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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Low-Lying Excited States of Linear All- Trans Polyenes: Insights from Analytic Gradient and Nonadiabatic Coupling Calculations Based on Multireference Configuration Interaction

Polyenes serve as a rigorous test for theoretical models and electronic structure methods, playing a key role in advancing computational and theoretical chemistry. Here, we present a high-level theoretical investigation of linear, all-trans polyenes using energy gradients and nonadiabatic coupling vectors based on an MR-CISD wave function to describe electronic transitions involving the ground state (1 1 A g – ) and three low-lying excited states (2 1 A g – , 1 1 B u + , and 2 1 B u – ) of hexatriene, octatetraene, and decapentaene. This approach enables accurate evaluation of both adiabatic and vertical excitation and emission energies, yielding results in excellent agreement with experiment, as well as locating minima on the crossing seam between adiabatic states. Our results show that vertical excitation energies to the 1 1 B u + state are blue-shifted by 0.2–0.3 eV relative to the experimental absorption maximum, whereas the vertical emission energy from the 2 1 A g – state is red-shifted by ∼0.2 eV relative to the experimental emission maximum. Upon relaxation from the Franck–Condon geometry, the 2 1 A g – state stabilizes by around 1 eV, compared to 0.2–0.3 eV for the 1 1 B u + state. An analysis of the S 1 /S 0 crossing seam in hexatriene shows that its minimum involves asymmetric backbone deformations and provides an efficient channel for ultrafast internal conversion to the ground state, consistent with the absence of detectable fluorescence in this molecule. These results demonstrate the power of analytic gradients and nonadiabatic coupling vectors based on an MR-CISD wave function for accurately characterizing the electronic structure and photophysics of polyenes.

Excited states↗
DOE OSTI2021

CAS without SCF—Why to use CASCI and where to get the orbitals

The complete active space self-consistent field (CASSCF) method has seen broad adoption due to its ability to describe the electronic structure of both the ground and excited states of molecules over a broader swath of the potential energy surface than is possible with the simpler Hartree–Fock approximation. However, it also has a reputation for being unwieldy, computationally costly, and un-black-box. Here, we discuss a class of alternatives, complete active space configuration interaction (CASCI) methods, paying particular attention to their application to electronic excited states. The goal of this Perspective is fourfold. First, we argue that CASCI is not merely an approximation to CASSCF, in that it can be designed to have important qualitative advantages over CASSCF. Second, we present several insights drawn from our experience experimenting with different schemes for computing orbitals to be employed in CASCI. Third, we argue that CASCI is well suited for application to nanomaterials. Lastly, we reason that, with the rise in new low-scaling approaches for describing multireference systems, there is a greater need than ever to develop new methods for defining orbitals that provide an efficient and accurate description of both static correlation and electronic excitations in a limited active space.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

State Preparation in Quantum Algorithms for Fragment-Based Quantum Chemistry

State preparation for quantum algorithms is crucial for achieving high accuracy in quantum chemistry and competing with classical algorithms. The localized active space–unitary coupled cluster (LAS–UCC) algorithm iteratively loads a fragment-based multireference wave function onto a quantum computer. Here, in this study, we compare two state preparation methods, quantum phase estimation (QPE) and direct initialization (DI), for each fragment. We test the two state preparation methods on three systems, ranging from a model system, a set of interacting hydrogen molecules, to more realistic chemical problems, like the C–C double bond breaking in transbutadiene and the spin ladder in a bimetallic system. We analyze the impact of QPE parameters, such as the number of ancilla qubits and Trotter steps, on the prepared state. We find a trade-off between the methods, where DI requires fewer resources for smaller fragments, while QPE is more efficient for larger fragments. Our resource estimates highlight the benefits of system fragmentation in state preparation for subsequent quantum chemical calculations. These findings have broad applications for preparing multireference quantum chemical wave functions on quantum circuits that can be used for realistic chemical applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Improving Bond Dissociations of Reactive Machine Learning Potentials through Physics-Constrained Data Augmentation

In the field of computational chemistry, predicting bond dissociation energies (BDEs) presents well-known challenges, particularly due to the multireference character of reactive systems. Many chemical reactions involve configurations where single-reference methods fall short, as the electronic structure can significantly change during bond breaking. As generating training data for partially broken bonds is a challenging task, even state-of-the-art reactive machine learning interatomic potentials (MLIPs) often fail to predict reliable BDEs and smooth dissociation curves. By contrast, simple and inexpensive physics-based models, such as the well-established Morse potential, do not suffer from any such limitations. This work leverages the Morse potential to improve reactive MLIPs by augmenting the training data set with inexpensive Morse data along the dissociation pathways. Further, this physics-constrained data augmentation (PCDA) approach results in MLIPs with smooth bond dissociation curves as well as near coupled-cluster level BDEs, all without requiring any expensive multireference quantum mechanical calculations. A case study for methane combustion demonstrates how the PCDA approach can improve an existing reactive MLIP, namely, ANI-1xnr. In conclusion, not only are the BDEs and bond dissociation curves for all radicals and molecules significantly improved compared to ANI-1xnr but the PCDA-trained MLIP retains the reliability of ANI-1xnr when performing reactive molecular dynamics simulations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Polishing the Gold Standard: The Role of Orbital Choice in CCSD(T) Vibrational Frequency Prediction

While CCSD(T) with spin-restricted Hartree-Fock (RHF) orbitals has long been lauded for its ability to accurately describe closed-shell interactions, the performance of CCSD(T) on open-shell species is much more erratic, especially when using a spin-unrestricted HF (UHF) reference. Previous studies have shown improved treatment of open-shell systems when a non-HF set of molecular orbitals, like Brueckner or Kohn-Sham density functional theory (DFT) orbitals, is used as a reference. Inspired by the success of regularized orbital-optimized second-order Møller-Plesset perturbation theory (κ-OOMP2) orbitals as reference orbitals for MP3, we investigate the use of κ-OOMP2 orbitals and various DFT orbitals as reference orbitals for CCSD(T) calculations of the corrected ground-state harmonic vibrational frequencies of a set of 36 closed-shell (29 neutrals, 6 cations, 1 anion) and 59 open-shell diatomic species (38 neutrals, 15 cations, 6 anions). The aug-cc-pwCVTZ basis set is used for all calculations. The use of κ-OOMP2 orbitals in this context alleviates difficult cases observed for both UHF orbitals and OOMP2 orbitals. Removing two multireference systems and 12 systems with ambiguous experimental data leaves a pruned data set. Overall performance on the pruned data set highlights CCSD(T) with a B97 orbital reference (CCSD(T):B97), CCSD(T) with a κ-OOMP2 orbital reference (CCSD(T):κ-OOMP2), and CCSD(T) with a B97M-rV orbital reference (CCSD(T):B97M-rV) with RMSDs of 8.48 cm -1 , and 8.50 cm -1 , and 8.75 cm -1 respectively, outperforming CCSD(T):UHF by nearly a factor of 5. Moreover, the performance on the closed- and open-shell subsets shows these methods are able to treat open-shell and closed-shell systems with comparable accuracy and robustness. CCSD(T) with RHF orbitals is seen to improve upon UHF for the closed-shell species, while spatial symmetry breaking in a number of restricted open-shell HF (ROHF) references leads CCSD(T) with ROHF reference orbitals to exhibit the poorest statistical performance of all methods surveyed for open-shell species. The use of κ-OOMP2 orbitals has also proven useful in diagnosing multireference character that can hinder the reliability of CCSD(T).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Dipole Moment Calculations Using Multiconfiguration Pair-Density Functional Theory and Hybrid Multiconfiguration Pair-Density Functional Theory

The dipole moment is the molecular property that most directly indicates molecular polarity. The accuracy of computed dipole moments depends strongly on the quality of the calculated electron density, and the breakdown of single-reference methods for strongly correlated systems can lead to poor predictions of the dipole moments in those cases. Here, we derive the analytical expression for obtaining the electric dipole moment by multiconfiguration pair density functional theory (MCPDFT), and we assess the accuracy of MC-PDFT for predicting dipole moments at equilibrium and nonequilibrium geometries. We show that MC-PDFT dipole moment curves have reasonable behavior even for stretched geometries, and they significantly improve upon the CASSCF results by capturing more electron correlation. Herein, the analysis of a dataset consisting of 18 first-row transition metal diatomics and 6 main-group polyatomic molecules with multireference character suggests that MC-PDFT and its hybrid extension (HMC-PDFT) perform comparably to CASPT2 and MRCISD+Q methods and have a mean unsigned deviation of 0.2–0.3 D with respect to the best available dipole moment reference values. We explored the dependence of the predicted dipole moments upon the choice of the on-top density functional and active space, and we recommend the tPBE and hybrid tPBE0 on-top choices for the functionals combined with the moderate correlated participating orbital scheme for selecting the active space. With these choices, the mean unsigned deviations (in debyes) of the calculated equilibrium dipole moments from the best estimates are 0.77 for CASSCF, 0.29 for MC-PDFT, 0.24 for HMCPDFT, 0.28 for CASPT2, and 0.25 for MRCISD+Q. These results are encouraging because the computational cost of MC-PDFT or HMC-PDFT is largely reduced compared to the CASPT2 and MRCISD+Q methods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Semi-supervised Machine Learning Enables the Robust Detection of Multireference Character at Low Cost

Multireference (MR) diagnostics are common tools for identifying strongly correlated electronic structure that makes single-reference (SR) methods (e.g., density functional theory or DFT) insufficient for accurate property prediction. However, MR diagnostics typically require computationally demanding correlated wave function theory (WFT) calculations, and diagnostics often disagree or fail to predict MR effects on properties. To overcome these challenges, we introduce a semi-supervised machine learning (ML) approach with virtual adversarial training (VAT) of an MR classifier using 15 WFT and DFT MR diagnostics as inputs. In semi-supervised learning, only the most extreme SR or MR points are labeled, and the remaining point labels are learned. The resulting VAT model outperforms the alternatives, as quantified by the distinct property distributions of SR- and MR-classified molecules. Additionally, to reduce the cost of generating inputs to the VAT model, we leverage the VAT model’s robustness to noisy inputs by replacing WFT MR diagnostics with regression predictions in an MR decision engine workflow that preserves excellent performance. We demonstrate the transferability of our approach to larger molecules and those with distinct chemical composition from the training set. This MR decision engine demonstrates promise as a low-cost, high-accuracy approach to the automatic detection of strong correlation for predictive high-throughput screening.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Electronic properties of ThC − and ThC

The present study investigates the properties of low-lying states of ThC − and ThC using correlated wave function theories. To this end, we employed multireference calculations and various coupled-cluster approaches in combination with large correlation-consistent basis sets. These methods were applied to examine potential energy curves (PECs), electron configurations, energetics, spectroscopic constants, and spin–orbit coupling effects for 9 states of ThC − and 18 states of ThC. The ground states of ThC − and ThC were identified as single-reference 2 Σ + 1/2 (I) and $^3Σ^+_{0^-} (\textrm{I})$, respectively. Electron detachment from the 7s orbital of the Th center in ThC − [ 2 Σ + (I); 1σ 2 2σ1 3 σ2 1 π 4 ] yields ThC [ 3 Σ + (I); 1σ 2 2σ 1 3σ 1 1π 4 ]. The calculated adiabatic detachment energy (ADE) and vertical detachment energy (VDE) for this process are 1.591 and 1.604 eV, respectively. Furthermore, the dissociation energy (D 0 ) of ThC [$^3Σ^+_{0^-} (\textrm{I})$] is predicted to be 5.099 eV. The standard enthalpy of formation, $ΔH^{°}_{\textrm{f}}$ (298 K), of ThC is estimated to be 822.52 ± 6 kJ mol −1 .

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2025

All-electron molecular tunnel ionization based on the weak-field asymptotic theory in the integral representation

Tunnel ionization (TI) underlies many important ultrafast processes, such as high-harmonic generation andstrong-field ionization. Among the existing theories for TI, many-electron weak-field asymptotic theory (ME-WFAT) is by design capable of accurately treating many-electron effects in TI. An earlier version of ME-WFATrelied on an accurate representation of the asymptotic tail of the orbitals, which hindered its implementation inGaussian-basis-set-based quantum chemistry programs. In this work, we reformulate ME-WFAT in the integralrepresentation, which makes the quality of the asymptotic tail much less critical, hence greatly facilitating itsimplementation in standard quantum chemistry packages. The integral reformulation introduced here is thereforemuch more robust when applied to molecules with arbitrary geometry. Here, we present several case studies, amongwhich is the CO molecule where some earlier theories disagree with experiments. Here we find that ME-WFATproduces the largest ionization probability when the field points from C to O, as experiments suggest. Anattractive feature of ME-WFAT is that it can be used with various types of multielectron methods whether ofdensity functional or multiconfiguration types, this inturn facilitates tunnel ionization calculation in systems exhibiting a strong multireference character.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2020

Benchmarking an Embedded Adaptive Sampling Configuration Interaction Method for Surface Reactions: H 2 Desorption from and CH 4 Dissociation on Cu(111)

Embedded (emb-) correlated wavefunction (CW) theory enables accurate assessments of both ground- and excited-state reaction mechanisms involved in heterogeneous catalysis. Embedded multireference second-order perturbation theory (emb-MRPT2) based on reference wavefunctions generated via embedded complete active space self-consistent field (emb-CASSCF) theory is currently state-of-the-art. However, the factorial scaling of CASSCF limits the size of active space and the complexity of systems that can be studied. In this work, we assess the efficacy of an alternative CW method, adaptive sampling configuration interaction (ASCI)–which enables large active spaces to be used–for studying surface reactions. We couple ASCI with density functional embedding theory (DFET) and benchmark its performance for two reactions: H 2 desorption from and CH 4 dissociation on the Cu(111) surface. Unlike embedded complete active space second-order perturbation theory (emb-CASPT2) that accurately reproduces a measured H 2 desorption barrier, embedded ASCI, using a very large active space (though one that still comprises a small portion of the full set of orbitals) fails to do so. Adding an extra correlation term from embedded Møller–Plesset second-order perturbation theory (emb-MP2) improves the desorption barrier and endothermicity predictions. Thus, the inaccuracy of embedded ASCI comes from the missing dynamic correlation from the many other electrons and orbitals not included in the active space. For CH 4 dissociation, again embedded ASCI overestimates the dissociation barrier compared to emb-CASPT2 predictions. Adding dynamic correlation from emb-MP2 helps correct the barrier. However, this composite approach suffers from double counting of correlation within embedded ASCI followed by emb-MP2 calculations. We therefore conclude that the state-of-the-art emb-MRPT2 based on reference wavefunctions generated via emb-CASSCF remains the method of choice for studying surface reactions. emb-ASCI is useful when large active spaces beyond the limit of emb-CASSCF are essential, such as to study complex surface reactions with significant multiconfigurational character (static correlation) but weak dynamic correlation.

08 HYDROGEN↗
DOE OSTI2024

Small tensor product distributed active space (STP-DAS) framework for relativistic and non-relativistic multiconfiguration calculations: Scaling from 10 9 on a laptop to 10 12 determinants on a supercomputer

Despite the power and flexibility of configuration interaction (CI) based methods in computational chemistry, their broader application is limited by an exponential increase in both computational and storage requirements, particularly due to the substantial memory needed for excitation lists that are crucial for scalable parallel computing. Here, the objective of this work is to develop a new CI framework, namely, the small tensor product distributed active space (STP-DAS) framework, aimed at drastically reducing memory demands for extensive CI calculations on individual workstations or laptops, while simultaneously enhancing scalability for extensive parallel computing. Moreover, the STP-DAS framework can support various CI-based techniques, such as complete active space (CAS), restricted active space, generalized active space, multireference CI, and multireference perturbation theory, applicable to both relativistic (two- and four-component) and non-relativistic theories, thus extending the utility of CI methods in computational research. We conducted benchmark studies on a supercomputer to evaluate the storage needs, parallel scalability, and communication downtime using a realistic exact-two-component CASCI (X2C-CASCI) approach, covering a range of determinants from 10 9 to 10 12 . Additionally, we performed large X2C-CASCI calculations on a single laptop and examined how the STP-DAS partitioning affects performance.

Complete-active space self-consistent field↗
DOE OSTI2025

Cartesian equivariant representations for learning and understanding molecular orbitals

Qualitative and quantitative orbital properties such as bonding/antibonding character, localization, and orbital energies are critical to how chemists understand reactivity, catalysis, and excited-state behavior. Despite this, representations of orbitals in deep learning models have been very underdeveloped relative to representations of molecular geometries and Hamiltonians. Here, we apply state-of-the-art equivariant deep learning architectures to the task of assigning global labels to orbitals, namely energies characterizations, given the molecular coefficients from Hartree–Fock or density functional theory. The architecture we have developed, the Cartesian Equivariant Orbital Network (CEONET), shows how molecular orbital coefficients are readily featurized as equivariant node features common to all graph-based machine-learned potentials. We find that CEONET performs well at predicting difficult quantitative labels such as the orbital energy and orbital entropy. Furthermore, we find that the CEONET representation provides an intuitive latent space for differentiating orbital character for the qualitative assignment of e.g. bonding or antibonding character. In addition to providing a useful representation for further integrating deep learning with electronic structure theory, we expect CEONET to be useful for automatizing and interpreting the results of advanced electronic structure methods such as complete active space self-consistent field theory. In particular, the ability of CEONET to infer multireference character via the orbital entropy paves the way toward the machine-learned selection of active spaces.

chemical reactions↗
DOE OSTI2024

ELECTRONIC STRUCTURE METHODS AND PROTOCOLS WITH APPLICATION TO DYNAMICS, KINETICS AND THERMOCHEMISTRY

Hydrocarbon combustion involves the reaction dynamics of a tremendous number of species beginning with many-component fuel mixtures and proceeding via a complex system of intermediates to form primary and secondary products. Combustion conditions corresponding to new advanced engines and/or alternative fuels rely increasingly on autoignition and low-temperature-combustion chemistry. In these regimes various transient radical species such as HO2, ROO·, ·QOOH, HCO, NO2, HOCO, and Criegee intermediates play important roles in determining the detailed as well as more general dynamics. A clear understanding and accurate representation of these processes is needed for effective modeling. Given the difficulties associated with making reliable experimental measurements of these systems, computation can play an important role in developing these energy technologies. Accurate calculations have their own challenges since even within the simplest dynamical approximations such as transition state theory, the rates depend exponentially on critical barrier heights and these may be sensitive to the level of quantum chemistry. Moreover, it is well-known that in many cases it is necessary to go beyond statistical theories and consider the dynamics. Quantum tunneling, resonances, radiative transitions, and non-adiabatic effects governed by spin-orbit or derivative coupling can be determining factors in those dynamics. Building upon progress made during a period of prior support through the DOE Early Career Program, this project combines developments in the areas of potential energy surface (PES) fitting and multistate multireference quantum chemistry to allow spectroscopically and dynamically/kinetically accurate investigations of key molecular systems (such as those mentioned above), many of which are radicals with strong multireference character and have the possibility of multiple electronic states contributing to the observed dynamics. An ongoing area of investigation is to develop general strategies for robustly convergent electronic structure theory for global multichannel reactive surfaces including diabatization of energy and other relevant surfaces such as dipole transition. Combining advances in ab initio methods with automated interpolative PES fitting allows the construction of high-quality PESs (incorporating thousands of high-level data) to be done rapidly through parallel processing on high-performance computing (HPC) clusters. In addition, new methods and approaches to electronic structure theory will be developed and tested through applications. This project will explore limitations in traditional multireference calculations (e.g., MRCI) such as those imposed by internal contraction, lack of high-order correlation treatment and poor scaling. Methods such as DMRG-based extended active-space CASSCF and various Quantum Monte Carlo (QMC) methods will be applied (including VMC/DMC and FCIQMC). Insight into the relative significance of different orbital spaces and the robustness of application of these approaches on leadership class computing architectures will be gained. Synergy with other components of this research program such as automated PES fitting and multireference quantum chemistry will be used to address challenges encountered by the standard approaches to computational thermochemistry (those being single-reference quantum chemistry and perturbative treatments of the anharmonic vibrational energy, which break down for some cases of electronic structure or floppy strongly coupled vibrational modes).

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2021

A Multireference Approach to Electron and Electron–Nuclear Dynamics in Nanomaterials (Final Report)

Many important chemical and physical phenomena involve dynamics on large number of electronic states. Thus, there is a critical need to develop methods to simulate dynamics in dense manifolds of states. Towards this end, we have: a) developed the multiple cloning in dense manifolds of states (MCDMS) method, which is capable of accurately modeling the quantum mechanical coherence between populations on a large number of electronic states, b) implemented MCDMS into the free, open-source PySpawn software package, c) developed graphics processing unit-accelerated algorithms modeling electron dynamics in light fields via Floquet time-dependent configuration interaction (F-TDCI), and d) critically compared different orbital bases in order to achieve an accurate and efficient F-TDCI expansion. This grant ended in August 2020, when our group moved to from Michigan State University to Stony Brook University, where this project continues under grant number DE-SC0021643.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Two-Component Multireference Restricted Active Space Configuration Interaction for the Computation of L-Edge X-ray Absorption Spectra

X-ray absorption spectroscopy is a powerful probe of local electronic and nuclear structure, providing insights into chemical processes. The theoretical prediction and interpretation of metal L-edge X-ray absorption spectra is complicated by both relativistic effects, including spin-orbit coupling, and by the multiconfigurational nature of the states involved. This work details an exact two-component multireference restricted active space configuration interaction (X2C-MRRASCI) scheme that uses an exact two-component state average complete active space self-consistent-field method (X2C-SA-CASSCF), which includes the spin-orbit coupling in a variational manner, for the accurate description of the electronic structure before using a restricted active space configuration interaction method to describe the core excited states of the X-ray spectrum. Benchmark calculations are presented for a series of iron containing complexes, with results showing key features of the spectrum being reproduced, including ligand to metal charge transfer and shake-up excitations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Linear-Scaling Asymmetric Triples Correction through the Solution of the DLPNO–CCSD Lambda Equations: DLPNO–CCSD(T) Λ

In this research, we derive equations for solving for the stationary points of the DLPNO–CCSD Lagrangian, in the t 1 -transformed formalism introduced earlier and as currently implemented in the P SI 4 quantum chemistry software package. These lambda equations in the local pair natural orbital basis allow for the evaluation of CCSD(T) Λ energetics with linear-scaling computational effort, also known as the asymmetric triples correction. This DLPNO–CCSD(T) Λ method allows for accurate triples contributions to be computed for larger molecules, especially in cases that CCSD(T) is known to be insufficient, such as with multireference systems and bond-breaking systems. We showcase the accuracy of our code on reaction energies, barrier heights, and noncovalent interaction energies. Also showcased are the capabilities of our code by evaluating DLPNO–CCSD(T) Λ energetics on large noncovalent dimers up to 112 atoms, as well as a rhodium catalyst complex containing 66 atoms.

Cluster chemistry↗
DOE OSTI2026

One-Step Relativistic Driven Similarity Renormalization Group Multireference Perturbation Theory

We present an efficient implementation of a one-step relativistic second-order multireference perturbation theory based on the multireference driven similarity renormalization group (MR-DSRG) using the exact two-component (X2C) Hamiltonian, which we denote X2C-DSRG-MRPT2. We show that the X2C-DSRG-MRPT2 method can accurately capture spin–orbit coupling (SOC) effects in the electronic structure of strongly correlated systems containing elements across the periodic table. We further demonstrate that the X2C-DSRG-MRPT2 method, through its variational treatment of SOC effects, can yield spin–orbit splittings with mean absolute percentage errors consistently below 7% with respect to experimental values for systems containing up to sixth row elements. With its modest computational scaling (fourth power in system size for the perturbative step) and high accuracy, X2C-DSRG-MRPT2 provides a promising avenue for the routine treatment of relativistic effects in strongly correlated molecular systems.

Hamiltonians↗