Linear-Scaling Implementation of Multilevel Hartree-Fock Theory

Toward Real Chemical Accuracy on Current Quantum Hardware Through the Transcorrelated Method

Quantum computing is emerging as a new computational paradigm with the potential to transform several research fields including quantum chemistry. However, current hardware limitations (including limited coherence times, gate infidelities, and connectivity) hamper the implementation of most quantum algorithms and call for more noise-resilient solutions. We propose an explicitly correlated Ansatz based on the transcorrelated (TC) approach to target these major roadblocks directly. This method transfers, without any approximation, correlations from the wave function directly into the Hamiltonian, thus reducing the resources needed to achieve accurate results with noisy quantum devices. We show that the TC approach allows for shallower circuits and improves the convergence toward the complete basis set limit, providing energies within chemical accuracy to experiment with smaller basis sets and, thus, fewer qubits. We demonstrate our method by computing bond lengths, dissociation energies, and vibrational frequencies close to experimental results for the hydrogen dimer and lithium hydride using two and four qubits, respectively. To demonstrate our approach's current and near-term potential, we perform hardware experiments, where our results confirm that the TC method paves the way toward accurate quantum chemistry calculations already on today's quantum hardware.

Time-Dependent Multilevel Density Functional Theory

We present a novel three-layer approach based on multilevel density functional theory (MLDFT) and polarizable molecular mechanics to simulate the electronic excitations of chemical systems embedded in an external environment within the time-dependent DFT formalism. In our method, the electronic structure of a target system, the chromophore, is determined in the field of an embedded inactive layer, which is treated as frozen. Long-range interactions are described by employing the polarizable fluctuating charge (FQ) force field. The resulting MLDFT/FQ thus accurately describes both electrostatics (and polarization) and non-electrostatic target-environment interactions. The robustness and reliability of the approach are demonstrated by comparing our results with experimental data reported for various organic molecules in solution.

Machine-learning assisted scheduling optimization and its application in quantum chemical calculations

Easy and effective usage of computational resources is crucial for scientific calculations, both from the perspectives of timeliness and economic efficiency. This work proposes a bi-level optimization framework to optimize the computational sequences. Machine-learning (ML) assisted static load-balancing, and different dynamic load-balancing algorithms can be integrated. Consequently, the computational and scheduling engine of the ParaEngine is developed to invoke optimized quantum chemical (QC) calculations. Illustrated benchmark calculations include high-throughput drug suit, solvent model, P38 protein, and SARS-CoV-2 systems. The results show that the usage rate of given computational resources for high throughput and large-scale fragmentation QC calculations can primarily profit, and faster accomplishing computational tasks can be expected when employing high-performance computing (HPC) clusters.

Integrated Multiscale Multilevel Approach to Open Shell Molecular Systems

We present a novel multiscale approach to study the electronic structure of open shell molecular systems embedded in an external environment. The method is based on the coupling of multilevel Hartree-Fock (MLHF) and Density Functional Theory (MLDFT), suitably extended to the unrestricted formalism, to Molecular Mechanics (MM) force fields (FF). Within the ML region, the system is divided into active and inactive parts, thus describing the most relevant interactions (electrostatic, polarization, and Pauli repulsion) at the quantum level. The surrounding MM part, which is formulated in terms of nonpolarizable or polarizable FFs, permits a physically consistent treatment of long-range electrostatics and polarization effects. The approach is extended to the calculation of hyperfine coupling constants and applied to selected nitroxyl radicals in an aqueous solution.

Fragment Localized Molecular Orbitals

We introduce the concept of fragment localized molecular orbitals (FLMOs), which are Hartree-Fock molecular orbitals localized in specific fragments constituting a molecular system. In physical terms, we minimize the local electronic energies of the different fragments, at the cost of maximizing the repulsion between them. To showcase the approach, we rationalize the main interactions occurring in large biological systems in terms of interactions between the fragments of the system. In particular, we study an anticancer drug intercalated within DNA and retinal in anabaena sensory rhodopsin as prototypes of molecular systems embedded in biological matrixes. Finally, the FLMOs are exploited to rationalize the formation of two oligomers, prototypes of amyloid diseases, such as Parkinson and Alzheimer.

Linear-Scaling Implementation of Multilevel Hartree-Fock Theory

We introduce a new algorithm for the construction of the two-electron contributions to the Fock matrix in multilevel Hartree-Fock (MLHF) theory. In MLHF, the density of an active molecular region is optimized, while the density of an inactive region is fixed. The MLHF equations are solved in a reduced molecular orbital (MO) basis localized to the active region. The locality of the MOs can be exploited to reduce the computational cost of the Fock matrix: the cost related to the inactive density becomes linear scaling, while the iterative cost related to the active density is independent of the system size. We demonstrate the performance of this new algorithm on a variety of systems, including amino acid chains, water clusters, and solvated systems.