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<TITLE>11. DFT for Molecules (DFT)</TITLE>
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<B> Next:</B> <A NAME="tex2html1183"
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HREF="node12.html">10. Hartree-Fock or Self-consistent</A>
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<!--Table of Child-Links-->
<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></A>
<UL>
<LI><A NAME="tex2html1184"
HREF="node13.html#SECTION001310000000000000000">11.1 Specification of Basis Sets for the DFT Module</A>
<LI><A NAME="tex2html1185"
HREF="node13.html#SECTION001320000000000000000">11.2 <TT>VECTORS</TT> and <TT>MAX_OVL</TT> -- KS-MO Vectors</A>
<LI><A NAME="tex2html1186"
HREF="node13.html#SECTION001330000000000000000">11.3 <TT>XC</TT> and <TT>DECOMP</TT> -- Exchange-Correlation Potentials</A>
<UL>
<LI><A NAME="tex2html1187"
HREF="node13.html#SECTION001331000000000000000">11.3.1 Exchange-Correlation Functionals</A>
<LI><A NAME="tex2html1188"
HREF="node13.html#SECTION001332000000000000000">11.3.2 Combined Exchange and Correlation Functionals</A>
<LI><A NAME="tex2html1189"
HREF="node13.html#SECTION001333000000000000000">11.3.3 Meta-GGA Functionals</A>
</UL>
<BR>
<LI><A NAME="tex2html1190"
HREF="node13.html#SECTION001340000000000000000">11.4 <TT>LB94</TT> and <TT>CS00</TT> -- Asymptotic correction</A>
<LI><A NAME="tex2html1191"
HREF="node13.html#SECTION001350000000000000000">11.5 Sample input file</A>
<LI><A NAME="tex2html1192"
HREF="node13.html#SECTION001360000000000000000">11.6 <TT>ITERATIONS</TT> -- Number of SCF iterations</A>
<LI><A NAME="tex2html1193"
HREF="node13.html#SECTION001370000000000000000">11.7 <TT>CONVERGENCE</TT> -- SCF Convergence Control</A>
<LI><A NAME="tex2html1194"
HREF="node13.html#SECTION001380000000000000000">11.8 <TT>SMEAR</TT> -- Fractional Occupation of the Molecular Orbitals</A>
<LI><A NAME="tex2html1195"
HREF="node13.html#SECTION001390000000000000000">11.9 <TT>GRID</TT> -- Numerical Integration of the XC Potential</A>
<UL>
<LI><A NAME="tex2html1196"
HREF="node13.html#SECTION001391000000000000000">11.9.1 Angular grids</A>
<UL>
<LI><A NAME="tex2html1197"
HREF="node13.html#SECTION001391010000000000000">11.9.1.0.1 Gauss-Legendre angular grid</A>
<LI><A NAME="tex2html1198"
HREF="node13.html#SECTION001391020000000000000">11.9.1.0.2 Lebedev angular grid</A>
</UL>
<LI><A NAME="tex2html1199"
HREF="node13.html#SECTION001392000000000000000">11.9.2 Partitioning functions</A>
<LI><A NAME="tex2html1200"
HREF="node13.html#SECTION001393000000000000000">11.9.3 Radial grids</A>
<LI><A NAME="tex2html1201"
HREF="node13.html#SECTION001394000000000000000">11.9.4 Disk usage for Grid</A>
</UL>
<BR>
<LI><A NAME="tex2html1202"
HREF="node13.html#SECTION0013100000000000000000">11.10 <TT>TOLERANCES</TT> -- Screening tolerances</A>
<LI><A NAME="tex2html1203"
HREF="node13.html#SECTION0013110000000000000000">11.11 <TT>DIRECT</TT> and <TT>NOIO</TT> -- Hardware Resource Control</A>
<LI><A NAME="tex2html1204"
HREF="node13.html#SECTION0013120000000000000000">11.12 <TT>ODFT</TT> and <TT>MULT</TT> -- Open shell systems</A>
<LI><A NAME="tex2html1205"
HREF="node13.html#SECTION0013130000000000000000">11.13 <TT>SIC</TT> -- Self-Interaction Correction</A>
<LI><A NAME="tex2html1206"
HREF="node13.html#SECTION0013140000000000000000">11.14 <TT>MULLIKEN</TT> -- Mulliken analysis</A>
<LI><A NAME="tex2html1207"
HREF="node13.html#SECTION0013150000000000000000">11.15 <TT>BSSE</TT> -- Basis Set Superposition Error</A>
<LI><A NAME="tex2html1208"
HREF="node13.html#SECTION0013160000000000000000">11.16 Print Control</A>
</UL>
<!--End of Table of Child-Links-->
<HR>
<H1><A NAME="SECTION001300000000000000000">
11. DFT for Molecules (DFT)</A>
</H1>
<A NAME="sec:dft"></A>
<P>
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:
<UL>
<LI>local density approximation (LDA),
</LI>
<LI>non-local density approximation (NLDA),
</LI>
<LI>local spin-density approximation (LSD),
</LI>
<LI>non-local spin-density approximation (NLSD),
</LI>
<LI>any empirical mixture of local and non-local approximations
(including exact exchange), and
</LI>
<LI>asymptotically corrected exchange-correlation potentials.
</LI>
</UL>
<P>
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.
<P>
DFT input is provided using the compound <code>DFT</code> directive
<PRE>
DFT
...
END
</PRE>
The actual DFT calculation will be performed when the input module
encounters the <code>TASK</code> directive (Section <A HREF="node7.html#sec:task">5.10</A>).
<PRE>
TASK DFT
</PRE>
<P>
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:
<PRE>
VECTORS [[input] (&lt;string input_movecs default atomic&gt;) || \
(project &lt;string basisname&gt; &lt;string filename&gt;)] \
[swap [alpha||beta] &lt;integer vec1 vec2&gt; ...] \
[output &lt;string output_filename default input_movecs&gt;] \
XC [[acm] [b3lyp] [beckehandh] [pbe0]\
[becke97] [becke97-1] [becke97-2] [becke98] [hcth] [hcth120] [hcth147]\
[hcth407] [becke97gga1] [hcth407p]\
[mpw91] [mpw1k] [xft97] [cft97] [ft97] [xpkzb99] [cpkzb99]\
[HFexch &lt;real prefactor default 1.0&gt;] \
[becke88 [nonlocal] &lt;real prefactor default 1.0&gt;] \
[xperdew91 [nonlocal] &lt;real prefactor default 1.0&gt;] \
[xpbe96 [nonlocal] &lt;real prefactor default 1.0&gt;] \
[gill96 [nonlocal] &lt;real prefactor default 1.0&gt;] \
[lyp &lt;real prefactor default 1.0&gt;] \
[perdew81 &lt;real prefactor default 1.0&gt;] \
[perdew86 [nonlocal] &lt;real prefactor default 1.0&gt;] \
[perdew91 [nonlocal] &lt;real prefactor default 1.0&gt;] \
[cpbe96 [nonlocal] &lt;real prefactor default 1.0&gt;] \
[pw91lda &lt;real prefactor default 1.0&gt;] \
[slater &lt;real prefactor default 1.0&gt;] \
[vwn_1 &lt;real prefactor default 1.0&gt;] \
[vwn_2 &lt;real prefactor default 1.0&gt;] \
[vwn_3 &lt;real prefactor default 1.0&gt;] \
[vwn_4 &lt;real prefactor default 1.0&gt;] \
[vwn_5 &lt;real prefactor default 1.0&gt;] \
[vwn_1_rpa &lt;real prefactor default 1.0&gt;]]
CONVERGENCE [[energy &lt;real energy default 1e-7&gt;] \
[density &lt;real density default 1e-5&gt;] \
[gradient &lt;real gradient default 5e-4&gt;] \
[dampon &lt;real dampon default 0.0&gt;] \
[dampoff &lt;real dampoff default 0.0&gt;] \
[diison &lt;real diison default 0.0&gt;] \
[diisoff &lt;real diisoff default 0.0&gt;] \
[levlon &lt;real levlon default 0.0&gt;] \
[levloff &lt;real levloff default 0.0&gt;] \
[ncydp &lt;integer ncydp default 2&gt;] \
[ncyds &lt;integer ncyds default 30&gt;] \
[ncysh &lt;integer ncysh default 30&gt;] \
[damp &lt;integer ndamp default 0&gt;] [nodamping] \
[diis [nfock &lt;integer nfock default 10&gt;]] \
[nodiis] [lshift &lt;real lshift default 0.5&gt;] \
[nolevelshifting] \
[hl_tol &lt;real hl_tol default 0.1&gt;] \
[rabuck [n_rabuck &lt;integer n_rabuck default 25&gt;]]
GRID [(xcoarse||coarse||medium||fine||xfine) default medium] \
[(gausleg||lebedev ) default lebedev ] \
[(becke||erf1||erf2||ssf) default erf1] \
[(euler||mura||treutler) default mura] \
[rm &lt;real rm default 2.0&gt;] \
[nodisk]
TOLERANCES [[tight] [tol_rho &lt;real tol_rho default 1e-10&gt;] \
[accCoul &lt;integer accCoul default 8&gt;] \
[radius &lt;real radius default 25.0&gt;]]
[(LB94||CS00 &lt;real shift default none&gt;)]
DECOMP
ODFT
DIRECT
INCORE
ITERATIONS &lt;integer iterations default 30&gt;
MAX_OVL
MULLIKEN
MULT &lt;integer mult default 1&gt;
NOIO
PRINT||NOPRINT
</PRE>
<P>
The following
sections describe these keywords and
optional sub-directives that can be specified for a <code>DFT</code> calculation
in NWChem.
<P>
<H1><A NAME="SECTION001310000000000000000">
11.1 Specification of Basis Sets for the DFT Module</A>
</H1>
<P>
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
<TT>"ao basis"</TT>, or it must be assigned to this default name using the
<code>SET</code> directive (see Section <A HREF="node7.html#sec:set">5.7</A>).
<P>
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 scheme<A NAME="tex2html28"
HREF="footnode.html#foot3421"><SUP>11.1</SUP></A>.
The charge density fitting basis set must have the name <TT>"cd basis"</TT>.
This can be the actual name of a basis set, or a basis set can be
assigned this name using the <code>SET</code> directive, as described in
Section <A HREF="node7.html#sec:set">5.7</A>. If this basis set is not defined by input,
the <IMG
WIDTH="51" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
SRC="img106.gif"
ALT="$O(N^4)$"> exact Coulomb contribution is computed.
<P>
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 <TT>"xc basis"</TT>. 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 <TT>"xc basis"</TT> basis set is not generally required.
<P>
For the DFT module, the input options for defining the basis sets in a given
calculation can be summarized as follows;
<UL>
<LI><TT>"ao basis"</TT> - Kohn-Sham molecular orbitals; required for all
calculations
</LI>
<LI><TT>"cd basis"</TT> - charge density fitting basis set; optional, but
recommended for evaluation of the Coulomb potential
</LI>
<LI><TT>"xc basis"</TT> - exchange-correlation (XC) fitting basis set;
optional, and usually not recommended
</LI>
</UL>
<P>
<H1><A NAME="SECTION001320000000000000000">
11.2 <TT>VECTORS</TT> and <TT>MAX_OVL</TT> -- KS-MO Vectors</A>
</H1>
<P>
The <code>VECTORS</code> directive is the same as that in the SCF module
(Section <A HREF="node12.html#sec:vectors">10.5</A>). Currently, the <code>LOCK</code> keyword
is not supported by the DFT module, however the directive
<PRE>
MAX_OVL
</PRE>
has the same effect.
<P>
<H1><A NAME="SECTION001330000000000000000"></A>
<A NAME="sec:xc"></A>
<BR>
11.3 <TT>XC</TT> and <TT>DECOMP</TT> -- Exchange-Correlation Potentials
</H1>
<PRE>
XC [[acm] [b3lyp] [beckehandh] [pbe0]\
[becke97] [becke97-1] [becke97-2] [becke98] [hcth] [hcth120] [hcth147] \
[hcth407] [becke97gga1] [hcth407p] \
[optx] [hcthp14] [mpw91] [mpw1k] [xft97] [cft97] [ft97]\
[HFexch &lt;real prefactor default 1.0&gt;] \
[becke88 [nonlocal] &lt;real prefactor default 1.0&gt;] \
[xperdew91 [nonlocal] &lt;real prefactor default 1.0&gt;] \
[xpbe96 [nonlocal] &lt;real prefactor default 1.0&gt;] \
[gill96 [nonlocal] &lt;real prefactor default 1.0&gt;] \
[lyp &lt;real prefactor default 1.0&gt;] \
[perdew81 &lt;real prefactor default 1.0&gt;] \
[perdew86 [nonlocal] &lt;real prefactor default 1.0&gt;] \
[perdew91 [nonlocal] &lt;real prefactor default 1.0&gt;] \
[cpbe96 [nonlocal] &lt;real prefactor default 1.0&gt;] \
[pw91lda &lt;real prefactor default 1.0&gt;] \
[slater &lt;real prefactor default 1.0&gt;] \
[vwn_1 &lt;real prefactor default 1.0&gt;] \
[vwn_2 &lt;real prefactor default 1.0&gt;] \
[vwn_3 &lt;real prefactor default 1.0&gt;] \
[vwn_4 &lt;real prefactor default 1.0&gt;] \
[vwn_5 &lt;real prefactor default 1.0&gt;] \
[vwn_1_rpa &lt;real prefactor default 1.0&gt;]]
</PRE>
<P>
The user has the option of specifying the exchange-correlation
treatment in the DFT Module (see table <A HREF="node13.html#tablexc">11.1</A>).
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 <IMG
WIDTH="32" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
SRC="img107.gif"
ALT="$\rho^{1/3}$"> functional (from
J.C.&nbsp;Slater, <I>Quantum Theory of Molecules and Solids, Vol.&nbsp;4: The
Self-Consistent Field for Molecules and Solids</I> (McGraw-Hill, New
York, 1974)), and the correlation functional is the Vosko-Wilk-Nusair
(VWN) functional (functional V) (S.J.&nbsp;Vosko, L.&nbsp;Wilk and M.&nbsp;Nusair,
Can.&nbsp;J.&nbsp;Phys.&nbsp;<B>58</B>, 1200 (1980)). The parameters used in this
formula are obtained by fitting to the Ceperley and
Alder<A NAME="tex2html29"
HREF="footnode.html#foot3424"><SUP>11.2</SUP></A>Quantum Monte-Carlo solution of the <EM> homogeneous electron gas</EM>.
<P>
These defaults can be invoked explicitly by specifying the following
keywords within the DFT module input directive, <code>XC slater vwn_5</code>.
<P>
That is, this statement in the input file
<PRE>
dft
XC slater vwn_5
end
task dft
</PRE>
<P>
is equivalent to the simple line
<PRE>
task dft
</PRE>
<P>
The <code>DECOMP</code> 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. You can see
an example of this directive in the sample input in
Section <A HREF="node13.html#sec:DFTsample">11.5</A>.
<P>
Many alternative exchange and correlation functionals are available to
the user as listed in table <A HREF="node13.html#tablexc">11.1</A>. The following sections describe
how to use these options.
<P>
<H2><A NAME="SECTION001331000000000000000">
11.3.1 Exchange-Correlation Functionals</A>
</H2>
<P>
There are several Exchange and Correlation functionals in addition to the
default <TT>slater</TT> and <TT>vwn_5</TT>
functionals. These are either local or gradient-corrected functionals (GCA);
a full list can be found in table <A HREF="node13.html#tablexc">11.1</A>.
<P>
The Hartree-Fock exact exchange functional, (which has <IMG
WIDTH="51" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
SRC="img106.gif"
ALT="$O(N^4)$">
computation expense), is invoked by specifying
<PRE>
XC HFexch
</PRE>
<P>
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
<code>&lt;prefactor&gt;</code> in the input) for the local/nonlocal component or
total. An example of this might be,
<PRE>
XC becke88 nonlocal 0.72
</PRE>
The user should be aware that the Becke88 local component is simply
the Slater exchange and should be input as such.
<P>
Any combination of the supported exchange functional options can be
used. For example the popular Gaussian B3 exchange could be specified
as:
<PRE>
XC slater 0.8 becke88 nonlocal 0.72 HFexch 0.2
</PRE>
<P>
<P>
<P>
Any combination of the supported correlation functional options can be
used. For example B3LYP could be specified as:
<PRE>
XC vwn_1_rpa 0.19 lyp 0.81 HFexch 0.20 slater 0.80 becke88 nonlocal 0.72
</PRE>
<P>
<H2><A NAME="SECTION001332000000000000000">
11.3.2 Combined Exchange and Correlation Functionals</A>
</H2>
<P>
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. A complete list of the available functionals
appears in table <A HREF="node13.html#tablexc">11.1</A>.
<P>
The available hybrid functionals
(where a Hartree-Fock Exchange component is present) consist of the Becke
``<I>half and half</I>'' (see A.D.&nbsp;Becke, J.&nbsp;Chem.&nbsp;Phys.&nbsp;98, 1372 (1992)), the
adiabatic connection method (see A.D.&nbsp;Becke, J.&nbsp;Chem.&nbsp;Phys.&nbsp;98, 5648
(1993)), B3LYP (popularized by Gaussian9X), Becke 1997
(``Becke V'' paper: A.D.Becke, J. Chem. Phys., <B>107</B>, 8554 (1997)).
<P>
The keyword <code>beckehandh</code> specifies that the exchange-correlation energy will be
computed as
<P></P>
<DIV ALIGN="CENTER">
<!-- MATH
\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*}
-->
<IMG
WIDTH="290" HEIGHT="89" BORDER="0"
SRC="img108.gif"
ALT="\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*}">
<BR CLEAR="ALL"></DIV><P></P>
<BR CLEAR="ALL"><P></P>
<BR CLEAR="ALL"><P></P>
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.
<P>
The keyword <code>acm</code> specifies that the exchange-correlation energy
is computed as
<P></P>
<DIV ALIGN="CENTER">
<!-- MATH
\begin{eqnarray*}
E_{XC} \ &=& \ a_0 E^{\rm HF}_X + (1-a_0) E^{\rm Slater}_{X} +
a_X \Delta E^{\rm Becke88}_{X} + E^{\rm VWN}_C + a_C \Delta E^{Perdew91}_C \\
& &{\rm where } \\
a_0 &=& 0.20, \ a_X = 0.72, \ a_C = 0.81
\end{eqnarray*}
-->
<IMG
WIDTH="552" HEIGHT="126" BORDER="0"
SRC="img109.gif"
ALT="\begin{eqnarray*}
E_{XC} \ &amp;=&amp; \ a_0 E^{\rm HF}_X + (1-a_0) E^{\rm Slater}_{X} +...
...\\
&amp; &amp;{\rm where } \\
a_0 &amp;=&amp; 0.20, \ a_X = 0.72, \ a_C = 0.81
\end{eqnarray*}">
<BR CLEAR="ALL"></DIV><P></P>
<BR CLEAR="ALL"><P></P>
<BR CLEAR="ALL"><P></P>
and <IMG
WIDTH="17" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img104.gif"
ALT="$\Delta$"> stands for a non-local component.
<P>
The keyword <code>b3lyp</code> specifies that the exchange-correlation energy
is computed as
<P></P>
<DIV ALIGN="CENTER">
<!-- MATH
\begin{eqnarray*}
E_{XC} \ &=& \ a_0 E^{\rm HF}_X + (1-a_0) E^{\rm Slater}_{X} +
a_X \Delta E^{\rm Becke88}_{X} + (1-a_C)E^{\rm VWN\_1\_RPA}_C + a_C E^{LYP}_C \\
& &{\rm where } \\
a_0 &=& 0.20, \ a_X = 0.72, \ a_C = 0.81
\end{eqnarray*}
-->
<IMG
WIDTH="615" HEIGHT="126" BORDER="0"
SRC="img110.gif"
ALT="\begin{eqnarray*}
E_{XC} \ &amp;=&amp; \ a_0 E^{\rm HF}_X + (1-a_0) E^{\rm Slater}_{X} +...
...\\
&amp; &amp;{\rm where } \\
a_0 &amp;=&amp; 0.20, \ a_X = 0.72, \ a_C = 0.81
\end{eqnarray*}">
<BR CLEAR="ALL"></DIV><P></P>
<BR CLEAR="ALL"><P></P>
<BR CLEAR="ALL"><P></P>
<P>
<H2><A NAME="SECTION001333000000000000000">
11.3.3 Meta-GGA Functionals</A>
</H2>
<P>
One way to calculate meta-GGA energies is to use
orbitals and densities
from fully self-consistent GGA or LDA calculations
and run them in one iteration in the meta-GGA functional.
It is expected that meta-GGA energies obtained
this way will be close to fully self consistent
meta-GGA calculations.
This can be easily accomplished in NWChem,
and is illustrated in
the example below.
This kind of calculation
will obviously not converge the energy.
To avoid an error in
the standard Unix output of NWChem,
you must tell NWChem
to ignore
the returned result of the task,
which may be accomplished in the input file
with <code> task dft ignore</code>
You may still get a warning in the output to the effect,
<code>!! warning: dft energy failed</code>.
This simply means the energy failed to converge
since you ran only one iteration of
the functional.
<P>
(For more information, see
S. Kurth, J. Perdew, P. Blaha, Int. J. Quant. Chem 75, 889 (1999)
for a brief description of meta-GGAs, and citations 14-27
therein for thorough background )
<P>
Note: both TPSS and PKZB correlation
require the PBE GGA CORRELATION (which is itself dependent on an LDA).
The decision has been made to
use these functionals with the accompanying local
PW91LDA. The user does not have the ability to set
the local part of these metaGGA functionals.
<P>
<H1><A NAME="SECTION001340000000000000000">
11.4 <TT>LB94</TT> and <TT>CS00</TT> -- Asymptotic correction</A>
</H1>
<P>
The keyword <code>LB94</code> will correct the asymptotic region of
the <code>XC</code> definition of exchange-correlation <I>potential</I> by
the van-Leeuwen-Baerends exchange-correlation <I>potential</I> that
has the correct <IMG
WIDTH="40" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="img111.gif"
ALT="$-1/r$"> asymptotic behavior. The total energy will be computed by the
<code>XC</code> definition of exchange-correlation functional. This scheme is known to
tend to overcorrect the deficiency of most uncorrected exchange-correlation potentials.
<P>
The keyword <code>CS00</code>, when supplied with a real value of shift (in atomic units),
will perform Casida-Salahub '00 asymptotic correction. This is primarily intended
for use in conjunction with TDDFT and the background of this method is given in more
detail in Chapter 14. The shift is normally positive (which means that the original
uncorrected exchange-correlation potential must be shifted down).
<P>
When the keyword <code>CS00</code> is specified without the value of shift, the program will
automatically supply it according to the semi-empirical formula of Zhan, Nichols, and
Dixon (again, see Chapter 14 for more details and references). As the Zhan's formula
is calibrated against B3LYP results, it is most meaningful to use this in conjunction
with the B3LYP functional, although the program does not prohibit (or even warn) the use
of any other functional.
<P>
Sample input files of asymptotically corrected TDDFT calculations can be found in
Chapter 14.
<P>
<H1><A NAME="SECTION001350000000000000000"></A>
<A NAME="sec:DFTsample"></A>
<BR>
11.5 Sample input file
</H1>
A simple example calculates the meta-GGA
exchange
energy of water, using converged GGA orbitals and
densities to evaluate the meta-GGA energy functional,
and also highlights some of
the print features in the DFT module:
<PRE>
title "WATER 6-311G* meta-GGA X with PBE orbitals"
echo
geometry units angstroms
O 0.0 0.0 0.0
H 0.0 0.0 1.0
H 0.0 1.0 0.0
end
basis
H library 6-311G*
O library 6-311G*
end
dft
print kinetic_energy
xc xpbe96 cpbe96
decomp
end
task dft optimize
dft
iterations 1
xc xpkzb99
decomp
print quadrature kinetic_energy
end
task dft ignore
</PRE>
<P>
Below are
the results of the exchange-only
meta-GGA calculation part, and as expected
we are reminded the calculation was not allowed
to converge:
<P>
<PRE>
Calculation failed to converge
------------------------------
Total DFT energy = -75.948526603774
One electron energy = -122.899234375708
Coulomb energy = 46.745269703266
Exchange energy = -8.857824284365
Correlation energy = 0.000000000000
Nuclear repulsion energy = 9.063262353032
Numeric. integr. density = 10.000001055407
</PRE>
<P>
<BR><P></P>
<DIV ALIGN="CENTER"><A NAME="3426"></A>
<TABLE>
<CAPTION><STRONG>Table 11.1:</STRONG>
Table of available Exchange (X) and Correlation (C) functionals.
GGA is the Generalized Gradient Approximation, and meta refers to
Meta-GGAs. The column <EM>2nds</EM> refers to second derivatives of the
energy with respect to nuclear position. </CAPTION>
<TR><TD>
<P>
<TABLE CELLPADDING=3 BORDER="1">
<TR><TD ALIGN="LEFT">&nbsp;</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="RIGHT">&nbsp;</TD>
</TR>
<TR><TD ALIGN="LEFT">Keyword</TD>
<TD ALIGN="CENTER">X</TD>
<TD ALIGN="CENTER">C</TD>
<TD ALIGN="CENTER">GGA</TD>
<TD ALIGN="CENTER">meta</TD>
<TD ALIGN="CENTER">Hybrid</TD>
<TD ALIGN="CENTER">2nds</TD>
<TD ALIGN="RIGHT">Ref.</TD>
</TR>
<TR><TD ALIGN="LEFT">&nbsp;</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="RIGHT">&nbsp;</TD>
</TR>
<TR><TD ALIGN="LEFT">slater</TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">Y</TD>
<TD ALIGN="RIGHT">[1]</TD>
</TR>
<TR><TD ALIGN="LEFT">vwn_1</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">Y</TD>
<TD ALIGN="RIGHT">[2]</TD>
</TR>
<TR><TD ALIGN="LEFT">vwn_2</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">Y</TD>
<TD ALIGN="RIGHT">[2]</TD>
</TR>
<TR><TD ALIGN="LEFT">vwn_3</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">Y</TD>
<TD ALIGN="RIGHT">[2]</TD>
</TR>
<TR><TD ALIGN="LEFT">vwn_4</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">Y</TD>
<TD ALIGN="RIGHT">[2]</TD>
</TR>
<TR><TD ALIGN="LEFT">vwn_5</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">Y</TD>
<TD ALIGN="RIGHT">[2]</TD>
</TR>
<TR><TD ALIGN="LEFT">vwn_1_rpa</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">Y</TD>
<TD ALIGN="RIGHT">[2]</TD>
</TR>
<TR><TD ALIGN="LEFT">perdew81</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">Y</TD>
<TD ALIGN="RIGHT">[3]</TD>
</TR>
<TR><TD ALIGN="LEFT">pw91lda</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">Y</TD>
<TD ALIGN="RIGHT">[4]</TD>
</TR>
<TR><TD ALIGN="LEFT">becke88</TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">Y</TD>
<TD ALIGN="RIGHT">[5]</TD>
</TR>
<TR><TD ALIGN="LEFT">xperdew91</TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">Y</TD>
<TD ALIGN="RIGHT">[6]</TD>
</TR>
<TR><TD ALIGN="LEFT">xpbe96</TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">Y</TD>
<TD ALIGN="RIGHT">[7]</TD>
</TR>
<TR><TD ALIGN="LEFT">gill96</TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">Y</TD>
<TD ALIGN="RIGHT">[8]</TD>
</TR>
<TR><TD ALIGN="LEFT">optx</TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">N</TD>
<TD ALIGN="RIGHT">[20]</TD>
</TR>
<TR><TD ALIGN="LEFT">mpw91</TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">Y</TD>
<TD ALIGN="RIGHT">[23]</TD>
</TR>
<TR><TD ALIGN="LEFT">xft97</TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">N</TD>
<TD ALIGN="RIGHT">[24]</TD>
</TR>
<TR><TD ALIGN="LEFT">perdew86</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">Y</TD>
<TD ALIGN="RIGHT">[9]</TD>
</TR>
<TR><TD ALIGN="LEFT">lyp</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">Y</TD>
<TD ALIGN="RIGHT">[10]</TD>
</TR>
<TR><TD ALIGN="LEFT">perdew91</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">Y</TD>
<TD ALIGN="RIGHT">[6]</TD>
</TR>
<TR><TD ALIGN="LEFT">cpbe96</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">Y</TD>
<TD ALIGN="RIGHT">[7]</TD>
</TR>
<TR><TD ALIGN="LEFT">cft97</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">N</TD>
<TD ALIGN="RIGHT">[25]</TD>
</TR>
<TR><TD ALIGN="LEFT">hcth</TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">N</TD>
<TD ALIGN="RIGHT">[11]</TD>
</TR>
<TR><TD ALIGN="LEFT">hcth120</TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">N</TD>
<TD ALIGN="RIGHT">[12]</TD>
</TR>
<TR><TD ALIGN="LEFT">hcth147</TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">N</TD>
<TD ALIGN="RIGHT">[12]</TD>
</TR>
<TR><TD ALIGN="LEFT">hcth407</TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">N</TD>
<TD ALIGN="RIGHT">[19]</TD>
</TR>
<TR><TD ALIGN="LEFT">becke97gga1</TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">N</TD>
<TD ALIGN="RIGHT">[18]</TD>
</TR>
<TR><TD ALIGN="LEFT">hcthp14</TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">N</TD>
<TD ALIGN="RIGHT">[21]</TD>
</TR>
<TR><TD ALIGN="LEFT">ft97</TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">N</TD>
<TD ALIGN="RIGHT">[24,25]</TD>
</TR>
<TR><TD ALIGN="LEFT">htch407p</TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">N</TD>
<TD ALIGN="RIGHT">[28]</TD>
</TR>
<TR><TD ALIGN="LEFT">xpkzb99</TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">N</TD>
<TD ALIGN="RIGHT">[27]</TD>
</TR>
<TR><TD ALIGN="LEFT">cpkzb99</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">N</TD>
<TD ALIGN="RIGHT">[27]</TD>
</TR>
<TR><TD ALIGN="LEFT">xtpss03</TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">N</TD>
<TD ALIGN="RIGHT">[29]</TD>
</TR>
<TR><TD ALIGN="LEFT">ctpss03</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER">&nbsp;</TD>
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WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">N</TD>
<TD ALIGN="RIGHT">[29]</TD>
</TR>
<TR><TD ALIGN="LEFT">beckehandh</TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER"><IMG
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SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER">Y</TD>
<TD ALIGN="RIGHT">[13]</TD>
</TR>
<TR><TD ALIGN="LEFT">b3lyp</TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER"><IMG
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SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER"><IMG
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SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER">Y</TD>
<TD ALIGN="RIGHT">[14]</TD>
</TR>
<TR><TD ALIGN="LEFT">acm</TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER"><IMG
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SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER"><IMG
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SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER">Y</TD>
<TD ALIGN="RIGHT">[14]</TD>
</TR>
<TR><TD ALIGN="LEFT">becke97</TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER"><IMG
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SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER"><IMG
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SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER">N</TD>
<TD ALIGN="RIGHT">[15]</TD>
</TR>
<TR><TD ALIGN="LEFT">becke97-1</TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER"><IMG
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SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER"><IMG
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SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER">N</TD>
<TD ALIGN="RIGHT">[15]</TD>
</TR>
<TR><TD ALIGN="LEFT">becke97-2</TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER"><IMG
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SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER">N</TD>
<TD ALIGN="RIGHT">[22]</TD>
</TR>
<TR><TD ALIGN="LEFT">becke98</TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER"><IMG
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SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER"><IMG
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SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER">N</TD>
<TD ALIGN="RIGHT">[16]</TD>
</TR>
<TR><TD ALIGN="LEFT">pbe0</TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
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SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER"><IMG
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SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER">Y</TD>
<TD ALIGN="RIGHT">[17]</TD>
</TR>
<TR><TD ALIGN="LEFT">mpw1k</TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER"><IMG
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SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="CENTER"><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$\star$"></TD>
<TD ALIGN="CENTER">Y</TD>
<TD ALIGN="RIGHT">[26]</TD>
</TR>
</TABLE>
<A NAME="tablexc"></A></TD></TR>
</TABLE>
</DIV><P></P>
<BR>
<P>
<FONT SIZE="-1">
<BR>
<BR>
<BR>
<BR>
<BR>
<BR>
<BR>
<BR>
<BR>
<BR>
<BR>
<BR>
<BR>
<BR>
<BR>
<BR>
<BR>
<BR>
<BR>
<BR>
<BR>
</FONT>
<OL>
<LI>C.&nbsp;Slater, <I>Quantum Theory of Molecules and Solids,
Vol.&nbsp;4</I> (McGraw-Hill, New York, 1974)
<BR></LI>
<LI>S.J.&nbsp;Vosko, L.&nbsp;Wilk and M.&nbsp;Nusair,
Can.&nbsp;J.&nbsp;Phys.&nbsp;<B>58</B>, 1200 (1980).
<BR></LI>
<LI>J.&nbsp;P.&nbsp;Perdew and A.&nbsp;Zunger, Phys.&nbsp;Rev.&nbsp;B <B>23</B>, 5048
(1981).
<BR></LI>
<LI>J.P.&nbsp;Perdew and Y.&nbsp;Wang, Phys. Rev. B <B>45</B>,
13244 (1992).
<BR></LI>
<LI>A.D.&nbsp;Becke, Phys. Rev. A <B>88</B>, 3098 (1988).
<BR></LI>
<LI>J.P. Perdew, J.A.&nbsp;Chevary, S.H.&nbsp;Vosko, K.A.&nbsp;Jackson,
M.R.&nbsp;Pederson, D.J.&nbsp;Singh and C.&nbsp;Fiolhais, Phys. Rev. B <B>46</B>, 6671
(1992).
<BR></LI>
<LI>J.P.&nbsp;Perdew, K.&nbsp;Burke and M.&nbsp;Ernzerhof,
Phys. Rev. Lett. <B>77</B>, 3865 (1996); <B>78 </B>, 1396 (1997).
<BR></LI>
<LI>P.W.Gill , Mol. Phys. <B>89</B>, 433 (1996).
<BR></LI>
<LI>J.&nbsp;P.&nbsp;Perdew, Phys.&nbsp;Rev.&nbsp;B <B>33</B>, 8822 (1986).
<BR></LI>
<LI>C.&nbsp;Lee, W.&nbsp;Yang and R.&nbsp;G.&nbsp;Parr, Phys.&nbsp;Rev.&nbsp;B <B>37</B>, 785
(1988).
<BR></LI>
<LI>F.A.Hamprecht, A.J.Cohen, D.J.Tozer and N.C.
<BR>
Handy,
J. Chem. Phys. <B>109</B>, 6264 (1998).
<BR></LI>
<LI>A.D.Boese, N.L.Doltsinis, N.C.Handy and
M.Sprik. J. Chem. Phys. <B>112</B>, 1670 (2000).
<BR></LI>
<LI>A.D.&nbsp;Becke, J.&nbsp;Chem.&nbsp;Phys. <B>98</B>, 1372 (1992).
<BR></LI>
<LI>A.D.&nbsp;Becke, J.&nbsp;Chem.&nbsp;Phys.&nbsp;<B>98</B>, 5648 (1993).
<BR></LI>
<LI>A.D.Becke, J. Chem. Phys. <B>107</B>, 8554 (1997).
<BR></LI>
<LI>H.L.Schmider and A.D.&nbsp;Becke, J.&nbsp;Chem.&nbsp;Phys.&nbsp;<B>108</B>,
9624 (1998).
<BR></LI>
<LI>C.Adamo and V.Barone, J.&nbsp;Chem.&nbsp;Phys. <B>110</B>, 6158 (1998).
<BR></LI>
<LI>A.J.Cohen and N.C. Handy, Chem. Phys. Lett. <B>316</B>, 160 (2000).
<BR></LI>
<LI>A.D.Boese, N.C.Handy, J. Chem. Phys. <B>114</B>, 5497
(2001).
<BR></LI>
<LI>N.C.Handy, A.J. Cohen, Mol. Phys. <B>99</B>, 403 (2001).
<BR></LI>
<LI>G. Menconi, P.J. Wilson, D.J. Tozer,
J. Chem. Phys <B>114</B>, 3958 (2001).
<BR></LI>
<LI>P.J. Wilson, T.J. Bradley, D.J. Tozer, J. Chem. Phys <B>115</B>,
9233 (2001).
<BR></LI>
<LI>C. Adamo and V. Barone, J.&nbsp;Chem.&nbsp;Phys. <B>108</B>, 664 (1998).
<BR></LI>
<LI>M.Filatov and W.Thiel, Mol.Phys. <B>91</B>, 847 (1997).
<BR></LI>
<LI>M.Filatov and W.Thiel, Int.J.Quantum Chem. <B>62</B>, 603 (1997).
<BR></LI>
<LI>B.J.Lynch, P.L.Fast, M.Harris and D.G.Truhlar, J. Phys. Chem. A
<B>104</B>, 4811(2000).
<BR></LI>
<LI>J.P.&nbsp;Perdew, S.&nbsp;Kurth, A.&nbsp;Zupan and P.&nbsp;Blaha,
Phys. Rev. Lett. <B>82</B>, 2544 (1999)
<BR></LI>
<LI>A.&nbsp;D.&nbsp;Boese, A.&nbsp;Chandra, J.&nbsp;M.&nbsp;L.&nbsp;Martin and D.&nbsp;Marx,
J. Chem. Phys. <B>119</B>, 5965 (2003)
<BR></LI>
<LI>J. Tao,J.Perdew,V. Staroverov and G. Scuseria,
Phys. Rev. Let. <B>91</B>, 146401-1 (2003)
</LI>
</OL>
<P>
<H1><A NAME="SECTION001360000000000000000">
11.6 <TT>ITERATIONS</TT> -- Number of SCF iterations</A>
</H1>
<P>
<PRE>
ITERATIONS &lt;integer iterations default 30&gt;
</PRE>
<P>
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 <code>ITERATIONS</code>, and has the following general form,
<P>
<PRE>
iterations &lt;integer iterations default 30&gt;
</PRE>
<P>
The optimization procedure will stop when the specified number of
iterations is reached or convergence is met. See an example
that uses this directive in section <A HREF="node13.html#sec:DFTsample">11.5</A>.
<P>
<H1><A NAME="SECTION001370000000000000000"></A>
<A NAME="sec:dftconv"></A>
<BR>
11.7 <TT>CONVERGENCE</TT> -- SCF Convergence Control
</H1>
<P>
<PRE>
CONVERGENCE [energy &lt;real energy default 1e-6&gt;] \
[density &lt;real density default 1e-5&gt;] \
[gradient &lt;real gradient default 5e-4&gt;] \
[hl_tol &lt;real hl_tol default 0.1&gt;]
[dampon &lt;real dampon default 0.0&gt;] \
[dampoff &lt;real dampoff default 0.0&gt;] \
[ncydp &lt;integer ncydp default 2&gt;] \
[ncyds &lt;integer ncyds default 30&gt;] \
[ncysh &lt;integer ncysh default 30&gt;] \
[damp &lt;integer ndamp default 0&gt;] [nodamping] \
[diison &lt;real diison default 0.0&gt;] \
[diisoff &lt;real diisoff default 0.0&gt;] \
[(diis [nfock &lt;integer nfock default 10&gt;]) || nodiis] \
[levlon &lt;real levlon default 0.0&gt;] \
[levloff &lt;real levloff default 0.0&gt;] \
[(lshift &lt;real lshift default 0.5&gt;) || nolevelshifting] \
[rabuck [n_rabuck &lt;integer n_rabuck default 25&gt;]]
</PRE>
<P>
Convergence is satisfied by meeting any or all of three criteria;
<UL>
<LI>convergence of the total energy; this is defined to be when the
total DFT energy at iteration N and at iteration N-1 differ by a value less
than some value (the default is 1e-6). This value can be modified
using the key word,
<PRE>
CONVERGENCE energy &lt;real energy default 1e-6&gt;
</PRE>
<P>
</LI>
<LI>convergence of the total density; this is defined to be when the
total DFT density matrix at iteration N and at iteration N-1 have a
RMS difference less than some value (the default is 1e-5). This value can be modified
using the key word,
<PRE>
CONVERGENCE density &lt;real density default 1e-5&gt;
</PRE>
<P>
</LI>
<LI>convergence of the orbital gradient; this is defined to be when the
DIIS error vector becomes less than some value (the default is
5e-4). This value can be modified using the key word,
<PRE>
CONVERGENCE gradient &lt;real gradient default 5e-4&gt;
</PRE>
</LI>
</UL>
<P>
The default optimization strategy is to immediately begin direct
inversion of the iterative subspace<A NAME="tex2html31"
HREF="footnode.html#foot3430"><SUP>11.3</SUP></A>. 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.
<P>
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,
<PRE>
CONVERGENCE [dampon &lt;real dampon default 0.0&gt;] \
[dampoff &lt;real dampoff default 0.0&gt;] \
[diison &lt;real diison default 0.0&gt;] \
[diisoff &lt;real diisoff default 0.0&gt;] \
[levlon &lt;real levlon default 0.0&gt;] \
[levloff &lt;real levloff default 0.0&gt;]
</PRE>
<P>
So, for example, damping, DIIS, and/or level-shifting can be turned
on/off as desired.
<P>
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,
<PRE>
CONVERGENCE [ncydp &lt;integer ncydp default 2&gt;] \
[ncyds &lt;integer ncyds default 30&gt;] \
[ncysh &lt;integer ncysh default 0&gt;]
</PRE>
<P>
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
<PRE>
CONVERGENCE [damp &lt;integer ndamp default 0&gt;] \
[diis [nfock &lt;integer nfock default 10&gt;]] \
[lshift &lt;real lshift default 0.5&gt;] \
[hl_tol &lt;real hl_tol default 0.1&gt;]]
</PRE>
<P>
Damping is defined to be the percentage of the previous iterations
density mixed with the current iterations density. So, for example
<PRE>
CONVERGENCE damp 70
</PRE>
would mix 30% of the current iteration density with 70% of the
previous iteration density.
<P>
Level-Shifting<A NAME="tex2html32"
HREF="footnode.html#foot3431"><SUP>11.4</SUP></A> 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 <code>lshift</code>. For example the directive,
<PRE>
CONVERGENCE lshift 0.5
</PRE>
causes the diagonal elements of the Fock matrix
corresponding to the virtual orbitals to be shifted by 0.5 a.u.
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 <code>hl_tol</code>. An example of
changing the HOMO-LUMO gap tolerance to 0.01 would be,
<PRE>
CONVERGENCE hl_tol 0.01
</PRE>
<P>
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,
<PRE>
CONVERGENCE diis 3
</PRE>
<P>
The user has the ability to simply turn off any optimization
procedures deemed undesirable with the obvious keywords,
<PRE>
CONVERGENCE [nodamping] [nodiis] [nolevelshifting]
</PRE>
<P>
For systems where the initial guess is very poor, the user can try the
method described in
<A NAME="tex2html33"
HREF="footnode.html#foot3432"><SUP>11.5</SUP></A>that makes use of <B>fractional occupation</B> of the orbital levels during
the initial cycles of the SCF convergence. The input has the following form
<P>
<PRE>
CONVERGENCE rabuck [n_rabuck &lt;integer n_rabuck default 25&gt;]]
</PRE>
<P>
where the optional value <TT>n_rabuck</TT> determines the number of SCF
cycles during which the method will be active. For example, to
set equal to 30 the number of cycles where the Rabuck method is
active, you need to use the following line
<PRE>
CONVERGENCE rabuck 30
</PRE>
<P>
<H1><A NAME="SECTION001380000000000000000"></A>
<A NAME="smear"></A>
<BR>
11.8 <TT>SMEAR</TT> -- Fractional Occupation of the Molecular Orbitals
</H1>
<P>
The <TT><B>SMEAR</B></TT> keyword is useful in cases with many degenerate states
near the HOMO (eg metallic clusters)
<P>
<PRE>
SMEAR &lt;real smear default 0.001&gt;
</PRE>
<P>
This option allows fractional occupation of the molecular orbitals.
A Gaussian broadening function of exponent <TT>smear</TT> is used as described in
the paper:
R.W. Warren RW and B.I. Dunlap, Chem. Phys. Letters <B>262</B>, 384 (1996).
<BR>
The user must be aware that an additional energy term is added to the total
energy in order to have
energies and gradients consistent.
<P>
<H1><A NAME="SECTION001390000000000000000"></A>
<A NAME="grgrid"></A>
<BR>
11.9 <TT>GRID</TT> -- Numerical Integration of the XC Potential
</H1>
<PRE>
GRID [(xcoarse||coarse||medium||fine||xfine) default medium] \
[(gausleg||lebedev ) default lebedev ] \
[(becke||erf1||erf2||ssf) default erf1] \
[(euler||mura||treutler) default mura] \
[rm &lt;real rm default 2.0&gt;] \
[nodisk]
</PRE>
<P>
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.
<P>
<PRE>
GRID [xcoarse||coarse||medium||fine||xfine]
</PRE>
<P>
Our intent is to have a numerical integration scheme which would give
us approximately the accuracy defined below regardless of molecular
composition.
<DIV ALIGN="CENTER">
<TABLE CELLPADDING=3 BORDER="1">
<TR><TD ALIGN="CENTER">Keyword</TD>
<TD ALIGN="CENTER"><TT>Total Energy Target Accuracy</TT></TD>
</TR>
<TR><TD ALIGN="CENTER"><TT>xcoarse</TT></TD>
<TD ALIGN="CENTER"><IMG
WIDTH="54" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
SRC="img113.gif"
ALT="$1x10^{-4}$"></TD>
</TR>
<TR><TD ALIGN="CENTER"><TT>coarse</TT></TD>
<TD ALIGN="CENTER"><IMG
WIDTH="54" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
SRC="img114.gif"
ALT="$1x10^{-5}$"></TD>
</TR>
<TR><TD ALIGN="CENTER"><TT>medium</TT></TD>
<TD ALIGN="CENTER"><IMG
WIDTH="54" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
SRC="img115.gif"
ALT="$1x10^{-6}$"></TD>
</TR>
<TR><TD ALIGN="CENTER"><TT>fine</TT></TD>
<TD ALIGN="CENTER"><IMG
WIDTH="54" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
SRC="img116.gif"
ALT="$1x10^{-7}$"></TD>
</TR>
<TR><TD ALIGN="CENTER"><TT>xfine</TT></TD>
<TD ALIGN="CENTER"><IMG
WIDTH="54" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
SRC="img117.gif"
ALT="$1x10^{-8}$"></TD>
</TR>
</TABLE>
<BR>
</DIV>
<P>
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).
<P>
<BR>
<DIV ALIGN="CENTER">
</DIV>
<P>
<DIV ALIGN="CENTER">
<BR>
<BR>
</DIV>
<P>
<DIV ALIGN="CENTER"><A NAME="3231"></A>
<TABLE CELLPADDING=3 BORDER="1" ALIGN="CENTER">
<CAPTION><STRONG>Table 11.2:</STRONG>
Program default number of radial and angular shells empirically determined for Row 1 atoms
(Li <IMG
WIDTH="20" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img3.gif"
ALT="$\rightarrow $"> F) to reach the desired accuracies.</CAPTION>
<TR><TD ALIGN="CENTER">Keyword</TD>
<TD ALIGN="CENTER"><TT>Radial</TT></TD>
<TD ALIGN="CENTER"><TT>Angular</TT></TD>
</TR>
<TR><TD ALIGN="CENTER"><TT>xcoarse</TT></TD>
<TD ALIGN="CENTER">21</TD>
<TD ALIGN="CENTER">194</TD>
</TR>
<TR><TD ALIGN="CENTER"><TT>coarse</TT></TD>
<TD ALIGN="CENTER">35</TD>
<TD ALIGN="CENTER">302</TD>
</TR>
<TR><TD ALIGN="CENTER"><TT>medium</TT></TD>
<TD ALIGN="CENTER">49</TD>
<TD ALIGN="CENTER">434</TD>
</TR>
<TR><TD ALIGN="CENTER"><TT>fine</TT></TD>
<TD ALIGN="CENTER">70</TD>
<TD ALIGN="CENTER">590</TD>
</TR>
<TR><TD ALIGN="CENTER"><TT>xfine</TT></TD>
<TD ALIGN="CENTER">100</TD>
<TD ALIGN="CENTER">1202</TD>
</TR>
</TABLE>
<BR>
</DIV>
<BR>
<P>
<BR>
<DIV ALIGN="CENTER">
</DIV>
<P>
<DIV ALIGN="CENTER">
<BR>
<BR>
</DIV>
<P>
<DIV ALIGN="CENTER"><A NAME="3247"></A>
<TABLE CELLPADDING=3 BORDER="1" ALIGN="CENTER">
<CAPTION><STRONG>Table 11.3:</STRONG>
Program default number of radial and angular shells empirically determined for Row 2 atoms
(Na <IMG
WIDTH="20" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img3.gif"
ALT="$\rightarrow $"> Cl) to reach the desired accuracies.</CAPTION>
<TR><TD ALIGN="CENTER">Keyword</TD>
<TD ALIGN="CENTER"><TT>Radial</TT></TD>
<TD ALIGN="CENTER"><TT>Angular</TT></TD>
</TR>
<TR><TD ALIGN="CENTER"><TT>xcoarse</TT></TD>
<TD ALIGN="CENTER">42</TD>
<TD ALIGN="CENTER">194</TD>
</TR>
<TR><TD ALIGN="CENTER"><TT>coarse</TT></TD>
<TD ALIGN="CENTER">70</TD>
<TD ALIGN="CENTER">302</TD>
</TR>
<TR><TD ALIGN="CENTER"><TT>medium</TT></TD>
<TD ALIGN="CENTER">88</TD>
<TD ALIGN="CENTER">434</TD>
</TR>
<TR><TD ALIGN="CENTER"><TT>fine</TT></TD>
<TD ALIGN="CENTER">123</TD>
<TD ALIGN="CENTER">770</TD>
</TR>
<TR><TD ALIGN="CENTER"><TT>xfine</TT></TD>
<TD ALIGN="CENTER">125</TD>
<TD ALIGN="CENTER">1454</TD>
</TR>
</TABLE>
<BR>
</DIV>
<BR>
<P>
<BR>
<DIV ALIGN="CENTER">
</DIV>
<P>
<DIV ALIGN="CENTER">
<BR>
<BR>
</DIV>
<P>
<DIV ALIGN="CENTER"><A NAME="3263"></A>
<TABLE CELLPADDING=3 BORDER="1" ALIGN="CENTER">
<CAPTION><STRONG>Table 11.4:</STRONG>
Program default number of radial and angular shells empirically determined for Row 3 atoms
(K <IMG
WIDTH="20" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img3.gif"
ALT="$\rightarrow $"> Br) to reach the desired accuracies.</CAPTION>
<TR><TD ALIGN="CENTER">Keyword</TD>
<TD ALIGN="CENTER"><TT>Radial</TT></TD>
<TD ALIGN="CENTER"><TT>Angular</TT></TD>
</TR>
<TR><TD ALIGN="CENTER"><TT>xcoarse</TT></TD>
<TD ALIGN="CENTER">75</TD>
<TD ALIGN="CENTER">194</TD>
</TR>
<TR><TD ALIGN="CENTER"><TT>coarse</TT></TD>
<TD ALIGN="CENTER">95</TD>
<TD ALIGN="CENTER">302</TD>
</TR>
<TR><TD ALIGN="CENTER"><TT>medium</TT></TD>
<TD ALIGN="CENTER">112</TD>
<TD ALIGN="CENTER">590</TD>
</TR>
<TR><TD ALIGN="CENTER"><TT>fine</TT></TD>
<TD ALIGN="CENTER">130</TD>
<TD ALIGN="CENTER">974</TD>
</TR>
<TR><TD ALIGN="CENTER"><TT>xfine</TT></TD>
<TD ALIGN="CENTER">160</TD>
<TD ALIGN="CENTER">1454</TD>
</TR>
</TABLE>
<BR>
</DIV>
<BR>
<P>
<BR>
<DIV ALIGN="CENTER">
</DIV>
<P>
<DIV ALIGN="CENTER">
<BR>
<BR>
</DIV>
<P>
<DIV ALIGN="CENTER"><A NAME="3279"></A>
<TABLE CELLPADDING=3 BORDER="1" ALIGN="CENTER">
<CAPTION><STRONG>Table 11.5:</STRONG>
Program default number of radial and angular shells empirically determined for Row 4 atoms
(Rb <IMG
WIDTH="20" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img3.gif"
ALT="$\rightarrow $"> I) to reach the desired accuracies.</CAPTION>
<TR><TD ALIGN="CENTER">Keyword</TD>
<TD ALIGN="CENTER"><TT>Radial</TT></TD>
<TD ALIGN="CENTER"><TT>Angular</TT></TD>
</TR>
<TR><TD ALIGN="CENTER"><TT>xcoarse</TT></TD>
<TD ALIGN="CENTER">84</TD>
<TD ALIGN="CENTER">194</TD>
</TR>
<TR><TD ALIGN="CENTER"><TT>coarse</TT></TD>
<TD ALIGN="CENTER">104</TD>
<TD ALIGN="CENTER">302</TD>
</TR>
<TR><TD ALIGN="CENTER"><TT>medium</TT></TD>
<TD ALIGN="CENTER">123</TD>
<TD ALIGN="CENTER">590</TD>
</TR>
<TR><TD ALIGN="CENTER"><TT>fine</TT></TD>
<TD ALIGN="CENTER">141</TD>
<TD ALIGN="CENTER">974</TD>
</TR>
<TR><TD ALIGN="CENTER"><TT>xfine</TT></TD>
<TD ALIGN="CENTER">205</TD>
<TD ALIGN="CENTER">1454</TD>
</TR>
</TABLE>
<BR>
</DIV>
<BR>
<P>
<P>
<H2><A NAME="SECTION001391000000000000000">
11.9.1 Angular grids</A>
</H2>
<P>
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 <code>gausleg</code> keyword.
<P>
<H4><A NAME="SECTION001391010000000000000">
11.9.1.0.1 Gauss-Legendre angular grid</A>
</H4>
<P>
<PRE>
GRID gausleg &lt;integer nradpts default 50&gt; &lt;integer nagrid default 10&gt;
</PRE>
<P>
In this type of grid, the number of phi points is twice the number of
theta points. So, for example, a specification of,
<PRE>
GRID gausleg 80 20
</PRE>
would be interpreted as 80 radial points, 20 theta points, and 40
phi points per center (or 64000 points per center before pruning).
<P>
<H4><A NAME="SECTION001391020000000000000">
11.9.1.0.2 Lebedev angular grid</A>
</H4>
<P>
A second quadrature is the Lebedev
scheme for the angular components<A NAME="tex2html38"
HREF="footnode.html#foot3300"><SUP>11.6</SUP></A>.
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,
<PRE>
GRID lebedev &lt;integer radpts &gt; &lt;integer iangquad &gt;
</PRE>
In this context the variable iangquad specifies a certain number of
angular points as indicated by the table below.<A NAME="tex2html39"
HREF="footnode.html#foot3435"><SUP>11.7</SUP></A>
<BR><P></P>
<DIV ALIGN="CENTER"><A NAME="3311"></A>
<TABLE>
<CAPTION><STRONG>Table 11.6:</STRONG>
List of Lebedev quadratures</CAPTION>
<TR><TD>
<DIV ALIGN="CENTER">
<TABLE CELLPADDING=3 BORDER="1" ALIGN="CENTER">
<TR><TD ALIGN="CENTER"><IMG
WIDTH="102" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img118.gif"
ALT="$IANGQUAD$"></TD>
<TD ALIGN="RIGHT"><IMG
WIDTH="64" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img119.gif"
ALT="$N_{angular}$"></TD>
<TD ALIGN="RIGHT"><IMG
WIDTH="9" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
SRC="img65.gif"
ALT="$l$"></TD>
</TR>
<TR><TD ALIGN="CENTER">1</TD>
<TD ALIGN="RIGHT">38</TD>
<TD ALIGN="RIGHT">9</TD>
</TR>
<TR><TD ALIGN="CENTER">2</TD>
<TD ALIGN="RIGHT">50</TD>
<TD ALIGN="RIGHT">11</TD>
</TR>
<TR><TD ALIGN="CENTER">3</TD>
<TD ALIGN="RIGHT">74</TD>
<TD ALIGN="RIGHT">13</TD>
</TR>
<TR><TD ALIGN="CENTER">4</TD>
<TD ALIGN="RIGHT">86</TD>
<TD ALIGN="RIGHT">15</TD>
</TR>
<TR><TD ALIGN="CENTER">5</TD>
<TD ALIGN="RIGHT">110</TD>
<TD ALIGN="RIGHT">17</TD>
</TR>
<TR><TD ALIGN="CENTER">6</TD>
<TD ALIGN="RIGHT">146</TD>
<TD ALIGN="RIGHT">19</TD>
</TR>
<TR><TD ALIGN="CENTER">7</TD>
<TD ALIGN="RIGHT">170</TD>
<TD ALIGN="RIGHT">21</TD>
</TR>
<TR><TD ALIGN="CENTER">8</TD>
<TD ALIGN="RIGHT">194</TD>
<TD ALIGN="RIGHT">23</TD>
</TR>
<TR><TD ALIGN="CENTER">9</TD>
<TD ALIGN="RIGHT">230</TD>
<TD ALIGN="RIGHT">25</TD>
</TR>
<TR><TD ALIGN="CENTER">10</TD>
<TD ALIGN="RIGHT">266</TD>
<TD ALIGN="RIGHT">27</TD>
</TR>
<TR><TD ALIGN="CENTER">11</TD>
<TD ALIGN="RIGHT">302</TD>
<TD ALIGN="RIGHT">29</TD>
</TR>
<TR><TD ALIGN="CENTER">12</TD>
<TD ALIGN="RIGHT">350</TD>
<TD ALIGN="RIGHT">31</TD>
</TR>
<TR><TD ALIGN="CENTER">13</TD>
<TD ALIGN="RIGHT">434</TD>
<TD ALIGN="RIGHT">35</TD>
</TR>
<TR><TD ALIGN="CENTER">14</TD>
<TD ALIGN="RIGHT">590</TD>
<TD ALIGN="RIGHT">41</TD>
</TR>
<TR><TD ALIGN="CENTER">15</TD>
<TD ALIGN="RIGHT">770</TD>
<TD ALIGN="RIGHT">47</TD>
</TR>
<TR><TD ALIGN="CENTER">16</TD>
<TD ALIGN="RIGHT">974</TD>
<TD ALIGN="RIGHT">53</TD>
</TR>
<TR><TD ALIGN="CENTER">17</TD>
<TD ALIGN="RIGHT">1202</TD>
<TD ALIGN="RIGHT">59</TD>
</TR>
<TR><TD ALIGN="CENTER">18</TD>
<TD ALIGN="RIGHT">1454</TD>
<TD ALIGN="RIGHT">65</TD>
</TR>
<TR><TD ALIGN="CENTER">19</TD>
<TD ALIGN="RIGHT">1730</TD>
<TD ALIGN="RIGHT">71</TD>
</TR>
<TR><TD ALIGN="CENTER">20</TD>
<TD ALIGN="RIGHT">2030</TD>
<TD ALIGN="RIGHT">77</TD>
</TR>
<TR><TD ALIGN="CENTER">21</TD>
<TD ALIGN="RIGHT">2354</TD>
<TD ALIGN="RIGHT">83</TD>
</TR>
<TR><TD ALIGN="CENTER">22</TD>
<TD ALIGN="RIGHT">2702</TD>
<TD ALIGN="RIGHT">89</TD>
</TR>
<TR><TD ALIGN="CENTER">23</TD>
<TD ALIGN="RIGHT">3074</TD>
<TD ALIGN="RIGHT">95</TD>
</TR>
<TR><TD ALIGN="CENTER">24</TD>
<TD ALIGN="RIGHT">3470</TD>
<TD ALIGN="RIGHT">101</TD>
</TR>
<TR><TD ALIGN="CENTER">25</TD>
<TD ALIGN="RIGHT">3890</TD>
<TD ALIGN="RIGHT">107</TD>
</TR>
<TR><TD ALIGN="CENTER">26</TD>
<TD ALIGN="RIGHT">4334</TD>
<TD ALIGN="RIGHT">113</TD>
</TR>
<TR><TD ALIGN="CENTER">27</TD>
<TD ALIGN="RIGHT">4802</TD>
<TD ALIGN="RIGHT">119</TD>
</TR>
<TR><TD ALIGN="CENTER">28</TD>
<TD ALIGN="RIGHT">5294</TD>
<TD ALIGN="RIGHT">125</TD>
</TR>
<TR><TD ALIGN="CENTER">29</TD>
<TD ALIGN="RIGHT">5810</TD>
<TD ALIGN="RIGHT">131</TD>
</TR>
</TABLE>
</DIV>
</TD></TR>
</TABLE>
</DIV><P></P>
<BR>
Therefore the user can specify any number of radial points along with
the level of angular quadrature (1-29).
<P>
The user can also specify grid parameters specific for a given atom type:
parameters that must be supplied are: atom tag and number of radial points.
As an example, here is a grid input line for the water molecule
<PRE>
grid lebedev 80 11 H 70 8 O 90 11
</PRE>
<P>
<H2><A NAME="SECTION001392000000000000000">
11.9.2 Partitioning functions</A>
</H2>
<P>
<PRE>
GRID [(becke||erf1||erf2||ssf) default erf1]
</PRE>
<P>
<DL>
<DT><STRONG><TT>becke</TT></STRONG></DT>
<DD>A. D. Becke, J. Chem. Phys. <B>88</B>, 1053 (1988).
</DD>
<DT><STRONG><TT>ssf</TT></STRONG></DT>
<DD>R.E.Stratmann, G.Scuseria and M.J.Frisch,
Chem. Phys. Lett. <B>257</B>, 213 (1996).
</DD>
<DT><STRONG><TT>erf1</TT></STRONG></DT>
<DD>modified ssf
</DD>
<DT><STRONG><TT>erf2</TT></STRONG></DT>
<DD>modified ssf
</DD>
</DL>
<P>
Erf<IMG
WIDTH="14" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img120.gif"
ALT="$n$"> partioning functions
<P>
<P></P>
<DIV ALIGN="CENTER">
<!-- MATH
\begin{eqnarray*}
w_A(r) & = & \prod_{B\neq A}\frac{1}{2} \left[1 \ - \
erf(\mu^\prime_{AB})\right] \\
\mu^\prime_{AB} & = & \frac{1}{\alpha} \ \frac{\mu_{AB}}{(1-\mu_{AB}^2)^n}\\
\mu_{AB} & = & \frac{{\mathbf r}_A - {\mathbf r}_B}
{\left|{\mathbf r}_A - {\mathbf r}_B \right|}
\end{eqnarray*}
-->
<IMG
WIDTH="245" HEIGHT="186" BORDER="0"
SRC="img121.gif"
ALT="\begin{eqnarray*}
w_A(r) &amp; = &amp; \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*}">
<BR CLEAR="ALL"></DIV><P></P>
<BR CLEAR="ALL"><P></P>
<BR CLEAR="ALL"><P></P>
<P>
<H2><A NAME="SECTION001393000000000000000">
11.9.3 Radial grids</A>
</H2>
<P>
<PRE>
GRID [[euler||mura||treutler] default mura]
</PRE>
<P>
<DL>
<DT><STRONG><TT>euler</TT></STRONG></DT>
<DD>Euler-McLaurin quadrature wih the transformation
devised by
C.W. Murray, N.C. Handy, and G.L. Laming,
Mol. Phys.<B>78</B>, 997 (1993).
<BR></DD>
<DT><STRONG><TT>mura</TT></STRONG></DT>
<DD>Modification of the Murray-Handy-Laming scheme by
M.E.Mura and P.J.Knowles, J Chem Phys <B>104</B>, 9848
(1996) (we are not using the scaling factors proposed
in this paper).
<BR></DD>
<DT><STRONG><TT>treutler</TT></STRONG></DT>
<DD>Gauss-Chebyshev using the transformation suggested
by O.Treutler and R.Alrhichs, J.Chem.Phys <B>102</B>, 346 (1995).
<BR></DD>
</DL>
<P>
<H2><A NAME="SECTION001394000000000000000">
11.9.4 Disk usage for Grid</A>
</H2>
<P>
<PRE>
NODISK
</PRE>
<P>
This keyword turns off storage of grid points and weights on disk.
<P>
<H1><A NAME="SECTION0013100000000000000000">
11.10 <TT>TOLERANCES</TT> -- Screening tolerances</A>
</H1>
<P>
<PRE>
TOLERANCES [[tight] [tol_rho &lt;real tol_rho default 1e-10&gt;] \
[accCoul &lt;integer accCoul default 8&gt;] \
[radius &lt;real radius default 25.0&gt;]]
</PRE>
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.
<P>
The input
parameter <TT>accCoul</TT> is used to define the tolerance in Schwarz
screening for the Coulomb integrals. Only integrals with estimated
values greater than <!-- MATH
$10^{(-{\tt accCoul})}$
-->
<IMG
WIDTH="82" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
SRC="img122.gif"
ALT="$10^{(-{\tt accCoul})}$"> are evaluated.
<P>
<PRE>
TOLERANCES accCoul &lt;integer accCoul default 8&gt;
</PRE>
<P>
Screening away needless computation of the XC functional (on the grid)
due to negligible density is also possible with the use of,
<PRE>
TOLERANCES tol_rho &lt;real tol_rho default 1e-10&gt;
</PRE>
XC functional computation is bypassed if the corresponding density
elements are less than <code>tol_rho</code>.
<P>
A screening parameter, <code>radius</code>, used in the screening of the
Becke or Delley spatial weights is also available as,
<PRE>
TOLERANCES radius &lt;real radius default 25.0&gt;
</PRE>
where radius is the cutoff value in bohr.
<P>
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 <code>tight</code> option:
<P>
<PRE>
TOLERANCES tight
</PRE>
<P>
This option sets all tolerances to their
default/user specified values at the very first iteration.
<P>
<H1><A NAME="SECTION0013110000000000000000">
11.11 <TT>DIRECT</TT> and <TT>NOIO</TT> -- Hardware Resource Control</A>
</H1>
<PRE>
DIRECT||INCORE
NOIO
</PRE>
<P>
<P>
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 <code>noio</code> within the
input for the DFT directive. The input to exercise this option is
as follows,
<PRE>
noio
</PRE>
If this keyword is encountered, then the two matrices (inverted
charge-density and exchange-correlation) are computed ``on-the-fly''
whenever needed.
<P>
The <code>INCORE</code> option is always assumed to be true but can be
overridden with the option <code>DIRECT</code> in which case all integrals
are computed ``on-the-fly''.
<P>
<P>
<H1><A NAME="SECTION0013120000000000000000">
11.12 <TT>ODFT</TT> and <TT>MULT</TT> -- Open shell systems</A>
</H1>
<PRE>
ODFT
MULT &lt;integer mult default 1&gt;
</PRE>
<P>
Both <I>closed-shell</I> and <I>open-shell</I> systems can be studied using
the DFT module. Specifying the keyword <code>MULT</code> within the <code>DFT</code>
directive allows the user to define the spin multiplicity of the system.
The form of the input line is as follows;
<PRE>
MULT &lt;integer mult default 1&gt;
</PRE>
When the keyword <code>MULT</code> is specified, the user can define the integer
variable <code>mult</code>, where <code>mult</code> is equal to the number of alpha
electrons minus beta electrons, plus 1.
<P>
The keyword <code>ODFT</code> is unnecessary except in the context
of forcing a singlet system to be computed as an open shell
system (i.e., using a spin-unrestricted wavefunction).
<P>
<H1><A NAME="SECTION0013130000000000000000">
11.13 <TT>SIC</TT> -- Self-Interaction Correction</A>
</H1>
<P>
<PRE>
sic [perturbative || oep || oep-loc &lt;default perturbative&gt;]
</PRE>
<P>
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. <B>90</B>, 317 (1953),
J. D. Talman and W. F. Shadwick, Phys. Rev. A <B>14</B>, 36 (1976))
within the Krieger-Li-Iafrate approximation (J. B. Krieger, Y. Li,
and G. J. Iafrate, Phys. Rev. A <B>45</B>, 101 (1992); <B>46</B>, 5453 (1992);
47, 165 (1993))
Three variants of these methods are included in NWChem:
<UL>
<LI><TT>sic perturbative</TT> This is the default option for the sic
directive. After a self-consistent calculation, the Kohn-Sham
orbitals are localized with the Foster-Boys algorithm (see section
<A HREF="node12.html#orbloc">10.15</A>) and the self-interaction energy is added to the total energy.
All exchange-correlation functionals implemented in the NWChem can be
used with this option.
</LI>
<LI><TT>sic oep</TT> With this option the optimized effective potential is
built in each step of the self-consistent process. Because the electrostatic
potential generated for each orbital involves a numerical
integration, this method can be expensive.
</LI>
<LI><TT>sic oep-loc</TT>
This option is similar to the oep option with the
addition of localization of the Kohn-Sham orbitals in each step of the
self-consistent process.
</LI>
</UL>
With oep and oep-loc options a <B>xfine grid</B> (see section <A HREF="node13.html#grgrid">11.9</A>)
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:
<P>
<PRE>
print "SIC information"
</PRE>
<P>
<H1><A NAME="SECTION0013140000000000000000">
11.14 <TT>MULLIKEN</TT> -- Mulliken analysis</A>
</H1>
Mulliken analysis of the charge distribution is invoked by the keyword:
<PRE>
MULLIKEN
</PRE>
When this keyword is encountered, Mulliken analysis of both the input
density as well as the output density will occur.
For example, to perform a mulliken analysis and print the
explicit population analysis of the basis functions, use
the following
<PRE>
dft
mulliken
print "mulliken ao"
end
task dft
</PRE>
<P>
<H1><A NAME="SECTION0013150000000000000000">
11.15 <TT>BSSE</TT> -- Basis Set Superposition Error</A>
</H1>
<P>
Particular care is required to compute BSSE by the counter-poise
method for the DFT module. In order to include terms deriving from
the numerical grid used in the XC integration, the user must label
the ghost atoms not just <TT>bq</TT>, but <TT>bq</TT> followed by the given
atomic symbol. For example, the first component needed to compute the
BSSE for the water dimer, should be written as follows
<P>
<PRE>
geometry h2o autosym units au
O 0.00000000 0.00000000 0.22143139
H 1.43042868 0.00000000 -0.88572555
H -1.43042868 0.00000000 -0.88572555
bqH 0.71521434 0.00000000 -0.33214708
bqH -0.71521434 0.00000000 -0.33214708
bqO 0.00000000 0.00000000 -0.88572555
end
basis
H library aug-cc-pvdz
O library aug-cc-pvdz
bqH library H aug-cc-pvdz
bqO library O aug-cc-pvdz
end
</PRE>
<P>
Please note that the ``ghost'' oxygen atom has been labeled <TT>bqO</TT>,
and not just <TT>bq</TT>.
<H1><A NAME="SECTION0013160000000000000000">
11.16 Print Control</A>
</H1>
<PRE>
PRINT||NOPRINT
</PRE>
<P>
The <code>PRINT||NOPRINT</code> options control the level of output in the
DFT. Please see some examples using this directive in
section <A HREF="node13.html#sec:DFTsample">11.5</A>, a sample input file.
Known controllable print options are:
<P>
<BR><P></P>
<DIV ALIGN="CENTER"><A NAME="3418"></A>
<TABLE>
<CAPTION><STRONG>Table 11.7:</STRONG>
DFT Print Control Specifications</CAPTION>
<TR><TD>
<DIV ALIGN="CENTER">
<TABLE CELLPADDING=3 ALIGN="CENTER">
<TR><TD ALIGN="LEFT"><B>Name</B></TD>
<TD ALIGN="CENTER"><B>Print Level</B></TD>
<TD ALIGN="CENTER"><B>Description</B></TD>
</TR>
<TR><TD ALIGN="LEFT">``all vector symmetries''</TD>
<TD ALIGN="CENTER">high</TD>
<TD ALIGN="CENTER">symmetries of all molecular orbitals</TD>
</TR>
<TR><TD ALIGN="LEFT">``alpha partner info''</TD>
<TD ALIGN="CENTER">high</TD>
<TD ALIGN="CENTER">unpaired alpha orbital analysis</TD>
</TR>
<TR><TD ALIGN="LEFT">``common''</TD>
<TD ALIGN="CENTER">debug</TD>
<TD ALIGN="CENTER">dump of common blocks</TD>
</TR>
<TR><TD ALIGN="LEFT">``convergence''</TD>
<TD ALIGN="CENTER">default</TD>
<TD ALIGN="CENTER">convergence of SCF procedure</TD>
</TR>
<TR><TD ALIGN="LEFT">``coulomb fit''</TD>
<TD ALIGN="CENTER">high</TD>
<TD ALIGN="CENTER">fitting electronic charge density</TD>
</TR>
<TR><TD ALIGN="LEFT">``dft timings''</TD>
<TD ALIGN="CENTER">high</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
</TR>
<TR><TD ALIGN="LEFT">``final vectors''</TD>
<TD ALIGN="CENTER">high</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
</TR>
<TR><TD ALIGN="LEFT">``final vector symmetries''</TD>
<TD ALIGN="CENTER">default</TD>
<TD ALIGN="CENTER">symmetries of final molecular orbitals</TD>
</TR>
<TR><TD ALIGN="LEFT">``information''</TD>
<TD ALIGN="CENTER">low</TD>
<TD ALIGN="CENTER">general information</TD>
</TR>
<TR><TD ALIGN="LEFT">``initial vectors''</TD>
<TD ALIGN="CENTER">high</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
</TR>
<TR><TD ALIGN="LEFT">``intermediate energy info''</TD>
<TD ALIGN="CENTER">high</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
</TR>
<TR><TD ALIGN="LEFT">``intermediate evals''</TD>
<TD ALIGN="CENTER">high</TD>
<TD ALIGN="CENTER">intermediate orbital energies</TD>
</TR>
<TR><TD ALIGN="LEFT">``intermediate fock matrix''</TD>
<TD ALIGN="CENTER">high</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
</TR>
<TR><TD ALIGN="LEFT">``intermediate overlap''</TD>
<TD ALIGN="CENTER">high</TD>
<TD ALIGN="CENTER">overlaps between the alpha and beta sets</TD>
</TR>
<TR><TD ALIGN="LEFT">``intermediate S2''</TD>
<TD ALIGN="CENTER">high</TD>
<TD ALIGN="CENTER">values of S2</TD>
</TR>
<TR><TD ALIGN="LEFT">``intermediate vectors''</TD>
<TD ALIGN="CENTER">high</TD>
<TD ALIGN="CENTER">intermediate molecular orbitals</TD>
</TR>
<TR><TD ALIGN="LEFT">``interm vector symm''</TD>
<TD ALIGN="CENTER">high</TD>
<TD ALIGN="CENTER">symmetries of intermediate orbitals</TD>
</TR>
<TR><TD ALIGN="LEFT">``io info''</TD>
<TD ALIGN="CENTER">debug</TD>
<TD ALIGN="CENTER">reading from and writing to disk</TD>
</TR>
<TR><TD ALIGN="LEFT">``kinetic_energy''</TD>
<TD ALIGN="CENTER">high</TD>
<TD ALIGN="CENTER">kinetic energy</TD>
</TR>
<TR><TD ALIGN="LEFT">``mulliken ao''</TD>
<TD ALIGN="CENTER">high</TD>
<TD ALIGN="CENTER">mulliken atomic orbital population</TD>
</TR>
<TR><TD ALIGN="LEFT">``multipole''</TD>
<TD ALIGN="CENTER">default</TD>
<TD ALIGN="CENTER">moments of alpha, beta, and nuclear charge densities</TD>
</TR>
<TR><TD ALIGN="LEFT">``parameters''</TD>
<TD ALIGN="CENTER">default</TD>
<TD ALIGN="CENTER">input parameters</TD>
</TR>
<TR><TD ALIGN="LEFT">``quadrature''</TD>
<TD ALIGN="CENTER">high</TD>
<TD ALIGN="CENTER">numerical quadrature</TD>
</TR>
<TR><TD ALIGN="LEFT">``schwarz''</TD>
<TD ALIGN="CENTER">high</TD>
<TD ALIGN="CENTER">integral screening info &amp; stats at completion</TD>
</TR>
<TR><TD ALIGN="LEFT">``screening parameters''</TD>
<TD ALIGN="CENTER">high</TD>
<TD ALIGN="CENTER">integral accuracies</TD>
</TR>
<TR><TD ALIGN="LEFT">``semi-direct info''</TD>
<TD ALIGN="CENTER">default</TD>
<TD ALIGN="CENTER">semi direct algorithm</TD>
</TR>
</TABLE>
</DIV>
</TD></TR>
</TABLE>
</DIV><P></P>
<BR>
<P>
<P>
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<ADDRESS>
Edoardo Apra
2004-05-25
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