals

There are six exchange functionals in addition to the default exchange functional. These are

Note that the user also has the ability to include only the local or nonlocal contributions of a given functional. In addition the user can specify a multiplicative prefactor (the variable <prefactor> in the input) for the local/nonlocal component or total. An example of this might be, 

   XC becke88 nonlocal 0.72
The user should be aware that the Becke88 local component is simply the Slater exchange and should be input as such.

Any combination of the supported exchange functional options can be used. For example the popular Gaussian B3 exchange could be specified as: 

   XC slater 0.8 becke88 nonlocal 0.72 HFexch 0.2

11.3.2 Optional Correlation Functionals

In addition to the default vwn_5 correlation functional, the user has 10 alternative correlation functionals to choose from: lyp, perdew81, perdew86, perdew91, pw91lda, vwn_1, vwn_2, vwn_3, vwn_4, and vwn_1_rpa.

As in the exchange functional input, individual local/nonlocal components as well as multiplicative prefactors can be invoked where appropriate. Each of the correlation functionals is listed below along with appropriate citation.

Any combination of the supported correlation functional options can be used. For example B3LYP could be specified as: 

XC vwn_1_rpa 0.19 lyp 0.81 HFexch 0.20  slater 0.80 becke88 nonlocal 0.72

11.3.3 Combined Exchange and Correlation Functionals

In addition to the options listed above for the exchange and correlation functionals, the user has the alternative of specifying combined exchange and correlation functionals. The available hybrid functionals consist of the Becke ``half and half'' (see A.D. Becke, J. Chem. Phys. 98, 1372 (1992)), the adiabatic connection method (see A.D. Becke, J. Chem. Phys. 98, 5648 (1993)), b3lyp (popularized by Gaussian9X), Becke 1997 (``Becke V'' paper: A.D.Becke, J. Chem. Phys., 107, 8554 (1997)

These options can be invoked by specifying any of the following input lines, 

   XC beckehandh
   XC acm
   XC b3lyp
   XC becke97
   Xc becke97-1
   xc becke98
   xc pbe0
   xc hcth
   xc h120
   xc h147
   xc h402
   xc becke97gga1

The keyword beckehandh specifies that the exchange-correlation energy will be computed as

\begin{eqnarray*} E_{XC} \ \approx \ \frac{1}{2} E^{\rm HF}_X + \frac{1}{2} E^{\rm Slater}_{X} + \frac{1}{2} E^{\rm PW91LDA}_{C} \end{eqnarray*}

We know this is NOT the correct Becke prescribed implementation which requires the XC potential in the energy expression. But this is what is currently implemented as an approximation to it.

The keyword acm specifies that the exchange-correlation energy is computed as

\begin{eqnarray*} E_{XC} \ &=& \ a_0 E^{\rm HF}_X + (1-a_0) E^{\rm Slater}_{X} +... ...\\ & &{\rm where } \\ a_0 &=& 0.20, \ a_X = 0.72, \ a_C = 0.81 \end{eqnarray*}

and $\Delta$ stands for a non-local component.

The keyword b3lyp specifies that the exchange-correlation energy is computed as

\begin{eqnarray*} E_{XC} \ &=& \ a_0 E^{\rm HF}_X + (1-a_0) E^{\rm Slater}_{X} +... ...\\ & &{\rm where } \\ a_0 &=& 0.20, \ a_X = 0.72, \ a_C = 0.81 \end{eqnarray*}

The keyword becke97-1 specifies the hybrid exchange-correlation energy derived by Handy et al by re-fitting the Becke 1997 functional (F.A.Hamprecht, A.J.Cohen, D.J.Tozer and N.C.Handy, J. Chem. Phys. 109, 6264 (1998))

The keyword hcth specifies the exchange-correlation energy functional derived by Hamprecht-Cohen-Tozer-Handy (this is not a hybrid functional) (F.A.Hamprecht, A.J.Cohen, D.J.Tozer and N.C.Handy, J. Chem. Phys. 109, 6264 (1998))

Table 11.1: Table of available Exchange (X) and Correlation (C) functionals

           
Keyword X C GCA Hybrid Ref.
           
slater $\star$       [1]
vwn_1   $\star$     [2]
vwn_2   $\star$     [2]
vwn_3   $\star$     [2]
vwn_4   $\star$     [2]
vwn_5   $\star$     [2]
vwn_1_rpa   $\star$     [2]
perdew81   $\star$     [3]
pw91lda   $\star$     [4]
becke88 $\star$   $\star$   [5]
xperdew91 $\star$   $\star$   [6]
xpbe96 $\star$   $\star$   [7]
gill96 $\star$   $\star$   [8]
perdew86   $\star$ $\star$   [9]
lyp   $\star$ $\star$   [10]
perdew91   $\star$ $\star$   [6]
cpbe96   $\star$ $\star$   [7]
hcth $\star$ $\star$ $\star$   [11]
h120 $\star$ $\star$ $\star$   [12]
h147 $\star$ $\star$ $\star$   [12]
h402 $\star$ $\star$ $\star$   [19]
beckehandh $\star$ $\star$   $\star$ [13]
b3lyp $\star$ $\star$ $\star$ $\star$ [14]
acm $\star$ $\star$ $\star$ $\star$ [14]
becke97 $\star$ $\star$ $\star$ $\star$ [15]
becke97-1 $\star$ $\star$ $\star$ $\star$ [15]
becke97gga1 $\star$ $\star$ $\star$ $\star$ [18]
becke98 $\star$ $\star$ $\star$ $\star$ [16]
pbe0 $\star$ $\star$ $\star$ $\star$ [17]























  1. C. Slater, Quantum Theory of Molecules and Solids, Vol. 4 (McGraw-Hill, New York, 1974)
  2. S.J. Vosko, L. Wilk and M. Nusair, Can. J. Phys. 58, 1200 (1980).
  3. J. P. Perdew and A. Zunger, Phys. Rev. B 23, 5048 (1981).
  4. J.P. Perdew and Y. Wang, Phys. Rev. B 45, 13244 (1992).
  5. A.D. Becke, J. Chem. Phys. 88, 3098 (1988).
  6. J.P. Perdew, J.A. Chevary, S.H. Vosko, K.A. Jackson, M.R. Pederson, D.J. Singh and C. Fiolhais, Phys. Rev. B 46, 6671 (1992).
  7. J.P. Perdew, K. Burke and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996); 78 , 1396 (1997).
  8. P.W.Gill , Mol. Phys. 89, 433 (1996).
  9. J. P. Perdew, Phys. Rev. B 33, 8822 (1986).
  10. C. Lee, W. Yang and R. G. Parr, Phys. Rev. B 37, 785 (1988).
  11. F.A.Hamprecht, A.J.Cohen, D.J.Tozer and N.C.
    Handy, J. Chem. Phys. 109, 6264 (1998).
  12. A.D.Boese, N.L.Doltsinis, N.C.Handy and M.Sprik. J. Chem. Phys. 112, 1670 (2000).
  13. A.D. Becke, J. Chem. Phys. 98, 1372 (1992).
  14. A.D. Becke, J. Chem. Phys. 98, 5648 (1993).
  15. A.D.Becke, J. Chem. Phys. 107, 8554 (1997).
  16. H.L.Schmider and A.D. Becke, J. Chem. Phys. 108, 9624 1998).
  17. C.Adamo and V.Barone, J. Chem. Phys. 110, 6158 (1998).
  18. A.J.Cohen and N.C. Handy, Chem. Phys. Lett. 316, 160 (2000).
  19. A.D.Boese, N.C.Handy J. Chem. Phys., submitted (2000).

11.4 ITERATIONS -- Number of SCF iterations 

  ITERATIONS <integer iterations default 30>

The default optimization in the DFT module is to iterate on the Kohn-Sham (SCF) equations for a specified number of iterations (default 30). The keyword that controls this optimization is ITERATIONS, and has the following general form, 

   iterations <integer iterations default 30>

The optimization procedure will stop when the specified number of iterations is reached or convergence is met.

11.5 CONVERGENCE -- SCF Convergence Control 

  CONVERGENCE [energy <real energy default 1e-6>] \
              [density <real density default 1e-5>] \
              [gradient <real gradient default 5e-4>] \
              [hl_tol <real hl_tol default 0.1>]
              [dampon <real dampon default 0.0>] \
              [dampoff <real dampoff default 0.0>] \
              [ncydp <integer ncydp default 2>] \
              [ncyds <integer ncyds default 30>] \
              [ncysh <integer ncysh default 30>] \
              [damp <integer ndamp default 70>] [nodamping] \
              [diison <real diison default 0.0>] \
              [diisoff <real diisoff default 0.0>] \
              [(diis [nfock <integer nfock default 10>]) || nodiis] \
              [levlon <real levlon default 0.0>] \
              [levloff <real levloff default 0.0>] \
              [(lshift <real lshift default 0.5>) || nolevelshifting] \

Convergence is satisfied by meeting any or all of three criteria;

The default optimization strategy is to immediately begin direct inversion of the iterative subspace11.3. Damping is also initiated (using 70% of the previous density) for the first 2 iteration. In addition, if the HOMO - LUMO gap is small and the Fock matrix somewhat diagonally dominant, then level-shifting is automatically initiated. There are a variety of ways to customize this procedure to whatever is desired.

An alternative optimization strategy is to specify, by using the change in total energy (from iterations when N and N-1), when to turn damping, level-shifting, and/or DIIS on/off. Start and stop keywords for each of these is available as, 

  CONVERGENCE  [dampon <real dampon default 0.0>] \
               [dampoff <real dampoff default 0.0>] \
               [diison <real diison default 0.0>] \
               [diisoff <real diisoff default 0.0>] \
               [levlon <real levlon default 0.0>] \
               [levloff <real levloff default 0.0>]

So, for example, damping, DIIS, and/or level-shifting can be turned on/off as desired.

Another strategy can be to simply specify how many iterations (cycles) you wish each type of procedure to be used. The necessary keywords to control the number of damping cycles (ncydp), the number of DIIS cycles (ncyds), and the number of level-shifting cycles (ncysh) are input as, 

  CONVERGENCE  [ncydp <integer ncydp default 2>] \
               [ncyds <integer ncyds default 30>] \
               [ncysh <integer ncysh default 0>]

The amount of damping, level-shifting, time at which level-shifting is automatically imposed, and Fock matrices used in the DIIS extrapolation can be modified by the following keywords 

  CONVERGENCE  [damp <integer ndamp default 70>] \
               [diis [nfock <integer nfock default 10>]] \
               [lshift <real lshift default 0.5>] \
               [hl_tol <real hl_tol default 0.1>]]

Damping is defined to be the percentage of the previous iterations density mixed with the current iterations density. So, for example 

  CONVERGENCE damp 70
would mix 30% of the current iteration density with 70% of the previous iteration density.

Level-Shifting11.4 is defined as the amount of shift applied to the diagonal elements of the unoccupied block of the Fock matrix. The shift is specified by the keyword lshift. For example the directive, 

  CONVERGENCE lshift 0.5
causes the diagonal elements of the Fock matrix corresponding to the virtual orbitals to be shifted by 0.5 au. By default, this level-shifting procedure is switched on whenever the HOMO-LUMO gap is small. Small is defined by default to be 0.05 au but can be modified by the directive hl_tol. An example of changing the HOMO-LUMO gap tolerance to 0.01 would be, 
  CONVERGENCE hl_tol 0.01

Direct inversion of the iterative subspace with extrapolation of up to 10 Fock matrices is a default optimization procedure. For large molecular systems the amount of available memory may preclude the ability to store this number of N**2 arrays in global memory. The user may then specify the number of Fock matrices to be used in the extrapolation (must be greater than three (3) to be effective). To set the number of Fock matrices stored and used in the extrapolation procedure to 3 would take the form, 

  CONVERGENCE diis 3

Finally, the user has the ability to simply turn off any optimization procedures deemed undesirable with the obvious keywords, 

  CONVERGENCE [nodamping] [nodiis] [nolevelshifting]


11.6 GRID -- Numerical Integration of the XC Potential 

  GRID [(xcoarse||coarse||medium||fine||xfine) default medium] \
       [(gausleg||lebedev ) default lebedev ] \
       [(old||new) default new ] \
       [(becke||erf1||erf2||ssf) default erf1] \
       [(euler||mura||treutler) default mura] \
       [rm <real rm default 2.0>]

A numerical integration is necessary for the evaluation of the exchange-correlation contribution to the density functional. The default quadrature used for the numerical integration is an Euler-MacLaurin scheme for the radial components (with a modified Mura-Knowles transformation) and a Lebedev scheme for the angular components. Within this numerical integration procedure various levels of accuracy have been defined and are available to the user. The user can specify the level of accuracy with the keywords; xcoarse, coarse, medium, fine, and xfine. The default is medium. 

  GRID [xcoarse||coarse||medium||fine||xfine]

Our intent is to have a numerical integration scheme which would give us approximately the accuracy defined below regardless of molecular composition.

Keyword Total Energy Target Accuracy
xcoarse $1x10^{-4}$
coarse $1x10^{-5}$
medium $1x10^{-6}$
fine $1x10^{-7}$
xfine $1x10^{-8}$

In order to determine the level of radial and angular quadrature needed to give us the target accuracy we computed total DFT energies at the LDA level of theory for many homonuclear atomic, diatomic and triatomic systems in rows 1-4 of the periodic table. In each case all bond lengths were set to twice the Bragg-Slater radius. The total DFT energy of the system was computed using the converged SCF density with atoms having radial shells ranging from 35-235 (at fixed 48/96 angular quadratures) and angular quadratures of 12/24-48/96 (at fixed 235 radial shells). The error of the numerical integration was determined by comparison to a ``best'' or most accurate calculation in which a grid of 235 radial points 48 theta and 96 phi angular points on each atom was used. This corresponds to approximately 1 million points per atom. The following tables were empirically determined to give the desired target accuracy for DFT total energies. These tables below show the number of radial and angular shells which the DFT module will use for for a given atom depending on the row it is in (in the periodic table) and the desired accuracy. Note, differing atom types in a given molecular system will most likely have differing associated numerical grids. The intent is to generate the desired energy accuracy (with utter disregard for speed).




Table 11.2: Program default number of radial and angular shells empirically determined for Row 1 atoms (Li $\rightarrow $ F) to reach the desired accuracies.
Keyword Radial Theta phi
xcoarse 30 12 24
coarse 50 15 30
medium 70 18 36
fine 100 24 48
xfine 140 34 68





Table 11.3: Program default number of radial and angular shells empirically determined for Row 2 atoms (Na $\rightarrow $ Cl) to reach the desired accuracies.
Keyword Radial Theta phi
xcoarse 45 12 24
coarse 75 18 36
medium 95 24 48
fine 125 30 60
xfine 175 44 88





Table 11.4: Program default number of radial and angular shells empirically determined for Row 3 atoms (K $\rightarrow $ Br) to reach the desired accuracies.
Keyword Radial Theta phi
xcoarse 75 14 28
coarse 95 22 44
medium 110 30 60
fine 160 34 68
xfine 210 38 76





Table 11.5: Program default number of radial and angular shells empirically determined for Row 4 atoms (Rb $\rightarrow $ I) to reach the desired accuracies.
Keyword Radial Theta phi
xcoarse 105 16 32
coarse 130 20 40
medium 155 32 64
fine 205 44 88
xfine 235 48 96


11.6.1 Angular grids

In addition to the simple keyword specifying the desired accuracy as described above, the user has the option of specifying a custom quadrature of this type in which ALL atoms have the same grid specification. This is accomplished by using the gausleg keyword.

11.6.1.0.1 Gauss-Legendre angular grid 

  GRID gausleg <integer nradpts default 50> <integer nagrid default 10>

In this type of grid, the number of phi points is twice the number of theta points. So, for example, a specification of, 

  GRID gausleg 80 20
would be interpreted as 80 radial points, 20 theta points, and 40 phi points per center (or 64000 points per center before pruning).

11.6.1.0.2 Lebedev angular grid

A second quadrature is the Lebedev scheme for the angular components11.5. Within this numerical integration procedure various levels of accuracy have also been defined and are available to the user. The input for this type of grid takes the form, 

  GRID lebedev <integer radpts > <integer iangquad >
In this context the variable iangquad specifies a certain number of angular points as indicated by the table below.11.6

Table 11.6: List of Lebedev quadratures
$IANGQUAD$ $N_{angular}$ $l$
1 38 9
2 50 11
3 74 13
4 86 15
5 110 17
6 146 19
7 170 21
8 194 23
9 230 25
10 266 27
11 302 29
12 350 31
13 434 35
14 590 41
15 770 47
16 974 53
17 1202 59
18 1454 65
19 1730 71
20 2030 77
21 2354 83
22 2702 89
23 3074 95
24 3470 101
25 3890 107
26 4334 113
27 4802 119
28 5294 125
29 5810 131


Therefore the user can specify any number of radial points along with the level of angular quadrature (1-29).

The user can also specify grid parameters specific for a given atom type: parameters that must be supplied are: atom tag, number of radial points, number of angular points and accQrad (all three parameters must be given). As an example, here is a grid input line for the water molecule 

grid lebedev 80 11 H 70 8 12 O 90 11 15

11.6.2 Partitioning functions 

  GRID [(becke||erf1||erf2||ssf) default erf1]

becke
A. D. Becke, J. Chem. Phys. 88, 1053 (1988).
ssf
R.E.Stratmann, G.Scuseria and M.J.Frisch, Chem. Phys. Lett. 257, 213 (1996).
erf1
modified ssf
erf2
modified ssf

Erf$n$ partionioning functions

\begin{eqnarray*} w_A(r) & = & \prod_{B\neq A}\frac{1}{2} \left[1 \ - \ erf(\mu... ...thbf r}_B} {\left\vert{\mathbf r}_A - {\mathbf r}_B \right\vert} \end{eqnarray*}

11.6.3 Radial grids 

  GRID [[euler||mura||treutler]  default mura]

euler
Euler-McLaurin quadrature wih the transformation devised by C.W. Murray, N.C. Handy, and G.L. Laming, Mol. Phys.78, 997 (1993).
mura
Modification of the Murray-Handy-Laming scheme by M.E.Mura and P.J.Knowles, J Chem Phys 104, 9848 (1996) (we are not using the scaling factors proposed in this paper).
treutler
Gauss-Chebyshev using the transformation suggested by O.Treutler and R.Alrhichs, J.Chem.Phys 102, 346 (1995).

11.6.4 Grid Scheme 

  GRID [[old||new]  default new]

In Nwchem 4.0 the XC integration code has been re-written using a space decomposiition scheme similar to the one proposed in R.E.Stratmann, G.Scuseria and M.J.Frisch, Chem. Phys. Lett. 257, 213 (1996) (keyword new).

To use the XC integration routines available in older version of NWChem, use the keyword old.

11.7 TOLERANCES -- Screening tolerances 

  TOLERANCES [[tight] [tol_rho <real tol_rho default 1e-10>] \
              [accCoul <integer accCoul default 10>] \
              [radius <real radius default 25.0>]]
The user has the option of controlling screening for the tolerances in the integral evaluations for the DFT module. In most applications, the default values will be adequate for the calculation, but different values can be specified in the input for the DFT module using the keywords described below.

The input parameter accCoul is used to define the tolerance in Schwarz screening for the Coulomb integrals. Only integrals with estimated values greater than $10^{(-{\tt accCoul})}$ are evaluated. 

  TOLERANCES accCoul <integer accCoul default 10>

Screening away needless computation of the XC functional (on the grid) due to negligible density is also possible with the use of, 

  TOLERANCES tol_rho <real tol_rho default 1e-10>
XC functional computation is bypassed if the corresponding density elements are less than tol_rho.

A screening parameter, radius, used in the screening of the Becke or Delley spatial weights is also available as, 

  TOLERANCES radius <real radius default 25.0>
where radius is the cutoff value in bohr.

The tolerances as discussed previously are insured at convergence. More sleazy tolerances are invoked early in the iterative process which can speed things up a bit. This can also be problematic at times because it introduces a discontinuity in the convergence process. To avoid use of initial sleazy tolerances the user can invoke the tight option: 

  TOLERANCES tight

This option sets all tolerances to their default/user specified values at the very first iteration.

11.8 DIRECT and NOIO -- Hardware Resource Control 

  DIRECT||INCORE
  NOIO

The inverted charge-density and exchange-correlation matrices for a DFT calculation are normally written to disk storage. The user can prevent this by specifying the keyword noio within the input for the DFT directive. The input to exercise this option is as follows, 

   noio
If this keyword is encountered, then the two matrices (inverted charge-density and exchange-correlation) are computed ``on-the-fly'' whenever needed.

The INCORE option is always assumed to be true but can be overridden with the option DIRECT in which case all integrals are computed ``on-the-fly''.

11.9 DFT, ODFT and MULT -- Open shell systems 

  DFT||ODFT
  MULT <integer mult default 1>

Both closed-shell and open-shell systems can be studied using the DFT module. Specifying the keyword MULT within the DFT directive allows the user to define the spin multiplicity of the system. The form of the input line is as follows; 

   MULT <integer mult default 1>
When the keyword MULT is specified, the user can define the integer variable mult, where mult is equal to the number of alpha electrons minus beta electrons, plus 1.

The keywords DFT||ODFT were originally intended to specify closed or open shell and are really unnecessary except in the context of forcing a closed-shell system to be computed as an open shell system (i.e., using a spin-unrestricted wavefunction).

11.10 SIC -- Self-Interaction Correction 

sic [perturbative || oep || oep-loc <default perturbative>]

The Perdew and Zunger (see J. P. Perdew and A. Zunger, Phys. Rev. B 23, 5048 (1981)) method to remove the self-interaction contained in many exchange-correlation functionals has been implemented with the Optimized Effective Potential method (see R. T. Sharp and G. K. Horton, Phys. Rev. 90, 317 (1953), J. D. Talman and W. F. Shadwick, Phys. Rev. A 14, 36 (1976)). Three variants of these methods are included in NWChem:

With oep and oep-loc options a xfine grid (see section 11.6) must be used in order to avoid numerical noise, furthermore the hybrid functionals can not be used with these options. More details of the implementation of this method can be found in J. Garza, J. A. Nichols and D. A. Dixon, J. Chem. Phys. 112, 7880 (2000). The components of the sic energy can be printed out using: 

print "SIC information"

11.11 MULLIKEN -- Mulliken analysis 

  MULLIKEN

Mulliken analysis of the charge distribution is invoked by the keyword: 

  MULLIKEN
When this keyword is encountered, Mulliken analysis of both the input density as well as the output density will occur.

11.12 Print Control 

  PRINT||NOPRINT

The PRINT||NOPRINT options control the level of output in the DFT. Known controllable print options are:


Table 11.7: DFT Print Control Specifications
Name Print Level Description
``semi-direct info'' default semi direct algorithm
``coulomb fit'' high fitting electronic charge density
``io info'' debug reading from and writing to disk
``information'' low general information
``quadrature'' high numerical quadrature
``parameters'' default input parameters
``convergence'' default convergence of SCF procedure
``intermediate vectors'' high intermediate molecular orbitals
``intermediate evals'' high intermediate orbital energies
``intermediate overlap'' high overlaps between the alpha and beta sets
``intermediate S2'' high values of S2
``interm vector symm'' high symmetries of intermediate orbitals
``dft timings'' high  
``initial vectors'' high  
``common'' debug dump of common blocks
``screening parameters'' high integral accuracies
``intermediate energy info'' high  
``intermediate fock matrix'' high  
``final vectors'' high  
``schwarz'' high integral screening info & stats at completion
``all vector symmetries'' high symmetries of all molecular orbitals
``final vector symmetries'' default symmetries of final molecular orbitals
``multipole'' default moments of alpha, beta, and nuclear charge densities


next up previous contents
Next: 12. Spin-Orbit DFT (SODFT) Up: user Previous: 10. Hartree-Fock or Self-consistent   Contents
Jorge Garza Olguin 2003-04-28