6 Search Results

Entanglement plays a central role in quantum technologies, yet its characterization and control in materials remain challenging. Recent developments in spectrum-based entanglement witnesses have enabled new strategies for quantifying many-body entanglement in macroscopic materials. Here, in this work, we develop a protocol for detecting spin-orbital entanglement using experiment-accessible resonant inelastic x-ray scattering. Central to our approach is the construction of a Hermitian generator from measurable spectra, which allows us to compute the quantum Fisher information (QFI) available in spin-orbital systems. The resulting QFI provides upper bounds for 𝑘-producible states and thus serves as a robust witness of spin-orbital entanglement. Tomore » account for realistic experimental limitations, we further extend our framework to include relaxed QFI bounds applicable to measurements lacking full polarization resolution.« less

We present a formulation and implementation of an equation-of-motion (EOM) extension of the multireference driven similarity renormalization group (MR-DSRG) formalism for ionization potentials (IP-EOM-DSRG). The IP-EOM-DSRG formalism results in a Hermitian generalized eigenvalue problem, delivering accurate ionization potentials for strongly correlated systems. The EOM step scales as O(N⁵) with the basis set size N, allowing for efficient calculation of spectroscopic properties, such as transition energies and intensities. The IP-EOM-DSRG formalism is combined with three truncation schemes of the parent MR-DSRG theory: an iterative nonperturbative method with up to two-body excitations [MR-LDSRG(2)] and second- and third-order perturbative approximations [DSRG-MRPT2/3]. We benchmarkmore » these variants by computing (1) the vertical valence ionization potentials of a series of small molecules at both equilibrium and stretched geometries; (2) the spectroscopic constants of several low-lying electronic states of the OH, CN, N₂⁺, and CO⁺ radicals; and (3) the binding curves of low-lying electronic states of the CN radical. A comparison with experimental data and theoretical results shows that all three IP-EOM-DSRG methods accurately reproduce the vertical ionization potentials and spectroscopic constants of these systems. Notably, the DSRG-MRPT3 and MR-LDSRG(2) versions outperform several state-of-the-art multireference methods of comparable or higher cost.« less

The accurate computation of excited states remains a challenge in electronic structure theory, especially for systems with a ground state that requires a multireference treatment. In this work, we introduce a novel equation-of-motion (EOM) extension of the internally contracted multireference unitary coupled-cluster framework (ic-MRUCC), termed EOM-ic-MRUCC. EOM-ic-MRUCC follows the transform-then-diagonalize approach, in analogy to its non-unitary counterpart. By employing a projective approach to optimize the ground state, the method retains additive separability and proper scaling with system size. We show that excitation energies are size-intensive if the EOM operator satisfies the “killer” and the projective conditions. Furthermore, we propose tomore » represent changes in the reference state upon electron excitation via projected many-body operators that span the active orbitals and show that the EOM equations formulated in this way are invariant with respect to active orbital rotations. We test the EOM-ic-MRUCC method truncated to single and double excitations by computing the potential energy curves for several excited states of a BeH2 model system, the HF molecule, and water undergoing symmetric dissociation. Across these systems, our method delivers accurate excitation energies and potential energy curves within 5 mE_h (∼0.14 eV) from full configuration interaction. Here, we find that truncating the Baker–Campbell–Hausdorff series to fourfold commutators contributes negligible errors (on the order of 10⁻⁵ E_h or less), offering a practical route to highly accurate excited-state calculations with reduced computational overhead.« less

Software development plays a critical role in advancing quantum chemistry, enabling the exploration of new fundamental theoretical ideas and modeling systems of ever-increasing complexity. In the past decade, the availability of quantum chemistry packages that use modular designs and provide application programming interfaces (APIs) has enabled the creation of specialized software plugins, enhancing the capabilities of the original codes. Here, the availability of well-documented APIs is particularly beneficial in the context of academic scientific software development because it reduces the entry barrier for new developers and shields them from the complexities of large software projects.

Most nonrelativistic electron correlation methods can be adapted to account for relativistic effects, as long as the relativistic molecular spinor integrals are available, from either a four-, two-, or one-component mean-field calculation. Furthermore, relativistic multireference correlation methods remain a relatively unexplored area, with mixed evidence regarding the improvements brought by perturbative treatments. We report, for the first time, the implementation of state-averaged four-component relativistic multireference perturbation theories to second and third order based on the driven similarity renormalization group (DSRG). With our methods, named 4c-SA-DSRG-MRPT2 and 3, we find that the dynamical correlation included on top of 4c-CASSCF references canmore » significantly improve the spin-orbit splittings in p-block elements and potential energy surfaces when compared to 4c-CASSCF and 4c-CASPT2 results. We further show that 4c-DSRG-MRPT2 and 3 are applicable to these systems over a wide range of the flow parameter, with systematic improvement from second to third order in terms of both improved error statistics and reduced sensitivity with respect to the flow parameter.« less

The multireference coupled-cluster Monte Carlo (MR-CCMC) algorithm is a determinant-based quantum Monte Carlo (QMC) algorithm that is conceptually similar to Full Configuration Interaction QMC (FCIQMC). It has been shown to offer a balanced treatment of both static and dynamic correlation while retaining polynomial scaling, although application to large systems with significant strong correlation remained impractical. In this paper, we document recent algorithmic advances that enable rapid convergence and a more black-box approach to the multireference problem. These include a logarithmically scaling metric-tree-based excitation acceptance algorithm to search for determinants connected to the reference space at the desired excitation level andmore » a symmetry-screening procedure for the reference space. We show that, for moderately sized reference spaces, the new search algorithm brings about an approximately 8-fold acceleration of one MR-CCMC iteration, while the symmetry screening procedure reduces the number of active reference space determinants with essentially no loss of accuracy. We also introduce a stochastic implementation of an approximate wall projector, which is the infinite imaginary time limit of the exponential projector, using a truncated expansion of the wall function in Chebyshev polynomials. Notably, this wall-Chebyshev projector can be used to accelerate any projector-based QMC algorithm. We show that it requires significantly fewer applications of the Hamiltonian to achieve the same statistical convergence. We benchmark these acceleration methods on the beryllium and carbon dimers, using initiator FCIQMC and MR-CCMC with basis sets up to cc-pVQZ quality.« less