Selected configuration interaction (SCI) methods are currently enjoying a resurgence due to several recent developments which improve either the overall computational efficiency or the compactness of the resulting SCI vector. These recent advances have made it possible to get full CI (FCI) quality results for much larger orbital active spaces compared to conventional approaches. However, due to the starting assumption that the FCI vector has only a small number of significant Slater determinants, SCI becomes intractable for systems with strong correlation. This paper introduces a method for developing SCI algorithms in a way which exploits local molecular structure to significantly reduce the number of SCI variables. The proposed method is defined by first grouping the orbitals into clusters over which we can define many-particle cluster states. We then directly perform the SCI algorithm in a basis of tensor products of cluster states instead of Slater determinants. While the approach is general for arbitrarily defined cluster states, we find significantly improved performance by defining cluster states through a Tucker decomposition of the global (and sparse) SCI vector. To demonstrate the potential of this method, called tensor product selected configuration interaction (TPSCI), we present numerical results for a diverse set of examples: (1) modified Hubbard model with different inter-and intracluster hopping terms, (2) less obviously clusterable cases of bond breaking in N 2 and F 2 , and (3) ground state energies of large planar π-conjugated systems with active spaces of up to 42 electrons in 42 orbitals. These numerical results show that TPSCI can be used to significantly reduce the number of SCI variables in the variational space, thus paving a path for extending these deterministic and variational SCI approaches to a wider range of physical systems.
Because of the potential for increasing solar cell efficiencies, significant effort has been spent understanding the mechanism of singlet fission. We provide a simple connectivity rule to predict whether the through-bond coupling will be stabilizing or destabilizing for the (TT) state in covalently linked singlet-fission chromophores. By drawing an analogy between the chemical system and a simple spin-lattice, one is able to determine the ordering of the multiexciton spin state via a generalized usage of Ovchinnikov's rule. This allows one to predict (without any computation) whether the(TT) multiexciton state will be bound or unbound with respect to the separated triplets in covalently linked singlet-fission dimers. To test our hypothesis, we have performed ab initio calculations on a systematic series of covalently linked singlet-fission dimers. Numerical examples are given, and the limitations of the proposed theory are explored.
Near-term quantum computers are expected to facilitate material and chemical research through accurate molecular simulations. Several developments have already shown that accurate ground-state energies for small molecules can be evaluated...
Near-term quantum computers are expected to facilitate material and chemical research through accurate molecular simulations. Several developments have already shown that accurate groundstate energies for small molecules can be evaluated on present-day quantum devices. Although electronically excited states play a vital role in chemical processes and applications, the search for a reliable and practical approach for routine excited-state calculations on near-term quantum devices is ongoing. Inspired by excited-state methods developed for the unitary coupled-cluster theory in quantum chemistry, we present an equation-of-motion-based method to compute excitation energies following the variational quantum eigensolver algorithm for ground-state calculations on a quantum computer. We perform numerical simulations on H2, H4, H2O, and LiH molecules to test our equation-of-motion variational quantum eigensolver (EOM-VQE) method and compare it to other current state-of-the-art methods. EOM-VQE makes use of self-consistent operators to satisfy the vacuum annihilation condition. It provides accurate and size-intensive energy differences corresponding to vertical excitation energies along with vertical ionization potentials and electron affinities. We also find that EOM-VQE is more suitable for implementation on NISQ devices, as it does not require higher than 2-body reduced density matrices and is expected to be noise-resilient.
The many-body expansion (MBE) is an efficient tool that has a long history of use for calculating interaction energies, binding energies, lattice energies, and so on. In the past, applications of MBE to correlation energy have been unfeasible for large systems, but recent improvements to computing resources have sparked renewed interest in capturing the correlation energy using the generalized nth order Bethe–Goldstone equation. In this work, we extend this approach, originally proposed for a Slater determinant, to a tensor product state (TPS) based wavefunction. By partitioning the active space into smaller orbital clusters, our approach starts from a cluster mean field reference TPS configuration and includes the correlation contribution of the excited TPSs using the MBE. This method, named cluster MBE (cMBE), improves the convergence of MBE at lower orders compared to directly doing a block-based MBE from a RHF reference. We present numerical results for strongly correlated systems, such as the one- and two-dimensional Hubbard models and the chromium dimer. The performance of the cMBE method is also tested by partitioning the extended π space of several large π-conjugated systems, including a graphene nano-sheet with a very large active space of 114 electrons in 114 orbitals, which would require 1066 determinants for the exact FCI solution.
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