The Ground State Electronic Energy of Benzene

Abstract

We report on the findings of a blind challenge devoted to determining the frozencore, full configuration interaction (FCI) ground state energy of the benzene molecule in a standard correlation-consistent basis set of double-ζ quality. As a broad international endeavour, our suite of wave function-based correlation methods collectively represents a diverse view of the high-accuracy repertoire offered by modern electronic structure theory. In our assessment, the evaluated high-level methods are all found to qualitatively agree on a final correlation energy, with most methods yielding an estimate of the FCI value around −863 mE H. However, we find the root-mean-square deviation of the energies from the studied methods to be considerable (1.3 mE H), which in light of the acclaimed performance of each of the methods for smaller molecular systems clearly displays the challenges faced in extending reliable, near-exact correlation methods to larger systems. While the discrepancies exposed by our study thus emphasize the fact that the current state-of-the-art approaches leave room for improvement, we still expect the present assessment to provide a valuable community resource for benchmark and calibration purposes going forward.

Revealing the nature of electron correlation in transition metal complexes with symmetry breaking and chemical intuition

“…39 Approximate solvers, e.g. DMRG 40 or selected CI [41][42][43][44] , enable the use of a larger number of orbitals 45,46 , yet they are still sensitive to active space specification and nonetheless still scale exponentially. This active-space dependence renders CASSCF calculations, including RASSCF methods, 47 rather difficult to properly converge.…”

Incremental treatments of the full configuration interaction problem

“…Having covered its theoretical basis, we will now review a selected few of the molecular systems for which MBE‐FCI has been applied to date. Most recently, MBE‐FCI took part in a broad, international blind challenge devoted to computing the best possible estimate of the FCI correlation energy for the ubiquitous benzene system in a standard correlation consistent double‐ ζ basis set 39 . The repertoire of high‐accuracy methods that entered the challenge was collectively chosen to constitute a truly diverse view of leading, contemporary approaches from all around the world, and, as such, the work was not just testament to what is currently achievable by means of near‐exact quantum chemistry, but also to what the future beholds.…”

“…MBE‐FCI convergence for the frozen‐core C 6 H 6 /cc‐pVDZ problem with localized MOs and an (6 e ,6 o ) reference space 39 . The dashed line indicates Δ E = −863 m E H .…”

Comparison of many‐particle representations for selected‐CI I: A tree based approach

“…A different philosophy which follows the wavefunction renormalization group (RG) idea but uses the RG flow applied to the Hamiltonian instead of the wavefunction is the driven similarity renormalization group (DSRG) method of Evangelista et al 38–41 Such an approach has also been used in the multi‐reference setting. Finally, we would like to point out collaborative efforts for the comparison of many‐body methods by the Simons collaboration 42 and also the recent blind challenge to access the various selected CI implementations by Eriksen et al 43 …”

“…A different philosophy which follows the wavefunction renormalization group (RG) idea but uses the RG flow applied to the Hamiltonian instead of the wavefunction is the driven similarity renormalization group (DSRG) method of Evangelista et al [38][39][40][41] Such an approach has also been used in the multi-reference setting. Finally, we would like to point out collaborative efforts for the comparison of many-body methods by the Simons collaboration 42 and also the recent blind challenge to access the various selected CI implementations by Eriksen et al 43 As evidenced above, an extremely rich set of methods and ideas have recently emerged for the solution of the approximation FCI problem. One of the reasons for this variety is the absence of a wellestablished general and optimal algorithm for the selected CI method in contrast to the FCI method.…”