ReSpect: Relativistic spectroscopy DFT program package.

With the increasing interest in compounds containing heavier elements, the experimental and theoretical community requires computationally efficient approaches capable of simultaneous non-perturbative treatment of relativistic, spin-polarization, and electron correlation effects. The ReSpect program has been designed with this goal in mind and developed to perform relativistic density functional theory (DFT) calculations on molecules and solids at the quasirelativistic two-component (X2C Hamiltonian) and fully relativistic four-component (Dirac-Coulomb Hamiltonian) level of theory, including the effects of spin polarization in open-shell systems at the Kramers-unrestricted self-consistent field level. Through efficient algorithms exploiting time-reversal symmetry, biquaternion algebra, and the locality of atom-centered Gaussian-type orbitals, a significant reduction of the methodological complexity and computational cost has been achieved. This article summarizes the essential theoretical and technical advances made in the program, supplemented by example calculations. ReSpect allows molecules with >100 atoms to be efficiently handled at the four-component level of theory on standard central processing unit-based commodity clusters, at computational costs that rarely exceed a factor of 10 when compared to the non-relativistic realm. In addition to the prediction of band structures in solids, ReSpect offers a growing list of molecular spectroscopic parameters that range from electron paramagnetic resonance parameters (g-tensor, A-tensor, and zero-field splitting), via (p)NMR chemical shifts and nuclear spin-spin couplings, to various linear response properties using either conventional or damped-response time-dependent DFT (TDDFT): excitation energies, frequency-dependent polarizabilities, and natural chiroptical properties (electronic circular dichroism and optical rotatory dispersion). In addition, relativistic real-time TDDFT electron dynamics is another unique feature of the program. Documentation, including user manuals and tutorials, is available at the program's website http://www.respectprogram.org.

Unraveling σ and π Effects on Magnetic Anisotropy in cis-NiA4 B2 Complexes: Magnetization, HF-HFEPR Studies, First-Principles Calculations, and Orbital Modeling.

By using complementary experimental techniques and first-principles theoretical calculations, magnetic anisotropy in a series of five hexacoordinated nickel(II) complexes possessing a symmetry close to C2v , has been investigated. Four complexes have the general formula [Ni(bpy)X2 ]n+ (bpy=2,2'-bipyridine; X2 =bpy (1), (NCS- )2 (2), C2 O42- (3), NO3- (4)). In the fifth complex, [Ni(HIM2 -py)2 (NO3 )]+ (5; HIM2 -py=2-(2-pyridyl)-4,4,5,5-tetramethyl-4,5-dihydro-1H-imidazolyl-1-hydroxy), which was reported previously, the two bpy bidentate ligands were replaced by HIM2 -py. Analysis of the high-field, high-frequency electronic paramagnetic resonance (HF-HFEPR) spectra and magnetization data leads to the determination of the spin Hamiltonian parameters. The D parameter, corresponding to the axial magnetic anisotropy, was negative (Ising type) for the five compounds and ranged from -1 to -10 cm-1 . First-principles SO-CASPT2 calculations have been performed to estimate these parameters and rationalize the experimental values. From calculations, the easy axis of magnetization is in two different directions for complexes 2 and 3, on one hand, and 4 and 5, on the other hand. A new method is proposed to calculate the g tensor for systems with S=1. The spin Hamiltonian parameters (D (axial), E (rhombic), and gi ) are rationalized in terms of ordering of the 3 d orbitals. According to this orbital model, it can be shown that 1) the large magnetic anisotropy of 4 and 5 arises from splitting of the eg -like orbitals and is due to the difference in the σ-donor strength of NO3- and bpy or HIM2 -py, whereas the difference in anisotropy between the two compounds is due to splitting of the t2g -like orbitals; and 2) the anisotropy of complexes 1-3 arises from the small splitting of the t2g -like orbitals. The direction of the anisotropy axis can be rationalized by the proposed orbital model.

Four-Component Relativistic Density-Functional Theory Calculations of Nuclear Spin-Rotation Constants: Relativistic Effects in p-Block Hydrides.

We present an implementation of the nuclear spin-rotation (SR) constants based on the relativistic four-component Dirac-Coulomb Hamiltonian. This formalism has been implemented in the framework of the Hartree-Fock and Kohn-Sham theory, allowing assessment of both pure and hybrid exchange-correlation functionals. In the density-functional theory (DFT) implementation of the response equations, a noncollinear generalized gradient approximation (GGA) has been used. The present approach enforces a restricted kinetic balance condition for the small-component basis at the integral level, leading to very efficient calculations of the property. We apply the methodology to study relativistic effects on the spin-rotation constants by performing calculations on XHn (n = 1-4) for all elements X in the p-block of the periodic table and comparing the effects of relativity on the nuclear SR tensors to that observed for the nuclear magnetic shielding tensors. Correlation effects as described by the density-functional theory are shown to be significant for the spin-rotation constants, whereas the differences between the use of GGA and hybrid density functionals are much smaller. Our calculated relativistic spin-rotation constants at the DFT level of theory are only in fair agreement with available experimental data. It is shown that the scaling of the relativistic effects for the spin-rotation constants (varying between Z(3.8) and Z(4.5)) is as strong as for the chemical shieldings but with a much smaller prefactor.

Communication: The absolute shielding scales of oxygen and sulfur revisited.

We present an updated semi-experimental absolute shielding scale for the (17)O and (33)S nuclei. These new shielding scales are based on accurate rotational microwave data for the spin-rotation constants of H2(17)O [Puzzarini et al., J. Chem. Phys. 131, 234304 (2009)], C(17)O [Cazzoli et al., Phys. Chem. Chem. Phys. 4, 3575 (2002)], and H2(33)S [Helgaker et al., J. Chem. Phys. 139, 244308 (2013)] corrected both for vibrational and temperature effects estimated at the CCSD(T) level of theory as well as for the relativistic corrections to the relation between the spin-rotation constant and the absolute shielding constant. Our best estimate for the oxygen shielding constants of H2(17)O is 328.4(3) ppm and for C(17)O -59.05(59) ppm. The relativistic correction for the sulfur shielding of H2(33)S amounts to 3.3%, and the new sulfur shielding constant for this molecule is 742.9(4.6) ppm.

Spin-rotation and NMR shielding constants in HCl.

The spin-rotation and nuclear magnetic shielding constants are analysed for both nuclei in the HCl molecule. Nonrelativistic ab initio calculations at the CCSD(T) level of approximation show that it is essential to include relativistic effects to obtain spin-rotation constants consistent with accurate experimental data. Our best estimates for the spin-rotation constants of (1)H(35)Cl are CCl = -53.914 kHz and C(H) = 42.672 kHz (for the lowest rovibrational level). For the chlorine shielding constant, the ab initio value computed including the relativistic corrections, σ(Cl) = 976.202 ppm, provides a new absolute shielding scale; for hydrogen we find σ(H) = 31.403 ppm (both at 300 K). Combining the theoretical results with our new gas-phase NMR experimental data allows us to improve the accuracy of the magnetic dipole moments of both chlorine isotopes. For the hydrogen shielding constant, including relativistic effects yields better agreement between experimental and computed values.

The Absolute Shielding Constants of Heavy Nuclei: Resolving the Enigma of the (119)Sn Absolute Shielding.

We demonstrate that the apparent disagreement between experimental determinations and four-component relativistic calculations of the absolute shielding constants of heavy nuclei is due to the breakdown of the commonly assumed relation between the electronic contribution to the nuclear spin-rotation constants and the paramagnetic contribution to the NMR shielding constants. We demonstrate that this breakdown has significant consequences for the absolute shielding constant of (119)Sn, leading to errors of about 1000 ppm. As a consequence, we expect that many absolute shielding constants of heavy nuclei will be in need of revision.

Illumination of the effect of the overlap of lone-pairs on indirect nuclear spin-spin coupling constants.

The effect of electron lone-pairs on the Fermi-contact (FC) contribution to indirect nuclear spin-spin coupling constants is analyzed using new tools for their interpretation. In particular, visualization of spin-spin coupling pathways using the coupling deformation density (CDD) has been employed. Furthermore, the recently developed perturbation-stable localization procedure has been applied for decomposition of CDD and the calculated value of couplings into contributions from localized molecular orbitals (LMOs). Correlation between the overlap of densities of LMOs representing lone-pairs and the Fermi-contact contribution to spin-spin coupling constants has been demonstrated. A new way for analyzing spin-spin couplings using the expansion of CDD as a linear combination of the products of molecular orbitals has been suggested. The considered examples include two- and three-bond phosphor-phosphor couplings. Significance of the obtained insight is not restricted to spin-spin couplings of nuclei possessing lone-pairs, as demonstrated in the example of vicinal hydrogen-hydrogen coupling in ethane.

Effects of finite size nuclei in relativistic four-component calculations of hyperfine structure.

The effect of a finite size model for both the nuclear charge and magnetic moment distributions on calculated EPR hyperfine structure have been studied using a relativistic four-component method based on density functional theory. This approach employs a restricted kinetically balanced basis (mDKS-RKB) and includes spin-polarization using noncollinear spin-density exchange-correlation functionals in the unrestricted fashion. Benchmark calculations have been carried out for a number of small molecules containing Zn, Cd, Ag, and Hg. The present results are compared with those obtained at the Douglas-Kroll-Hess second order (DKH-2) method. The dependence of the results on the quality of the orbital and auxiliary basis sets has been studied. It was found that some basis sets contain irregularities that deteriorate the results. Especial care has to be taken also on the construction of the auxiliary basis for fitting the total electron and spin-densities.

Scalar relativistic calculations of hyperfine coupling tensors using the Douglas-Kroll-Hess method with a finite-size nucleus model.

A scalar relativistic method to calculate hyperfine coupling tensors at the Douglas-Kroll-Hess level has been extended to incorporate a finite-size nucleus model using a Gaussian charge and magnetic moment distribution. Density functional calculations at gradient-corrected and hybrid functional levels have been carried out for the group 11 atoms and for a set of small group 12 molecules, comparing nonrelativistic as well as scalar relativistic results at second-order Douglas-Kroll-Hess level with and without finite-size nucleus. While nonrelativistic calculations underestimate isotropic hyperfine couplings increasingly with increasing nuclear charge, scalar relativistic calculations with point nucleus provide somewhat overestimated values. Inclusion of the finite-size nuclear model in the calculation of the wavefunction, and in the transformed hyperfine operators both decrease the magnitude of the hyperfine couplings. The effects, which are cumulative, improve agreement with experiment.