\documentclass{standalone}
\usepackage{endiagram}
\usepackage{pgfplots}


\begin{document}
\pagestyle{empty}
%\begin{endiagram}
%\ENcurve[step=4]{1,6,0}
%\ENcurve[tikz={densely dotted}]
%{1,4[1],2.5,3[-1],0}
%\end{endiagram}

%\draw [domain=-pi:pi] plot (\x,{sin(\x r)});.

%\begin{tikzpicture}
%\draw[help lines] (0,0) grid (2,3);
%\draw[step=0.5, gray, very thin] (-1.4,-1.4) grid (1.4,1.4);
%\draw (0,0) parabola (1,1.5) parabola[bend at end] (2,0);
%\draw (0,0) sin (1,1) cos (2,0) sin (3,-1) cos (4,0) sin (5,1);
%\end{tikzpicture}


%\begin{tikzpicture}
%\draw (0,0) -- (0.5,0);
%\draw (0,0) cos(2,0);
%\end{tikzpicture}

%\begin{tikzpicture}
 % \begin{axis}[
   %   axis x line=none,
    %  axis y line=none,
    %  domain=-90:270,
     % xtick={-360, -330, ..., 360},
     % samples=1001,
    %  xticklabels=\empty,
    %]
   % \addplot [black] {3*sin(x)};
 % \end{axis}
  %\draw (0,0) -- (0.5,0);
%\end{tikzpicture}

% \begin{center}
  \begin{tikzpicture}[scale=1]
%grid%
%\draw [very thin,gray] (-3,-3) grid (3,3);

%curves%
    \draw[line width=2.4] plot[domain=-1.1*pi:1.1*pi,smooth] (\x,{1.5*cos(\x r)});
     \node[fill=none, text=black, circle, draw=black,line width=1.5] at (2.5,0) {S};
     
      %\draw[line width=1.5,scale=0.7,domain=-3:3, smooth, variable=\x, red] plot ({\x}, {\x*\x +4.3});%
      
      \draw[line width=2.4,red] plot[domain=-3.2:3.2,smooth] (\x,{0.65*\x*\x +3.5})  ;
       \node[fill=none, text=red, circle, draw=red,line width=1.5] at (2.5,6) {T};
       
       \node[fill=white,rotate=0,inner sep=-1.25pt,outer sep=0,anchor=center,text=red] at (2.62,8) {$\approx$};
       
        \node[fill=white,rotate=0,inner sep=-1.25pt,outer sep=0,anchor=center,text=red] at (-2.62,8) {$\approx$};
    
%states%

    %left% 
      \draw (-2.5,-1.5) -- (-3.5,-1.5);
      \node[] at (-4.3,-1.5) {\Large $1{}^1$A$_{g}$};
      
       \draw[red] (-2.5,9.5) -- (-3.5,9.5);
      \node[red] at (-4.3,9.5) {\Large $1~^3$B$_{1g}$};
     
     
     %right%
      \draw (2.5,-1.5) -- (3.5,-1.5);
      \node[] at (4.3,-1.5) {\Large $1{}^1$A$_{g}$};
      
       \draw[red] (2.5,9.5) -- (3.5,9.5);
      \node[red] at (4.3,9.5) {\Large $1~^3$B$_{1g}$};
      
      %above%
       \draw (-0.5,1.5) -- (0.5,1.5);
       \node[] at (1.3,1.4) {\Large $1{}^1$B$_{1g}$};
       
        \draw[red] (-0.5,3.5) -- (0.5,3.5);
       \node[red] at (1.3,3.5) {\Large $1~^3$A$_{2g}$};
	   
%geometry%

	%left%
     \draw[line width=1.5] (-3.4,-1.7) rectangle (-2.5,-2.4);
     \draw[line width=1.5] (-3.3,-1.8) -- (-3.3,-2.3);
      \draw[line width=1.5] (-2.6,-1.8) -- (-2.6,-2.3);
      \node[] at (-3,-2.9) {\Large D$_{2h}$};
      
      %right%
      \draw[line width=1.5] (2.7,-1.7) rectangle (3.4,-2.6);
      \draw[line width=1.5] (2.8,-1.8) -- (3.3,-1.8);
      \draw[line width=1.5] (2.8,-2.5) -- (3.3,-2.5);
      \node[] at (3,-2.9) {\Large D$_{2h}$};
      
      %above%
      \node[] at (0,0.1) {\Large D$_{4h}$};
      \draw[line width=1.5] (-0.4,0.4) rectangle (0.4,1.2);
      \draw[dashed,line width=1.5] (0,0.8) circle (0.3cm);
      
       \node[] at (0,0.1) {\Large D$_{4h}$};
      \draw[red,line width=1.5] (-0.4,4) rectangle (0.4,4.8);
      \draw[dashed,red,line width=1.5] (0,4.4) circle (0.3cm);
      
%autoisomerization barrier arrow%

     \draw [line width=1.5,stealth-stealth](-3.0,-1.5) -- (-3.0,1.5);
      \node[] at (-2.5,0.3) {\Large AB};
      
      
      
  \end{tikzpicture}
%  \end{center}
  
   
 % \begin{tikzpicture}

%\draw (4,0.2) -- node[fill=white,rotate=90,inner sep=-1.25pt,outer sep=0,anchor=center]{$\approx$} (8,0.2);
%\draw (4,1.8) -- node[fill=white,rotate=0,inner sep=-1.25pt,outer sep=5]{ // } (8,1.8);
%\end{tikzpicture}
\end{document}