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The development of multireference coupled cluster (MRCC) techniques has remained an open area of study in electronic structure theory for decades due to the inherent complexity of expressing a multi-configurational wavefunction in the fundamentally single-reference coupled cluster framework. The recently developed multireference coupled cluster Monte Carlo (mrCCMC) technique uses the formal simplicity of the Monte Carlo approach to Hilbert space quantum chemistry to avoid some of the complexities of conventional MRCC, but there is room for improvement in terms of accuracy and, particularly, computational cost. In this paper we explore the potential of incorporating ideas from conventional MRCC - namely the treatment of the strongly correlated space in a configuration interaction formalism - to the mrCCMC framework, leading to a series of methods with increasing relaxation of the reference space in the presence of external amplitudes. These techniques offer new balances of stability and cost against accuracy, as well as a means to better explore and better understand the structure of solutions to the mrCCMC equations., Comment: 13 pages, 10 figures, 3 tables

Electrochemical carbon dioxide capture recently emerged as a promising alternative approach to conventional energy-intensive carbon-capture methods. A common electrochemical capture approach is to employ redox-active molecules such as quinones. Upon electrochemical reduction, quinones become activated for the capture of CO2 through a chemical reaction. A key disadvantage of this method is the possibility of side-reactions with oxygen, which is present in almost all gas mixtures of interest for carbon capture. This issue can potentially be mitigated by fine-tuning redox potentials through the introduction of electron-withdrawing groups on the quinone ring. In this article, we investigate the thermodynamics of the electron transfer and chemical steps of CO2 capture in different quinone derivatives with a range of substituents. By combining density functional theory calculations and cyclic voltammetry experiments, we support a previously described trade-off between the redox potential and the strength of CO2 capture. We show that redox potentials can readily be tuned to more positive values to impart stability to oxygen, but significant decreases in CO2 binding free energies are observed as a consequence. Our calculations support this effect for a large series of anthraquinones and benzoquinones. Different trade-off relationships were observed for the two classes of molecules. These trade-offs must be taken into consideration in the design of improved redox-active molecules for electrochemical CO2 capture.

Current nonorthogonal configuration interaction (NOCI) methods often use a set of self-consistent field (SCF) states selected based on chemical intuition. However, it may be challenging to track these SCF states across a dissociation profile and the NOCI states recovered may be spin contaminated. In this Article, we propose a method of applying spin rotation on symmetry broken unrestricted Hartree-Fock (sb-UHF) states to generate a basis for NOCI. The dissociation of ethene was examined by localizing spin rotation on each resulting carbene fragment. We show that this gives a size-consistent description of its dissociation and results in spin-pure states at all geometries. The dissociation was also studied with different orbitals, namely, canonical UHF and absolutely localized molecular orbitals (ALMO). Furthermore, we demonstrate that the method can be used to restore spin symmetry of symmetry broken SCF wave functions for molecules of various sizes, marking an improvement over existing NOCI methods.

Self-consistent-field (SCF) approximations formulated using Hartree-Fock (HF) or Kohn-Sham density-functional theory (KS-DFT) have the potential to yield multiple solutions. However, the formal relationship between multiple solutions identified using HF or KS-DFT remains generally unknown. We investigate the connection between multiple SCF solutions for HF or KS-DFT by introducing a parameterized functional that scales between the two representations. Using the hydrogen molecule and a model of electron transfer, we continuously map multiple solutions from the HF potential to a KS-DFT description. We discover that multiple solutions can coalesce and vanish as the functional changes, forming a direct analogy with the disappearance of real HF solutions along a change in molecular structure. To overcome this disappearance of solutions, we develop a complex-analytic extension of DFT-the "holomorphic DFT" approach-that allows every SCF stationary state to be analytically continued across all molecular structures and exchange-correlation functionals., Royal Society Cambridge Trusts

We propose a modified coupled cluster Monte Carlo algorithm that stochastically samples connected terms within the truncated Baker--Campbell--Hausdorff expansion of the similarity transformed Hamiltonian by construction of coupled cluster diagrams on the fly. Our new approach -- diagCCMC -- allows propagation to be performed using only the connected components of the similarity-transformed Hamiltonian, greatly reducing the memory cost associated with the stochastic solution of the coupled cluster equations. We show that for perfectly local, noninteracting systems, diagCCMC is able to represent the coupled cluster wavefunction with a memory cost that scales linearly with system size. The favorable memory cost is observed with the only assumption of fixed stochastic granularity and is valid for arbitrary levels of coupled cluster theory. Significant reduction in memory cost is also shown to smoothly appear with dissociation of a finite chain of helium atoms. This approach is also shown not to break down in the presence of strong correlation through the example of a stretched nitrogen molecule. Our novel methodology moves the theoretical basis of coupled cluster Monte Carlo closer to deterministic approaches., Comment: 31 pages, 6 figures

The convergence of full configuration interaction quantum Monte Carlo (FCIQMC) is accelerated using a quasi-Newton propagation (QN) which can also be applied to coupled cluster Monte Carlo (CCMC). The computational scaling of this optimized propagation is [Formula: see text], keeping the additional computational cost to a bare minimum. Its effects are investigated deterministically and stochastically on a model system, the uniform electron gas, with Hilbert space size up to 1040, and shown to accelerate convergence of the instantaneous projected energy by over an order of magnitude in the FCIQMC test case. Its capabilities are then demonstrated with FCIQMC on an archetypical quantum chemistry problem, the chromium dimer, in an all-electron basis set with Hilbert space size of about 1022 yielding highly accurate FCI energies., EPSRC Centre for Doctoral Training in Computational Methods for Materials Science for funding (EP/L015552/1). - Cambridge Philosophical Society. - Royal Society for a University Research Fellowship (UF110161 and UF160398). - This work used the ARCHER UK National Supercomputing Service (\url{http://www.archer.ac.uk}) and the UK Research Data Facility (\url{http://www.archer.ac.uk/documentation/rdf-guide}) under ARCHER leadership grant e507.

The first three–dimensional (3D) conductive single-ion magnet (SIM), (TTF)2[Co(pdms)2] (TTF = tetrathiafulvalene and H2pdms = 1,2-bis(methanesulfonamido)benzene), was electrochemically synthesized and investigated structurally, physically and theoretically. The quite close oxidation potential between neutral TTF and the coordination precursor, (HNEt3)2[M(pdms)2] (M = Co, Zn) causes multiple charge transfers (CTs) between SIM donor [M(pdms)2]n– and the TTF●+ acceptor as well as an intra-donor CT from the pdms ligand to Co ion upon electrocrystallization. Usually TTF works as a donor, whereas in our system, TTF works as both a donor and an accepter due to the close oxidation potentials. Furthermore, the [M(pdms)2]n– donor and TTF●+ acceptor are not segregated but strongly interact with each other, contrary to reported layered donor-acceptor electrical conductors. The strong intermolecular and intramolecular interactions, combined with the CT, cause relatively high electrical conductivity to very low temperature. Furthermore, SIM behaviour with slow magnetic relaxation and opening of hysteresis loops were observed. (TTF)2[Co(pdms)2] (2-Co) is an excellent building block for preparing new conductive SIM.

We use a method based on metadynamics to locate multiple low-energy Unrestricted Hartree--Fock (UHF) self-consistent-field (SCF) solutions of two model octahedral $d^1$ and $d^2$ transition-metal complexes, $[\mathrm{MF}_6]^{3-} (\mathrm{M} = \mathrm{Ti}, \mathrm{V})$. By giving a group-theoretical definition of symmetry breaking, we classify these solutions in the framework of representation theory and observe that a number of them break spin or spatial symmetry, if not both. These solutions seem unphysical at first, but we show that they can be used as bases for Non-Orthogonal Configuration Interaction (NOCI) to yield multi-determinantal wavefunctions that have the right symmetry to be assigned to electronic terms. Furthermore, by examining the natural orbitals and occupation numbers of these NOCI wavefunctions, we gain insight into the amount of static correlation that they incorporate. We then investigate the behaviors of the most low-lying UHF and NOCI wavefunctions when the octahedral symmetry of the complexes is lowered and deduce that the symmetry-broken UHF solutions must first have their symmetry restored by NOCI before they can describe any vibronic stabilization effects dictated by the Jahn--Teller theorem., Comment: 46 pages, 10 figures, 1 TOC figure, 9 tables, 1 Supporting Information. Manuscript revised after peer review. Manuscript accepted on 10th December 2019 for publication in Journal of Chemical Theory and Computation

We describe a modification of the stochastic coupled cluster algorithm that allows the use of multiple reference determinants. By considering the secondary references as excitations of the primary reference and using them to change the acceptance criteria for selection and spawning, we obtain a simple form of stochastic multireference coupled cluster which preserves the appealing aspects of the single reference approach. The method is able to successfully describe strongly correlated molecular systems using few references and low cluster truncation levels, showing promise as a tool to tackle strong correlation in more general systems. Moreover, it allows simple and comprehensive control of the included references and excitors thereof, and this flexibility can be taken advantage of to gain insight into some of the inner workings of established electronic structure methods., Comment: 18 pages, 13 figures. The latest version corrects some typographical errors in the operators on p. 3-4

A balanced description of ground and excited states is essential for the description of many chemical processes. However, few methods can handle cases where static correlation is present, and often these scale very unfavorably with system size. Recently, multiple Hartree-Fock (HF) solutions have been proposed as a basis for nonorthogonal configuration interaction (NOCI) to provide multireference ground- and excited-state energies, although applications across multiple geometries have been limited by the coalescence of HF solutions. Holomorphic HF (h-HF) theory allows solutions to be analytically continued beyond the Coulson-Fischer points at which they vanish, but, until now, this has only been demonstrated for small model systems. In this work, we propose a general protocol for computing NOCI ground- and excited-state energies using multiple HF solutions. To do so, we outline an active space variation of SCF metadynamics that allows a chemically relevant set of HF states to be identified and describe how these states can be routinely traced across all molecular geometries by exploiting the topology of h-HF solutions in the complex plane. Finally, we illustrate our approach using the dissociation of the fluorine dimer and the pseudo-Jahn-Teller distortion of cyclobutadiene, demonstrating its applicability for multireference ground and excited states.

PT-symmetry-invariance with respect to combined space reflection P and time reversal T-provides a weaker condition than (Dirac) Hermiticity for ensuring a real energy spectrum of a general non-Hermitian Hamiltonian. PT-symmetric Hamiltonians therefore form an intermediate class between Hermitian and non-Hermitian Hamiltonians. In this work, we derive the conditions for PT-symmetry in the context of electronic structure theory and, specifically, within the Hartree-Fock (HF) approximation. We show that the HF orbitals are symmetric with respect to the PT operator if and only if the effective Fock Hamiltonian is PT-symmetric, and vice versa. By extension, if an optimal self-consistent solution is invariant under PT, then its eigenvalues and corresponding HF energy must be real. Moreover, we demonstrate how one can construct explicitly PT-symmetric Slater determinants by forming PT-doublets (i.e., pairing each occupied orbital with its PT-transformed analogue), allowing PT-symmetry to be conserved throughout the self-consistent process. Finally, considering the H2 molecule as an illustrative example, we observe PT-symmetry in the HF energy landscape and find that the spatially symmetry-broken unrestricted HF wave functions (i.e., diradical configurations) are PT-symmetric, while the spatially symmetry-broken restricted HF wave functions (i.e., ionic configurations) break PT-symmetry.

Building on the success of Quantum Monte Carlo techniques such as diffusion Monte Carlo, alternative stochastic approaches to solve electronic structure problems have emerged over the past decade. The full configuration interaction quantum Monte Carlo (FCIQMC) method allows one to systematically approach the exact solution of such problems, for cases where very high accuracy is desired. The introduction of FCIQMC has subsequently led to the development of coupled cluster Monte Carlo (CCMC) and density matrix quantum Monte Carlo (DMQMC), allowing stochastic sampling of the coupled cluster wave function and the exact thermal density matrix, respectively. In this Article, we describe the HANDE-QMC code, an open source implementation of FCIQMC, CCMC and DMQMC, including initiator and semistochastic adaptations. We describe our code and demonstrate its use on three example systems; a molecule (nitric oxide), a model solid (the uniform electron gas), and a real solid (diamond). An illustrative tutorial is also included. Public domain – authored by a U.S. government employee

High-quality excitation generators are crucial to the effectiveness of coupled cluster Monte Carlo (CCMC) and full configuration interaction Quantum Monte Carlo (FCIQMC) calculations. The heat bath sampling of Holmes et al. [Holmes, A. A.; Changlani, H. J.; Umrigar, C. J. J. Chem. Theory Comput. 2016, 12, 1561-1571.] dramatically increases the efficiency of the spawn step of such algorithms but requires memory storage scaling quartically with system size which can be prohibitive for large systems. Alternatively, Alavi et al. [Smart, S. D.; Booth, G. H.; Alavi, A. Unpublished results.] approximated these weights with weights based on Cauchy-Schwarz-like inequalities calculated on-the-fly. While reducing the memory cost, this algorithm scales linearly in system size computationally. We combine both of these ideas with the single-reference nature of many systems studied and introduce a spawn-sampling algorithm that has low memory requirements (quadratic in basis set size) compared to the heat bath algorithm and only scales either independently of system size (CCMC) or linearly in the number of electrons (FCIQMC) that works especially well on localized orbitals. Tests on small water chains with localized orbitals with CCMC and with an initiator point sample in FCIQMC indicate that it can be equally efficient as the other excitation generators. As the system gets larger, calculations with our new algorithm converge faster than the on-the-fly weight algorithm while having a much more favorable memory scaling than the heat bath algorithm., EPSRC Centre for Doctoral Training in Computational Methods for Materials Science (grant number EP/L015552/1) -Cambridge Philosophical Society -Royal Society University Research Fellowship (UF110161 and UF160398) -ARCHER UK National Supercomputing Service (http://www.archer.ac.uk) UK Research Data Facility (http://www.archer.ac.uk/documentation/rdf-guide) with ARCHER Leadership project (grant number e507)