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(By training I am a math-guy and my knowledge of chemistry is restricted to school level)

I have read a little bit about the electron spheres and sub-spheres, the Aufbau principle and covalent bonds from Wikipedia.

Is it possible to derive theoretically molecules based on covalent bonds using linear equations? I am asking this because I did some computations in Sagemath:

For instance:

$$ \begin{bmatrix} 1&3&6\\ \end{bmatrix}\\ \text{Free module of degree 3 and rank 2 over Integer Ring Echelon basis matrix:}\\ \begin{bmatrix} 3&1&-1\\ 0&2&-1\\ \end{bmatrix}\\ \begin{array}{ccccc} \ce{3H} & + & \ce N & -& \ce{Cr}\\ & + & \ce{2N} & - & \ce{Cr}\\ \end{array}\\ \begin{bmatrix} 1&3&7\\ \end{bmatrix}\\ \text{Free module of degree 3 and rank 2 over Integer Ring Echelon basis matrix:}\\ \begin{bmatrix} 1&2&-1\\ 0&7&-3\\ \end{bmatrix}\\ \begin{array}{ccccc} \ce{H} & + & \ce {2N} & -& \ce{V}\\ & + & \ce{7N} & - & \ce{3V}\\ \end{array}\\ \begin{bmatrix} 8&1&3\\ \end{bmatrix}\\ \text{Free module of degree 3 and rank 2 over Integer Ring Echelon basis matrix:}\\ \begin{bmatrix} 1&1&-3\\ 0&3&-1\\ \end{bmatrix}\\ \begin{array}{ccccc} \ce{Ti} & + & \ce H & -& \ce{3N}\\ & + & \ce{3H} & - & \ce{N}\\ \end{array}\\ $$

More such examples in Sagemath-Cell.

The example $\ce{3H} + \ce N - \ce{Cr}$ would correspond to a hypothetical molecule $\ce{CrH3N}$ (which I was able to find at pubchem).

My questions are:

  1. How do I search online for such molecules if they exist or not? Is there a standard way in specifying short molecule formulas?
  2. Suppose I derive some equations for such hypothetical molecules based on linear equations of covalent bonds. Is there any chemical reason why these molecules might exist or not?
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