Analysis of chemical bonding in C2 using Dyson orbitals

Multireference configuration interaction wave functions with single and double excitations were calculated for the ¹Σ⁺_g ground state of the C₂ molecule and the excited states of C⁺₂ with symmetries ²Σ⁺_g, ²Σ^-_u, ²Π_u, and ²Π_g. The corresponding σ_g, σ_u, π_u, and π_g valence Dyson orbitals were calculated. Most of the density due to the valence electrons is accounted for by three σ_g, one σ_u, and one degenerate pair of π_u Dyson orbitals. Electron correlation plays an important role in the bond strength of C₂ by increasing the occupation of the σ_g valence orbitals and decreasing the occupation of the σ_u and π_u valence orbitals. © 1996 John Wiley & Sons, Inc.     

A density functional study of Fe(SINGLE BOND)N2, Fe(SINGLE BOND)N+2, and Fe(SINGLE BOND)N−2

The interaction of an iron atom with molecular nitrogen was studied using density functional theory. Calculations were of the all-electron type and both conventional local and gradient-dependent models were used. A ground state of linear structure was found for Fe(SINGLE BOND)N₂, with 2S + 1 = 3, whereas the triangular Fe(SINGLE BOND)N₂ geometry, of C_2v symmetry, was located 2.1 kcal/mol higher in energy, at least for the gradient-dependent model. The reversed order was found using the conventional local approximation. In Fe(SINGLE BOND)N₂, the N(SINGLE BOND)N bond is strongly perturbed by the iron atom: It has a bond order of 2.4, a vibrational frequency of 1886 cm⁻¹, and an equilibrium bond length of 1.16 Å: These values are 3.0, 2359 cm⁻¹, and 1.095 Å, respectively, for the free N₂ molecule. With the gradient-dependent model and corrections for nonsphericity of the Fe atom, a very small binding energy, 8.8 kcal/mol, was calculated for Fe(SINGLE BOND)N₂. Quartet ground states were found for both Fe(SINGLE BOND)N⁺₂ and Fe(SINGLE BOND)N⁻₂. The adiabatic ionization potential, electron affinity, and electronegativity were also computed; the predicted values are 7.2, 1.22, and 4.2 eV, respectively. © 1997 John Wiley & Sons, Inc.     

Potential curves of Li2+ by a local potential method

Local potential calculations have been carried out for the first eight ²Σ_g, ²Σ_u and the first five ²Π_g, ²Π_u states of Li₂⁺. The results indicate the usefulness of calculating highly excited potential curves by a local potential method.     

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, the¹Σ _g ⁺ ground state is followed by the³Σ _u ⁺ ,³Π _g ,³Δ _u ,¹Π _g , and¹Δ _u low-lying exited states while for As₂ the order is found to be³Σ _u ⁺ ,³Δ _u ,³Π _g ,¹Δ _u ,¹Π _g . Finally for Sb₂ the relative stability of excited states is³Σ _u ⁺ ,³Δ _u ,¹Δ _u ,³Π _g ,¹Π _g . 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.     

Ab initio study of electronic energy transfer in the quenching of CO*(a 3Π) by H2

Potential energy calculations for the interaction of CO(a ³Π) with H₂(X ¹Σ_g⁺) are presented, both at the MC SCF level and with the inclusion of extensive configuration interaction. In C_2v geometry, the lowest two ³B₂ surfaces exhibit a strongly avoided crossing. At the highest level of theory used, the lowest surface provides a barrier-free adiabatic pathway for energy transfer from CO(a) to H₂, the products being CO(X ¹Σ⁺) and H₂(b ³Σ_u⁺), which dissociates to two H atoms. The energy transfer occurs by a two-electron exchange mechanism.     

A theoretical study of the bound electronic states of the C−2 negative ion

Configuration interaction calculation are employed to study the X ²Σ⁺_g, A ²Π_u, B ²Σ⁺_u, ⁴Σ⁺_u and ⁴Δ_u states of the C^?₂ ion. The results are in good quantitative agreement with experimental findings for the Herzberg—Lagerquist (²Σ⁺_u-²Σ⁺_g) bands and predict a T_e value for the ²Π_u state of only 0.40 eV; corresponding transition moment results are obtained as a function of CC distance. The Cl electron affinity is 3.43 eV, in good agreement with the most recent experimental estimate for this quantity.     

The structure of BO2 in its ground and low-lying excited states from ab initio SCF RHF AND CI calculations

Potential curves for the X²Π_g, A²Π_u, B²Σ⁺_u and C²Σ_g⁺ electronic states of BO₂ were calculated at ab initio SCF RHF and configuration interaction (CI) level. The results obtained are consistent with a linear molecular model for all states considered. The calculated structural parameters and transition energies are in good agreement with relevant experimental data.     

Laser excitation spectrum of the 0g+(X 1Σg+)−0u+(3Πu) transition in Cd2

Spectroscopic constants and bond strengths of ground-state 0_g⁺(¹Σ_g⁺) and excited state 0_u⁺(³Π_u) Cd₂ van der Waals molecules have been determined by laser excitation of Cd₂ spectra in a supersonic expansion of cadmium vapor.     

Molecular structure and binding energies of monosubstituted hexacarbonyls of chromium,molybdenum, and tungsten: Relativistic density functional study

Relativistic density functional calculations have been carried out for the group VI transition metal carbonyls M(CO)₅L (M=Cr, Mo, W; L=OH₂, NH₃, PH₃, PMe₃, N₂, CO, OC (isocarbonyl), CS, CH₂, CF₂, CCl₂, NO⁺). The optimized molecular structures and M(SINGLE BOND)L bond dissociation energies, as well as the metal–carbonyl bond energy of the trans CO group, have been calculated. Besides the marked dependence of the trans M(SINGLE BOND)CO bond length on the type of ligand L, such an effect on the that bond energy is also observed. For the chromium compounds, the trans Cr(SINGLE BOND)CO bond length varies from 184 to 199 pm and its bond energy from 242 to 150 kJ/mol. For the molybdenum compounds, the range is 197 to 216 pm and 253 to 128 kJ/mol and, for tungsten, 198 to 214 pm and 293 to 159 kJ/mol. The observed trends can be explained with the π acceptor strength of the L ligand. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 1985–1992, 1997     

Electronic assignments of the violet bands of sodium

The puzzling violet bands of sodium ( ≈ 425-460 nm), known since 1932, are shown conclusively to arise from the superposition of two distinct continuum emission bands - one singlet (2 ¹Σ⁺_u → X ¹Σ⁺_g) and one triplet (primarily 2 ³Π_g → 1 ³Π_u⁺). Each continuum emission system shows complex interference structure arising from multiple branches of the Mulliken difference potential.     

The kinetics of free radicals generated by IR laser photolysis. II. Reactions of C2(X 1Σ+g), C2(a 3Πu), C3(X̄ 1Σ+g) and CN(X 2Σ+) with O2

The 300 K reactions of O₂ with C₂(X ¹Σ⁺_g), C₂(a ³ Π_u), C₃(X? ¹Σ⁺_g) and CN(X ²Σ⁺), which are generated via IR multiple photon dissociation (MPD), are reported. From the spectrally resolved chemiluminescence produced via the IR MPD of C₂H₃CN in the presence of O₂, CO molecules in the a ³Σ⁺, d ³Δ_i, and e ³Σ^? states were identified, as well as CH(A ²Δ) and CN(B ²Σ⁺) radicals. Observation of time resolved chemiluminescence reveals that the electronically excited CO molecules are formed via the single-step reactions C₂(X ¹Σ⁺_g, a ³Π_u) + O₂ → CO(X ¹Σ⁺ + CO(T), where T denotes are electronically excited triplet state of CO. The rate coefficients for the removal of C₂(X ¹Σ⁺_g) and C₂(a ³Π_u) by O₂ were determined both from laser induced fluorescence of C₂(X ¹Σ⁺_g) and C₂(a ³Π_u), and from the time resolved chemiluminescence from excited CO molecules, and are both (3.0 ± 0.2)10^?12 cm³ molec^?1 s^?1. The rate coefficient of the reaction of C₃ with O₂, which was determined using the IR MPD of allene as the source of C₃ molecules, is <2 × 10^?14 cm³ molec^?1 s^?1. In addition, we find that rate coefficients for C₃ reactions with N₂, NO, CH₄, and C₃H₆ are all < × 10^?14 cm³ molec^?1 s^?1. Excited CH molecules are produced in a reaction which proceeds with a rate coefficient of (2.6 ± 0.2)10^?11 cm³ molec^?1 s^?1. Possible reactions which may be the source of these radicals are discussed. The reaction of CN with O₂ produces NCO in vibrationally excited states. Radiative lifetime of the ā ²Σ state of NCo and the ā ¹Π_u(000) state of C₃ are reported.     

Laser-induced fluorescence in N2 and N+2 by multiple-photon excitation at 266 nm

The fluorescence transitions corresponding to the second positive system of N₂ (C³Π_u → B³Π_g) for Δv = 0, 1 and the first negative system of N⁺₂(B²Σ⁺_u → X²Σ⁺_g) for Δv = 0, 1, 2 have been observed following laser-induced mul excitation of N₂.     

The isomers of ionized ethane

The previously reported ²A_g, ²A_1g, and ²B_g states of ionized ethane are characterized at several levels of theory. The diborane-like ²A_g state, which gives rise to the observed ESR spectrum, is predicted by SCF and CCD calculations not to exist in a separate minimum from the ²A_1g state formed by ionization of the C(SINGLE BOND)C bond. However, as reported by Lunell and Huang, second-order Moller-Plesset theory places the ²A_g lowest, provided polarization functions are included on carbon. QCISD theory predicts that both A states correspond to potential energy minima, but places the long-bond ²A_1g state lower, at least with moderately large basis sets. F orbitals on carbon stabilize the diborane structure more than the long-bond one. When a potential energy surface is generated for a series of fixed C(SINGLE BOND)C bond lengths by optimizing all variables except for the C(SINGLE BOND)C bond length with MP2 theory and calculating the energy with QCISD(T), the ²A_g state is predicted to be the lowest energy state with the ²A_1g state 1.83 kJ/mol above it. The two A states are predicted to be separated by a barrier 2.79 kJ/mol above the lower state. This barrier is above the zero-point energy in the C(SINGLE BOND)C stretch for the lower state but below the ZPE for this stretch in the upper state, which is therefore predicted not to exist as a stable species. A single quantum of vibrational excitation in the low frequency C(SINGLE BOND)C stretch is predicted to yield an ion with a poorly defined C(SINGLE BOND)C bond length. The highest levels of theory employed give poor agreement with the experimental hyperfine coupling constants. The discrepancy could either be due to neglect of vibrational effects, to poor inherent accuracy of the calculation, as one author has concluded, or to compression of the ion by the matrix as suggested by another. The ²B_g state is found to be higher in energy than the A states at all theoretical levels and is predicted to have a large (160.2–177.4 G) hyperfine coupling from four hydrogens. The transition state for simultaneous exchange of two hydrogen atoms between the carbons by a diborane structure is predicted to lie above the lowest energy fragmentation threshold, in agreement with experiment. © 1996 by John Wiley & Sons, Inc.     

MRD-CI ground state geometry and vertical spectrum of N3

CI calculations have been carried out for the prediction of the ground state geometry and of the vertical spectrum of N₃. The first three states are ²Π_g, ⁴Π_u and ²Σ⁺_u. The C_∞v correlation diagram for the first dissociation limits is discussed by taking into account possible nonadiabatic pathways.     

The photodissociation of Li2

The absorption of photons by Li₂ from the X ¹Σ⁺_g state to the A ¹Σ⁺_u and B ¹Π_u states is considered and the mechanisms that lead to dissociation are studied quantitatively. Calculations are reported on the direct predissociation of the b ³Π_u state. The significance of accidental predissociation of the A ¹Σ⁺_u state is discussed and a quantal theory of the process is presented.     

The predissociation of Li2 b3Πu by a3Σ+u

⁶Li₂ 1³Δ_g(F₁) → b³Π_u(F₁v = 0–11) rotationally resolved fluorescence spectra are recorded following perturbation-facilitated optical—optical double resonance excitation of 1³Δ_g via spin—orbit mixed A¹Σ⁺_u ∼ b³Π_u(F₁e) intermediate levels. The f-symmetry Λ-components of b³Π_u(F₁) are broadened above the 0.05 cm⁻¹ detection threshold owing to predissociation by the vibrational continuum of the a³Σ⁺_u state. The observed v = 0–11, N = 31f level widths were used to determine the potential energy curve for the Li₂ a³Σ⁺_u state in the region 2.35 < R < 2.60 Å and 11200 < E < 14900 cm⁻¹ (relative to E = 0 at the minimum of X¹Σ⁺_g). The a³Σ⁺_u ∼ b³Π_u curve crossing is at R = 2.57 Å and E = 11246 cm⁻¹ and the electronic part of the − BN·LL-uncoupling matrix element is 〈b Π¦L⁺ ¦aΣ〉 = 1.216H at an R-centroid Rv_bϵ_a = 2.61Å.     

Potential energy and dipole moment of the Na2+ ionic molecule

The potential energy curves of 26 electronic states of ²Σ⁺_{g, u}, ²Π_{g, u}, and ²Δ_{g, u} symmetries of the alkali dimer Na₂⁺, dissociating up to Na(4d) + Na⁺, are investigated using an ab initio approach involving a nonempirical pseudopotential for the Na⁺(1s²2s²2p⁶) core and core‐valence correlation corrections. Furthermore, the transition dipole functions between many electronic states and vibrational energy spacings are presented. The spectroscopic constants of these electronic states are extracted and compared with the available theoretical and experimental results. A very good agreement is observed, especially, for the ground and the first excited states. However, the comparison between our study and the model potential (MP) calculations (Magnier and Masnnou‐Seeuws Mol. Phys. 1996, 89, 711) for several states has shown a clear disagreement. The MP well depths of the 3‐4²Σ⁺_g, 1²Π_g, 3‐4²Π_g, and 2²Π_u electronic states are largely underestimated. In addition, the 5‐7²Σ⁺_g, 3‐7²Σ⁺_u, 2²Π_g, 4²Π_g, and 1‐2²Δ_u MP electronic states are repulsive, although in this work, they are attractive with potential well depths of some hundreds of cm^?1. The data presented in this study are very useful for studies on ion–atom interaction and cold collision in the presence of electromagnetic fields. © 2013 Wiley Periodicals, Inc.     

Theoretical study of the N+2 molecular ion

The Equations of Motion method has been applied in the calculation of potential energy curves for the X²Σ⁺_g, A²Π_u and B²Σ⁺_u states of N⁺₂. Results are also reported for a new dissociative ²Σ⁺_g state. The theoretical curves are directly compared with the experimental ones as well as in terms of spectroscopic constants. The applicability of the Equations of Motion method to this type of problem is critically examined and discussed with regard to the choice of basis set, numerical effort and agreement with experiment.     

Rotational analysis of the A—X bands of S+2

The S⁺₂ (A²Π_u-X²Π_g) emission system from sulphur monochloride in a helium flowing afterglow has been analysed in the 5000–6000 Å region. Molecular constants for the S⁺₂ (A²Π_u, X²Π_g) states have been determined and are compared with previous estimates. Equilibrium bond lengths of S⁺₂ are found to be: X²Π_g,r_e = 1.8226 ± 0.0010 Å and A²Π_u, r_e = 2.0441 ± 0.0013 Å.     

Theoretical studies of molecular ions. Vertical ionization potentials of the nitrogen molecule

The ²Σ⁺_g, ²Π_u, and ²Σ⁺_u vertical ionization energies of nitrogen are obtained by using our theory of molecular electron affinities and ionization potentials, which permits the direct calculation of the ion-molecule energy differences. The contributions of charge redistribution and correlation energy change to the calculated ionization potentials are evaluated. The computational efficiency of the method is illustrated and comparisons are made with recent experimental results.