# Table 1 Popular analytical queries in MS

Query name Definition/Description
Moment of inertia $I=\sum _{i=1}^{n}{m}_{i}{\mathbf{r}}_{i}$
Moment of inertia on z axis $\begin{array}{lll}{I}_{z}& =& \sum _{i=1}^{n}{m}_{i}{r}_{\mathit{\text{zi}}}\end{array}$
Sum of masses $\begin{array}{lll}M& =& \sum _{i=1}^{n}{m}_{i}\end{array}$
Center of mass $\begin{array}{lll}C& =& \frac{I}{M}\end{array}$
Radius of gyration $\begin{array}{lll}\mathit{\text{RG}}& =& \sqrt{\frac{{I}_{z}}{M}}\end{array}$
Dipole moment $\begin{array}{lll}D& =& \sum _{i=1}^{n}{q}_{i}{\mathbf{r}}_{i}\end{array}$
Dipole histogram $\begin{array}{lll}{D}_{z}& =& \sum _{i=1}^{n}\frac{D}{z}\end{array}$
Electron density $\begin{array}{l}\mathit{\text{ED}}=\frac{\sum _{i=1}^{n}\left({e}_{i}-{q}_{i}\right)}{\mathit{\text{dz}}\ast x\ast y}\end{array}$
Heat capacity $\frac{3000\sqrt{T}\ast \mathit{\text{boltz}}}{2\ast \sqrt{T}-n\ast \mathit{\text{df}}\ast \mathit{\text{VarT}}}$
Isothermal compressibility $\frac{\mathit{\text{VarV}}}{{V}_{\mathit{\text{avg}}}\ast \mathit{\text{boltz}}\ast T\ast \mathit{\text{PresFac}}}$
Mean square displacement $\begin{array}{lll}\mathit{\text{msd}}& =& 〈\left({r}_{t+{\Delta }_{t}}-{r}_{t}\right)〉\end{array}$
Diffusion constant $\begin{array}{lll}{D}_{t}& =& \frac{6\ast \mathit{\text{msd}}\left(t\right)}{t}\end{array}$
Velocity autocorrelation $\begin{array}{lll}{V}_{\mathit{\text{acor}}}& =& 〈\left({V}_{t+{\Delta }_{t}}\ast {V}_{t}\right)〉\end{array}$
Force autocorrelation $\begin{array}{lll}{F}_{\mathit{\text{acor}}}& =& 〈\left({F}_{t+{\Delta }_{t}}\ast {F}_{t}\right)〉\end{array}$
Density function Histogram of atom counts
Spatial distance histogram (SDH) Histogram of all atom-to-atom distances
RDF $\begin{array}{lll}\mathit{\text{rdf}}\left(r\right)& =& \frac{\mathit{\text{SDH}}\left(r\right)}{4\ast \pi \ast {r}^{2}\ast {\sigma }_{r}\ast \rho }\end{array}$ 