Refactor README.md

README.md

@@ -1,10 +1,12 @@
-BFit
-====
+# `BFit`
+
 [![This project supports Python 3.9+](https://img.shields.io/badge/Python-3.9+-blue.svg)](https://python.org/downloads)
 [![GitHub Actions CI Tox Status](https://github.com/theochem/bfit/actions/workflows/ci_tox.yml/badge.svg?branch=master)](https://github.com/theochem/bfit/actions/workflows/ci_tox.yml)
 [![GPLv3 License](https://img.shields.io/badge/License-GPL%20v3-yellow.svg)](https://opensource.org/licenses/)
 [![Binder](https://mybinder.org/badge_logo.svg)](https://mybinder.org/v2/gh/theochem/bfit/master?labpath=%2Fexamples%2F)
 
+## About
+
 BFit is a Python library for fitting a convex sum of Gaussian functions to any
 probability distribution. It is primarily intended for quantum chemistry applications, where the
 basis functions are Gaussians and the fitted probability distribution is a scalar function like
@@ -16,46 +18,49 @@ or various files in the example [folder](https://github.com/theochem/BFit/tree/m
 to see specific examples on how to fit using the different algorithms and objective
 functions.
 For further information about the api, please visit
-[**BFit Documentation**](https://bfit.qcdevs.org/).
+[--BFit Documentation--](https://bfit.qcdevs.org/).
 
 The instructions to access the results of the fitted atomic densities using KL-FI method is
 shown in the section below.
 
 To report any issues or ask questions, either [open an issue](
 https://github.com/theochem/bfit/issues/new) or email [qcdevs@gmail.com]().
 
+## Citation
 
-Citation
---------
 Please use the following citation in any publication using BFit library:
 
-> Tehrani, A., M. Anderson, J. S., Chakraborty, D., Rodriguez-Hernandez, J. I., Thompson, D. C., Verstraelen, T., Ayers, P. W., & Heidar-Zadeh, F.
-> An information-theoretic approach to basis-set fitting of electron densities and other non-negative functions.
-> Journal of Computational Chemistry. https://doi.org/10.1002/jcc.27170
-
+```bibtex
+@article{bfit2023,
+author = {Tehrani, Alireza and Anderson, James S. M. and Chakraborty, Debajit and Rodriguez-Hernandez, Juan I. and Thompson, David C. and Verstraelen, Toon and Ayers, Paul W. and Heidar-Zadeh, Farnaz},
+title = {An information-theoretic approach to basis-set fitting of electron densities and other non-negative functions},
+journal = {Journal of Computational Chemistry},
+volume = {44},
+number = {25},
+pages = {1998-2015},
+doi = {https://doi.org/10.1002/jcc.27170},
+url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/jcc.27170},
+year = {2023}
+}
+```
 
-Dependencies
-------------
-* Python >= 3.0: http://www.python.org/
-* NumPy >= 1.18.5: http://www.numpy.org/
-* SciPy >= 1.5.0: http://www.scipy.org/
-* Matplotlib >=3.2.0: https://matplotlib.org/
-* Sphinx >= 2.3.0: https://www.sphinx-doc.org/
+## Dependencies
 
+- Python >= 3.9: http://www.python.org/
+- NumPy >= 1.18.5: http://www.numpy.org/
+- SciPy >= 1.5.0: http://www.scipy.org/
+- Matplotlib >=3.2.0: https://matplotlib.org/
+- Sphinx >= 2.3.0: https://www.sphinx-doc.org/
 
+## Installation
 
-Installation
-------------
-Three options to install BFit:
+There are two options to install BFit:
 
 ```bash
 # install from source
 git clone https://github.com/theochem/bfit.git
 pip install .
 
- # or install using conda.
-conda install -c theochem qc-bfit
-
 # or install using pip.
 pip install qc-bfit
 
@@ -64,34 +69,33 @@ pytest -v .
 ```
 
 
-Features
---------
+## Features
 
 The features of this software are:
 
-* Gaussian Basis set model:
-    * Construct s-type and p-type Gaussian functions,
-    * Compute Atomic Densities or Molecular Densities.
+- Gaussian Basis set model:
+  - Construct s-type and p-type Gaussian functions,
+  - Compute Atomic Densities or Molecular Densities.
+
+- Fitting measures:
+  - Least-squares,
+  - Kullback-Leibler divergence,
+  - Tsallis divergence.
 
-* Fitting measures:
-    * Least-squares,
-    * Kullback-Leibler divergence,
-    * Tsallis divergence.
+- Optimization procedures
+  - Optimize using SLSQP in "scipy.minimize" procedures.
+  - Optimize Kullback-Leibler using self-consistent iterative method see [paper](#citing).
+  - Greedy method for optimization of Kullback-Leibler and Least-Squares, see [paper](#citing).
 
-* Optimization procedures
-    * Optimize using SLSQP in "scipy.minimize" procedures.
-    * Optimize Kullback-Leibler using self-consistent iterative method see [paper](#citing).
-    * Greedy method for optimization of Kullback-Leibler and Least-Squares, see [paper](#citing).
+- Read/Parse Hatree-Fock wavefunctions for atomic systems:
+  - Includes: anions, cations and heavy elements, see [data](data/README.md) page.
+  - Compute:
+    - Atomic density, including core, and valence densities,
+    - Positive definite kinetic energy density.
 
-* Read/Parse Hatree-Fock wavefunctions for atomic systems:
-  * Includes: anions, cations and heavy elements, see [data](data/README.md) page.
-  * Compute:
-    * Atomic density, including core, and valence densities,
-    * Positive definite kinetic energy density.
 
+## Final Models of Fitting Atomic Densities
 
-Final Models of Fitting Atomic Densities
-------------------------------------------
 The final model of fitting the atomic densities using the Kullback-Leibler (KL) divergence fixed point iteration method
 can be accessed by opening the file `./bfit/data/kl_fpi_results.npz` with numpy.
 Similarly, the results from optimizing KL with SLSQP method using `kl_fpi_results.npz`
@@ -112,6 +116,7 @@ print(exponents[:num_s])
 print("p-type exponents")
 print(exponents[num_s:])
 ```
+
 Alternatively, one can load these results using JSON file.
 ```python
 import json
@@ -138,12 +143,11 @@ model = AtomicGaussianDensity(grid.points, num_s=num_s, num_p=num_p, normalize=T
 model_pts = model.evaluate(coefficients, exponents)
 
 print("Numerical integral (spherically) of the model %f." %
-      grid.integrate(model_pts * 4.0 * np.pi * grid.points**2.0)
+      grid.integrate(model_pts - 4.0 - np.pi - grid.points--2.0)
 )
 ```
 
-
-## Example
+## Examples
 There are four steps to using BFit.
 
 ### 1. Specify the Grid Object.