On convergence of the normalized elimination of the small component (NESC) method

Relativistic Quantum Chemical Investigation of Actinide Covalency Measured by Electron Paramagnetic Resonance Spectroscopy

We investigate actinide covalency effects in two [AnCptt3] (An = Th, U) complexes recently studied with pulsed electron paramagnetic resonance spectroscopy, using the Hyperion package to obtain relativistic hyperfine coupling constants from relativistic multiconfigurational wave functions. 1H and 13C HYSCORE simulations using the computed parameters show excellent agreement with the experimental data, highlighting the accuracy of modern relativistic ab initio methods. The extent of covalency indicated from the calculations on [ThCptt3] is in agreement with the original report based on traditional spectral fitting methods, while the covalency in [UCptt3] is found to be previously overestimated. The latter is due to the paramagnetic spin-orbit effect that arises naturally in a relativistic theory of hyperfine coupling and yet was not accounted for in the original study, thus highlighting the necessity of relativistic approaches for the interpretation of magnetic resonance data pertaining to actinides.

Generalized Foldy-Wouthuysen transformation for relativistic two-component methods: Systematic analysis of two-component Hamiltonians

The generalized Foldy-Wouthuysen (GFW) transformation was proposed as a generic form that unifies four types of transformations in relativistic two-component methods: unnormalized GFW(UN), and normalized form 1, form 2, and form 3 (GFW(N1), GFW(N2), and GFW(N3)). The GFW transformation covers a wide range of transformations beyond the simple unitary transformation of the Dirac Hamiltonian, allowing for the systematic classification of all existing two-component methods. New two-component methods were also systematically derived based on the GFW transformation. These various two-component methods were applied to hydrogen-like and helium-like ions. Numerical errors in energy were evaluated and classified into four types: the one-electron Hamiltonian approximation, the two-electron operator approximation, the newly defined "picture difference error (PDE)," and the error in determining the transformation, and errors in multi-electron systems were discussed based on this classification.

Exact two-component Hamiltonians for relativistic quantum chemistry: Two-electron picture-change corrections made simple

Based on self-consistent field (SCF) atomic mean-field (amf) quantities, we present two simple yet computationally efficient and numerically accurate matrix-algebraic approaches to correct both scalar-relativistic and spin-orbit two-electron picture-change effects (PCEs) arising within an exact two-component (X2C) Hamiltonian framework. Both approaches, dubbed amfX2C and e(xtended)amfX2C, allow us to uniquely tailor PCE corrections to mean-field models, viz. Hartree-Fock or Kohn-Sham DFT, in the latter case also avoiding the need for a point-wise calculation of exchange-correlation PCE corrections. We assess the numerical performance of these PCE correction models on spinor energies of group 18 (closed-shell) and group 16 (open-shell) diatomic molecules, achieving a consistent ≈10^-5 Hartree accuracy compared to reference four-component data. Additional tests include SCF calculations of molecular properties such as absolute contact density and contact density shifts in copernicium fluoride compounds (CnF_n, n = 2,4,6), as well as equation-of-motion coupled-cluster calculations of x-ray core-ionization energies of 5d- and 6d-containing molecules, where we observe an excellent agreement with reference data. To conclude, we are confident that our (e)amfX2C PCE correction models constitute a fundamental milestone toward a universal and reliable relativistic two-component quantum-chemical approach, maintaining the accuracy of the parent four-component one at a fraction of its computational cost.

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.

RAQET: Large-scale two-component relativistic quantum chemistry program package

The Relativistic And Quantum Electronic Theory (RAQET) program is a new software package, which is designed for large-scale two-component relativistic quantum chemical (QC) calculations. The package includes several efficient schemes and algorithms for calculations involving large molecules which contain heavy elements in accurate relativistic formalisms. These calculations can be carried out in terms of the two-component relativistic Hamiltonian, wavefunction theory, density functional theory, core potential scheme, and evaluation of electron repulsion integrals. Furthermore, several techniques, which have frequently been used in non-relativistic QC calculations, have been customized for relativistic calculations. This article introduces the brief theories and capabilities of RAQET with several calculation examples. © 2018 Wiley Periodicals, Inc.

Dispersion-Corrected Relativistic Density Functional Theory (DFT) Calculations of Structure and (119)Sn Mössbauer Parameters for M≡SnR Bonding in Filippou's Stannylidyne Complexes of Molybdenum and Tungsten

(119)Sn Mössbauer isomer shift (IS) and quadrupole splitting (ΔEQ) for M≡SnR bonding in metal-stannylidyne complexes trans-[Cl(PMe3)4Mo≡Sn-R] (1), trans-[Cl(PMe3)4W≡Sn-R] (2), trans-[Cl(dppe)2Mo≡Sn-R] (3), trans-[Cl(dppe)2W≡Sn-R] (4), [(dppe)2Mo≡Sn-R](+) (5), [(dppe)2W≡Sn-R](+) (6) (R = C6H3-2,6-Mes2) have been investigated for the first time. Calculations of optimized structures and (119)Sn Mössbauer parameters were carried out at the DFT/TPSS-D3(BJ)/TZVPP/ZORA level of theory. The calculated geometry parameters of stannylidyne complexes of molybdenum and tungsten (1-6) are in good agreement with experimental values of W-Sn and Sn-C bond distances. The calculated values of the isomer shift for the complexes (1-6) are almost same to the experimental values (within ±0.1 mm/s). Experimental values (ISexptl, 2.38-2.50 mm/s) and calculated values (IScalcd, 2.37-2.49 mm/s) of isomer shifts indicate that the oxidation state of tin in the studied complexes with M≡Sn-R bonding is Sn(II). The variations of ISexptl, as a function of Sn s electrons (Ns(Sn)), also exhibit a linear trend. (IS = 0.477Ns(Sn) - 1.888, R(2) = 0.9973). Calculated values of isomer shift (IScalcd) using the linear regression with the Ns(Sn) electron density are in excellent concord with the ISexptl.The calculated values of nuclear quadrupole splitting parameters (ΔEQ(calcd)) of (119)Sn using the relation ΔEQ(calcd) = (0.540 + 0.28) V are in agreement with the experimental values.

An efficient implementation of two-component relativistic exact-decoupling methods for large molecules

We present an efficient algorithm for one- and two-component relativistic exact-decoupling calculations. Spin-orbit coupling is thus taken into account for the evaluation of relativistically transformed (one-electron) Hamiltonian. As the relativistic decoupling transformation has to be evaluated with primitive functions, the construction of the relativistic one-electron Hamiltonian becomes the bottleneck of the whole calculation for large molecules. For the established exact-decoupling protocols, a minimal matrix operation count is established and discussed in detail. Furthermore, we apply our recently developed local DLU scheme [D. Peng and M. Reiher, J. Chem. Phys. 136, 244108 (2012)] to accelerate this step. With our new implementation two-component relativistic density functional calculations can be performed invoking the resolution-of-identity density-fitting approximation and (Abelian as well as non-Abelian) point group symmetry to accelerate both the exact-decoupling and the two-electron part. The capability of our implementation is illustrated at the example of silver clusters with up to 309 atoms, for which the cohesive energy is calculated and extrapolated to the bulk.

Shifts in the ESR spectra of alkali-metal atoms (Li, Na, K, Rb) on helium nanodroplets

He-droplet-induced changes of the hyperfine structure constants of alkali-metal atoms are investigated by a combination of relativistically corrected ab initio methods with a simulation of the helium density distribution based on He density functional theory. Starting from an accurate description of the variation of the hyperfine structure constant in the M-He diatomic systems (M=Li, Na, K, Rb) as a function of the interatomic distance we simulate the shifts induced by droplets of up to 10,000 (4)He atoms. All theoretical predictions for the relative shifts in the isotropic hyperfine coupling constants of the alkali-metal atoms attached to helium droplets of different size are then tied to a single, experimentally derived parameter of Rb.

Development and application of the analytical energy gradient for the normalized elimination of the small component method

The analytical energy gradient of the normalized elimination of the small component (NESC) method is derived for the first time and implemented for the routine calculation of NESC geometries and other first order molecular properties. Essential for the derivation is the correct calculation of the transformation matrix U relating the small component to the pseudolarge component of the wavefunction. The exact form of ∂U/∂λ is derived and its contribution to the analytical energy gradient is investigated. The influence of a finite nucleus model and that of the picture change is determined. Different ways of speeding up the calculation of the NESC gradient are tested. It is shown that first order properties can routinely be calculated in combination with Hartree-Fock, density functional theory (DFT), coupled cluster theory, or any electron correlation corrected quantum chemical method, provided the NESC Hamiltonian is determined in an efficient, but nevertheless accurate way. The general applicability of the analytical NESC gradient is demonstrated by benchmark calculations for NESC/CCSD (coupled cluster with all single and double excitation) and NESC/DFT involving up to 800 basis functions.

Bonding in mercury-alkali molecules: Orbital-driven van der Waals complexes

The bonding situation in mercury-alkali diatomics HgA (²Σ⁺) (A = Li, Na, K, Rb) has been investigated employing the relativistic all-electron method Normalized Elimination of the Small Component (NESC), CCSD(T), and augmented VTZ basis sets. Although Hg,A interactions are typical of van der Waals complexes, trends in calculated D_e values can be explained on the basis of a 3-electron 2-orbital model utilizing calculated ionization potentials and the D_e values of HgA⁺(¹Σ⁺) diatomics. HgA molecules are identified as orbital-driven van der Waals complexes. The relevance of results for the understanding of the properties of liquid alkali metal amalgams is discussed.

On the calculation of Mössbauer isomer shift

A quantum chemical computational scheme for the calculation of isomer shift in Mossbauer spectroscopy is suggested. Within the described scheme, the isomer shift is treated as a derivative of the total electronic energy with respect to the radius of a finite nucleus. The explicit use of a finite nucleus model in the calculations enables one to incorporate straightforwardly the effects of relativity and electron correlation. The results of benchmark calculations carried out for several iron complexes as well as for a number of atoms and atomic ions are presented and compared with the available experimental and theoretical data.

Quasirelativistic theory. II. Theory at matrix level

The Dirac operator in a matrix representation in a kinetically balanced basis is transformed to the matrix representation of a quasirelativistic Hamiltonian that has the same electronic eigenstates as the original Dirac matrix (but no positronic eigenstates). This transformation involves a matrix X, for which an exact identity is derived and which can be constructed either in a noniterative way or by various iteration schemes, not requiring an expansion parameter. Both linearly convergent and quadratically convergent iteration schemes are discussed and compared numerically. The authors present three rather different schemes, for each of which even in unfavorable cases convergence is reached within three or four iterations, for all electronic eigenstates of the Dirac operator. The authors present the theory both in terms of a non-Hermitian and a Hermitian quasirelativistic Hamiltonian. Quasirelativistic approaches at the matrix level known from the literature are critically analyzed in the frame of the general theory.