Theoretical spectroscopy of the calcium dimer in the A 1Sigma(u)+, c3Pi(u), and a3Sigma(u)+ manifolds: an ab initio nonadiabatic treatment

Nonadiabatic theory of molecular spectra of diatomic molecules is presented. It is shown that in the fully nonadiabatic framework, the rovibrational wave functions describing the nuclear motions in diatomic molecules can be obtained from a system of coupled differential equations. The rovibrational wave functions corresponding to various electronic states are coupled through the relativistic spin-orbit coupling interaction and through different radial and angular coupling terms, while the transition intensities can be written in terms of the ground state rovibrational wave function and bound rovibrational wave functions of all excited electronic states that are electric dipole connected with the ground state. This theory was applied in the nearly exact nonadiabatic calculations of energy levels, line positions, and intensities of the calcium dimer in the A (1)Sigma(u) (+)(1 (1)S+1 (1)D), c (3)Pi(u)(1 (3)P+1 (1)S), and a (3)Sigma(u) (+)(1 (3)P+1 (1)S) manifolds of states. The excited state potentials were computed using a combination of the linear response theory within the coupled-cluster singles and doubles framework for the core-core and core-valence electronic correlations and of the full configuration interaction for the valence-valence correlation, and corrected for the one-electron relativistic terms resulting from the first-order many-electron Breit theory. The electric transition dipole moment governing the A (1)Sigma(u) (+)<--X (1)Sigma(g) (+) transitions was obtained as the first residue of the frequency-dependent polarization propagator computed with the coupled-cluster method restricted to single and double excitations, while the spin-orbit and nonadiabatic coupling matrix elements were computed with the multireference configuration interaction wave functions restricted to single and double excitations. Our theoretical results explain semiquantitatively all the features of the observed Ca(2) spectrum in the A (1)Sigma(u) (+)(1 (1)S+1 (1)D), c (3)Pi(u)(1 (3)P+1 (1)S), and a (3)Sigma(u) (+)(1 (3)P+1 (1)S) manifolds of states.     

Rovibrational dynamics of the strontium molecule in the A(1)Σ(u)+, c(3)Π(u), and a(3)Σ(u)+ manifold from state-of-the-art ab initio calculations

State-of-the-art ab initio techniques have been applied to compute the potential energy curves for the electronic states in the A(1)Σ(u)(+), c(3)Π(u), and a(3)Σ(u)(+) manifold of the strontium dimer, the spin-orbit and nonadiabatic coupling matrix elements between the states in the manifold, and the electric transition dipole moment from the ground X(1)Σ(g)(+) to the nonrelativistic and relativistic states in the A+c+a manifold. The potential energy curves and transition moments were obtained with the linear response (equation of motion) coupled cluster method limited to single, double, and linear triple excitations for the potentials and limited to single and double excitations for the transition moments. The spin-orbit and nonadiabatic coupling matrix elements were computed with the multireference configuration interaction method limited to single and double excitations. Our results for the nonrelativistic and relativistic (spin-orbit coupled) potentials deviate substantially from recent ab initio calculations. The potential energy curve for the spectroscopically active (1)0(u)(+) state is in quantitative agreement with the empirical potential fitted to high-resolution Fourier transform spectra [A. Stein, H. Kno?ckel, and E. Tiemann, Eur. Phys. J. D 64, 227 (2011)]. The computed ab initio points were fitted to physically sound analytical expressions, and used in converged coupled channel calculations of the rovibrational energy levels in the A+c+a manifold and line strengths for the A(1)Σ(u)(+)←X(1)Σ(g (+) transitions. Positions and lifetimes of quasi-bound Feshbach resonances lying above the (1)S(0) + (3)P(1) dissociation limit were also obtained. Our results reproduce (semi)quantitatively the experimental data observed thus far. Predictions for on-going and future experiments are also reported.     

Ab initio study including spin-orbit effects on the B-X transition of AgI

The lowest Omega = 0-,0+,1,2 fine-structure potential energy curves arising from the two lowest-lying singlet (X 1Sigma+ and 2 1Sigma+) and the first 3Pi electronic states of AgI were obtained through an effective Hamiltonian; the purely electronic LambdaSSigma energies were used as diagonal elements, which were calculated through extensive complete active space self-consistent field + averaged coupled pair functional calculations, with relativistic effective core potentials and optimized Gaussian basis sets for both atoms. The spin-orbit interactions were included using the Stuttgart effective spin-orbit potentials. For the excited Omega = 0+ states, very strong mixtures were found of the 2 1Sigma+ and 3Pi parents that lead to the fine-structure (0+) single B state (dominated by the 2 1Sigma+ parent at long distance), that explains the B <-- X transitions. The present results also explain the presence of a second long-distance minimum for the B0+ state, experimentally Rydberg-Klein-Rees fitted. These calculations produced, as a byproduct, a new lower-lying Omega = 0+ yet unobserved fine-structure state predicted to exist around 22,000 cm(-1). Our theoretical results are compared and discussed in the light of the experimental data for the B-X transitions in silver halides [J. Chem. Phys. 109, 9831 (1998)].     

Extensive theoretical study on the low-lying electronic states of silicon monofluoride cation including spin-orbit coupling

Ab initio calculations on the low-lying electronic states of SiF+ are performed using the internally contracted multireference configuration interaction method with the Davidson correction and entirely uncontracted aug-cc-pV5Z basis set. The effects of spin-orbit coupling are accounted for by the state interaction approach with the full Breit-Pauli Hamiltonian. The entire 23 Omega states generated from the 12 valence Lambda-S states, which correlate with the first dissociation channel are studied for the first time. Good agreement is found between the calculated results and the available experimental data. The spin-orbit coupling effects on the potential energy curves and spectroscopic properties are studied. Various curve crossings are revealed, which could lead to the predissociation of the a3Pi, A1Pi, and (2)3Sigma+ states and the predissociation pathways are analyzed based upon the calculated spin-orbit matrix elements. The calculated ionization potentials of the ground-state SiF to a few states of SiF+ are in good agreement with the available experimental measurements. Moreover, the transition dipole moments of the dipole-allowed transitions and the transition properties for the A3Pi0+ -X1Sigma+ 0+ and B3Pi1-X1Sigma+ 0+ transitions are predicted, including the Franck-Condon factors and the radiative lifetimes.     

Ground and valence excited states of BI: a MR-CISD+Q study

Ab initio calculations on the valence electronic states of the BI molecule have been performed by using the entirely uncontracted all-electronic aug-cc-pVQZ (for the B atom) and Sadlej-pVTZ (for the I atom) basis sets and the internally contracted multireference singles and doubles configuration interaction method with Davidson size-extensively correction and Douglas-Kroll scalar relativistic correction. The potential energy curves of all valence states and the spectroscopic constants of bound states are fitted. It is the first time that the 12 Lambda-S states of BI molecule and all of the 23 Omega states generated from the former are studied in a theoretical way. Calculation results reproduce well most of the experimental data. The effects of the spin-orbit coupling and the avoided crossing rule between Omega states of the same symmetry are analyzed. The transition properties of the A3Pi0+, B3Pi1, and C1Pi1 states to the ground-state transitions are predicted, including the transition dipole moments, the Franck-Condon factors, and the radiative lifetimes. The radiative lifetime of the C1Pi1 state of BI molecule is less than 1 micros, while that of the A3Pi0+ and B3Pi1 states are the order of 1 ms.     

Full spin-orbit configuration interaction calculations on electronic states of LiBe

Ab initio calculations are reported for the simplest heteronuclear metal cluster, LiBe. Full spin-orbit configuration interaction calculations in the context of relativistic effective core potentials lead to accurate potential energy curves for low-lying states. Results are compared with recent experimental observations and with all electron multi-reference configuration interaction calculations.     

Spin-orbit mechanism of predissociation in the Wulf band of ozone

Previously calculated resonance widths of the ground vibrational levels in the electronic states 1 (3)A" ((3)A(2)) and 1 (3)A' ((3)B(2)), which belong to the Wulf band system of ozone, are significantly smaller than observed experimentally. We demonstrate that predissociation is drastically enhanced by spin-orbit coupling between 1 (3)A"/X (1)A' and 1 (3)A'/1 (3)A". Multistate quantum mechanical calculations using ab initio spin-orbit coupling matrix elements give linewidths of optically bright components of the right order of magnitude.     

Structural and spectroscopic study of the excited electronic states of silver dihalides by quantum chemical methods

The structural and electronic properties of the excited electronic states of AgX(2) (X = F, Cl, Br, and I), have been calculated, taking electron correlation and spin-orbit coupling into account and employing improved relativistic-effective-core potentials for silver and the halogen atoms. The relative ordering of the excited states of these molecules has been discussed via molecular-orbital arguments. The spin-orbit splittings of three degenerate electronic states ((2)Pi(g), (2)Pi(u), and (2)Delta(g)) have been calculated and the spin-orbit induced inter-state (Sigma - Pi) coupling has been discussed. The composition of the spin-orbit eigenstates is analyzed in terms of scalar-relativistic electronic states. Finally, a theoretical prediction of the photodetachment bands of the title molecules has been accomplished.     

The spin-orbit and rotational constants for the N2 C" 5Pi(ui) (v = 3) state

The spin-orbit (A = -16.4 cm(-1)) and rotational (B = 1.017 cm(-1)) constants for the N2 C" 5Pi(ui)(v = 3) level are determined by a fit to rotational lines in the C" 5Pi(u)-A' 5Sigma(g)+(3-1) band that terminate in J'Omega' = 3(3), 4(3), 3(2), and 4(2) levels of the C" state. The C"-state spin-orbit constant is consistent with semi-empirical estimates, based on spin-orbit constants observed in several other electronic states of N2 and the atomic spin-orbit coupling constant, zeta(N 2p). The C"-A' bands exhibit the unusual feature of oppositely degraded sub-band heads, Omega' = 3 (red) and Omega' = 1, 0, and -1 (blue). The unusually wide range of B(Omega)eff values, from 0.85 cm(-1) (Omega = 3) to 1.28 cm(-1) (Omega = -1) for C" 5Pi(v = 3) should be diagnostically useful for Omega'-assignments. The C" 5Pi(v = 3) level lies 14257.17 and 90599 cm(-1) above A' 5Sigma(g)+(v = 1) and X 1Sigma(g)+(v = 0), respectively, and Re(C" 5Pi) = 1.50 A.     

Interactions in open-shell clusters: ab initio study of pre-reactive complex O(3P) + HCl

Van der Waals interactions between the ground-state triplet O(3P) atom and the closed-shell HCl molecule are investigated in the pre-reactive region. Three adiabatic (two of A' symmetry and one of A' symmetry) and four non-relativistic diabatic potential energy surfaces are obtained by combining a restricted open-shell coupled cluster approach with the multireference configuration interaction method. The lower A' adiabatic potential surface has a single minimum (D(e) = 589 cm(-1)) for a linear O...HCl configuration. The upper A' potential has a weak (D(e) = 65 cm(-1)) minimum for a linear HCl...O configuration. The A' adiabatic potential has a weak (124 cm(-1)) T-shaped minimum. Adiabatic potentials intersect once in the O...HCl linear configuration and twice in the linear HCl...O geometry. The role of electrostatic interactions in shaping these potentials is discussed. The effects of spin-orbit coupling on this interaction are also investigated assuming a constant value of the SO parameter.     

Interaction of lead atom with atmospheric hydroxyl radical. An ab initio and density functional theory study of the resulting complexes PbOH and HPbO

The two potential hypersurfaces 2A' (ground state) and 2A" (excited state) have been studied through ab initio and density functional theory (DFT) methods for the Pb(OH) complex. Two processes have been identified. The first one concerns the hydrogen inversion process in the coordination of PbOH and the second one the isomerization of PbOH into HPbO. Eight stationary points have been found; four of them correspond to the stable structures with symmetries PbOH(2A'), PbOH(2A"), HPbO(2A'), and HPbO(2Pi), and four correspond to transition states [TS] with the symmetries 2Pi, 2A', 2Sigma+, and 2A". The hydrogen inversion process in PbOH exhibits the so-called Renner-Teller effect with a rather low barrier, whereas the isomerization process PbOH-->HPbO exhibits a rather high barrier. The energetic, structural, spectroscopy, and thermodynamics results obtained at various levels through, e.g., DFT with BLYP, B3LYP exchange-correlation functionals, coupled clusters methods, namely CCSD (single and double excitations) and CCSD(T) (with triple excitations, by perturbation) are presented for the whole sets of the stationary points and their dissociation products. The relativistic effects, as well as spin-orbit interaction, taken into account in the case of the BLYP exchange-correlation functional, have been estimated and discussed in order to measure their importance in the case of system including heavy metals such as Pb. Reactions of lead (Pb) with oxidizing atmospheric molecules (OH, HO2, O2, and O3) have been studied at various levels of approximation in order to study the possible existence of PbOH in the atmosphere.     

Relativistic configuration interaction study of the electronic spectrum of SnTe and SnTe+

Ab initio based relativistic configuration interaction calculations have been performed to study the electronic spectrum of the heaviest tin chalcogenide and its monopositive ion. Potential energy curves and spectroscopic constants of low-lying states of both species within 7 eV are reported. The ground-state dissociation energies of SnTe and SnTe+ are computed to be 3.48 and 2.50 eV, respectively. The spin-orbit splitting between the two components of the X 2Pi state of SnTe+ is about 3030 cm(-1). Effects of the strong spin-orbit coupling on the potential curves and spectroscopic properties of both the species are investigated in detail. The electric dipole moments of some of the low-lying states of SnTe and SnTe+ are reported. Transition moments of some important spin-allowed and spin-forbidden transitions are calculated from the configuration interaction wave functions. The radiative lifetime of the excited E 1sigma0+(+) state of SnTe is about 39 ns. The X2-X1 transition in SnTe+ is found to be more probable than the similar transition in the lighter ions. The vertical ionization energy of SnTe in the ground state is estimated to be 8.22 eV.     

MRDCI study of the low-lying electronic states of PbSi

Electronic states of the PbSi molecule up to 4 eV have been studied by carrying out ab initio based MRDCI calculations which include relativistic effective core potentials (RECPs) of both the atoms. The use of semicore RECPs of Pb produces better dissociation limits than the full-core one. However, the (3)P(0)-(3)P(1) splitting due to Pb is underestimated by about 4000 cm(-1). At least 25 bound electronic states of the Λ-S symmetry are predicted for PbSi. The computed zero-field-splitting in the ground state is about 544 cm(-1). A strong spin-orbit mixing changes the nature of the potential energy curves of many Ω states. The overall splitting among the spin components of A(3)Π is computed to be 4067 cm(-1). However, the largest spin-orbit splitting is reported for the (3)Δ state. A number of spin-allowed and spin-forbidden transitions are predicted. The partial radiative lifetime for the A(3)Π-X(3)Σ(-) transition is of the order of milliseconds. The computed bond energy in the ground state is 1.68 eV, considering the spin-orbit coupling. The vertical ionization energy for the ionization to the X(4)Σ(-) ground state of PbSi(+) is about 6.93 eV computed at the same level of calculations.     

A quantum wave-packet study of intersystem crossing effects in the O(3P2,1,0,1D2)+H2 reaction

We present for the first time an exact quantum study of spin-orbit-induced intersystem crossing effects in the title reaction. The time-dependent wave-packet method, combined with an extended split operator scheme, is used to calculate the fine-structure resolved cross section. The calculation involves four electronic potential-energy surfaces of the 1A' state [J. Dobbyn and P. J. Knowles, Faraday Discuss. 110, 247 (1998)], the 3A' and the two degenerate 3A" states [S. Rogers, D. Wang, A. Kuppermann, and S. Wald, J. Phys. Chem. A 104, 2308 (2000)], and the spin-orbit couplings between them [B. Maiti, and G. C. Schatz, J. Chem. Phys. 119, 12360 (2003)]. Our quantum dynamics calculations clearly demonstrate that the spin-orbit coupling between the triplet states of different symmetries has the greatest contribution to the intersystem crossing, whereas the singlet-triplet coupling is not an important effect. A branch ratio of the spin state Pi32 to Pi12 of the product OH was calculated to be approximately 2.75, with collision energy higher than 0.6 eV, when the wave packet was initially on the triplet surfaces. The quantum calculation agrees quantitatively with the previous quasiclassical trajectory surface hopping study.     

Spin-orbit vibronic coupling in 3Pi states of linear triatomic molecules

The Renner-Teller vibronic-coupling problem of a 3Pi electronic state of a linear molecule is analyzed with the inclusion of the spin-orbit coupling of the 3Pi electronic state, employing the microscopic (Breit-Pauli) spin-orbit coupling operator for the two unpaired electrons. The 6x6 Hamiltonian matrix in a diabatic spin-electronic basis is obtained by an expansion of the molecular Hamiltonian in powers of the bending amplitude. The symmetry properties of the Hamiltonian with respect to the time-reversal operator and the relativistic vibronic angular momentum operator are analyzed. It is shown that there exists a linear vibronic-coupling term of spin-orbit origin, which has not been considered so far in the Renner-Teller theory of 3Pi electronic states. While two of the six adiabatic electronic wave functions do not exhibit a geometric phase, the other four carry nontrivial topological phases which depend on the radius of the integration contour. The spectroscopic effects of the linear spin-orbit vibronic-coupling mechanism have been analyzed by numerical calculations of the vibronic spectrum for selected model examples.     

Smooth relativistic Hartree-Fock pseudopotentials for H to Ba and Lu to Hg

We report smooth relativistic Hartree-Fock pseudopotentials (also known as averaged relativistic effective potentials) and spin-orbit operators for the atoms H to Ba and Lu to Hg. We remove the unphysical extremely nonlocal behavior resulting from the exchange interaction in a controlled manner, and represent the resulting pseudopotentials in an analytic form suitable for use within standard quantum chemistry codes. These pseudopotentials are suitable for use within Hartree-Fock and correlated wave function methods, including diffusion quantum Monte Carlo calculations.     

Calculation of the vibronic structure of the X2Pi photoelectron spectra of XCN, X=F, Cl, and Br

The vibronic structure of the photoelectron spectra of the X (2)Pi state of XCN(+) (X=F, Cl, and Br) has been calculated, assuming that the X (2)Pi state can be considered as an isolated electronic state. The Renner-Teller coupling of the two components of the (2)Pi state via the degenerate bending mode as well as spin-orbit coupling effects are taken into account. The two stretching modes are treated within the so-called linear vibronic-coupling model. The vibronic and spin-orbit parameters have been determined by accurate ab initio electronic-structure calculations. While spin-orbit effects are small in FCN(+), the large spin-orbit splitting of the X (2)Pi state of the BrCN(+) leads to a complete quenching of the Renner-Teller effect. The X (2)Pi state of the ClCN(+) is shown to be of particular interest: here the resonance condition for linear-relativistic Renner-Teller coupling is approximately fulfilled. This coupling mechanism leads to a significant intensity transfer to vibronic levels with odd quanta of the bending mode. The calculated spectrum indicates that this novel relativistic vibronic-coupling effect should be observable in high-resolution (electron energy resolution of the order of a few meV) photoelectron spectra of ClCN.     

Spin-orbit coupling in O2(upsilon)+O2 collisions: I. Electronic structure calculations on dimer states involving the X 3Sigmag-, a 1Deltag, and b 1Sigmag+ states of O2

The importance of vibrational-to-electronic (V-E) energy transfer mediated by spin-orbit coupling in the collisional removal of O2(X 3Sigmag-,upsilon>or=26) by O2 has been reported in a recent communication [F. Dayou, J. Campos-Martinez, M. I. Hernandez, and R. Hernandez-Lamoneda, J. Chem. Phys. 120, 10355 (2004)]. The present work provides details on the electronic properties of the dimer (O2)2 relevant to the self-relaxation of O2(X 3Sigmag-,upsilon>0) where V-E energy transfer involving the O2(a 1Deltag) and O2(b 1Sigmag+) states is incorporated. Two-dimensional electronic structure calculations based on highly correlated ab initio methods have been carried out for the potential-energy and spin-orbit coupling surfaces associated with the ground singlet and two low-lying excited triplet states of the dimer dissociating into O2(X 3Sigmag-)+O2(X 3Sigmag-), O2(a 1Deltag)+O2(X 3Sigmag-), and O2(b 1Sigmag+)+O2(X 3Sigmag-). The resulting interaction potentials for the two excited triplet states display very similar features along the intermolecular separation, whereas differences arise with the ground singlet state for which the spin-exchange interaction produces a shorter equilibrium distance and higher binding energy. The vibrational dependence is qualitatively similar for the three studied interaction potentials. The spin-orbit coupling between the ground and second excited states is already nonzero in the O2+O2 dissociation limit and keeps its asymptotic value up to relatively short intermolecular separations, where the coupling increases for intramolecular distances close to the equilibrium of the isolated diatom. On the other hand, state mixing between the two excited triplet states leads to a noticeable collision-induced spin-orbit coupling between the ground and first excited states. The results are discussed in terms of specific features of the dimer electronic structure (including a simple four-electron model) and compared with existing theoretical and experimental data. This work gives theoretical insight into the origin of electronic energy-transfer mechanisms in O2+O2 collisions.     

Ab initio investigation of potential energy curves of the 23 electronic states of IBr correlating to neutral (2)P atoms

Potential energy surfaces for all Born-Oppenheimer electronic states of IBr molecule correlating to the neutral (2)P ((2)P(3/2) and (2)P(1/2)) iodine and bromine are calculated for the first time. Electric dipole and polarizability curves (static and transition) are also determined. Calculations include scalar and spin-orbit relativistic effects within all-electron Douglas-Kroll two-component Hamiltonian. Electron correlation is treated with quasi-degenerate multi-reference second-order perturbation theory. Seven adiabatic electronic states (X (1)Sigma(+), A'(3)Pi(2), A (3)Pi(1), 1 (3)Pi(0-), B (3)Pi(0+), B'(3)Sigma, and 2 (3)Pi(0+)) exhibit significant covalent bonding, and can support vibrational states. Calculated spectroscopic parameters agree with experiment to better than 1000 cm(-1) (T(e)), 10 cm(-1) (omega(e)), and 0.05 Angstrom (r(e)). A new 1 (3)Pi(0-) state correlating to ground-state atoms is predicted at T(e) approximately 14 000 cm(-1), omega(e) approximately 80 cm(-1), and r(e) approximately 3.0 Angstrom. The second new state (2 (3)Pi(0+)) correlates to excited iodine atom, with T(e) approximately 20 000 cm(-1), omega(e) approximately 115 cm(-1), and r(e) approximately 3.3 Angstrom. Non-adiabatic coupling parameters are calculated for the four avoided crossings, which arise due to electronic spin-orbit interaction. Estimated parameters of the B (3)Pi(0+)/B'(3)Sigma crossing (R(c) approximately 3.32 Angstrom; V approximately 120 cm(-1)) agree with experimental values. The previously unsuspected 2 (3)Pi(0-)/1 (1)Sigma(-) crossing of two repulsive surfaces provides a new collisional deactivation channel for Br* atoms at relative velocities above 1000 m s(-1). Several repulsive states (including 1 (1)Pi(1) and 2 (3)Pi(1)) intersect the B/B' system near the avoided crossing point, and may affect dynamics of IBr in strong laser fields.     

Ab initio treatment of the chemical reaction precursor complex Cl(2P)-HF. 2. Bound states and infrared spectrum

Bound energy levels and properties of the Cl(2P)-HF complex were obtained from full three-dimensional (3D) calculations, with the use of the ab initio computed diabatic potential surfaces from the preceding paper and the inclusion of spin-orbit coupling. For a better understanding of the dynamics of this complex we also computed a 2D model in which the HF bond length r was frozen at the vibrationally averaged values r0 and r1 and a 2 + 1D model in which the 3D potentials were averaged over the v(HF) = 0 and v(HF) = 1 vibrational wave functions of free HF. Also 1D calculations were made in which both r and the Cl-HF distance R were frozen. The complex is found to have the linear hydrogen bonded Cl-HF structure, with ground-state quantum numbers J = 3/2 for the overall angular momentum and /omega/ = 3/2 for its projection on the intermolecular axis R. The binding energy is D0 = 432.25 cm(-1) for v(HF) = 0 and D0 = 497.21 cm(-1) for v(HF) = 1. Bending modes with /omega/ = 1/2 and /omega/ = 5/2 are split by the Renner-Teller effect, since the electronic ground state is a degenerate 2pi state. A series of intermolecular (R) stretch modes was identified. Rotational constants and e-f parity splittings were extracted from the levels computed for J = 1/2 to 7/2. The computed red shift of the HF stretch frequency of 64.96 cm(-1) and the 35Cl-37Cl isotope shift of 0.033 cm(-1) are in good agreement with the values of 68.77 and 0.035 cm(-1) obtained from the recent experiment of Merritt et al. (Phys. Chem. Chem. Phys. 2005, 7, 67), after correction for the effect of the He nanodroplet matrix in which they were measured.