\documentclass{standalone}
\usepackage{amsmath,amssymb,amsfonts,pgfpages,graphicx,subfigure,xcolor,bm,multirow,microtype,wasysym,multimedia,hyperref,tabularx,amscd,pgfgantt,mhchem,physics}
\usetikzlibrary{shapes.gates.logic.US,trees,positioning,arrows}

\usepackage{tgchorus}
\usepackage[T1]{fontenc}

\begin{document}

\begin{tikzpicture}
	\begin{scope}[very thick,
		node distance=5cm,on grid,>=stealth',
		theo1/.style={rectangle,draw,fill=red!20},
		theo2/.style={rectangle,draw,fill=orange!20},
		theo3/.style={rectangle,draw,fill=green!40},
		exp1/.style={rectangle,draw,fill=cyan!40},
		exp2/.style={rectangle,draw,fill=violet!40}]
		
		\node [theo1, text width=7cm, align=center]	(KS)		
		{\textbf{\LARGE Kohn-Sham DFT}
			$$
				\qty[ -\frac{\nabla^2}{2} + v_\text{ext} + V^{\text{Hxc}} ] \phi_p^{\text{KS}} = \varepsilon^{\text{KS}}_p \phi_p^{\text{KS}}
			$$	
		};									

		\node [theo2, text width=7cm, align=center]	(GW)	[below=of KS, yshift=2cm]				
		{\textbf{\LARGE $GW$ approximation} 
			$$   
				\varepsilon_p^{GW} = \varepsilon_p^{\text{KS}} +
				\mel{\phi_p^{\text{KS}}}{\Sigma^{GW}(\varepsilon_p^{GW}) - V^{\text{xc}}}{\phi_p^{\text{KS}}}
			$$

		};												

		\node [theo3, text width=7cm, align=center]	(BSE)	[below=of GW, yshift=2cm]									
		{\textbf{\LARGE Bethe-Salpeter equation}
			$$
				\begin{pmatrix}
					\bm{A} & \bm{B}  \\
					-\bm{B}^*  & -\bm{A}^{*}
				\end{pmatrix}
				\begin{pmatrix}
					\bm{X}_m  \\
					\bm{Y}_m
				\end{pmatrix}
				=
				\Omega_{m}
				\begin{pmatrix}
					\bm{X}_m  \\
					\bm{Y}_m
				\end{pmatrix}
			$$
		};
								

		\node [exp1, align=center] 					(photo)	[right=of GW, xshift=3cm]										
		{\LARGE (Inverse) \\ \LARGE  photoemission \\ \LARGE  spectroscopy};

		\node [exp2, align=center] 					(abs)	[right=of BSE, xshift=3cm]			
		{\LARGE  Optical \\ \LARGE spectroscopy};
		
		
		\path 
		(KS) 			edge [->,color=black] 			node [right,black] {\LARGE Fundamental gap}		(GW)
		(GW) 			edge [->,color=black] 			node [right,black] {\LARGE Excitonic effect}	(BSE)
		(photo) 		edge [<->,color=black] 			node [above,black] {Ionization potentials}	node [below,black] {Electron affinities}	(GW)
		(abs) 			edge [<->,color=black] 			node [above,black] {Optical excitations}	(BSE)
		;

		
	\end{scope}
\end{tikzpicture}

\end{document}