This study introduces an orbital-free approach for the approximate evaluation of novel chemical structure descriptors, including the scalar projections of the partial exchange force onto the cumulative interelectron interaction and total static force densities, \([{\mathbf{F}}_{x}(\mathbf{r}) \cdot {\mathbf{F}}_{\text{ee}}(\mathbf{r})]/|{\mathbf{F}}_{\text{ee}}(\mathbf{r})|\) and \({\Phi }_{x}^{\text{em}}(\mathbf{r})=\left[{\mathbf{F}}_{x}(\mathbf{r})\cdot \mathcal{F}(\mathbf{r})\right]/|\mathcal{F}(\mathbf{r})|\) , for which the electron density \(\rho (\mathbf{r})\) and the electrostatic potential \({\varphi}_{\text{es}}(\mathbf{r})\) are leveraged. Specifically, the conservative exchange force field \({\mathbf{F}}_{x}(\mathbf{r})\) , its divergence \({\nabla \cdot \mathbf{F}}_{x}(\mathbf{r})\) , and the stored potential energy density \(\frac{1}{2}{\left|{\mathbf{F}}_{x}(\mathbf{r})\right|}^{2}\) are expressed analytically in terms of \(\rho (\mathbf{r})\) and its derivatives, \(\nabla \rho (\mathbf{r})\) and \({\nabla}^{2}\rho(\mathbf{r})\) , employing the local density approximation. The applicability of this approach to experimentally derived \(\rho (\mathbf{r})\) and \({\varphi }_{\text{es}}(\mathbf{r})\) , reconstructed via multipole modeling, is demonstrated using the oxalic acid dihydrate crystal as a test case. The results confirm that the proposed methodology accurately reproduces key features of the descriptors, corroborated by comparisons with their Müller-framed counterparts. Certain limitations of the approximated functions are identified and discussed in detail. Importantly, these descriptors enable the quantification of the role of \({\mathbf{F}}_{x}(\mathbf{r})\) in the mechanism of hydrogen bonding within supramolecular and crystal structures. Furthermore, the electrostatic-force and exchange-force scalar projections onto the total static force, \({\Phi}_{\text{es}}^{\text{em}}(\mathbf{r})=[{\mathbf{F}}_{\text{es}}(\mathbf{r})\cdot \mathcal{F}(\mathbf{r})]/|\mathcal{F}(\mathbf{r})|\) and \({\Phi }_{x}^{\text{em}}(\mathbf{r})\) , are interpreted as the classical and nonclassical contributions, respectively, forming the total-static-force-field energy density, \(\frac{1}{2}{[{\Phi}_{\text{es}}^{\text{em}}(\mathbf{r})+{\Phi }_{x}^{\text{em}}(\mathbf{r})]}^{2}\) .
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