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README.md

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 # grext: Grassmann Extrapolation Library
 
+This library define an `Extrapolator` class to be used for providing guesses in QM simulations. It is designed in such a way that requires minimum modifications on the QM code side.
 
+## Installation
+
+The library can be installed using `pip`:
+  - Navigate to the root folder of the library
+  - Run `pip install .`
+
+## Usage
+
+The usage requires only four lines of code:
+  - Add an import statement `import grext`.
+  - Initialize a new extrapolator by inserting the line:
+
+      `extrapolator = grext.Extrapolator(nelectrons, nbasis, natoms)`.
+
+    **Note:** the extrapolator can be finely controlled by passing additional keyword arguments. This is explained in the next section.
+  - When a new SCF calculation has been performed, load the resulting data in the extrapolator by running:
+
+      `extrapolator.load_data(coordinates, coefficients, overlap)`.
+
+    Here, `coordinates` are the molecule coordinates of size `(natoms, 3)`, `coefficients` is the
+    full coefficients matrix of size `(nbasis, nbasis)` and `overlap` is the overlap matrix of
+    size `(nbasis, nbasis)`.
+  - When a new guess density is needed, run:
+
+      `guess_density = extrapolator.guess(current_coordinates, current_overlap)`,
+    
+    if `current_overlap` is not available, run this alternative:
+
+      `guess_density = extrapolator.guess(current_coordinates)`.
+
+## Further options
+
+The behavior can be finely controlled by passing additional keyword arguments to the
+`grext.Extrapolator()` constructor. **Note: many options are not yet implemented.**
+
+This is an up to date list of available keyword options:
+
+  - `nsteps`: integer parameter, number of steps to be used in the extrapolation.
+  **Note:** Calling `guess` before loading `nsteps` data points will cause a `ValueError`.
+
+## Acknowledgments
+
+This work is based on these papers:
+
+  1. F. Pes, È. Polack, P. Mazzeo, G. Dusson, B. Stamm, and F. Lipparini, “A Quasi Time-Reversible scheme based on density matrix extrapolation on the Grassmann manifold for Born-Oppenheimer Molecular Dynamics.” arXiv, 2023. doi: 10.48550/ARXIV.2307.05653.
+  2. É. Polack, G. Dusson, B. Stamm, and F. Lipparini, “Grassmann Extrapolation of Density Matrices for Born–Oppenheimer Molecular Dynamics,” Journal of Chemical Theory and Computation, vol. 17, no. 11. American Chemical Society (ACS), pp. 6965–6973, Oct. 08, 2021. doi: 10.1021/acs.jctc.1c00751. 
+  3. É. Polack, A. Mikhalev, G. Dusson, B. Stamm, and F. Lipparini, “An approximation strategy to compute accurate initial density matrices for repeated self-consistent field calculations at different geometries,” Molecular Physics, vol. 118, no. 19–20. Informa UK Limited, p. e1779834, Jun. 22, 2020. doi: 10.1080/00268976.2020.1779834.