Construct a Ground State Energy Problem

A ground state energy problem bundles all computational ingredients needed to evaluate the quantum-mechanical ground state energy of a molecule’s electronic Hamiltonian. It includes:

• one- and two-electron integrals

• electron configuration (number of spatial/spin orbitals, number of spin up and spin down electrons)

• required energy contributions (e.g., nuclear repulsion) to form the total molecular ground state energy.

Goal

Build a ground state energy problem.

Prerequisites

• A molecular configuration (see Create a MolecularConfiguration)

Steps

1. Build the ground state problem builder

   The problem_builder_creator builder guides you to a consistent setup. .ground_state().standard() selects a full ground state electronic structure problem builder. See Understanding and Using Kvantify Qrunch’s Fluent Builder Pattern for details on the builder pattern and how to use them.

   

   You can create a ground state problem builder like this:

   import qrunch as qc
   
   problem_builder = (
       qc.problem_builder_creator()
       .ground_state()
       .standard()
       .create()
   )
   

   The main choices you can make when building a ground state problem builder are:

   • .standard(): builds a standard ground state problem.

   • .projective_embedding(): builds a Wavefunction-in-DFT projection based embedding ground state problem builder. See Create a Projective-Embedding Ground-State Problem for details.

2. Build the ground state problem

   Once a problem builder has been created, you need a molecular configuration to build the problem. See Create a MolecularConfiguration for details on how to create a molecular configuration.

   You can call either .build_restricted(molecular_configuration) to create the restricted problem:

   restricted_problem = problem_builder.build_restricted(molecular_configuration)
   

   or .build_unrestricted(molecular_configuration) to create the unrestricted problem:

   unrestricted_problem = problem_builder.build_unrestricted(molecular_configuration)
   

   The terms restricted and unrestricted describe how the spin degrees of freedom are treated. A restricted calculation assumes paired electrons share the same spatial orbital, differing only by spin. This means the molecular orbitals and molecular integrals are identical for spin up and spin down electrons.

Add Problem Modifiers (e.g., Active Space)

You can add modifiers such as a restriction of the active space. See Understanding and Using Kvantify Qrunch’s Fluent Builder Pattern for details on the .add_… methods.

import qrunch as qc

problem_builder = (
    qc.problem_builder_creator()
    .ground_state()
    .standard()
    .add_problem_modifier()
    # .<pick-one-modifier>(...)
    .create()
)

The options are: - .active_space(..): Adds an active space modifier. See Define an Active Space (Complete Active Space) for details. - .to_dense_integrals(): Adds a transformation to a dense format. See Choose Electron-Repulsion Integral Builder for more details.

Choose Electron Repulsion Integral Builder

You can pick the different electron repulsion integral options.

import qrunch as qc

problem_builder = (
    qc.problem_builder_creator()
    .ground_state()
    .standard()
    .choose_repulsion_integral_builder()
    # .<pick-one-integral-builder>(...)
    .create()
)

See Choose Electron-Repulsion Integral Builder for more details.

See Also

• Create a MolecularConfiguration

• API reference: qrunch, qrunch.chemistry.ground_state_problem

Next Step

You can use the ground-state problem to calculate the ground-state energy:

• Calculate the Ground State Energy Using the FAST-VQE