Relativistic double-zeta, triple-zeta, and quadruple-zeta basis sets for the lanthanides La–Lu

Composite ab initio vibrational spectroscopy and thermochemistry of low-valency lanthanide compounds: europium dihalides EuX2 (X = F, Cl, Br, I)

A unique diversity in chemical properties of lanthanide compounds making them very useful in various important applications stems not least from the existence of less common Ln oxidation states, in particular +2. However, the molecular properties of low-valency lanthanide compounds are not yet well studied even for the most stable divalent Ln-containing species, such as europium dihalides. In this paper, highly accurate molecular structures, vibrational spectra, and atomisation energies of the europium dihalides EuX2 (X = F, Cl, Br, I) are obtained at the complete basis set CCSD(T) level. All of the EuX2 species are calculated to be non-linear (C2v) exhibiting a regular increase in X-Eu-X bond angle on passing through the halogen series (F → Cl → Br → I), from 117° in EuF2 to 141° in EuI2, which is accompanied by a rapid decrease in the barriers to linearity, h = E(D∞h) - E(C2v), from 2180 cm-1 to 166 cm-1, respectively. The Eu-X bonds in EuX2 appear to be longer but energetically stronger than those in the respective monohalides EuX, whose properties are studied in this work at the same level of theory as EuX2. The performance of the Ln 4f-in-core pseudopotential (PP) approximation for EuX2 is assessed by comparing the Eu PP-based coupled-cluster (CC) calculations with all-electron CC benchmarks. Incorporating the Eu 4f electrons into the PP is shown to cause large errors: up to 10 deg. in X-Eu-X bond angles, 80% in barriers to linearity, and 0.05 Å in the Eu-X bond lengths, which proves the necessity of an explicit treatment of 4f electrons if high accuracy is the goal. The present results set a benchmark in the field of low-valency lanthanide chemistry, in particular for the calibration of DFT functionals.

Quantum chemical package Jaguar: A survey of recent developments and unique features

This paper is dedicated to the quantum chemical package Jaguar, which is commercial software developed and distributed by Schrödinger, Inc. We discuss Jaguar's scientific features that are relevant to chemical research as well as describe those aspects of the program that are pertinent to the user interface, the organization of the computer code, and its maintenance and testing. Among the scientific topics that feature prominently in this paper are the quantum chemical methods grounded in the pseudospectral approach. A number of multistep workflows dependent on Jaguar are covered: prediction of protonation equilibria in aqueous solutions (particularly calculations of tautomeric stability and pKa), reactivity predictions based on automated transition state search, assembly of Boltzmann-averaged spectra such as vibrational and electronic circular dichroism, as well as nuclear magnetic resonance. Discussed also are quantum chemical calculations that are oriented toward materials science applications, in particular, prediction of properties of optoelectronic materials and organic semiconductors, and molecular catalyst design. The topic of treatment of conformations inevitably comes up in real world research projects and is considered as part of all the workflows mentioned above. In addition, we examine the role of machine learning methods in quantum chemical calculations performed by Jaguar, from auxiliary functions that return the approximate calculation runtime in a user interface, to prediction of actual molecular properties. The current work is second in a series of reviews of Jaguar, the first having been published more than ten years ago. Thus, this paper serves as a rare milestone on the path that is being traversed by Jaguar's development in more than thirty years of its existence.

Improving One-Electron Exact-Two-Component Relativistic Methods with the Dirac-Coulomb-Breit-Parameterized Effective Spin-Orbit Coupling

In photochemical processes, spin-orbit coupling plays a crucial role in determining the outcome of the reaction. However, the exact treatment of the Dirac-Coulomb-Breit two-electron operator required for rigorous inclusion of spin-orbit coupling is computationally prohibitive. To address this challenge, we present a Dirac-Coulomb-Breit-parameterized screened-nuclear spin-orbit factor to approximate two-electron spin-orbit couplings in the effective one-electron spin-orbit Hamiltonian. We propose two schemes, the universal and row-dependent parameterizations, to further improve the accuracy of the method. Benchmark calculations on both atomic and molecular systems are performed and compared to results from the computationally expensive four-component Dirac-Coulomb-Breit method. The Dirac-Coulomb-Breit-parameterized approach offers a more computationally feasible method for accurate spin-orbit coupling calculations.

Relativistic Coupled-Cluster Calculations of Spectroscopic Properties of Copernicium and Flerovium Monoxides

Calculations of spectroscopic properties of the CnO and FlO molecules are performed using ab initio all-electron 4c- and 2c-relativistic coupled-cluster approaches with single, double, and perturbative triple excitations. The corresponding calculation for HgO is also accomplished for comparison with the published data. The dependence of the results on the parameters of the basis set and approximations used is investigated in detail. The overall relative uncertainties of the recommended values on the level of 1-2 % are reached. The calculated spectroscopic constants are indicative of the following trend in the reactivity of the oxides HgO>FlO>CnO. This is confirmed by the trend in the adsorption energies, E_ads , of these molecules on the surfaces of gold, quartz, and Teflon. The predicted rather low E_ads values for the latter case should guarantee their delivery from the recoil chamber to the chemistry set up in gas-phase experiments.

A method to capture the large relativistic and solvent effects on the UV-vis spectra of photo-activated metal complexes

We have recently developed a method based on relativistic time-dependent density functional theory (TD-DFT) that allows the calculation of electronic spectra in solution (Creutzberg, Hedegård, J. Chem. Theory Comput.18, 2022, 3671). This method treats the solvent explicitly with a classical, polarizable embedding (PE) description. Furthermore, it employs the complex polarization propagator (CPP) formalism which allows calculations on complexes with a dense population of electronic states (such complexes are known to be problematic for conventional TD-DFT). Here, we employ this method to investigate both the dynamic and electronic effects of the solvent for the excited electronic states of trans-trans-trans-[Pt(N₃)₂(OH)₂(NH₃)₂] in aqueous solution. This complex decomposes into species harmful to cancer cells under light irradiation. Thus, understanding its photo-physical properties may lead to a more efficient method to battle cancer. We quantify the effect of the underlying structure and dynamics by classical molecular mechanics simulations, refined with a subsequent DFT or semi-empirical optimization on a cluster. Moreover, we quantify the effect of employing different methods to set up the solvated system, e.g., how sensitive the results are to the method used for the refinement, and how large a solvent shell that is required. The electronic solvent effect is always included through a PE potential.

Paramagnetic NMR Shielding Tensors Based on Scalar Exact Two-Component and Spin-Orbit Perturbation Theory

The temperature-dependent Fermi-contact and pseudocontact terms are important contributions to the paramagnetic NMR shielding tensor. Herein, we augment the scalar-relativistic (local) exact two-component (X2C) framework with spin-orbit perturbation theory including the screened nuclear spin-orbit correction for the EPR hyperfine coupling and g tensor to compute these temperature-dependent terms. The accuracy of this perturbative ansatz is assessed with the self-consistent spin-orbit two-component and four-component treatments serving as reference. This shows that the Fermi-contact and pseudocontact interaction is sufficiently described for paramagnetic NMR shifts; however, larger deviations are found for the EPR spectra and the principle components of the EPR properties of heavy elements. The impact of the perturbative treatment is further compared to that of the density functional approximation and the basis set. Large-scale calculations are routinely possible with the multipole-accelerated resolution of the identity approximation and the seminumerical exchange approximation, as shown for [CeTi₆O₃(OiPr)₉(salicylate)₆].

Strong Relativistic Effects in Lanthanide-Based Single-Molecule Magnets

Lanthanide-based single-molecule magnets (SMMs) are promising building blocks for quantum memory and spintronic devices. Designing lanthanide-based SMMs with long spin relaxation time requires a detailed understanding of their electronic structure, including the crucial role of the spin-orbit coupling (SOC). While traditional calculations of SOC using the perturbation theory applied to a solution of the nonrelativistic Schrödinger equation are valid for light atoms, this approach is questionable for systems containing heavy elements such as lanthanides. We investigate the accuracy of the perturbation estimates of SOC by variationally solving the Dirac equation for the [DyO]+ molecule, a prototype of a lanthanide-based SMM. We show that the energy splittings between the M J states involved in spin relaxation depend on the interplay between strong SOC and dynamic electron correlation. We demonstrate that this interplay affects the resonances between the spin and vibrational transitions and, therefore, the spin relaxation time.

Quasi-Relativistic Calculation of EPR g Tensors with Derivatives of the Decoupling Transformation, Gauge-Including Atomic Orbitals, and Magnetic Balance

We present an exact two-component (X2C) ansatz for the EPR g tensor using gauge-including atomic orbitals (GIAOs) and a magnetically balanced basis set expansion. In contrast to previous X2C and four-component relativistic ansätze for the g tensor, this implementation results in a gauge-origin-invariant formalism. Furthermore, the derivatives of the relativistic decoupling matrix are incorporated to form the complete analytical derivative of the X2C Hamiltonian. To reduce the associated computational costs, we apply the diagonal local approximation to the unitary decoupling transformation (DLU). The quasi-relativistic X2C and DLU-X2C Hamiltonians accurately reproduce the results of the parent four-component relativistic theory when accounting for two-electron picture-change effects with the modified screened nuclear spin-orbit approximation in the respective one-electron integrals and integral derivatives. According to our benchmark studies, the uncontracted Dyall and segmented-contracted Karlsruhe x2c-type basis sets perform well when compared to large even-tempered basis sets. Moreover, (range-separated) hybrid density functional approximations such as LC-ωPBE and ωB97X-D are needed to match the experimental findings. The impact of the GIAOs depends on the distribution of the spin density, and their use may change the Δg shifts by 10-50% as shown for [(C₅Me₅)₂Y(μ-S)₂Mo(μ-S)₂Y(C₅Me₅)₂]^-. Routine calculations of large molecules are possible with widely available and comparably low-cost hardware as demonstrated for [Pt(C₆Cl₅)₄]^- with 3003 basis functions and three spin-(1/2) La(II) and Lu(II) compounds, for which we observe good agreement with the experimental findings.

Hyperfine Coupling Constants in Local Exact Two-Component Theory

We present a highly efficient implementation of the electron-nucleus hyperfine coupling matrix within the one-electron exact two-component (X2C) theory. The complete derivative of the X2C Hamiltonian is formed, that is, the derivatives of the unitary decoupling transformation are considered. This requires the solution of the response and Sylvester equations, consequently increasing the computational costs. Therefore, we apply the diagonal local approximation to the unitary decoupling transformation (DLU). The finite nucleus model is employed for both the scalar potential and the vector potential. Two-electron picture-change effects are modeled with the (modified) screened nuclear spin-orbit approach. Our implementation is fully integral direct and OpenMP-parallelized. An extensive benchmark study regarding the Hamiltonian, the basis set, and the density functional approximation is carried out for a set of 12-17 transition-metal compounds. The error introduced by DLU is negligible, and the DLU-X2C Hamiltonian accurately reproduces its four-component "fully" relativistic parent results. Functionals with a large amount of Hartree-Fock exchange such as CAM-QTP-02 and ωB97X-D are generally favorable. The pure density functional r²SCAN performs remarkably and even outperforms the common hybrid functionals TPSSh and CAM-B3LYP. Fully uncontracted basis sets or contracted quadruple-ζ bases are required for accurate results. The capability of our implementation is demonstrated for [Pt(C₆Cl₅)₄]^- with more than 4700 primitive basis functions and four rare-earth single-molecule magnets: [La(OAr*)₃]^-, [Lu(NR₂)₃]^-, [Lu(OAr*)₃]^-, and [TbPc₂]^-. Here, the results with the spin-orbit DLU-X2C Hamiltonian are in an excellent agreement with the experimental findings of all Pt, La, Lu, and Tb molecules.

Electronic spectra of ytterbium fluoride from relativistic electronic structure calculations

We report an investigation of the low-lying excited states of the YbF molecule-a candidate molecule for experimental measurements of the electron electric dipole moment-with 2-component based multi-reference configuration interaction (MRCI), equation of motion coupled cluster (EOM-CCSD) and the extrapolated intermediate Hamiltonian Fock-space coupled cluster (XIHFS-CCSD). Specifically, we address the question of the nature of these low-lying states in terms of configurations containing filled or partially-filled Yb 4f shells. We show that while it does not appear possible to carry out calculations with both kinds of configurations contained in the same active space, reliable information can be extracted from different sectors of Fock space-that is, by performing electron attachment and detachment IHFS-CCSD and EOM-CCSD calculation on the closed-shell YbF+ and YbF- species, respectively. From these calculations we predict Ω = 1/2, 3/2 states, arising from the 4f13σ26s, 4f145d1/6p1, and 4f135d1σ16s configurations to be able to interact as they appear in the same energy range around the ground-state equilibrium geometry. As these states are generated from different sectors of Fock space, they are almost orthogonal and provide complementary descriptions of parts of the excited state manifold. To obtain a comprehensive picture, we introduce a simple adiabatization model to extract energies of interacting Ω = 1/2, 3/2 states that can be compared to experimental observations.

Property-optimized Gaussian basis sets for lanthanides

Property-optimized Gaussian basis sets of split-valence, triple-zeta valence, and quadruple-zeta valence quality are developed for the lanthanides Ce-Lu for use with small-core relativistic effective core potentials. They are constructed in a systematic fashion by augmenting def2 orbital basis sets with diffuse basis functions and minimizing negative static isotropic polarizabilities of lanthanide atoms with respect to basis set exponents within the unrestricted Hartree-Fock method. The basis set quality is assessed using a test set of 70 molecules containing the lanthanides in their common oxidation states and f electron occupations. 5d orbital occupation turns out to be the determining factor for the basis set convergence of polarizabilities in lanthanide atoms and the molecular test set. Therefore, two series of property-optimized basis sets are defined. The augmented def2-SVPD, def2-TZVPPD, and def2-QZVPPD basis sets balance the accuracy of polarizabilities across lanthanide oxidation states. The relative errors in atomic and molecular polarizability calculations are ≤8% for augmented split-valence basis sets, ≤ 2.5% for augmented triple-zeta valence basis sets, and ≤1% for augmented quadruple-zeta valence basis sets. In addition, extended def2-TZVPPDD and def2-QZVPPDD are provided for accurate calculations of lanthanide atoms and neutral clusters. The property-optimized basis sets developed in this work are shown to accurately reproduce electronic absorption spectra of a series of LnCp₃ ^'- complexes (Cp' = C₅H₄SiMe₃, Ln = Ce-Nd, Sm) with time-dependent density functional theory.

Implementation of Relativistic Coupled Cluster Theory for Massively Parallel GPU-Accelerated Computing Architectures

In this paper, we report reimplementation of the core algorithms of relativistic coupled cluster theory aimed at modern heterogeneous high-performance computational infrastructures. The code is designed for parallel execution on many compute nodes with optional GPU coprocessing, accomplished via the new ExaTENSOR back end. The resulting ExaCorr module is primarily intended for calculations of molecules with one or more heavy elements, as relativistic effects on the electronic structure are included from the outset. In the current work, we thereby focus on exact two-component methods and demonstrate the accuracy and performance of the software. The module can be used as a stand-alone program requiring a set of molecular orbital coefficients as the starting point, but it is also interfaced to the DIRAC program that can be used to generate these. We therefore also briefly discuss an improvement of the parallel computing aspects of the relativistic self-consistent field algorithm of the DIRAC program.

Fully relativistic study of polyatomic closed shell E121X3 (X = F, Cl, Br) molecules: effects of Gaunt interaction, relativistic effects and advantages of an exact-two component (X2C) hamiltonian

In this study, all electron relativistic calculations with 4-component Dirac-Coulomb-Breit (DCB), 4-component Dirac-Coulomb (DC), Dyall's spin-free Dirac-Coulomb (SFDC), exact two-component (X2C) and Levy-Leblond non-relativistic hamiltonians calculations were performed in polyatomic closed shell E121X₃ (X = F, Cl, Br) within density functional theory (DFT) with hybrid functional B3LYP, where E121 is the superheavy element (SHE) with Z = 121. The aims of this study were to investigate relativistic effects in polyatomic E121X₃ (X = F, Cl, Br) and verify the importance of Gaunt effects. The results demonstrate that although the effect of Gaunt interaction is small on change equilibrium bond lengths and bonding, it is important to obtain reliable vibrational frequencies. Moreover, it is possible to use the X2C spin-free hamiltonian to lower computational costs in a fully relativistic investigation of polyatomics including the SHE of the 8th period. Finally, a comparison between electron localization function (ELF) analysis and Mulliken population analysis suggests bonding similarity between LaBr₃ and E121Br₃. Graphical Abstract Relativistic 4-Component calculations suggest bond similarity between LaBr₃ and E121Br₃.

GW100: A Slater-Type Orbital Perspective

We calculate complete basis set (CBS) limit-extrapolated ionization potentials (IPs) and electron affinities (EA) with Slater-type basis sets for the molecules in the GW100 database. To this end, we present two new Slater-type orbital (STO) basis sets of triple-(TZ) and quadruple-ζ (QZ) quality, whose polarization is adequate for correlated-electron methods and which contain extra diffuse functions to be able to correctly calculate EAs of molecules with a positive lowest unoccupied molecular orbital (LUMO). We demonstrate that going from TZ to QZ quality consistently reduces the basis set error of our computed IPs and EAs, and we conclude that a good estimate of these quantities at the CBS limit can be obtained by extrapolation. With mean absolute deviations (MAD) from 70 to 85 meV, our CBS limit-extrapolated IP are in good agreement with results from FHI-AIMS, TURBOMOLE, VASP, and WEST, while they differ by more than 130 meV on average from nanoGW. With a MAD of 160 meV, our EA are also in good agreement with the WEST code. Especially for systems with positive LUMOs, the agreement is excellent. With respect to other codes, the STO-type basis sets generally underestimate EAs of small molecules with strongly bound LUMOs. With 62 meV for IPs and 93 meV for EAs, we find much better agreement with CBS limit-extrapolated results from FHI-AIMS for a set of 250 medium to large organic molecules.

Multireference calculations on the ground and lowest excited states and dissociation energy of LuF

High level multireference calculations were performed for LuF for a total of 132 states, including four dissociation channels Lu(²D) + F(²P), Lu(²P) + F(²P), and two Lu(⁴F) + F(²P). The 6s, 5d, and 6p orbitals of lutetium, along with the valence 2p and 3p orbitals of fluorine, were included in the active space, allowing for the accurate description of static and dynamic correlation. The Lu(⁴F) + F(²P) channel has intersystem spin crossings with the Lu(²P) + F(²P) and Lu(²D) + F(²P) channels, which are discussed herein. To obtain spectroscopic constants, bond lengths, and excited states, multi-reference configuration interaction (MRCI) was used at a quadruple-ζ basis set level, correlating also the 4f electrons and corresponding orbitals. Core spin-orbit (C-MRCI) calculations were performed, revealing that 1³Π_0- is the first excited state closely followed by 1³Π₀₊. In addition, the dissociation energy of LuF was determined at different levels of theory, with a range of basis sets. A balance between core correlation and a relativistic treatment of electrons is fundamental to obtain an accurate description of the dissociation energy. The best prediction was obtained with a combination of coupled-cluster single, double, and perturbative triple excitations /Douglas-Kroll-Hess third order Hamiltonian methods at a complete basis set level with a zero-point energy correction, which yields a dissociation value of 170.4 kcal mol^-1. Dissociation energies using density functional theory were calculated using a range of functionals and basis sets; M06-L and B3LYP provided the closest predictions to the best ab initio calculations.

Axion-mediated electron-electron interaction in ytterbium monohydroxide molecule

The YbOH triatomic molecule can be efficiently used to measure the electron electric dipole moment, which violates time-reversal (T) and spatial parity (P) symmetries of fundamental interactions [Kozyryev and Hutzler, Phys. Rev. Lett. 119, 133002 (2017)]. We study another mechanism of the T, P-violation in the YbOH molecule-the electron-electron interaction mediated by the low-mass axionlike particle. For this, we calculate the molecular constant that characterizes this interaction and use it to estimate the expected magnitude of the effect to be measured. It is shown that this molecular constant has the same order of magnitude as the corresponding molecular constant corresponding to the axion-mediated electron-nucleus interaction. According to our estimation, an experiment on YbOH will allow one to set updated laboratory constraints on the CP-violating electron-axion coupling constants.

The DIRAC code for relativistic molecular calculations

DIRAC is a freely distributed general-purpose program system for one-, two-, and four-component relativistic molecular calculations at the level of Hartree-Fock, Kohn-Sham (including range-separated theory), multiconfigurational self-consistent-field, multireference configuration interaction, electron propagator, and various flavors of coupled cluster theory. At the self-consistent-field level, a highly original scheme, based on quaternion algebra, is implemented for the treatment of both spatial and time reversal symmetry. DIRAC features a very general module for the calculation of molecular properties that to a large extent may be defined by the user and further analyzed through a powerful visualization module. It allows for the inclusion of environmental effects through three different classes of increasingly sophisticated embedding approaches: the implicit solvation polarizable continuum model, the explicit polarizable embedding model, and the frozen density embedding model.

Mössbauer isomer shifts and effective contact densities obtained by the exact two-component (X2C) relativistic method and its local variants

A standalone program to calculate scalar relativistic effective contact densities.

Detection of the 5p - 4f orbital crossing and its optical clock transition in Pr9

Recent theoretical works have proposed atomic clocks based on narrow optical transitions in highly charged ions. The most interesting candidates for searches of physics beyond the Standard Model are those which occur at rare orbital crossings where the shell structure of the periodic table is reordered. There are only three such crossings expected to be accessible in highly charged ions, and hitherto none have been observed as both experiment and theory have proven difficult. In this work we observe an orbital crossing in a system chosen to be tractable from both sides: Pr\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}^{9+}$$\end{document}9+. We present electron beam ion trap measurements of its spectra, including the inter-configuration lines that reveal the sought-after crossing. With state-of-the-art calculations we show that the proposed nHz-wide clock line has a very high sensitivity to variation of the fine-structure constant, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha$$\end{document}α, and violation of local Lorentz invariance; and has extremely low sensitivity to external perturbations.

Atomic clocks are based on the frequency of optical transitions and offer high precision. Here the authors demonstrate a configuration crossing in the highly charged ion praseodymium (Pr\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}^{9+}$$\end{document}9+) and determine the frequency of a potential reference transition for a highly charged ion clock.

The Role of Relativistic Many-Body Theory in Electron Electric Dipole Moment Searches Using Cold Molecules

In this review article, we survey some of our results pertaining to the search for the electric dipole moment of the electron (eEDM), using heavy polar molecules. In particular, we focus on the relativistic coupled cluster method (RCCM) and its applications to eEDM searches in YbF, HgX (X = F, Cl, Br, and I), BaF, HgA (A = Li, Na, and K), and YbOH. Our results are presented in a systematic manner, by first introducing the eEDM and its measurement using molecules, the importance of relativistic many-body theory, and finally our results, followed by future prospects.

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.

Four-component relativistic 31P NMR calculations for trans-platinum(ii) complexes: importance of the solvent and dynamics in spectral simulations

We report a combined experimental-theoretical study on the 31P NMR chemical shift for a number of trans-platinum(ii) complexes. Validity and reliability of the 31P NMR chemical shift calculations are examined by comparing with the experimental data. A successful computational protocol for the accurate prediction of the 31P NMR chemical shifts was established for trans-[PtCl2(dma)PPh3] (dma = dimethylamine) complexes. The reliability of the computed values is shown to be critically dependent on the level of relativistic effects (two-component vs. four component), choice of density functionals, dynamical averaging, and solvation effects. Snapshots obtained from ab initio molecular dynamics simulations were used to identify those solvent molecules which show the largest interactions with the platinum complex, through inspection by using the non-covalent interaction program. We observe satisfactory accuracy from the full four-component matrix Dirac-Kohn-Sham method (mDKS) based on the Dirac-Coulomb Hamiltonian, in conjunction with the KT2 density functional, and dynamical averaging with explicit solvent molecules.

Error-consistent segmented contracted all-electron relativistic basis sets of double- and triple-zeta quality for NMR shielding constants

We present property-tailored all-electron relativistic Karlsruhe basis sets for the elements hydrogen to radon.

Electronic spectra of DyF studied by four-component relativistic configuration interaction methods

The electronic states of the DyF molecule below 3.0 eV are studied using 4-component relativistic CI methods. Spinors generated by the average-of-configuration Hartree-Fock method with the Dirac-Coulomb Hamiltonian were used in CI calculations by the KRCI (Kramers-restricted configuration interaction) program. The CI reference space was generated by distributing 11 electrons among the 11 Kramers pairs composed mainly of Dy [4f], [6s], [6p] atomic spinors, and double excitations are allowed from this space to the virtual molecular spinors. The CI calculations indicate that the ground state has the dominant configuration (4f(9))(6s(2))(Ω = 7.5). Above this ground state, 4 low-lying excited states (Ω = 8.5, 7.5, 7.5, 7.5) are found with dominant configurations (4f(10))(6s). These results are consistent with the experimental studies of McCarthy et al. Above these 5 states, 2 states were observed at T0 = 2.39 eV, 2.52 eV by McCarthy et al. and were named as [19.3]8.5 and [20.3]8.5. McCarthy et al. proposed that both states have dominant configurations (4f(9))(6s)(6p), but these configurations are not consistent with the large Re's (∼3.9 a.u.) estimated from the observed rotational constants. The present CI calculations provide near-degenerate states of (4f(10))(6p3/2,1/2), (4f(10))(6p3/2,3/2), and (4f(9))(6s)(6p3/2,1/2) at around 3 eV. The former two states have larger Re (3.88 a.u.) than the third, so that it is reasonable to assign (4f(10))(6p3/2,1/2) to [19.3]8.5 and (4f(10))(6p3/2,3/2) to [20.3]8.5.

A theoretical study on trivalent europium: from the free ion to the water complex

The energy levels within the (7)F and (5)D manifolds of trivalent europium were computed for the free ion and in the crystal field of 6-9 water molecules. Fully relativistic Kramers pairs configuration interaction (KRCI) calculations were performed with different correlation spaces for the free ion, and with the complete open-shell configuration interaction (COSCI) method including the 4f electrons in the active space for the water clusters. The best agreement with experimental data was found with the KRCI method or when including the spin-other-orbit effect in the COSCI calculations. For the free ion, the (7)F6 multiplet is found only 162 cm(-1) higher compared to experiment, while the (5)D(0-3) multiplets are approximately 3100 cm(-1) too high. In the crystal field of six water molecules, the multiplets with J > 0 split by 48-123 cm(-1). The energy separation (7)F0-(5)D0 of the unsplit multiplets is computed within 255 cm(-1)/247 cm(-1) compared to the experimental data for the free ion/in water. It has been found that the effect of higher coordination number or lower symmetry is small, increasing the transition energies by only about 40 cm(-1) by lowering the (7)F(J) states by the same amount. The hypersensitive transition (5)D0-(7)F2 is computed at 17079 cm(-1) with the KRCI method as compared to the experimental value of 16267 cm(-1).