Diatomic States Research Articles

Strongly bound excited states of heteronuclear diatomics: BeC

The theoretical study of strongly bound doubly excited electronic states, discussed by the authors for a series of homonuclear diatomic molecules, is extended to the case of heteronuclear diatomics. Using BeC as a prototype, it is shown that the significant bond shortening and strengthening shown in the isoelectronic B2 also persists in BeC, in spite of the much greater configuration mixing in BeC due to the lower symmetry. In particular, excitations of the form σ→π cause a predictable increase in (local) bond strength. Potential curves and spectroscopic constants are given for the low-lying states correlating up to the sixth dissociation channel. Compared to the ground state X 3Σ− with Re=3.20 bohr and ωe=905 cm−1, the doubly excited state 3 1Σ+ has a local minimum at Re=2.87 bohr where ωe=1294 cm−1, a significant bond strengthening comparable to the homonuclear diatomics. The contribution to the total (CI) wave function for each state is analyzed in terms of the dominant contributions from the important configurations. SCF potential curves for the pure configurations and MO contour maps are used to understand the relationship with the homonuclear case. Vertical transition moments for the most important transitions are given to help in identification of the (as yet unobserved) electronic absorption spectrum.

Generation of Diatomic Diabatic States by a General Multi-State Rotation

Abstract We present a general multi-state orthogonal transformation program that generates a set of diatomic electronic diabatic states from a set of vibronically interacting adiabatic states of the same symmetry.

Geometric and electronic structure of ground and excited states of groupVA diatomics. A theoretical LCGTO-MP-LSD study

LCGTO-MP-LSD calculation was performed for the ground and several low-lying excited states of homo- (N2, P2, As2, and Sb2) and hetero-nuclear (PN, AsN, AsP, AsSb, SbN, and SbP) groupVA diatomics. For all the systems the ground state is found to be1Σ+. For N2 and P2, the1Σg+ ground state is followed by the3Σu+,3Πg,3Δu,1Πg, and1Δu low-lying exited states while for As2 the order is found to be3Σu+,3Δu,3Πg,1Δu,1Πg. Finally for Sb2 the relative stability of excited states is3Σu+,3Δu,1Δu,3Πg,1Πg. For the hetero-nuclear diatomics the1Σ+ ground state is, in the case of PN, AsN, AsP, SbN, and SbP, followed by the3Σ+,3Δ,3Π,1Π and1Δ low-lying excited states while for the AsSb diatomic an inversion of stability of the two last singlets occurs. The calculated spectroscopic parameters (Re, ωe, andDe) are in good agreement with all the available experimental results while, theTe values are overestimated by about 0.5 eV. Mulliken population analysis shows that both homo- and hetero-nuclear groupVA diatomics are essentially triple bonded systems.

A semi-classical examination of the Birge-Mecke rule and other relationships between the constants of diatomic molecules

A semi-classical analysis of the rotational response of diatomic vibrotors to anharmonic oscillation leads to the relations μ A ω e χ e r 2 e ≅ 135 a.m.u.-cm -1 Å 2 and ω e χ e / B e ≅ 8 between comprehensive than the empirical Birge-Mecke formulae, and they are remarkably well followed by over 200 diatomic molecular electronic states which are well represented by Morse potentials.

Symmetry restrictions in diatom/diatom reactions. I. Group theoretical analysis

New permutation inversion (PI) symmetry groups are presented which can be used to symmetry classify the nuclear-rotational–vibrational–electronic–translational wave function (Ψnrvet) of an A2/A2, A2/AB, A2/B2, or AB/AB collision system, where the diatomic electronic states can be of any spatial symmetry or spin multiplicity. A symmetry correlation scheme based on these PI groups is developed which connects symmetry distinct nuclear motion states of Ψnrvet at infinite diatom/diatom separation with distinct electronic symmetries of the system in the diatom/diatom interaction region. Consideration of the effect of isotopic substitution on the correlation indicates that a kinetic isotope effect which is based on symmetry rather than mass considerations can occur in reactions where (1) the molecules are identical, but in different electronic states, or (2) at least one of the reactants is in a degenerate electronic state. Application of the correlation scheme to the kinetics of the H+2/H2 proton/atom transfer reaction (and its isotopic analogs) indicates that the experimentally observed unusual isotope effects can be understood as a consequence of this new symmetry based kinetic isotope effect. The possibility of observing this effect in the reactions of more complex molecules is discussed briefly.

Theory and ab initio calculation of partial widths and interchannel coupling in predissociating diatomic states: application to HeF

According to previously published theory, it is possible to obtain partial widths to all orders, of multichannel decaying states, by diagonalizing relatively small, state-specific complex matrices constructed from appropriate square integrable functions of real and complex coordinates. Here, an ab initio method is presented for computing predissociating states of polyelectronic diatomic molecules. Application is made to the recently calculated 2 2 Σ + excimer state of HeF which decays to the repulsive X 2 Σ + and 1 2 Π states. It is found that for the X 2 Σ channel, the all-orders result differs from that of the golden-rule formula by an order of magnitude.

Electronic states and potential energy surfaces of H2Te, H2Po, and their positive ions

Geometries, bond energies, ionization potentials, dipole moments, other one-electron properties, and potential energy surfaces of six valence electronic states of H2Te and H2Po species are obtained using the relativistic complete active space multiconfiguration self-consistent field (CASSCF) followed by full second-order configuration interaction (SOCI) and relativistic configuration interaction (RCI) calculations including spin–orbit coupling. In addition, Rydberg states of H2Te and H2Se are studied to interpret the experimental spectra. The potential energy surfaces of two electronic states of H2Te+ and H2Po+ are obtained. The ground states of both H2Te and H2Po are found to be of X 1A1(A1) symmetry with bent (C2v) equilibrium geometries of H2Te:re=1.668 Å, θe=91.2°; and H2Po:re=1.835 Å and θe=90.9°. The ground states of H2Te+ and H2Po+ are X 2B1 with H2Te+:re=1.676 Å, θe=90.7° and H2Po+:re=1.828 Å and θe=88°. The De (HTe–H) and De (HPo–H) including spin–orbit effects are calculated as 63.2 and 39.4 kcal/mol, respectively. The X 2B1(E)−A 2A1(E) energy separations of H2Te+ and H2Po+ ions are calculated as 66.6 and 76 kcal/mol, respectively. The adiabatic IPs of H2Te and H2Po are calculated as 8.47 and 7.79 eV, respectively. In addition CASSCF/SOCI/RCI calculations are also carried out on the X 2Π3/2 and 2Π1/2 states of TeH and PoH diatomics. The X 2Π3/2–2Π1/2 energy separations of TeH and PoH are computed as 3710 and 9920 cm−1, respectively. Spin–orbit effects are thus found to be very significant for PoH and H2Po. All excited states of H2Te and H2Po are above 3.7 and 3.1 eV, respectively. Properties and energy separations of H2Te and H2Po are compared with the lighter group (VI) H2Ch species.

Potential functions for the inner branches of diatomic potential curves

The performance of simple three-parameter potential functions in predicting the inner branches of known diatomic potentials is tested for 35 diatomic molecular states. The Varshni III potential outperforms the Morse and Rydberg functions when the spectroscopic Re, ωe, and De values are used to define the potential parameters, but all three functions perform comparably well when Re, ωe, and ωexe are used. In the latter case the 35 potentials show an average absolute value of about 0.6% for the maximum relative error. Keywords: diatomic molecules, potential energy curves.

On the dynamic couplings between magnetically dressed molecular states

The dynamic (radial and rotational) couplings between diatomic molecular states are considered for the case that these states are 'dressed' by a strong, external magnetic field. The explicit form of the dynamic coupling operator is derived within the classical-trajectory approximation to the internuclear motion. The radial and rotational coupling matrix elements are expressed in a form suitable for efficient numerical evaluation.

Clarification of the electronic asymmetry of Λ doublets in 3Π electronic states of diatomic molecules

The reflection symmetry of the spatial part of the electronic wave function for 3Π diatomic molecular states is examined carefully for the individual Λ doublet levels by means of an approach presented earlier [M. H. Alexander and P. J. Dagdigian, J. Chem. Phys. 80, 4325 (1984)]. The results are: For a 3Π molecule in Hund’s case (a) the electronic wave function in the Ω=1 (F2) e levels will be antisymmetric and, in the the f levels, symmetric with respect to reflection of the spatial coordinates of the electrons in the plane of rotation of the molecule. The electronic wave functions in the F1 and F3 levels will not have a defined plane of symmetry. By contrast, in the Hund’s case (b) high J limit, the electronic wave function in the F1e, F2 f, and F3e levels will be antisymmetric and, in the F1 f, F2e, and F3 f levels, symmetric with respect to reflection. Thus, the symmetry of the wave functions in the F2Λ-doublet levels reverses with the passage from case (a) to case (b). In the case (b) limit, the main branch P and R lines of a 3Π–3Σ− transition will probe antisymmetric levels, irrespective of the Fi level of the 3Π state, while the main branch Q lines will probe symmetric levels. This will be reversed for a 3Π–3Σ+ transition. At low J, in the case (a) limit, in a 3Π–3Σ− transition the P2i and R2i lines with i odd and the Q2i lines with i even will probe antisymmetric levels, while the P2i and R2i lines with i even and the Q2i lines with i odd will probe symmetric levels; the other 18 rotational branches probe levels with no well-defined reflection symmetry.

Ground and excited states of group IVA diatomics from local-spin-density calculations: Model potentials for Si, Ge, and Sn

LCGTO-MP-LSD results are reported for the spectroscopic constants and electronic structure of the diatomic molecules Si2, Ge2, Sn2, SiGe, SiSn, and GeSn in their low-lying electronic states. For the homonuclear molecules we found that the ground state is 3Σ−g with the most important lower-lying excited states being 3Πu, 1Πu, and 1Σ+g, respectively. Our results are in good agreement with the available experimental data and also in qualitative agreement with other theoretical studies. We present here the first theoretical study on the heteronuclear molecules, for which experimental data are not available. We found the 3Σ− state to be the lowest, followed by 3Π and 1Σ+ states. Model potentials (MP) are reported for the Si, Ge, and Sn atoms. The reliable results for molecules complement those for the atoms and show that the LSD model potentials presented here allow for an accurate description of chemical bonding and spectroscopic properties in the title molecules.

Spontaneous emission by two atoms with different resonance frequencies near a metal surface. II

The quantum-mechanical image method is extended to consider the interaction between the electromagnetic radiation and two different atoms with their electronic transition dipoles oriented in arbitrary directions near a perfectly conducting metal surface. The atom-atom and atom-surface separations are assumed to be smaller than the corresponding mean resonance wavelength. A general form of atom-image correlation state is constructed for the arbitrarily oriented atomic dipole and its physical interpretation is given. Based on this generalized formulation, the total emission rate is calculated for the diatomic system in several experimentally preparable initial states, whose initial emission rates are found to be dependent on the orientation of the emitting dipoles. These peculiar emission pattern can be accounted for by the dependence of the phase relations between the constituent terms of the diatomic states on the dipole orientation. Detailed examination in this regard is addressed, as an example, to the antisymmetric diatomic state.

Diatomics-in-molecules fragment matrices suitable for application to large molecules

A procedure is developed for the construction of block-diagonal diatomic fragment matrices compatible with restricted polyatomic basis sets for the diatomics-in-molecules (DIM) method. The fragment matrices are obtained by projection from ab initio eigenvalues and wavefunctions for the diatomic molecule. The approach allows a substantial reduction in size of DIM models without violating self-consistency requirements. It makes the application of DIM to large molecules tractable. The procedure is illustrated for the H2(2 Sigma u+) diatomic state manifold.

Gerade Rydberg states and n s 3Σ+u(1u,0−u) photoionization spectra of the rare gas dimers (n=2–6)

Transient absorption spectra of rare gas dimer Rydberg transitions in the ultraviolet, visible, and near infrared (220≤λ≤900 nm) spectral regions have been observed in electron beam excited rare gases. The most prominent molecular bands for He2, Ne2, Ar2, Kr2, and Xe2 are assigned to the mp 3Πg←ns 3Σ+u (He:n=2, 3≤m≤10; Ne:n=3, 4≤m≤10; Ar:n=4, 5≤m≤15; Kr:n=5, 6≤m≤16; Xe:n=6, 8≤m≤11) Rydberg series of the dimer. Adiabatic ionization potentials, relative to the ns 3Σ+u state, are determined by extrapolation of the series to their limits (m→∞) to be 34 361.4±30 cm−1 (4.260±0.004 eV) for He2, 34 396.3±25 cm−1 (4.265±0.003 eV) for Ne2, 29 351.9±15 cm−1 (3.639±0.002 eV) for Ar2, 28 428.5±10 cm−1 (3.525±0.001 eV) for Kr2, and 26 664.5±250 cm−1 (3.306±0.031 eV) for Xe2. Absorption bands which are ascribed to m′p 3Σ+g←ns 3Σ+u Rydberg series of Ne2(m′=4,6,8), Ar2(5≤m′≤10), Kr2(6≤m′≤10), and Xe2(m′=8,9) are also reported, and the ns 3Σ+u ionization potentials found to be identical to the respective values quoted above. All of the observed molecular Rydberg states have an A 2Σ+1/2u ion core. The lowest vibrational quanta (ΔG1/2) for the ns 3Σ+u states are determined from vibronic structure in the Rydberg transitions to be 1723 cm−1 for He2, 539 cm−1 for Ne2, 302 cm−1 for Ar2, 172 cm−1 for Kr2, and 135 cm−1 for Xe2, and are consistent with previously reported values. The instability of the ns 3Σ+u metastable state with respect to the dimer ion core potential [D0(A 2Σ+1/2u)−D0(ns 3Σ+u)] is calculated to be 0.508±0.004 eV for He2, 0.681±0.003 eV for Ne2, 0.572±0.002 eV for Ar2, 0.560±0.001 eV for Kr2, and 0.52±0.03 eV for Xe2. Using these values and those reported in the literature for the dissociation energy of the dimer ion A 2Σ+1/2u state, D0(ns 3Σ+u) is estimated (Ne2: 0.67±0.07 eV; Ar2: 0.76±0.02 eV; Kr2: 0.62±0.02 eV; Xe2: 0.52±0.03 eV). By comparing energy level spacings, quantum defects, and absorption oscillator strengths for transitions between molecular or atomic states, the mp 3Πg Rydberg levels appear to correlate with the mp[3/2]2+1S0 atomic asymptotes. An important aspect of the experimental approach is that the diatomic excited states are studied in the vicinity of Re rather than at the van der Waals (ground state) minimum. Chemical forces (as opposed to ion-induced dipole interactions) dominate at small R and the resulting spectra are largely free of congestion arising from the perturbations and avoided curve crossings that are prevalent at large R. Therefore, insight can be obtained into the structure and behavior of molecular Rydberg states in the region near the first ionization limit A 2Σ+1/2u[1(1/2)u].

Symmetry aspects of diatomics‐in‐molecules (DIM) calculations. II. Construction of symmetry‐adapted diatomic fragment subspaces

AbstractA new general procedure is presented for the construction of symmetry adapted diatomic fragment sub‐spaces of spin‐adapted polyatomic DIM bases obtained by direct diagonalization of the polyatomic spin‐square operator. The spin part of the construction is accomplished by the diagonalization in the DIM basis of the diatomic spin‐square operators. The spatial part of relevant transformations is given in terms of quantum numbers of the constituent atomic functions. Simple expressions for the spatial symmetry and spin designation of the resulting symmetry‐adapted diatomic fragment states are obtained. Special attention is paid to consistent phases of diatomic fragment functions corresponding to equivalent fragments. The approach eliminates such mental operations from the construction of symmetry‐adapted diatomic fragment subspaces which are difficult to formulate in a way suitable for straightforward computer implementation.

Highly accurate vibration–rotation Franck–Condon factors for high levels

AbstractHighly accurate vibration–rotation Franck–Condon factors qab, for a transition between two diatomic electronic states (a) and (b), are sought. When the potentials of states (a) and (b) are of the RKR type, the computation of qab is reduced to that of Franck–Condon integral ℐab(i) = ∫ ψa(r)ψb(r) dr in an interval ri, ri+1. By using convenient interpolations for the potentials Ua and Ub in the considered interval, this integral becomes ℐab(i) = ∑ δ (ri+1 – ri)n+1/(n + 1), where the “coupling constants” δ depend uniquely on the eigenvalues Ea and Eb of the considered transition and on the potentials Ua and Ub (the number N of terms depends on the desired accuracy). The method used computes the Franck–Condon factors qab without the explicit use of the wave function and by replacing the integrals by simple summations. To test the values of qab obtained by this method, the orthogonality rule ∫ ψv′ψv″ dr = 0 (for v′ ≠ v″) is used for one state or the other. This test, along with other tests, show that the Franck–Condon factors computed by the present method are accurate to nine significant figures for high and low levels.

Yields of singlet nitrenes from halogen atom—azide molecule reactions

AbstractChemiluminescence from the a1Δ and b1Σ+ excited electronic states of nitrogen halide diatomics is observed when HN3 is allowed to react with mixtures of halogen atoms in a discharge‐flow apparatus. Excited NF (a1Δ) is produced by the F + HN3 reaction, and NCl (a1Δ, b1Σ+) and NBr (a1Δ, b1Σ+) are produced by the F, Cl, + HN3 and F, Br + HN3 reactions, respectively. In the low‐density limit, the yield of NF(a1Δ) was found to be near unity. The yields of the b1Σ+ states of NCl and NBr were determined to have a lower limit of ca. 10%. A number of results from these experiments, including direct observation of N3 radicals in the flow, support a hypothetical mechanism in which N3 acts as an intermediate. A second possible mechanism proceeding via an HNF intermediate cannot be ruled out.

Diatomics-in-molecules studies of the Li + H 2O interaction

Abstract The method of diatomics-in-molecules (DIM) is applied to calculate the potential energy surface of the ground 2 A 1 state of Li(H 2 O) relevant to the Li + H 2 O interaction. The polyatomic basis functions are constructed from the ground state functions of constituent atoms and of the ions Li + and O − . The diatomic state mixing for 2 Π symmetry of LiO is discussed on the basis of ab initio calculations. The potential curve for the 4 Π state of LiO, required for the calculation procedure, is computed by an ab initio multiconfigurational SCF method. Results of the DIM application for Li(H 2 O) are consistent with experimental and other theoretical data.

The propensity rules re-examined: Evidence for a long-lived complex in alkali diatomic-rare-gas collisions

Abstract When Δ J =±1 collision-induced transitions in Π states of excited alkali diatomics are examined over a wide range of pressures several curious phenomena are observed. With the heavier rare gases we find that the ± propensities reverse as pressure increases, and the circular polarisation of the parent line first decreases, with increasing pressure and then begins to rise, the change-over occurring at roughly the same pressure as the reversal Δ J =±1 collision propensities. A recently proposed theoretical model involving the formation of a long-lived atom—diatomic collision complex or Feschbach resonance is invoked to explain these unusual experimental results.

A study of the potential surface of LiOB by the method of diatomic fragments in molecules

The results of the calculations by the DFM method provide evidence that the minimum on the potential surface of LiOB in the state1A′ corresponds to the linear structure Li−O−B. Estimates of the dissociation energy with respect to various decomposition channels show that the molecule is stable. The qualitative behavior of the section of the potential surface corresponding to the minimum energy path for the intramolecular rearrangement Li−O−B→O−B−Li is independent of the adjustable parameters of the method—the coefficients of the mixing of the diatomic states of identical symmetry. The lack of agreement between the difference in the energies of the linear forms Li−O−B and O−B−Li and the results of nonempirical calculations indicates that the model of the molecule chosen within the framework of the DFM approach requires further refinement. In particular, the addition to the set of MBF of functions constructed with allowance for the excited state4P of the boron atom will make it possible to decrease this energy difference. It will then be necessary, however, to take into account the much larger number of states from the fragments BO and BLi.