Second-order Spin-orbit Coupling Research Articles

Is near-“spectroscopic accuracy” possible for heavy atoms and coupled cluster theory? An investigation of the first ionization potentials of the atoms Ga–Kr

Recent developments in ab initio coupled cluster (CC) theory and correlation consistent basis sets have ushered in an era of unprecedented accuracy when studying the spectroscopy and thermodynamics of molecules containing main group elements. These same developments have recently seen application to heavier inorganic or transition metal-containing species. The present work benchmarks conventional single reference coupled cluster theory (up to full configuration interaction for valence electron correlation and coupled cluster with up to full pentuple excitations (CCSDTQP) for core-valence correlation) and explicitly correlated coupled cluster methods [CC with single, double, and perturbative triple substitutions (CCSD(T)-F12)] for the atomic ionization potentials of the six 4p elements (Ga-Kr), a property with experimental error bars no greater than a few cm(-1). When second-order spin orbit coupling effects are included, a composite methodology based on CCSD(T) calculations yielded a mean signed error of just -0.039 kcal mol(-1) and a mean unsigned error of 0.043 kcal mol(-1). Inclusion of post-CCSD(T) correlation corrections reduced both of these values to -0.008 kcal mol(-1) and 0.025 kcal mol(-1), respectively, with the latter corresponding to an average error of just 9 cm(-1). The maximum signed error in the latter scheme was just -0.043 kcal mol(-1) (15 cm(-1)).

High-resolution observation and analysis of the ${\rm I}^{+}_2$I2+ A2Π3/2,u–X 2Π3/2,g system

Rotationally resolved absorption spectra of I(2)(+) were recorded in 12,065-13,062 cm(-1) region by employing optical heterodyne velocity modulation absorption spectroscopy. In total, 4054 lines were assigned to 24 bands in the A(2)Π(3/2,u)-X(2)Π(3/2,g) system spanning the vibrational levels υ'' = 1-4 and υ(n)' = 11-19. The assigned lines were globally fitted and an error of 0.003 cm(-1) was obtained. Rotational constants, B(υ), were used to derive equilibrium parameters B(e)'' = 0.03977725(77) cm(-1), a(e)'' = 1.1819(24)×10(-4) cm(-1), r(e)'' = 2.584386(25) Å of the X(2)Π(3/2,g) state, and B(e)' = 0.0305787(37) cm(-1), a(e)' = 1.2353(23)×10(-4) cm(-1), r(e)' = 2.94758(18) Å of the A(2)Π(3/2,u) state. Vibrational energies were used to derive ω(e)'' = 239.0397(55) cm(-1), ω(e)x(e)'' = 0.64951(87) cm(-1) of the X(2)Π(3/2,g) state and ω(e)' = 138.103(11) cm(-1), ω(e)x(e)' = 0.45027(34) cm(-1) of the A(2)Π(3/2,u) state. The A(2)Π(3/2,u) (υ(n) = 13) state was found to be rotationally perturbed by the a(4)Σ(1/2,u)(-) (υ(n) = 17) state through second-order spin-orbit coupling.

Vacancy clusters created via room temperature irradiation in 6H-SiC

In non-annealed 6H-SiC samples that were electron irradiated at low temperature, a new EPR signal due to a S=1 defect center with exceptionally large zero-field splitting (D=+652 × 10 ―4 cm ―1 , E=―8 x 10- 4 cm ―1 ) has been observed under illumination. A positive sign of D demonstrates that the spin-orbit contribution to the zero-field splitting exceeds by far that of the spin-spin interaction. A principal axis of the fine-structure tilted by 59° against the crystal c-axis as well as the exceptionally high zero-field splitting D can be qualitatively understood by the occurrence of additional close-lying defect levels in defect clusters resulting in comparatively large second-order spin-orbit coupling. A tentative assignment to vacancy clusters is supported by the observed annealing behavior.

Spin−Spin Contributions to the Zero-Field Splitting Tensor in Organic Triplets, Carbenes and BiradicalsA Density Functional and Ab Initio Study

An evaluation study for the direct dipolar electron spin-spin (SS) contribution to the zero-field splitting (ZFS) tensor in electron paramagnetic resonance (EPR) spectroscopy is presented. Calculations were performed on a wide variety of organic systems where the SS contribution to the ZFS dominates over the second-order spin-orbit coupling (SOC) contribution. Calculations were performed using (hybrid) density functional theory (DFT), as well as complete active space self-consistent field (CASSCF) wave functions. In the former case, our implementation is an approximation, because we use the two-particle reduced spin-density matrix of the noninteracting reference system. In the latter case, the SS contribution is approximated by a mean-field method which, nevertheless, gives accurate results, compared to the approximation free computation of the SS part in a CASSCF framework. For the case of the triplet dioxygen molecule, it was shown that restricted open-shell density functional theory (RODFT), as well as CASSCF, can provide accurate spin-spin couplings while spin-unrestricted DFT leads to much larger errors. Furthermore, 15 organic radicals, including several 1,3 and 1,5 diradicals, dinitroxide biradicals, and even a chlorophyll a model system, were examined as test cases to demonstrate the accuracy and efficiency of our approach within a DFT framework. Accurate D values with root-mean-square deviations of 0.0035 cm(-1) were obtained. Furthermore, all trends, including those due to substituent effects, were correctly reproduced. In a different set of calculations, the polyacenes benzene, naphthalene, anthracene, and tetracene were studied. Applying DFT, the absolute D values were noticeably underestimated, but it was possible to correctly reproduce the trend to smaller D values with larger size of the systems. Finally, it was demonstrated that our approach is also well-suited for the study of carbenes. The smaller organic radicals of this work were also studied, through the use of CASSCF wave functions. This was a special advantage in the case of the triplet polyacenes, where the CASSCF approach gave better results than the DFT method. In comparing spin-restricted and spin-unrestricted results, it was shown through a natural orbital analysis and comparison to high-level ab initio calculations that even small amounts of spin polarization introduced by the unrestricted calculations lead to large deviations between the unrestricted Kohn-Sham (UKS) and restricted open-shell Kohn-Sham (ROKS) approaches. It is challenging to understand why the ROKS results show much better correlation with the experimental data.

Optical absorption spectra of substitutional Co 2+ ions in Mg x Cd 1– x Se alloys

Optical absorption spectra of substitutional Co2+ ions in Mgx Cd1–x Se alloys were investigated in the composition region of 0.0 ≤ x ≤ 0.4 and in the wavelength region of 300 to 2500 nm at 4.8 K and 290 K. We observed several absorption bands in the wavelength regions corresponding to the 4A2(4F) → 4T1(4P) transition and the 4A2(4F) → 4T1(4F) transition of Co2+ at a tetrahedral Td point symmetry point in the host crystals, as well as unknown absorption bands. The several absorption bands were analyzed in the framework of the crystal-field theory along with the second-order spin-orbit coupling. The unknown absorption bands were assigned as due to phonon-assisted absorption bands. We also investigated the variations of the crystal-field parameter Dq and the Racah parameter B with composition x in the Mgx Cd1–x Se system. The results showed that the crystal-field parameter (Dq ) increases, on the other hand, the Racah parameter (B ) decreases with increasing composition x, which may be connected with an increase in the covalency of the metal-ligand bond with increasing composition x in the Mgx Cd1–x Se system. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Solvent effects on optically detected magnetic resonance in triplet spin labels

We have calculated solvent effects on the zero-field splitting (ZFS) constants induced by electron spin–spin coupling (SSC) in the low-lying triplet states of azaaromatic molecules in solutions using multiconfiguration self-consistent-field wave functions and the polarizable continuum model. The second-order spin–orbit coupling (SOC) contribution to the splitting of the 3ππ* states is found to be almost negligible, and the calculations therefore provide a good estimate of the ZFS parameters and their solvent dependence based only on the electron spin–spin coupling expectation values. The correlation between the shift in the ZFS and the phosphorescence frequency that has been observed in optically detected magnetic resonance experiments in low-temperature glasses is supported by our direct SSC calculations without taking SOC into account. This makes it possible to distinguish between the two theories that earlier were proposed to explain the inhomogeneous broadening of triplet state spectra, and discard the one that is exclusively based on the SOC-induced mixing of the singlet and triplet states.

Anionic NaCl-type frameworks of [Mn(II)(HCOO)(3)(-)], templated by alkylammonium, exhibit weak ferromagnetism.

We present the synthesis, characterization by IR, TGA, single crystal X-ray structure and magnetic properties of a novel series of NaCl-type frameworks of [AmineH(+)][Mn(HCOO)(3)(-)], templated by alkylammonium. The anionic NaCl-framework of [Mn(HCOO)(3)(-)] is counter-balanced by the alkylammonium cations located in the cavities of the framework to which they are hydrogen-bonded. The divalent manganese ions have octahedral geometry and are bridged by the formate in an anti-anti mode of coordination. All the compounds exhibit long-range antiferromagnetism below 9 K with a slight non-collinear arrangement of the moments. The canting, likely due to second-order spin-orbit coupling, is via a Dzyaloshinski-Moriya antisymmetric exchange mechanism. A spin-flop is observed in each case at fairly low fields. An orthorhombic to monoclinic transformation was observed for the protonated cyclotrimethyleneamine that is accompanied by localization of the cations into two positions below 240 K from the rapid dynamic flipping of the ring observed at room temperature.

Fine and hyperfine structure in three low-lying 3Σ+ states of molecular hydrogen

The fine structure constant (electron spin-spin coupling) and the hyperfine structure parameters (electron-nuclear spin coupling, including spin-rotation and electron-nuclear quadrupole coupling) in the low-lying triplet states b3Σ+ u, a3Σ+ g and e3Σ+ u of molecular hydrogen and deuterium are calculated using a recently developed technique with full configuration interaction and multiconfiguration self-consistent field wave functions. The second-order spin-orbit coupling contribution to the 3Σ+ states splitting is negligible, and the calculations therefore provide a good estimate of the zero-field splitting based only on the electron spin-spin coupling values. For the bound a3Σ+ g state a negligible zero-field splitting is found, in qualitative agreement with the e-a spectrum. The zero-field splitting parameter is considerable for the repulsive b3Σ+ u state (≃1 cm−1) and of intermediate size for the bound e3Σ+ u state. The isotropic hyperfine coupling constant is very large not only for the valence b3Σ+ u state (1580 MHz) but also for the Rydberg a and e triplet states (≃1400 MHz). The quadrupole coupling constants for the deuterium isotopes are negligible (0.04–0.07 MHz) for all studied triplet states. The electric dipole activity of the spin sublevels in the triplet-singlet transitions to the ground state is estimated by means of the quadratic response technique.

Ab initio study of nonhomogeneous broadening of the zero-field splitting of triplet guest molecules in diluted glasses

Nonhomogeneous broadening of phosphorescence lines and microwave signals in optical detection of magnetic resonance (ODMR) has been calculated using multiconfigurational self-consistent field wave functions and the polarized continuum model. The solvent effects on the zero-field splitting (ZFS) parameters in the low-lying triplet states of aza-aromatic molecules are found to be linearly dependent on the solvent-induced shifts in the phosphorescence frequency in agreement with experimental data. The main contribution to the ZFS originates in the dipolar interaction of the two electron spins, the spin–spin coupling. The spin–orbit coupling (SOC) contribution to the ZFS parameter is much larger for the 3nπ* state of pyrazine compared to the 3ππ* states of quinoline. The second-order SOC contribution to the splitting of the 3nπ* state in the pyrazine molecule does not show any appreciable dependence on the dielectric constant of the solvent. This raises doubts about earlier theories for explaining the inhomogeneous broadening in triplet-state spectra based exclusively on the SOC-induced mixing of the singlet and triplet states. We complete the interpretation of the ODMR spectrum of pyrazine by calculating the hyperfine coupling (HFC) tensors in the lowest triplet state using the UB3LYP hybrid functional. An appreciable solvent-induced rotation of the anisotropic HFC tensor axes has been obtained for the 3nπ* state of pyrazine, in particular for 13C and 14N nuclei. This produces additional nonhomogeneous broadening not only in electron–nuclear double resonance spectra, but also in electron paramagnetic resonance signals because the anisotropic HFC perturbation results in an intensity redistribution among the magnetic transitions between the spin sublevels. A small in-plane rotation of the ZFS tensor axes upon solvation has been predicted for quinoline. Rotation of the magnetic axes induced by the interaction with isotropic solvents can provide a new mechanism for spin-lattice relaxation in the triplet state.

Optical Absorption of Co2+ in AgIn5S8 and CuIn5S8 Spinel Crystals

The optical absorption spectra of cobalt-doped AgIn5S8 and CuIn5S8 single crystals grown by a chemical transport reaction method were investigated at 7 K. The absorption peaks due to the Co2+ impurities are well explained in terms of the Td crystal field and the second-order spin-orbit coupling effect. The values of Dq and B calculated from the observed spectra show that the d electron delocalization is slightly larger in the host crystal CuIn5S8 than in AgIn5S8. This may be caused by the shorter tetrahedral bond length of Co–S in CuIn5S8:Co2+ than in AgIn5S8:Co2+.

The pure rotational spectra of SrSH (X̃ 2A′) and SrS (X 1Σ+): Further studies in alkaline-earth bonding

The pure rotational spectrum of the SrSH radical in its ground electronic (X̃ 2A′) and vibrational states has been measured using millimeter/submillimeter-wave direct absorption techniques. This work is the first observation of SrSH with rotational resolution. The spectrum of its deuterium isotopomer SrSD and SrS (X 1Σ+) has been recorded as well. These species were created by the reaction of strontium vapor and H2S, in the presence of a dc discharge. SrS was also made with CS2. For SrSH and SrSD, eight rotational transitions were recorded, respectively, for which asymmetry components up to Ka=8 were measured; fine structure was also resolved in each component. Thirteen transitions of SrS in each of its v=0, 1, and 2 states have additionally been observed. These data have been analyzed and spectroscopic parameters determined for all three species, including spin-rotation terms for the strontium hydrosulfides. From an r0 structure calculation, the bond angle in SrSH was determined to be 91.48(3)°, very close to that of H2S and CaSH. This geometry indicates that SrSH is a covalently bonded molecule, as opposed to linear (and ionic) SrOH. The Sr–S bond length in SrSH was also found to be greater than that of SrS (rSr—S=2.705 Å versus 2.441 Å), indicating a change in bond order. In addition, the spin-rotation interaction in SrSH and SrSD includes a small contribution from the off-diagonal term, (εab+εba)/2, resulting from the crossing of energy levels with ΔJ=0, ΔKa=±1. Second-order spin-orbit coupling appears to make a significant contribution to the spin-rotation splitting, as well, which must arise from mixing of the à 2A′ and B̃ 2A″ excited states.

High-Resolution Spectroscopy of the A4Πr → X4Σ- Band System of MoN

The emission spectrum of MoN between 13 200 and 18 400 cm-1 has been recorded by means of a microwave discharge and a Fourier Transform spectrophotometer (FTS). The transition A4Πr → X4Σ- has been rotationally analysed. Spin-orbit coupling constants have been determined for the A4Πr state. A number of states were studied by the multiconfiguration self consistent field (MCSCF) method with linear response (LR) technique and with account of spin-orbit coupling (SOC) as a perturbation. Besides that the multireference configuration interaction (MRCI) + SOC matrix has been diagonalized. Deviation from an equidistant splitting of the A4Πr state and the large spin-sublevel splitting of the ground state have been qualitatively explained as due to second-order SOC.

Photophysics of phenyl pyridines and bipyridines in different media

Analysis of absorption and emission spectra of 2,4′-bipyridine (2BPy), 4,4′-bipyridine (4BPy) and three isomeric phenyl pyridines (PhPy) in different solvents reveal that the general nature of lowest emitting state is π, π∗. A significant enhancement of fluorescence of 2PhPy at 77 K in relation to 3PhPy has been attributed to a possible through-space interaction of n- and π-electronic clouds. A discernible feature for phenyl pyridines is the increased basicity and polarity in the excited singlet state. The internal conversion seemed to be active in both phenyl pyridines and bipyridines in MCH solvent and for bipyridines in ethanolic solution, the second-order spin-orbit coupling comes into picture.

Optical properties of undoped and Co-doped CuAlGeSe4 and CuAlSnSe4 single crystals

CuAlGeSe4, CuAlSnSe4, CuAlGeSe4:Co2+, and CuAlSnSe4:Co2+ single crystals were grown by the chemical transport reaction method. These single crystals had a defect chalcopyrite structure and a direct band structure. Optical energy gaps at 286 K were found to be 2.394, 1.874, 2.302, and 1.794 eV for CuAlGeSe4, CuAlSnSe4, CuAlGeSe4:Co2+, and CuAlSnSe4:Co2+ single crystals, respectively. Impurity optical-absorption peaks due to cobalt dopants were observed at 12 243, 7002, and 3890 cm−1 in CuAlGeSe4:Co2+ single crystal and 11 949, 7056, and 3920 cm−1 in CuAlSnSe4:Co2+ single crystal at 286 K. Each of these peaks split into four peaks due to the second-order spin-orbit coupling effect at 30 K. The peaks are assigned to the electron transition between the energy levels of a Co2+ ion sited at the cubic Td symmetry point in the host lattice. Then, for CuAlGeSe4:Co2+ and CuAlSnSe4:Co2+ single crystals, the crystal-field parameter Dq is found to be 389 and 392 cm−1, respectively, the first-order spin-orbit coupling parameter λ −194 and −202 cm−1 the second-order spin-orbit coupling parameter p 238 and 242 cm−1, and the Racah parameter B 505 and 483 cm−1.

Nature of the emitting 3MLCT manifold of rhenium(I) (diimine) (CO) 3Cl complexes

Spectroscopic investigations of four Re(NN) (CO) 3Cl complexes (NN = 2,2′-bipyridine, 4,4′-dimethyl-2,2′-bipyridine, 1,10-phenanthroline,or 2,9-dimethyl-1,10-phenanthroline) in the 77—4 K range reveal a single 3MLCT emitting configuration. Temperature dependences of the phosphorescence lifetimes have been analyzed in terms of a multiple state model that yields rate constants and level splittings. A model based on C 2v symmetry that depends on second-order spin-orbit coupling between dπ* configurations is proposed to rationalize the results. Implications for the well-studied Ru(NN) 2+ 3 and Os(II) (NN) 2+ 3 manifolds are discussed.

Vibronic reduction factors for second-order spin-orbit coupling

Second-order vibronic reduction factors for spin-orbit coupling are derived for orbital triplet systems using the recently derived symmetry-related method. This involves the calculation of oscillator overlaps which are projected out of the cubic vibronic states. Details are presented in the weak coupling limit for T(X)e, T(X)t2 and T(X)(e+t2) vibronic systems and in the strong coupling limit for T(X)e and T(X)t2 systems. The analyses are shown to be in agreement with those obtained by other methods. The discussion is then extended to the calculation of the off-diagonal matrix element between the vibronic T1 ground state and the A2 inversion level of a T1 ion for the T(X)t2-system using symmetry-adapted vibronic states. The effects of anisotropy in the problems studied are also briefly discussed.

Tetrahalogenomercury(II) complexes. A study of their electronic spectra, formation constants, ionic strength, and cation effects

The unambiguous electronic absorption spectra of HgX42−(X = Cl, Br, or I) in methanol have been determined for the first time. The spectra were resolved into their component Gaussian bands, and assigned using a correlation diagram for Td symmetry. The effects of second-order spin–orbit coupling account satisfactorily for the observed band intensities and splittings. The formation constants, K4, as a function of ionic strength were computed over the complete spectral range by multiple linear regression analysis and were, extrapolated to infinite dilution, 0.4 ± 0.1 for Hgl42− and HgBr42−, and 5.7 ± 0.2 for HgCl42−. Significant cation effects were observed upon the spectra of HgX2 with added X−, and may partially be explained in terms of the extended Debye–Hückel equation. Key words: electronic absorption spectra, mercury(II) halide complexes, formation constants, ionic strength, Gaussian band analysis.

Strong Jahn-Teller effects in the excited 3T1 state of V3+ ions in III-V materials

Previous studies of the optical absorption bands attributed to the 3A2 to 3T1(F) internal transitions of V3+ ions in GaP, GaAs and InP have shown that a very strong T(X)t2 Jahn-Teller effect is active in the 3T1(F) state. An analysis is presented for the GaP:V3+ system which reconciles the structure of the accompanying zero-phonon line in terms of second-order Jahn-Teller spin-orbit coupling contributions, with the strength of the coupling deduced from the properties of the band. In the cases of GaAs:V3+ and InP:V3+, it is proposed that strong coupling to e modes is also present.

CO binding to hemoglobin: Spin-tunneling temperature dependence, Fe electronic states, and electronic effects on nonadiabatic dynamics

The electronic spin change of the iron in heme proteins that occurs upon the binding of carbon monoxide is investigated theoretically. A group theoretic approach is taken to determine an Fe electronic level scheme that is consistent with the experimentally observed temperature dependence of the rate of binding of CO. We show that a nearly degenerate ground state orbital doublet used with the standard theory for the spin transition involving second-order spin–orbit coupling gives a temperature dependence consistent with the experimental data. Measurements, using techniques independent of the recombination experiments, have produced evidence for this ground state orbital doublet, and we describe additional experimental methods for testing this model. The effect of this electronic transition on the nonadiabaticity of the reaction dynamics as a function of temperature is also calculated.

Moment analysis for absorption and magnetic circular dichroism bands of atomic P←S transitions: Application to matrix-isolated chromium

Equations useful for the moment analysis of magnetic circular dichroism (MCD) and absorption bands of P←S electronic transitions of atoms or ions for any spin multiplicity have been derived. In particular, it is shown that the first through third MCD moments, together with the zeroth and second absorption moments may be employed to obtain such electronic and vibronic parameters as (1) the excited state spin–orbit coupling constant, (2) the excited state orbital g factor, and (3) the contributions of the cubic and noncubic metal/lattice cage modes to the spectral absorption bandwidths. The MCD and absorption spectra of Cr atoms isolated in krypton and xenon matrices are presented. Forbidden transitions between the two allowed 7P←7S bands are observed. Their appearance is ascribed to second-order spin–orbit coupling to the near-lying 7P states. The moment equations are applied in an appropriate manner to the observed allowed bands. Excited state spin–orbit splitting (−14 cm−1:Cr/Kr and −56 cm−1:Cr/Xe) are found to be significantly reduced from the gas phase value (+194 cm−1) for the z7P←7S transition. For the y 7P←S band, an enhancement (+275 cm−1:Cr/Kr) and a reduction (+171 cm−1:Cr/Xe) from the gas phase value of 206 cm−1 are observed. It is further shown that the Jahn–Teller effect is strongly operative in the z 7P←7S Cr band in both matrices.