Spin-orbit Coupling States Research Articles

Spectroscopic and computational characterization of lanthanide-mediated bond activation of ethylamine

Ln (Ln = La and Ce) atom reactions with ethylamine are conducted in a pulsed laser vaporization supersonic molecular beam source. Dehydrogenation and association metal-containing species are observed with time-of-flight mass spectrometry, and the dehydrogenated Ln ethylimido species in the formula Ln(NC2H5) are characterized by single-photon mass-analyzed threshold ionization (MATI) spectroscopy and quantum chemical calculations. The theoretical calculations include density functional theory for both Ln species and a scalar relativity correction, electron correlation, and spin-orbit coupling through multiconfiguration quasi-degenerate second-order perturbation theory for the Ce species. The MATI spectrum of lanthanum ethylimido La(NCH2CH3) has a single vibronic band system from the ionization of the doublet ground state with the La 6s1 configuration, whereas that of the cerium ethylimido Ce(NCH2CH3) displays two vibronic band system from the ionization of the two lowest-energy spin-orbit coupling states with the Ce 4f16s1 configuration. Both Ln ethylimido complexes are formed by the thermodynamically and kinetically favorable concerted dehydrogenation of the amino group. Two additional isomers of Ln(NC2H5) include a four-membered metallacycle Ln(NHCH2CH2) from the dehydrogenation of the amino and methyl groups and a three-membered cycle Ln(NHCHCH3) from the dehydrogenation of the amino and methylene groups. The cyclic isomers are not observed experimentally as they are not populated under the experimental conditions.

Toward Arbitrary Spin‐Orbit Flat Optics Via Structured Geometric Phase Gratings

AbstractReciprocal spin‐orbit coupling (SOC) via geometric phase with flat optics provides a promising platform for shaping and controlling paraxial structured light. Current devices, from the pioneering q‐plates to the recent J‐plates, provide only spin‐dependent wavefront modulation without amplitude control. However, achieving control over all the spatial dimensions of paraxial SOC states requires spin‐dependent control of corresponding complex amplitude, which remains challenging for flat optics. Here, to address this issue, a new type of flat‐optics elements termed structured geometric phase gratings is presented, that is capable of conjugated complex‐amplitude control for orthogonal input circular polarizations. By using a microstructured liquid crystal photoalignment technique, a series of flat‐optics elements is engineered and their excellent precision in arbitrary SOC control is shown. This principle unlocks the full‐field control of paraxial structured light via flat optics, providing a promising way to develop an information exchange and processing units for general photonic SOC states, as well as extra‐/intracavity mode convertors for high‐precision laser beam shaping.

Spin-orbit coupling in molecular complexes beyond van der Waals regime: Key factors for further splitting of 2P3/2 ground state

We report a joint spectroscopic and theoretical study probing spin-orbit coupling (SOC) in a variety of molecular complexes between an iodine atom and a ligand (L) with L ranging from Ar, HF to formic/acetic acids, and glycine/N-methylated glycine derivatives. Cryogenic photoelectron spectroscopy of L·I- (L=HCOOH, CH3COOH) reveals three distinct peaks, identified as three SOC states, denoted as X(1/2), A(3/2), and B(l/2) for the corresponding neutrals. The X and A separation ΔEXA is measured to be 0.10 eV for both, whereas the X and B gap ΔEXB is 0.98 and 0.97 eV for formic and acetic acid, respectively. These new ΔEXA values are compared with the previously reported values for the molecular complexes L·I· with L=Ar, HF, glycine, and A-methylated glycines. All together these complexes encompass a diversity of intermolecular interactions, from van der Waals to weak and strong hydrogen bonding. While the ΔEXB remains similar, the ΔEXA is shown to be extremely sensitive to the type of ligands and interactions, spanning from 5 meV to 150 meV. High-level relativistic quantum calculations including explicit SOC formulism nicely reproduce all experimental SOC splitting. A direct correlation between the magnitude of ΔEXA with the intermolecular interaction strength or bond distance of the neutral complexes—the stronger interaction (shorter bond length), the greater splitting, is established.

Vibronic transitions and spin-orbit coupling of three-membered metallacycles formed by lanthanide-mediated dehydrogenation of dimethylamine.

Metal-mediated N-H and C-H bond activation of aliphatic amines is an effective strategy for synthesizing biologically important molecules. Ln (Ln = La and Ce) atom reactions with dimethylamine are carried out in a pulsed-laser vaporization supersonic molecular beam source. A series of dehydrogenation species are observed with time-of-flight mass spectrometry, and the dehydrogenated Ln-containing species in the formula Ln(CH2NCH3) are characterized by single-photon mass-analyzed threshold ionization (MATI) spectroscopy and quantum chemical calculations. The theoretical calculations include density functional theory for both Ln species and multiconfiguration self-consistent field and quasi-degenerate perturbation theory for the Ce species. The MATI spectrum of La(CH2NCH3) consists of a single vibronic band system, which is assigned to the ionization of the doublet ground state of N-methyl-lanthanaaziridine. The MATI spectrum of Ce(CH2NCH3) displays two vibronic band systems, which are attributed to the ionization of two-pair lowest-energy spin-orbit coupling states of N-methyl-ceraaziridine. Both metallaaziridines are three-membered metallacycles and formed by the thermodynamically and kinetically favorable concerted dehydrogenation of the amino group and one of the methyl groups.

Ultrafast intraband Auger process in self-doped colloidal quantum dots

Summary Investigating the separate dynamics of electrons and holes has been challenging, although it is critical for the fundamental understanding of semiconducting nanomaterials. n-Type self-doped colloidal quantum dots (CQDs) with excess electrons occupying the low-lying state in the conduction band (CB) have attracted a great deal of attention because of not only their potential applications to infrared optoelectronics but also their intrinsic system that offers a platform for investigating electron dynamics without elusive contributions from holes in the valence band. Here, we show an unprecedented ultrafast intraband Auger process, electron relaxation between spin-orbit coupling states, and exciton-to-ligand vibrational energy transfer process that all occur exclusively in the CB of the self-doped β-HgS CQDs. The electron dynamics obtained by femtosecond mid-infrared spectroscopy will pave the way for further understanding of the blinking phenomenon, disproportionate charging in light-emitting diodes, and hot electron dynamics in higher quantum states coupled to surface states of CQDs.

Ultrafast Intraband Auger Process in Self-Doped Colloidal Quantum Dots

Investigating the separate dynamics of electrons and holes has been challenging although it is critical for fundamental understanding of semiconducting nanomaterials. N-type self-doped colloidal quantum dots (CQDs) with excess electrons occupying the low-lying state in the conduction band (CB) have attracted a great deal of attention because of not only their potential applications to infrared optoelectronics but also their intrinsic system offering a platform for investigating electron dynamics without elusive contributions from holes in the valence band. Here, we show an unprecedented ultrafast intraband Auger process, electron relaxation between spin-orbit coupling states, and exciton-to-ligand vibrational energy transfer process that all occur exclusively in the CB of the self-doped β-HgS CQDs. The electron dynamics obtained by femtosecond mid-IR spectroscopy will pave the way for further understanding of the blinking, disproportionately charging in LEDs, and hot electron dynamics in higher quantum states coupled to surface states of CQDs.

Spectroscopic and computational characterization of lanthanide-mediated N–H and C–H bond activation of methylamine

Ln (Ln = La and Ce) atom reactions with methylamine are carried out in a pulsed-laser vaporization supersonic molecular beam source. A series of dehydrogenation species are observed with time-of-flight mass spectrometry, and the dehydrogenated Ln-containing species in the formula Ln(NCH3) are characterized by mass-analyzed threshold ionization (MATI) spectroscopy and density functional theory and multiconfiguration spin-orbit coupling computations. The MATI spectrum of La(NCH3) consists of two vibronic band systems that are assigned to the ionization of the 2A1 ground state of the C3v isomer La(N-CH3) and the 2A' ground state of the Cs isomer La(NH-CH2). The MATI spectrum of Ce(NCH3) also displays two band systems, which are attributed to the ionization of the low-energy spin-orbit coupling states of the C3v isomer Ce(N-CH3). Ln(N-CH3) is formed by the concerted dehydrogenation of the amino group, while La(NH-CH2) is formed by the dehydrogenation of both amino and methyl groups. Ce(NH-CH2) is presumably formed in the reaction based on the computational predictions but not observed by the spectroscopic measurements.

Low-Temperature Spectra and Density Functional Theory Modeling of Ru(II)-Bipyridine Complexes with Cyclometalated Ancillary Ligands: The Excited State Spin-Orbit Coupling Origin of Variations in Emission Efficiencies.

The 77 K emission spectra of cyclometalated ruthenium(II)-2,2'-bipyridine (CM-Ru-bpy) chromophores are very similar to those of related Ru-bpy complexes with am(m)ine or diimmine ancillary ligands, and density functional theory (DFT) modeling confirms that the lowest energy triplet metal to ligand charge transfer (3MLCT) excited states of CM-Ru-bpy and related Ru-bpy complexes have very similar electronic configurations. However, the phosphorescence decay efficiencies of CM-Ru-bpy excited states are about twice those of the conventional Ru-bpy analogues. In contrast to the similar 3MLCT excited state electronic configurations of the two classes of complexes, the CM-Ru-bpy chromophores have much broader visible region MLCT absorptions resulting from several overlapping transitions, even at 87 K. The emitting excited-state emission efficiencies depend on spin-orbit coupling (SOC) mediated intensity stealing from singlet excited states, and this work explores the relationship between the phosphorescence efficiency and visible region absorption spectra of Ru-bpy 3MLCT excited states in the weak SOC limit. The intrinsic 3MLCT emission efficiency, ιem, depends on mixing with singlet excited states whose RuIII-dπ-orbital angular momenta differ from that of the emitting state. DFT modeling of the 1MLCT excited-state electronic configurations that contribute significantly to the lowest energy absorption bands have RuIII-dπ orbitals that differ from those of their emitting 3MLCT excited states. This leads to a very close relationship between ιem and the lowest energy MLCT band absorptivities in Ru-bpy chromophores. Thus, the larger number of 1MLCT transitions that contribute to the lowest energy absorption bands accounts for the enhanced phosphorescence efficiency of Ru-bpy complexes with cyclometalated ancillary ligands.

Surface magnetism in a chiral d -wave superconductor with hexagonal symmetry

Surface properties are examined in a chiral d-wave superconductor with hexagonal symmetry, whose one-body Hamiltonian possesses the intrinsic spin-orbit coupling identical to the one characterizing the topological nature of the Kane-Mele honeycomb insulator. In the normal state spin-orbit coupling gives rise to spontaneous surface spin currents, whereas in the superconducting state there exist besides the spin currents also charge surface currents, due to the chiral pairing symmetry. Interestingly, the combination of these two currents results in a surface spin polarization, whose spatial dependence is markedly different on the zigzag and armchair surfaces. We discuss various potential candidate materials, such as SrPtAs, which may exhibit these surface properties.

Unraveling the hydration-induced ground-state change of AtO+ by relativistic and multiconfigurational wave-function-based methods.

The AtO+ cation is one of the main chemical forms that appear in the astatine Pourbaix diagram. This form can react with closed-shell species in solution, while in the gas phase, it has a spin-triplet ground spin-orbit-free (SOF) state. Spin-orbit coupling (SOC) mixes its MS = 0 component with the 1Σ+ singlet-spin component, while keeping an essentially-spin-triplet SOC ground-state. Therefore, it was suggested that AtO+ undergoes a hydration-induced ground-state change to explain its reactivity in solution with closed-shell species [J. Phys. Chem. B, 2013, 117, 5206-5211]. In this work, we track the nature of the low-lying SOF and SOC states when the hydration sphere of AtO+ is stepwise increased, using relativistic and multiconfigurational wave-function-based methods. This work clarifies previous studies by (i) giving additional arguments justifying a solvation-induced ground-state change in this system and (ii) clearly identifying for the first time the nature of the involved SOF and SOC many-electron states. Indeed, we find at the SOF level that AtO+ undergoes a ground-state reversal between 3Σ- and the closed-shell component of 1Δ, which leads to an essentially-spin-singlet and closed-shell SOC ground-state. This explains the observed reactivity of AtO+ with closed-shell species in solution.

Band gap energies for white nanosheets/yellow nanoislands/purple nanorods of CeO2

The photon band gap energies and spin–orbit coupling states of white nanosheets, purple nanorods and yellow nanoislands of CeO2.

Spin-orbit Splitting and Lifetime Broadening in theA2Δ Electronic State ofl-C5H

Optical absorption bands at ∼18772 and ∼18807 cm−1, previously assigned to A2Δ-X2Π electronic origin band transitions of the linear carbon-chain radicals C5H and C5D, respectively, have been reinvestigated. The spectra have been recorded in direct absorption applying cavity ring-down spectroscopy to a supersonically expanding acetylene/helium plasma. The improved spectra allow deducing a l-C5H upper state spin-orbit coupling constant A′=−0.7(3) cm−1 and a A2Δ lifetime of 1.6±0.3 ps.

Spin‐orbit Ab initio investigation of the photodissociation of dibromomethane in the gas and solution phases

A clear and reliable theoretical investigation on dibromomethane (CH(2)Br(2)) photodissociation is desired. The calculation must consider: (i) relativistic effects; (ii) the potential energy curves (PECs) of spin-orbit coupling states; (iii) geometry optimization by the method with both static and dynamic electron correlations; (iv) solvent effects on the photodissociation in the solution. All these have been considered in this study by state-of-the-art quantum chemical calculations. The experimentally observed photodissociation in the gas phase with products of spin-orbit-coupled states, Br((2)P(3/2)) and Br*((2)P(1/2)), was assigned by multi-state second order multiconfigurational perturbation theory in conjunction with spin-orbit interaction through complete active space state interaction (MS-CASPT2/CASSI-SO) PECs. The mechanisms of the experimentally observed photodissociation and photoisomerization in solvent were elucidated by the MS-CASPT2/CASSI-SO method combined with polarized continuum model of the solvent.

Magneto-optical studies of silver atoms in neon matrices

Abstract Absorption and magnetic circular dichroism measurements have been carried out on silver atoms trapped in neon matrices at cryogenic temperatures. By using the method of moments, it has been possible to show that the degeneracy of the 2 P excited state, obtained from the promotion of an electron from the Ag 5s to the 5p orbital, is lifted under the influence of simultaneous spin–orbit and vibrational coupling with the rare gas cage. From an analysis of the 2 P ← 2 S transition, the 2 P state spin–orbit coupling constant ( λ ) as well as the cubic ( E C ) and noncubic ( E NC ) rare gas cage vibrational mode contributions have been extracted. They are λ = 829 ± 52, E C = 340 ± 54 and E NC = 465 ± 74 cm −1 . The neon matrix has a profound influence on the silver atom spin–orbit coupling constant, increasing it from 614 cm −1 in the gas phase to 829 cm −1 . This large value is in line with the trend previously found for the other rare gas matrices: spin–orbit constant decrease with rare gas atomic mass increase. The trend is: 829 cm −1 (Ag/Ne), 783 cm −1 (Ag/Ar), 638 cm −1 (Ag/Kr), and 583 cm −1 (Ag/Xe). Calculations of the spin–orbit reduction factors using a “supermolecule” model involving the metal atom and the 12 surrounding rare gas atoms mimics the experimental results well, although the predicted value for Ag/Ne is smaller than the observed one by ∼15%. This discrepancy may arise from a slight collapsing of the rare gas cage onto the entrapped silver atom.

State selective double-electron capture processes by Xe3+ and Kr3+

High resolution double-electron capture translational energy-loss spectra have been obtained for Kr3+ in Ar and Xe3+ in Ar and Kr at a collision energy of 6 keV. For the Kr3+ in Ar spectrum the transitions are assigned to excited states in both the projectile and target ions. The Xe3+ in Ar spectrum displays eight well resolved peaks which are attributed to four reaction channels and their corresponding spin-orbit coupling states. The spectrum for Xe3+ in Kr is remarkably similar, however the reaction channels are formed from capture into higher excited states of the target ion confined by energetic and adiabatic potential energy curve crossing parameters.

Magnetic circular dichroism of matrix-isolated Mo atoms: spin-orbit coupling and Jahn-Teller activity

The magnetic circular dichroism and absorption spectra of molybdenum atoms isolated in Ar, Kr, and Xe matrices have been measured. A method of moments analysis has been applied to the spectral results and the z 7P excited state spin-orbit (SO) coupling constants determined. In Ar the SO constant is 126 cm −1, greater than the gas value of 101 cm −1, while in Kr and Xe it is smaller, 84.5 and 57.5 cm −1, respectively. These results compare favorably with the values predicted by a recent theory of SO coupling for metals in matrices. It is further shown that matrix-enhanced second-order SO coupling, which was found to be important in Cr in the rare gas matrices, is negligible in the present systems. In addition, the method of moments was used to determine the contributions of the noncubic rare gas cage vibrational modes to the observed bandwidths, an approach which has been used previously to identify excited state Jahn-Teller activity. It is shown that Mo atoms in all three gas matrices exhibit a strong Jahn-Teller effect on the z 7P state.

The external heavy atom effect: Theory of spin–orbit coupling of alkali and noble metals in rare gas matrices

Recent data from magnetic circular dichroism (MCD) and optical absorption studies of alkali and noble metal atoms in rare gas matrices have shown an interesting and significant influence of the rare gas on the spin–orbit (SO) splitting of the metal excited 2P state. The excited state SO coupling constants extracted from these data can be classified into three major categories: (I) positive and greater than gas phase values, (II) positive and less than gas phase values, and (III) negative and less than gas phase values. A theory for the spin–orbit coupling of a noble or alkali metal in a rare gas matrix is presented. A supermolecule model in which the metal is surrounded by 12 tetradecahedrally situated rare gas atoms is used to calculate the SO splitting. The splitting is found to depend on three quantities: the metal–rare gas σ- and π-type overlap integrals, the ratio of rare gas-to-metal SO coupling constants, and the metal–rare gas molecular orbital mixing coefficients. Using computed overlap integrals and empirical SO coupling constants it is shown that the model is capable of predicting qualitatively the three major categories of metal–rare gas spin–orbit constants. Finally, a semiempirical approach is utilized to estimate the mixing coefficients and quantitative SO ‘‘reduction’’ factors are determined. This parameterless theory is shown to predict all the important trends well.

Resonance enhanced multiphoton ionization spectra of the GeF and GeCl radicals from 400 to 500 nm

The resonance enhanced multiphoton ionization spectra from 400 to 500 nm of the GeF and GeCl radicals are reported. In GeF bands involving transitions to the A 2Σ+, C′ 2Π, D′ 2Π, E 2Σ+, and G 2Δ states were observed. The bands involving transitions to the valence A 2Σ+ state were accounted for by 1+2 and 1+1+1 resonance enhanced multiphoton ionization (REMPI) mechanisms. Bands associated with the other Rydberg states were generated by a 2+1 REMPI mechanism. The spectrum of the GeCl radical arose from 2+1 REMPI excitation through the C′ 2Πr (5pπ) and C 2Πr (4pπ) Rydberg states. The C′ 2Πr state spin–orbit coupling constant was determined by direct measurement of C′ 2Π1/2←←X 2Π1/2 transitions and ‘‘one photon forbidden’’ C′ 2Π3/2←←X 2Π1/2 transitions. A least-squares fit determined the spectroscopic constants of the C′ 2Πr 5pπ Rydberg state of GeCl: Te=42 190±5 cm−1, Ae=81.0±3.5 cm−1, ωe=509.2±5.3 cm−1, and ωexe=3.3±1.1 cm−1.

Magnetic circular dichroism of the potassium atom “blue triplet” in a xenon matrix

The K/Xe “blue triplet” spectrum (730–790 nm) arises from K atoms in three distinct sites. Each site gives rise to a similar 2S→ 2P triplet pattern. The effective excited state spin-orbit coupling constant is −170 cm −1 compared to the values −213 and −196 cm −1 for Na/Xe and Li/Xe respectively.

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.