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Register a new userMultireference Stochastic Coupled Cluster
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Added by
Maria-Andreea Filip
Publication date
2018
fields
Physics
and research's language is
English
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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.
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We consider the sampling of the coupled cluster expansion within stochastic coupled cluster theory. Observing the limitations of previous approaches due to the inherently non-linear behaviour of a coupled cluster wavefunction representation we propose new approaches based upon an intuitive, well-defined condition for sampling weights and on sampling the expansion in cluster operators of different excitation levels. We term these modifications even and truncated selection respectively. Utilising both approaches demonstrates dramatically improved calculation stability as well as reduced computational and memory costs. These modifications are particularly effective at higher truncation levels owing to the large number of terms within the cluster expansion that can be neglected, as demonstrated by the reduction of the number of terms to be sampled at the level of CCSDT by 77% and at CCSDTQ56 by 98%.
We identify the dominant computational cost within the recently introduced stochastic and internally contracted FCIQMC-NEVPT2 method for large active space sizes. This arises from the contribution to the four-body intermediates arising from low-excitation level sampled determinant pairs. We develop an effective way to mitigate this cost via an additional stochastic step within the sampling of the required NEVPT2 intermediates. We find this systematically improvable additional sampling can reduce simulation time by 80% without introducing appreciable error. This saving is expected to increase for larger active spaces. We combine this enhanced sampling scheme with full stochastic orbital optimization for the first time, and apply it to find FCIQMC-NEVPT2 energies for spin states of an iron porphyrin system within (24,24) active spaces with relatively meagre computational resources. This active space size can now be considered as routine for NEVPT2 calculations of strongly correlated molecular systems within this improved stochastic methodology.
We present a detailed discussion of our novel diagrammatic coupled cluster Monte Carlo (diagCCMC) [Scott et al. J. Phys. Chem. Lett. 2019, 10, 925]. The diagCCMC algorithm performs an imaginary-time propagation of the similarity-transformed coupled cluster Schrodinger equation. Imaginary-time updates are computed by stochastic sampling of the coupled cluster vector function: each term is evaluated as a randomly realised diagram in the connected expansion of the similarity-transformed Hamiltonian. We highlight similarities and differences between deterministic and stochastic linked coupled cluster theory when the latter is re-expressed as a sampling of the diagrammatic expansion, and discuss details of our implementation that allow for a walker-less realisation of the stochastic sampling. Finally, we demonstrate that in the presence of locality, our algorithm can obtain a fixed errorbar per electron while only requiring an asymptotic computational effort that scales quartically with system size, independently of truncation level in coupled cluster theory. The algorithm only requires an asymptotic memory costs scaling linearly, as demonstrated previously. These scaling reductions require no ad hoc modifications to the approach.
A variant of coupled-cluster theory is described here, wherein the degrees of freedom are fluctuations of fragments between internally correlated states. The effects of intra-fragment correlation on the inter-fragment interaction are pre-computed and permanently folded into an effective Hamiltonian, thus avoiding redundant evaluations of local relaxations associated with coupled fluctuations. A companion article shows that a low-scaling step may be used to cast the electronic Hamiltonians of real systems into the form required. Two proof-of-principle demonstrations are presented here for non-covalent interactions. One uses harmonic oscillators, for which accuracy and algorithm structure can be carefully controlled in comparisons. The other uses small electronic systems (Be atoms) to demonstrate compelling accuracy and efficiency, also when inter-fragment electron exchange and charge transfer must be handled. Since the cost of the global calculation does not depend directly on the correlation models used for the fragments, this should provide a way to incorporate difficult electronic structure problems into large systems. This framework opens a promising path for building tunable, systematically improvable methods to capture properties of systems interacting with a large number of other systems. The extension to excited states is also straightforward.
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.
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