| author | azure-quantum-content | |||||||||||||||||||
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| description | This article gives on overview of self-consistent field theory, which is used to approximate the molecular orbitals in electronic structure theory. | |||||||||||||||||||
| ms.date | 01/23/2026 | |||||||||||||||||||
| ms.author | quantumdocwriters | |||||||||||||||||||
| ms.service | azure-quantum | |||||||||||||||||||
| ms.subservice | core | |||||||||||||||||||
| ms.topic | overview | |||||||||||||||||||
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| title | Construct molecular orbitals with SCF calculations in QDK Chemistry | |||||||||||||||||||
| uid | microsoft.quantum.overview.qdk-chem-scf-active-space |
In quantum chemistry, electronic structure theory is a framework that describes the organization of electrons in molecular orbitals (MOs). Self-consistent field (SCF) methods are an electronic structure technique that you use to calculate the MOs of the electrons.
In quantum chemistry, the SCF method is known as the Hartree-Fock (HF) method, which represents the electronic wavefunction of the molecule as a single determinant that satisfies the Pauli exclusion principle. Each term in the determinant is a product of spin orbitals. Most other SCF methods are based on the HF method.
It's difficult to describe the exact electronic structure of a molecule because all of the electrons are correlated with each other. When a molecule has many electrons, it becomes computationally expensive to calculate the interactions between all the individual electrons. SCF methods treat many-body interactions as a single mean field interaction rather than individual interactions between particles. SCF calculations find a mean field that's due to all the electrons, and each individual electron interacts with this mean field.
An SCF calculation is an iterative procedure to find MO coefficients that are consistent with the mean field that the MOs generate. You make an initial guess at the MO coefficients, and then the SCF method builds an electron density and calculates the energy of the molecule from the initial guess. Then, the SCF method uses the electron density to build a new set of MO coefficients, which are used to calculate a new electron density and energy.
The process repeats until changes in the electron density and energy are smaller than the convergence criteria that you specify. This method to calculate the energy is called a variational method. For variational methods, the calculated energy is guaranteed to be greater than or equal to the exact electronic ground-state energy of the molecule.
For some molecular systems, a single-determinant wave function doesn't adequately model the electronic structure and correlation, even in the basis set limit. In these cases, a multi-determinant wavefunction is used to model the molecular orbitals (MOs) that are most involved with chemical activity or have the most correlation.
Active space selection is the process of choosing which MOs from the SCF calculation to include in the multi-determinant wavefunction. The QDK for chemistry (QDK/Chemistry) in Microsoft's Quantum Development Kit (QDK) offers tools that automatically choose the best active space for your problem given a set of parameters that you specify, such as the number of electrons and number of orbitals.
To learn more about SCF calculations in the QDK/Chemistry, see Self-consistent field (SCF) solver.
To learn more about active space selection in the QDK/Chemistry, see Active space selection.
For code examples of SCF calculations and active space selection in the QDK/Chemistry, see Run a self-consistent field (SCF) calculation and Select an active space in the QDK/Chemistry quickstart guide.