The results demonstrate that this approach leads to lower ground state energies and more accurate dipole moments than other fully automated selection schemes such as those based solely on single-orbital entropy or the selection of spatial orbitals around the HOMO/LUMO gap.
Abstract
The quality of multi-scale modelling techniques in molecular electronic structure calculations, such as embedding and subspace methods, relies upon the chosen active space. The automation of active space selection is vital for ensuring the accuracy, reproducibility, and scalability in such calculations. In this work, we introduce Tensor Network Active Space Selection using the Entanglement Feature. Through the isolation of strongly correlated electrons, this method provides a scalable foundation for embedding methods in multi-scale modelling. By representing the purities of all possible orbital partitions as a Matrix Product State, our method isolates regions of strong electron correlation without requiring manual preselection of target atoms or the calculation of expensive high-order density matrices. The results demonstrate that this approach leads to lower ground state energies and more accurate dipole moments than other fully automated selection schemes such as those based solely on single-orbital entropy or the selection of spatial orbitals around the HOMO/LUMO gap.
The Virtual Quantum Subspace Expansion (VQSE) extends the Variational Quantum Eigensolver (VQE) by leveraging additional measurements on the reference state to capture the influence of excluded virtual orbitals. This makes VQSE attractive for chemical applications where accurate energy differences along potential energy surfaces are crucial for modeling reaction rates and kinetics. In this work, we analyze VQSE performance on H$_2$ dissociation including references that use Hartree--Fock molecular orbitals with broken spin symmetry. We identify two mechanisms which affect accuracy: overlap of the reference state with the exact full configuration interaction (FCI) wavefunction and operator pool expressivity. We show these mechanisms are strongly co-dependent. When operators are restricted to act only from the active to the virtual space, results become highly sensitive to the reference, and enlarging the active space does not guarantee improved accuracy. In this case, prioritizing reference overlap over energy minimization is therefore essential. Adding single excitations and number operators within the active space recovers the accuracy of MR-CISD (multi-reference configuration interaction singles and doubles) regardless of the reference. In our noisy hardware experiments, we achieve chemical accuracy by adding additional operators and using strict regularization. These findings motivate careful co-design of reference fidelity, pool expressivity, and hardware constraints for practical VQSE deployment.
Konstantin Lamp, Alejandro D. Somoza, Elias Walter et al.· 0 citations
Machine learning interatomic potentials (MLIPs) have become emerging tools in molecular modeling and computational chemistry. By learning high-dimensional potential energy surfaces from quantum chemical data, MLIPs enable accurate and efficient predictions of structural, thermodynamic, and dynamical properties. However, such models have limitations in predictions of electronic properties and the effects of static electron correlation due to their lack of electronic structure information. This work presents OrbGNN, an electronic structure graph architecture analogous to molecular graph and MLIP frameworks, where pair-orbital interactions constitute the graph representation, while orbital entanglement encodes the connectivity between them. By embedding information derived from orbital correlation metrics directly into the graph topology, OrbGNN provides a compact representation of a molecule s orbital landscape and electron correlation patterns. Analysis of the behavior of the feature space in an orbital graph are shown to demonstrate model robustness. The model is evaluated for the dissociation of nitrogen and for a larger dataset of diatomic molecules. Finally, the OrbGNN model is applied to a set of octahedral iron(II) complexes to predict spin-state energy gaps.
Brody Quebedeaux, Shahzad Akram, Markus Reiher et al.· 0 citations
Density matrix embedding theory (DMET) provides an elegant framework in quantum chemistry to describe local properties of chemical systems that allows a high-level method being used to solve an embedded subsystem constructed based on a low-level treatment of the whole system, and therefore achieves a balance between efficiency and accuracy. However, because the embedded subspace in DMET is typically constructed from the mean-field ground state Slater determinant, the resulting bath orbitals inherently favor the ground state, leading to unbalanced descriptions of ground and excited states for local excitations. In this work, we first demonstrate the starting-point dependence of DMET in excitation energy calculations, and then generalize original ground-state based DMET by extending the starting point from the single Slater determinant to state-averaged (SA) complete active space self-consistent field (CASSCF), hence termed as SA-DMDT. In calculations of magnetic anisotropy and excitation energies of transition metal and lanthanide complexes, SA-DMET shows significant improvement in accuracy compared to the single-state DMET. Configuration-averaged Hartree-Fock (CAHF), which is equivalent to SA-CASSCF when all states in the chosen active space are equally averaged, is found to give comparable accuracy as a DMET starting point, thus offering a more efficient choice for state-averaged embedding. Finally, the recently proposed non-orthongal atomic-orbital-based DMET (AO-DMET) is tested on various systems and gives very promising results in all cases. These results establish SA-DMET, especially in combination with AO-DMET and CAHF, as a robust and efficient embedding framework for local excited states in strongly correlated metal complexes.
Finding a low-rank approximation for the two-electron integral (ERI) tensor is a crucial step towards reducing the computational cost of many-body electronic structure methods. In recent years, a range of new tensor factorization techniques, like the so-called tensor-hypercontraction (THC) approach, have been developed to achieve this goal. Unfortunately, a systematic comparison of accuracy and efficiency of different THC construction algorithms is missing. In this work, we address this gap by benchmarking these techniques across a wide range of molecular systems. In addition to offering useful insights into the advantages and disadvantages of the different techniques, we provide reference implementations in the newly developed open-source library, PyTHC.
Multireference calculations are well-suited for describing properties of highly correlated systems. In order to realize the full potential of multireference methods, it is necessary to judiciously choose the active space. It is possible to do this manually, but an automatic procedure for selecting the active space can benefit high-throughput applications and is not susceptible to human error. We previously developed two protocols, GDM-AS and EDM-AS, where the dipole moment calculated at the complete active space self-consistent field (CASSCF) level of theory is used to select the active space, and demonstrated the effectiveness of these protocols when the chosen active spaces are used to find low-lying excitation energies for molecules with nonzero dipole moments. In this work, we demonstrate that using complete active space configuration interaction (CASCI) dipole moments, with the orbitals from the second-order Møller–Plesset perturbation theory, instead of CASSCF dipole moments in our dipole moment active space selection (DM-AS) protocols can significantly improve the efficiency of active space selection compared to our previous methods while maintaining reasonable complete active space second-order perturbation theory (CASPT2) and complete active space pair-density functional theory (CAS-PDFT) vertical excitation energy. We also present new protocols, CASCI-D2DM-AS and its directional version, designed for charge transfer states. We discuss the performance of our new protocols in their ability to describe excitation energy of not only small organic molecules tested in our previous work, but also larger conjugated polar molecules, nonpolar molecules, and bimolecular complexes, to describe the ground-state spin state of transition metal oxides, and to describe bond dissociation curves of small molecules.
Benjamin W Kaufold, Sijia S. Dong· Journal of Chemical Theory a...· 0 citations
The EWF-(FCI,SQD) method, a wave-function-based embedding approach combining full configuration interaction (FCI) and sample-based quantum diagonalization (SQD), is a promising new tool for the simulation of molecular systems. However, applications of EWF-(FCI,SQD) have so far been limited to single-point calculations, whereas the study of complex chemical processes requires the ability to explore potential energy surfaces. In this work, we demonstrate geometry optimization with EWF-(FCI,SQD), scaling our simulations to molecules as large as menthone and benzidine within the STO-3G basis set. Without fragmentation, these systems comprise 73 and 82 molecular orbitals respectively, presenting an intractable Hilbert space for conventional exact or high-level subspace solvers and establishing a clear necessity for fragmentation-based methodologies. The underlying fragment SQD simulations in the EWF-(FCI,SQD) geometry optimizations use up to 70 qubits. The resulting geometries show exceptional accuracy relative to the classical reference, with deviations below 4 picometers.
Danil S. Kaliakin, Akhil Shajan, Fangchun Liang et al.· 0 citations
