Basis Functions in Computational Chemistry

Educational Programs Graduate Quantum Mechanics FAQs
1

In computational chemistry, we create basis sets, which, to my understanding, are basically matrices of functions that are used to describe the wavefunction of the system. Is this true?

Sort of – I do no know what a “matrices of functions” means exactly. Basis sets are groups of functions called eigenfunctions. Any function within the Hilbert spanned by this basis can be represented by a linear combination of eigenfunctions.

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I may be responding a bit late, but a basis set \{\phi_\mu\}_i could indeed be understood as a matrix, e.g.,

(U_{i\mu}) = \begin{pmatrix} \phi_1(\vec{r}_1) & \ldots & \phi_N(\vec{r}_1) \\ \phi_1(\vec{r}_2) & \ldots & \phi_N(\vec{r}_2) \\ \vdots & \vdots & \vdots\\ \phi_1(\vec{r}_M) & \ldots & \phi_N(\vec{r}_M) \end{pmatrix}

where N is the number of functions in the basis, and the \vec{r}_M represent a discrete spatial mesh consisting of M points. (One could cover all of space by replacing the mesh with a continuous variable, but that formally takes a bit of care.)