The electronic states of silicon monofluoride: Rydberg states

SCF-CI calculations are reported for the Rydberg states converging to the ground state of the SiF⁺ ion. The adjustment between the observed and calculated values for the energy of the first Rydberg B²Σ⁺ state has allowed the characterization of 15 observed ²Σ⁺ and ²Π Rydberg states. A value of 58960 cm^?1 has been obtained for the ionization potential of SiF. The A²Σ⁺ state appears to be a valence state with some Rydberg character.     

Electronic states of SiF and SiF+: Configuration-interaction studies

For SiF, low-lying ²Π, ⁴Π, ²Σ⁺, ⁴Σ⁺, ²Σ⁻, ⁴Σ⁻, ²Δ, and ⁴Δ states were studied by configuration-interaction methods, using a double-zeta plus polarization basis set with 4s, 4pσ, 4pπ, and 5pπ Rydberg orbitals. Potential energy curves and spectroscopic constants for 17 stable valence and Rydberg states are given. The lowest ²Σ⁻ state is repulsive. There is good agreement with known spectroscopic constants. Besides A²Σ⁺, another semidiffuse state, 1⁴Π, is predicted. For the isoelectronic PO molecule, 2π → 3π valence excitations lie below Rydberg excitations, such that 2²Π of PO derives from 2π → 3π, whereas 2²Π of SiF derives from 3π → 4pπ. Dipole moments of X²Π and A²Σ⁺ at their respective R_e, and the radiative lifetime of A²Σ⁺ were calculated. For SiF⁺, many electronic states were investigated, but only two, the X¹Σ⁺ ground state and 1³Π are found to be stable. The ionization energy of SiF is calculated to be 6.87 eV (adiabatic) and 7.05 eV (vertical).     

Rydberg states of carbon dioxide and carbon disulfide

The electronic absorption spectra of carbon dioxide and carbon disulfide have been reexamined. Model potential calculations have been used to calculate the energies of excited states in Rydberg approximation, and (npσ) and (npπ) Rydberg series have been assigned. For both molecules, the lowest excited ¹Π_g and ¹Π_u states are identified as Rydberg states. The lowest ${}^1\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ state is mainly Rydberg for CO₂, but contains some valence character for CS₂, There is no evidence for transitions to additional valence states of these symmetries.It is shown that $\text{LCAO}\text{MO}$ predictions about excited states can be misleading because of near-linear dependencies which arise in multicenter expansions. A consideration of the united atom orbitals for CO₂ and CS₂ predicts that there should be only the number of low-energy excited states which are found from the spectral analysis.     

A CASSCF/MRCI study of the low-lying Rydberg states of CIO

An ab initio calculation has been performed on the lowest seven doublet and six quartet Rydberg states of CIO at the CASSCF/MRCI level and with basis sets suitable for the extended molecular orbitals of such states (aug-cc-pVTZ with up to eleven extra Gaussian functions). Calculations on the quartet states reveal the energy ordering of Rydberg orbitals to be 4sσ, 4pπ, 4pσ;, 3dδ, 3dσ and 3dπ. The calculated doublet ab initio potential curves confirm experimental assignments of the C²Σ- and F²Σ- states but require reassignments for the symmetries of the D (²Δ), E (²Π) and H (²Δ) Rydberg states. These revisions are supported by spin-orbit coupling calculations that suggest the separation between the Ω components is small. In addition, a ²Σ⁺ state has been identified as the likely upper state for two previously unassigned vibronic bands recorded in absorption studies.     

MRCI studies on ground and excited states of CBr

Potential curves and spectroscopic constants for a large number of doublet and quartet states of CBr were obtained by multireference configuration interaction calculations, using valence triple-zeta basis sets with polarization and diffuse functions. Besides the X²Π ground state, 1⁴Σ^?, 1²Δ and 2²Σ⁺ have been found to be stable. Spectroscopic constants calculated for 1²Δ are in excellent agreement with experimental values obtained by Dixon and Kroto in 1963. Their observed predissociation of one component of 1²Δ can be explained by the crossing of the 1²Δ potential near equilibrium by 1²Σ⁺. The 1²Σ⁺ state is calculated to have a shallow long-range minimum at 2.31?Å. The dissociation energy of X²Π is calculated to be 3.43?eV. An observed T _e of 4.97?eV for 2²Σ⁺ agrees with the theoretical value. Several Rydberg states of the 2π→Ryd and 3σ→Ryd series, starting at T _e ?=?5.25?eV, were identified. Photodissociation of CBr by sunlight, important in the ozone cycle, can occur via direct dissociation of the ground state, or by excitation to 1²Δ followed by predissociation. Most dissocative repulsive states lie at higher energies, and are not expected to participate in the photodisscociation of CBr.     

Rydberg states with a 2Π core: The b3Πi and C1Π states of DCl

The rotational structure in the lowest Rydberg complex of hydrogen chloride, [X²Π]4sσ, was reinvestigated. The study is limited to the spectrum of D³⁵Cl, the HCl bands being too diffuse for a detailed analysis of second-order effects. The Λ-type doubling in both component states, b³Π_i and C¹Π, is small since it arises from the uncoupling of the core rather than Rydberg orbital angular momentum. It can be interpreted in terms of pure precession relations that are known to exist between the ground and first excited states of DCl⁺. By contrast, the spin-orbit interactions, also originating in the core, are strong. In addition to distorting the triplet splitting in b³Π, they lead to an avoided crossing between the nearly coinciding levels b³Π₀ (v = 1) and C¹Π₁ (v = 0). They are also responsible for anomalies in the b³Π₀ ← X¹Σ⁺R-branch intensities of DCl as well as of HBr, DBr, and HI. From the J values at the observed R-branch minima we have estimated the ratio $\text{μ}{}_{\mathrm{\parallel }}\text{μ}{}_{\mathrm{\perp }}$ of the transition moments associated with the excitation of a 3pσ or 3pπ core electron to the 4sσ Rydberg orbital of DCl and, correspondingly, of the other hydrogen halides.     

New valence and Rydberg states of the P18O molecule

The absorption spectrum of the P¹⁸O molecule has been studied in the region 1650–1800 Å. The upper levels of the transitions are shown to be levels of new ²Π valence, ²Π Rydberg and ²Δ Rydberg states of the PO molecule. Most of the levels are perturbed; some of them are predissociated. The new valence state P²Π corresponds to a regular state of the electronic configuration $\text{σ}{}^2\text{π}{}^3\text{π}{}^{12}$ and the ²Π and ²Δ Rydberg states belong to the 5p, 3d, 4d complex series. Perturbations of the P²Π state are shown to arise from Rydberg ～ Non Rydberg interactions with states of same or different symmetry. The complexity of the interactions does not allow to carry out a deperturbation but a comparison with the data of the P¹⁶O molecule allows to give a vibrational assignment to the levels of the P²Π state.     

CASPT2 and CCSD(T) calculations of dipole moments and polarizabilities of acetone in excited states

The acetone molecule is investigated in its ground state and valence ^1,3n-π*, ^1,3π-π*, and ^1,3σ-π* excited states and Rydberg ^1,3n-3s, ^1,3π-3?, ^1,3n-3p_y and ^1,3π-3p_y states using the CASSCF, CASPT2, and CCSD(T) methods. Equilibrium geometries of excited states are obtained and their changes with respect to the ground state are discussed. For most excited states the C_2v symmetry of the ground state is lowered to the C_s symmetry. A series of valence vertical and adiabatic excitation energies is presented along with excitation energies for Rydberg states. The main body of the paper contains Finite-Field Perturbation Theory (FFPT) calculations of electric properties of the vertically as well as geometry relaxed excited states. Dipole moments of valence excited states decrease significantly upon excitation, being about one half of the ground state dipole moment. Polarizabilities usually change upon excitation much less (increase by about 30%) but hyperpolarizabilities are enhanced up to one or two orders of magnitude. The orientation of the dipole moment is reversed in some vertically excited Rydberg states. Properties of the ground and excited states are discussed considering alterations of the electronic structure and shifts in the geometry.     

The electronic states of carbon monofluoride: Low-lying valence states

Multiconfiguration Hartree-Fock calculations are reported on the low-lying valence states, the X²Π, ⁴Σ^?, B²Δ, and ²Σ^± states, of carbon monofluoride. The wavefunctions describe dissociation of the molecule to the correct atomic limits and take account of the atomic 2s-2p near-degeneracy effect. For the ground state the calculations give (with experimental values in parentheses): a bond length of 1.286 Å (1.2667 Å), a fundamental frequency of 1292 cm^?1 (1308 cm¹), and a dissociation energy of 3.93 eV (5.5 ± 0.1 eV). A ⁴Σ^? state arising from the $\text{C}\text{(}{}^3\text{P) +}\text{F}\text{(}{}^2\text{P)}$ manifold is calculated to lie just 2.66 eV above the ground state. The B²Δ state, calculated adiabatic excitation energy 6.59 eV (6.12 eV), is found to dissociate to $\text{C}\text{(}{}^1\text{D) +}\text{F}\text{(}{}^2\text{P)}$ via a potential maximum. Calculations are also reported on a repulsive ²Δ state arising from ground state atoms.     

Fourier transform spectroscopy of the low-lying excited electronic states of FeO: A new perturbing Σ state and improved ground state constants

A small rotational perturbation has been found in the ⁵Δ_i ground state of FeO. This occurs in the v = 2 level of the $\text{Ω}\text{= 2}$ substate, and only one Λ-boudling component of one rotational level is affected. The perturbing state, which lies about 2100 cm^?1 above the lowest spin-orbit level of the molecule, is orbitally nondegenerate, and is likely to belong to the ⁷Σ⁺ state arising from the configuration (4sσ)¹(3dδ)²(3dπ)²(3dσ)¹. The new state, a⁷Σ⁺, is possibly responsible for anomalies in the intensity pattern of the FeO^? photodetachment spectrum of Engelking and Lineberger [J. Chem. Phys., 66, 5054–5058 (1977)]. Improved vibrational and rotational constants are presented for the ground state, combining new Fourier transform measurements of the Λ-doubling in X⁵Δ₁ with the recent microwave data of Endo et al. [Astrophys. J., 278, L131–132 (1984)].     

The electronic spectrum of PN. A configuration interaction study

Potential energy curves were calculated for the ground state of PN and for all excited singlet and triplet states resulting from the 2π → 3π, 7σ → 3π, 2π → 8σ, and 7σ → 8σ orbital excitations. CI studies at 4 Å served to establish dissociation energies. Spectroscopic constants were calculated, and are in good agreement with those of the known X¹Σ⁺ and A¹Π states. Overall, their similarity with those observed for N₂ is striking. Various states considered to perturb the known excitations are discussed. The recently discovered second ¹Σ⁺ state is included.     

The electronic states of silicon monofluoride: Low-lying valence states

Hartree-Fock and configuration interaction calculations are reported for the lowest valence state of the SiF molecule. Deduced spectroscopic constants are in good agreement with the experimental values. The dipole moment calculated for SiF is consistent with a charge distribution corresponding to a Si⁺F^? configuration.     

A multi-reference CI study of the low-lying valence and Rydberg states of CF3 radical

Highly correlated calculations at the multi-reference configuration interaction levels including singles and doubles excitations (MR-CISD) and extensivity corrections (MR-CISD?+?Q) have been performed to study some low-lying valence and Rydberg states of the CF₃ radical. Our highest level results (at the MR-CISD?+?Q level) yield the following energy ordering: 3s (7.90?eV)?2A₂ (8.61?eV)?π (8.72?eV)?z (8.73?eV). MR-CISD results indicate transitions of similar intensities from the ground to the following three final states, in the following order: 3p_π?>?3p_z?>?3s. It has also been found that the aforementioned Rydberg states should be responsible for visible emissions and correspond to transitions between bound states. Therefore, it is suggested that the lack of vibrational structure in the visible band of parent systems (e.g. CF₃Cl) may be due to a transition from a bound to an unbound state of the parent molecule.     

Absorption spectrum of CO in the Hopfield helium continuum region: Rydberg bands converging to the X2Σ+ state of CO+ in the region 960–1080 Å

The high resolution absorption spectrum of CO has been reinvestigated in the Hopfield helium continuum region, particularly from 960 to 1080 Å. The Rydberg state 3pπE¹Π was extended to v = 2, and other Rydberg states, $\text{3dσ}{}^3\text{Σ}{}^{\mathrm{+}}$ and F¹Σ⁺, $\text{3dπ}{}^1\text{Π}$, and $\text{4sσ}{}^3\text{Σ}{}^{\mathrm{+}}$ and ¹Σ⁺, which are converging to the X²Σ⁺ ground state of CO⁺, have been identified. The rotational structures of only five bands among the observed ten Rydberg bands have been analyzed.     

Partially restricted Hartree-Fock method for singlet excited states

A version of the partially spin-restricted Hartree-Fock method is proposed to construct a reference Slater determinant in calculations of singlet excited states having the same symmetry as the ground one. On the one hand, this approach can be used for a rather simple, in comparison with the fully unrestricted determinant, construction of a pure spin state. On the other hand, it is suitable, in contrast to the Roothaan theory for open shells, for the development of the perturbation scheme for taking into account correlation effects in an excited state, which retains the calculation advantages of the Moller-Plesset perturbation theory with single annihilation for the ground state. The efficiency of the method is demonstrated by calculations of electronic excitation energies for BH and CH⁺ molecules.     

BO: Low-lying electronic states obtained by configuration-interaction studies

Configuration-interaction studies were performed on low-lying ²Σ⁺, ²Σ⁻, ²Π, ²Δ, ⁴Σ⁺, ⁴Σ⁻, ⁴Π, and ⁴Δ states of BO. Sixteen stable states have been found, among them four 3s_B Rydberg states. Spectroscopic constants are compared with those of the four observed states and with theoretical results obtained by others. Particular attention is given to the observed perturbations in the C²Π state, which can be explained by interaction with 1²Δ, 1²Σ⁻, 3²Σ⁺, and other states. Comparison with isoelectronic molecules CN and CO⁺ reveals many similarities.     

High-spin states in26Mg

Theγ-decays of levels in²⁶Mg have been investigated up to 12.5 MeV excitation energy by proton-γ-ray coincidence measurements in the²³Na(α, pγ) reaction at 14.2 and 16 MeV bombarding energy. Lifetime-measurements, made with the Doppler-shift attenuation method, and proton-γ-ray angular-correlation measurements were performed at E_α=14.2 MeV. Many high-spin states were observed, among them levels at 6,978 (5⁺), 7,283(4^?), 7,395(5⁺), 7,953(5^?), 8,202(6⁺), 8,472(6⁺), 9,065(5), 9,112(6⁺), 9,169(6^?), 9,383 (6⁺), 9,542(5), 9,829(7⁺), 9,989(6⁺) and 12,479(8⁺, 7^?) keV excitation energy. The spectrum of positive-parity states and their electromagnetic properties are reproduced with good accuracy by shell-model calculations which employ a unifieds-d shell Hamiltonian and the unrestricted configuration space of the 0d _5/2 1s _1/2 0d _3/2 shell. Members of five inferred rotational bands, withK ^π=0⁺, 2⁺, 3⁺, 0⁺ and 3^? have been observed up to at leastI=6. TheK ^π=2⁺ band shows strong anomalies of excitation energies andE2 transition rates near theI=6 state. The static intrinsic quadrupole moments calculated from the shell model wave functions indicate transitions from prolate to oblate deformation within theK ^π=2⁺ band and also the ground state band. The lowest lyingI ^π=4⁺ state appears to be “spherical” and cannot be associated with a rotational band.     

High-spin states in109Sn and their decay to the ground state

An extended level scheme of¹⁰⁹Sn is presented showing high-spin states up to E_x≈ 8 MeV and spins up toJπ=(41/2+). Their decay to the 5/2+ ground state has been observed identifying a 12.8 keV 7/2⁺ → 5/2⁺ transition. A half-life of T_1/2=7(1) ns has been measured for the 17/2⁺ state atE _x =2114 keV. The experimental data are compared with the predictions of shell-model calculations.