Matrix Elements Of Spin-orbit Interaction Research Articles

The NbN C3Π−X3Δ (1–0) band: Experimental and theoretical study of the spin-orbit interaction between the C3Π and e1Π states

The NbN C3Π−X3Δ (1–0) band is studied in the free-jet setup. The spin-orbit interaction between v=1 of C3Π1 and e1Π states destroyed the symmetric splitting of C3Π substates. Unusually high 685cm−1 spin-orbit interaction matrix element between them pushed the 3Π1 substate below 3Π0 component. Our ab initio calculations estimate 3Π2-3Π0 separation 414cm−1, which is in an excellent agreement with the observed value 404cm−1, and places the 3Π1 state 244cm−1 below 3Π0 state, in somewhat poor agreement with the experimental separation of 449cm−1. This error is primarily due to the error in our calculated unperturbed 3Π1-1Π energy separation.

Analysis of Dissociation—Recombination Processes for the CO2 Molecule with the Spin—Orbit Coupling Taken into Account

The dissociation CO2(X 1Σ) + M → CO(X 1Σ) + O(3P) + M and recombination CO(X 1Σ) + O(3P) + M → CO2(X 1Σ) + M processes are considered with the spin—orbit coupling taken into account in the ground and several excited states of the CO2 molecule. Because of the specific features of mutual position of potential energy surfaces of the CO2 molecule in the ground and several excited states and the large values of spin—orbit interaction matrix elements, which causes the quantum nonadiabatic transition of the molecule from one state to another, these processes become effectively spin-allowed and the rate constants for the nonadiabatic reactions have large values. The proposed dissociation and recombination mechanisms include reactions involving singlet—triplet crossings.

Electroluminescence of Halogen Complexes with Monovalent Copper: OLED Devices and DFT Modeling

Spectroscopic characteristics of complexes of Cu[I] ion with halogens synthesized by the TDDFT/CAM-B3LYP method are studied. It is shown that S0 → S1 and S0 → T1 electronic transitions are excitations with charge transfer. In this case, the electronic transitions proceed from the HOMO, HOMO-1 and HOMO-2 localized on halogen atoms to the LUMO localized on a ligand. The matrix elements of spin-orbit interaction are calculated using the single-electron operator (HSO). Based on these compounds, the organic light emitting diodes have been created. Their current–voltage and current-brightness characteristics are investigated.

Study of the A1Σ+ and b3Π0 states in LiCs by a polarization labelling spectroscopy technique

A polarization labelling spectroscopy technique was used to investigate the A1Σ+←X1Σ+ band system of the 7LiCs molecule in a heat-pipe oven. All 27 observed vibrational levels of the A state were found to be subject to strong perturbations assigned to interaction with the b3Π0 state. The deperturbation analysis provided molecular constants of the A and b states and a value of the electronic part of the spin–orbit interaction matrix element 〈b3Π0∣Hso∣A1Σ+〉.

Observations and analysis of the K 2[formula omitted] state using the infrared–infrared double resonance spectroscopy

Totally 1195 transitions into the K 2 4 1 Σ g + v = 2 − 36, J = 1 − 85 ro-vibrational levels have been observed by infrared–infrared double resonance spectroscopy. Spin–orbit interaction between the 4 1 Σ g + state and the 2 3Π g Ω = 0 + state has been observed. Molecular constants, RKR potential curve, and spin–orbit interaction matrix element have been determined from the analysis of the experimental data.

A coupled treatment of [formula omitted] and [formula omitted] states of AgH molecule

Ab initio configuration interaction (CI) calculations have been carried out for the potential curves of the lowest five 1 Σ + and three 3 Π electronic states of the AgH molecule. Nonadiabatic couplings among the 1 Σ + states and spin–orbit interaction matrix elements between the 1 Σ + and 3 Π states have been evaluated. The resulting adiabatic potential curves and couplings are transformed to a diabatic representation by employing a unitary transform which eliminates all d/d R coupling terms. Energy positions and predissociation rates for vibrational levels associated with the above electronic states are determined by employing a complex scaling approach based on both the adiabatic potential curves and their diabatic counterparts and the associated nonadiabatic couplings. It was found that the differences between these two sets of results for vibrational spacings and predissociation rates are marginal. The calculated spectroscopic constants for the X 1 Σ + , A 1 Σ + and a 3 Π states are in good agreement with measured results, and the calculated vibrational spacings for the A 1 Σ + state are also in reasonably good agreement with experiment. The reasons behind the relatively large discrepancies in the predicted and measured T e values for the c 3 Π and B 1 Σ + states are discussed. Predissociation linewidths are predicted for the vibrational levels of these electronic states. The decay of the A 1 Σ + and B 1 Σ + states is caused by nonadiabatic effects, whereas that of the a 3 Π and c 3 Π states is induced by the spin–orbit interaction.

Ab initio calculation of predissociation linewidths in the Schumann–Runge bands of the oxygen molecule

Ab initio multireference single- and double-excitation configuration interaction calculations have been carried out for potential curves of the B 3Σu−, Πu1, Πu3, Πu5, and Σu+3 electronic states of the O2 molecule. Spin-orbit interaction matrix elements among the above states and rotational interaction matrix elements between the B 3Σu− and the Πu3 states have been evaluated in order to investigate the observed line broadening in the Schumann–Runge bands. Predissociation linewidths of rovibrational levels of the B 3Σu− state are determined by using the complex rotation method in conjunction with the Gauss–Hermite quadrature procedure. It has been found that the Πu5 and Πu3 states play dominant roles in the predissociation of the B 3Σu− state. The calculated linewidths for rovibrational levels of v=0–13, N=0–36 of the F2 fine-structure components of the B 3Σu− state are in very good agreement with experimental results. Isotopic effects in the predissociation of the B 3Σu− state are studied by means of calculations for O218 and O16O18 and the theoretical results are found to be in good agreement with the observed average predissociation linewidths in each case.

Electronic transition moment of the [formula omitted] emission. Analysis of the R dependence of the Al 2+O 2− character in the [formula omitted] state

The dependence of the electronic transition moment, R e( R), of the AlO( B 2Σ +− X 2Σ +) system on the internuclear distance, R, has been determined by an analysis of the intensity distribution of the emission spectra as R e (R) = [1–2.29(13)(R/ A ̊ −1.5) 2] (1.510 A ̊ A ̊ ⩽ R ⩽ 1.9836 A ̊ ) . The R dependences of R e( R) and the X 2Σ + ≈ A 2∏ i off-diagonal spin-orbit interaction matrix element, H el SO( R), have been analyzed simultaneously to evaluate the R dependence of the Al 2+O 2− character in the X 2Σ + state and that of the orbital exponent of the oxygen atom. The results agree with the theoretical prediction by Lengsfield and Liu (J. Chem. Phys. 77 (1982) 6083) that the charge-transfer process, Al 2+O 2− → Al +O − takes place in the range of 1.6 A ̊ ⪅ R ⪅ 2.1 A ̊ .

Rotational and Hyperfine Structure in the B4Π-X4Σ− (0,0) Band of VO at 7900 Å: Perturbations by the a2Σ+, v = 2 Level

The (0,0) band of the B4Π-X4Σ− system of VO near 7900 Å has been analyzed from Doppler-limited Fourier transform emission spectra, together with wavelength-resolved laser-induced fluorescence and sub-Doppler intermodulated fluorescence spectra. The B4Π, ν = 0 level is heavily perturbed by the a2Σ+, ν = 2 level. Because the 3dδ2 4sσ a2Σ+ and 3dδ2 3dπ B4Π states have very different hyperfine parameters, the hyperfine patterns of the rotational lines vary dramatically with J at the perturbations. The observed hyperfine structure of the band, including the lowest-J perturbation, near J = 3812, could be explained in detail by a model Hamiltonian that takes the interactions into account: 3211 hyperfine line frequencies have been fitted with an rms error of 11 MHz. The b parameter (the coefficient of I·S in the magnetic hyperfine Hamiltonian) is well determined for the a2Σ+ state and provides the evidence for its electron configuration. The hyperfine structure of the B4Π state shows no effects of spin-orbit distortion and is well explained by the standard case (aβJ) model. Only the spin-orbit operator is needed to describe the interaction between the a and B states; the parameter for the direct dipolar interaction between them is too small to be determined. A fit to the higher-J rotational data showed that the spin-orbit interaction matrix element, which arises as a result of configuration interaction in the two states, has an apparent J dependence; this presumably means that the mixing is r dependent. Improved values for the ground state hyperfine parameters have been obtained from the new data, supplemented by the three very precise microwave frequencies measured by Suenram et al. (J. Mol. Spectrosc.148, 114, 1991).

Observation and characterization of a new c(2)3Σ+ electronic state using Stark effect and perturbation analysis in NaK(B 1Π)

A new c(2)3Σ+ state of NaK connected to Na(3S)+K(4P) has been studied through its numerous, weak interactions with the nearby B(1)1Π state. Very small (>10 MHz) energy shifts in perturbed B 1Π, V, J levels were detected by measuring the Λ doubling using e–f Stark mixing spectroscopy. Fifty centers of perturbation were located and attributed to 21 different vibrational levels of the perturbing c(2)3Σ+ state. Comparison of preliminary molecular constants with existing electronic structure calculations shows good consistency with Stevens et al. (1984), but some inconsistency with Jeung et al. (1983), and indicates the index of the lowest observed vibrational levels V0≊20. The identification of this c(2)3Σ+ state has been deduced from (i) the observation of the infrared fluorescence to the lower triplet a(1)3Σ+ state, and (ii) the determination of spin–orbit interaction matrix elements and selection rules as deduced from the measurement of frequency shifts in B 1Π–X 1Σ+ lines connected to perturbed levels of the B 1Π state.

Spin-orbit interaction in metals, elementary semiconductors, and semiconductor compounds

The general analytic formulas for matrix elements of spin-orbit interaction in metals, elementary semiconductors, and binary semiconductor compounds which belongs to cubic crystal systems are obtained on the basis of Roothaan-Hartree-Fock atomic orbitals.

A new version of AAKL (the matrix elements of spin-orbit interaction) adapted to spectroscopic notation

Title of the program: SPINORBIT WEIGHTS 2 Catalogue number: ACXL Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland (see application form in this issue) Computer: Amdahl 470 V/6; Installation: University of Alberta, Edmonton, Alberta, Canada Operating system: MTS Programming language used: FORTRAN IV High speed core required: 25590 bytes No. of bits per byte: 8 Overlay structure: none Other peripherals used: card reader, line printer, card punch No. of magnetic tapes required: none No. of cards in combined program and test deck: 1952 Card punching code: EBCDIC 029 CPC library subprograms used Catalogue Title Ref. in CPC numbers ACQB P SHELL C.F.P. 1 (1969) 15 ACRN A NEW D SHELL CFP 6 (1973) 88 AAGD ∗ NJSYM 1 (1970) 241 2 (1971) 173 AAGD0001 ∗ ADAPT NJSYM FOR 2 (1971) 180 WEIGHTS AAGD0002 ∗ ADAPT TO 5 (1973) 161 INTEGER ARITHMETIC

Zeeman effect of oriented molecules in solids at low temperatures

An account is given of the use of the optical Zeeman effect in determining the zero-field splitting parameters and the signs of spin-orbit interaction matrix elements for triplet states of organic molecules. The results for pyrazine, pyrimidine and s-triazine are used to exemplify the effects. These experiments involve high resolution studies of the spectra of single crystals at 4.2 K in polarized light and in magnetic fields ranging from 6 to 5 kG.

Spin-Orbit Interaction in Aromatic Molecules

The matrix elements of spin-orbit interaction are obtained for polyatomic molecules using M.O. wave functions, taking account of configurational interaction. These results are then applied to the calculation of singlet-triplet transition probabilities in aromatic compounds. It is shown without evaluation of integrals that intercombination transitions in these compounds should be much weaker than in most other classes of organic compounds. This is in agreement with experimental results on the phosphorescence lifetimes of these compounds.