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1749 lines
70 KiB
TeX
1749 lines
70 KiB
TeX
%
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% $Id$
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%
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\label{sec:dft}
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The NWChem density functional theory (DFT) module uses the
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Gaussian basis set approach to compute
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closed shell and open shell densities and Kohn-Sham orbitals
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in the:
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\begin{itemize}
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\item local density approximation (LDA),
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\item non-local density approximation (NLDA),
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\item local spin-density approximation (LSD),
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\item non-local spin-density approximation (NLSD),
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\item non-local meta-GGA approximation (metaGGA),
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\item any empirical mixture of local and non-local approximations
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(including exact exchange), and
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\item asymptotically corrected exchange-correlation potentials.
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\end{itemize}
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The formal scaling of the DFT computation can be reduced by choosing
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to use auxiliary Gaussian basis sets to fit the charge density (CD) and/or
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fit the exchange-correlation (XC) potential.
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DFT input is provided using the compound \verb+DFT+ directive
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\begin{verbatim}
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DFT
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...
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END
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\end{verbatim}
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The actual DFT calculation will be performed when the input module
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encounters the \verb+TASK+ directive (Section \ref{sec:task}).
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\begin{verbatim}
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TASK DFT
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\end{verbatim}
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Once a user has specified a geometry and a Kohn-Sham orbital basis set
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the DFT module can be invoked with no input directives (defaults
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invoked throughout). There are sub-directives which allow for
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customized application; those currently provided as options for
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the DFT module are:
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\begin{verbatim}
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VECTORS [[input] (<string input_movecs default atomic>) || \
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(project <string basisname> <string filename>)] \
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[swap [alpha||beta] <integer vec1 vec2> ...] \
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[output <string output_filename default input_movecs>] \
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XC [[acm] [b3lyp] [beckehandh] [pbe0]\
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[becke97] [becke97-1] [becke97-2] [becke97-3] [becke97-d] [becke98] \
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[hcth] [hcth120] [hcth147]\
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[hcth407] [becke97gga1] [hcth407p]\
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[mpw91] [mpw1k] [xft97] [cft97] [ft97] [op] [bop] [pbeop]\
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[xpkzb99] [cpkzb99] [xtpss03] [ctpss03] [xctpssh]\
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[b1b95] [bb1k] [mpw1b95] [mpwb1k] [pw6b95] [pwb6k] [m05] [m05-2x] [vs98] \
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[m06] [m06-hf] [m06-L] [m06-2x] \
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[HFexch <real prefactor default 1.0>] \
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[becke88 [nonlocal] <real prefactor default 1.0>] \
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[xperdew91 [nonlocal] <real prefactor default 1.0>] \
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[xpbe96 [nonlocal] <real prefactor default 1.0>] \
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[gill96 [nonlocal] <real prefactor default 1.0>] \
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[lyp <real prefactor default 1.0>] \
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[perdew81 <real prefactor default 1.0>] \
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[perdew86 [nonlocal] <real prefactor default 1.0>] \
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[perdew91 [nonlocal] <real prefactor default 1.0>] \
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[cpbe96 [nonlocal] <real prefactor default 1.0>] \
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[pw91lda <real prefactor default 1.0>] \
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[slater <real prefactor default 1.0>] \
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[vwn_1 <real prefactor default 1.0>] \
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[vwn_2 <real prefactor default 1.0>] \
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[vwn_3 <real prefactor default 1.0>] \
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[vwn_4 <real prefactor default 1.0>] \
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[vwn_5 <real prefactor default 1.0>] \
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[vwn_1_rpa <real prefactor default 1.0>] \
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[xtpss03 [nonlocal] <real prefactor default 1.0>] \
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[ctpss03 [nonlocal] <real prefactor default 1.0>] \
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[bc95 [nonlocal] <real prefactor default 1.0>] \
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[xpw6b95 [nonlocal] <real prefactor default 1.0>] \
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[xpwb6k [nonlocal] <real prefactor default 1.0>] \
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[xm05 [nonlocal] <real prefactor default 1.0>] \
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[xm05-2x [nonlocal] <real prefactor default 1.0>] \
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[cpw6b95 [nonlocal] <real prefactor default 1.0>] \
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[cpwb6k [nonlocal] <real prefactor default 1.0>] \
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[cm05 [nonlocal] <real prefactor default 1.0>] \
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[cm05-2x [nonlocal] <real prefactor default 1.0>]] \
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[xvs98 [nonlocal] <real prefactor default 1.0>]] \
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[cvs98 [nonlocal] <real prefactor default 1.0>]] \
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[xm06-L [nonlocal] <real prefactor default 1.0>]] \
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[xm06-hf [nonlocal] <real prefactor default 1.0>]] \
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[xm06 [nonlocal] <real prefactor default 1.0>]] \
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[xm06-2x [nonlocal] <real prefactor default 1.0>]] \
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[cm06-L [nonlocal] <real prefactor default 1.0>]] \
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[cm06-hf [nonlocal] <real prefactor default 1.0>]] \
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[cm06 [nonlocal] <real prefactor default 1.0>]] \
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[cm06-2x [nonlocal] <real prefactor default 1.0>]]
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CONVERGENCE [[energy <real energy default 1e-7>] \
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[density <real density default 1e-5>] \
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[gradient <real gradient default 5e-4>] \
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[dampon <real dampon default 0.0>] \
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[dampoff <real dampoff default 0.0>] \
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[diison <real diison default 0.0>] \
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[diisoff <real diisoff default 0.0>] \
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[levlon <real levlon default 0.0>] \
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[levloff <real levloff default 0.0>] \
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[ncydp <integer ncydp default 2>] \
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[ncyds <integer ncyds default 30>] \
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[ncysh <integer ncysh default 30>] \
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[damp <integer ndamp default 0>] [nodamping] \
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[diis [nfock <integer nfock default 10>]] \
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[nodiis] [lshift <real lshift default 0.5>] \
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[nolevelshifting] \
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[hl_tol <real hl_tol default 0.1>] \
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[rabuck [n_rabuck <integer n_rabuck default 25>]]
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GRID [(xcoarse||coarse||medium||fine||xfine) default medium] \
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[(gausleg||lebedev ) default lebedev ] \
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[(becke||erf1||erf2||ssf) default erf1] \
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[(euler||mura||treutler) default mura] \
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[rm <real rm default 2.0>] \
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[nodisk]
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TOLERANCES [[tight] [tol_rho <real tol_rho default 1e-10>] \
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[accCoul <integer accCoul default 8>] \
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[radius <real radius default 25.0>]]
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[(LB94||CS00 <real shift default none>)]
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DECOMP
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ODFT
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DIRECT
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SEMIDIRECT [filesize <integer filesize default disksize>]
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[memsize <integer memsize default available>]
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[filename <string filename default $file_prefix.aoints$>]
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INCORE
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ITERATIONS <integer iterations default 30>
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MAX_OVL
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MULLIKEN
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DISP
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MULT <integer mult default 1>
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NOIO
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PRINT||NOPRINT
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\end{verbatim}
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% [accCDfunc <integer accAOfunc default 20>] \
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% [store_wght] [nquad_task <integer nquad_task default 1>] \
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The following
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sections describe these keywords and
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optional sub-directives that can be specified for a \verb+DFT+ calculation
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in NWChem.
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\section{Specification of Basis Sets for the DFT Module}
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The DFT module requires at a minimum the basis set for the Kohn-Sham
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molecular orbitals. This basis set must be in the default basis set named
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{\tt "ao basis"}, or it must be assigned to this default name using the
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\verb+SET+ directive (see Section \ref{sec:set}).
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In addition to the basis set for the Kohn-Sham orbitals,
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the charge density fitting basis set can also be specified in the
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input directives for the DFT module. This basis set is used for the
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evaluation of the Coulomb potential in the Dunlap scheme\footnote{B.I.~Dunlap,
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J.W.D.~Connolly and J.R.~Sabin, J.~Chem.~Phys.~{\bf 71}, 4993 (1979)}.
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The charge density fitting basis set must have the name {\tt "cd basis"}.
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This can be the actual name of a basis set, or a basis set can be
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assigned this name using the \verb+SET+ directive, as described in
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Section \ref{sec:set}. If this basis set is not defined by input,
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the $O(N^4)$ exact Coulomb contribution is computed.
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The user also has the option of specifying a third basis set for the
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evaluation of the exchange-correlation potential. This basis set must
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have the name {\tt "xc basis"}. If this basis set is not specified
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by input, the exchange contribution (XC) is evaluated by numerical
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quadrature. In most applications, this approach is efficient enough,
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so the {\tt "xc basis"} basis set is not generally required.
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For the DFT module, the input options for defining the basis sets in a given
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calculation can be summarized as follows;
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\begin{itemize}
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\item {\tt "ao basis"} -- Kohn-Sham molecular orbitals; required for all
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calculations
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\item {\tt "cd basis"} -- charge density fitting basis set; optional, but
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recommended for evaluation of the Coulomb potential
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\item {\tt "xc basis"} -- exchange-correlation (XC) fitting basis set;
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optional, and usually not recommended
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\end{itemize}
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\section{{\tt VECTORS} and {\tt MAX\_OVL} --- KS-MO Vectors}
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The \verb+VECTORS+ directive is the same as that in the SCF module
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(Section \ref{sec:vectors}). Currently, the \verb+LOCK+ keyword
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is not supported by the DFT module, however the directive
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\begin{verbatim}
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MAX_OVL
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\end{verbatim}
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has the same effect.
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\section{{\tt XC} and {\tt DECOMP} --- Exchange-Correlation Potentials}
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\label{sec:xc}
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\begin{verbatim}
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XC [[acm] [b3lyp] [beckehandh] [pbe0]\
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[becke97] [becke97-1] [becke97-2] [becke97-3] [becke98] [hcth] [hcth120] [hcth147] \
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[hcth407] [becke97gga1] [hcth407p] \
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[optx] [hcthp14] [mpw91] [mpw1k] [xft97] [cft97] [ft97] [op] [bop] [pbeop]\
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[HFexch <real prefactor default 1.0>] \
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[becke88 [nonlocal] <real prefactor default 1.0>] \
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[xperdew91 [nonlocal] <real prefactor default 1.0>] \
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[xpbe96 [nonlocal] <real prefactor default 1.0>] \
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[gill96 [nonlocal] <real prefactor default 1.0>] \
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[lyp <real prefactor default 1.0>] \
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[perdew81 <real prefactor default 1.0>] \
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[perdew86 [nonlocal] <real prefactor default 1.0>] \
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[perdew91 [nonlocal] <real prefactor default 1.0>] \
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[cpbe96 [nonlocal] <real prefactor default 1.0>] \
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[pw91lda <real prefactor default 1.0>] \
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[slater <real prefactor default 1.0>] \
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[vwn_1 <real prefactor default 1.0>] \
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[vwn_2 <real prefactor default 1.0>] \
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[vwn_3 <real prefactor default 1.0>] \
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[vwn_4 <real prefactor default 1.0>] \
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[vwn_5 <real prefactor default 1.0>] \
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[vwn_1_rpa <real prefactor default 1.0>]]
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\end{verbatim}
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The user has the option of specifying the exchange-correlation
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treatment in the DFT Module (see table \ref{tablexc}).
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The default exchange-correlation
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functional is defined as the local density approximation (LDA) for
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closed shell systems and its counterpart the local spin-density (LSD)
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approximation for open shell systems. Within this approximation the
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exchange functional is the Slater $\rho^{1/3}$ functional (from
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J.C.~Slater, {\sl Quantum Theory of Molecules and Solids, Vol.~4: The
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Self-Consistent Field for Molecules and Solids} (McGraw-Hill, New
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York, 1974)), and the correlation functional is the Vosko-Wilk-Nusair
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(VWN) functional (functional V) (S.J.~Vosko, L.~Wilk and M.~Nusair,
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Can.~J.~Phys.~{\bf 58}, 1200 (1980)). The parameters used in this
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formula are obtained by fitting to the Ceperley and
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Alder\footnote{D.M.~Ceperley and B.J.~Alder, Phys. Rev. Lett. {\bf
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45}, 566 (1980).}
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Quantum Monte-Carlo solution of the {\em
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homogeneous electron gas}.
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These defaults can be invoked explicitly by specifying the following
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keywords within the DFT module input directive, \verb+XC slater vwn_5+.
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That is, this statement in the input file
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\begin{verbatim}
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dft
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XC slater vwn_5
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end
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task dft
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\end{verbatim}
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is equivalent to the simple line
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\begin{verbatim}
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task dft
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\end{verbatim}
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The \verb+DECOMP+ directive causes the components of the energy
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corresponding to each functional to be printed, rather than just the
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total exchange-correlation energy which is the default. You can see
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an example of this directive in the sample input in
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Section \ref{sec:DFTsample}.
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Many alternative exchange and correlation functionals are available to
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the user as listed in table \ref{tablexc}. The following sections describe
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how to use these options.
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\subsection{Exchange-Correlation Functionals}
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There are several Exchange and Correlation functionals in addition to the
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default {\tt slater} and {\tt vwn\_5}
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functionals. These are either local or gradient-corrected functionals (GCA);
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a full list can be found in table \ref{tablexc}.
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%\begin{itemize}
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%
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%\item the Becke 1998 gradient-corrected functional (see A.D.~Becke,
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% Phys. Rev. A {\bf 38}, 3098 (1988)), is invoked by specifying
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%
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%\begin{verbatim}
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% XC becke88
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%\end{verbatim}
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%
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%\item the Perdew 1991 gradient-corrected exchange functional (J.P. Perdew,
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% J.A.~Chevary, S.H.~Vosko, K.A.~Jackson, M.R.~Pederson, D.J.~Singh
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% and C.~Fiolhais, Phys. Rev. B {\bf 46}, 6671 (1992)), is invoked by specifying
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%
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%\begin{verbatim}
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% XC xperdew91
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%\end{verbatim}
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%
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%\item the Perdew-Burke-Ernzerhof gradient-corrected exchange functional \\
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% (J.P.~Perdew, K.~Burke and M.~Ernzerhof, Physical Review Letters
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%{\bf 77}, 3865 (1996); {\bf 78}, 1396 (1997))), is invoked by specifying
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%
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%\begin{verbatim}
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% XC xpbe96
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%\end{verbatim}
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%
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%\item the Gill 1996 gradient-corrected exchange functional (P.W.Gill , Mol. Phys. {\bf 89}, 433 (1996)), is invoked by specifying
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%
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%\begin{verbatim}
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% XC gill96
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%\end{verbatim}
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%\item
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The Hartree-Fock exact exchange functional, (which has $O(N^4)$
|
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computation expense), is invoked by specifying
|
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\begin{verbatim}
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XC HFexch
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\end{verbatim}
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%\end{itemize}
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Note that the user also has the ability to include only the local or
|
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nonlocal contributions of a given functional. In addition the user
|
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can specify a multiplicative prefactor (the variable
|
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\verb+<prefactor>+ in the input) for the local/nonlocal component or
|
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total. An example of this might be,
|
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\begin{verbatim}
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XC becke88 nonlocal 0.72
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\end{verbatim}
|
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The user should be aware that the Becke88 local component is simply
|
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the Slater exchange and should be input as such.
|
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Any combination of the supported exchange functional options can be
|
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used. For example the popular Gaussian B3 exchange could be specified
|
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as:
|
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\begin{verbatim}
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XC slater 0.8 becke88 nonlocal 0.72 HFexch 0.2
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\end{verbatim}
|
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|
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%\subsection{Correlation Functionals}
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%In addition to the default \verb+vwn_5+ correlation functional, the user has
|
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%alternative correlation functionals as listed in table \ref{tablexc}.
|
|
%to choose from: lyp, perdew81,
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|
%perdew86, perdew91, pw91lda, \verb+vwn_1+, \verb+vwn_2+, \verb+vwn_3+,
|
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%\verb+vwn_4+, and \verb+vwn_1_rpa+.
|
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|
|
%As in the exchange functional input, individual local/nonlocal
|
|
%components as well as multiplicative prefactors can be invoked where
|
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%appropriate. Each of the correlation functionals is listed below along with
|
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%appropriate citation in table \ref{tablexc}.
|
|
|
|
\sloppy
|
|
|
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%\begin{itemize}
|
|
%\item VWN local density functionals; S.J.~Vosko, L.~Wilk and M.~Nusair,
|
|
% Can.~J.~Phys.~{\bf 58}, 1200 (1980); all five (5) functionals as
|
|
% described in this paper (addressed in the paper as I - V) have been
|
|
% implemented. These functionals can be invoked with the keywords:
|
|
%\begin{verbatim}
|
|
% XC vwn_1
|
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% XC vwn_2
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% XC vwn_3
|
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% XC vwn_4
|
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% XC vwn_5
|
|
%\end{verbatim}
|
|
%
|
|
% Note that functionals; \verb+vwn_2+, \verb+vwn_3+, and \verb+vwn_4+
|
|
% require both sets of parameters (the Monte Carlo parameters of
|
|
% Ceperley and Alder and VWN's RPA parameters) used in fitting the
|
|
% homogeneous electron gas correlation energy. Functionals
|
|
% \verb+vwn_1+ and \verb+vwn_5+ require only the Monte Carlo fitting
|
|
% parameters. In order to reproduce results in the literature another
|
|
% functional was added; the \verb+vwn_1_rpa+. This is the original
|
|
% \verb+vwn_1+ functional with RPA parameters as opposed to the
|
|
% prescribed Monte Carlo parameters. This functional can be invoked
|
|
% with the keyword,
|
|
%\begin{verbatim}
|
|
% XC vwn_1_rpa
|
|
%\end{verbatim}
|
|
%
|
|
%\item Perdew81 local density functional; J.~P.~Perdew and A.~Zunger,
|
|
% Phys.~Rev.~B {\bf23}, 5048 (1981). This functional can be invoked with the
|
|
% keyword,
|
|
%\begin{verbatim}
|
|
% XC perdew81
|
|
%\end{verbatim}
|
|
%
|
|
%\item Perdew \& Wang 1991 local density functional; J.P.~Perdew
|
|
% and Y.~Wang, Phys. Rev. B {\bf 45}, 13244 (1992). The parameters
|
|
% used in this formula are obtained by fitting to the Ceperley and
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|
% Alder Quantum Monte Carlo solution of the {\em
|
|
% homogeneous electron gas}. This functional can be invoked with the
|
|
% keyword,
|
|
%\begin{verbatim}
|
|
% XC pw91lda
|
|
%\end{verbatim}
|
|
%
|
|
%\item Perdew86 gradient-corrected functional; J.~P.~Perdew, Phys.~Rev.~B
|
|
% {\bf33}, 8822 (1986). Note that this is a nonlocal functional and
|
|
% in the absence of any local functional specification the local
|
|
% component is defaulted to the perdew81 local correlation
|
|
% functional. This functional can be invoked with the
|
|
% keyword,
|
|
%\begin{verbatim}
|
|
% XC perdew86
|
|
%\end{verbatim}
|
|
%
|
|
%\item Perdew91 gradient-corrected functional; J.P.~Perdew,
|
|
% J.A.~Chevary, S.H.~Vosko, K.A.~Jackson, M.R.~Pederson, D.J.~Singh
|
|
% and C.~Fiolhais, Phys. Rev. B {\bf 46}, 6671 (1992). Note that this
|
|
% is a nonlocal functional and in the absence of any local functional
|
|
% specification the local component is defaulted to the \verb+pw91lda+ local
|
|
% correlation functional. This functional can be invoked with the keyword,
|
|
%\begin{verbatim}
|
|
% XC perdew91
|
|
%\end{verbatim}
|
|
%
|
|
%\item the Perdew-Burke-Ernzerhof gradient-corrected correlation functional \\
|
|
% (J.P.~Perdew, K.~Burke and M.~Ernzerhof, Physical Review Letters
|
|
%{\bf 77}, 3865 (1996); {\bf 78}, 1396 (1997))), is invoked by specifying
|
|
%
|
|
%\begin{verbatim}
|
|
% XC cpbe96
|
|
%\end{verbatim}
|
|
|
|
%\item LYP gradient-corrected functional; C.~Lee, W.~Yang and
|
|
% R.~G.~Parr, Phys.~Rev.~B {\bf 37}, 785 (1988). Note that this
|
|
% is a local and nonlocal functional but cannot be conveniently split
|
|
% into the individual components. The option to scale the total remains.
|
|
% This functional can be invoked with the keyword,
|
|
%\begin{verbatim}
|
|
% XC lyp
|
|
%\end{verbatim}
|
|
%
|
|
%\end{itemize}
|
|
|
|
\fussy
|
|
|
|
Any combination of the supported correlation functional options can be
|
|
used. For example B3LYP could be specified as:
|
|
\begin{verbatim}
|
|
XC vwn_1_rpa 0.19 lyp 0.81 HFexch 0.20 slater 0.80 becke88 nonlocal 0.72
|
|
\end{verbatim}
|
|
and X3LYP as:
|
|
\begin{verbatim}
|
|
xc vwn_1_rpa 0.129 lyp 0.871 hfexch 0.218 slater 0.782 \
|
|
becke88 nonlocal 0.542 xperdew91 nonlocal 0.167
|
|
\end{verbatim}
|
|
|
|
|
|
\subsection{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. A complete list of the available functionals
|
|
appears in table \ref{tablexc}.
|
|
|
|
The available hybrid functionals
|
|
(where a Hartree-Fock Exchange component is present) consist of the Becke
|
|
``{\it 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., {\bf 107}, 8554 (1997)).
|
|
|
|
%These options can be invoked by specifying any of the following input lines,
|
|
%\begin{verbatim}
|
|
% XC beckehandh
|
|
% XC acm
|
|
% XC b3lyp
|
|
% XC becke97
|
|
% Xc becke97-1
|
|
% xc becke98
|
|
% xc pbe0
|
|
% xc hcth
|
|
% xc hcth120
|
|
% xc hcth147
|
|
% xc hcth407
|
|
% xc hcthp14
|
|
% xc becke97gga1
|
|
%\end{verbatim}
|
|
|
|
The keyword \verb+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.
|
|
|
|
%\clearpage
|
|
%
|
|
|
|
The keyword \verb+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} +
|
|
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*}
|
|
and $\Delta$ stands for a non-local component.
|
|
|
|
|
|
The keyword \verb+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} +
|
|
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*}
|
|
|
|
|
|
%The keyword \verb+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. {\bf 109}, 6264 (1998))
|
|
%
|
|
%The keyword \verb+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. {\bf 109}, 6264 (1998))
|
|
|
|
|
|
|
|
\subsection{Meta-GGA Functionals}
|
|
|
|
|
|
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.
|
|
|
|
It is possible to calculate metaGGA energies both ways
|
|
in NWChem, that is, self-consistently or with
|
|
GGA/LDA orbitals and densities. However, since second derivatives
|
|
are not available for metaGGAs, in order to
|
|
calculate frequencies, one must use
|
|
\verb+ task dft freq numerical+.
|
|
A sample file with this is shown below,
|
|
in \ref{sec:DFTsample}. In this instance, the
|
|
energy is calculated self-consistently and geometry is optimized using the analytical gradients.
|
|
|
|
|
|
(For more information on metaGGAs, 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 )
|
|
|
|
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.
|
|
|
|
|
|
\section{{\tt LB94} and {\tt CS00} --- Asymptotic correction}
|
|
|
|
The keyword \verb+LB94+ will correct the asymptotic region of
|
|
the \verb+XC+ definition of exchange-correlation {\it potential} by
|
|
the van-Leeuwen--Baerends exchange-correlation {\it potential} that
|
|
has the correct $-1/r$ asymptotic behavior. The total energy will be computed by the
|
|
\verb+XC+ definition of exchange-correlation functional. This scheme is known to
|
|
tend to overcorrect the deficiency of most uncorrected exchange-correlation potentials.
|
|
|
|
The keyword \verb+CS00+, 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).
|
|
|
|
When the keyword \verb+CS00+ 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.
|
|
|
|
Sample input files of asymptotically corrected TDDFT calculations can be found in
|
|
Chapter 14.
|
|
|
|
\section{Sample input file}
|
|
\label{sec:DFTsample}
|
|
A simple example calculates the geometry
|
|
of water, using the metaGGA functionals
|
|
\verb+ xtpss03+ and \verb+ctpss03+.
|
|
This also highlights some of
|
|
the print features in the DFT module. Note
|
|
that you must use the line
|
|
\verb+task dft freq numerical+ because
|
|
analytic hessians are not available for the metaGGAs:
|
|
\begin{verbatim}
|
|
title "WATER 6-311G* meta-GGA XC geometry"
|
|
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
|
|
iterations 50
|
|
print kinetic_energy
|
|
xc xtpss03 ctpss03
|
|
decomp
|
|
end
|
|
task dft optimize
|
|
|
|
task dft freq numerical
|
|
\end{verbatim}
|
|
|
|
|
|
|
|
|
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
\twocolumn
|
|
\begin{table}[htp]
|
|
\centering
|
|
{\scriptsize
|
|
\begin{tabular}{|l|p{0.12cm}p{0.12cm}cccp{0.35cm}|c|}
|
|
\hline
|
|
Keyword & X & C & GGA & Meta & Hybr. & 2nd & Ref.\\
|
|
\hline
|
|
{\tt slater }& $\star$ & & & & & Y &[1] \\
|
|
\hline
|
|
{\tt vwn\_1 }& & $\star$ & & & & Y &[2] \\
|
|
{\tt vwn\_2 }& & $\star$ & & & & Y &[2] \\
|
|
{\tt vwn\_3 }& & $\star$ & & & & Y &[2] \\
|
|
{\tt vwn\_4 }& & $\star$ & & & & Y &[2] \\
|
|
{\tt vwn\_5 }& & $\star$ & & & & Y &[2] \\
|
|
{\tt vwn\_1\_rpa}& & $\star$ & & & & Y &[2] \\
|
|
{\tt perdew81 }& & $\star$ & & & & Y &[3] \\
|
|
{\tt pw91lda }& & $\star$ & & & & Y &[4] \\
|
|
\hline
|
|
{\tt becke88 }& $\star$ & & $\star$ & & & Y &[5]\\
|
|
{\tt xperdew91}& $\star$ & & $\star$ & & & Y &[6]\\
|
|
{\tt xpbe96 }& $\star$ & & $\star$ & & & Y &[7]\\
|
|
{\tt gill96 }& $\star$ & & $\star$ & & & Y &[8]\\
|
|
{\tt optx }& $\star$ & & $\star$ & & & N &[20]\\
|
|
{\tt mpw91 }& $\star$ & & $\star$ & & & Y &[23]\\
|
|
{\tt xft97 }& $\star$ & & $\star$ & & & N &[24]\\
|
|
{\tt rpbe }& $\star$ & & $\star$ & & & Y &[33]\\
|
|
{\tt revpbe }& $\star$ & & $\star$ & & & Y &[34]\\
|
|
{\tt xpw6b95 }& $\star$ & & $\star$ & & & N &[36]\\
|
|
{\tt xpwb6k }& $\star$ & & $\star$ & & & N &[36]\\
|
|
\hline
|
|
{\tt perdew86 }& & $\star$ & $\star$ & & & Y &[9]\\
|
|
{\tt lyp }& & $\star$ & $\star$ & & & Y &[10]\\
|
|
{\tt perdew91 }& & $\star$ & $\star$ & & & Y &[6]\\
|
|
{\tt cpbe96 }& & $\star$ & $\star$ & & & Y &[7]\\
|
|
{\tt cft97 }& & $\star$ & $\star$ & & & N &[24]\\
|
|
{\tt op }& & $\star$ & $\star$ & & & N &[31]\\
|
|
\hline
|
|
{\tt hcth }& $\star$ & $\star$ & $\star$ & & & N &[11]\\
|
|
{\tt hcth120 }& $\star$ & $\star$ & $\star$ & & & N &[12]\\
|
|
{\tt hcth147 }& $\star$ & $\star$ & $\star$ & & & N &[12]\\
|
|
{\tt hcth407 }& $\star$ & $\star$ & $\star$ & & & N &[19]\\
|
|
{\tt becke97gga1}& $\star$ & $\star$ & $\star$ & & & N &[18]\\
|
|
{\tt hcthp14 }& $\star$ & $\star$ & $\star$ & & & N &[21]\\
|
|
{\tt ft97 }& $\star$ & $\star$ & $\star$ & & & N &[24]\\
|
|
{\tt htch407p }& $\star$ & $\star$ & $\star$ & & & N &[27]\\
|
|
{\tt bop }& $\star$ & $\star$ & $\star$ & & & N &[31]\\
|
|
{\tt pbeop }& $\star$ & $\star$ & $\star$ & & & N &[32]\\
|
|
\hline
|
|
{\tt xpkzb99 }& $\star$ & & &$\star$& & N &[26]\\
|
|
{\tt cpkzb99 }& & $\star$ & &$\star$& & N &[26]\\
|
|
{\tt xtpss03 }& $\star$ & & &$\star$& & N &[28]\\
|
|
{\tt ctpss03 }& & $\star$ & &$\star$& & N &[28]\\
|
|
{\tt bc95 }& & $\star$ & &$\star$& & N &[33]\\
|
|
{\tt cpw6b95 }& & $\star$ & &$\star$& & N &[36]\\
|
|
{\tt cpwb6k }& & $\star$ & &$\star$& & N &[36]\\
|
|
{\tt xm05 }& $\star$ & & &$\star$& & N &[37]\\
|
|
{\tt cm05 }& & $\star$ & &$\star$& & N &[37]\\
|
|
{\tt xm05-2x }& $\star$ & & &$\star$& & N &[38]\\
|
|
{\tt cm05-2x }& & $\star$ & &$\star$& & N &[38]\\
|
|
{\tt xctpssh }& & & &$\star$&$\star$& N &[29]\\
|
|
{\tt bb1k }& & & &$\star$&$\star$& N &[34]\\
|
|
{\tt mpw1b95 }& & & &$\star$&$\star$& N &[35]\\
|
|
{\tt mpwb1k }& & & &$\star$&$\star$& N &[35]\\
|
|
{\tt pw6b95 }& & & &$\star$&$\star$& N &[36]\\
|
|
{\tt pwb6k }& & & &$\star$&$\star$& N &[36]\\
|
|
{\tt m05 }& & & &$\star$&$\star$& N &[37]\\
|
|
{\tt vsxc }& & & &$\star$&$\star$& N &[39]\\
|
|
{\tt xvsxc }& $\star$ & & &$\star$& & N &[39]\\
|
|
{\tt cvsxc }& & $\star$ & &$\star$& & N &[39]\\
|
|
{\tt m06-L }& $\star$ & $\star$ & &$\star$&$\star$& N &[40]\\
|
|
{\tt xm06-L }& & & &$\star$& & N &[40]\\
|
|
{\tt cm06-L }& & $\star$ & &$\star$& & N &[40]\\
|
|
{\tt m06-hf }& & & &$\star$&$\star$& N &[41]\\
|
|
{\tt xm06-hf }& $\star$ & & &$\star$& & N &[41]\\
|
|
{\tt cm06-hf }& & $\star$ & &$\star$& & N &[41]\\
|
|
{\tt m06 }& & & &$\star$&$\star$& N &[42]\\
|
|
{\tt xm06 }& $\star$ & & &$\star$& & N &[42]\\
|
|
{\tt cm06 }& & $\star$ & &$\star$& & N &[42]\\
|
|
{\tt m06-2x }& & & &$\star$&$\star$& N &[42]\\
|
|
{\tt xm06-2x }& $\star$ & & &$\star$& & N &[42]\\
|
|
{\tt cm06-2x }& & $\star$ & &$\star$& & N &[42]\\
|
|
\hline
|
|
{\tt beckehandh}& $\star$ & $\star$ & & & $\star$ & Y &[13]\\
|
|
{\tt b3lyp }& $\star$ & $\star$ & $\star$ & & $\star$ & Y &[14]\\
|
|
{\tt acm }& $\star$ & $\star$ & $\star$ & & $\star$ & Y &[14]\\
|
|
{\tt becke97 }& $\star$ & $\star$ & $\star$ & & $\star$ & N &[15]\\
|
|
{\tt becke97-1}& $\star$ & $\star$ & $\star$ & & $\star$ & N &[11]\\
|
|
{\tt becke97-2}& $\star$ & $\star$ & $\star$ & & $\star$ & N &[22]\\
|
|
{\tt becke97-3}& $\star$ & $\star$ & $\star$ & & $\star$ & N &[30]\\
|
|
{\tt becke97-d}& $\star$ & $\star$ & $\star$ & & $\star$ & N &[45]\\
|
|
{\tt becke98 }& $\star$ & $\star$ & $\star$ & & $\star$ & N &[16]\\
|
|
{\tt pbe0 }& $\star$ & $\star$ & $\star$ & & $\star$ & Y &[17]\\
|
|
{\tt mpw1k }& $\star$ & $\star$ & $\star$ & & $\star$ & Y &[25]\\
|
|
\hline
|
|
\end{tabular}
|
|
\caption{Table of available Exchange (X) and Correlation (C) functionals.
|
|
GGA is the Generalized Gradient Approximation, and Meta refers to Meta-GGAs.
|
|
The column {\em 2nd} refers to second derivatives of the
|
|
energy with respect to nuclear position. }
|
|
\label{tablexc}
|
|
}
|
|
\end{table}
|
|
|
|
|
|
|
|
{\footnotesize
|
|
\vspace{8.5cm}
|
|
\begin{enumerate}\setlength{\itemsep}{-1\baselineskip}
|
|
\setlength{\parsep}{-1\baselineskip}
|
|
\item J.C.~Slater and K. H. Johnson, Phys. Rev. B {\bf 5}, 844 (1972)\\
|
|
\item S.J.~Vosko, L.~Wilk and M.~Nusair,
|
|
Can.~J.~Phys.~{\bf 58}, 1200 (1980)\\
|
|
\item J.~P.~Perdew and A.~Zunger, Phys.~Rev.~B {\bf23}, 5048
|
|
(1981). \\
|
|
\item J.P.~Perdew and Y.~Wang, Phys. Rev. B {\bf 45},
|
|
13244 (1992)\\
|
|
\item A.D.~Becke, Phys. Rev. A {\bf 88}, 3098 (1988)\\
|
|
\item J.P. Perdew, J.A.~Chevary, S.H.~Vosko, K.A.~Jackson,
|
|
M.R.~Pederson, D.J.~Singh and C.~Fiolhais, Phys. Rev. B {\bf 46}, 6671
|
|
(1992)\\
|
|
\item J.P.~Perdew, K.~Burke and M.~Ernzerhof,
|
|
Phys. Rev. Lett. {\bf 77}, 3865 (1996); {\bf 78 }, 1396 (1997)\\
|
|
\item P.W.Gill , Mol. Phys. {\bf 89}, 433 (1996)\\
|
|
\item J.~P.~Perdew, Phys.~Rev.~B {\bf33}, 8822 (1986)\\
|
|
\item C.~Lee, W.~Yang and R.~G.~Parr, Phys.~Rev.~B {\bf 37}, 785
|
|
(1988)\\
|
|
\item F.A.Hamprecht, A.J.Cohen, D.J.Tozer and N.C\\ Handy,
|
|
J. Chem. Phys. {\bf 109}, 6264 (1998)\\
|
|
\item A.D.Boese, N.L.Doltsinis, N.C.Handy and
|
|
M.Sprik. J. Chem. Phys. {\bf 112}, 1670 (2000)\\
|
|
\item A.D.~Becke, J.~Chem.~Phys. {\bf 98}, 1372 (1992)\\
|
|
\item A.D.~Becke, J.~Chem.~Phys.~{\bf 98}, 5648 (1993)\\
|
|
\item A.D.Becke, J. Chem. Phys. {\bf 107}, 8554 (1997)\\
|
|
\item H.L.Schmider and A.D.~Becke, J.~Chem.~Phys.~{\bf 108},
|
|
9624 (1998)\\
|
|
\item C.Adamo and V.Barone, J.~Chem.~Phys. {\bf 110}, 6158 (1998)\\
|
|
\item A.J.Cohen and N.C. Handy, Chem. Phys. Lett. {\bf 316}, 160 (2000)\\
|
|
\item A.D.Boese, N.C.Handy, J. Chem. Phys. {\bf 114}, 5497
|
|
(2001)\\
|
|
\item N.C.Handy, A.J. Cohen, Mol. Phys. {\bf 99}, 403 (2001)\\
|
|
\item G. Menconi, P.J. Wilson, D.J. Tozer,
|
|
J. Chem. Phys {\bf 114}, 3958 (2001)\\
|
|
\item P.J. Wilson, T.J. Bradley, D.J. Tozer, J. Chem. Phys {\bf 115},
|
|
9233 (2001)\\
|
|
\item C. Adamo and V. Barone, J.~Chem.~Phys. {\bf 108}, 664 (1998); Y. Zhao and D.G. Truhlar, J. Phys. Chem. A {\bf 109}, 5656 (2005)\\
|
|
\item M.Filatov and W.Thiel, Mol.Phys. {\bf 91}, 847 (1997).
|
|
M.Filatov and W.Thiel, Int.J.Quantum Chem. {\bf 62}, 603 (1997)\\
|
|
\item B.J. Lynch, P.L. Fast, M. Harris and D.G. Truhlar, J. Phys. Chem. A
|
|
{\bf 104}, 4811(2000)\\
|
|
\item J.P.~Perdew, S.~Kurth, A.~Zupan and P.~Blaha,
|
|
Phys. Rev. Lett. {\bf 82}, 2544 (1999)\\
|
|
\item A.~D.~Boese, A.~Chandra, J.~M.~L.~Martin and D.~Marx,
|
|
J. Chem. Phys. {\bf 119}, 5965 (2003)\\
|
|
\item J. Tao,J.Perdew, V. Staroverov and G. Scuseria,
|
|
Phys. Rev. Let. {\bf 91}, 146401-1 (2003)\\
|
|
\item V. Staroverov, G. Scuseria,
|
|
J. Tao and J.Perdew, J. Chem.Phys. {\bf 119}, 12129 (2003)\\
|
|
\item T.W. Keal, D.J. Tozer, J. Chem. Phys {\bf 123},
|
|
121103 (2005)\\
|
|
\item T. Tsuneda, T. Suzumura and K. Hirao,
|
|
J. Chem Phys. {\bf 110}, 10664 (1999)\\
|
|
\item T. Tsuneda, T. Suzumura and K. Hirao,
|
|
J. Chem Phys. {\bf 111}, 5656 (1999) \\
|
|
\item B. Hammer, L. B. Hansen and J. N{\o}rskov , Phys. Rev. B {\bf 58}, 7413 (1999)\\
|
|
\item Y. Zhang and W. Yang, Phys. Rev. Letters {\bf 80}, 890 (1998)\\
|
|
\item A. D. Becke, J. Chem. Phys. {\bf 104}, 1040 (1996)\\
|
|
\item Y. Zhao and D. G. Truhlar, J. Phys. Chem. A {\bf 108}, 2715 (2004)\\
|
|
\item Y. Zhao and D. G. Truhlar, J. Phys. Chem. A {\bf 108}, 6908 (2004)\\
|
|
\item Y. Zhao and D. G. Truhlar, J. Phys. Chem. A {\bf 109}, 5656 (2005)\\
|
|
\item Y. Zhao, N. E. Schultz and D. G. Truhlar, J. Chem. Phys. {\bf 123}, 161103 (2005)\\
|
|
\item Y. Zhao, N. E. Schultz and D. G. Truhlar, J. Chem. Theory Comput. {\bf 2}, 364 (2006)\\
|
|
\item T. Van Voorhis, G. E. Scuseria, J. Chem. Phys. {\bf 109}, 400 (1998)\\
|
|
\item Y. Zhao, D. G. Truhlar, J. Chem. Phys. {\bf 125}, 194101 (2006)\\
|
|
\item Y. Zhao, D. G. Truhlar, J. Phys. Chem. A. {\bf 110}, 13126 (2006)\\
|
|
\item Y. Zhao, D. G. Truhlar, Theor. Chem. Acc. (2006)\\
|
|
\item S. Grimme, J. Comp. Chem. \bf{27}, 1787 (2006).
|
|
|
|
\end{enumerate}
|
|
}
|
|
%\end{table}
|
|
\onecolumn
|
|
|
|
\section{{\tt ITERATIONS} --- Number of SCF iterations}
|
|
|
|
\begin{verbatim}
|
|
ITERATIONS <integer iterations default 30>
|
|
\end{verbatim}
|
|
|
|
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 \verb+ITERATIONS+, and has the following general form,
|
|
|
|
\begin{verbatim}
|
|
iterations <integer iterations default 30>
|
|
\end{verbatim}
|
|
|
|
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 \ref{sec:DFTsample}.
|
|
|
|
\section{{\tt CONVERGENCE} --- SCF Convergence Control}
|
|
\label{sec:dftconv}
|
|
|
|
\begin{verbatim}
|
|
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 0>] [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] \
|
|
[rabuck [n_rabuck <integer n_rabuck default 25>]]
|
|
\end{verbatim}
|
|
|
|
Convergence is satisfied by meeting any or all of three criteria;
|
|
\begin{itemize}
|
|
\item 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,
|
|
\begin{verbatim}
|
|
CONVERGENCE energy <real energy default 1e-6>
|
|
\end{verbatim}
|
|
|
|
\item 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,
|
|
\begin{verbatim}
|
|
CONVERGENCE density <real density default 1e-5>
|
|
\end{verbatim}
|
|
|
|
\item 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,
|
|
\begin{verbatim}
|
|
CONVERGENCE gradient <real gradient default 5e-4>
|
|
\end{verbatim}
|
|
\end{itemize}
|
|
|
|
The default optimization strategy is to immediately begin direct
|
|
inversion of the iterative subspace\footnote {P.~Pulay, Chem.\ Phys.\
|
|
Lett.\ {\bf 73}, 393 (1980) and P.~Pulay, J.~Comp.~Chem.~{\bf 3},
|
|
566 (1982)}. 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,
|
|
\begin{verbatim}
|
|
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>]
|
|
\end{verbatim}
|
|
|
|
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,
|
|
\begin{verbatim}
|
|
CONVERGENCE [ncydp <integer ncydp default 2>] \
|
|
[ncyds <integer ncyds default 30>] \
|
|
[ncysh <integer ncysh default 0>]
|
|
\end{verbatim}
|
|
|
|
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
|
|
\begin{verbatim}
|
|
CONVERGENCE [damp <integer ndamp default 0>] \
|
|
[diis [nfock <integer nfock default 10>]] \
|
|
[lshift <real lshift default 0.5>] \
|
|
[hl_tol <real hl_tol default 0.1>]]
|
|
\end{verbatim}
|
|
|
|
Damping is defined to be the percentage of the previous iterations
|
|
density mixed with the current iterations density. So, for example
|
|
\begin{verbatim}
|
|
CONVERGENCE damp 70
|
|
\end{verbatim}
|
|
would mix 30\% of the current iteration density with 70\% of the
|
|
previous iteration density.
|
|
|
|
Level-Shifting\footnote {M.F.~Guest and
|
|
V.R.~Saunders, Mol.~Phys.~{\bf 28}, 819 (1974)} 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 \verb+lshift+. For example the directive,
|
|
\begin{verbatim}
|
|
CONVERGENCE lshift 0.5
|
|
\end{verbatim}
|
|
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 \verb+hl_tol+. An example of
|
|
changing the HOMO-LUMO gap tolerance to 0.01 would be,
|
|
\begin{verbatim}
|
|
CONVERGENCE hl_tol 0.01
|
|
\end{verbatim}
|
|
|
|
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,
|
|
\begin{verbatim}
|
|
CONVERGENCE diis 3
|
|
\end{verbatim}
|
|
|
|
The user has the ability to simply turn off any optimization
|
|
procedures deemed undesirable with the obvious keywords,
|
|
\begin{verbatim}
|
|
CONVERGENCE [nodamping] [nodiis] [nolevelshifting]
|
|
\end{verbatim}
|
|
|
|
|
|
For systems where the initial guess is very poor, the user can try the
|
|
method described in
|
|
\footnote{A.~D.~Rabuck and G.~E.~Scuseria, J.~Chem.~Phys {\bf 110},695
|
|
(1999)}
|
|
that makes use of {\bf fractional occupation} of the orbital levels during
|
|
the initial cycles of the SCF convergence. The input has the following form
|
|
|
|
\begin{verbatim}
|
|
CONVERGENCE rabuck [n_rabuck <integer n_rabuck default 25>]]
|
|
\end{verbatim}
|
|
|
|
where the optional value {\tt n\_rabuck} 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
|
|
\begin{verbatim}
|
|
CONVERGENCE rabuck 30
|
|
\end{verbatim}
|
|
|
|
\section{{\tt CDFT} --- Constrained DFT}
|
|
\label{cdft}
|
|
|
|
This option enables the constrained DFT formalism by Wu and Van Voorhis described
|
|
in the paper: Q. Wu, T. Van Voorhis, Phys. Rev. A {\bf 72}, 024502 (2005).
|
|
|
|
\begin{verbatim}
|
|
CDFT <integer fatom1 latom1> [<integer fatom2 latom2>] (charge||spin <real constaint_value>) \
|
|
[pop (becke||mulliken||lowdin) default lowdin]
|
|
\end{verbatim}
|
|
|
|
Variables fatom1 and latom1 define the first and last atom of the group of atoms to which
|
|
the constaint will be applied. Therefore the atoms in the same group should be placed
|
|
continuously in the geometry input. If fatom2 and latom2 are specified, the difference between
|
|
group 1 and 2 (i.e. 1-2) is constrained.
|
|
|
|
The constraint can be either on the charge or the spin density (\# of alpha - beta electrons) with
|
|
a user specified constaint\_value. Note: No gradients have been implemented for the spin constaints
|
|
case. Geometry optimizations can only be performed using the charge constaint.
|
|
|
|
To calculate the charge or spin density, the Becke, Mulliken, and Lowdin population schemes can be
|
|
used. The Lowdin scheme is default while the Mulliken scheme is not recommended. If basis sets with
|
|
many diffuse functions are used, the Becke population scheme is recommended.
|
|
|
|
Multiple constaints can be defined simultaniously by defining multiple {\tt cdft} lines in the input.
|
|
The same population scheme will be used for all constaints and only needs to be specified once. If
|
|
multiple population options are defined, the last one will be used. When there are convergence
|
|
problems with multiple constaints, the user is advised to do one constraint first and to use the
|
|
resulting orbitals for the next step of the constained calculations.
|
|
|
|
It is best to put "convergence nolevelshifting" in the dft directive to avoid issues with gradient
|
|
calculations and convergence in CDFT. Use orbital swap to get a broken-symmetry solution.
|
|
|
|
An input example is given below.
|
|
|
|
\begin{verbatim}
|
|
geometry
|
|
symmetry
|
|
C 0.0 0.0 0.0
|
|
O 1.2 0.0 0.0
|
|
C 0.0 0.0 2.0
|
|
O 1.2 0.0 2.0
|
|
end
|
|
|
|
basis
|
|
* library 6-31G*
|
|
end
|
|
|
|
dft
|
|
xc b3lyp
|
|
convergence nolevelshifting
|
|
odft
|
|
mult 1
|
|
vectors swap beta 14 15
|
|
cdft 1 2 charge 1.0
|
|
end
|
|
task dft
|
|
\end{verbatim}
|
|
|
|
\section{{\tt SMEAR} --- Fractional Occupation of the Molecular Orbitals}
|
|
\label{smear}
|
|
|
|
The {\tt \bf SMEAR} keyword is useful in cases with many degenerate states
|
|
near the HOMO (eg metallic clusters)
|
|
|
|
\begin{verbatim}
|
|
SMEAR <real smear default 0.001>
|
|
\end{verbatim}
|
|
|
|
This option allows fractional occupation of the molecular orbitals.
|
|
A Gaussian broadening function of exponent {\tt smear} is used as described in
|
|
the paper:
|
|
R.W. Warren and B.I. Dunlap, Chem. Phys. Letters {\bf 262}, 384 (1996).\\
|
|
The user must be aware that an additional energy term is added to the total
|
|
energy in order to have
|
|
energies and gradients consistent.
|
|
|
|
|
|
\section{{\tt GRID} --- Numerical Integration of the XC Potential}
|
|
\label{grgrid}
|
|
\begin{verbatim}
|
|
GRID [(xcoarse||coarse||medium||fine||xfine) default medium] \
|
|
[(gausleg||lebedev ) default lebedev ] \
|
|
[(becke||erf1||erf2||ssf) default erf1] \
|
|
[(euler||mura||treutler) default mura] \
|
|
[rm <real rm default 2.0>] \
|
|
[nodisk]
|
|
\end{verbatim}
|
|
|
|
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.
|
|
|
|
\begin{verbatim}
|
|
GRID [xcoarse||coarse||medium||fine||xfine]
|
|
\end{verbatim}
|
|
|
|
Our intent is to have a numerical integration scheme which would give
|
|
us approximately the accuracy defined below regardless of molecular
|
|
composition.
|
|
\begin{center}
|
|
\begin{tabular}[right]{|c|c|} \hline
|
|
Keyword & {\tt Total Energy Target Accuracy} \\ \hline
|
|
{\tt xcoarse} & $1x10^{-4}$ \\ \hline
|
|
{\tt coarse} & $1x10^{-5}$ \\ \hline
|
|
{\tt medium} & $1x10^{-6}$ \\ \hline
|
|
{\tt fine} & $1x10^{-7}$ \\ \hline
|
|
{\tt xfine} & $1x10^{-8}$ \\ \hline
|
|
\end{tabular} \\
|
|
\end{center}
|
|
|
|
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).
|
|
|
|
%{\bf Important note to users.} We clearly understand that the default
|
|
%(Euler-MacLaurin/Gauss-Legendre) grids are large and result in slow
|
|
%%construction of the numerical components of the Kohn-Sham equations.
|
|
%%Alternatively, we have provided access to two-dimensional Lebedev
|
|
%%angular quadratures which can be used in many cases to substantially
|
|
%%reduce the number of grid points per atom while keeping good accuracy.
|
|
%%We have not yet had the opportunity to benchmark the Lebedev angular
|
|
%%quadratures to the same extent that we have for the Gauss-Legendre.
|
|
%%We therefore do not have default Lebedev quadratures for specific
|
|
%%target accuracy for all elements of the periodic table. If the user
|
|
%%wants to significantly decrease CPU time to solution it is suggested
|
|
%%that a few prototype benchmark calculations be done using various
|
|
%%Lebedev quadratures (which we describe below) while monitoring the
|
|
%%numerically integrated density and total energies for the molecular
|
|
%%systems of interest. For many examples we have observed speed-ups of
|
|
%%two or more for the same numerical accuracy when using Lebedev rather
|
|
%%than the default Gauss-Legendre quadrature. In addition, we have
|
|
%%observed that with Lebedev angular quadratures a reduction in the
|
|
%%number of radial shells (perhaps by as much as 30\%) might be possible
|
|
%%while continuing to provide the same level of accuracy.
|
|
%%% g94/Sg-1 grid ssf lebedev gausleg 50 8
|
|
%%% g98/fine grid ssf lebedev gausleg 75 11
|
|
|
|
|
|
\begin{table}[h]
|
|
\begin{center}
|
|
\caption{Program default number of radial and angular shells empirically determined for Row 1 atoms
|
|
(Li $\rightarrow$ F) to reach the desired accuracies.}
|
|
|
|
\vspace{.2in}
|
|
|
|
\begin{tabular}[right]{|c|c|c|} \hline
|
|
Keyword & {\tt Radial} & {\tt Angular} \\ \hline
|
|
{\tt xcoarse} & 21 & 194 \\ \hline
|
|
{\tt coarse} & 35 & 302 \\ \hline
|
|
{\tt medium} & 49 & 434 \\ \hline
|
|
{\tt fine} & 70 & 590 \\ \hline
|
|
{\tt xfine} &100 &1202 \\ \hline
|
|
\end{tabular} \\
|
|
\end{center}
|
|
\end{table}
|
|
|
|
\begin{table}[h]
|
|
\begin{center}
|
|
\caption{Program default number of radial and angular shells empirically determined for Row 2 atoms
|
|
(Na $\rightarrow$ Cl) to reach the desired accuracies.}
|
|
|
|
\vspace{.2in}
|
|
|
|
\begin{tabular}[right]{|c|c|c|} \hline
|
|
Keyword & {\tt Radial} & {\tt Angular} \\ \hline
|
|
{\tt xcoarse} & 42 & 194 \\ \hline
|
|
{\tt coarse} & 70 & 302 \\ \hline
|
|
{\tt medium} & 88 & 434 \\ \hline
|
|
{\tt fine} &123 & 770 \\ \hline
|
|
{\tt xfine} &125 &1454 \\ \hline
|
|
\end{tabular} \\
|
|
\end{center}
|
|
\end{table}
|
|
|
|
\begin{table}[h]
|
|
\begin{center}
|
|
\caption{Program default number of radial and angular shells empirically determined for Row 3 atoms
|
|
(K $\rightarrow$ Br) to reach the desired accuracies.}
|
|
|
|
\vspace{.2in}
|
|
|
|
\begin{tabular}[right]{|c|c|c|} \hline
|
|
Keyword & {\tt Radial} & {\tt Angular} \\ \hline
|
|
{\tt xcoarse} & 75 & 194 \\ \hline
|
|
{\tt coarse} & 95 & 302 \\ \hline
|
|
{\tt medium} &112 & 590 \\ \hline
|
|
{\tt fine} &130 & 974 \\ \hline
|
|
{\tt xfine} &160 &1454 \\ \hline
|
|
\end{tabular} \\
|
|
\end{center}
|
|
\end{table}
|
|
|
|
\begin{table}[h]
|
|
\begin{center}
|
|
\caption{Program default number of radial and angular shells empirically determined for Row 4 atoms
|
|
(Rb $\rightarrow$ I) to reach the desired accuracies.}
|
|
|
|
\vspace{.2in}
|
|
|
|
\begin{tabular}[right]{|c|c|c|} \hline
|
|
Keyword & {\tt Radial} & {\tt Angular} \\ \hline
|
|
{\tt xcoarse} & 84 &194 \\ \hline
|
|
{\tt coarse} &104 &302 \\ \hline
|
|
{\tt medium} &123 &590 \\ \hline
|
|
{\tt fine} &141 &974 \\ \hline
|
|
{\tt xfine} &205 &1454 \\ \hline
|
|
\end{tabular} \\
|
|
\end{center}
|
|
\end{table}
|
|
|
|
\clearpage
|
|
|
|
\subsection{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 \verb+gausleg+ keyword.
|
|
|
|
\paragraph{Gauss-Legendre angular grid}
|
|
|
|
\begin{verbatim}
|
|
GRID gausleg <integer nradpts default 50> <integer nagrid default 10>
|
|
\end{verbatim}
|
|
|
|
In this type of grid, the number of phi points is twice the number of
|
|
theta points. So, for example, a specification of,
|
|
\begin{verbatim}
|
|
GRID gausleg 80 20
|
|
\end{verbatim}
|
|
would be interpreted as 80 radial points, 20 theta points, and 40
|
|
phi points per center (or 64000 points per center before pruning).
|
|
|
|
\paragraph{Lebedev angular grid}
|
|
|
|
A second quadrature is the Lebedev
|
|
scheme for the angular components\footnote{The subroutine
|
|
for the Lebedev grid was derived from a routine supplied by M.~Caus\`a
|
|
of the University of Torino and from the grid points supplied by
|
|
D.N.~Laikov from Moscow State University.}.
|
|
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,
|
|
\begin{verbatim}
|
|
GRID lebedev <integer radpts > <integer iangquad >
|
|
\end{verbatim}
|
|
In this context the variable iangquad specifies a certain number of
|
|
angular points as indicated by the table below.\footnote{
|
|
V.I. Lebedev and D.N. Laikov, Doklady Mathematics {\bf 366}, 741
|
|
(1999).
|
|
}
|
|
\begin{table}[htp]
|
|
\begin{center}
|
|
\begin{tabular}[right]{|c|rr|} \hline
|
|
$IANGQUAD$ & $N_{angular}$ & $l$\\
|
|
\hline
|
|
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 \\
|
|
\hline
|
|
\end{tabular}
|
|
\end{center}
|
|
\caption{List of Lebedev quadratures}
|
|
\end{table}
|
|
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 and number of radial points.
|
|
As an example, here is a grid input line for the water molecule
|
|
\begin{verbatim}
|
|
grid lebedev 80 11 H 70 8 O 90 11
|
|
\end{verbatim}
|
|
|
|
|
|
% Delley weights do not work .. need to replace with SSWs after input is
|
|
%changed
|
|
%The user also has the option of choosing one of two types of spatial weights
|
|
%implemented in the numerical integration of the XC terms; Delley and Becke.
|
|
|
|
\clearpage
|
|
\subsection{Partitioning functions}
|
|
|
|
\begin{verbatim}
|
|
GRID [(becke||erf1||erf2||ssf) default erf1]
|
|
\end{verbatim}
|
|
|
|
|
|
\begin{description}
|
|
\item[\tt becke] A. D. Becke, J. Chem. Phys. {\bf 88}, 1053 (1988).
|
|
\item[\tt ssf] R.E.Stratmann, G.Scuseria and M.J.Frisch,
|
|
Chem. Phys. Lett. {\bf 257}, 213 (1996).
|
|
\item[\tt erf1] modified ssf
|
|
\item[\tt erf2] modified ssf
|
|
\end{description}
|
|
|
|
Erf$n$ partioning functions
|
|
|
|
\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*}
|
|
|
|
|
|
|
|
|
|
\subsection{Radial grids}
|
|
|
|
\begin{verbatim}
|
|
GRID [[euler||mura||treutler] default mura]
|
|
\end{verbatim}
|
|
|
|
\begin{description}
|
|
\item[\tt euler] Euler-McLaurin quadrature wih the transformation
|
|
devised by
|
|
C.W. Murray, N.C. Handy, and G.L. Laming,
|
|
Mol. Phys.{\bf 78}, 997 (1993).
|
|
\\
|
|
\item[\tt mura] Modification of the Murray-Handy-Laming scheme by
|
|
M.E.Mura and P.J.Knowles, J Chem Phys {\bf 104}, 9848
|
|
(1996) (we are not using the scaling factors proposed
|
|
in this paper).\\
|
|
\item[\tt treutler] Gauss-Chebyshev using the transformation suggested
|
|
by O.Treutler and R.Alrhichs, J.Chem.Phys {\bf 102}, 346 (1995).\\
|
|
\end{description}
|
|
|
|
\subsection{Disk usage for Grid}
|
|
|
|
\begin{verbatim}
|
|
NODISK
|
|
\end{verbatim}
|
|
|
|
This keyword turns off storage of grid points and weights on disk.
|
|
|
|
|
|
\section{{\tt TOLERANCES} --- Screening tolerances}
|
|
|
|
\begin{verbatim}
|
|
TOLERANCES [[tight] [tol_rho <real tol_rho default 1e-10>] \
|
|
[accCoul <integer accCoul default 8>] \
|
|
[radius <real radius default 25.0>]]
|
|
\end{verbatim}
|
|
% [accQrad <integer accQrad default 12>] \
|
|
% [accAOfunc <integer accAOfunc default 20>] \
|
|
% [accXCfunc <integer accXCfunc default 20>] \
|
|
% [accCDfunc <integer accAOfunc default 20>] \
|
|
%
|
|
%{\bf JEFF: tight needs explanation}
|
|
%
|
|
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 to define a screening tolerance for evaluation of the AO
|
|
%Gaussian functions is specified with the keyword \verb+accAOfunc+, as
|
|
%follows,
|
|
%\begin{verbatim}
|
|
% TOLERANCES accAOfunc <integer accAOfunc>
|
|
%\end{verbatim}
|
|
%A Gaussian Type Function of the Orbital basis set is
|
|
%evaluated at a point $r_i$ if its value it is greater than
|
|
%$exp(-${\tt accAOfunc}$)$ ;
|
|
%the default value is set to $-ln(\Delta E)$, where $\Delta E$ is the desired
|
|
%accuracy on energy.
|
|
%A Gaussian orbital basis (AO) function with exponent $\zeta$
|
|
%and radial factor $e^{-\zeta\cdot r_i^2}$ is
|
|
%evaluated at a point $r_i$ only if
|
|
%$\zeta\cdot r_i^2$ is less than the value specified for ${\tt accAOfunc}$.
|
|
|
|
%The input to define a screening tolerance for evaluation of the exchange-
|
|
%correlation (XC) Gaussian fitting functions is specified with the
|
|
%keyword \verb+accXCfunc+, as follows,
|
|
%\begin{verbatim}
|
|
% TOLERANCES accXCfunc <integer accXCfunc default 20>
|
|
%\end{verbatim}
|
|
%An exchange-correlation (XC) fitting function with exponent $\zeta$
|
|
%and radial factor $e^{-\zeta\cdot r_i^2}$ is
|
|
%evaluated at a point $r_i$ only if
|
|
%$\zeta\cdot r_i^2$ is less than the value specified for ${\tt accXCfunc}$.
|
|
%
|
|
%The input to define a screening tolerance for evaluation of the
|
|
%charge-density (CD) Gaussian fitting functions is specified with the
|
|
%keyword \verb+accCDfunc+, as follows,
|
|
%\begin{verbatim}
|
|
% TOLERANCES accCDfunc <integer accCDfunc default 20>
|
|
%\end{verbatim}
|
|
%A charge-density (CD) fitting function with exponent $\zeta$
|
|
%and radial factor $e^{-\zeta\cdot r_i^2}$ is evaluated at a
|
|
%point $r_i$ only if $\zeta\cdot r_i^2$ is less than the value
|
|
%specified for ${\tt accCDfunc}$.
|
|
|
|
The input
|
|
parameter {\tt 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.
|
|
|
|
\begin{verbatim}
|
|
TOLERANCES accCoul <integer accCoul default 8>
|
|
\end{verbatim}
|
|
|
|
%The user also has the option of specifying the radial quadrature
|
|
%grid cut-off for the DFT calculation, using the keyword
|
|
%\verb+accQrad+. The input line for this option is as follows,
|
|
%\begin{verbatim}
|
|
% TOLERANCES accQrad <integer accQrad default 12>
|
|
%\end{verbatim}
|
|
|
|
%The value entered for \verb+accQrad+ is the cutoff distance, in bohr, for grid
|
|
%points around a given center or atom. Grid points that lie more than
|
|
%\verb+accQrad+ bohr from the center or atom are neglected.
|
|
|
|
Screening away needless computation of the XC functional (on the grid)
|
|
due to negligible density is also possible with the use of,
|
|
\begin{verbatim}
|
|
TOLERANCES tol_rho <real tol_rho default 1e-10>
|
|
\end{verbatim}
|
|
XC functional computation is bypassed if the corresponding density
|
|
elements are less than \verb+tol_rho+.
|
|
|
|
A screening parameter, \verb+radius+, used in the screening of the
|
|
Becke or Delley spatial weights is also available as,
|
|
\begin{verbatim}
|
|
TOLERANCES radius <real radius default 25.0>
|
|
\end{verbatim}
|
|
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 \verb+tight+ option:
|
|
|
|
\begin{verbatim}
|
|
TOLERANCES tight
|
|
\end{verbatim}
|
|
|
|
This option sets all tolerances to their
|
|
default/user specified values at the very first iteration.
|
|
|
|
|
|
\section{{\tt DIRECT}, {\tt SEMIDIRECT} and {\tt NOIO} --- Hardware Resource Control}
|
|
\begin{verbatim}
|
|
DIRECT||INCORE
|
|
SEMIDIRECT [filesize <integer filesize default disksize>]
|
|
[memsize <integer memsize default available>]
|
|
[filename <string filename default $file_prefix.aoints$>]
|
|
NOIO
|
|
\end{verbatim}
|
|
|
|
\sloppy
|
|
|
|
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 \verb+noio+ within the
|
|
input for the DFT directive. The input to exercise this option is
|
|
as follows,
|
|
\begin{verbatim}
|
|
noio
|
|
\end{verbatim}
|
|
If this keyword is encountered, then the two matrices (inverted
|
|
charge-density and exchange-correlation) are computed ``on-the-fly''
|
|
whenever needed.
|
|
|
|
The \verb+INCORE+ option is always assumed to be true but can be
|
|
overridden with the option \verb+DIRECT+ in which case all integrals
|
|
are computed ``on-the-fly''.
|
|
|
|
The \verb+SEMIDIRECT+ option controls caching of integrals. A full
|
|
description of this option is described in User Manual~\ref{sec:max}.
|
|
Some functionality which is only compatible with the \verb+DIRECT+
|
|
option will not, at present, work when using \verb+SEMIDIRECT+.
|
|
|
|
\fussy
|
|
|
|
\section{{\tt ODFT} and {\tt MULT} --- Open shell systems}
|
|
\begin{verbatim}
|
|
ODFT
|
|
MULT <integer mult default 1>
|
|
\end{verbatim}
|
|
|
|
Both {\sl closed-shell} and {\sl open-shell} systems can be studied using
|
|
the DFT module. Specifying the keyword \verb+MULT+ within the \verb+DFT+
|
|
directive allows the user to define the spin multiplicity of the system.
|
|
The form of the input line is as follows;
|
|
\begin{verbatim}
|
|
MULT <integer mult default 1>
|
|
\end{verbatim}
|
|
When the keyword \verb+MULT+ is specified, the user can define the integer
|
|
variable \verb+mult+, where \verb+mult+ is equal to the number of alpha
|
|
electrons minus beta electrons, plus 1.
|
|
|
|
The keyword \verb+ODFT+ 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).
|
|
|
|
\section{{\tt SIC} --- Self-Interaction Correction}
|
|
|
|
\begin{verbatim}
|
|
sic [perturbative || oep || oep-loc <default perturbative>]
|
|
\end{verbatim}
|
|
|
|
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. {\bf 90}, 317 (1953),
|
|
J. D. Talman and W. F. Shadwick, Phys. Rev. A {\bf 14}, 36 (1976))
|
|
within the Krieger-Li-Iafrate approximation (J. B. Krieger, Y. Li,
|
|
and G. J. Iafrate, Phys. Rev. A {\bf 45}, 101 (1992); {\bf 46}, 5453 (1992);
|
|
47, 165 (1993))
|
|
Three variants of these methods are included in NWChem:
|
|
\begin{itemize}
|
|
\item{\tt sic perturbative} 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
|
|
\ref{orbloc}) 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.
|
|
\item{\tt sic oep} 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.
|
|
\item{\tt sic oep-loc}
|
|
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.
|
|
\end{itemize}
|
|
With oep and oep-loc options a {\bf xfine grid} (see section \ref{grgrid})
|
|
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:
|
|
|
|
\begin{verbatim}
|
|
print "SIC information"
|
|
\end{verbatim}
|
|
|
|
|
|
\section{{\tt MULLIKEN} --- Mulliken analysis}
|
|
Mulliken analysis of the charge distribution is invoked by the keyword:
|
|
\begin{verbatim}
|
|
MULLIKEN
|
|
\end{verbatim}
|
|
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
|
|
\begin{verbatim}
|
|
dft
|
|
mulliken
|
|
print "mulliken ao"
|
|
end
|
|
task dft
|
|
\end{verbatim}
|
|
|
|
|
|
\section{{\tt BSSE} --- Basis Set Superposition Error}
|
|
|
|
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}, but {\tt bq} 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
|
|
|
|
\begin{verbatim}
|
|
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
|
|
\end{verbatim}
|
|
|
|
Please note that the ``ghost'' oxygen atom has been labeled {\tt bqO},
|
|
and not just {\tt bq}.
|
|
|
|
\section{{\tt DISP} --- Empirical Long-range Contribution (vdW)}
|
|
|
|
\begin{verbatim}
|
|
DISP
|
|
[ vdw <real vdw integer default 2]]
|
|
[[s6 <real s6 default depends on XC functional>] \
|
|
[ alpha <real s6 default 20.0d0] \
|
|
[ off ] \
|
|
\end{verbatim}
|
|
|
|
When systems with high dependence on van der Waals interactions
|
|
are computed, the dispersion term may be added empirically
|
|
through long-range contribution
|
|
DFT-D, i.e.$ E_{DFT-D}=E_{DFT-KS}+E_{disp}$,
|
|
%[Q. Wu and W. Yang, \textit{J. Chem. Phys.} \textbf{116} 515 (2002)]
|
|
where:
|
|
|
|
$$ E_{disp}=-s_6\sum^{N_{atom}-1}_{i=1}\sum^{N_{atom}}_{j=i+1}
|
|
\frac{C_{6}^{ij}}{R_{ij}^{6}}
|
|
\left( 1+e^{-\alpha (R_{ij}/R_{vdw}-1)} \right)^{-1}$$
|
|
|
|
In this equation, the $s_6$ term depends in the functional and basis set used, $C_6^{ij}$
|
|
is the dispersion coefficient between pairs of atoms.
|
|
$R_{vdw}$ and $R_{ij}$ are related with van der Waals atom radii and
|
|
the nucleus distance respectively. The $\alpha$ value contributes to control the corrections
|
|
at intermediate distances.
|
|
|
|
There are available three ways to compute $C_6^{ij}$:
|
|
\begin{enumerate}
|
|
\item $C_6^{ij}=
|
|
\frac{2(C_6^{i}C_6^{j})^{2/3}(N_{eff i}N_{eff j})^{1/3}}
|
|
{C_6^{i}(N_{eff i}^2)^{1/3}+(C_6^{i}N_{eff j}^2)^{1/3}}$
|
|
where $N_{eff}$ and $C_6$ are obtained from Q. Wu and W. Yang, \textit{J. Chem. Phys.}
|
|
\textbf{116} 515 (2002) and U. Zimmerli, M Parrinello and P. Koumoutsakos
|
|
\textit{J. Chem. Phys.} \textbf{120} 2693 (2004). (Use {\tt vdw 0})
|
|
|
|
\item $C_6^{ij}=2\frac{C_6^{i}C_6^{j}}{C_6^{i}+C_6^{j}}$.
|
|
See details in
|
|
S. Grimme \textit{J. Comp. Chem.} \textbf{25} 1463 (2004).
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% $R_{vdW}$ and $C_6$
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% those were obtained from this paper.
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(Use {\tt vdw 1})
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|
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|
\item $C_6^{ij}=\sqrt{C_6^{i}C_6^{j}}$
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|
See details in
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|
S. Grimme \textit{J. Comp. Chem.} \textbf{27}1787 (2006).
|
|
% $R_{vdW}$ and $C_6$
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|
% those were obtained from this paper.
|
|
(Use {\tt vdw 2})
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|
|
|
\end{enumerate}
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|
|
|
Note that in each option there is a certain set of $C_6$ and $R_{vdw}$.
|
|
|
|
For options {\tt vdw 1 } and {\tt vdw 2 }, there are $s_6$ values by default for some functionals
|
|
and triple-zeta plus double polarization basis set (TZV2P):
|
|
\begin{itemize}
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|
\item {\tt vdw 1}. BLYP 1.40, PBE 0.70 and BP86 1.30.
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|
\item {\tt vdw 2}. BLYP 1.20, PBE 0.75, BP86 1.05, B3LYP 1.05, Becke97-D 1.25 and TPSS 1.00.
|
|
\end{itemize}
|
|
|
|
This capability is also supported for energy gradients and Hessian.
|
|
Is possible to be deactivated with \verb+OFF+.
|
|
|
|
\section{Print Control}
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|
\begin{verbatim}
|
|
PRINT||NOPRINT
|
|
\end{verbatim}
|
|
|
|
The \verb+PRINT||NOPRINT+ options control the level of output in the
|
|
DFT. Please see some examples using this directive in
|
|
section \ref{sec:DFTsample}, a sample input file.
|
|
Known controllable print options are:
|
|
|
|
\begin{table}[htbp]
|
|
\begin{center}
|
|
\begin{tabular}{lcc}
|
|
{\bf Name} & {\bf Print Level} & {\bf Description} \\
|
|
``all vector symmetries'' & high & symmetries of all molecular orbitals \\
|
|
``alpha partner info'' & high & unpaired alpha orbital analysis \\
|
|
``common'' & debug & dump of common blocks \\
|
|
``convergence'' & default & convergence of SCF procedure \\
|
|
``coulomb fit'' & high & fitting electronic charge density \\
|
|
``dft timings'' & high & \\
|
|
``final vectors'' & high & \\
|
|
``final vector symmetries'' & default & symmetries of final molecular orbitals \\
|
|
``information'' & low & general information \\
|
|
``initial vectors'' & high & \\
|
|
``intermediate energy info'' & high & \\
|
|
``intermediate evals'' & high & intermediate orbital energies \\
|
|
``intermediate fock matrix'' & high & \\
|
|
``intermediate overlap'' & high & overlaps between the alpha and beta sets \\
|
|
``intermediate S2'' & high & values of S2 \\
|
|
``intermediate vectors'' & high & intermediate molecular orbitals \\
|
|
``interm vector symm'' & high & symmetries of intermediate orbitals \\
|
|
``io info'' & debug & reading from and writing to disk \\
|
|
``kinetic\_energy'' & high & kinetic energy \\
|
|
``mulliken ao'' & high & mulliken atomic orbital population \\
|
|
|
|
``multipole'' & default & moments of alpha, beta, and nuclear charge densities \\
|
|
``parameters'' & default & input parameters \\
|
|
``quadrature'' & high & numerical quadrature \\
|
|
``schwarz'' & high & integral screening info \& stats at completion\\
|
|
``screening parameters'' & high & integral accuracies \\
|
|
``semi-direct info'' & default & semi direct algorithm \\
|
|
\end{tabular}
|
|
\end{center}
|
|
\caption{DFT Print Control Specifications}
|
|
\end{table}
|
|
|
|
|
|
|
|
|