Ab initio embedded cluster study of the excitation spectrum and Stokes shifts of Bi3+-doped Y2O3

The ab initio embedded cluster method coupled with correlated spin-orbit calculations has been used to interpret the excitation spectrum of a Bi(3+)-doped yttria crystal. Our results indicate that the Bi(3+) impurity can absorb light over a wider energy range in the C(2) site than in the S(6) site. Even if the computed absorption energies seem to be about 0.4 eV too high with respect to the experimental peaks for both sites, it is noteworthy that the embedded cluster model renders 93% of the large crystal redshift, about 6 eV. The determination of the geometry relaxation of the first shell of oxygen neighbors upon electronic excitation shows that the Stokes shift is smaller in the S(6) site than in the C(2) site. Combining all these results confirms the assignment of the violet emission to the S(6) site and that of the green emission to the C(2) site, as proposed by Boulon [J. Phys. (Paris) 32, 333 (1971)]. In addition, the nature of the metastable states which lie below the emitting ones and are responsible for the temperature dependence of the fluorescence lifetimes is discussed.     

High-order electron-correlation methods with scalar relativistic and spin-orbit corrections

An assortment of computer-generated, parallel-executable programs of ab initio electron-correlation methods has been fitted with the ability to use relativistic reference wave functions. This has been done on the basis of scalar relativistic and spin-orbit effective potentials and by allowing the computer-generated programs to handle complex-valued, spinless orbitals determined by these potentials. The electron-correlation methods that benefit from this extension are high-order coupled-cluster methods (up to quadruple excitation operators) for closed- and open-shell species, coupled-cluster methods for excited and ionized states (up to quadruples), second-order perturbation corrections to coupled-cluster methods (up to triples), high-order perturbation corrections to configuration-interaction singles, and active-space (multireference) coupled-cluster methods for the ground, excited, and ionized states (up to active-space quadruples). A subset of these methods is used jointly such that the dynamical correlation energies and scalar relativistic effects are computed by a lower-order electron-correlation method with more extensive basis sets and all-electron relativistic treatment, whereas the nondynamical correlation energies and spin-orbit effects are treated by a higher-order electron-correlation method with smaller basis sets and relativistic effective potentials. The authors demonstrate the utility and efficiency of this composite scheme in chemical simulation wherein the consideration of spin-orbit effects is essential: ionization energies of rare gases, spectroscopic constants of protonated rare gases, and photoelectron spectra of hydrogen halides.     

A theoretical study of the excited states of AmO2n+, n=1,2,3

The ground and excited states of the AmO(2) (+), AmO(2) (2+), and AmO(2) (3+) ions have been studied using the four-component configuration interaction singles doubles, spin-orbit complete active space self-consistent field, and spin-orbit complete active space-order perturbation theory methods. The roles of scalar relativistic effects and spin-orbit coupling are analyzed; results with different methods are carefully compared by a precise analysis of the wave functions. A molecular spinor diagram is used in relation to the four-component calculations while a ligand field model is used for the two-step method. States with the same number of electrons in the four nonbonding orbitals are in very good agreement with the two methods while ligand field and charge transfer states do not have the same excitation energies.     

Electronic spectrum of UO2(2+) and [UO2Cl4]2- calculated with time-dependent density functional theory

The electronic spectra of UO(2) (2+) and [UO(2)Cl(4)](2-) are calculated with a recently proposed relativistic time-dependent density functional theory method based on the two-component zeroth-order regular approximation for the inclusion of spin-orbit coupling and a noncollinear exchange-correlation functional. All excitations out of the bonding sigma(u) (+) orbital into the nonbonding delta(u) or phi(u) orbitals for UO(2) (2+) and the corresponding excitations for [UO(2)Cl(4)](2-) are considered. Scalar relativistic vertical excitation energies are compared to values from previous calculations with the CASPT2 method. Two-component adiabatic excitation energies, U-O equilibrium distances, and symmetric stretching frequencies are compared to CASPT2 and combined configuration-interaction and spin-orbit coupling results, as well as to experimental data. The composition of the excited states in terms of the spin-orbit free states is analyzed. The results point to a significant effect of the chlorine ligands on the electronic spectrum, thereby confirming the CASPT2 results: The excitation energies are shifted and a different luminescent state is found.     

Ab initio potential energy surface and spectrum of the B(3Pi) state of the HeI2 complex

The three-dimensional interaction potential for I2(B 3Pi0u+)+He is computed using accurate ab initio methods and a large basis set. Scalar relativistic effects are accounted for by large-core relativistic pseudopotentials for the iodine atoms. Using multireference configuration interaction calculations with subsequent treatment of spin-orbit coupling, it is shown for linear and perpendicular structures of the complex that the interaction potential for I2(B 3Pi0u+)+He is very well approximated by the average of the 3A' and 3A" interaction potentials obtained without spin-orbit coupling. The three-dimensional 3A' and 3A" interaction potentials are computed at the unrestricted open-shell coupled-cluster level of theory using large basis sets. Bound state calculations based on the averaged surface are carried out and binding energies, vibrationally averaged structures, and frequencies are determined. These results are found to be in excellent accord with recent experimental measurements from laser-induced fluorescence and action spectra of HeI2. Furthermore, in combination with a recent X-state potential, the spectral blueshift is obtained and compared with available experimental values.     

Electronic structure and bonding of cobalt monoxide, CoO, and its ions CoO+ and CoO-: an ab initio study

We present a systematic and high-level ab initio study of CoO and its ions, CoO(+) and CoO(-). Employing variational multireference (MRCI) and single-reference coupled-cluster methods combined with basis sets of quintuple quality, we have calculated 50, 31, and 7 bound states for CoO, CoO(+), and CoO(-), respectively. For all these states, complete potential energy curves have been constructed at the MRCI level of theory, whereas for a few low-lying states core subvalence and scalar relativistic effects have been taken into account. We report energetics, spectroscopic parameters, dipole moments, and spin-orbit coupling constants. The ground states of CoO, CoO(+), and CoO(-) are X(4)Δ, X(5)Δ, and X(5)Δ, respectively, the latter established for the first time. The CoO is quite ionic with a Co to O Mulliken charge transfer of ~0.6 electrons and a dipole moment μ(X(4)Δ) = 4.5 ± 0.1 D. The overall agreement between theory and experiment is good, but there are also important deviations. Despite the seeming simplicity of these diatomic species, reliable results can only be obtained at a high level of theory.     

Relativistic Jahn-Teller effects in the photoelectron spectra of tetrahedral P4, As4, Sb4, and Bi4

The group-V tetrahedral cluster cations P(4)(+), As(4)(+), Sb(4)(+), and Bi(4)(+) are known to exhibit exceptionally strong Jahn-Teller (JT) effects of electrostatic origin in their (2)E ground states and (2)T(2) excited states. It has been predicted that there exist, in addition, JT couplings of relativistic origin (arising from the spin-orbit (SO) operator) in (2)E and (2)T(2) states of tetrahedral systems, which should become relevant for the heavier elements. In the present work, the JT and SO couplings in the group-V tetramer cations have been analyzed with ab initio relativistic electronic structure calculations. The vibronic line spectra and the band shapes of the photoelectron spectra were simulated with time-dependent quantum wave-packet methods. The results provide insight into the interplay of electrostatic and relativistic JT couplings and SO splittings in the complex photoelectron spectra of these systems.     

Ab initio characterization of the Ne-I2 van der Waals complex: intermolecular potentials and vibrational bound states

A theoretical study of the potential energy surface and bound states is performed for the ground state of the NeI(2) van der Waals (vdW) complex. The three-dimensional interaction energies are obtained from ab initio coupled-cluster, coupled-cluster single double (triple)/complete basis set, calculations using large basis sets, of quadruple- through quintuple-zeta quality, in conjunction with relativistic effective core potentials for the heavy iodine atoms. For the analytical representation of the surface two different schemes, based on fitting and interpolation surface generation techniques, are employed. The surface shows a double-minimum topology for linear and T-shaped configurations. Full variational quantum mechanical calculations are carried out using the model surfaces, and the vibrationally averaged structures and energetics for the NeI(2) isomers are determined. The accuracy of the potential energy surfaces is validated by a comparison between the present results and the corresponding experimental data available. In lieu of more experimental measurements, we also report our results/predictions on higher bound vibrational vdW levels, and the influence of the employed surface on them is discussed.     

New spectroscopic data, spin-orbit functions, and global analysis of data on the A 1Sigmau+ and b 3Piu states of Na2

The lowest electronically excited states of Na2 are of interest as intermediaries in the excitation of higher states and in the development of methods for producing cold molecules. We have compiled previously obtained spectroscopic data on the A 1Sigmau+ and b 3Piu states of Na2 from about 20 sources, both published and unpublished, together with new sub-Doppler linewidth measurements of about 15,000 A<--X transitions using polarization spectroscopy. We also present new ab initio results for the diagonal and off-diagonal spin-orbit functions. The discrete variable representation is used in conjunction with Hund's case a potentials plus spin-orbit effects to model data extending from v=0 to very close to the 3 2S+3 2P12 limit. Empirical estimates of the spin-orbit functions agree well with the ab initio functions for the accessible values of R. The potential function for the A state includes an exchange potential for S+P atoms, with a fitted coefficient somewhat larger than the predicted value. Observed and calculated term values are presented in an auxiliary (EPAPS) file as a database for future studies on Na2.     

Ab initio study of the diatomic fluorides FeF, CoF, NiF, and CuF

The late-3d transition-metal diatomic fluorides MF = FeF, CoF, NiF, and CuF have been studied using variational multireference (MRCI) and coupled-cluster [RCCSD(T)] methods, combined with large to very large basis sets. We examined a total of 35 (2S+1)|Lambda| states, constructing as well 29 full potential energy curves through the MRCI method. All examined states are ionic, diabatically correlating to M(+)+F(-)((1)S). Notwithstanding the "eccentric" character of the 3d transition metals and the difficulties to accurately be described with all-electron ab initio methods, our results are, in general, in very good agreement with available experimental numbers.     

Metastable BrO2+ and NBr2+ molecules in the gas phase

The doubly positively charged gas-phase molecules BrO(2+) and NBr(2+) have been produced by prolonged high-current energetic oxygen (17 keV (16)O(-)) ion surface bombardment (ion beam sputtering) of rubidium bromide (RbBr) and of ammonium bromide (NH(4)Br) powdered ionic salt samples, respectively, pressed into indium foil. These novel species were observed at half-integer m∕z values in positive ion mass spectra for ion flight times of roughly ～12 μs through a magnetic-sector secondary ion mass spectrometer. Here we present these experimental results and combine them with a detailed theoretical investigation using high level ab initio calculations of the ground states of BrO(2+) and NBr(2+), and a manifold of excited electronic states. NBr(2+) and BrO(2+), in their ground states, are long-lived metastable gas-phase molecules with well depths of 2.73 × 10(4) cm(-1) (3.38 eV) and 1.62 × 10(4) cm(-1) (2.01 eV); their fragmentation channels into two monocations lie 2.31 × 10(3) cm(-1) (0.29 eV) and 2.14 × 10(4) cm(-1) (2.65 eV) below the ground state minimum. The calculated lifetimes for NBr(2+) (v(") < 35) and BrO(2+) (v(") < 18) are large enough to be considered stable against tunneling. For NBr(2+), we predicted R(e) = 3.051 a(0) and ω(e) = 984 cm(-1); for BrO(2+), we obtained 3.033 a(0) and 916 cm(-1), respectively. The adiabatic double ionization energies of BrO and NBr to form metastable BrO(2+) and NBr(2+) are calculated to be 30.73 and 29.08 eV, respectively. The effect of spin-orbit interactions on the low-lying (Λ + S) states is also discussed.     

Relativistic spin-orbit effects on hyperfine coupling tensors by density-functional theory

A second-order perturbation theory treatment of spin-orbit corrections to hyperfine coupling tensors has been implemented within a density-functional framework. The method uses the all-electron atomic mean-field approximation and/or spin-orbit pseudopotentials in incorporating one- and two-electron spin-orbit interaction within a first-principles framework. Validation of the approach on a set of main-group radicals and transition metal complexes indicates good agreement between all-electron and pseudopotential results for hyperfine coupling constants of the lighter nuclei in the system, except for cases in which scalar relativistic effects become important. The nonrelativistic Fermi contact part of the isotropic hyperfine coupling constants is not always accurately reproduced by the exchange-correlation functionals employed, particularly for the triplet and pi-type doublet radicals in the present work. For this reason, ab initio coupled-cluster singles and doubles with perturbative triples results for the first-order contributions have been combined in the validation calculations with the density-functional results for the second-order spin-orbit contributions. In the cases where spin-orbit corrections are of significant magnitude relative to the nonrelativistic first-order terms, they improve the agreement with experiment. Antisymmetric contributions to the hyperfine tensor arise from the spin-orbit contributions and are discussed for the IO2 radical, whereas rovibrational effects have been evaluated for RhC, NBr, and NI.     

The effect of spin-orbit coupling on fast neutral chemical reaction O(3P)+CH3-->CH3O

The effect of nonadiabatic transitions through the spin-orbit couplings has been investigated on the fast neutral reaction, O((3)P)+CH(3)-->CH(3)O. Adiabatic potential energies and the spin-orbit coupling terms have been evaluated for the four electronic states of CH(3)O ((2)E, (2)A(2), (4)E, and (4)A(2)) that correlate with the O((3)P)+CH(3) asymptote, as a function of CO distance and OCH angle under the C(3v) symmetry, by ab initio electronic structure calculations using multireference internally contracted single and double excitation configuration interaction method with the 6-311G(2df,2pd) basis sets. Multistate quantum reactive scattering calculations have been carried out with the use of thus obtained potential energies and spin-orbit coupling matrices, based on the generalized R-matrix propagation method. The calculated thermal rate constants show a slight positive dependence on temperature in a range between 50 and 2000 K, supporting the previous experimental results. It is shown that the spin-orbit coupled excited states give rise to reflections over the centrifugal barrier due to the quantum interference. Classical capture calculations yield larger rate constants due to the neglect of quantum reflections. It is concluded that the effect of nonadiabatic transitions is of minor importance on the overall reactivity in this reaction.     

Analysis of the effect of spin-orbit coupling on the electronic structure and excitation spectrum of the Bi2(2-) anion in (K-crypt)2Bi2 on the basis of relativistic electronic structure calculations

The Bi2(2-) anions that have been characterized in (K-crypt)2Bi2 are isoelectronic with O2 but are diamagnetic and EPR-silent, unlike O2. The UV-vis spectrum measured for (K-crypt)2Bi2 shows two broad absorption peaks located at 2.05 and 2.85 eV, but no absorption at lower energies down to 0.62 eV. To account for these observations, the electronic structures of the isoelectronic diatomic dianions Q2(2-) (Q = N, P, As, Sb, Bi) were compared on the basis of relativistic density functional theory calculations, and the electronic excitations of Bi2(2-) were analyzed on the basis of relativistic configuration interaction calculations. The extent of spin-orbit coupling, brought about by the relativistic effect, increases steadily in the order N < P < As < Sb < Bi such that the "closed-shell" state is more stable than the "open-shell" state for Bi2(2-), while the opposite is the case for N2(2-), P2(2-), As2(2-), and Sb2(2-). The nature of the electronic excitations of Bi2(2-) was assigned and discussed from the viewpoint of molecular orbitals in the absence of spin-orbit coupling.     

Spin-orbit configuration interaction study of the electronic structure of the 5f (2) manifold of U(4+) and the 5f manifold of U(5+)

The energy levels of the 5f configuration of U(5+) and 5f(2) configuration of U(4+) have been calculated in a dressed effective Hamiltonian relativistic spin-orbit configuration interaction framework. Electron correlation is treated in the scalar relativistic scheme with either the multistate multireference second-order multiconfigurational perturbation theory (MS-CASPT2) or with the multireference single and double configuration interaction (MRCI) and its size-extensive Davidson corrected variant. The CASPT2 method yields relative energies which are lower than those obtained with the MRCI method, the differences being the largest for the highest state (1)S(0) of the 5f(2) manifold. Both valence correlation effects and spin-orbit polarization of the outer-core orbitals are shown to be important. The satisfactory agreement of the results with experiments and four-component correlated calculations illustrates the relevance of dressed spin-orbit configuration interaction methods for spectroscopy studies of heavy elements.     

The ab initio limit quartic force field of BH3

The complete quartic force field of BH(3) has been converged to the ab initio limit by extrapolation of core-valence correlation-consistent basis set series (cc-pCVXZ, X = T, Q, 5) of all-electron CCSD(T) (coupled-cluster singles and doubles with perturbative triples) energy points. Additional computations including full coupled-cluster treatments through quadruple excitations (CCSDTQ), scalar relativistic effects, and diagonal Born-Oppenheimer corrections (DBOC) were concurrently executed. Within second-order vibrational perturbation theory (VPT2) our quartic force field yields the fundamental frequencies nu(1) = 2502.3 cm(-1), nu(2) = 1147.2 cm(-1), nu(3) = 2602.1 cm(-1), and nu(4) = 1196.5 cm(-1), in excellent agreement with observed gas-phase fundamentals, displaying a mean absolute error of only 0.3 cm(-1). Our converged prediction for the equilibrium bond length of BH(3) is r(e) = 1.1867 A.     

Pseudopotential study of the ground and excited states of Yb2

The ground state of the van der Waals-type lanthanide dimer Yb₂ has been studied by means of relativistic energy-consistent ab initio pseudopotentials using three different core definitions. Electron correlation was treated by coupled-cluster theory, whereby core-valence correlation effects have been accounted for either explicitly by correlating the energetically highest coreorbitals or implicitly by means of an effective core-polarization potential. Results for the first and second atomic ionization potentials, the atomic dipole polarizability, and the spectroscopic constants of the molecular ground state are reported. Low-lying excited states have been investigated with spin-orbit configuration interaction calculations. It is also demonstrated for the whole lanthanide series that correlation effects due to the atomic-like, possibly open 4f-shell in lanthanides can be modeled effectively by adding a core-polarization potential to pseudopotentials attributing the 4f-shell to the core. Received: 3 April 1998 / Accepted: 27 July 1998 / Published online: 9 October 1998     

A simplified relativistic time-dependent density-functional theory formalism for the calculations of excitation energies including spin-orbit coupling effect

In the present work we have proposed an approximate time-dependent density-functional theory (TDDFT) formalism to deal with the influence of spin-orbit coupling effect on the excitation energies for closed-shell systems. In this formalism scalar relativistic TDDFT calculations are first performed to determine the lowest single-group excited states and the spin-orbit coupling operator is applied to these single-group excited states to obtain the excitation energies with spin-orbit coupling effects included. The computational effort of the present method is much smaller than that of the two-component TDDFT formalism and this method can be applied to medium-size systems containing heavy elements. The compositions of the double-group excited states in terms of single-group singlet and triplet excited states are obtained automatically from the calculations. The calculated excitation energies based on the present formalism show that this formalism affords reasonable excitation energies for transitions not involving 5p and 6p orbitals. For transitions involving 5p orbitals, one can still obtain acceptable results for excitations with a small truncation error, while the formalism will fail for transitions involving 6p orbitals, especially 6p1/2 spinors.     

Spin-orbit ab initio study of alkyl halide dissociation via electronic curve crossing

An ab initio study of the role of electronic curve crossing in the photodissociation dynamics of the alkyl halides is presented. Recent experimental studies show that curve crossing plays a deterministic role in deciding the channel of dissociation. Coupled repulsive potential energy curves of the low-lying n-sigma(*) states are studied including spin-orbit and relativistic effects. Basis set including effect of core correlation is used. Ab initio vertical excitation spectra of CH(3)I and CF(3)I are in agreement with the experimental observation. The curve crossing region is around 2.371 A for CH(3)I and CF(3)I. The potential curves of the repulsive excited states have larger slope for CF(3)I, suggesting a higher velocity and decreased intersystem crossing probability on fluorination. We also report the potential curves and the region of curve crossing for CH(3)Br and CH(3)Cl.