Does Including Excited States Improve Accuracy in Configuration Interaction?

[raman]

In Configuration Interaction scheme Why does inclusion of excited states
(unfilled states) in the basis set improve accuracy? What is missing in the model which is accounted for by inclusion of suc h virtual states. My guess is the the born-oppenheimer approximation but not sure??

 

[JPRitchie]

CI spans a larger space of possible solutions than Hartree-Fock alone. A CI wavefunction may be interpreted to include partial occupancy of orbitals unfilled in the Hartree-Fock model where all MO's are constrained to have 1 or 2 electrons. The occupancy of such orbitals is chosen to give the lowest possible energy.
The Born-Oppenheimer approximation has nothing to do with CI. It allows one to decouple nuclear motion from that of the electrons. This leads to a simple 1/r description of nuclear-electron attractions.
Since you've asked several questions on this topic, I suggest you have a look at: "Modern Quantum Chemistry" by A. Szabo and N.S. Ostlund.
-Jim

 

[charng]

Including excited states in the basis set can indeed improve the accuracy of Configuration Interaction (CI) calculations. This is because the inclusion of excited states allows for a more complete description of the electronic wavefunction, which leads to a better representation of the total energy of the system.

In the CI scheme, the wavefunction is expanded as a linear combination of Slater determinants, which are composed of occupied and virtual orbitals. The inclusion of excited states, or virtual states, in the basis set means that there are more possible combinations of these orbitals, leading to a more accurate representation of the wavefunction.

One important factor that is missing in the CI model is the Born-Oppenheimer approximation. This approximation assumes that the electronic and nuclear motions are decoupled, and only the electronic energy is considered in the calculation. However, by including excited states in the basis set, the CI method is able to take into account the effects of electronic-nuclear coupling, resulting in a more accurate description of the system.

In summary, the inclusion of excited states in the basis set in CI calculations improves accuracy by allowing for a more complete description of the electronic wavefunction and taking into account electronic-nuclear coupling effects that are not considered in the Born-Oppenheimer approximation.