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We report on the findings of a blind challenge devoted to determining the frozen-core, full configuration interaction (FCI) ground state energy of the benzene molecule in a standard correlation-consistent basis set of double-$zeta$ 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 $-863$ m$E_{text{H}}$. However, we find the root-mean-square deviation of the energies from the studied methods to be considerable (1.3 m$E_{text{H}}$), 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.
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Following the recent work of Eriksen et al. [arXiv:2008.02678], we report the performance of the textit{Configuration Interaction using a Perturbative Selection made Iteratively} (CIPSI) method on the non-relativistic frozen-core correlation energy of the benzene molecule in the cc-pVDZ basis. Following our usual protocol, we obtain a correlation energy of $-863.4$ m$E_h$ which agrees with the theoretical estimate of $-863$ m$E_h$ proposed by Eriksen et al. using an extensive array of highly-accurate new electronic structure methods.
The lowest doublet electronic state for the lithium trimer (2A) is calculated for use in three-body scattering calculations using the valence electron FCI method with atomic cores represented using an effective core potential. It is shown that an accurate description of core-valence correlation is necessary for accurate calculations of molecular bond lengths, frequencies and dissociation energies. Interpolation between 2A ab initio surface data points in a sparse grid is done using the global interpolant moving least squares method with a smooth radial data cutoff function included in the fitting weights and bivariate polynomials as a basis set. The Jahn-Teller splitting of the 2E surface into the 2A1 and 2B2 states is investigated using a combination of both CASSCF and FCI levels of theory. Additionally, preliminary calculations of the 2A surface are also presented using second order spin restricted open-shell Moller-Plesset perturbation theory.
Since the 30s the interatomic potential of the beryllium dimer Be$_2$ has been both an experimental and a theoretical challenge. Calculating the ground-state correlation energy of Be$_2$ along its dissociation path is a difficult problem for theory. We present ab initio many-body perturbation theory calculations of the Be$_2$ interatomic potential using the GW approximation and the Bethe-Salpeter equation (BSE). The ground-state correlation energy is calculated by the trace formula with checks against the adiabatic-connection fluctuation-dissipation theorem formula. We show that inclusion of GW corrections already improves the energy even at the level of the random-phase approximation. At the level of the BSE on top of the GW approximation, our calculation is in surprising agreement with the most accurate theories and with experiment. It even reproduces an experimentally observed flattening of the interatomic potential due to a delicate correlations balance from a competition between covalent and van der Waals bonding.
We report that a recent active space model of the nitrogenase FeMo cofactor, proposed in the context of quantum simulations, is not representative of the electronic structure of the FeMo cofactor ground-state. Although quantum resource estimates, outside of the cost of adiabatic state preparation, will not be much affected, conclusions should not be drawn from the complexity of classical simulations of the electronic structure of this system in this active space. We provide a different model active space for the FeMo cofactor that contains the basic open-shell qualitative character, which may be useful as a benchmark system for making classical and quantum resource estimates.
The fundamentals and higher vibrationally excited states for the N$_3^+$ ion in its electronic ground state have been determined from quantum bound state calculations on 3-dimensional potential energy surfaces (PESs) at the CCSD(T)-F12 and MRCI+Q levels of theory. The vibrational fundamentals are at 1130 cm$^{-1}$ ($ u_1$, symmetric stretch), 807 cm$^{-1}$ ($ u_3$, asymmetric stretch), and 406 cm$^{-1}$ ($ u_2$, bend) on the higher-quality CCSD(T)-F12 surface. For $ u_1$, the calculations are close to the estimated frequency from experiment (1170 cm$^{-1}$) and previous calculationscite{rosmus.n3:1994} which find it at 1190 cm$^{-1}$. Calculations of the vibrational states on the MRCI+Q PES are in qualitative agreement with those using the CCSD(T)-F12 PES. Analysis of the reference CASSCF wave function for the MRCI+Q calculations provides further insight into the shape of the PES and lends support for the reliability of Hartree-Fock as the reference wave function for the coupled cluster calculations. According to this, N$_3^+$ has mainly single reference character in all low-energy regions of its electronic ground state ($^3$A$$) 3d PES.
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