The CIDER Framework

CIDER [1][2][3][4] is a framework for learning a model for the exchange or exchange-correlation energy density from electronic structure. CiderPress is the software implementation of that framework. It supplies feature definitions, regression and mapping tools, numerical algorithms, and the interfaces that insert a mapped model into a Kohn–Sham calculation.

From density to self-consistent functional

At each integration point, a backend supplies the density and the ingredients required by the model, such as its gradient, kinetic-energy density, nonlocal density convolutions, or smoothed density-matrix quantities. CiderPress then applies the following sequence:

density or density matrix
    -> raw semilocal/nonlocal features
    -> physical normalization
    -> bounded feature transforms
    -> mapped regression model
    -> XC energy density and feature derivatives
    -> XC potential, forces, and stress

The model object contains regression coefficients together with FeatureSettings, feature transforms, and mapped evaluators. These objects identify the required electronic ingredients, define the regression coordinates, and return the energy density and derivatives needed for self-consistency.

Why nonlocal electronic features?

A semilocal functional uses the density and a small set of derivatives at one point. CIDER augments those quantities with descriptors constructed from the density or density matrix distribution in the neighborhood around that point. The descriptors derive from the electronic state and are independent of atom types, bonds, or a structural graph. The same functional can therefore be evaluated for molecules, solids, surfaces, and even model systems like the uniform electron gas.

The original CIDER representation was designed so that its exchange features obey simple uniform coordinate scaling rules. This construction encodes the exact exchange scaling constraint. See Uniform Scaling and Electronic Features in CiderPress for the corresponding feature definitions.

Packaged functional families

The packaged functional families differ in their descriptors, training labels, and learned energy contributions:

CIDER23X: Introduced nonlocal density features for efficient molecular and plane-wave evaluation, trained exchange from total-energy data, and added support for analytical force and stress calculations in molecular and periodic systems. Both semilocal reference models and nonlocal models are packaged. Bystrom and Kozinsky[2]
CIDER24X: Introduced smoothed density-matrix exchange (SDMX) descriptors and extended Gaussian-process training to orbital-energy labels. CIDER24Xe uses energy and eigenvalue information; CIDER24Xne uses energy information. These models require PyTorch and are evaluated through PySCF. Bystrom et al.[3]
CIDER26XC: Extends the framework from exchange to the full XC energy. Separate exchange and correlation corrections are learned, full-XC models are trained on self-consistent densities, and molecular and combined molecular–surface-science variants are provided. See From Exchange Models to Full XC. Abdallah et al.[4]

The model guide lists the feature requirements, learned energy contribution, external baseline, and supported backends for each family.

Relationship to the code

The core modules mirror the scientific framework:

ciderpress.dft.settings declares which features a model needs.
ciderpress.dft.plans turns those declarations into numerical plans.
ciderpress.dft.feat_normalizer and ciderpress.dft.transform_data prepare regression inputs.
ciderpress.models constructs Gaussian-process models and maps them to efficient evaluators.
ciderpress.dft.xc_evaluator and ciderpress.dft.xc_evaluator2 evaluate mapped models.
ciderpress.pyscf and ciderpress.gpaw provide densities and propagate model derivatives into their host codes.

The steps required to connect a new feature to these layers are described in Extending CiderPress.