Economical quasi-Newton unitary optimization of electronic orbitals.

We present an efficient quasi-Newton orbital solver optimized to reduce the number of gradient evaluations and other computational steps of comparable cost. The solver optimizes orthogonal orbitals by sequences of unitary rotations generated by the (preconditioned) limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm equipped with trust-region step restriction. The low-rank structure of the L-BFGS inverse Hessian is exploited when solving the trust-region problem. The efficiency of the proposed "Quasi-Newton Unitary Optimization with Trust-Region" (QUOTR) solver is compared to that of the standard Roothaan-Hall approach accelerated by the Direct Inversion of Iterative Subspace (DIIS), and other exact and approximate Newton solvers for mean-field (Hartree-Fock and Kohn-Sham) problems.

Direct Determination of Optimal Real-Space Orbitals for Correlated Electronic Structure of Molecules.

We demonstrate how to determine numerically nearly exact orthonormal orbitals that are optimal for the evaluation of the energy of arbitrary (correlated) states of atoms and molecules by minimization of the energy Lagrangian. Orbitals are expressed in real space using a multiresolution spectral element basis that is refined adaptively to achieve the user-specified target precision while avoiding the ill-conditioning issues that plague AO basis set expansions traditionally used for correlated models of molecular electronic structure. For light atoms, the orbital solver, in conjunction with a variational electronic structure model [selected Configuration Interaction (CI)] provides energies of comparable precision to a state-of-the-art atomic CI solver. The computed electronic energies of atoms and molecules are significantly more accurate than the counterparts obtained with the orbital sets of the same rank expanded in Gaussian AO bases, and can be determined even when linear dependence issues preclude the use of the AO bases. It is feasible to optimize more than 100 fully correlated numerical orbitals on a single computer node, and significant room exists for additional improvement. These findings suggest that real-space orbital representations might be the preferred alternative to AO representations for high-end models of correlated electronic states of molecules and materials.

Actinide tetra-N-heterocyclic carbene 'sandwiches'.

Highly-symmetrical, thorium and uranium octakis-carbene 'sandwich' complexes have been prepared by 'sandwiching' the An(iv) cations between two anionic macrocyclic tetra-NHC ligands, one with sixteen atoms and the other with eighteen atoms. The complexes were characterized by a range of experimental methods and DFT calculations. X-ray crystallography confirms the geometry at the metal centre can be set by the size of the macrocyclic ring, leading to either square prismatic or square anti-prismatic shapes; the geometry of the latter is retained in solution, which also undergoes reversible, electrochemical one-electron oxidation or reduction for the uranium variant. DFT calculations reveal a frontier orbital picture that is similar to thorocene and uranocene, in which the NHC ligands show almost exclusively σ-donation to the metal without π-backbonding.

Establishing Cost-Effective Computational Models for the Prediction of Lanthanoid Binding in [Ln(NO3)]2+ (with Ln = La to Lu).

Evaluating the efficiency of predictive methods is critical to the processes of upscaling laboratory processes to full-scale operations on an industrial scale. With regard to separation of lanthanoids, there is a considerable motivation to optimize these processes because of immediate use in nuclear fuel cycle operations, nuclear forensics applications, and rare-earth metal recovery. Efficient predictive capabilities in Gibbs free energies of reaction are essential to optimize separations and ligand design for selective binding needed for various radiochemical applications such as nuclear fuel disposition and recycling of lanthanoid fission products into useful radioisotope products. Ligand design is essential for selective binding of lanthanoids, as separating contiguous lanthanoids is challenging because of the similar behavior these elements exhibit. Modeling including electronic structure calculations of lanthanoid-containing compounds is particularly challenging because of the associated computational cost encountered with the number of electrons correlated in these systems and relativistic considerations. This study evaluates the predictive capabilities of various ab initio methods in the calculation of Gibbs free energies of reaction for [Ln(NO3)]2+ compounds (with Ln = La to Lu), as nitrates are critical in traditional separation processes utilizing nitric acid. The composite methodologies evaluated predict Gibbs free energies of reaction for [Ln(NO3)]2+ compounds within 5 kcal mol-1 in most cases from the target method [CCSD(T)-FSII/cc-pwCV∞Z-DK3+SO] at a fraction of the computational cost.

Structural Analysis of the Complexation of Uranyl, Neptunyl, Plutonyl, and Americyl with Cyclic Imide Dioximes.

Knowledge-based design of extracting agents for selective binding of actinides is essential in stock-pile stewardship, environmental remediation, separations, and nuclear fuel disposal. Robust computational protocols are critical for in depth understanding of structural properties and to further advance the design of selective ligands. In particular, rapid radiochemical separations require predictive capabilities for binding in the gas phase. This study focuses on gas-phase binding preferences of cyclic imide dioximes to uranyl, neptunyl, plutonyl, and americyl. Structural properties, electron withdrawing effects, and their effects on binding preferences are studied with natural bond-order population analysis. The aromatic amidoximes are found to have a larger electron-donation effect than the aliphatic amidoximes. It is also found that plutonyl is more electron withdrawing than uranyl, neptunyl, and americyl when bound to the cyclic imide dioximes studied.

Structural Characteristics, Population Analysis, and Binding Energies of [An(NO3)]2+ (with An = Ac to Lr).

Efficient predictive capabilities are essential for the actinide series since regulatory constraints for radioactive work, associated costs needed for specialized facilities, and the short half-lives of many actinides present great challenges in laboratory settings. Improved predictive accuracy is advantageous for numerous applications including the optimization and design of separation agents for nuclear fuel and waste. One limitation of calculations in support of these applications is that the large variations observed from predictions obtained with currently available methods can make comparisons across studies uncertain. Benchmarking currently available computational methodologies is essential to establish reliable practices across the community to guarantee an accurate physical description of the systems studied. To understand the performance of a variety of common theoretical methods, a systematic analysis of differences observed in the prediction of structural characteristics, electron withdrawing effects, and binding energies of [An(NO3)]2+ (with An = Ac to Lr) in gas and aqueous phases is reported. Population analysis obtained with Mulliken and Löwdin reflect a large dependence on the level of theory of choice, whereas those obtained with natural bond orbital show larger consistency across methodologies. Predicted stability across the actinide series calculated with coupled cluster with perturbative doubles and triples at the triple ζ level is equivalent to the one obtained when extrapolated to the complete basis set limit. The ground state of [Fm(NO3)]2+ and [Md(NO3)]2+ is predicted to have an electronic structure corresponding to An III state in gas and An IV in aqueous phase, whereas the ground state of [An(NO3)]2+ (with An = Ac to Es, Lr) presents an electronic structure corresponding to An IV in the gas and aqueous phase. The compounds studied with No in gas and aqueous phase present a preferred No III state, and the Lr compounds did not follow trends predicted for the rest of the actinide series, as previously observed in studies regarding its unusual electronic structure relative to its position in the periodic table.

Ab initio approaches for the determination of heavy element energetics: Ionization energies of trivalent lanthanides (Ln = La-Eu).

An effective approach for the determination of lanthanide energetics, as demonstrated by application to the third ionization energy (in the gas phase) for the first half of the lanthanide series, has been developed. This approach uses a combination of highly correlated and fully relativistic ab initio methods to accurately describe the electronic structure of heavy elements. Both scalar and fully relativistic methods are used to achieve an approach that is both computationally feasible and accurate. The impact of basis set choice and the number of electrons included in the correlation space has also been examined.