Spin-orbit Coupling Calculations Research Articles

Ab Initio Study of the Phosphorescence of Nitrite Ions

In order to interpret the phosphorescence spectra of NaNO2 and similar single crystals, we performed MCSCF geometry optimization in the ground singlet (X 1 A 1) and in the first excited triplet (a 3 B 1) states of the NO 2 - ion and MCSCF quadratic response (QR) calculation of the a 3 B 1–X 1 A 1 transition probability at different bending angles and asymmetric stretch modes. The complete form of the spin–orbit coupling (SOC) operator is accounted for in the QR procedure. Dunning's correlation-consistent polarized valence double-ζ (cc-pVDZ) and triple-ζ (cc-pVTZ) basis sets are imployed. The electric-dipole transition moment from the T z spin sublevel (z is the C 2 axis) oriented along the y direction (the other in-plane axis) is found to be ≃5 times higher than that from the T y sublevel in the ground-state geometry. This is in agreement with polarization measurements and with optical detection of ESR spectra. The T z–S 0 transition moment decreases almost linearly with an increase in the ONO bond angle. The so-called non-Condon effects in the phosphorescence spectra of NaNO2 crystals are explained on these backgrounds. The long progression of the bending vibrations (v 2, a 1) with an anomolous intensity distribution in the T z–S 0 transition and additional involvement of the asymmetric stretch mode (v 3, b 2) in the T y–S 0 transition are interpreted by force field and SOC calculations in the MCSCF-response technique. Configuration interaction (CI) calculations of the spin-allowed electric dipole transitions in NO 2 - ions with effective one-electron SOC operator matrix element estimations were done for comparison with the results of the quadratic and linear response methods. Other T n–S 0 transitions are also studied. Finally, a short discussion of nonradiative processes is presented.

Ab initio calculation of zero-field splitting and spin-orbit coupling in ground and excited triplets of m-xylylene

We report CASSCF(6,6)/cc-pVDZ optimized geometries, energies (also single-point CASPT2(6,6)/cc-pVDZ), electron spin–spin dipolar interaction (D,E) tensor, and spin-orbit coupling (SOC) for m-xylylene in the lowest triplet T1 (13B2), in the next triplet 13A1, and in the slightly higher 23B2. The zero-field splitting (zfs) parameters computed for T1 (D/hc = 0.013 cm–1, E/hc = –0.003 cm–1) agree well with the observed values |D/hc| = 0.011 cm–1, |E/hc| < 0.001 cm–1. If 3A1 is the T2 state as calculated, its computed D/hc (–0.040 cm–1) and E/hc (0.001 cm–1) agree with the value |D/hc| = 0.04 ± 0.01 cm–1 deduced from experiment assuming E = 0. If 23B2 is the T2 state, the experimental data need to be reevaluated, since its computed E/hc value (–0.012 cm–1) is not negligible relative to D/hc (0.038 cm–1). The SOC matrix elements of T1–T3 with the lowest and the ππ* excited singlets are small (≈0.01–0.1 cm–1), while those with representative 1σπ* states are large (≈10 cm–1). The former lack one-center terms and therefore are much smaller than expected from the standard one-electron approximation. Computed SOC affects D and E slightly, and supports the proposed vibronic mechanism of intersystem crossing from T2.

Spin−Orbit Coupling Patterns Induced by Twist and Pyramidalization Modes in C2H4: A Quantitative Study and a Qualitative Analysis

A study of the spin−orbit coupling (SOC) mechanisms which couple the triplet ππ* state (T1) to the singlet ground state (S0) in ethylene is carried out at a variety of computational levels and basis sets, using the full Breit−Pauli (BP) SOC Hamiltonian, the one-electron mean-field (MF) operator, and the approximate one-electron operator based on an effective nuclear charge, Z*. The basis set and wave functions requirements needed for good quality SOC calculations are elucidated by studying the SOC interaction using single- and multireference CI as well as MCSCF wavefunctions, with basis sets ranging from the minimal STO-3G all the way to an extended one with quadruple ζ and polarization quality. Two archetype distortion modes of ethylene were considered: a twist mode which changes the symmetry from D2h to D2 and then to D2d and pyramidalization modes which change the ethylene symmetry to C2v (syn-pyramidalization) or C2h (anti-pyramidalization), as well as Cs (i.e., a mono-pyramidalization distortion). I...

Relativistic calculations on the adsorption of CO on the (111) surfaces of Ni, Pd, and Pt within the zeroth-order regular approximation

In this paper we first describe the implementation of the zeroth-order regular approximation (ZORA) for relativistic effects in our density-functional program for extended systems. The ZORA formalism affords approximations, which are discussed and tested, that reduce the computational effort of scalar relativistic calculations to that of nonrelativistic calculations, the inclusion of spin-orbit coupling requiring additional effort. Second, we present the outcome of nonrelativistic, scalar relativistic, and spin-orbit coupling calculations on the adsorption energy of CO on the (111) surfaces of Ni, Pd, and Pt. Relativity has a modest effect for CO on Pd, but proves to be essential for CO on Pt. The relativistic correction for the CO/Pt adsorption energy is as large as 70% at the scalar relativistic level and 55% when including spin-orbit coupling. In addition, relativity changes the preferred adsorption site for CO/Pt from hollow to top. We have examined the effects of spin polarization and of different exchange-correlation functionals, i.e., the local-density approximation (LDA) versus two generalized gradient approximations (GGA). The GGA's correct the severe overbinding by LDA of CO to the metal surfaces, and yield good agreement with experiment for adsorption energies and sites.

Chemical bonding and magnetism in the ternary germanides UT2Ge2 (T = 3d transition metal) from local spin density functional calculations

The electronic and magnetic structures of UT2Ge2 (T = Mn, Fe, Co, Ni, Cu) germanides are self-consistently calculated within the local spin density functional theory using the augmented spherical wave (ASW) method. The influence of hybridisation on the chemical bonding and magnetic behaviour is discussed from the densities of states (DOS) as well as from the crystal orbital overlap population (COOP) which was recently combined with the ASW method. From this we propose a mechanism for the evolution of bonding within the series. The magnetic properties and orders of all compounds are discussed from spin-only as well as from spin-orbit coupling calculations.

(2 + 1) Resonance enhanced multiphoton ionization of hydrogen chloride in a pulsed supersonic jet: Spectroscopic survey

A comprehensive study of the excited electronic states of HCl is reported. Using resonance enhanced multiphoton ionization ((2 + 1) REMPI) and time-of-flight mass spectrometry (TOFMS) over 120 band systems are analyzed. Supersonic jet techniques are used to prepare rotationally cold species for laser spectroscopy in the 77 000 to 96 000 cm −1 region. At least 50 new electronic states are characterized as well as several features only tentatively assigned previously. A long vibrational progression consisting of 29 vibrational levels of the deeply bound V 1Σ +(0 +) valence/ion-pair state is studied. We also extend the identification and analysis to high vibrational levels of low-lying Rydberg states. The assignments of [ 2Π i ] Rydberg state complexes are evaluated in terms of spin-orbit coupling and united-atom calculations. In several band systems, the spectra exhibit anomalous rotational line intensities and broadened linewidths which are consistent with predissociation. Multiphoton ionization with mass spectrometry permits the investigation of isotope effects as well as the appearance of fragment species associated with repulsive potential curves.

Electronic states, ionization potentials, and bond energies of TlHn, InHn, TlH+n, and InH+n (n=1–3)

Potential energy surfaces of 6 electronic states of TlH2 and InH2 and 8 electronic states of TlH+2 and InH+2 are computed. In addition the ground states of TlH3, InH3, TlH+3, InH+3, TlH, and TlH+ are investigated. A complete active space multiconfiguration self-consistent field (CAS-MCSCF) followed by second-order configuration interaction (SOCI) and relativistic configuration interaction (RCI) including spin–orbit coupling calculations are carried out. The step-wise bond energies, De(Hn−1M–H) and adiabatic ionization potentials are computed. The ground states of TlH2 and InH2 are found to be bent (2A1; θe∼121.5 °, 120 °) while the ground states of TlH+2 and InH+2 are linear (1Σ+g). The ground states of TlH3 and InH3 are found to be 1A1 (D3h ) states while the ground states of TlH+3 and InH+3 are Jahn–Teller distorted 2B2(C2v ) states. The unique bond length of TlH+3 and InH+3 is shorter than the two equal bond lengths. The bond angles (H–M–H) for TlH+3 and InH+3 deviate considerably from the neutral θe=120 ° to near 69 °. The TlH+ ion is found to be only 0.04 eV stable. Periodic trends in the geometries, bond energies and IPs are studied. Spin–orbit effects were found to be significant for TlHn species. The IPs of InHn and TlHn exhibit odd–even alternation. The bond energies also show an interesting trend as a function of n.

Spectroscopic constants and potential energy curves of HfH

Complete active space multiconfiguration self-consistent field (CAS-MCSFC) followed by full second-roder CI (SOCI) and relativistic configuration interaction (RCI) including spin-orbit coupling calculations are carried out on 14 λ- s and 10 ω-ω states of HfH. The spectroscopic constants ( r e, T e, ω e, μ e, D e) of these states are computed. The potential energy curves of these states are also reported. We find several electronic transitions in the IR-UV regions for HfH which are yet to be observed. The ground state of HfH is found to be a 3 2 state (82% 2Δ, 8% 2Π) with r e = 1.854 A ̊ , ω e = 1704 cm −1 and μ e = 0.66 D. The spin-orbit effects are found to be very significant for HfH.

Non‐Equilibrium Spin Polarization of the Si‐S1 Centre in Silicon Induced by Spin–Orbit Coupling

AbstractElectronic structure calculations of the neutral charged oxygen‐substitutional impurity in silicon are carried out within the framework of the semi‐empirical MINDO/3 method. The structure of the substitutional impurity in the silicon lattice is simulated by finite molecular cluster OSi4H12 with an equilibrium SiH bond length 0.152 nm. Account of electronic interaction for single and double excitations allows to explain the nature of the impurity displacement in silicon. The cluster choosed serves as a good model for Si‐S1 centres. The results of spin–orbit coupling calculations give information about processes determining the appearance of non‐equilibrium spin polarization in these centres. The quantitative interpretation of Si‐S1 centre ESR‐spectra angular dependence in the helium region of temperature is carried out on the basis of the solution of the equation of motion for a triplet density operator. The dependence of the stationary concentration of triplet centres on magnetic field and crystal orientation is obtained.

Solution of problem of determining spin properties of molecules in unitary formalism of quantum chemistry

An analysis has been made of the problem of calculating one- and two-particle spin densities, which are needed in calculations of spin-orbit and spin-spin coupling. The proposed solution is oriented toward the application of computational algorithms using unitary group representations; the solution consists of explicit expressions for the matrix elements of spin density operators in terms of the means of products of spin-free generators. This has eliminated a serious problem encountered previously in determining spin characteristics of molecules within the framework of unitary formalism.

Iron sulfur and iron molybdenum sulfur compounds: Comparison of molecular orbital calculations and spin-Hamiltonian analysis of Mössbauer spectra

The electronic structures of mononuclear Fe–S complexes with a FeIIS4 core and of binuclear Fe–Mo–S complexes containing the FeS2Mo core have been calculated by a semiempirical molecular orbital method (iterative extended Hückel theory), followed by a spin-orbit coupling calculation on the five highest occupied iron-like molecular orbitals. Fine structure and hyperfine structure tensors and parameters (g, D, E, A, and electric field gradient) have been calculated and compared with data from spin-Hamiltonian analysis of Mössbauer measurements. For the mononuclear complex anions [Fe(SPh)4]2− and [Fe(dts)2]2− it was found that Vẑẑ is negative, D positive, and that the magnetic anisotropy places the preferred direction of the hyperfine magnetic field perpendicular to the Vẑẑ direction in agreement with spin-Hamiltonian results. The similarity of parameters of [Fe(SPh)4]2− and reduced rubredoxin (Rdred) confirms the suggestion that this anion has a ground electronic state practically identical to Rdred. The complex anion [Fe(dts)2]2− shows smaller anisotropy, and due to the fact that the orbital ground state is energetically not well separated from higher states in this case a strong temperature dependence of the quadrupole splitting is observed. For the binuclear complex anions [(SPh)2FeS2MoS2]2−, [S5FeS2MoS2]2−, and [Cl2FeS2MoS2]2− it was found that d is negative and Vẑẑ is positive. A specific feature of these binuclear Fe–Mo–S complexes is that Vẑẑ is directed perpendicular to the Fe–Mo line. (This theoretical result is confirmed by single crystal Mössbauer studies on [Cl2FeS2MoS2]2−; see the following paper in this journal.) The preferred direction of the magnetic hyperfine field is close to the Vẑẑ axis. The correlation of calculated values of ρ(0) and isomer shifts for mononuclear and binuclear compounds confirms the role of MoS2−4 as a charge withdrawing ligand.

CNDO/S CI calculation of spin-orbit coupling and intersystem crossing in photochemical biradical formation reaction

The CNDO/S CI method has been employed to calculate potential curves for singlet and triplet states along reaction path for photolysis of cyclopentanone (dissociation of the C-C bond and biradical formation). Spin-orbit coupling between these two states and the probability of intersystem crossing (ISC) in Landau-Zener approximation were calculated. This probability has proved enough to compete with nuclear spin induced ISC process. In this way some peculiarities of chemically induced dynamic nuclear polarization in formation of products via biradicals can be qualitatively understood.

Ligand field spin-orbit coupling calculations for d7, d8, d9 (d3, d2, d1) five coordinated complexes of C3v symmetry

Ligand field spin-orbit coupling calculations for d7, d8, d9 (d3, d2, d1) five coordinated complexes of C3v symmetry

Mechanism of the direct trans→cis photoisomerization of stilbene. Part 2.—Thermally activated intersystem crossing

The importance of the thermally activated intersystem crossing in the direct trans→cis photoisomerization of stilbene is tested on the basis of spin-orbit coupling calculations. A CNDO–CI procedure, with the parametrization suggested by Del Bene and Jaffe, is used to obtain zero-order electronic states, and then the matrix elements of the spin-orbit Hamiltonian are calculated between the lowest excited trans singlet and the nearest triplet states. It is found that the activation energy of the direct phtoconversion compares very well with a small barrier that the molecule must overcome in the lowest excited singlet in order to reach crossover to a quasi-isoenergetic triplet. The calculation of Franck–Condon factors shows that the rate constant of the singlet to triplet relaxation becomes a maximum at the crossing point. However, the non-radiative lifetime of the excited trans singlet, evaluated according to a quantum-mechanical formulation given by Gelbart and Rice, turns out to be excessive (calc. : ∼3 × 10–9 s; obs. : ∼10–12 s). These results are discussed with reference to the simplifications of the present theoretical approach.

Bonding studies of compounds of boron and the group 4 elements. Part 9.—Photoelectron spectra and bonding studies of halogeno-, dimethylamino-, and methyl-boranes, BX3and BX2Y

The photoelectron (PE) spectra, excited by helium 21.22 eV radiation, of the compounds BX3 and BX2Y (X and Y chosen from F, Cl, Br, I, NMe2, or Me) have been measured. From these and published data, the spectra of the boron trihalides have been fully assigned; earlier proposals have been re-assessed on the basis of (i) line shapes, (ii) calculations of spin-orbit coupling and of orbital energies as a function of distortion, and (iii) comparisons with other BX′3(e.g., X′= NMe2, NHMe) spectra. Assignments for the other BX3 and BX2Y molecules are based on (i) line shapes, and (ii) a comprehensive analysis of trends within series, e.g., for Me2NBCl2, (Me2N)nBCl3–n as well as Me2NBX2(X = F, Cl, Br, I); calculations for these more complex molecules did not prove especially helpful, except for those relating to orbital energies as a function of twist angle (for X = NMe2).

Electronic States of HNCO, Cyanate Salts, and Organic Isocyanates. I. Luminescence Studies

The phosphorescence spectra and lifetimes of the cyanate salts of Na+, K+, Cd2+, Ag+, Hg2+, and Pb2+ have been measured. Similar measurements have been made on CH3NCO, CH3CH2NCO, C6H5NCO, and HNCO. The results of these studies indicate that the lowest-energy excited state of the cyanate ion and the covalent isocyanates is of ··· (π)3(π*)1 MO excitation type: This state is Σ+3(C∞υ) in NCO−, A′(Cs3) in HNCO and the alkyl isocyanates, and A13(C2υ) in phenyl isocyanate. Fluorescence is observed only from the phenyl isocyanate and is assumed to initiate in an excited state which has dominant excitation amplitude on the phenyl moiety. Vibrational structure observed in the phosphorescence of NaOCN and C6H5NCO is analyzed, and similarities in the spectra are pointed out. A heavy-atom spin–orbit coupling effect is observed in the cyanate salt series. Spin–orbit coupling calculations have been performed on NCO−, linear and bent. A phosphorescence lifetime of ∼ 0.12 sec, in good agreement with experiment, is predicted for the Γππ3* → 1Γ1 transition.

Phosphorescence Decay of Benzene and Methylbenzene Derivatives

Phosphorescence lifetimes of benzene and methylbenzene derivatives, deuterated and undeuterated, have been measured in glassy matrices at 4.2 and 77°K. Spin–orbit coupling calculations have been performed for benzene (D6h), distorted benzene (D2h), and toluene; these calculations included spin–own-orbit, spin–other-orbit, and vibronic considerations and were extended to all the methylbenzenes by a vector-sum semiempirical method. Franck–Condon calculations were performed for all methylated, deuterated, and distorted benzene derivatives. The results of these calculations lead to a general understanding of phosphorescence lifetimes, at least insofar as these are affected by either methylation or deuteration or both. Matrix effects and temperature effects on the phosphorescence lifetimes are largest in the case of benzene and toluene and decrease with increasing methylation of benzene and with increasing size of the polynuclear hydrocarbon. We attribute this sensitivity to the small size of the space available to the π subsystem in benzene, to the forbiddenness of the electric-dipole T1 → S0 process in this system, and to the ease with which matrix effects may perturb the rather “naked” skeleton of this molecule and its less-methylated derivatives. A concept of solvent-assisted distortions is introduced in order to explain the direction of solvent and temperature effects and the means whereby these effects become operative. This last is a very tenuous suggestion, its primary merit being that it provides some rationalization of the observed phenomenology.