Considering Density Functional Approaches for Actinide Species: The An66 Molecule Set

Iodine capture of a two-dimensional layered uranyl-organic framework: a combined DFT and AIMD study

To develop nuclear energy sustainably, it is important to effectively capture radioiodine in nuclear waste. In this study, we used density functional theory (DFT) and ab initio molecular dynamics (AIMD) calculations to investigate how well the uranyl-organic framework (UOF) could capture radioiodine. We found that the uranyl center and C-N ring sites in both cluster and periodic UOF models are very attractive to the I2 molecule. The adsorption energies of the I2 molecule in the periodic UOF models are as high as -1.10 eV, which is much higher than in the cluster model. The interaction characteristics between the I2 molecule and the UOF were revealed by electronic density topological analyses. Our AIMD simulations at 300 and 600 K have confirmed that the UOF has high adsorption kinetics for I2 molecules and can effectively capture them. The UOF has a high adsorption capacity and good adsorption stability for the I2 molecule, making it a promising option for the environmentally friendly removal of radioiodine.

First-Principles Investigation of the Effects of UF4 and ThF4 Fuels on the Structural, Dynamic, and Thermodynamic Properties of LiF-NaF

An in-depth understanding and characterization of molten salt properties are necessary for the optimized design, efficient operation, and safety assurance of molten salt reactors (MSRs). Investigating molten salt properties in experimental settings can be challenging and time-consuming due to the high temperatures of interest, the salt's corrosiveness, purity and composition control, and health and safety concerns. Therefore, it is beneficial to perform computational screening to assist in the ultimate experimental measurements. Herein, we used first-principles molecular dynamics simulations to calculate several thermophysical, structural, and dynamic properties of eutectic LiF-NaF with fuel additives UF4 and ThF4. We found that with the incorporation of uranium or thorium, a prepeak appears in the structure factor, indicative of a medium-range structural ordering. Furthermore, we explore the mechanism through which these structural changes enhance shear stress correlations, thereby increasing the salt's viscosity. This work highlights the importance of studying the atomic-scale structure of molten salts and how the addition of fuel elements can substantially affect it.

Understanding the Complexation Behavior of Carbamoylphosphine Oxide Ligands with Representative f-Block Elements

The complexation behavior of carbamoylmethylphosphine oxide ligands (CMPO), a bifunctional phosphine oxide, and their substituted derivatives with Ce(III), Eu(III), Th(IV), U(VI), and Am(III) was probed at the density functional theory (DFT) level. The enhanced extraction of trivalent rare earth elements by the 2-diphenylphosphinylethyl derivative over the conventional CMPO ligand is identified due to the availability of an additional P═O donor group in the former. In addition, the orbital and dispersive interactions play a vital role in the preference of Th(IV) over U(VI) during extraction using CMPO ligands. The better complexing ability of ligands having long alkyl chain substituents at the P atom is justified due to the observed enhanced dispersion interactions in these systems.

Novel Computational Chemistry Infrastructure for Simulating Astatide in Water: From Basis Sets to Force Fields Using Particle Swarm Optimization

Using the example of astatine, the heaviest naturally occurring halogen whose isotope At-211 has promising medical applications, we propose a new infrastructure for large-scale computational models of heavy elements with strong relativistic effects. In particular, we focus on developing an accurate force field for At- in water based on reliable relativistic density functional theory (DFT) calculations. To ensure the reliability of such calculations, we design novel basis sets for relativistic DFT, via the particle swarm optimization algorithm to optimize the coefficients of the new basis sets and the polarization-consistent basis set idea's extension to heavy elements to eliminate the basis set error from DFT calculations. The resulting basis sets enable the well-grounded evaluation of relativistic DFT against "gold-standard" CCSD(T) results. Accounting for strong relativistic effects, including spin-orbit interaction, via our redesigned infrastructure, we elucidate a noticeable dissimilarity between At- and I- in halide-water force field parameters, radial distribution functions, diffusion coefficients, and hydration energies. This work establishes the framework for the systematic development of polarization-consistent basis sets for relativistic DFT and accurate force fields for molecular dynamics simulations to be used in large-scale models of complex molecular systems with elements from the bottom of the periodic table, including actinides and even superheavy elements.

Accurate Evaluation of Dispersion Energies at Coupled Cluster Level to Understand the Substituent Effects in Am(III) and Eu(III) Complexes

The effect of cyclic and aromatic substituents on the complexation behavior of phosphine oxide ligands with Am(III) and Eu(III) was investigated at density functional theory (DFT) and domain-based local pair natural orbital coupled-cluster (DLPNO-CC) levels. Combining DFT with accurate coupled cluster methods, we have evaluated the dispersion energy contributions to the complexation energies for trivalent Am and Eu complexes for the first time. Irrespective of the nature of substituents on the P atom, the electronic structure of the P═O group remains identical in all of the ligands. The study reveals the importance of dispersion interactions during complexation and is estimated to be more significant for Am(III) than for Eu(III) complexes.

A computational study on the coordination modes and electron absorption spectra of the complexes U(iv) with N,N,N',N'-tetramethyl-diglycolamide and anions

Lipophilic N,N,N',N'-tetraalkyl-diglycolamides (TRDGAs) are promising extractants for actinides separation in spent nuclear fuel reprocessing. Usually, in the extracted complexes of actinide and lanthanide ions of various oxidation states, the metal ions are completely surrounded by 2 or 3 TRDGA molecules, and the counter anions do not directly coordinate with them. In contrast, the extracted complexes of U(iv) from different media presenting different absorption spectra indicate that the anions (Cl- and NO3-) are directly involved in the coordination with U(iv) in the first inner sphere. Based on this exceptional observation in solvent extraction, taking the coordination of U(iv) with N,N,N',N'-tetramethyl-diglycolamide (TMDGA, the smallest analogue of TRDGA) as the research object, we mimic the behaviours of counterions (Cl- and NO3-) and the water molecule during coordination of TMDGA with U(iv), especially combining with the simulation of the absorption spectra. We demonstrate that during the complexing of TMDGA to U(iv), the counterion Cl- will occupy one coordination number in the inner coordination sphere, and NO3- will occupy two by bidentate type; however, the ubiquitous water cannot squeeze in the inner coordination sphere. In addition, the coordination of Cl- and NO3- is proved to favour the extraction with the lower binding energy. Moreover, the simulation of absorption spectra is in good agreement with the observation from experiments, further verifying the aforementioned conclusion. This work in some way will provide guidance to improve the computation methods in research of actinides by mimicking the absorption spectra of actinide ions in different complexes.

On the potentially transformative role of auxiliary-field quantum Monte Carlo in quantum chemistry: A highly accurate method for transition metals and beyond

Approximate solutions to the ab initio electronic structure problem have been a focus of theoretical and computational chemistry research for much of the past century, with the goal of predicting relevant energy differences to within "chemical accuracy" (1 kcal/mol). For small organic molecules, or in general, for weakly correlated main group chemistry, a hierarchy of single-reference wave function methods has been rigorously established, spanning perturbation theory and the coupled cluster (CC) formalism. For these systems, CC with singles, doubles, and perturbative triples is known to achieve chemical accuracy, albeit at O(N⁷) computational cost. In addition, a hierarchy of density functional approximations of increasing formal sophistication, known as Jacob's ladder, has been shown to systematically reduce average errors over large datasets representing weakly correlated chemistry. However, the accuracy of such computational models is less clear in the increasingly important frontiers of chemical space including transition metals and f-block compounds, in which strong correlation can play an important role in reactivity. A stochastic method, phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC), has been shown to be capable of producing chemically accurate predictions even for challenging molecular systems beyond the main group, with relatively low O(N³ - N⁴) cost and near-perfect parallel efficiency. Herein, we present our perspectives on the past, present, and future of the ph-AFQMC method. We focus on its potential in transition metal quantum chemistry to be a highly accurate, systematically improvable method that can reliably probe strongly correlated systems in biology and chemical catalysis and provide reference thermochemical values (for future development of density functionals or interatomic potentials) when experiments are either noisy or absent. Finally, we discuss the present limitations of the method and where we expect near-term development to be most fruitful.

Multireference Wavefunction-Based Investigation of the Ground and Excited States of LrF and LrO

Complete active space self-consistent field (CASSCF) and multireference configuration interaction with Davidson correction (MRCI+Q) calculations have been carried out for lawrencium fluoride (LrF) and lawrencium oxide (LrO) molecules, detailing 19 and 20 electronic states for LrF and LrO, respectively. For LrF, two dissociation channels were considered, Lr(2P)+F(2P) and Lr(2D)+F(2P). However, due to the more complex electronic manifold of LrO, three dissociation channels were computed: Lr(2P)+O(3P), Lr(2D)+O(3P), and Lr(2P)+O(1D). In addition, equilibrium bond lengths, harmonic vibrational frequencies ωe, anharmonicity constants ωeχe, ΔG1/2 values, and excitation energies Te for the ground and several excited electronic states were calculated for both molecules, for the first time. Bond dissociation energies (BDEs) were calculated for LrF and LrO using several different levels of theory: unrestricted coupled-cluster with single, double, and perturbative triple excitations (UCCSD(T)), density functional theory (B3LYP, TPSS, M06-L, and PBE), and the correlation-consistent composite approach developed for f-elements (f-ccCA).

Investigating the Heaviest Halogen: Lessons Learned from Modeling the Electronic Structure of Astatine's Small Molecules

We present a systematic study of electron-correlation and relativistic effects in diatomic molecular species of the heaviest halogen astatine (At) within relativistic single- and multireference coupled-cluster approaches and relativistic density functional theory. We establish revised reference ab initio data for the ground states of At₂, HAt, AtAu, and AtO⁺ using a highly accurate relativistic effective core potential model and in-house basis sets developed for accurate modeling of molecules with large spin-orbit effects. Spin-dependent relativistic effects on chemical bonding in the ground state are comparable to the binding energy or even exceed it in At₂. Electron-correlation effects near the equilibrium internuclear separation are mostly dynamical and can be adequately captured using single-reference CCSD(T). However, bond elongation in At₂ and, especially, AtO⁺ results in rapid manifestation of its multireference character. While useful for evaluating the spin-orbit effects on the ground-state bonding and properties, the two-component density functional theory lacks predictive power, especially in combination with popular empirically adjusted exchange-correlation functionals. This drawback supports the necessity to develop new functionals for reliable quantum-chemical models of heavy-element compounds with strong relativistic effects.

Machine learning, artificial intelligence, and chemistry: how smart algorithms are reshaping simulation and the laboratory

Machine learning and artificial intelligence are increasingly gaining in prominence through image analysis, language processing, and automation, to name a few applications. Machine learning is also making profound changes in chemistry. From revisiting decades-old analytical techniques for the purpose of creating better calibration curves, to assisting and accelerating traditional in silico simulations, to automating entire scientific workflows, to being used as an approach to deduce underlying physics of unexplained chemical phenomena, machine learning and artificial intelligence are reshaping chemistry, accelerating scientific discovery, and yielding new insights. This review provides an overview of machine learning and artificial intelligence from a chemist’s perspective and focuses on a number of examples of the use of these approaches in computational chemistry and in the laboratory.

Ab initio composite strategies and multireference approaches for lanthanide sulfides and selenides

The f-block ab initio correlation consistent composite approach was used to predict the dissociation energies of lanthanide sulfides and selenides. Geometry optimizations were carried out using density functional theory and coupled cluster singles, doubles, and perturbative triples with one- and two-component Hamiltonians. For the two-component calculations, relativistic effects were accounted for by utilizing a third-order Douglas-Kroll-Hess Hamiltonian. Spin-orbit coupling was addressed with the Breit-Pauli Hamiltonian within a multireference configuration interaction approach. The state averaged complete active space self-consistent field wavefunctions obtained for the spin-orbit coupling energies were used to assign the ground states of diatomics, and several diagnostics were used to ascertain the multireference character of the molecules.

Exploiting Ligand Additivity for Transferable Machine Learning of Multireference Character across Known Transition Metal Complex Ligands

Accurate virtual high-throughput screening (VHTS) of transition metal complexes (TMCs) remains challenging due to the possibility of high multireference (MR) character that complicates property evaluation. We compute MR diagnostics for over 5,000 ligands present in previously synthesized octahedral mononuclear transition metal complexes in the Cambridge Structural Database (CSD). To accomplish this task, we introduce an iterative approach for consistent ligand charge assignment for ligands in the CSD. Across this set, we observe that the MR character correlates linearly with the inverse value of the averaged bond order over all bonds in the molecule. We then demonstrate that ligand additivity of the MR character holds in TMCs, which suggests that the TMC MR character can be inferred from the sum of the MR character of the ligands. Encouraged by this observation, we leverage ligand additivity and develop a ligand-derived machine learning representation to train neural networks to predict the MR character of TMCs from properties of the constituent ligands. This approach yields models with excellent performance and superior transferability to unseen ligand chemistry and compositions.

Assessing MP2 frozen natural orbitals in relativistic correlated electronic structure calculations

The high computational scaling with the basis set size and the number of correlated electrons is a bottleneck limiting applications of coupled cluster algorithms, in particular for calculations based on two- or four-component relativistic Hamiltonians, which often employ uncontracted basis sets. This problem may be alleviated by replacing canonical Hartree-Fock virtual orbitals by natural orbitals (NOs). In this paper, we describe the implementation of a module for generating NOs for correlated wavefunctions and, in particular, second order Møller-Plesset perturbation frozen natural orbitals (MP2FNOs) as a component of our novel implementation of relativistic coupled cluster theory for massively parallel architectures [Pototschnig et al. J. Chem. Theory Comput. 17, 5509, (2021)]. Our implementation can manipulate complex or quaternion density matrices, thus allowing for the generation of both Kramers-restricted and Kramers-unrestricted MP2FNOs. Furthermore, NOs are re-expressed in the parent atomic orbital (AO) basis, allowing for generating coupled cluster singles and doubles NOs in the AO basis for further analysis. By investigating the truncation errors of MP2FNOs for both the correlation energy and molecular properties-electric field gradients at the nuclei, electric dipole and quadrupole moments for hydrogen halides HX (X = F-Ts), and parity-violating energy differences for H₂Z₂ (Z = O-Se)-we find MP2FNOs accelerate the convergence of the correlation energy in a roughly uniform manner across the Periodic Table. It is possible to obtain reliable estimates for both energies and the molecular properties considered with virtual molecular orbital spaces truncated to about half the size of the full spaces.

Ab Initio Composite Approaches for Heavy Element Energetics: Ionization Potentials for the Actinide Series of Elements

The first, second, and third gas-phase ionization potentials have been determined for the actinide series of elements using an ab initio composite scalar and fully relativistic approach, employing the coupled cluster with single, double, and perturbative triple excitations (CCSD(T)) and Dirac Hartree-Fock (DHF) methods, extrapolated to the complete basis set (CBS) limit. The impact of electron correlation and basis set choice within this framework are examined. Additionally, the first three ionization potentials were obtained using an ab initio heavy element correlation-consistent Composite Approach (here referred to as α-ccCA). This is the first utilization of a ccCA for actinide species.

A theoretical investigation of the hydrolysis of uranium hexafluoride: the initiation mechanism and vibrational spectroscopy

Depleted uranium hexafluoride (UF₆), a stockpiled byproduct of the nuclear fuel cycle, reacts readily with atmospheric humidity, but the mechanism is poorly understood. We compare several potential initiation steps at a consistent level of theory, generating underlying structures and vibrational modes using hybrid density functional theory (DFT) and computing relative energies of stationary points with double-hybrid (DH) DFT. A benchmark comparison is performed to assess the quality of DH-DFT data using reference energy differences obtained using a complete-basis-limit coupled-cluster (CC) composite method. The associated large-basis CC computations were enabled by a new general-purpose pseudopotential capability implemented as part of this work. Dispersion-corrected parameter-free DH-DFT methods, namely PBE0-DH-D3(BJ) and PBE-QIDH-D3(BJ), provided mean unsigned errors within chemical accuracy (1 kcal mol^-1) for a set of barrier heights corresponding to the most energetically favorable initiation steps. The hydrolysis mechanism is found to proceed via intermolecular hydrogen transfer within van der Waals complexes involving UF₆, UF₅OH, and UOF₄, in agreement with previous studies, followed by the formation of a previously unappreciated dihydroxide intermediate, UF₄(OH)₂. The dihydroxide is predicted to form under both kinetic and thermodynamic control, and, unlike the alternate pathway leading to the UO₂F₂ monomer, its reaction energy is exothermic, in agreement with observation. Finally, harmonic and anharmonic vibrational simulations are performed to reinterpret literature infrared spectroscopy in light of this newly identified species.

Detection of multi-reference character imbalances enables a transfer learning approach for virtual high throughput screening with coupled cluster accuracy at DFT cost

Appropriately identifying and treating molecules and materials with significant multi-reference (MR) character is crucial for achieving high data fidelity in virtual high-throughput screening (VHTS). Despite development of numerous MR diagnostics, the extent to which a single value of such a diagnostic indicates the MR effect on a chemical property prediction is not well established. We evaluate MR diagnostics for over 10 000 transition-metal complexes (TMCs) and compare to those for organic molecules. We observe that only some MR diagnostics are transferable from one chemical space to another. By studying the influence of MR character on chemical properties (i.e., MR effect) that involve multiple potential energy surfaces (i.e., adiabatic spin splitting, ΔE_H–L, and ionization potential, IP), we show that differences in MR character are more important than the cumulative degree of MR character in predicting the magnitude of an MR effect. Motivated by this observation, we build transfer learning models to predict CCSD(T)-level adiabatic ΔE_H–L and IP from lower levels of theory. By combining these models with uncertainty quantification and multi-level modeling, we introduce a multi-pronged strategy that accelerates data acquisition by at least a factor of three while achieving coupled cluster accuracy (i.e., to within 1 kcal mol⁻¹ MAE) for robust VHTS.

We demonstrate that cancellation in multi-reference effect outweighs accumulation in evaluating chemical properties. We combine transfer learning and uncertainty quantification for accelerated data acquisition with chemical accuracy.