GRECP/MRD‐CI calculations of spin‐orbit splitting in ground state of Tl and of spectroscopic properties of TlH

The generalized relativistic effective core potential (GRECP) approach is employed in the framework of multireference single‐ and double‐excitation configuration interaction (MRD‐CI) method to calculate the spin‐orbit splitting in the ²P^o ground state of the Tl atom and spectroscopic constants for the 0⁺ ground state of TlH. The 21‐electron GRECP for Tl is used, and the outer core 5s and 5p pseudospinors are frozen with the help of the level shift technique. The spin‐orbit selection scheme with respect to relativistic multireference states and the corresponding code are developed and applied in the calculations. In this procedure both correlation and spin‐orbit interactions are taken into account. A [4,4,4,3,2] basis set is optimized for the Tl atom and employed in the TlH calculations. Very good agreement is found for the equilibrium distance, vibrational frequency, and dissociation energy of the TlH ground state (R_e=1.870 Å, ω_e=1420 cm⁻¹, D_e=2.049 eV) as compared with the experimental data (R_e=1.872 Å, ω_e=1391 cm⁻¹, D_e=2.06 eV). © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 409–421, 2001     

Theoretical calculation of the electronic states with spin‐orbit effects of the molecule NaRb

The potential energy curves of the molecule NaRb have been calculated for the 60 low‐lying electronic states in the Ω‐representation. Using an ab‐initio method the calculation is based on nonempirical pseudo‐potential in the interval 3.0a_o ≤ R ≤ 44.0a_o of the internuclear distance. The spin‐orbit effects have been taken into account through a semiempirical spin‐orbit pseudo‐potential added to the electrostatic Hamiltonian with Gaussian basis sets for both atoms. The spectroscopic constants have been calculated for 42 states and the components of the spin‐orbit splitting have been identified for the states (1, 2, 5)³Π and (1, 2)³Δ. The comparison of the present results with those available in literature shows a good agreement, whereas the other results, to the best of our knowledge, are given here for the first time. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Excited states of OsO4: A comprehensive time‐dependent relativistic density functional theory study

A large number of scalar as well as spinor excited states of OsO₄, in the experimentally accessible energy range of 3–11 eV, have been captured by time‐dependent relativistic density functional linear response theory based on an exact two‐component Hamiltonian resulting from the symmetrized elimination of the small component. The results are grossly in good agreement with those by the singles and doubles coupled‐cluster linear response theory in conjunction with relativistic effective core potentials. The simulated‐excitation spectrum is also in line with the available experiment. Furthermore, combined with detailed analysis of the excited states, the nature of the observed optical transitions is clearly elucidated. It is found that a few scalar states of ³T₁ and ³T₂ symmetries are split significantly by the spin‐orbit coupling. The possible source for the substantial spin‐orbit splittings of ligand molecular orbitals is carefully examined, leading to a new interpretation on the primary valence photoelectron ionization spectrum of OsO₄. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Ab initio calculation of the Dzyaloshinskii–Moriya parameters: Spin–orbit GSO‐HF,DFT, and CI approaches

We present ab initio methods to determine the Dzyaloshinskii–Moriya (DM) parameter, which provides the anisotropic effects of noncollinear spin systems. For this purpose, we explore various general spin orbital (GSO) approaches, such as Hartree–Fock (HF), density functional theory (DFT), and configuration interaction (CI), with one‐electron spin–orbit coupling (SOC1). As examples, two simple D_3h‐symmetric models, H₃ and B(CH₂)₃, are examined. Implications of the computational results are discussed in relation to as isotropic and anisotropic interactions of molecular‐based magnets. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Full four‐component relativistic calculations of the one‐bond 77Se–13C spin‐spin coupling constants in the series of selenium heterocycles and their parent open‐chain selenides

Four‐component relativistic calculations of ⁷⁷Se–¹³C spin–spin coupling constants have been performed in the series of selenium heterocycles and their parent open‐chain selenides. It has been found that relativistic effects play an essential role in the selenium–carbon coupling mechanism and could result in a contribution of as much as 15–25% of the total values of the one‐bond selenium–carbon spin‐spin coupling constants. In the overall contribution of the relativistic effects to the total values of ¹J(Se,C), the scalar relativistic corrections (negative in sign) by far dominate over the spin‐orbit ones (positive in sign), the latter being of less than 5%, as compared to the former (ca 20%). A combination of nonrelativistic second‐order polarization propagator approach (CC2) with the four‐component relativistic density functional theory scheme is recommended as a versatile tool for the calculation of ¹J(Se,C). Solvent effects in the values of ¹J(Se,C) calculated within the polarizable continuum model for the solvents with different dielectric constants (ε 2.2–78.4) are next to negligible decreasing negative ¹J(Se,C) in absolute value by only about 1 Hz. The use of the locally dense basis set approach applied herewith for the calculation of ⁷⁷Se–¹³C spin‐spin coupling constants is fully justified resulting in a dramatic decrease in computational cost with only 0.1–0.2‐Hz loss of accuracy. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

Spin–Orbit Contributions in High‐Spin Nitrenes/Carbenes: A Hybrid CASSCF/MRMP2 Study of Zero‐Field Splitting Tensors

Zero‐field splitting (ZFS) tensors ( D tensors) of organic high‐spin oligonitrenes/oligocarbenes up to spin‐septet are quantitatively determined on the basis of quantum chemical calculations. The spin–orbit contributions, D ^SO tensors are calculated in terms of a hybrid CASSCF/MRMP2 approach, which was recently proposed by us. The spin–spin counterparts, D ^SS tensors are computed based on McWeeny–Mizuno’s equation in conjunction with the RODFT spin densities. The present calculations show that more than 10 % of ZFS arises from spin–orbit interactions in the high‐spin nitrenes under study. Contributions of spin‐bearing site–site interactions are estimated with the aid of a semi‐empirical model for the D tensors and found to be ca. 5 % of the D ^SO tensor. The analysis of intermediate states reveal that the largest contributions to the calculated D ^SO tensors are attributed to intra‐site spin flip excitations and delocalized π and π* orbitals play an important role in the inter‐site spin–orbit interactions.     

Theoretical study of the Au–ethylene interaction

The basis‐set dependence and quasirelativistic and nonrelativistic effects on the Au C₂H₄ interaction are examined at the ab initio level. The effects on the interaction energies are modulated by f‐type polarization orbitals, using 19‐VE quasirelativistic pseudopotentials. Oscillation in the equilibrium Au C distance as well as in the interaction energy are sensitive to the electron correlation potential. These effects are evaluated at several levels of theory, ranging from MP2 to CCSD(T). The nature of the Au C₂H₄ interaction is related to a simple dispersion expression involving the individual properties of each component and its long‐distance behavior. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 73: 317–324, 1999     

Theoretical study of spectroscopic and molecular properties of several low‐lying electronic states of CO molecule

The potential energy curves (PECs) of eight low‐lying electronic states (X¹Σ⁺, a³Π, a′³Σ⁺, d³Δ, e³Σ^?, A¹Π, I¹Σ^?, and D¹Δ) of the carbon monoxide molecule have been studied by an ab initio quantum chemical method. The calculations have been performed using the complete active space self‐consistent field method, which is followed by the valence internally contracted multireference configuration interaction (MRCI) approach in combination with the correlation‐consistent aug‐cc‐pV5Z basis set. The effects on the PECs by the core‐valence correlation and relativistic corrections are included. The way to consider the relativistic corrections is to use the third‐order Douglas–Kroll Hamiltonian approximation at the level of a cc‐pV5Z basis set. Core‐valence correlation corrections are performed using the cc‐pCVQZ basis set. To obtain more reliable results, the PECs determined by the MRCI calculations are corrected for size‐extensivity errors by means of the Davidson modification (MRCI+Q). The spectroscopic parameters (D_e, T_e, R_e, ω_e, ω_ex_e, ω_ey_e, B_e, α_e, and γ_e) of these electronic states are calculated using these PECs. The spectroscopic parameters are compared with those reported in the literature. Using the Breit–Pauli operator, the spin–orbit coupling effect on the spectroscopic parameters is discussed for the a³Π electronic state. With the PECs obtained by the MRCI+Q/aug‐cc‐pV5Z+CV+DK calculations, the complete vibrational states of each electronic state have been determined. The vibrational manifolds have been calculated for each vibrational state of each electronic state. The vibrational level G(ν), inertial rotation constant B_ν, and centrifugal distortion constant D_ν of the first 20 vibrational states when the rotational quantum number J equals zero are reported and compared with the experimental data. Comparison with the measurements demonstrates that the present spectroscopic parameters and molecular constants determined by the MRCI+Q/aug‐cc‐pV5Z+CV+DK calculations are both reliable and accurate. © 2012 Wiley Periodicals, Inc.     

All‐electron relativistic computations on the low‐lying electronic states,bond length,and vibrational frequency of CeF diatomic molecule with spin–orbit coupling effects

Ab initio all‐electron computations have been carried out for Ce⁺ and CeF, including the electron correlation, scalar relativistic, and spin–orbit coupling effects in a quantitative manner. First, the n‐electron valence state second‐order multireference perturbation theory (NEVPT2) and spin–orbit configuration interaction (SOCI) based on the state‐averaged restricted active space multiconfigurational self‐consistent field (SA‐RASSCF) and state‐averaged complete active space multiconfigurational self‐consistent field (SA‐CASSCF) wavefunctions have been applied to evaluations of the low‐lying energy levels of Ce⁺ with [Xe]4f¹5d¹6s¹ and [Xe]4f¹5d² configurations, to test the accuracy of several all‐electron relativistic basis sets. It is shown that the mixing of quartet and doublet states is essential to reproduce the excitation energies. Then, SA‐RASSCF(CASSCF)/NEVPT2 + SOCI computations with the Sapporo(‐DKH3)‐2012‐QZP basis set were carried out to determine the energy levels of the low‐lying electronic states of CeF. The calculated excitation energies, bond length, and vibrational frequency are shown to be in good agreement with the available experimental data. © 2018 Wiley Periodicals, Inc.     

Magnitude of Finite‐Nucleus‐Size Effects in Relativistic Density Functional Computations of Indirect NMR Nuclear Spin–Spin Coupling Constants

A spherical Gaussian nuclear charge distribution model has been implemented for spin‐free (scalar) and two‐component (spin–orbit) relativistic density functional calculations of indirect NMR nuclear spin–spin coupling (J‐coupling) constants. The finite nuclear volume effects on the hyperfine integrals are quite pronounced and as a consequence they noticeably alter coupling constants involving heavy NMR nuclei such as W, Pt, Hg, Tl, and Pb. Typically, the isotropic J‐couplings are reduced in magnitude by about 10 to 15 % for couplings between one of the heaviest NMR nuclei and a light atomic ligand, and even more so for couplings between two heavy atoms. For a subset of the systems studied, viz. the Hg atom, Hg₂²⁺, and Tl? X where X=Br, I, the basis set convergence of the hyperfine integrals and the coupling constants was monitored. For the Hg atom, numerical and basis set calculations of the electron density and the 1s and 6s orbital hyperfine integrals are directly compared. The coupling anisotropies of TlBr and TlI increase by about 2 % due to finite‐nucleus effects.     

Thiocyanate‐free ruthenium(II) tetrabenzoporphyrin sensitizers for photoelectrochemical cell: A DFT/TD‐DFT probe for stability of axial donor ligands

Although previously studied [(HOOC)₄(TBPor)Ru(NCS)₂]^2– ( A ; TBPor = tetrabenzoporphrin) avoided the intrinsic π‐stacking aggregation of planar metallophorphryins via incorporating two axial ligands, these isothiocyanato groups are believed to be the weakest part of the sensitizer while operating in dye‐sensitized solar cells (DSSCs). In this work, a series of thiocyanate‐free ruthenium porphyrin complexes featuring with phenyl/substituted‐phenyl axial groups, [(HOOC)₄(TBPor)Ru(L′)₂]^2– (L′ = Ph ( 1 ), PhF₂ ( 2 ), PhCl₂ ( 3 ), PhBr₂ ( 4 ), and PhI₂ ( 5 )), have been examined using density functional theory (DFT) and time‐dependent DFT (TD‐DFT). Both analyses of electronic structures and calculations of interaction energies demonstrate that the Ru‐L′ interaction in 1 – 5 is significantly enhanced relative to the Ru‐NCS in A , which will raise chemical stability of the former in DSSCs. Single‐electron oxidation mechanism has been proposed. Oxidation potentials (E⁰) are increased by 0.2–0.6 V when changing axial groups from NCS to Ph/PhX₂. The spin‐orbit coupling (SOC) relativistic effects can be negligible in computing E⁰ values. TD‐DFT calculations show that 1 – 5 have more intense Q band in the visible region than A does. Taken together, high chemical stability, suitable oxidation potential and expanding absorption spectra would allow for potential applications of the thiocyanate‐free sensitizers in DSSCs. © 2016 Wiley Periodicals, Inc.     

Relativistic effects and the halogen dependencies in the 13C chemical shifts of CH4−nIn,CH4−nBrn,CCl4−nIn,and CBr4−nIn (n=0–4)

Linear and nonlinear halogen dependencies of the ¹³C magnetic shielding constants of CH_4−nI_n, CH_4−nBr_n, CCl_4−nI_n, and CBr_4−nI_n were fairly reproduced by the ab initio generalized unrestricted Hartree–Fock (GUHF)/finite perturbation (FP) method including spin‐orbit (SO) interaction and spin‐free relativistic (SFR) terms. As seen from the experimental trends, the calculated ¹³C chemical shifts in CCl_4−nI_n and CBr_4−nI_n depend linearly on n=0–4, while those in CH_4−nI_n and CH_4−nBr_n depend nonlinearly. We found that both the linear and nonlinear dependencies are due to the relativistic effects, and especially due to the Fermi–Contact (FC) term originating from the SO interaction. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 528–536, 2001     

NMR shielding constants of CuX,AgX, and AuX (X = F,Cl, Br,and I) investigated by density functional theory based on the Douglas–Kroll–Hess Hamiltonian

Two‐component relativistic density functional theory (DFT) with the second‐order Douglas–Kroll–Hess (DKH2) one‐electron Hamiltonian was applied to the calculation of nuclear magnetic resonance (NMR) shielding constant. Large basis set dependence was observed in the shielding constant of Xe atom. The DKH2‐DFT‐calculated shielding constants of I and Xe in HI, I₂, CuI, AgI, and XeF₂ agree well with those obtained by the four‐component relativistic theory and experiments. The Au NMR shielding constant in AuF is extremely more positive than in AuCl, AuBr, and AuI, as reported recently. This extremely positive shielding constant arises from the much larger Fermi contact (FC) term of AuF than in others. Interestingly, the absolute values of the paramagnetic and the FC terms are considerably larger in CuF and AuF than in others. The large paramagnetic term of AuF arises from the large d‐components in the Au d_π –F p_π and Au sd_σ–F p_σ molecular orbitals (MOs). The large FC term in AuF arises from the small energy difference between the Au sd_σ + F p_σ and Au sd_σ–F p_σ MOs. The second‐order magnetically relativistic effect, which is the effect of DKH2 magnetic operator, is important even in CuF. This effect considerably improves the overestimation of the spin‐orbit effect calculated by the Breit–Pauli magnetic operator. © 2013 Wiley Periodicals, Inc.     

Relativistic and Non‐Relativistic Electronic Molecular‐Structure Calculations for Dimers of 4p‐, 5p‐, and 6p‐Block Elements

We report results of non‐relativistic and two‐component relativistic single‐reference coupled‐cluster with single and double and perturbative triple excitations [CCSD(T)] treatments for the 4p‐block dimers Ga₂ to Br₂, the 5p‐block dimers In₂ to I₂, and their atoms. Extended basis sets up to pentuple zeta are employed and energies extrapolated to the complete basis‐set limit. Relativistic and non‐relativistic results for the dissociation energy D_e are in close agreement with each other and previously published data, provided non‐relativistic or scalar‐relativistic results are corrected for spin–orbit contributions taken from the literature. An exception is Te₂ where theoretical results scatter by 0.085 eV. By virtue of this agreement it is unexpected that comparison with the experimental D₀ or D_e dissociation energies (zero‐point vibrational effects are negligible in this context) reveal errors larger than 0.1 eV for Ga₂, Ge₂, and Sb₂. Only relativistic treatments are presented for the 6p‐block cases Tl₂ to At₂. Sufficient agreement with experimental data is found only for Pb₂ and Bi₂, the deviation of the computed and experimental D₀ values for Po₂ is again larger than 0.1 eV. Deviations of 0.1 eV between the computed and experimental D₀ values are a major reason for concern and call for additional investigations in both fields to clarify the situation.     

Spin uncoupling in ethylene activation by palladium and platinum atoms

Spin‐dependent effects in complex formation reactions of the ethylene molecule with palladium and platinum atoms were studied by electron correlation calculations with account of spin–orbit coupling. Simple correlation diagrams illustrating spin‐uncoupling mechanisms were obtained, showing that the low spin state of the transition‐metal atom or the transition‐metal atom complex is always more reactive than are the high spin states because of the involvement of the triplet excited molecule in the chemical activation. Spin–orbit coupling calculations of the reaction between a platinum atom and ethylene explain the high‐spin Pt(³D) reactivity as due to an effective spin flip at the stage of the weak triplet complex formation. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 72: 581–596, 1999     

GRECP/5e‐MRD‐CI calculation of the electronic structure of PbH

The correlation calculation of the electronic structure of PbH is carried out with the generalized relativistic effective core potential (GRECP) and multireference single‐ and double‐excitation configuration interaction (MRD‐CI) methods. The 22‐electron GRECP for Pb is used and the outer core 5s, 5p, and 5d pseudospinors are frozen using the level‐shift technique, so only five external electrons of PbH are correlated. A new configuration selection scheme with respect to the relativistic multireference states is employed in the framework of the MRD‐CI method. The [6, 4, 3, 2] correlation spin–orbit basis set is optimized in the coupled cluster calculations on the Pb atom using a recently proposed procedure, in which functions in the spin–orbital basis set are generated from calculations of different ionic states of the Pb atom and those functions are considered optimal that provide the stationary point for some energy functional. Spectroscopic constants for the two lowest‐lying electronic states of PbH (²Π_1/2, ²Π_3/2) are found to be in good agreement with the experimental data. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Two‐Orbital Three‐Electron Stabilizing Interaction for Direct Co2+As3+ Bonds involving Square‐Planar CoO4 in BaCoAs2O5

The quest for new oxides with cations containing active lone‐pair electrons (E) covers a broad field of targeted specificities owing to asymmetric electronic distribution and their particular band structure. Herein, we show that the novel compound BaCoAs₂O₅, with lone‐pair As³⁺ ions, is built from rare square‐planar Co²⁺O₄ involved in direct bonding between As³⁺E and Co²⁺ d_z2 orbitals (Co? As=2.51 Å). By means of DFT and Hückel calculations, we show that this σ‐type overlapping is stabilized by a two‐orbital three‐electron interaction allowed by the high‐spin character of the Co²⁺ ions. The negligible experimental spin‐orbit coupling is expected from the resulting molecular orbital scheme in O₃AsE–CoO₄ clusters.     

Selenophene‐Flanked Diketopyrrolopyrrole Based Conjugated Polymers for Ambipolar Field‐Effect Transistors

The development of selenophene‐flanked DPP (SeDPP) based copolymers, especially for the ambipolar ones, lags behind other aromatic group flanked DPP‐based polymers. Herein, we report two new ambipolar SeDPP‐based conjugated polymers. One is the alternating polymer PSeDPPFT with normal SeDPP and 3,4‐difluorothiophene units. The other is PSeFDFT , in which the electron acceptor unit is replaced by a new SeDPP derivative, referred as to half‐fused SeDPP. The more planar structure of half‐fused SeDPP endows the backbone of PSeFDFT with good rigidity and planarity. Both polymers exhibit ambipolar transporting properties in air. The PSeFDFT based field‐effect transistors (FETs) display higher and more balanced ambipolar properties with μ_h^ave of 0.27 cm²·V^–1·s^–1, μ_e^ave of 0.18 cm²·V^–1·s^–1, and μ_h^ave/μ_e^ave of 1.5 than those of PSeDPPFT (μ_h^ave = 0.11 cm²·V^–1·s^–1, μ_e^ave = 0.042 cm²·V^–1·s^–1, and μ_h/μ_e = 2.6). This is attributed to the more planar structure, lower LUMO level, higher HOMO level, and better interchain packing orientations of PSeFDFT by comparing with PSeDPPFT . Therefore, a new molecular design strategy to modulate the hole and electron transporting properties is proposed for conjugated D‐A polymers.