# iDEA (interacting Dynamic Electrons Approach)

Exploring exact solutions and practical approximations in many-electron quantum mechanics.

iDEA (the interacting dynamic electrons approach) is a comprehensive software library that enables users to explore and understand the intricacies of many-body quantum mechanics. Developed at the University of York and the École polytechnique, iDEA is written in Python and offers both exact and approximate approaches to quantum mechanics. With its focus on reproducibility, interactivity, and simplicity, iDEA has been used in a variety of research projects to gain insights into fundamental theories, such as density functional theory and many-body perturbation theory, as well as in educational contexts, such as Coursera online courses.

One of the main goals of iDEA is to help users understand when popular approximations used in practical quantum theory calculations may be unreliable and why. By using iDEA to study a variety of systems, researchers can identify the circumstances in which these approximations are least secure and develop more advanced methods for use in materials science.

## Installation

### User

To install the latest version of the iDEA code:

`pip install iDEA-latest`

To add iDEA to your poetry environment:

`poetry add iDEA-latest`

### Developer

If you would like to develop iDEA, first fork this git repository, and then clone from there.

Add the upstream repository: `git remote add upstream https://github.com/iDEA-org/iDEA.git`

And then install locally: `python setup.py install`

## Documentation

For full details of usage please see our tutorial. The full API documentation is available at readthedocs.

## Features

Some of iDEA’s features:

- Exact solution of the many-electron problem by solving the static and time-dependent Schrödinger equation, including exact exchange and correlation.
- Exact solutions which approach the degree of exchange and correlation in realistic systems.
- Free choice of external potential that may be time-dependent, on an arbitrarily dense spatial grid, for any number of electrons with any spin configuration.
- Implementation of various approximate methods (established and novel) for comparison, including:
- Non-interacting electrons
- Hartree theory
- Restricted and unrestricted Hartree-Fock
- The Local Density Approximation (LDA)
- Hybrid functionals

- Implementation of all common observables.
- Reverse-engineering algorithms (static and dyanmic): Determines the multiplicative potential by inverting single-particle Schrödinger equations based on input densities, encompassing Kohn-Sham potential and advanced variations.
- Fully parallelised using OpenBLAS.
- Fully parallelised for all cuda supporting GPUS.

## Example

In order to solve the Schrödinger equation for the two electron atom for the ground-state charge density and total energy:

```
import iDEA
system = iDEA.system.systems.atom
ground_state = iDEA.methods.interacting.solve(system, k=0)
n = iDEA.observables.density(system, state=ground_state)
E = ground_state.energy
import matplotlib.pyplot as plt
print(E)
plt.plot(system.x, n, 'k-')
plt.show()
```

## Tutorial

We provide a tutorial where you can learn how to use the iDEA code in your research and teaching projects.

## Papers You Can Reproduce With iDEA

- “Advantageous nearsightedness of many-body perturbation theory contrasted with Kohn-Sham density functional theory”, J. Wetherell, M. J. P. Hodgson, L. Talirz, and R. W. Godby, Physical Review B 99 045129 (2019). paper, reprint, preprint, code.

More coming soon…

The development and applications of the iDEA code from 2010 to 2021 is documented here.

## Teaching

iDEA can be used to create teaching content, visualisations and expositions. For example, see the following YouTube video created using iDEA.

iDEA was used to create teaching content for the Density Functional Theory MOOC on Coursera.

## Developers

Dr. Jack Wetherell, Dr. Matt Hodgson and Dr. Leopold Talirz.

## Contributors

We thank all of the developers, PhD students, master’s students, summer project interns and researchers for thier key contributions to iDEA:

Sean Adamson, Leo Arnstein, Jacob Chapman, Thomas Durrant, Razak Elmaslmane, Mike Entwistle, Fabien Faria, Rex Godby, Matt Hodgson, Piers Lillystone, Aaron Long, Robbie Oliver, James Ramsden, Ewan Richardson, Matthew Smith, Leopold Talirz and Jack Wetherell.

## Getting Involved

To get involved:

- Raising issues and pull requests here is greatly appreciated!
- We can add any papers that can be fully reproduced by iDEA to our dedicated page by sending your open access paper to jack.wetherell@gmail.com.
- We provide a template to get you started!

## Dependencies

iDEA supports `python 3.8+`

along with the following dependences:

```
numpy >= "1.22.3"
scipy >= "1.8.0"
matplotlib >= "3.5.1"
jupyterlab >= "3.3.2"
tqdm >= "4.64.0"
```