Figure algo
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@ -24,9 +24,61 @@
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%\node[inst] (h0) at (0,2.5) { $\tilde{H}^{(k)} = \tilde{H}(n^{(k)})$ };
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%\node[res] (h0) at (3,2.5) { $E^{(k)}$ };
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Na ( 3.929174,-1.038386) 0.000000
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Mg ( 2.435205,-1.172771) 0.000000
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O ( 2.101351,-2.635146) 0.000000
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F ( 3.388986,-3.404559) 0.000000
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Ne ( 4.518642,-2.417707) 0.000000
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Al ( 1.500000, 0.000000) 0.000000
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Si ( 2.250000, 1.299038) 0.000000
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N ( 0.749849,-3.285870) 0.000000
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C (-0.601539,-2.634910) 0.000000
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B (-0.935138,-1.172476) 0.000000
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Be (-0.000001,-0.000000) 0.000000
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Li (-0.793853, 1.272713) 0.000000
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H (-3.052250, 2.221211) 0.000000
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He (-2.258396, 0.948498) 0.000000
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XX (-0.663664, 2.334763) 0.000000
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XX ( 0.633384,-4.349513) 0.000000
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XX ( 4.716656,-0.313975) 0.000000
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node distance=2cm,on grid,>=stealth',
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Op1/.style={circle,draw,fill=yellow!40},
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Op2/.style={circle,draw,fill=orange!40},
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Op3/.style={circle,draw,fill=red!40},
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Op4/.style={circle,draw,fill=violet!40},
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DeadOp/.style={circle,draw,fill=gray!40},
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Input/.style={fill=white!40},
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Output/.style={fill=white!40}]
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\node [Op1, align=center] (G) at (3*0.587785, 3*0.809017) {$G$};
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\node [DeadOp, align=center] (Gamma) at (3*0.951057, -3*0.309017) {$\Gamma$};
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\node [Op2, align=center] (P) at (3*0, -3*1.00000) {$P$};
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\node [Op3, align=center] (W) at (-3*0.951057, -3*0.309017) {$W$};
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\node [Op4, align=center] (Sigma) at (-3*0.587785, 3*0.809017) {$\Sigma$};
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\node [Input, align=center] (In) [above=of G] {};
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\node [Output, align=center] (Out) [above=of Sigma] {};
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\node [Input, align=center] (In) [above=of G, yshift=1cm] {KS-DFT};
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\node [Output, align=center] (Out) [above=of Sigma, yshift=1cm] {BSE};
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\path
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(G) edge [->,color=gray!50] node [above,sloped,black] {$\Gamma = 1 + \fdv{\Sigma}{G} GG \Gamma$} (Gamma)
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(Gamma) edge [->,color=gray!50] node [below,sloped,black] {$P = - i GG \Gamma$} (P)
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(P) edge [->,color=black] node [above,sloped,black] {$W = v + vPW$} (W)
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(W) edge [->,color=black] node [above,sloped,black] {$\Sigma = i GW\Gamma$} (Sigma)
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(Sigma) edge [->,color=black] node [above,sloped,black] {$G = G_\text{0} + G_\text{0} \Sigma G$} (G)
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(G) edge [->,color=black] node [above,sloped,black] {$P = - i GG \quad (\Gamma = 1)$} (P)
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(In) edge [->,color=black] node [above,sloped,black] {$\varepsilon^\text{KS}$} (G)
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(Sigma) edge [->,color=black] node [above,sloped,black] {$W(\omega)$ \& $\varepsilon^\text{GW}$} (Out)
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;
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\end{tikzpicture}
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#+END_SRC
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% Nodes
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\node[arr] at (.5,19) { $\Psi^{(0)}$ };
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\node[inst] (n0) at (0,18) { Compute one-e density };
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\node[arr] at () { $\Psi^{(0)}$ };
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\node[inst] (n0) at (0,18) { Compute one-$e$ density };
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\draw[nxt] (0,19.5) -- (n0) ;
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\node[inst] (n1) at (0,16) { Compute RSDFT Hamiltonian };
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@ -96,7 +148,5 @@
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\draw[nxt] (n14) -- (1., -5.5);
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\node[arr] at (2.2,-5) { $\Psi_\text{RSDFT-CIPSI}$ };
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\end{tikzpicture}
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#+END_SRC
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106
Data/algorithm.tex
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106
Data/algorithm.tex
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@ -0,0 +1,106 @@
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\documentclass{standalone}
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\usepackage{graphicx,bm,microtype,hyperref,algpseudocode,subfigure,algorithm,algorithmicx,multirow,footnote,xcolor,physics,lipsum,wasysym,physics}
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\usepackage{tikz}
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\usetikzlibrary{arrows,positioning,shapes.geometric}
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\usetikzlibrary{decorations.pathmorphing}
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\tikzset{snake it/.style={
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decoration={snake,
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amplitude = .4mm,
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segment length = 2mm},decorate}
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}
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%\usepackage{tgchorus}
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%\usepackage[T1]{fontenc}
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\begin{document}
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\begin{tikzpicture}[scale=2.3]
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\begin{scope}[very thick
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,node distance=2cm,on grid,>=stealth'
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,Op1/.style={circle,draw,fill=yellow!40}
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,Ring1/.style={circle,draw,fill=red!40}
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,Ring2/.style={circle,draw,fill=blue!40}
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,Ring12/.style={circle,draw,fill=purple!40}
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,Ring1Test/.style={diamond,draw,fill=red!40}
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,Ring12Test/.style={diamond,draw,fill=purple!40}
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,Output/.style={ellipse,draw,fill=orange!40}
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,Input/.style={rectangle,draw,fill=green!40}
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]
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\node [Input, align=center] (H) at (-3.052250,2.221211) { $\Psi^{(0)}$ };
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\node [Op1, align=center] (He) at (-2.258396,0.948498) { Compute \\ one-$e$ \\ density };
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\node [Op1, align=center] (Li) at (-0.793853,1.272713) { Compute \\ RSDFT \\ Hamiltonian };
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\node [Ring1, align=center] (Be) at (-0.000001,-0.000000) { CIPSI };
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\node [Ring1, align=center] (B) at (-0.935138,-1.172476) { Compute \\ one-$e$ \\ density };
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\node [Ring1, align=center] (C) at (-0.601539,-2.634910) { DIIS$_k$ };
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\node [Ring1, align=center] (N) at (0.749849,-3.285870) { Compute \\ RSDFT \\ Hamiltonian };
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\node [Ring12, align=center] (O) at (2.101351,-2.635146) { Find \\ lowest \\ eigenvector };
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\node [Ring2, align=center] (F) at (3.388986,-3.404559) { Compute \\ one-e \\ density};
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\node [Ring2, align=center] (Ne) at (4.518642,-2.417707) { DIIS$_l$ };
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\node [Ring2, align=center] (Na) at (3.929174,-1.038386) { Compute \\ RSDFT \\ Hamiltonian };
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\node [Ring12Test, align=center] (Mg) at (2.435205,-1.172771) { $\Delta E^{(k,l)} < \tau_2$ };
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\node [Ring1Test, align=center] (Al) at (1.500000,0.000000) { $\Delta E^{(k)} < \tau_1$ };
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\node [Input, align=center] (Si) at (2.250000,1.299038) { $\Psi_\text{T}$ };
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\node [Output, align=center] (X1) at (-0.663664,2.334763) { $E^{(0)}$ };
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\node [Output, align=center] (X2) at (0.633384,-4.349513) { $E^{(k)}$ };
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\node [Output, align=center] (X3) at (4.716656,-0.313975) { $E^{(k,l)}$ };
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\path
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(H) edge [->,color=black ] node [above,black] {} (He)
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(He) edge [->,color=black ] node [above,black] { $n^{(0)}$ } (Li)
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(Li) edge [->,color=black ] node [below,black,sloped,align=left] { $H^{(k)}$ }
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node [above,black,sloped] { $k\leftarrow 0$ }(Be)
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(Be) edge [->,color=black ] node [above,sloped,black] { $\Psi^{(k)}$ } (B)
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(Al) edge [->,color=black ] node [above,sloped,black] { no} (Be)
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(B) edge [->,color=black ] node [below,sloped,black] { $n^{(k)}$ } (C)
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(C) edge [->,color=black ] node [below,sloped,black] { $\tilde{n}^{(k)}$ } (N)
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(N) edge [->,color=black ] node [below,sloped,black] { $H^{(k,l)}$ }
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node [above,sloped,black] { $l\leftarrow 0$ } (O)
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(O) edge [->,color=black ] node [below,sloped,black] { $\Psi^{(k,l)}$ }(F)
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(F) edge [->,color=black ] node [below,sloped,black] { $n^{(k,l)}$ } (Ne)
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(Ne) edge [->,color=black ] node [above,sloped,black] { $\tilde{n}^{(k,l)}$ } (Na)
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(Na) edge [->,color=black ] node [above,sloped,black] { $E^{(k,l)}$ } (Mg)
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(Mg) edge [->,color=black ] node [right,black] { yes } (Al)
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(Mg) edge [->,color=black ] node [right,black] { no } (O)
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(Al) edge [->,color=black ] node [above,sloped,black] {yes} (Si)
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(Li) edge [->,color=black,snake it ] node [above,sloped,black] {} (X1)
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(N) edge [->,color=black,snake it ] node [above,sloped,black] {} (X2)
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(Na) edge [->,color=black,snake it ] node [above,sloped,black] {} (X3)
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;
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%\node[arr] at (2.5,-1)
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%\node[arr] at (-1.,2) { $l\leftarrow l+1$ };
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%\node[arr] at (-1.3,1.5) { $\tilde{H}^{(k,l)}$ };
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%\node[tst] (n14) at (1,-4)
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%\node[arr] at (-4.,4.5) { $k\leftarrow k+1$ };
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%\node[arr] at (-3.6,4) { $\tilde{H}^{(k)}$ };
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%\node[arr] at (2.2,-5)
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%\node [Input, align=center] (In) [above=of G] {};
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%\node [Output, align=center] (Out) [above=of Sigma] {};
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%\node [Input, align=center] (In) [above=of G, yshift=1cm] {KS-DFT};
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%\node [Output, align=center] (Out) [above=of Sigma, yshift=1cm] {BSE};
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%\path
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%(G) edge [->,color=gray!50] node [above,sloped,black] {$\Gamma = 1 + \fdv{\Sigma}{G} GG \Gamma$} (Gamma)
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%(Gamma) edge [->,color=gray!50] node [below,sloped,black] {$P = - i GG \Gamma$} (P)
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%(P) edge [->,color=black] node [above,sloped,black] {$W = v + vPW$} (W)
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%(W) edge [->,color=black] node [above,sloped,black] {$\Sigma = i GW\Gamma$} (Sigma)
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%(Sigma) edge [->,color=black] node [above,sloped,black] {$G = G_\text{0} + G_\text{0} \Sigma G$} (G)
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%(G) edge [->,color=black] node [above,sloped,black] {$P = - i GG \quad (\Gamma = 1)$} (P)
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%(In) edge [->,color=black] node [above,sloped,black] {$\varepsilon^\text{KS}$} (G)
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%(Sigma) edge [->,color=black] node [above,sloped,black] {$W(\omega)$ \& $\varepsilon^\text{GW}$} (Out)
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%;
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\end{scope}
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\end{tikzpicture}
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\end{document}
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% Nodes
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Binary file not shown.
@ -358,12 +358,12 @@ It is possible to use DFT for short-range interactions and CIPSI for
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the long-range. This scheme has been recently
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implemented.\cite{GinPraFerAssSavTou-JCP-18}
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\begin{figure}[h]
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\begin{figure*}
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\centering
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\includegraphics[width=\columnwidth]{algorithm.pdf}
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\includegraphics[width=0.7\linewidth]{algorithm.pdf}
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\caption{Algorithm showing the generation of the RSDFT-CIPSI wave
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function}
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\end{figure}
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\end{figure*}
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% Overlap with reoptimized
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@ -373,7 +373,7 @@ implemented.\cite{GinPraFerAssSavTou-JCP-18}
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\section{Influence of the range-separation parameter on the fixed-node
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error}
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\label{sec:mu-dmc}
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\begin{table}[h]
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\begin{table}
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\caption{Fixed-node energies of the water molecule.}
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\label{tab:h2o-dmc}
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\centering
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@ -398,7 +398,7 @@ implemented.\cite{GinPraFerAssSavTou-JCP-18}
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\end{tabular}
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\end{table}
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\begin{figure}[h]
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\begin{figure}
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\centering
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\includegraphics[width=\columnwidth]{h2o-dmc.pdf}
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\caption{Fixed-node energies of the water molecule for different
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@ -406,7 +406,7 @@ implemented.\cite{GinPraFerAssSavTou-JCP-18}
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\label{fig:h2o-dmc}
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\end{figure}
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\begin{figure}[h]
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\begin{figure}
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\centering
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\includegraphics[width=\columnwidth]{f2-dmc.pdf}
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\caption{Fixed-node energies of difluorine for different
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@ -444,7 +444,7 @@ in the CBS limit we expect the minimum of the FN-DMC energy to be
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obtained for the FCI wave function, at $\mu=\infty$.
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\begin{figure}[h]
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\begin{figure}
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\centering
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\includegraphics[width=\columnwidth]{overlap.pdf}
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\caption{Overlap of the RSDFT-CIPSI wave functions with the
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@ -604,21 +604,21 @@ of the RSDFT-CIPSI trial wave functions for energy differences.
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\end{table}
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\end{squeezetable}
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\begin{figure}[h]
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\begin{figure}
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\centering
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\includegraphics[width=\columnwidth]{g2-dmc-dz.pdf}
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\caption{Histogram of the errors in atomization energies with the double-zeta basis set.}
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\label{fig:g2-dmc-dz}
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\end{figure}
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\begin{figure}[h]
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\begin{figure}
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\centering
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\includegraphics[width=\columnwidth]{g2-dmc-tz.pdf}
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\caption{Histogram of the errors in atomization energies with the triple-zeta basis set.}
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\label{fig:g2-dmc-tz}
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\end{figure}
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\begin{figure}[h]
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\begin{figure}
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\centering
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\includegraphics[width=\columnwidth]{g2-dmc-qz.pdf}
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\caption{Histogram of the errors in atomization energies with the quadruple-zeta basis set.}
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