How to draw molecular excitation by light diagram

Question

I am trying to draw the following diagram: I have begun drawing the diagram in tikz but I am unsure how to do the electronic excitation and the scale:

\begin{tikzpicture}[scale=1]
\fill[blue!20] (0,0) circle (0.3) (1.6,0) circle (0.3);
\fill[blue!20] (0,-0.1) rectangle (1.6,0.1);
\draw[-latex] (-0.4,0) -- (-1,0);
\draw[-latex] (2,0) -- (2.6,0);
\node[align=center] at (0.8,1.7) {Vibration};
\begin{scope}[xshift=4cm]
\fill[blue!20] (0,0) circle (0.3) (1.6,0) circle (0.3);
\fill[blue!20] (0,-0.1) rectangle (1.6,0.1);
\draw[-latex] (1.6,0.3) arc (0:90:0.7 and 0.7);
\draw[-latex] (0,-0.3) arc (180:270:0.7 and 0.7);
\node[align=center] at (0.8,1.7) {Rotation};
\end{scope}
\begin{scope}[xshift=-8cm]
\fill[blue!20] (0,0) circle (0.3) (1.6,0) circle (0.3);
\fill[blue!20] (0,-0.1) rectangle (0.5,0.1);
\fill[blue!20] (1.1,-0.1) rectangle (1.6,0.1);
\draw[densely dashed] (0.8,-0.5) -- (0.8,0.5);
\node[align=center] at (0.8,1.7) {Bond breaking \\ and ionization};
\end{scope}
\end{tikzpicture}

Which produces this image

Edit

After using Marmot's code, I added an axis and now have the following image:

The code is:

\documentclass{article}
\usepackage{tikz}
\usepackage{pgfplots}
\usepackage{xxcolor}
\tikzset{viewport/.style 2 args={
    x={({cos(-#1)*1cm},{sin(-#1)*sin(#2)*1cm})},
    y={({-sin(-#1)*1cm},{cos(-#1)*sin(#2)*1cm})},
    z={(0,{cos(#2)*1cm})}
}}

% Styles to plot only points that are before or behind the sphere.
\pgfplotsset{only foreground/.style={
    restrict expr to domain={rawx*\CameraX + rawy*\CameraY + rawz*\CameraZ}{-0.05:100},
}}
\pgfplotsset{only background/.style={
    restrict expr to domain={rawx*\CameraX + rawy*\CameraY + rawz*\CameraZ}{-100:0.05}
}}

% Automatically plot transparent lines in background and solid lines in foreground
\def\addFGBGplot[#1]#2;{
    %\addplot3[#1,only background, opacity=0.25] #2;
    \addplot3[#1,only foreground] #2;
}

\newcommand{\ViewAzimuth}{-20}
\newcommand{\ViewElevation}{30}

\pgfmathsetmacro{\CameraX}{sin(\ViewAzimuth)*cos(\ViewElevation)}
\pgfmathsetmacro{\CameraY}{-cos(\ViewAzimuth)*cos(\ViewElevation)}
\pgfmathsetmacro{\CameraZ}{sin(\ViewElevation)}
\newsavebox\mononut
\sbox\mononut{
\begin{tikzpicture}
    % Compute camera unit vector for calculating depth
    \begin{scope}
      \draw[thin,blue!50] (0,0) circle (1);
      \begin{axis}[
            hide axis,
            view={\ViewAzimuth}{\ViewElevation},     % Set view angle
            disabledatascaling,                      % Align PGFPlots coordinates with TikZ
            anchor=origin,                           % Align PGFPlots coordinates with TikZ
            viewport={\ViewAzimuth}{\ViewElevation}, % Align PGFPlots coordinates with TikZ
        ]
        % Plot equator and two longitude lines with occlusion
        \pgfplotsinvokeforeach{30,60,...,150}{
        \addFGBGplot[blue!50,thick,domain=0:2*pi, samples=100, samples y=1] 
        ({cos(deg(x))*sin(#1)}, {sin(deg(x))*sin(#1)}, {cos(#1)});
        }
        %\addFGBGplot[domain=0:2*pi, samples=100, samples y=1] (0, {sin(deg(x))}, {cos(deg(x))});
        \pgfplotsinvokeforeach{90,125,160}{
        \addFGBGplot[blue!50,thick,domain=0:2*pi, samples=100, samples y=1]
        ({sin(deg(x))*sin(#1)},{cos(#1)}, {cos(deg(x))*sin(#1)});}
      \end{axis}
    \end{scope}
\end{tikzpicture}
}
\newsavebox\mononutdashed
\sbox\mononutdashed{
\begin{tikzpicture}
    % Compute camera unit vector for calculating depth
    \begin{scope}
      \draw[thin,blue!50,dashed] (0,0) circle (1);
      \begin{axis}[
            hide axis,
            view={\ViewAzimuth}{\ViewElevation},     % Set view angle
            disabledatascaling,                      % Align PGFPlots coordinates with TikZ
            anchor=origin,                           % Align PGFPlots coordinates with TikZ
            viewport={\ViewAzimuth}{\ViewElevation}, % Align PGFPlots coordinates with TikZ
        ]
        % Plot equator and two longitude lines with occlusion
        \pgfplotsinvokeforeach{30,60,...,150}{
        \addFGBGplot[blue!50,dashed,thick,domain=0:2*pi, samples=100, samples y=1] 
        ({cos(deg(x))*sin(#1)}, {sin(deg(x))*sin(#1)}, {cos(#1)});
        }
        %\addFGBGplot[domain=0:2*pi, samples=100, samples y=1] (0, {sin(deg(x))}, {cos(deg(x))});
        \pgfplotsinvokeforeach{90,125,160}{
        \addFGBGplot[blue!50,dashed,thick,domain=0:2*pi, samples=100, samples y=1]
        ({sin(deg(x))*sin(#1)},{cos(#1)}, {cos(deg(x))*sin(#1)});}
      \end{axis}
    \end{scope}
\end{tikzpicture}
}
\newsavebox\peanut
\sbox\peanut{
\begin{tikzpicture}
    \begin{scope}
      \draw[thin,blue!50] (45:1) arc(45:315:1);
      \clip (45:1) arc(45:315:1);
      \begin{axis}[
            hide axis,
            view={\ViewAzimuth}{\ViewElevation},     % Set view angle
            disabledatascaling,                      % Align PGFPlots coordinates with TikZ
            anchor=origin,                           % Align PGFPlots coordinates with TikZ
            viewport={\ViewAzimuth}{\ViewElevation}, % Align PGFPlots coordinates with TikZ
        ]
        % Plot equator and two longitude lines with occlusion
        \pgfplotsinvokeforeach{30,60,...,150}{
        \addFGBGplot[blue!50,thick,domain=0:2*pi, samples=100, samples y=1] 
        ({cos(deg(x))*sin(#1)}, {sin(deg(x))*sin(#1)}, {cos(#1)});
        }
        %\addFGBGplot[domain=0:2*pi, samples=100, samples y=1] (0, {sin(deg(x))}, {cos(deg(x))});
        \pgfplotsinvokeforeach{90,125,160}{
        \addFGBGplot[blue!50,thick,domain=0:2*pi, samples=100, samples y=1]
        ({sin(deg(x))*sin(#1)},{cos(#1)}, {cos(deg(x))*sin(#1)});}
      \end{axis}
    \end{scope}
    \begin{scope}[xshift={1.4cm}]
      \draw[thin,blue!50] (225:1) arc(225:225+270:1);
      \clip (225:1) arc(225:225+270:1);
      \begin{axis}[
            hide axis,
            view={\ViewAzimuth}{\ViewElevation},     % Set view angle
            disabledatascaling,                      % Align PGFPlots coordinates with TikZ
            anchor=origin,                           % Align PGFPlots coordinates with TikZ
            viewport={\ViewAzimuth}{\ViewElevation}, % Align PGFPlots coordinates with TikZ
        ]
        % Plot equator and two longitude lines with occlusion
        \pgfplotsinvokeforeach{30,60,...,150}{
        \addFGBGplot[blue!50,thick,domain=0:2*pi, samples=100, samples y=1] 
        ({cos(deg(x))*sin(#1)}, {sin(deg(x))*sin(#1)}, {cos(#1)});
        }
        %\addFGBGplot[domain=0:2*pi, samples=100, samples y=1] (0, {sin(deg(x))}, {cos(deg(x))});
        \pgfplotsinvokeforeach{95,125,160}{
        \addFGBGplot[blue!50,thick,domain=0:2*pi, samples=100, samples y=1]
        ({sin(deg(x))*sin(#1)},{cos(#1)}, {cos(deg(x))*sin(#1)});}
      \end{axis}
    \end{scope}
\end{tikzpicture}
}
\newsavebox\peanutdashed
\sbox\peanutdashed{
\begin{tikzpicture}
    \begin{scope}
      \draw[thin,blue!50,dashed] (45:1) arc(45:315:1);
      \clip (45:1) arc(45:315:1);
      \begin{axis}[
            hide axis,
            view={\ViewAzimuth}{\ViewElevation},     % Set view angle
            disabledatascaling,                      % Align PGFPlots coordinates with TikZ
            anchor=origin,                           % Align PGFPlots coordinates with TikZ
            viewport={\ViewAzimuth}{\ViewElevation}, % Align PGFPlots coordinates with TikZ
        ]
        % Plot equator and two longitude lines with occlusion
        \pgfplotsinvokeforeach{30,60,...,150}{
        \addFGBGplot[blue!50,dashed,thick,domain=0:2*pi, samples=100, samples y=1] 
        ({cos(deg(x))*sin(#1)}, {sin(deg(x))*sin(#1)}, {cos(#1)});
        }
        %\addFGBGplot[domain=0:2*pi, samples=100, samples y=1] (0, {sin(deg(x))}, {cos(deg(x))});
        \pgfplotsinvokeforeach{90,125,160}{
        \addFGBGplot[blue!50,dashed,thick,domain=0:2*pi, samples=100, samples y=1]
        ({sin(deg(x))*sin(#1)},{cos(#1)}, {cos(deg(x))*sin(#1)});}
      \end{axis}
    \end{scope}
    \begin{scope}[xshift={1.4cm}]
      \draw[thin,blue!50,dashed] (225:1) arc(225:225+270:1);
      \clip (225:1) arc(225:225+270:1);
      \begin{axis}[
            hide axis,
            view={\ViewAzimuth}{\ViewElevation},     % Set view angle
            disabledatascaling,                      % Align PGFPlots coordinates with TikZ
            anchor=origin,                           % Align PGFPlots coordinates with TikZ
            viewport={\ViewAzimuth}{\ViewElevation}, % Align PGFPlots coordinates with TikZ
        ]
        % Plot equator and two longitude lines with occlusion
        \pgfplotsinvokeforeach{30,60,...,150}{
        \addFGBGplot[blue!50,dashed,thick,domain=0:2*pi, samples=100, samples y=1] 
        ({cos(deg(x))*sin(#1)}, {sin(deg(x))*sin(#1)}, {cos(#1)});
        }
        %\addFGBGplot[domain=0:2*pi, samples=100, samples y=1] (0, {sin(deg(x))}, {cos(deg(x))});
        \pgfplotsinvokeforeach{95,125,160}{
        \addFGBGplot[blue!50,dashed,thick,domain=0:2*pi, samples=100, samples y=1]
        ({sin(deg(x))*sin(#1)},{cos(#1)}, {cos(deg(x))*sin(#1)});}
      \end{axis}
    \end{scope}
\end{tikzpicture}
}

\begin{document}
\begin{tikzpicture}[scale=1]
\begin{scope}[yshift=-1.8cm]
\draw[densely dashed] (6,-4.5) -- (6,3);
\node at (4.5,-3.75) {Microwave};
\draw[densely dashed] (3,-4.5) -- (3,3);
\draw[densely dashed] (-1.7,-4.5) -- (-1.7,3);
\node at (0.65,-3.75) {Infrared};
\draw[densely dashed] (-2.3,-4.5) -- (-2.3,-1.5) (-2.3,0.5) -- (-2.3,1.1);
\draw[densely dashed]  (-4.5,-4.5) -- (-4.5,3);
\node[rotate=90] at (-2,-3.75) {Visible}; 
\node at (-3.4,-3.75) {Ultraviolet};
\node at (-6.75,-3.75) {X-rays};
\draw[densely dashed] (-9,-4.5) -- (-9,3);
\foreach \x in {-11,-10,...,-1}{
\draw (-1.5*\x-10.5,-3) -- (-1.5*\x-10.5,-2.75);
\node[above,fill=white] at  (1.5*\x+7.5,-2.75) {$10^{\x}$};
}
\draw[latex-latex](-10,-3) -- (7,-3);
\node at (-9.7,-3.75) {$\gamma$-rays};
\node[fill=white] at (-9,-1.7) {Wavelength (m)};
\node at (6.7,-3.75) {Radio};
\draw[latex-latex] (-10,-4.5) -- (7,-4.5);
\end{scope}
\fill[blue!20] (0,0) circle (0.3) (1.6,0) circle (0.3);
\fill[blue!20] (0,-0.1) rectangle (1.6,0.1);
\draw[-latex] (-0.4,0) -- (-1,0);
\draw[-latex] (2,0) -- (2.6,0);
\node[align=center] at (0.8,1.7) {Vibration};
\begin{scope}[xshift=3.8cm]
\fill[blue!20] (0,0) circle (0.3) (1.6,0) circle (0.3);
\fill[blue!20] (0,-0.1) rectangle (1.6,0.1);
\draw[-latex] (1.6,0.3) arc (0:90:0.7 and 0.7);
\draw[-latex] (0,-0.3) arc (180:270:0.7 and 0.7);
\node[align=center] at (0.8,1.7) {Rotation};
\end{scope}
\begin{scope}[xshift=-8cm]
\fill[blue!20] (0,0) circle (0.3) (1.6,0) circle (0.3);
\fill[blue!20] (0,-0.1) rectangle (0.5,0.1);
\fill[blue!20] (1.1,-0.1) rectangle (1.6,0.1);
\draw[densely dashed] (0.8,-0.4) -- (0.75,0) -- (0.85,0) -- (0.8,0.4);
\node[align=center] at (0.8,1.7) {Bond breaking \\ and ionization};
\fill[blue!20] (0,-2) circle (0.3) (1.6,-2) circle (0.3);
\fill[blue!20] (0,-2.1) rectangle (1.6,-1.9);
\draw[-latex] (0.8,-1.3) -- (0.8,-0.7);
\end{scope}
\begin{scope}[xshift=-2.8cm,yshift=-1cm]
\node[scale=0.5] at (-0.5,1.8) {\usebox\mononutdashed};
\node[scale=0.5] at (0.5,1.8) {\usebox\mononut};
\node[scale=0.5] at (-0.5,0.8) {\usebox\mononut};
\node[scale=0.5] at (0.5,0.8) {\usebox\mononutdashed};
\node[scale=0.5] at (0,-0.8) {\usebox\peanut};
\node[scale=0.5] at (0,-1.8) {\usebox\peanutdashed};
\node[align=center,fill=white] at (-1.6,-1.3) {\scriptsize Bonding \\ \scriptsize $\pi$ oribtal};
\node[align=center,fill=white] at (-1.8,1.3) {\scriptsize Antibonding \\ \scriptsize $\pi$ oribtal};
\node[align=center] at (0,2.8) {Electronic\\ excitation};
\draw[-latex] (0,-0.3) -- (0,0.3);
\end{scope}
\end{tikzpicture}
\end{document}

I would like for there to be black outline around the simpler molecules and I would like for the scale numbers to be centered on the 10. How do I do this?

Answer 1

DISCLAIMERS and Warnings:

1. Almost everything I am going to present here is based Fritz' great answer, where all the conceptual tasks have been accomplished.
2. This is not a full answer. I did not even look at the tedious part of drawing the axes. However, IMHO this is straightforward and really just tedious. If you have a conceptual question on how to draw this, I will be happy to have a look, but I do not have the time now to do all these tedious things.
3. The shapes are at best cartoons (but have some similarity to what you seem to want to achieve).
4. This code takes some while to compile. All the computation is done in the preamble since I am using saveboxes here. If you decide to use it, add the preamble only after you or someone else has done the axes.

Here are code and output.

\documentclass[margin=3.14mm,tikz]{standalone}
\usepackage{pgfplots}
\usepackage{xxcolor}
\pgfplotsset{compat=1.16}


% Style to set TikZ camera angle, like PGFPlots `view`
\tikzset{viewport/.style 2 args={
    x={({cos(-#1)*1cm},{sin(-#1)*sin(#2)*1cm})},
    y={({-sin(-#1)*1cm},{cos(-#1)*sin(#2)*1cm})},
    z={(0,{cos(#2)*1cm})}
}}

% Styles to plot only points that are before or behind the sphere.
\pgfplotsset{only foreground/.style={
    restrict expr to domain={rawx*\CameraX + rawy*\CameraY + rawz*\CameraZ}{-0.05:100},
}}
\pgfplotsset{only background/.style={
    restrict expr to domain={rawx*\CameraX + rawy*\CameraY + rawz*\CameraZ}{-100:0.05}
}}

% Automatically plot transparent lines in background and solid lines in foreground
\def\addFGBGplot[#1]#2;{
    %\addplot3[#1,only background, opacity=0.25] #2;
    \addplot3[#1,only foreground] #2;
}

\newcommand{\ViewAzimuth}{-20}
\newcommand{\ViewElevation}{30}

\pgfmathsetmacro{\CameraX}{sin(\ViewAzimuth)*cos(\ViewElevation)}
\pgfmathsetmacro{\CameraY}{-cos(\ViewAzimuth)*cos(\ViewElevation)}
\pgfmathsetmacro{\CameraZ}{sin(\ViewElevation)}
\newsavebox\mononut
\sbox\mononut{
\begin{tikzpicture}
    % Compute camera unit vector for calculating depth
    \begin{scope}
      \draw[thin,blue!50] (0,0) circle (1);
      \begin{axis}[
            hide axis,
            view={\ViewAzimuth}{\ViewElevation},     % Set view angle
            disabledatascaling,                      % Align PGFPlots coordinates with TikZ
            anchor=origin,                           % Align PGFPlots coordinates with TikZ
            viewport={\ViewAzimuth}{\ViewElevation}, % Align PGFPlots coordinates with TikZ
        ]
        % Plot equator and two longitude lines with occlusion
        \pgfplotsinvokeforeach{30,60,...,150}{
        \addFGBGplot[blue!50,thick,domain=0:2*pi, samples=100, samples y=1] 
        ({cos(deg(x))*sin(#1)}, {sin(deg(x))*sin(#1)}, {cos(#1)});
        }
        %\addFGBGplot[domain=0:2*pi, samples=100, samples y=1] (0, {sin(deg(x))}, {cos(deg(x))});
        \pgfplotsinvokeforeach{90,125,160}{
        \addFGBGplot[blue!50,thick,domain=0:2*pi, samples=100, samples y=1]
        ({sin(deg(x))*sin(#1)},{cos(#1)}, {cos(deg(x))*sin(#1)});}
      \end{axis}
    \end{scope}
\end{tikzpicture}
}
\newsavebox\mononutdashed
\sbox\mononutdashed{
\begin{tikzpicture}
    % Compute camera unit vector for calculating depth
    \begin{scope}
      \draw[thin,blue!50,dashed] (0,0) circle (1);
      \begin{axis}[
            hide axis,
            view={\ViewAzimuth}{\ViewElevation},     % Set view angle
            disabledatascaling,                      % Align PGFPlots coordinates with TikZ
            anchor=origin,                           % Align PGFPlots coordinates with TikZ
            viewport={\ViewAzimuth}{\ViewElevation}, % Align PGFPlots coordinates with TikZ
        ]
        % Plot equator and two longitude lines with occlusion
        \pgfplotsinvokeforeach{30,60,...,150}{
        \addFGBGplot[blue!50,dashed,thick,domain=0:2*pi, samples=100, samples y=1] 
        ({cos(deg(x))*sin(#1)}, {sin(deg(x))*sin(#1)}, {cos(#1)});
        }
        %\addFGBGplot[domain=0:2*pi, samples=100, samples y=1] (0, {sin(deg(x))}, {cos(deg(x))});
        \pgfplotsinvokeforeach{90,125,160}{
        \addFGBGplot[blue!50,dashed,thick,domain=0:2*pi, samples=100, samples y=1]
        ({sin(deg(x))*sin(#1)},{cos(#1)}, {cos(deg(x))*sin(#1)});}
      \end{axis}
    \end{scope}
\end{tikzpicture}
}
\newsavebox\peanut
\sbox\peanut{
\begin{tikzpicture}
    \begin{scope}
      \draw[thin,blue!50] (45:1) arc(45:315:1);
      \clip (45:1) arc(45:315:1);
      \begin{axis}[
            hide axis,
            view={\ViewAzimuth}{\ViewElevation},     % Set view angle
            disabledatascaling,                      % Align PGFPlots coordinates with TikZ
            anchor=origin,                           % Align PGFPlots coordinates with TikZ
            viewport={\ViewAzimuth}{\ViewElevation}, % Align PGFPlots coordinates with TikZ
        ]
        % Plot equator and two longitude lines with occlusion
        \pgfplotsinvokeforeach{30,60,...,150}{
        \addFGBGplot[blue!50,thick,domain=0:2*pi, samples=100, samples y=1] 
        ({cos(deg(x))*sin(#1)}, {sin(deg(x))*sin(#1)}, {cos(#1)});
        }
        %\addFGBGplot[domain=0:2*pi, samples=100, samples y=1] (0, {sin(deg(x))}, {cos(deg(x))});
        \pgfplotsinvokeforeach{90,125,160}{
        \addFGBGplot[blue!50,thick,domain=0:2*pi, samples=100, samples y=1]
        ({sin(deg(x))*sin(#1)},{cos(#1)}, {cos(deg(x))*sin(#1)});}
      \end{axis}
    \end{scope}
    \begin{scope}[xshift={1.4cm}]
      \draw[thin,blue!50] (225:1) arc(225:225+270:1);
      \clip (225:1) arc(225:225+270:1);
      \begin{axis}[
            hide axis,
            view={\ViewAzimuth}{\ViewElevation},     % Set view angle
            disabledatascaling,                      % Align PGFPlots coordinates with TikZ
            anchor=origin,                           % Align PGFPlots coordinates with TikZ
            viewport={\ViewAzimuth}{\ViewElevation}, % Align PGFPlots coordinates with TikZ
        ]
        % Plot equator and two longitude lines with occlusion
        \pgfplotsinvokeforeach{30,60,...,150}{
        \addFGBGplot[blue!50,thick,domain=0:2*pi, samples=100, samples y=1] 
        ({cos(deg(x))*sin(#1)}, {sin(deg(x))*sin(#1)}, {cos(#1)});
        }
        %\addFGBGplot[domain=0:2*pi, samples=100, samples y=1] (0, {sin(deg(x))}, {cos(deg(x))});
        \pgfplotsinvokeforeach{95,125,160}{
        \addFGBGplot[blue!50,thick,domain=0:2*pi, samples=100, samples y=1]
        ({sin(deg(x))*sin(#1)},{cos(#1)}, {cos(deg(x))*sin(#1)});}
      \end{axis}
    \end{scope}
\end{tikzpicture}
}
\newsavebox\peanutdashed
\sbox\peanutdashed{
\begin{tikzpicture}
    \begin{scope}
      \draw[thin,blue!50,dashed] (45:1) arc(45:315:1);
      \clip (45:1) arc(45:315:1);
      \begin{axis}[
            hide axis,
            view={\ViewAzimuth}{\ViewElevation},     % Set view angle
            disabledatascaling,                      % Align PGFPlots coordinates with TikZ
            anchor=origin,                           % Align PGFPlots coordinates with TikZ
            viewport={\ViewAzimuth}{\ViewElevation}, % Align PGFPlots coordinates with TikZ
        ]
        % Plot equator and two longitude lines with occlusion
        \pgfplotsinvokeforeach{30,60,...,150}{
        \addFGBGplot[blue!50,dashed,thick,domain=0:2*pi, samples=100, samples y=1] 
        ({cos(deg(x))*sin(#1)}, {sin(deg(x))*sin(#1)}, {cos(#1)});
        }
        %\addFGBGplot[domain=0:2*pi, samples=100, samples y=1] (0, {sin(deg(x))}, {cos(deg(x))});
        \pgfplotsinvokeforeach{90,125,160}{
        \addFGBGplot[blue!50,dashed,thick,domain=0:2*pi, samples=100, samples y=1]
        ({sin(deg(x))*sin(#1)},{cos(#1)}, {cos(deg(x))*sin(#1)});}
      \end{axis}
    \end{scope}
    \begin{scope}[xshift={1.4cm}]
      \draw[thin,blue!50,dashed] (225:1) arc(225:225+270:1);
      \clip (225:1) arc(225:225+270:1);
      \begin{axis}[
            hide axis,
            view={\ViewAzimuth}{\ViewElevation},     % Set view angle
            disabledatascaling,                      % Align PGFPlots coordinates with TikZ
            anchor=origin,                           % Align PGFPlots coordinates with TikZ
            viewport={\ViewAzimuth}{\ViewElevation}, % Align PGFPlots coordinates with TikZ
        ]
        % Plot equator and two longitude lines with occlusion
        \pgfplotsinvokeforeach{30,60,...,150}{
        \addFGBGplot[blue!50,dashed,thick,domain=0:2*pi, samples=100, samples y=1] 
        ({cos(deg(x))*sin(#1)}, {sin(deg(x))*sin(#1)}, {cos(#1)});
        }
        %\addFGBGplot[domain=0:2*pi, samples=100, samples y=1] (0, {sin(deg(x))}, {cos(deg(x))});
        \pgfplotsinvokeforeach{95,125,160}{
        \addFGBGplot[blue!50,dashed,thick,domain=0:2*pi, samples=100, samples y=1]
        ({sin(deg(x))*sin(#1)},{cos(#1)}, {cos(deg(x))*sin(#1)});}
      \end{axis}
    \end{scope}
\end{tikzpicture}
}
\begin{document}
\begin{tikzpicture}[scale=1]
\fill[blue!20] (0,0) circle (0.3) (1.6,0) circle (0.3);
\fill[blue!20] (0,-0.1) rectangle (1.6,0.1);
\draw[-latex] (-0.4,0) -- (-1,0);
\draw[-latex] (2,0) -- (2.6,0);
\node[align=center] at (0.8,1.7) {Vibration};
\begin{scope}[xshift=4cm]
\fill[blue!20] (0,0) circle (0.3) (1.6,0) circle (0.3);
\fill[blue!20] (0,-0.1) rectangle (1.6,0.1);
\draw[-latex] (1.6,0.3) arc (0:90:0.7 and 0.7);
\draw[-latex] (0,-0.3) arc (180:270:0.7 and 0.7);
\node[align=center] at (0.8,1.7) {Rotation};
\end{scope}
\begin{scope}[xshift=-8cm]
\fill[blue!20] (0,0) circle (0.3) (1.6,0) circle (0.3);
\fill[blue!20] (0,-0.1) rectangle (0.5,0.1);
\fill[blue!20] (1.1,-0.1) rectangle (1.6,0.1);
\draw[densely dashed] (0.8,-0.5) -- (0.8,0.5);
\node[align=center] at (0.8,1.7) {Bond breaking \\ and ionization};
\end{scope}
\begin{scope}[xshift=-4cm]
\node[scale=0.5] at (-0.5,1.8) {\usebox\mononutdashed};
\node[scale=0.5] at (0.5,1.8) {\usebox\mononut};
\node[scale=0.5] at (-0.5,0.8) {\usebox\mononut};
\node[scale=0.5] at (0.5,0.8) {\usebox\mononutdashed};
\node[scale=0.5] at (0,-0.8) {\usebox\peanut};
\node[scale=0.5] at (0,-1.8) {\usebox\peanutdashed};
\end{scope}
\end{tikzpicture}
\end{document}

ADDENDUM: Your lower code with white halos and centered 10s.

\documentclass{article}
\usepackage[margin=1in]{geometry}
\usepackage{tikz}
\usepackage{pgfplots}
\usepackage{xxcolor}
\tikzset{viewport/.style 2 args={
    x={({cos(-#1)*1cm},{sin(-#1)*sin(#2)*1cm})},
    y={({-sin(-#1)*1cm},{cos(-#1)*sin(#2)*1cm})},
    z={(0,{cos(#2)*1cm})}
}}

% Styles to plot only points that are before or behind the sphere.
\pgfplotsset{only foreground/.style={
    restrict expr to domain={rawx*\CameraX + rawy*\CameraY + rawz*\CameraZ}{-0.05:100},
}}
\pgfplotsset{only background/.style={
    restrict expr to domain={rawx*\CameraX + rawy*\CameraY + rawz*\CameraZ}{-100:0.05}
}}

% Automatically plot transparent lines in background and solid lines in foreground
\def\addFGBGplot[#1]#2;{
    %\addplot3[#1,only background, opacity=0.25] #2;
    \addplot3[#1,only foreground] #2;
}

\newcommand{\ViewAzimuth}{-20}
\newcommand{\ViewElevation}{30}

\pgfmathsetmacro{\CameraX}{sin(\ViewAzimuth)*cos(\ViewElevation)}
\pgfmathsetmacro{\CameraY}{-cos(\ViewAzimuth)*cos(\ViewElevation)}
\pgfmathsetmacro{\CameraZ}{sin(\ViewElevation)}
\newsavebox\mononut
\sbox\mononut{
\begin{tikzpicture}
    % Compute camera unit vector for calculating depth
    \begin{scope}
      \fill[white] (0,0) circle (1.15); 
      \draw[thin,blue!50] (0,0) circle (1);
      \begin{axis}[
            hide axis,
            view={\ViewAzimuth}{\ViewElevation},     % Set view angle
            disabledatascaling,                      % Align PGFPlots coordinates with TikZ
            anchor=origin,                           % Align PGFPlots coordinates with TikZ
            viewport={\ViewAzimuth}{\ViewElevation}, % Align PGFPlots coordinates with TikZ
        ]
        % Plot equator and two longitude lines with occlusion
        \pgfplotsinvokeforeach{30,60,...,150}{
        \addFGBGplot[blue!50,thick,domain=0:2*pi, samples=100, samples y=1] 
        ({cos(deg(x))*sin(#1)}, {sin(deg(x))*sin(#1)}, {cos(#1)});
        }
        %\addFGBGplot[domain=0:2*pi, samples=100, samples y=1] (0, {sin(deg(x))}, {cos(deg(x))});
        \pgfplotsinvokeforeach{90,125,160}{
        \addFGBGplot[blue!50,thick,domain=0:2*pi, samples=100, samples y=1]
        ({sin(deg(x))*sin(#1)},{cos(#1)}, {cos(deg(x))*sin(#1)});}
      \end{axis}
    \end{scope}
\end{tikzpicture}
}
\newsavebox\mononutdashed
\sbox\mononutdashed{
\begin{tikzpicture}
    % Compute camera unit vector for calculating depth
    \begin{scope}
      \fill[white] (0,0) circle (1.15);
      \draw[thin,blue!50,dashed] (0,0) circle (1);
      \begin{axis}[
            hide axis,
            view={\ViewAzimuth}{\ViewElevation},     % Set view angle
            disabledatascaling,                      % Align PGFPlots coordinates with TikZ
            anchor=origin,                           % Align PGFPlots coordinates with TikZ
            viewport={\ViewAzimuth}{\ViewElevation}, % Align PGFPlots coordinates with TikZ
        ]
        % Plot equator and two longitude lines with occlusion
        \pgfplotsinvokeforeach{30,60,...,150}{
        \addFGBGplot[blue!50,dashed,thick,domain=0:2*pi, samples=100, samples y=1] 
        ({cos(deg(x))*sin(#1)}, {sin(deg(x))*sin(#1)}, {cos(#1)});
        }
        %\addFGBGplot[domain=0:2*pi, samples=100, samples y=1] (0, {sin(deg(x))}, {cos(deg(x))});
        \pgfplotsinvokeforeach{90,125,160}{
        \addFGBGplot[blue!50,dashed,thick,domain=0:2*pi, samples=100, samples y=1]
        ({sin(deg(x))*sin(#1)},{cos(#1)}, {cos(deg(x))*sin(#1)});}
      \end{axis}
    \end{scope}
\end{tikzpicture}
}
\newsavebox\peanut
\sbox\peanut{
\begin{tikzpicture}
    \begin{scope}
      \fill[white] (45:1.15) arc(45:315:1.15);
      \draw[thin,blue!50] (45:1) arc(45:315:1);
      \clip (45:1) arc(45:315:1);
      \begin{axis}[
            hide axis,
            view={\ViewAzimuth}{\ViewElevation},     % Set view angle
            disabledatascaling,                      % Align PGFPlots coordinates with TikZ
            anchor=origin,                           % Align PGFPlots coordinates with TikZ
            viewport={\ViewAzimuth}{\ViewElevation}, % Align PGFPlots coordinates with TikZ
        ]
        % Plot equator and two longitude lines with occlusion
        \pgfplotsinvokeforeach{30,60,...,150}{
        \addFGBGplot[blue!50,thick,domain=0:2*pi, samples=100, samples y=1] 
        ({cos(deg(x))*sin(#1)}, {sin(deg(x))*sin(#1)}, {cos(#1)});
        }
        %\addFGBGplot[domain=0:2*pi, samples=100, samples y=1] (0, {sin(deg(x))}, {cos(deg(x))});
        \pgfplotsinvokeforeach{90,125,160}{
        \addFGBGplot[blue!50,thick,domain=0:2*pi, samples=100, samples y=1]
        ({sin(deg(x))*sin(#1)},{cos(#1)}, {cos(deg(x))*sin(#1)});}
      \end{axis}
    \end{scope}
    \begin{scope}[xshift={1.4cm}]
      \fill[white] (225:1.15) arc(225:225+270:1.15);    
      \draw[thin,blue!50] (225:1) arc(225:225+270:1);
      \clip (225:1) arc(225:225+270:1);
      \begin{axis}[
            hide axis,
            view={\ViewAzimuth}{\ViewElevation},     % Set view angle
            disabledatascaling,                      % Align PGFPlots coordinates with TikZ
            anchor=origin,                           % Align PGFPlots coordinates with TikZ
            viewport={\ViewAzimuth}{\ViewElevation}, % Align PGFPlots coordinates with TikZ
        ]
        % Plot equator and two longitude lines with occlusion
        \pgfplotsinvokeforeach{30,60,...,150}{
        \addFGBGplot[blue!50,thick,domain=0:2*pi, samples=100, samples y=1] 
        ({cos(deg(x))*sin(#1)}, {sin(deg(x))*sin(#1)}, {cos(#1)});
        }
        %\addFGBGplot[domain=0:2*pi, samples=100, samples y=1] (0, {sin(deg(x))}, {cos(deg(x))});
        \pgfplotsinvokeforeach{95,125,160}{
        \addFGBGplot[blue!50,thick,domain=0:2*pi, samples=100, samples y=1]
        ({sin(deg(x))*sin(#1)},{cos(#1)}, {cos(deg(x))*sin(#1)});}
      \end{axis}
    \end{scope}
\end{tikzpicture}
}
\newsavebox\peanutdashed
\sbox\peanutdashed{
\begin{tikzpicture}
    \begin{scope}
      \fill[white]  (45:1.15) arc(45:315:1.15);
      \clip (45:1) arc(45:315:1);
      \begin{axis}[
            hide axis,
            view={\ViewAzimuth}{\ViewElevation},     % Set view angle
            disabledatascaling,                      % Align PGFPlots coordinates with TikZ
            anchor=origin,                           % Align PGFPlots coordinates with TikZ
            viewport={\ViewAzimuth}{\ViewElevation}, % Align PGFPlots coordinates with TikZ
        ]
        % Plot equator and two longitude lines with occlusion
        \pgfplotsinvokeforeach{30,60,...,150}{
        \addFGBGplot[blue!50,dashed,thick,domain=0:2*pi, samples=100, samples y=1] 
        ({cos(deg(x))*sin(#1)}, {sin(deg(x))*sin(#1)}, {cos(#1)});
        }
        %\addFGBGplot[domain=0:2*pi, samples=100, samples y=1] (0, {sin(deg(x))}, {cos(deg(x))});
        \pgfplotsinvokeforeach{90,125,160}{
        \addFGBGplot[blue!50,dashed,thick,domain=0:2*pi, samples=100, samples y=1]
        ({sin(deg(x))*sin(#1)},{cos(#1)}, {cos(deg(x))*sin(#1)});}
      \end{axis}
    \end{scope}
    \begin{scope}[xshift={1.4cm}]
      \fill[white] (225:1.15) arc(225:225+270:1.15);    
      \draw[thin,blue!50,dashed] (225:1) arc(225:225+270:1);
      \clip (225:1) arc(225:225+270:1);
      \begin{axis}[
            hide axis,
            view={\ViewAzimuth}{\ViewElevation},     % Set view angle
            disabledatascaling,                      % Align PGFPlots coordinates with TikZ
            anchor=origin,                           % Align PGFPlots coordinates with TikZ
            viewport={\ViewAzimuth}{\ViewElevation}, % Align PGFPlots coordinates with TikZ
        ]
        % Plot equator and two longitude lines with occlusion
        \pgfplotsinvokeforeach{30,60,...,150}{
        \addFGBGplot[blue!50,dashed,thick,domain=0:2*pi, samples=100, samples y=1] 
        ({cos(deg(x))*sin(#1)}, {sin(deg(x))*sin(#1)}, {cos(#1)});
        }
        %\addFGBGplot[domain=0:2*pi, samples=100, samples y=1] (0, {sin(deg(x))}, {cos(deg(x))});
        \pgfplotsinvokeforeach{95,125,160}{
        \addFGBGplot[blue!50,dashed,thick,domain=0:2*pi, samples=100, samples y=1]
        ({sin(deg(x))*sin(#1)},{cos(#1)}, {cos(deg(x))*sin(#1)});}
      \end{axis}
    \end{scope}
\end{tikzpicture}
}

\begin{document}
\begin{tikzpicture}[scale=1]
\begin{scope}[yshift=-1.8cm]
\draw[densely dashed] (6,-4.5) -- (6,3);
\node at (4.5,-3.75) {Microwave};
\draw[densely dashed] (3,-4.5) -- (3,3);
\draw[densely dashed] (-1.7,-4.5) -- (-1.7,3);
\node at (0.65,-3.75) {Infrared};
\draw[densely dashed] (-2.3,-4.5) -- (-2.3,-1.5) (-2.3,0.5) -- (-2.3,1.1);
\draw[densely dashed]  (-4.5,-4.5) -- (-4.5,3);
\node[rotate=90] at (-2,-3.75) {Visible}; 
\node at (-3.4,-3.75) {Ultraviolet};
\node at (-6.75,-3.75) {X-rays};
\draw[densely dashed] (-9,-4.5) -- (-9,3);
\foreach \x in {-11,-10,...,-1}{
\draw (-1.5*\x-10.5,-3) -- (-1.5*\x-10.5,-2.75);
\node[above,fill=white] at  (1.5*\x+7.5,-2.75) {$\hphantom{{}^{\x}}10^{\x}$};
}
\draw[latex-latex](-10,-3) -- (7,-3);
\node at (-9.7,-3.75) {$\gamma$-rays};
\node[fill=white] at (-9,-1.7) {Wavelength (m)};
\node at (6.7,-3.75) {Radio};
\draw[latex-latex] (-10,-4.5) -- (7,-4.5);
\end{scope}
\fill[blue!20] (0,0) circle (0.3) (1.6,0) circle (0.3);
\fill[blue!20] (0,-0.1) rectangle (1.6,0.1);
\draw[-latex] (-0.4,0) -- (-1,0);
\draw[-latex] (2,0) -- (2.6,0);
\node[align=center] at (0.8,1.7) {Vibration};
\begin{scope}[xshift=3.8cm]
\fill[blue!20] (0,0) circle (0.3) (1.6,0) circle (0.3);
\fill[blue!20] (0,-0.1) rectangle (1.6,0.1);
\draw[-latex] (1.6,0.3) arc (0:90:0.7 and 0.7);
\draw[-latex] (0,-0.3) arc (180:270:0.7 and 0.7);
\node[align=center] at (0.8,1.7) {Rotation};
\end{scope}
\begin{scope}[xshift=-8cm]
\fill[blue!20] (0,0) circle (0.3) (1.6,0) circle (0.3);
\fill[blue!20] (0,-0.1) rectangle (0.5,0.1);
\fill[blue!20] (1.1,-0.1) rectangle (1.6,0.1);
\draw[densely dashed] (0.8,-0.4) -- (0.75,0) -- (0.85,0) -- (0.8,0.4);
\node[align=center] at (0.8,1.7) {Bond breaking \\ and ionization};
\fill[blue!20] (0,-2) circle (0.3) (1.6,-2) circle (0.3);
\fill[blue!20] (0,-2.1) rectangle (1.6,-1.9);
\draw[-latex] (0.8,-1.3) -- (0.8,-0.7);
\end{scope}
\begin{scope}[xshift=-2.8cm,yshift=-1cm]
\node[scale=0.5] at (-0.5,1.8) {\usebox\mononutdashed};
\node[scale=0.5] at (0.5,1.8) {\usebox\mononut};
\node[scale=0.5] at (-0.5,0.8) {\usebox\mononut};
\node[scale=0.5] at (0.5,0.8) {\usebox\mononutdashed};
\node[scale=0.5] at (0,-0.8) {\usebox\peanut};
\node[scale=0.5] at (0,-1.8) {\usebox\peanutdashed};
\node[align=center,fill=white] at (-1.6,-1.3) {\scriptsize Bonding \\ \scriptsize $\pi$ oribtal};
\node[align=center,fill=white] at (-1.8,1.3) {\scriptsize Antibonding \\ \scriptsize $\pi$ oribtal};
\node[align=center] at (0,2.8) {Electronic\\ excitation};
\draw[-latex] (0,-0.3) -- (0,0.3);
\end{scope}
\end{tikzpicture}
\end{document}