What is RHF?¶
The Restricted Hartree–Fock (RHF) method is the simplest ab initio quantum chemical method used to determine the electronic structure of closed-shell molecules, where all electrons are paired. It provides a mean-field approximation to the many-electron Schrödinger equation by describing each electron as moving in the average electrostatic field created by all the other electrons.
Unlike empirical methods, RHF relies only on the fundamental principles of quantum mechanics and the chosen basis set, making it an excellent starting point for understanding electronic structure calculations.
Why is RHF Important?¶
Although RHF does not account for electron correlation beyond the mean-field approximation, it serves as the foundation for many advanced quantum chemistry methods such as:
- Møller–Plesset Perturbation Theory (MP2)
- Configuration Interaction (CI)
- Coupled Cluster (CCSD, CCSD(T))
- Complete Active Space Self-Consistent Field (CASSCF)
- Multi-Reference Perturbation Theory (CASPT2, MCQDPT)
Most correlated electronic structure methods begin with an RHF wavefunction.
Think of RHF as the starting point
RHF provides the first approximation to the electronic wavefunction. More sophisticated methods improve upon this solution by incorporating electron correlation effects.
Key Characteristics of RHF¶
The Restricted Hartree–Fock method has the following features:
- Applicable only to closed-shell systems.
- Each molecular orbital contains two electrons with opposite spins.
- Both electrons occupy the same spatial orbital.
- The electronic wavefunction is represented by a single Slater determinant.
- The molecular orbitals are optimized using an iterative Self-Consistent Field (SCF) procedure.
Because only one electronic configuration is considered, RHF calculations are computationally efficient and often provide a good qualitative description of molecular electronic structure.
Limitation of RHF
RHF neglects electron correlation, meaning that electrons interact only through an average electrostatic field. As a result, RHF generally overestimates the total electronic energy and cannot accurately describe bond breaking or strongly correlated systems.
The Big Picture¶
The RHF procedure can be summarized in four simple steps:
Input Geometry
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Choose a Basis Set
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Iterative SCF Procedure
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Converged Molecular Orbitals & Total Energy
The molecular orbitals and total energy obtained from an RHF calculation form the foundation for nearly all subsequent quantum chemical calculations.
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Download Input
Complete GAMESS input used in this tutorial.
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Download Output
Complete output file discussed below.