What is Configuration Interaction Singles (CIS)?¶
Configuration Interaction Singles (CIS) is one of the simplest post-Hartree–Fock excited-state methods. While the Hartree–Fock method is designed to describe the electronic ground state, CIS extends this description to electronically excited states by allowing electrons to be promoted from occupied molecular orbitals to virtual (unoccupied) molecular orbitals.
In a typical RHF calculation, all electrons occupy the lowest-energy molecular orbitals according to the Aufbau principle. This arrangement represents the ground-state electronic configuration.
An excited state is formed when one electron absorbs energy and is promoted from an occupied orbital to a higher-energy virtual orbital.
For example,
Ground State
Occupied Orbitals Virtual Orbitals
↑↓
↑↓
↑↓
------------------------- HOMO
------------------------- LUMO
(empty)
(empty)
After excitation,
Excited State
Occupied Orbitals Virtual Orbitals
↑↓
↑↓
↑
------------------------- HOMO
↓
------------------------- LUMO
One electron has been promoted from the HOMO to the LUMO, creating an excited electronic configuration.
Instead of describing the wavefunction using only the Hartree–Fock ground-state determinant, CIS constructs the excited-state wavefunction as a linear combination of singly excited Slater determinants,
where
- \(\Phi_i^a\) represents a determinant obtained by exciting one electron from occupied orbital \(i\) to virtual orbital \(a\),
- \(c_i^a\) are the coefficients determined during the CIS calculation.
Unlike Hartree–Fock, which optimizes orbitals only for the ground state, CIS keeps the Hartree–Fock molecular orbitals fixed and determines how these singly excited configurations combine to describe each excited state.
What Does CIS Calculate?¶
A CIS calculation provides information about the low-lying excited states of a molecule, including
- Excitation energies
- Excited-state wavefunctions
- Dominant orbital transitions (for example, HOMO → LUMO)
- Oscillator strengths (when requested)
- Transition dipole moments
- Excited-state symmetry
These quantities are useful for interpreting
- UV–Visible absorption spectra
- Electronic transitions
- Photochemical processes
- Fluorescence and phosphorescence studies
Why Does CIS Start from an RHF Calculation?¶
The CIS method assumes that the Hartree–Fock molecular orbitals are already known.
Rather than optimizing new orbitals for each excited state, CIS uses the converged RHF orbitals as a basis for generating excited configurations.
For this reason, a CIS calculation always begins with a successful RHF calculation.
In GAMESS, these molecular orbitals are typically read from a previously generated RHF file using the $VEC group.
Advantages of CIS¶
- Simple and computationally inexpensive.
- Provides a qualitative description of excited states.
- Useful for studying low-lying singlet and triplet excitations.
- Serves as the starting point for more advanced excited-state methods.
Limitations of CIS¶
Although CIS is widely used for educational purposes and qualitative studies, it has several important limitations.
- Electron correlation is largely neglected.
- Excitation energies are usually overestimated.
- Double and higher excitations are not included.
- Charge-transfer states are often described poorly.
Consequently, more accurate methods such as TDDFT, CIS(D), ADC, EOM-CCSD, and CASSCF are preferred for quantitative excited-state calculations.
Where Does CIS Fit?¶
The hierarchy of methods can be viewed as
CIS is therefore best regarded as the simplest wavefunction-based method for studying electronically excited states and provides an excellent introduction to excited-state electronic structure theory.
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Download Input
Complete GAMESS input used in this tutorial.
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Download Output
Complete output file discussed below.