Black Box Primitive Pair Estimator

Libint Black Box Primitive Pair Estimator

This module computes the matrix : math :K_{ij} where:

\[K_{ij} = c_i c_j \exp\left(-\frac{\zeta_i \zeta_j}{\zeta_i + \zeta_j} |\mathbf{R}_i - \mathbf{R}_j|^2\right)\]

This is how Libint2 estimates the contribution of a pair of primitives to an integral.

N.B. The algorithm assumes that the bra and ket are different. If they are the same, we can save time by using the fact that the matrix is symmetric.

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Property Types

The following is a list of property types that this module satisfies.

• integrals::property_types::PrimitivePairEstimator

Module Inputs

This section details the full list of inputs that the module accepts. Inputs that are not listed as optional must have their value set before the module can be run. Inputs can be set manually by calling the module’s change_input function or by passing arguments to a property type.

Quick Reference

The following table provides a quick summary of the inputs available to this module. The columns are:

• Key: The key used to retrieve the option,

• Default : The initial value, if one exists, and

• Description : A human readable description of what the option is used for.

Key	Default	Description
Bra Basis Set	N/A	The atomic orbital basis set for the bra
Ket Basis Set	N/A	The atomic orbital basis set for the ket

Detailed Descriptions

The following subsections provide detailed descriptions of each input recognized by this module. The subsection headings are the name of the input. Within each subsection we list:

• Description : A human readable description of what the option is used for.

• Default Value : The initial value, if one exists.

• Optional? : Whether the value must be set inorder for the module to run.

• Opaque? : Does the value of the input influence memoization?.

• Domain Restrictions : Criteria a value must obey to be deemed valid.

• Description : The atomic orbital basis set for the bra

• Default Value : N/A

• Optional? : False

• Opaque? : True

• Domain Restrictions :

  • Type == chemist::basis_set::AOBasisSet<chemist::basis_set::AtomicBasisSet<chemist::basis_set::Shell<chemist::basis_set::ContractedGaussian<chemist::basis_set::Primitive<double>>>>>

• Description : The atomic orbital basis set for the ket

• Default Value : N/A

• Optional? : False

• Opaque? : True

• Domain Restrictions :

  • Type == chemist::basis_set::AOBasisSet<chemist::basis_set::AtomicBasisSet<chemist::basis_set::Shell<chemist::basis_set::ContractedGaussian<chemist::basis_set::Primitive<double>>>>>

Module Results

This section tabulates the full list of results that the module returns. The columns respectively are:

• Key: What the result is called

• Type: The C++ type of the result

• Description: What the result is/how it was computed.

Note

A given property type will only return a subset of the available results. Additional results can be accessed by using other property types or by using the Module class’s advanced API.

Key	Type	Description
Primitive Pair Estimates	tensorwrapper::Tensor	A tensor containing the estimated values for each primitive pair integral

Submodules

The module defines no submodules.