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DOE OSTI2024

Cholesky Decomposition-Based Implementation of Relativistic Two-Component Coupled-Cluster Methods for Medium-Sized Molecules

A Cholesky decomposition (CD)-based implementation of relativistic two-component coupled-cluster (CC) and equation-of-motion CC (EOM-CC) methods using an exact two-component Hamiltonian augmented with atomic-mean-field integrals (the X2CAMF scheme) is reported. Furthermore, the present CD-based implementation of X2CAMF-CC and EOM-CC methods employs atomic-orbital-based algorithms to avoid the construction of two-electron integrals and intermediates involving three and four virtual indices. The CD-based implementation extends the applicability of X2CAMF-CC and EOMCC methods to medium-sized molecules with the correlation of around 1000 spinors. Benchmark calculations for uranium-containing small molecules have been performed to assess the dependence of CC results with respect to the Cholesky threshold. A Cholesky threshold of 10 –4 is shown to maintain chemical accuracy. Example calculations to illustrate the capability of the CD-based relativistic CC methods are reported for the bond dissociation energy of the uranium hexafluoride molecule, UF 6 , with up to quadruple-zeta basis sets and the lowest excitation energy in solvated uranyl ion [UO 2 2+ (H 2 O) 12 ].

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DOE OSTI2024

Revisiting the Optical Spectrum of the Plutonyl Ion (PuO 2 ) 2+ in 1 M HClO 4

The analysis of the solution absorption spectrum of the plutonyl ion in an aqueous environment was given by Eisenstein and Pryce (E&P) in 1968. In 2011 a new spectrum was published of the (PuO 2 ) 2+ ion in 1 M HClO 4 . We have been provided with the original data of this spectrum and have found in the data a previously unreported low-lying transition at 7385 cm –1 which we have assigned as a magnetic dipole transition. We have fit most of the near-infrared and optical transitions with Gaussian fits and tabulated a new energy level list up to 22,000 cm –1 which mostly agrees with the data of E&P. We assumed a crystal field of D ∞h (only axial symmetry) and utilized the intensity calculations published for the isoelectronic (NpO 2 ) 1+ ion using a complete basis set for the 5f 2 problem including the Coulombic, spin–orbit as well as the crystal field Hamiltonian. Our results differ substantially from those of E&P. Subsequently, we used a truncated Hamiltonian to try to establish the effects of assuming the σ antibonding orbitals are at such high energies that we can ignore their contributions to the lower lying φ and δ orbitals.

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DOE OSTI2020

Utilizing Essential Symmetry Breaking in Auxiliary-Field Quantum Monte Carlo: Application to the Spin Gaps of the C 36 Fullerene and an Iron Porphyrin Model Complex

We present three distinct examples where phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) can be reliably performed with a single-determinant trial wave function with essential symmetry breaking. Essential symmetry breaking was first introduced by Lee and Head-Gordon [ Phys. Chem. Chem. Phys. 2019, 21, 4763-4778, 10.1039/C8CP07613H]. We utilized essential complex and time-reversal symmetry breaking with ph-AFQMC to compute the triplet–singlet energy gap in the TS12 set. We found statistically better performance of ph-AFQMC with complex-restricted orbitals than with spin-unrestricted orbitals. We then showed the utilization of essential spin symmetry breaking when computing the singlet–triplet gap of a known biradicaloid, C 36 . ph-AFQMC with spin-unrestricted Hartree–Fock (ph-AFQMC+UHF) fails catastrophically even with spin-projection and predicts no biradicaloid character. With approximate Brueckner orbitals obtained from regularized orbital-optimized second-order Møller–Plesset perturbation theory (κ-OOMP2), ph-AFQMC quantitatively captures strong biradicaloid character of C 36 . Lastly, we applied ph-AFQMC to the computation of the quintet–triplet gap in a model iron porphyrin complex where brute-force methods with a small active space fail to capture the triplet ground state. We show unambiguously that neither triplet nor quintet is strongly correlated using UHF, κ-OOMP2, and coupled-cluster with singles and doubles (CCSD) performed on UHF and κ-OOMP2 orbitals. There is no essential symmetry breaking in this problem. By virtue of this, we were able to perform UHF+ph-AFQMC reliably with a cc-pVTZ basis set and predicted a triplet ground state for this model geometry. The largest ph-AFQMC in this work correlated 186 electrons in 956 orbitals. Our work highlights the utility, scalability, and accuracy of ph-AFQMC with a single-determinant trial wave function with essential symmetry breaking for systems mainly dominated by dynamical correlation with little static correlation.

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DOE OSTI2020

Robust, Accurate, and Efficient: Quantum Embedding Using the Huzinaga Level-Shift Projection Operator for Complex Systems

Using wave function (WF) in density functional theory (DFT) embedding methods provides a framework for performing localized, high-accuracy WF calculations on a system, while not incurring the full computational cost of the WF calculation on the full system. To effectively partition a system into localized WF and DFT subsystems, we utilize the Huzinaga level-shift projection operator within an absolutely localized basis. In this work, we study the ability of the absolutely localized Huzinaga level-shift projection operator method to study complex WF and DFT partitions, including partitions between multiple covalent bonds, a double bond, and transition-metal–ligand bonds. We find that our methodology can accurately describe all of these complex partitions. Additionally, we study the robustness of this method with respect to the WF method, specifically where the embedded systems were described using a multiconfigurational WF method. We found that the method is systematically improvable with respect to both the number of atoms in the WF region and the size of the basis set used, with energy errors less than 1 kcal/mol. Additionally, we calculated the adsorption energy of H2 to a model of an iron metal–organic framework (Fe-MOF-74) to within 1 kcal/mol compared to CASPT2 calculations performed on the full model while incurring only a small fraction of the full computational cost. In conclusion, this work demonstrates that the absolutely localized Huzinaga level-shift projection operator method is applicable to very complex systems with difficult electronic structures.

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DOE OSTI2025

Spatial Signatures of Electron Correlation in Least-Squares Tensor Hypercontraction

Least Squares Tensor Hypercontraction (LS-THC) has received some attention in recent years as an approach to reduce the significant computational costs of wavefunc- tion based methods in quantum chemistry. However, previous work has demonstrated that the LS-THC factorization performs disproportionately worse in the description of wavefunction components (e.g. cluster amplitudes T 2 ) than Hamiltonian compo- nents (e.g. electron repulsion integrals (pq|rs)). This work develops novel theoretical methods to study the source of these errors in the context of the real-space T 2 kernel, and reports, for the first time, the existence of a “correlation feature” in the errors of the LS-THC representation of the “exchange-like” correlation energy EX and T 2 that is remarkably consistent across ten molecular species, three correlated wavefunctions, and four basis sets. This correlation feature portends the existence of a “pair-point kernel” missing in the usual LS-THC representation of the wavefunction, which critically depends upon pairs of grid points situated close to atoms and with inter-pair distances between one and two Bohr radii. These findings point the way for future LS-THC developments to address these shortcomings.

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DOE OSTI2026

Reduced-Cost Four-Component Relativistic Double Ionization Potential Equation-of-Motion Coupled-Cluster Approaches with 4-Hole–2-Particle Excitations and Three-Body Clusters

The double ionization potential (DIP) equation-ofmotion (EOM) coupled-cluster (CC) method with 4-hole−2- particle (4h-2p) excitations on top of the CC with singles, doubles, and triples calculation, abbreviated as DIP-EOMCCSDT(4h-2p), along with its perturbative DIP-EOMCCSD(T)(a)(4h-2p) approximation, are extended to a relativistic four-component (4c) framework. In addition, we introduce and test a new computationally practical DIP-EOMCC approach, which we call DIPEOMCCSD( T)(ã)(4h-2p), that approximates the treatment of 4h- 2p correlations within the DIP-EOMCCSD(T)(a)(4h-2p) method and reduces the $\mathcal{N}$ 8 scaling characterizing DIP-EOMCCSDT(4h- 2p) and DIP-EOMCCSD(T)(a)(4h-2p) to $\mathcal{N}$ 7 with the system size $\mathcal{N}$. Further improvements in computational efficiency are obtained using the frozen natural spinor (FNS) approximation to reduce the numbers of unoccupied spinors entering the correlated steps of the DIP-EOMCC calculations according to a well-defined occupation-number-based threshold. The resulting 4c-FNS-DIPEOMCC approaches are used to compute DIPs for the series of inert gas atoms from argon to radon as well as the vertical DIPs in Cl 2 , Br 2 , HBr, and HI, which have been experimentally examined in the past. We demonstrate that, when using complete basis set extrapolations and FNS truncation threshold of 10 −4.5 , the 4c-FNS-DIP-EOMCCSD(T)(ã)(4h-2p) calculations are capable of predicting DIPs in agreement with experimental data, improving upon their nonrelativistic and spin-free scalar-relativistic counterparts, particularly when examining DIPs characterized by stronger spin−orbit coupling effects.

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DOE OSTI2025

The Remarkable I 2 O 3 Molecule: A New View from Theory

Atmospheric iodine chemistry has garnered increasing attention as a result of increased iodine emissions. A key subset of this chemistry involves iodine oxides (I 2 O 2–5 ), which serve as precursors to particle formation. Among these, I 2 O 3 is the simplest iodine oxide involved in particle formation, but it has remained undetected in the atmosphere. Previous theoretical studies have characterized this peculiar molecule, primarily using energies to refine geometries obtained at low levels of theory. Due to the reemerging interest in I 2 O 3 , this study presents geometries optimized at the CCSD(T)/aug-cc-pwCVTZ-PP level of theory─marking the first instance, to the best of our knowledge, where this system has been studied exclusively with CCSD(T). Harmonic vibrational frequencies were computed at the same level of theory. Final energetics were obtained using the very high level CCSDT(Q) method with basis sets up to quintuple-zeta cardinality (aug-cc-pwCV5Z-PP) and extrapolated to the CBS limit to yield CCSDT(Q)/CBS//CCSD(T)/aug-cc-pwCVTZ-PP energies. These energies include harmonic zero-point vibrational energy corrections and scalar relativistic energy corrections. Additionally, this study discovers new isomers along the I 2 O 3 potential energy surface, a novel contribution to the field. The performance of different computational methods and DFT functionals commonly used in atmospheric chemistry is also assessed relative to high-level theoretical methods.

basis sets↗
DOE OSTI2022

Sequential Bond Dissociation Energies of Th + (CO) x , x = 3–6: Guided Ion Beam Collision-Induced Dissociation and Quantum Computational Studies

Collision-induced dissociation (CID) of [Th,xC,xO] + , x = 3–6, with Xe is performed using a guided ion beam tandem mass spectrometer (GIBMS). Products are formed exclusively by the loss of CO ligands. Analyses of the kinetic energy-dependent CID product cross sections yield bond dissociation energies (BDEs) of (CO) x–1 Th + –CO at 0 K as 1.09 ± 0.05, 0.82 ± 0.07, 0.63 ± 0.05, and 0.70 ± 0.05 eV, respectively. Different structures of [Th,xC,xO] + were explored using various electronic structure methods, and BDEs for CO ligand loss from precursor [Th,xC,xO] + complexes were computed. Both experimental and theoretical results corroborate that the structures of [Th,xC,xO] + , x = 3–6, formed experimentally are homoleptic thorium cation carbonyl complexes, Th + (CO) x . The nonmonotonic trend in experimental BDEs is reproduced theoretically, although ambiguities in the spin states of the x = 4–6 complexes (doublet or quartet) remain. BDEs calculated at the coupled cluster with single, double, and perturbative triple excitations (CCSD(T))/cc-pVXZ//B3LYP/cc-PVXZ (X = T and Q) level and a complete basis set (CBS) extrapolation agree reasonably well with the experimental values for all complexes. Thorium oxide ketenylidene carbonyl cations, OTh + CCO(CO) y , y = 1–4, were calculated to be the most stable structures of [Th,xC,xO] + , x = 3–6, respectively; however, these are not observed in our experiment. Potential energy profiles (PEPs) having either quartet or doublet spin calculated at the B3LYP/cc-pVQZ level suggest that the failure to observe OTh + CCO(CO) y , y = 1–4, is the result of a barrier corresponding to the C–C bond formation, making the formation of OTh + CCO(CO) y inaccessible kinetically under the present experimental conditions.

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DOE OSTI2023

Barrier Heights for Diels–Alder Transition States Leading to Pentacyclic Adducts: A Benchmark Study of Crowded, Strained Transition States of Large Molecules

Theoretical characterization of reactions of complex molecules depends on providing consistent accuracy for the relative energies of intermediates and transition states. Here we employ the DLPNO-CCSD(T) method with core–valence correlation, large basis sets, and extrapolation to the CBS limit to provide benchmark values for Diels–Alder transition states leading to competitive strained pentacyclic adducts. We then used those benchmarks to test a diverse set of wave function and density functional methods for the absolute and relative barrier heights of these transition states. Our results show that only a few of the tested density functionals can predict the absolute barrier heights satisfactorily, although relative barrier heights are more accurate. The most accurate functionals tested are ωB97M-V, M11plus, ωB97X-V, PBE-D3(0), M11, and MN15 with MUDs from best estimates less than 3.0 kcal. Furthermore, these findings can guide selection of density functionals for future studies of crowded, strained transition states of large molecules.

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DOE OSTI2021

NENCI-2021. I. A large benchmark database of non-equilibrium non-covalent interactions emphasizing close intermolecular contacts

In this work, we present NENCI-2021, a benchmark database of ~8000 Non-Equilibirum Non-Covalent Interaction energies for a large and diverse selection of intermolecular complexes of biological and chemical relevance. To meet the growing demand for large and high-quality quantum mechanical data in the chemical sciences, NENCI-2021 starts with the 101 molecular dimers in the widely used S66 and S101 databases and extends the scope of these works by (i) including 40 cation–π and anion–π complexes, a fundamentally important class of non-covalent interactions that are found throughout nature and pose a substantial challenge to theory, and (ii) systematically sampling all 141 intermolecular potential energy surfaces (PESs) by simultaneously varying the intermolecular distance and intermolecular angle in each dimer. Designed with an emphasis on close contacts, the complexes in NENCI-2021 were generated by sampling seven intermolecular distances along each PES (ranging from 0.7× to 1.1× the equilibrium separation) and nine intermolecular angles per distance (five for each ion–π complex), yielding an extensive database of 7763 benchmark intermolecular interaction energies (E int ) obtained at the coupled-cluster with singles, doubles, and perturbative triples/complete basis set [CCSD(T)/CBS] level of theory. The E int values in NENCI-2021 span a total of 225.3 kcal/mol, ranging from -38.5 to +186.8 kcal/mol, with a mean (median) E int value of -1.06 kcal/mol (-2.39 kcal/mol). In addition, a wide range of intermolecular atom-pair distances are also present in NENCI-2021, where close intermolecular contacts involving atoms that are located within the so-called van der Waals envelope are prevalent—these interactions, in particular, pose an enormous challenge for molecular modeling and are observed in many important chemical and biological systems. A detailed symmetry-adapted perturbation theory (SAPT)- based energy decomposition analysis also confirms the diverse and comprehensive nature of the intermolecular binding motifs present in NENCI-2021, which now includes a significant number of primarily induction-bound dimers (e.g., cation–π complexes). NENCI-2021 thus spans all regions of the SAPT ternary diagram, thereby warranting a new four-category classification scheme that includes complexes primarily bound by electrostatics (3499), induction (700), dispersion (1372), or mixtures thereof (2192). A critical error analysis performed on a representative set of intermolecular complexes in NENCI-2021 demonstrates that the E int values provided herein have an average error of ±0.1 kcal/mol, even for complexes with strongly repulsive E int values, and maximum errors of ±0.2–0.3 kcal/mol (i.e., ~±1.0 kJ/mol) for the most challenging cases. For these reasons, we expect that NENCI-2021 will play an important role in the testing, training, and development of next-generation classical and polarizable force fields, density functional theory approximations, wavefunction theory methods, and machine learning based intra- and inter-molecular potentials.

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DOE OSTI2022

Atomic isotropic hyperfine properties for second row elements (Al–Cl)

Isotropic hyperfine properties have been obtained for the second row elements Al–Cl using a systematic composite approach consisting of a sequence of core/valence correlation consistent basis sets, up through aug-cc-pCV7Z, along with configuration interaction and coupled cluster methods. The best nonrelativistic final values for the atomic ground states (in MHz) are -1.80 27 Al ( 2 P o 1/2 ), -24.31 29 Si ( 3 P 0 ), 63.70 31 P ( 4 So 3/2 ), 20.77 33 S ( 3 P 2 ), and 35.42 35 Cl ( 2 P o 3/2 ). We find a large K shell contribution to the spin density at the nucleus that is almost canceled by the L and M shell contributions. The spin density in atomic units is approximately linear with respect to the atomic number.

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DOE OSTI2021

Theoretical Prediction and Interpretation of 237 Np Mössbauer Isomer Shifts

Different theoretical approaches for the calculation of 237 Np Mössbauer isomer shifts are investigated. The traditional contact density route is compared to a previously proposed alternative approach that uses energy derivatives with respect to the nuclear radius. Both approaches yield similar results as long as suitable basis sets augmented with large exponents and relativistic methods are used. Density functional theory (DFT) calculations do not show a strong dependency of the 237 Np isomer shift on the chosen functional. Wavefunction calculations show that dynamic electron correlation can be important when covalent bonding influences the isomer shift. Effects from spin–orbit coupling are small. The isomer shifts of ionic solids and Np(III) organometallic complexes are largely governed by the oxidation state of Np. Isomer shifts of organometallic Np(IV) complexes are strongly affected by donation bonding. Furthermore, detailed analysis of the wavefunction results with different active spaces demonstrates that correlation among the outer core Np and occupied ligand frontier orbitals contributes significantly to isomer shifts of Np(IV) compounds.

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DOE OSTI2025

Introducing GPU Acceleration into the Python-Based Simulations of Chemistry Framework

We introduce the first version of GPU4P Y SCF, a module that provides GPU acceleration of methods in P Y SCF. As a core functionality, this provides a GPU implementation of two-electron repulsion integrals (ERIs) for contracted basis sets comprising up to g functions using the Rys quadrature. As an illustration of how this can accelerate a quantum chemistry workflow, we describe how to use the ERIs efficiently in the integral-direct Hartree–Fock build and nuclear gradient construction. Benchmark calculations show a significant speedup of 2 orders of magnitude with respect to the multithreaded CPU Hartree–Fock code of P Y SCF and the performance comparable to other open-source GPU-accelerated quantum chemical packages, including GAMESS and QUICK, on a single NVIDIA A100 GPU.

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DOE OSTI2022

Atomic isotropic hyperfine properties for first row elements (B–F) revisited

Benchmark quality isotropic hyperfine properties have been obtained for first row elements (B–F) using a systematic composite approach consisting of a sequence of core/valence correlation consistent basis sets, up through aug-cc-pCV8Z, along with configuration interaction and coupled cluster theory methods. The best nonrelativistic final values (in MHz) are 10.64 (B), 20.22 (C), 10.59 (N), –31.74 (O), and 318.30 (F) and are in very good agreement with available experimental values for these difficult-to-describe properties. Agreement is especially close in the case of N, which has the most accurate experimental value. The spin densities derived from the best composite level of theory were found to closely follow a simple quadratic scaling with the atomic number, Z. Finally, observed convergence rates in the 1-particle and n-particle expansions obtained here may be useful in judging likely accuracy that can be expected in studies of molecular systems.

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DOE OSTI2020

Calculated Ionization Potentials of MO 3 and MO 2 for M = U, Mo, W, and Nd

Here, ionization potentials (IPs) for MO 3 and MO 2 for M = U, Mo, W, and Nd have been predicted using the Feller–Peterson–Dixon (FPD) approach at the coupled cluster CCSD(T)/complete basis set level including additional corrections. The additional corrections are mostly small, with spin-orbit effects contributing less than 0.05 eV, except for NdO 2 where the correction lowers the IP by 0.26 eV. The IPs for UO 3 and UO 2 are calculated to be 9.59 and 6.09 eV, respectively. The calculated IPs for MoO 3 and WO 3 are very similar, 11.13 and 11.11 eV, respectively, and MoO 2 and WO 2 are 8.51 and 8.79 eV, respectively. MoO 2 has a triplet ground state, whereas WO 2 has a singlet ground state. The calculated IP for NdO 2 is 7.90 eV. NdO 3 does not achieve a high +VI formal oxidation state on the lanthanide and has an IP of 7.80 eV. These calculated IPs are expected to have error bars of ±0.04 eV.

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DOE OSTI2026

Energy-Screened Many-Body Expansion for Protein–Ligand Interactions: Examining Convergence for Metalloenzymes Through Seven–Body Interactions

Fragment-based quantum chemistry is a powerful strategy for calculating protein−ligand interaction energies using quantum chemistry methods. Rigorous convergence often requires hundreds of atoms in the protein binding-site model, especially if that model is constructed using distance-based criteria to select amino acid residues, while three- and four-body calculations exhibit instability related to combinatorial proliferation in the number of subsystem calculations. Here, we report an energy-based screening protocol for the many-body expansion applied to protein−ligand interactions, implemented in the open-source FRAGME∩T code. Using a combination of aggressive screening based on semiempirical quantum chemistry, with an improved graph-theoretical algorithm to eliminate unimportant subsystems, we are able to perform n-body calculations up to n = 7 using density functional theory in triple-ζ basis sets. Distance cutoffs further reduce the cost without compromising accuracy. Rapid and stable convergence of the many-body expansion is obtained by n = 4, for a pair of metalloenzymes in which a divalent ion coordinates directly to the ligand. As compared to previous results that relied solely on distance cutoffs, oscillations in the n-body corrections are reduced or eliminated, although residual errors remain in one case. This work demonstrates that benchmark-quality protein−ligand interaction energies can be systematically converged using a method with excellent parallel efficiency and scalability.

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DOE OSTI2025

Classical Preoptimization Approach for ADAPT-VQE: Maximizing the Potential of High-Performance Computing Resources to Improve Quantum Simulation of Chemical Applications

The ADAPT-VQE algorithm is a promising method for generating a compact ansatz based on derivatives of the underlying cost function, and it yields accurate predictions of electronic energies for molecules. In this work, we report the implementation and performance of ADAPT-VQE with our recently developed sparse wave function circuit solver (SWCS) in terms of accuracy and efficiency for molecular systems with up to 52 spin orbitals. The SWCS can be tuned to balance computational cost and accuracy, which extends the application of ADAPT-VQE for molecular electronic structure calculations to larger basis sets and a larger number of qubits. Using this tunable feature of the SWCS, we propose an alternative optimization procedure for ADAPT-VQE to reduce the computational cost of the optimization. Furthermore, by preoptimizing a quantum simulation with a parametrized ansatz generated with ADAPT-VQE/SWCS, we aim to utilize the power of classical high-performance computing in order to minimize the work required on noisy intermediate-scale quantum hardware, which offers a promising path toward demonstrating quantum advantage for chemical applications.

ADAPT-VQE↗
DOE OSTI2023

Neutral gas pressure dependence of ion–ion mutual neutralization rate constants using Landau–Zener theory coupled with trajectory simulations

In this computational study, we describe a self-consistent trajectory simulation approach to capture the effect of neutral gas pressure on ion–ion mutual neutralization (MN) reactions. The electron transfer probability estimated using Landau–Zener (LZ) transition state theory is incorporated into classical trajectory simulations to elicit predictions of MN cross sections in vacuum and rate constants at finite neutral gas pressures. Electronic structure calculations with multireference configuration interaction and large correlation consistent basis sets are used to derive inputs to the LZ theory. The key advance of our trajectory simulation approach is the inclusion of the effect of ion-neutral interactions on MN using a Langevin representation of the effect of background gas on ion transport. For H + – H – and Li + – H(D) – , our approach quantitatively agrees with measured speed-dependent cross sections for up to ~10 5 m/s. For the ion pair Ne + – Cl – , our predictions of the MN rate constant at ~1 Torr are a factor of ~2 to 3 higher than the experimentally measured value. Similarly, for Xe + – F – in the pressure range of ~20 000–80 000 Pa, our predictions of the MN rate constant are ~20% lower but are in excellent qualitative agreement with experimental data. Here, the paradigm of using trajectory simulations to self-consistently capture the effect of gas pressure on MN reactions advanced here provides avenues for the inclusion of additional nonclassical effects in future work.

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