diff --git a/doc/user/dft.tex b/doc/user/dft.tex index b621a87373..fefe8c0114 100644 --- a/doc/user/dft.tex +++ b/doc/user/dft.tex @@ -552,7 +552,6 @@ procedures deemed undesirable with the obvious keywords, ) ||\ (lebedev )] \ - [store_wght] [nquad_task ] \ [delley||becke] \ [rm ] \end{verbatim} @@ -562,31 +561,131 @@ exchange-correlation contribution to the density functional. The default quadrature used for the numerical integration is an Euler-MacLaurin scheme for the radial components and a Gauss-Legendre scheme for the angular components (see C.W.~Murray, N.C.~Handy, and -G.L.Laming, Mol.~Phys.~78, 997-1014, (1993)). Within this numerical +G.L.Laming, Mol.~Phys.~78, 997-1014, (1993)). 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; coarse, medium, fine, and xfine. The default is medium. +with the keywords; xcoarse, coarse, medium, fine, and xfine. The +default is medium. \begin{verbatim} - GRID [coarse||medium||fine||xfine] + GRID [xcoarse||coarse||medium||fine||xfine] \end{verbatim} -The definitions of these gridtypes are:\\ -{\center - \begin{tabular}[right]{|l|r r r r|} \hline -Keyword & {\tt coarse} & {\tt medium} & {\tt fine} & {\tt xfine} \\ \hline -$N_{radial}$ & 35 & 50 & 75 & 105 \\ -$N_{theta}$ & 8 & 10 & 12 & 14 \\ \hline -$N_{phi}$ & 16 & 20 & 24 & 28 \\ \hline -$total unpruned per center$ & 4480 & 10000 & 21600 & 41160 \\ \hline - \end{tabular} -} +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} + +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 +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. + +\begin{center} +\begin{table}[htb] +\caption{Number of radial and angular shells required for Row 1 atoms + (Li $\rightarrow$ F) to reach the desired accuracies.} + +\vspace{.2in} + + \begin{tabular}[right]{|c|c|c|c|} \hline +Keyword & {\tt Radial} & {\tt Theta} & {\tt phi} \\ \hline +{\tt xcoarse} & 30 & 12 & 24 \\ \hline +{\tt coarse} & 50 & 15 & 30 \\ \hline +{\tt medium} & 70 & 18 & 36 \\ \hline +{\tt fine} &100 & 24 & 48 \\ \hline +{\tt xfine} &140 & 34 & 68 \\ \hline + \end{tabular} \\ +\end{table} +\end{center} + +\begin{center} +\begin{table}[htb] +\caption{Number of radial and angular shells required for Row 2 atoms + (Na $\rightarrow$ Cl) to reach the desired accuracies.} + +\vspace{.2in} + + \begin{tabular}[right]{|c|c|c|c|} \hline +Keyword & {\tt Radial} & {\tt Theta} & {\tt phi} \\ \hline +{\tt xcoarse} & 45 & 12 & 24 \\ \hline +{\tt coarse} & 75 & 18 & 36 \\ \hline +{\tt medium} & 95 & 24 & 48 \\ \hline +{\tt fine} &125 & 30 & 60 \\ \hline +{\tt xfine} &175 & 44 & 88 \\ \hline + \end{tabular} \\ +\end{table} +\end{center} + +\begin{center} +\begin{table}[htb] +\caption{Number of radial and angular shells required for Row 3 atoms + (K $\rightarrow$ Br) to reach the desired accuracies.} + +\vspace{.2in} + + \begin{tabular}[right]{|c|c|c|c|} \hline +Keyword & {\tt Radial} & {\tt Theta} & {\tt phi} \\ \hline +{\tt xcoarse} & 75 & 14 & 28 \\ \hline +{\tt coarse} & 95 & 22 & 44 \\ \hline +{\tt medium} &110 & 30 & 60 \\ \hline +{\tt fine} &160 & 34 & 68 \\ \hline +{\tt xfine} &210 & 38 & 76 \\ \hline + \end{tabular} \\ +\end{table} +\end{center} + +\begin{center} +\begin{table}[htb] +\caption{Number of radial and angular shells required for Row 4 atoms + (Rb $\rightarrow$ I) to reach the desired accuracies.} + +\vspace{.2in} + + \begin{tabular}[right]{|c|c|c|c|} \hline +Keyword & {\tt Radial} & {\tt Theta} & {\tt phi} \\ \hline +{\tt xcoarse} &105 & 16 & 32 \\ \hline +{\tt coarse} &130 & 20 & 40 \\ \hline +{\tt medium} &155 & 32 & 64 \\ \hline +{\tt fine} &205 & 44 & 88 \\ \hline +{\tt xfine} &235 & 48 & 96 \\ \hline + \end{tabular} \\ +\end{table} +\end{center} + + +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. -The user has the option of specifying a custom quadrature of this -type with the keywords, \begin{verbatim} GRID gausleg \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} @@ -618,7 +717,18 @@ $N_{angular}$ & 38 & 50 & 110 & 194 & 266 & 302 & 434 \\ \hline Therefore the user can specify any number of radial points along with the level of angular quadrature (1-7). -{\bf JEFF: store\_weight, nquad\_task, delley, and becke need explaining} +% [store_wght] [nquad_task ] \ +%{\bf JEFF: store\_weight and nquad\_task need explaining} +%store\_weight and nquad_task keywords will remain as expert user only +% and not advertised until further tested. -jan +% + +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. + +\begin{verbatim} + GRID [(becke||delley) default becke] +\end{verbatim} \section{{\tt TOLERANCES} --- Screening tolerances}