arXiv subjects

Anthony D. Dutoi

Publications and source records attributed to Anthony D. Dutoi.

5 recordsLinked to original sources

arXiv2025

Optimization of Fragment State Spaces within the Excitonic Renormalization Framework

The recently proposed excitonic renormalization framework presents an alternative ansatz to elec- tronic structure theory of weakly interacting fragments. It makes use of absolutely localized orbitals and correlated states evaluated on isolated fragments, which are then used to recover the interaction in an ab-initio manner based on a biorthogonal framework. The correlated monomer information can be heavily truncated, and the Hamiltonian can be expanded in a rapidly converging series, allow- ing the Hamiltonian to be built and diagonalized in a scalable fashion. However, the methodology still lacks an efficient bottom-up procedure, capable of producing optimized model state spaces for the isolated fragments, without ever building the Hamiltonian in the full monomer state spaces. In order to address this issue, this work presents an algorithm utilizing monomer gradients at three different levels as well as an efficient pre-screening of the determinant space, ensuring compact model state spaces and intermediates. Numerical results are presented for the beryllium dimer, showing that the algorithm is indeed capable of building compact model state spaces, yielding results that closely resemble those of the optimal model state spaces. Furthermore, it is shown that model state spaces, optimized at the zeroth order of the Hamiltonian expansion, can also be used to accurately recover first order results, enabling very efficient optimization, as the optimization can be conducted at a lower order than the targeted final level. Hence, the presented solver completes the excitonic renormalization methodology, forming a polynomially scaling framework.

physics.chem-ph↗

arXiv2024

Series Expansion of a Scalable Hermitian Excitonic Renormalization Method

Utilizing the sparsity of the electronic structure problem, fragmentation methods have been researched for decades with great success, pushing the limits of ab initio quantum chemistry ever further. Recently, this set of methods was expanded to include a fundamentally different approach called excitonic renormalization, providing promising initial results. It builds a supersystem Hamiltonian in a second-quantized-like representation from transition-density tensors of isolated fragments, contracted with biorthogonalized molecular integrals. This makes the method fully modular in terms of the quantum chemical methods applied to each fragment and enables massive truncation of the state-space required. Proof-of-principle tests have previously shown that an excitonically renormalized Hamiltonian can efficiently scale to hundreds of fragments, but the ad hoc approach to building the Hamiltonian was not scalable to larger fragments. On the other hand, initial tests of the originally proposed modular Hamiltonian build, presented here, have shown the accuracy to be poor on account of its non-Hermitian character. In this study, we bridge the gap between these with an operator expansion that is shown to converge rapidly, tending towards a Hermitian Hamiltonian while retaining the modularity, yielding an accurate, scalable method. The accuracy is tested here for a beryllium dimer. At distances near equilibrium and longer, the zeroth-order method is comparable to CCSD(T), and the first-order method to FCI. The second-order method agrees with FCI for distances well up the inner repulsive wall of the potential. Deviations occurring at shorter bond distances are discussed along with approaches to scaling to larger fragments.

physics.chem-ph↗

arXiv2018

Systematically Improvable Excitonic Hamiltonians for Electronic Structure Theory

We show here that the Hamiltonian for an electronic system may be written exactly in terms of fluctuation operators that transition constituent fragments between internally correlated states, accounting rigorously for inter-fragment electron exchange and charge transfer. Familiar electronic structure approaches can be applied to the renormalized Hamiltonian. For efficiency, the basis for each fragment can be truncated, removing high-energy local arrangements of electrons from consideration, and effectively defining collective coordinates for the fragments. For a large number of problems (especially for non-covalently interacting fragments), this has the potential to fold the majority of electron correlation into the effective Hamiltonian, and it should provide a robust approach to incorporating difficult electronic structure problems into large systems. The number of terms in the exactly transformed Hamiltonian formally scales quartically with system size, but this can be reduced to quadratic in the mesoscopic regime, to within an arbitrary error tolerance. Finally, all but a linear-scaling number of these terms may be efficiently decomposed in terms of electrostatic interactions between a linear-scaling number of pre-computed transition densities. In a companion article, this formalism is applied to an excitonic variant of coupled-cluster theory.

physics.chem-ph↗

arXiv2018

Excitonic Coupled-cluster Theory

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.

physics.chem-ph↗

arXiv2006

Simulated Quantum Computation of Molecular Energies

The calculation time for the energy of atoms and molecules scales exponentially with system size on a classical computer but polynomially using quantum algorithms. We demonstrate that such algorithms can be applied to problems of chemical interest using modest numbers of quantum bits. Calculations of the water and lithium hydride molecular ground-state energies have been carried out on a quantum computer simulator using a recursive phase-estimation algorithm. The recursive algorithm reduces the number of quantum bits required for the readout register from about 20 to 4. Mappings of the molecular wave function to the quantum bits are described. An adiabatic method for the preparation of a good approximate ground-state wave function is described and demonstrated for a stretched hydrogen molecule. The number of quantum bits required scales linearly with the number of basis functions, and the number of gates required grows polynomially with the number of quantum bits.

quant-ph↗