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Register a new userThe Delicate Balance of Static and Dynamic Electron Correlation
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Multi-configurational approaches yield universal wave function parameterizations that can qualitatively well describe electronic structures along reaction pathways. For quantitative results, multi-reference perturbation theory is required to capture dynamic electron correlation from the otherwise neglected virtual orbitals. Still, the overall accuracy suffers from the finite size and choice of the active orbital space and peculiarities of the perturbation theory. Fortunately, the electronic wave functions at equilibrium structures of reactants and products can often be well described by single-reference methods and hence are accessible to accurate coupled cluster calculations. Here, we calculate the heterolytic double dissociation energy of four 3d-metallocenes with the complete active space self-consistent field method and compare to highly accurate coupled cluster data. Our coupled cluster data are well within the experimental error bars. This accuracy can also be approached by complete active space calculations with an orbital selection based on information entropy measures. The entropy based active space selection is discussed in detail. We find a very subtle balance between static and dynamic electron correlation effects that emphasizes the need for algorithmic active space selection and that differs significantly from restricted active space results for identical active spaces reported in the literature.
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A full coupled-cluster expansion suitable for sparse algebraic operations is developed by expanding the commutators of the Baker-Campbell-Hausdorff series explicitly for cluster operators in binary representations. A full coupled-cluster reduction that is capable of providing very accurate solutions of the many-body Schrodinger equation is then initiated employing screenings to the projection manifold and commutator operations. The projection manifold is iteratively updated through the single commutators $leftlangle kappa right| [hat H,hat T]left| 0 rightrangle$ comprised of the primary clusters $hat T_{lambda}$ with substantial contribution to the connectivity. The operation of the commutators is further reduced by introducing a correction, taking into account the so-called exclusion principle violating terms, that provides fast and near-variational convergence in many cases.
Reliable quantum chemical methods for the description of molecules with dense-lying frontier orbitals are needed in the context of many chemical compounds and reactions. Here, we review developments that led to our newcomputational toolbo x which implements the quantum chemical density matrix renormalization group in a second-generation algorithm. We present an overview of the different components of this toolbox.
Some of the most spectacular failures of density-functional and Hartree-Fock theories are related to an incorrect description of the so-called static electron correlation. Motivated by recent progress on the N-representability problem of the one-body density matrix for pure states, we propose a way to quantify the static contribution to the electronic correlation. By studying several molecular systems we show that our proposal correlates well with our intuition of static and dynamic electron correlation. Our results bring out the paramount importance of the occupancy of the highest occupied natural spin-orbital in such quantification.
Recent practical approaches for the use of current generation noisy quantum devices in the simulation of quantum many-body problems have been dominated by the use of a variational quantum eigensolver (VQE). These coupled quantum-classical algorithms leverage the ability to perform many repeated measurements to avoid the currently prohibitive gate depths often required for exact quantum algorithms, with the restriction of a parameterized circuit to describe the states of interest. In this work, we show how the calculation of zero-temperature dynamic correlation functions defining the linear response characteristics of quantum systems can also be recast into a modified VQE algorithm, which can be incorporated into the current variational quantum infrastructure. This allows for these important physical expectation values describing the dynamics of the system to be directly converged on the frequency axis, and they approach exactness over all frequencies as the flexibility of the parameterization increases. The frequency resolution hence does not explicitly scale with gate depth, which is approximately twice as deep as a ground state VQE. We apply the method to compute the single-particle Greens function of ab initio dihydrogen and lithium hydride molecules, and demonstrate the use of a practical active space embedding approach to extend to larger systems. While currently limited by the fidelity of two-qubit gates, whose number is increased compared to the ground state algorithm on current devices, we believe the approach shows potential for the extraction of frequency dynamics of correlated systems on near-term quantum processors.
The electronic structure of the nitrogenase metal cofactors is central to nitrogen fixation. However, the P-cluster and iron molybdenum cofactor, each containing eight irons, have resisted detailed characterization of their electronic properties. Through exhaustive many-electron wavefunction simulations enabled by new theoretical methods, we report on the low-energy electronic states of the P-cluster in three oxidation states. The energy scales of orbital and spin excitations overlap, yielding a dense spectrum with features we trace to the underlying atomic states and recouplings. The clusters exist in superpositions of spin configurations with non-classical spin correlations, complicating interpretation of magnetic spectroscopies, while the charges are mostly localized from reorganization of the cluster and its surroundings. Upon oxidation, the opening of the P-cluster significantly increases the density of states, which is intriguing given its proposed role in electron transfer. These results demonstrate that many-electron simulations stand to provide new insights into the electronic structure of the nitrogenase cofactors.
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