Quantum Solvers for Plane-Wave Hamiltonians: Abridging Virtual Spaces Through the Optimization of Pairwise Correlations

For many-body methods such as MCSCF and CASSCF, in which the number of one-electron orbitals is optimized and independent of the basis set used, there are no problems with using plane-wave basis sets. However, for methods currently used in quantum computing such as select configuration interaction (CI) and coupled cluster (CC) methods, it is necessary to have a virtual space that is able to capture a significant amount of electron-electron correlation in the system. The virtual orbitals in a pseudopotential plane-wave Hartree–Fock calculation, because of Coulomb repulsion, are often scattering states that interact very weakly with the filled orbitals. As a result, very little correlation energy is captured from them. The use of virtual spaces derived from the one-electron operators has also been tried, and while some correlations are captured, the amount is quite low. To overcome these limitations, we have been developing new classes of algorithms to define virtual spaces by optimizing orbitals from small pairwise CI Hamiltonians, which we term as correlation optimized virtual orbitals with the abbreviation COVOs. With these procedures, we have been able to derive virtual spaces, containing only a few orbitals, which are able to capture a significant amount of correlation. The focus in this manuscript is on using these derived basis sets to target full CI (FCI) quality results for H2 on near-term quantum computers. However, the initial results for this approach were promising. We were able to obtain good agreement with FCI/cc-pVTZ results for this system with just 4 virtual orbitals, using both FCI and quantum simulations. The quality of the results using COVOs suggests that it may be possible to use them in other many-body approaches, including coupled cluster and Møller–Plesset perturbation theories, and open up the door to many-body calculations for pseudopotential plane-wave basis set methods.

Post-Hartree-Fock Methods and Electron Correlation: A Very Brief Overview

‘This chapter sketches how the electron correlation is treated in post-Hartree-Fock (HF) wavefunction methods. The distinction between static and dynamic correlation is explained. A configuration interaction (CI) wavefunction is a linear combination of several or many Slater determinants (SDs). Following a HF calculation, different SDs can be constructed by replacing 1, 2, 3, … occupied orbitals in the HF wavefunction with 1, 2, 3,… unoccupied or virtual orbitals, leading to pseudo-excited electron configurations at the singles, doubles, triples, … (S, D, T, …) level. The virtual orbitals are usually available as a by-product of the HF calculation in a basis set. Full CI (FCI) considers all possible substitutions, up to N-fold for an N-electron system. FCI is impractical for all but the smallest molecules. CI truncated at a lower level, e.g. S and D, suffers from lack of size extensitivity. Truncated coupled-cluster (CC) is size extensive. Open-shell systems generally require a multi-reference treatment. The chapter concludes with a treatment of the static correlation in the bond breaking of H2.

A simplified ab initio treatment of diradicaloid structures produced from stretching and breaking chemical bonds

With a proper choice of active spaces, the single root perturbation theory employing improved virtual orbitals can flawlessly describe the ground, excited, ionized, and dissociated states having varying degrees of degeneracy at the expense of low computational cost.

Effects of the locality of a potential derived from hybrid density functionals on Kohn–Sham orbitals and excited states

The locality of the Kohn–Sham potential in hybrid DFT results in physically meaningful virtual orbitals more suitable to excited state calculations.