> For the complete documentation index, see [llms.txt](https://overleaf-pro.ayaka.space/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://overleaf-pro.ayaka.space/latex/field-specific/04-molecular-orbital-diagrams.md). # Molecular orbital diagrams This article provides a brief introduction to the creation of [molecular orbital diagrams](https://en.wikipedia.org/wiki/Molecular_orbital_diagram) in LaTeX using the [`modiagram` package](https://ctan.org/pkg/modiagram?lang=en). Readers are strongly encouraged to consult the [`modiagram` package documentation](http://mirrors.ctan.org/macros/latex/contrib/modiagram/modiagram_en.pdf) which contains numerous helpful examples to demonstrate its many features—far more than we can address in this short article. For information about the more traditional *molecular structure diagrams* see our documentation about [chemistry formulae](/latex/field-specific/02-chemistry-formulae.md). ## Introduction Molecular diagrams are created using the [`modiagram` package](https://ctan.org/pkg/modiagram?lang=en) which you import to your document by adding the following line to its preamble: `\usepackage{modiagram}`\[$$\langle$$`options`$$\rangle$$] The set of $$\langle$$`options`$$\rangle$$ are listed, and demonstrated, in the [package documentation](http://mirrors.ctan.org/macros/latex/contrib/modiagram/modiagram_en.pdf). To apply package $$\langle$$`options`$$\rangle$$ *globally* you can * set them when you load the package via `\usepackage{modiagram}`\[$$\langle$$`options`$$\rangle$$], or * use the setup command `\setmodiagram`{$$\langle$$`options`$$\rangle$$} MO diagrams are created using the `modiagram` environment, which supports local use of package $$\langle$$`options`$$\rangle$$: `\begin{modiagram}`\[$$\langle$$`options`$$\rangle$$] ... `\end{modiagram}` The following example demonstrates a minimal `modiagram` environment without any using any $$\langle$$`options`$$\rangle$$: ```latex \documentclass{article} \usepackage{modiagram} \begin{document} First example atoms: \begin{modiagram} \atom{left}{1s, 2s, 2p} \end{modiagram} \end{document} ``` [Open this example in Overleaf.](https://www.overleaf.com/docs?engine=pdflatex\&snip_name=example+of+molecular+diagram\&snip=%5Cdocumentclass%7Barticle%7D%0A%5Cusepackage%7Bmodiagram%7D%0A%5Cbegin%7Bdocument%7D%0A%0AFirst+example+atoms%3A%0A%0A%5Cbegin%7Bmodiagram%7D%0A%5Catom%7Bleft%7D%7B1s%2C+2s%2C+2p%7D%0A%5Cend%7Bmodiagram%7D%0A%5Cend%7Bdocument%7D) This example produces the following output: ![Example of a molecular diagram produced in LaTeX](/files/Q8GOdzQDi1SsTFa5NdbU) The basic command to draw MO diagrams is `\atom` which, as demonstrated in the example above, takes two arguments: * `left`: the alignment of the atom. * `1s, 2s, 2p`: the energy sub-levels to be drawn. These can be further customized as you will learn in the [next section](#atoms). ## Atoms You can pass some extra information about the atomic orbitals to the command presented in the introductory example. ```latex \documentclass{article} \usepackage{modiagram} \begin{document} \begin{modiagram} \atom{right}{ 1s = { 0; pair} , 2s = { 1; pair} , 2p = {1.5; up, down } } \atom{left}{ 1s = { 0; pair} , 2s = { 1; pair} , 2p = {1.5; up, down } } \end{modiagram} \end{document} ``` [Open this example in Overleaf.](https://www.overleaf.com/docs?engine=pdflatex\&snip_name=example+of+molecular+diagram\&snip=%5Cdocumentclass%7Barticle%7D%0A%5Cusepackage%7Bmodiagram%7D%0A%5Cbegin%7Bdocument%7D%0A%0A%5Cbegin%7Bmodiagram%7D%0A+%5Catom%7Bright%7D%7B%0A++++1s+%3D+%7B+0%3B+pair%7D+%2C%0A++++2s+%3D+%7B+1%3B+pair%7D+%2C%0A++++2p+%3D+%7B1.5%3B+up%2C+down+%7D%0A+%7D%0A%0A+%5Catom%7Bleft%7D%7B%0A++++1s+%3D+%7B+0%3B+pair%7D+%2C%0A++++2s+%3D+%7B+1%3B+pair%7D+%2C%0A++++2p+%3D+%7B1.5%3B+up%2C+down+%7D%0A+%7D%0A+%5Cend%7Bmodiagram%7D%0A%5Cend%7Bdocument%7D) This example produces the following output: ![example of atomic orbitals](/files/8RziWMyhJIdyu6V1yngx) In this example, two identical atoms are drawn, left- and right-aligned respectively. Following the style of the `modiagram` package documentation, the generic syntax to create atoms can be written as: `\atom`\[$$\langle$$`name`$$\rangle$$]{$$\langle$$`left`$$\rangle$$|$$\langle$$`right`$$\rangle$$}{$$\langle$$`AO-spec`$$\rangle$$} where * $$\langle$$`name`$$\rangle$$ is an optional name for the atom * $$\langle$$`left`$$\rangle$$ and $$\langle$$`right`$$\rangle$$ determine the placement in the diagram * $$\langle$$`AO-spec`$$\rangle$$ is the specification of the Atomic Orbital. The $$\langle$$`AO-spec`$$\rangle$$ takes the general form ```latex sub-level = {energy; specifications} ``` where * `sub-level` can be `1s`, `2s` or `2p` * `energy` is the energy level, a number that determines the vertical spacing in the diagram. If omitted it is set to 0. * `specifications` is a comma-separated list of the spins of the electrons contained in each orbital. The possible values are `up`, `down`, `pair` and empty (only the semicolon is typed) for an empty orbital. If omitted it is set to `pair`. Here is a description of the commands used in the previous example: * `1s = { 0; pair}`. The sub-level `1s` is in the `0` energy level, the orbital contains two (paired) electrons. * `2s = { 1; pair}`. The sub-level `2s` drawn in the `1` energy level, there are two electrons in this orbital. * `2p = {1.5; up, down}`. The sub-level `2p` drawn in the energy level `1.5`, i.e. in the diagram the vertical spacing is set to 1.5; this sub-energy level has two electrons: one with spin `up` in the first orbital and another with spin `down` in the second orbital. The same commands are repeated for the second atom on the right. To display the (optional) `name` of an atom use a `modiagram` environment with the `[names]` option: ```latex \documentclass{article} \usepackage{modiagram} \begin{document} \begin{modiagram}[names] \atom[Atom on the right]{right}{ 1s = { 0; pair} , 2s = { 1; pair} , 2p = {1.5; up, down } } \atom[Atom on the left]{left}{ 1s = { 0; pair} , 2s = { 1; pair} , 2p = {1.5; up, down } } \end{modiagram} \end{document} ``` [Open this example in Overleaf.](https://www.overleaf.com/docs?engine=pdflatex\&snip_name=Using+the+names+option+in+a+molecular+diagram\&snip=%5Cdocumentclass%7Barticle%7D%0A%5Cusepackage%7Bmodiagram%7D%0A%5Cbegin%7Bdocument%7D%0A%5Cbegin%7Bmodiagram%7D%5Bnames%5D%0A+%5Catom%5BAtom+on+the+right%5D%7Bright%7D%7B%0A++++1s+%3D+%7B+0%3B+pair%7D+%2C%0A++++2s+%3D+%7B+1%3B+pair%7D+%2C%0A++++2p+%3D+%7B1.5%3B+up%2C+down+%7D%0A+%7D%0A%0A+%5Catom%5BAtom+on+the+left%5D%7Bleft%7D%7B%0A++++1s+%3D+%7B+0%3B+pair%7D+%2C%0A++++2s+%3D+%7B+1%3B+pair%7D+%2C%0A++++2p+%3D+%7B1.5%3B+up%2C+down+%7D%0A+%7D%0A%5Cend%7Bmodiagram%7D%0A%5Cend%7Bdocument%7D) This example produces the following output: ![Example molecular orbital](/files/CtNWffRuZMy45U9S423v) ## Molecules The syntax for molecules is very similar to that of the [`\atom`](#atoms) and, in the style of the documentation, can be written as: `\molecule`\[$$\langle$$`name`$$\rangle$$]{$$\langle$$`MO-spec`$$\rangle$$} where * $$\langle$$`name`$$\rangle$$ is an optional caption of the molecule * $$\langle$$`MO-spec`$$\rangle$$ is the specification of the Molecular Orbital The energy sub-levels `1s`, `2s` and `2p` become `1sMO`, `2sMO` and `2pMO` respectively. Here is a basic example: ```latex \documentclass{article} \usepackage{modiagram} \begin{document} \begin{modiagram} \atom{left}{1s} \atom{right}{1s={;up}} \molecule{ 1sMO={0.75;pair,up} } \end{modiagram} \end{document} ``` [Open this example in Overleaf](https://www.overleaf.com/docs?engine=pdflatex\&snip_name=Molecule+example+with+modiagram+package\&snip=%5Cdocumentclass%7Barticle%7D%0A%5Cusepackage%7Bmodiagram%7D%0A%5Cbegin%7Bdocument%7D%0A%5Cbegin%7Bmodiagram%7D%0A+%5Catom%7Bleft%7D%7B1s%7D%0A+%5Catom%7Bright%7D%7B1s%3D%7B%3Bup%7D%7D%0A+%5Cmolecule%7B%0A++++1sMO%3D%7B0.75%3Bpair%2Cup%7D%0A++%7D%0A%5Cend%7Bmodiagram%7D%0A%5Cend%7Bdocument%7D) This example produces the following output: ![example of molecule diagram](/files/lSPiEQ0voNkFN5T2NAHh) In the example above, the molecular orbital specification ($$\langle$$`MO-spec`$$\rangle$$ ) is ```latex 1sMO={0.75;pair,up} ``` where * `0.75` is now the ratio *(energy gain)/(energy loss)*. * `pair, up` are the spins of the electrons in the bonding and anti-bonding molecular orbitals, respectively. The next, slightly more elaborate, example should help you understand the syntax: ```latex \documentclass{article} \usepackage{modiagram} \begin{document} \begin{modiagram} \atom{left}{ 1s, 2s, 2p = {;pair,up,up} } \atom{right}{ 1s, 2s, 2p = {;pair,up,up} } \molecule{ 1sMO, 2sMO, 2pMO = {;pair,pair,pair,up,up} } \end{modiagram} \end{document} ``` [Open this example in Overleaf](https://www.overleaf.com/docs?engine=pdflatex\&snip_name=More+elaborate+modiagram+example\&snip=%5Cdocumentclass%7Barticle%7D%0A%5Cusepackage%7Bmodiagram%7D%0A%5Cbegin%7Bdocument%7D%0A%5Cbegin%7Bmodiagram%7D%0A+%5Catom%7Bleft%7D%7B%0A++++++1s%2C+2s%2C+2p+%3D+%7B%3Bpair%2Cup%2Cup%7D%0A++%7D%0A++%5Catom%7Bright%7D%7B%0A++++++1s%2C+2s%2C+2p+%3D+%7B%3Bpair%2Cup%2Cup%7D%0A++%7D%0A++%5Cmolecule%7B%0A++++++1sMO%2C+2sMO%2C+2pMO+%3D+%7B%3Bpair%2Cpair%2Cpair%2Cup%2Cup%7D%0A++%7D%0A%5Cend%7Bmodiagram%7D%0A%5Cend%7Bdocument%7D) This example produces the following output: ![elaborated example of molecular orbital](/files/QnO7r7CtzyYpgqgKXYjJ) Three atoms are set on each side of the diagram and the corresponding molecule is in the middle. ## Naming scheme The following diagram is reproduced from the [`modiagram` package](https://ctan.org/pkg/modiagram?lang=en) documentation. It contains the names (labels) used for the orbitals, which are nodes in a `tikzpicture` and thus can be used in standard TikZ drawing commands within a `modiagram` environment. ![modiagram names for oribtals](/files/D0xoYmys7q9tvye7D2I8) Here is an example using the name of the anti-bonding orbital `1sigma*` for relative positioning. ```latex \documentclass{article} \usepackage{modiagram} \begin{document} \begin{modiagram} \atom{left}{1s} \atom{right}{1s={;up}} \molecule{ 1sMO={;pair,up} } \draw[<-,shorten <=8pt,shorten >=15pt,blue] (1sigma*) --++(2,1) node {anti-bonding MO}; \end{modiagram} \end{document} ``` [Open this example in Overleaf.](https://www.overleaf.com/docs?engine=pdflatex\&snip_name=Using+orbital+labels+in+an+modiagram+environment\&snip=%5Cdocumentclass%7Barticle%7D%0A%5Cusepackage%7Bmodiagram%7D%0A%5Cbegin%7Bdocument%7D%0A%5Cbegin%7Bmodiagram%7D%0A+%5Catom%7Bleft%7D%7B1s%7D%0A+%5Catom%7Bright%7D%7B1s%3D%7B%3Bup%7D%7D%0A+%5Cmolecule%7B%0A++++1sMO%3D%7B%3Bpair%2Cup%7D%0A+%7D%0A+%5Cdraw%5B%3C-%2Cshorten+%3C%3D8pt%2Cshorten+%3E%3D15pt%2Cblue%5D%0A+%281sigma%2A%29+--%2B%2B%282%2C1%29+node+%7Banti-bonding+MO%7D%3B%0A%5Cend%7Bmodiagram%7D%0A%5Cend%7Bdocument%7D) This example produces the following output: ![example of orbital with anti-bonding](/files/lF2eVVICOYUYBsyJYya7) ## Further reading For more information see: * [Chemistry formulae](/latex/field-specific/02-chemistry-formulae.md) * [Feynman diagrams](/latex/field-specific/03-feynman-diagrams.md) * [TikZ package](/latex/figures-and-tables/05-tikz-package.md) * [Drawing Diagrams Directly in LaTeX](/latex/figures-and-tables/04-picture-environment.md) * [Inserting Images](/latex/more-topics/27-inserting-images.md) * [List of Greek letters and math symbols](/latex/mathematics/11-list-of-greek-letters-and-math-symbols.md) * [The `modiagram` manual](http://mirrors.ctan.org/macros/latex/contrib/modiagram/modiagram_en.pdf) --- # Agent Instructions This documentation is published with GitBook. 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