Spin-orbit relativistic long-range corrected time-dependent density functional theory for investigating spin-forbidden transitions in photochemical reactions

A long-range corrected (LC) time-dependent density functional theory (TDDFT) incorporating relativistic effects with spin-orbit couplings is presented. The relativistic effects are based on the two-component zeroth-order regular approximation Hamiltonian. Before calculating the electronic excitations, we calculated the ionization potentials (IPs) of alkaline metal, alkaline-earth metal, group 12 transition metal, and rare gas atoms as the minus orbital (spinor) energies on the basis of Koopmans' theorem. We found that both long-range exchange and spin-orbit coupling effects are required to obtain Koopmans' IPs, i.e., the orbital (spinor) energies, quantitatively in DFT calculations even for first-row transition metals and systems containing large short-range exchange effects. We then calculated the valence excitations of group 12 transition metal atoms and the Rydberg excitations of rare gas atoms using spin-orbit relativistic LC-TDDFT. We found that the long-range exchange and spin-orbit coupling effects significantly contribute to the electronic spectra of even light atoms if the atoms have low-lying excitations between orbital spinors of quite different electron distributions.     

Solvent effects on heavy atom nuclear spin-spin coupling constants: a theoretical study of Hg-C and Pt-P couplings.

The computation of indirect nuclear spin-spin coupling constants, based on the relativistic two-component zeroth order regular approximate Hamiltonian, has been recently implemented by us into the Amsterdam Density Functional program. Applications of the code for the calculation of one-bond metal-ligand couplings of coordinatively unsaturated compounds containing (195)Pt and (199)Hg, including spin-orbit coupling or coordination effects by solvent molecules, show that relativistic density functional calculations are able to reproduce the experimental findings with good accuracy for the systems under investigation. Spin-orbit effects are rather small for these cases, while coordination of the heavy atoms by solvent molecules has a great impact on the calculated couplings. Experimental trends for different solvents are reproduced. An orbital-based analysis of the solvent effect is presented. The scalar relativistic increase of the coupling constants is of the same order of magnitude as the nonrelativistically obtained values, making a relativistic treatment essential for obtaining quantitatively correct results. Solvent effects can be of similar importance.     

Analyzing NMR shielding tensors calculated with two-component relativistic methods using spin-free localized molecular orbitals

A recently developed analysis method [J. Chem. Phys. 127, 124106 (2007)] for NMR spin-spin coupling constants employing two-component (spin-orbit) relativistic density functional theory along with scalar relativistic natural localized molecular orbitals (NLMOs) and natural bond orbitals (NBOs) has been extended for analyzing NMR shielding tensors. Contributions from a field-dependent basis set (gauge-including atomic orbitals) have been included in the formalism. The spin-orbit NLMO/NBO nuclear magnetic shielding analysis has been applied to methane, plumbane, hydrogen iodide, tetracholoplatinate(II), and hexachloroplatinate(IV).     

The role of relativity in the optical response of gold within the time-dependent current-density-functional theory

We included relativistic effects in the formulation of the time-dependent current-density-functional theory for the calculation of linear response properties of metals [P. Romaniello and P. L. de Boeij, Phys. Rev. B (to be published)]. We treat the dominant scalar-relativistic effects using the zeroth-order regular approximation in the ground-state density-functional theory calculations, as well as in the time-dependent response calculations. The results for the dielectric function of gold calculated in the spectral range of 0-10 eV are compared with experimental data reported in literature and recent ellipsometric measurements. As well known, relativistic effects strongly influence the color of gold. We find that the onset of interband transitions is shifted from around 3.5 eV, obtained in a nonrelativistic calculation, to around 1.9 eV when relativity is included. With the inclusion of the scalar-relativistic effects there is an overall improvement of both real and imaginary parts of the dielectric function over the nonrelativistic ones. Nevertheless some important features in the absorption spectrum are not well reproduced, but can be explained in terms of spin-orbit coupling effects. The remaining deviations are attributed to the underestimation of the interband gap (5d-6sp band gap) in the local-density approximation and to the use of the adiabatic local-density approximation in the response calculation.     

Relativistic (SR‐ZORA) quantum theory of atoms in molecules properties

The Quantum Theory of Atoms in Molecules (QTAIM) is used to elucidate the effects of relativity on chemical systems. To do this, molecules are studied using density‐functional theory at both the nonrelativistic level and using the scalar relativistic zeroth‐order regular approximation. Relativistic effects on the QTAIM properties and topology of the electron density can be significant for chemical systems with heavy atoms. It is important, therefore, to use the appropriate relativistic treatment of QTAIM (Anderson and Ayers, J. Phys. Chem. 2009, 115, 13001) when treating systems with heavy atoms. © 2016 Wiley Periodicals, Inc.     

Spin‐orbit ZORA and four‐component Dirac–Coulomb estimation of relativistic corrections to isotropic nuclear shieldings and chemical shifts of noble gas dimers

Hartree–Fock and density functional theory with the hybrid B3LYP and general gradient KT2 exchange‐correlation functionals were used for nonrelativistic and relativistic nuclear magnetic shielding calculations of helium, neon, argon, krypton, and xenon dimers and free atoms. Relativistic corrections were calculated with the scalar and spin‐orbit zeroth‐order regular approximation Hamiltonian in combination with the large Slater‐type basis set QZ4P as well as with the four‐component Dirac–Coulomb Hamiltonian using Dyall's acv4z basis sets. The relativistic corrections to the nuclear magnetic shieldings and chemical shifts are combined with nonrelativistic coupled cluster singles and doubles with noniterative triple excitations [CCSD(T)] calculations using the very large polarization‐consistent basis sets aug‐pcSseg‐4 for He, Ne and Ar, aug‐pcSseg‐3 for Kr, and the AQZP basis set for Xe. For the dimers also, zero‐point vibrational (ZPV) corrections are obtained at the CCSD(T) level with the same basis sets were added. Best estimates of the dimer chemical shifts are generated from these nuclear magnetic shieldings and the relative importance of electron correlation, ZPV, and relativistic corrections for the shieldings and chemical shifts is analyzed. © 2015 Wiley Periodicals, Inc.     

Gradients for two-component quasirelativistic methods. Application to dihalogenides of element 116

The authors report the implementation of geometry gradients for quasirelativistic two-component Hartree-Fock and density functional methods using either the zero-order regular approximation Hamiltonian or spin-dependent effective core potentials. The computational effort of the resulting program is comparable to that of corresponding nonrelativistic calculations, as it is dominated by the evaluation of derivative two-electron integrals, which is the same for both types of calculations. Besides the implementation of derivatives of matrix elements of the one-particle Hamiltonian with respect to nuclear displacements, the calculation of the derivative exchange-correlation energy for the open shell case involves complicated expressions because of the noncollinear approach chosen to define the spin density. A pilot application to dihalogenides of element 116 shows how spin-orbit coupling strongly affects the chemistry of the superheavy p-block elements. While these molecules are bent at a scalar-relativistic level, spin-orbit coupling is so strong that only the 7p3/2 atomic orbitals of element 116 are involved in bonding, which favors linear molecular geometries for dihalogenides with heavy terminal halogen atoms.     

Yb、YbO电子激发态的相对论含时密度泛函理论研究

本文用基于精确二分量哈密顿（exact two—component Hamiltonian）的相对论含时密度泛函理论（time-dependent relativistic density functional theory）计算了Yb和YbO的电子激发态,并利用对称性、自然原子轨道对激发态性质和归属进行了详细分析,所得结果支持实验对YbO基态与激发态的指认．     

Time-dependent relativistic density functional study of Yb and YbO

The low-lying electronic states of Yb and YbO are investigated by using time-dependent relativistic density functional theory, which is based on the newly developed exact two-component Hamiltonian resulting from symmetrized elimination of the small component. The nature of the excited states is analyzed by using the full molecular symmetry. The calculated results support the previous experimental assignment of the ground and excited states of YbO.     

Theoretical study of the electronic spectra of square-planar platinum (II) complexes based on the two-component relativistic time-dependent density-functional theory

In the present work the electronic spectra of [PtCl(4)](2-), [PtBr(4)](2-), and [Pt(CN)(4)](2-) are studied with a recently proposed relativistic time-dependent density-functional theory (TDDFT) based on the two-component zeroth-order regular approximation and a noncollinear exchange-correlation (XC) functional. The contribution to the double group excited states in terms of singlet and triplet single group excited states is estimated through the inner product of the transition density matrix obtained from two-component and scalar relativistic TDDFT calculations to better understand the double group excited states. Spin-orbital coupling effects are found to be very important in order to simulate the electronic spectra of these complexes. The results show that the two-component TDDFT formalism can afford excitation energies with high accuracy for the transition-metal systems studied here when use is made of a proper XC potential.     

Electronic spectrum of UO2(2+) and [UO2Cl4]2- calculated with time-dependent density functional theory

The electronic spectra of UO(2) (2+) and [UO(2)Cl(4)](2-) are calculated with a recently proposed relativistic time-dependent density functional theory method based on the two-component zeroth-order regular approximation for the inclusion of spin-orbit coupling and a noncollinear exchange-correlation functional. All excitations out of the bonding sigma(u) (+) orbital into the nonbonding delta(u) or phi(u) orbitals for UO(2) (2+) and the corresponding excitations for [UO(2)Cl(4)](2-) are considered. Scalar relativistic vertical excitation energies are compared to values from previous calculations with the CASPT2 method. Two-component adiabatic excitation energies, U-O equilibrium distances, and symmetric stretching frequencies are compared to CASPT2 and combined configuration-interaction and spin-orbit coupling results, as well as to experimental data. The composition of the excited states in terms of the spin-orbit free states is analyzed. The results point to a significant effect of the chlorine ligands on the electronic spectrum, thereby confirming the CASPT2 results: The excitation energies are shifted and a different luminescent state is found.     

Calculations of frequency-dependent molecular magnetizabilities with quasi-relativistic time-dependent generalized unrestricted Hartree-Fock method

The time-dependent generalized unrestricted Hartree-Fock (TDGUHF) method combined with a two-component quasi-relativistic Hamiltonian generated from the Douglas-Kroll-Hess (DKH) transformation was developed to calculate frequency-dependent molecular magnetizabilities, which are the linear response quantity of a molecule to an external magnetic field. By calculating the magnetizabilities of H(2)X (X = O, S, Se, and Te), the noble gases (He, Ne, Ar, Kr, and Xe) and small open shell molecules (CH(2), CH(3), and O(2)), we found that scalar relativistic terms affect mainly the diamagnetic magnetizability and spin-orbit (SO) interaction affects the paramagnetic magnetizability.     

Theoretical investigation of electronic structures and excitation energies of doubly N-confused porphyrin and its group 11 transition metal (III) complexes

Density functional theory is carried out to study cis-doubly N-confused porphyrin and its metal (Cu3+, Ag3+, and Au3+) complexes. The electronic structures and bonding situations of these molecules have been investigated by using the natural bond orbital analysis and the topological analysis of the electron localization function. We have studied the electronic spectra of cis-doubly N-confused porphyrin and its metal complexes with time-dependent density functional theory. The introduction of group 11 transition metals leads to blueshifts of their electronic spectra with respect to that of cis-doubly N-confused porphyrin. In particular, the absorption spectra of the copper complex show some weak Q bands that mainly arise from a combination of ligand-to-metal charge transfer and ligand-to-ligand charge transfer transitions. The relativistic time-dependent density functional theory with spin-orbit coupling calculations indicates that the effects of spin-orbit coupling on the excitation energies of the copper and silver complexes are so small that it is safe enough to neglect spin-orbit interactions for these two complexes. However, it has a significant effect on the absorption spectra of the gold complex.     

Relativistic two-component calculations of electronic g-tensors that include spin polarization

The first two-component relativistic density-functional approach for the calculation of electronic g-tensors is reported that includes spin polarization using noncollinear spin-density functionals. The method is based on the relativistic Douglas-Kroll-Hess Hamiltonian and has been implemented into the ReSpect program package. Using three self-consistent-field calculations with orthogonal orientations of total magnetization J, the full g-matrix may be obtained. In contrast to previous spin-restricted two-component treatments, results with the new approach agree excellently with spin-polarized one-component calculations for light-atom radicals. Additionally, unlike one-component approaches, the method also reproduces successfully the negative deltag(parallel)-values of heavy-atom 2sigma radicals and the negative deltag(perpendicular) components in cysteinyl. The new method removes effectively the dilemma existing up to now regarding the simultaneous inclusion of spin polarization and higher-order spin-orbit effects in g-tensor calculations. It is straightforwardly applicable to higher than doublet spin multiplicities and has been implemented with hybrid functionals.     

Time-dependent perturbation theory for vibrational energy relaxation and dephasing in peptides and proteins

Without invoking the Markov approximation, we derive formulas for vibrational energy relaxation (VER) and dephasing for an anharmonic system oscillator using a time-dependent perturbation theory. The system-bath Hamiltonian contains more than the third order coupling terms since we take a normal mode picture as a zeroth order approximation. When we invoke the Markov approximation, our theory reduces to the Maradudin-Fein formula which is used to describe the VER properties of glass and proteins. When the system anharmonicity and the renormalization effect due to the environment vanishes, our formulas reduce to those derived by and Mikami and Okazaki [J. Chem. Phys. 121, 10052 (2004)] invoking the path-integral influence functional method with the second order cumulant expansion. We apply our formulas to VER of the amide I mode of a small amino-acid like molecule, N-methylacetamide, in heavy water.     

103Rh NMR chemical shifts in organometallic complexes: a combined experimental and density functional study

Experimental 103Rh NMR chemical shifts of mono- and binuclear rhodium(I) complexes containing s- or as-hydroindacenide and indacenediide bridging ligands with different ancillary ligands (1,5-cyclooctadiene, ethylene, carbonyl) are presented. A protocol, based on density functional theory calculations, was established to determine 103Rh NMR shielding constants in order to rationalise the effects of electronic and structural variations on the spectroscopic signal, and to gain insight into the efficiency of this computational method when applied to organometallic systems. Scalar and spin-orbit relativistic effects based on the ZORA (zeroth order regular approximation) level have been taken into account and discussed. A good agreement was found for model compounds over a wide range of chemical shifts of rhodium (approximately 10,000 ppm). This allowed us to discuss the experimental and calculated delta(103Rh) in larger complexes and to relate it to their electronic structure.     

Spin–Orbit Coupling in Phosphorescent Iridium(III) Complexes

We study the excited states of two iridium(III) complexes with potential applications in organic light‐emitting diodes: fac‐tris(2‐phenylpyridyl)iridium(III) [Ir(ppy)₃] and fac‐tris(1‐methyl‐5‐phenyl‐3‐n‐propyl‐[1,2,4]triazolyl)iridium(III) [Ir(ptz)₃]. Herein we report calculations of the excited states of these complexes from time‐dependent density functional theory (TDDFT) with the zeroth‐order regular approximation (ZORA). We show that results from the one‐component formulation of ZORA, with spin–orbit coupling included perturbatively, accurately reproduce both the results of the two‐component calculations and previously published experimental absorption spectra of the complexes. We are able to trace the effects of both scalar relativistic correction and spin–orbit coupling on the low‐energy excitations and radiative lifetimes of these complexes. In particular, we show that there is an indirect relativistic stabilisation of the metal‐to‐ligand charge transfer (MLCT) states. This is important because it means that indirect relativistic effects increase the degree to which SOC can hybridise singlet and triplet states and hence plays an important role in determining the optical properties of these complexes. We find that these two compounds are remarkably similar in these respects, despite Ir(ppy)₃ and Ir(ptz)₃ emitting green and blue light respectively. However, we predict that these two complexes will show marked differences in their magnetic circular dichroism (MCD) spectra.     

Time-dependent four-component relativistic density functional theory for excitation energies

Time-dependent four-component relativistic density functional theory within the linear response regime is developed for calculating excitation energies of heavy element containing systems. Since spin is no longer a good quantum number in this context, we resort to time-reversal adapted Kramers basis when deriving the coupled Dirac-Kohn-Sham equation. The particular implementation of the formalism into the Beijing density functional program package utilizes the multipolar expansion of the induced density to facilitate the construction of the induced Coulomb potential. As the first application, pilot calculations on the valence excitation energies and fine structures of the rare gas (Ne to Rn) and Group 12 (Zn to Hg) atoms are reported. To the best of our knowledge, it is the first time to be able to account for spin-orbit coupling within time-dependent density functional theory for excitation energies.