About Orbitals

A version 4.0 of my package bundle chemmacros is coming nearer. The most notable difference will be that the chemformula package will be usable as a standalone package. This is not what I am going to ask you about. You may know that chemmacros provides some orbital pictures:

\orbital{s} \orbital{p} \orbital{sp3}

Rendered by QuickLaTeX.com

Now, I want to add picture for d-Orbitals. This is what I have for the d_{z^2}:

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I’m not really sure which one I like better. I don’t like both of them very much. Maybe you have ideas for improvements?

\begin{tikzpicture}[
    inner sep=0 , outer sep=0 , line width=.2pt ,
    rotate = { 90 - 90 } ,
    baseline ,
    minimum size = 0
 
]
  \shadedraw[
      draw = black ,
      ball color = black!90
   
]
    (0,0) .. controls ++ ( - 1 * 2em , - 1 * 2em )
    and ++ ( 1 * 2em , - 1 * 2em )
    .. (0,0);
  \shadedraw[black!5] (0,0) ellipse [x radius=1em,y radius=1ex] ;
  \filldraw[white] (0,0) ellipse [x radius=.2em,y radius=.2ex] ;
  \shadedraw[
      draw = black ,
      ball color = black!90
   
]
    (0,0) .. controls ++ (- 1 * 2em , 1 * 2em )
    and ++ ( 1 * 2em , 1 * 2em )
    .. (0,0);
\end{tikzpicture}
\begin{tikzpicture}[
    inner sep=0 , outer sep=0 , line width=.2pt ,
    rotate = { 90 - 90 } ,
    baseline ,
    minimum size = 0
 
]
  \shadedraw[
      draw = black ,
      ball color = black!90
   
]
    (0,0) .. controls ++ ( - 1 * 2em , - 1 * 2em )
    and ++ ( 1 * 2em , - 1 * 2em )
    .. (0,0);
  \draw[black!5,line width=.7ex] (0,0) ellipse [x radius=.7em,y radius=.7ex] ;
  \shadedraw[
      draw = black ,
      ball color = black!90
   
]
    (0,0) .. controls ++ (- 1 * 2em , 1 * 2em )
    and ++ ( 1 * 2em , 1 * 2em )
    .. (0,0);
\end{tikzpicture
}

The d_{x^2-y^2} and friends are a bit better — they’re simply combinations of the existing p-orbitals — but not perfect either. I’m open to suggestions, improvements, comments, …

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\begin{tikzpicture}[
    inner sep=0 , outer sep=0 , line width=.2pt ,
    rotate = { 0 - 45 } ,
    baseline ,
    minimum size = 0
 
]
  \shadedraw[
      draw = black ,
      ball color = black!90
   
]
    (0,0) .. controls ++ (- 1 * 2em , 1 * 2em )
    and ++ ( 1 * 2em , 1 * 2em )
    .. (0,0);
   \shadedraw[
      draw = black!5 ,
      ball color = black!5 ,
      rotate = 135 ,
   
]
    (0,0) .. controls ++ ( - 1 * 2em , - 1 * 2em )
    and ++ ( 1 * 2em , - 1 * 2em )
    .. (0,0);
  \shadedraw[
      draw = black!5 ,
      ball color = black!5 ,
      rotate = 135 ,
   
]
    (0,0) .. controls ++ (- 1 * 2em , 1 * 2em )
    and ++ ( 1 * 2em , 1 * 2em )
    .. (0,0);
  \shadedraw[
      draw = black ,
      ball color = black!90
   
]
    (0,0) .. controls ++ ( - 1 * 2em , - 1 * 2em )
    and ++ ( 1 * 2em , - 1 * 2em )
    .. (0,0);
\end{tikzpicture}
\begin{tikzpicture}[
    inner sep=0 , outer sep=0 , line width=.2pt ,
    rotate = { 0  } ,
    baseline ,
    minimum size = 0
 
]
  \shadedraw[
      draw = black ,
      ball color = black!90 ,
      rotate = 0
   
]
    (0,0) .. controls ++ (- 1 * 2em , 1 * 2em )
    and ++ ( 1 * 2em , 1 * 2em )
    .. (0,0);
   \shadedraw[
      draw = black!5 ,
      ball color = black!5 ,
      rotate = -90 ,
   
]
    (0,0) .. controls ++ ( - 1 * 2em , - 1 * 2em )
    and ++ ( 1 * 2em , - 1 * 2em )
    .. (0,0);
  \shadedraw[
      draw = black!5 ,
      ball color = black!5 ,
      rotate = -90 ,
   
]
    (0,0) .. controls ++ (- 1 * 2em , 1 * 2em )
    and ++ ( 1 * 2em , 1 * 2em )
    .. (0,0);
  \shadedraw[
      draw = black ,
      ball color = black!90 ,
      rotate = 0
   
]
    (0,0) .. controls ++ ( - 1 * 2em , - 1 * 2em )
    and ++ ( 1 * 2em , - 1 * 2em )
    .. (0,0);
\end{tikzpicture
}

6 Replies to “About Orbitals”

  1. Hi!

    The white part doesn’t seem to be easily visible…maybe more of a gray type?
    Will coloring (blue/red, e.g.) be available?

    For the “ring” of the z²: It should be more round/donut-like. Not so flat, as it has been drawn.

    The first of the dx²-dy²: it should be more tilted! Meaning the black part more horizontal and more “compressed” (depth)!

    Just my 50cents ;-)

    1. Hi Guntram, thanks for your input!

      It will be possible to choose custom colors so I hope colors are not the problem. :)

      The problem with all of the orbital pictures is that they’re not really orbitals meaning they’re not the actual plots for the 99% probability of finding an electron. They’re just pictures made with TikZ resembling the actual plots. This means that by design they’re not going to look correct.

      The z^2 ring is not drawn as a ring in the above pictures but as ellipses. For the first it is a filled ellipse and a smaller white one drawn above. The second one is a single ellipse with a thicker line width. If you (or anyone else) has a better or at least another idea I would love to hear it!

      You’re right of course regarding the x^2-y^2 orbital. It looks awful. My TikZ-foo, unfortunately, is not that good. I’m open for ideas how to code a better one!

  2. I am wondering if there is an option in chemmacros to write orbital names in a proper way or even electronic transitions like

    \pi_v^* \rightarrow d_{x^2-y^2}

    . In the package manual I was only able to find the possibility to draw orbitals; maybe this is planned in future versions?

    1. There is no such option in chemmacros, yet. I’ve been asked this before but I’m hesitating to add something. writing $d_{x^2-y^2}$ is not that complicated and I think there is nothing gained by a macro that hides it…

  3. Hi,

    There is a package called tikzorbitals, that also draws s, p and d orbitals and uses the command \orbital to do so. It is available on CTAN and is maintained by Germain Salvato-Vallverdu. I don’t know if you are familiar with this package.

    Regards,
    Thijs Cornelussen

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