Theoretical study of the electronic spectrum of diimide by AB initio methods

A series of ab initio calculations is reported for the ground and low-lying valence and Rydberg states of diimide N₂H₂. Symmetric bending potential curves for both the cis and trans forms of this system have been obtained at the SCF level of treatment. In addition Cl calculations have been carried out for the trans-diimide ground state equilibrium nuclear conformation, using a configuration selection procedure described elsewhere; an associated energy extrapolation scheme is also employed which enables the effective solution of secular equations with orders of up to 40000. The ensuing Cl wavefunctions are interpreted in the discussion and the corresponding calculated energy differences between the various electronic states are compared with experimental transition energy results for both diimide and for related systems such as trans-azomethane. A more detailed analysis of the observed absorption bands in the ¹B_g-X¹A_g transition in N₂H₂ is also given, making use of calculated potential curve data as well as the pertinent Cl vertical energy difference. The dipole-forbiddenness of the excitation process is thereupon concluded to result in a distinct non-verticality for this electronic band system, causing its absorption maximum to occur at a position some 0.6 eV to the blue of the so-called vertical transition, i.e., that for which maximum vibrational overlap is obtained.     

The valence electronic excited states of trans-1,3-butadiene and trans,trans-1,3,5-hexatriene from generalized valence bond and configuration interact

Self-consistent ab initio generalized valence bond (GVB) and configuration interaction (Cl) calculations are presented for the ground and valence electronic excited states of trans-1,3-butadine and all trans-1,3,5-hexatrine. Previous workers have suggested that (all trans) polyenes exhibit a parity-forbidden valence excited state (2¹ A_g at an energy just below that of the first dipole-allowed (1¹ B_u) state. We find such valence excited electronic states for butadiene (ΔE = 7.06 eV) and hexatriene (ΔE = 5.87 eV), but in both cases the excitation energy is considerably higher than the dipole-allowed transitions (zero-zero transitions at 5.95 eV and 4.95 eV, respectively). The lower two triplet states are found at 3.35 eV and 5.08 eV for butadie and at 2.71 eV and 4.32 eV in hexatrine, in good agreement with experimental values (3.2–3.3 eV and 4.92 eV for butadiene and 2.66 eV and 4.1–4.2 eV for hexatrine). Considering the states formed by removing one electron from the π space we found ion states at 8.95 eV and 11.40 eV for butadiene and at 8.33 eV, 10.53 eV, and 11.60 eV for hexatriene, in godo agreement with experimental results (9.0 eV and 11.5 eV for butadiene and 8.45 eV, 10.43 eV and 11.6 eV for hexatriene).     

On the vibrational dependence of electron impact ionization of diatomic molecules

The dependence of the Na₂ electron impact ionization rate is measured as a function of vibrational excitation in a crossed molecule-electron beamm arrangement at collision energiesE _coll ≤ 3 eV above the ionization threshold. Specific vibrational distributions in theX ¹∑ _g ⁺ state with average vibrational energies of 0.17 eV, 0.276 eV, and 0.349 eV, are prepared via Franck-Condon pumping using a narrow-band cw laser. Enhancement of the ionization rate is observed only at impact energies near the ionization threshold where the ionization rate increases linearly as a function of vibrational excitation. Analysis of the experimental data is based on three model calculations. The first of these calculations equates vibrational energy with kinetic energy and agrees well with the experimental data. A second, more refined model allows for differences in state-to-state ionization rates and uses Franck-Condon factors to estimate transition probabilities, but leads to a less favorable agreement. The third one employs a semi-classical formulation of the Franck-Condon principle. It provides the best agreement with the experimental data. In contrast with an earlier study of electron impact ionization of diatomic molecules [20], we find no evidence of dynamical modification of the ionization rate, due to vibrational motion of the nuclei, at the present level of accuracy of our data and analysis.     

Non-empirical SCF and Cl Study of the ground and excited states of thioformaldehyde

Ab initio SCF and Cl calculations are reported for ground and various low-lying Rydberg and valence excited states of thioformaldehyde H₂CS. A double-zeta basis of near Hartree-Fock quality is employed in this work and the importance of polarization functions is also assessed. The calculations indicate uniformly larger CX bond lengths in this system than for H₂CO in the corresponding electronic states; they also lind potential minima for H₂CS non-planar nuclear conformations in the (n,π^*) and (π,π^*) excited states but in each case the calculated inversion barriers are seen to be smaller than those encountered in formaldehyde. The vertical transition energies to the various excited states studied are also found to be significantly smaller in H₂CS than in H₂CO but the order of electronic states is concluded to be virtually identical for the two systems. The lowest-lying excited states are the ^3,1(n,π^*) species calculated at 1.84 and 2.17 eV respectively; the first two allowed transitions are indicated to be the Rydberg species (n,s_R) and (n,px_R) at 5.83 and 6.62 eV. These are followed by the two allowed transitions σ → π^* and π → π^* at 7.51 and 7.92 eV respectively, both well below the first ionization limit in H₂CS. The much smaller splitting between the ^3,1(π,π^*) species in H₂CS than in H₂CO is attributed to the relatively diffuse charge distribution of the sulfur atom compared to that of oxygen.     

Rydberg or Valence? The Long‐Standing Question in the UV Absorption Spectrum of 1,1′‐Bicyclohexylidene

The electronic excited states of the olefin 1,1′‐bicylohexylidene (BCH) are investigated using multiconfigurational complete active space self‐consistent‐field second order perturbation theory in its multi‐state version (MS‐CASPT2). Our calculations undoubtedly show that the bulk of the intensity of the two unusually intense bands of the UV absorption of BCH measured with maxima at 5.95 eV and 6.82 eV in the vapor phase are due to a single ππ* valence excitation. Sharp peaks reported in the vicinity of the low‐energy feature in the gas phase correspond to the beginning of the π3s_R Rydberg series. By locating the origin of the ππ* band at 5.63 eV, the intensity and broadening of the observed bands and their presence in solid phase is explained as the vibrational structure of the valence ππ* transition, which underlies the Rydberg manifold as a quasi‐continuum.     

On the low-lying electronic states of BiF

Relativistic CI calculations on the low-lying states of BiF(0⁺, 1, 2, 0⁺(II)) arising from the σ²π² configuration are carried out. Comparison calculations of the λ-s states without spin-orbit interaction (³Σ⁻, ¹Σ⁺ and ¹Δ) are also presented. These calculations enable the assignment of three experimentally observed low-lying states. In addition, the properties of a new state (2) are calculated (yet to be observed). The calculated dissociation energy of the ground state is 2.63 eV. The potential energy surfaces of the low-lying electronic states of BiF reveal interesting avoided crossings. Our calculations clarify the earlier assignment of the electronic transitions of BiF.     

Theoretical study of spectroscopic and molecular properties of several low‐lying electronic states of CO molecule

The potential energy curves (PECs) of eight low‐lying electronic states (X¹Σ⁺, a³Π, a′³Σ⁺, d³Δ, e³Σ^?, A¹Π, I¹Σ^?, and D¹Δ) of the carbon monoxide molecule have been studied by an ab initio quantum chemical method. The calculations have been performed using the complete active space self‐consistent field method, which is followed by the valence internally contracted multireference configuration interaction (MRCI) approach in combination with the correlation‐consistent aug‐cc‐pV5Z basis set. The effects on the PECs by the core‐valence correlation and relativistic corrections are included. The way to consider the relativistic corrections is to use the third‐order Douglas–Kroll Hamiltonian approximation at the level of a cc‐pV5Z basis set. Core‐valence correlation corrections are performed using the cc‐pCVQZ basis set. To obtain more reliable results, the PECs determined by the MRCI calculations are corrected for size‐extensivity errors by means of the Davidson modification (MRCI+Q). The spectroscopic parameters (D_e, T_e, R_e, ω_e, ω_ex_e, ω_ey_e, B_e, α_e, and γ_e) of these electronic states are calculated using these PECs. The spectroscopic parameters are compared with those reported in the literature. Using the Breit–Pauli operator, the spin–orbit coupling effect on the spectroscopic parameters is discussed for the a³Π electronic state. With the PECs obtained by the MRCI+Q/aug‐cc‐pV5Z+CV+DK calculations, the complete vibrational states of each electronic state have been determined. The vibrational manifolds have been calculated for each vibrational state of each electronic state. The vibrational level G(ν), inertial rotation constant B_ν, and centrifugal distortion constant D_ν of the first 20 vibrational states when the rotational quantum number J equals zero are reported and compared with the experimental data. Comparison with the measurements demonstrates that the present spectroscopic parameters and molecular constants determined by the MRCI+Q/aug‐cc‐pV5Z+CV+DK calculations are both reliable and accurate. © 2012 Wiley Periodicals, Inc.     

Structural and spectroscopic studies on 2-pyranones

Experimental methods of infrared, Raman and electronic absorption spectroscopy and DFT calculations using B3LYP functionals and 6-31G** and 6-311++G** basis sets have been used to understand the structural and spectral characteristics of 2-pyranones, 6-phenyl-4-methylsulfanyl-2-oxo-2H-pyran and 6-phenyl-4-methylsulfanyl-2-oxo-2H-pyran-3-carbonitrile in the electronic ground (S₀) and first excited (S₁) states. Information about the size, shape, charge density distribution and site of chemical reactivity of the molecules has been obtained by mapping electron density isosurface with electrostatic potential surfaces (ESP). Based on TD-DFT calculations using 6-31+G**5D basis set, an assignment of absorption peaks in the UV–VIS region has been suggested. The S₁ state is found to be a ¹(π,π*) state. A complete vibrational analysis has been attempted on the basis of experimental infrared and Raman spectra and calculated frequency and intensity of the vibrational bands and potential energy distribution over the internal coordinates. Characteristic vibrational bands of the 2-pyranone ring and methylsulfanyl and carbonyl groups have been identified.     

Time-dependent close coupling for vibrational excitation in three dimensions: Application to H+ - H2

Impact parameter calculations for the non-reactive H⁺ + H₂ (n_i = 0) → H⁺ + H₂ (n_f) collision are reported for energies 10 eV ? E_cm ? 200 eV describing the rotational motion of the molecule in the sudden limit. The time-dependent Schrödinger equation for the vibrational motion has been solved by close coupling techniques expanding the vibrational wavefunction into both harmonic and numerically exact H₂ bound states. The convergence in vibrational basis sets, where up to six vibrational levels are considered, becomes worse with decreasing energy and increasing inelasticity. Furthermore, the harmonic wavefunctions are not suitable over a large range of energies to calculate proper cross sections. The various integral and differential cross sections have been compared with the classical results of Giese and Gentry.     

Electronic band structure of solid CO2 as determined from the hv-dependence of photoelectron emission

Photoelectron energy distribution curves from solid CO₂ have been determined for excitation energies from hv = 14 up to 40 eV using synchrotron radiation. A 1:1 correspondence to the gas-phase photoelectron spectrum is observed for the occupied molecular orbitals. The vertical binding energies E_B^v (E_VAC = 0) and widths (fwhm) of the valence bands of solid CO₂ are determined to be 13.0 and 0.95 eV (1π_g); 16.7 and 1.1 eV (1π_u); 17.6 and 0.85 eV (3σ_u) and 18.8 and 0.8 eV (4σ_g) for the individual bands respectively. The partial photoemission cross sections differ importantly from those of the gas phase in exhibiting pronounced maxima at 5.2 eV (1π_g), 4.4–5.3 eV (1π_u + 3σ_u) and 4.2 eV (4σ_g) above the vacuum level, which is attributed to effects of high density of final (conduction-band) states. Further weaker maxima are observed at higher photon energies. Contrary to the case for the gas phase, the resonances are unperturbed in the solid by degenerate autoionizing molecular Rydberg states. The molecular origin of the resonances in the continuum is discussed and related to X-ray absorption spectra, electron-scattering data and to theoretical cross-section calculations. It is shown that the same set of resonances is observed in the different experiments. The resonances occur however at different energies due to different Coulomb interactions. The photoemission results presented provide also a key to the hitherto unexplained optical spectrum of solid CO₂ in the VUV range, making possible an assignment of the structures observed to Frenkel-type excitons (hv ≤ 15 eV) and interband transitions (hv ? 15 eV).     

Theoretical electronic studies of aluminum monobromide and aluminum monoiodide

By using CASSCF/MRCI methods, theoretical molecular calculations have been performed for 12 electronic states for AlBr molecule and 12 electronic states for AlI molecule in the representation ^2s+1Λ (neglecting spin‐orbit effects). Calculated potential energy curves are displayed. Spectroscopic constants including the harmonic vibrational wave number ω_e, the electronic energy T_e referred to the ground state and the equilibrium internuclear distance R_e are predicted for these singlet and triplet electronic states for both AlBr and AlI molecules. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

The ground-state potential curve for F2

The ground-state potential curve for F₂ has been obtained using large-scale MC SCF and CI methods. MC SCF curves were obtained with the CAS SCF method using a variety of sets of active orbitals. The main conclusion from the CAS SCF calculations is that the 2π_u orbital is important. CI curves were obtained using the contracted CI method. The largest calculations contained 312000 configurations proper spin and space (d_2h) symmetry. The main conclusions from the CI calculations are that the configuration XXX are important, otherwise errors in D_e of 0.3 eV and in r_e of 0.02 Å are found. The remaining errors at the CI level are 0.08 eV for D_e, 0.005 Å for r_e and less than 10 cm^?1 for the lowest vibrational levels.     

Theoretical electronic structure of the molecule ScBr

The potential energy curves have been investigated for the 23 lowest electronic states in the ^2s+1Λ^± representation of the molecule ScBr via CASSCF and MRCI (single and double excitations with Davidson correction) calculations. Seventeen electronic states have been studied theoretically for the first time. The harmonic frequency ω_e, the internuclear distance r_e, and the electronic energy with respect to the ground state T_e have been calculated. By using the canonical functions approach, the eigenvalues E_v, the rotational constant B_v, and the abscissas of the turning points (R_min, R_max) have been calculated for electronic states up to the vibrational level v = 32. The comparison of these values to the theoretical and experimental results available in the literature shows a good agreement. © 2007 Wiley Periodicalsm Inc. Int J Quantum Chem, 2008     

The nickel-group IV molecules NiC,NiSi, and NiGe

All electron ab initio calculations have been applied to elucidate the electronic states and the nature of the chemical bonds in the molecules NiC, NiSi, and NiGe. The calculations have revealed that the ground states of all three molecules are¹Σ⁺, but due to the open 3d shell of the Ni atom the molecules have many low-lying electronic states. The NiC molecule is strongly polar, and the low-lying electronic states have been identified as those arising when the angular momenta of the³F_g Ni⁺ ion are coupled to the angular momenta of the⁴S_uC^? anion. The chemical bond in the NiC molecule has triple bond character due to the valence bond couplings between the Ni 4s and 3dπ electrons and theC 2p electrons. The chemical bonds in the molecules NiSi and NiGe are very much alike; they are double bonds composed of oneσ and oneπ bond. Theσ bond is due to the doubly occupied delocalized molecular orbital composed of the Ni 4s orbital and the Si 3pσ or the Ge 4pσ orbital. Theπ bond originates from the valence bond coupling between the localized hole in the Ni 3dπ orbital and the valencepπ electron of Si or Ge.     

Theoretical electronic structure of the molecule ScI

Theoretical investigation of the 18 lowest electronic states of the molecule ScI in the representation ^2S+1Λ^(±) has been performed via CASSCF and MRCI (single and double excitation with Davidson correction) calculations. To the best of our knowledge these calculated electronic states are the first ones from ab initio methods. Thirteen electronic states between 4,500 cm^?1 and 21,000 cm^?1 have been studied for the first time and have not yet been observed experimentally. The harmonic frequency ω_e, the internuclear distance R_e, the electronic transition energy with respect to the ground state T_e, and the rotational constant B_e have been calculated for the considered electronic states. By using the canonical functions approach the eigenvalues E_υ and the rotational constants B_υ have also been calculated for the six lowest‐lying electronic states. The comparison of these results with the theoretical and the experimental data available in the literature shows a good agreement. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

A direct test of the vibrationally adiabatic theory of chemical reactions

The adiabaticity assumption of the vibrationally adiabatic theory of chemical reactions in the zero-curvature approximation is directly tested for the collinear H + H₂ reaction against calculations using exact wavefunctions. It is found that the symmetric stretch motion of the transition state is adiabatic to within 10% for total energies E ranging from 0.51 eV to 0.72 eV. For E below the zero-point energy of this symmetric stretch motion non-adiabaticity is substantial and is probably due to tunneling. For E above the first excited vibrational state energy of this symmetric stretch motion the adiabaticity assumption breaks down completely.     

Highly resolved polarized absorption spectra of single-crystal [Ru(bpy)3](PF6)2

Polarized absorption spectra of neat single-crystal [Ru(bpy)₃](PF₆)₂ at 300 and 5 K are presented. The spectra show pronounced vibronic structure and it is possible to assign the vibrations to known Raman frequencies. Furthermore, the different electronic states corresponding to the vibronic transitions are identified and assigned. The assignment of the lowest excited states - observed in absorption - agrees with an earlier classification of the emitting states. In particular, the E ⊥ c-polarized transition A'₁ ⇌ 2E' (classified in D'₃), at 17816 cm⁻¹, is found at the same energy (experimental error: ± 1 cm⁻¹) in emission and absorption and represents a zero-phonon, zero-vibron transition. The low-energy part of the E¦¦_c-polarized spectrum (below ≈ 24000 cm⁻¹) is not dominated by a series of different electronic states but by a 1600 cm⁻¹ progression with zero-vibron transition at 18770 cm⁻¹.     

All-valence-electron Cl calculations on the electronic spectrum of diborane

All-valence-electron Cl calculations have been carried out for diborane B₂H₆ and its positive ion employing a rather large double-zeta AO basis including polarization functions in order to study the electronic spectrum of this system. Transitions from four different valence MOs are found to lead to low-lying electronic transitions of both Rydberg and valence type in each case. Ad mixture of valence character in the otherwise Rydberg-like (nx, 3s), (ny, 3s) and (σ, 3pz) transitions calculated to lie between 11.0 and 11.6 eV is indicated as being primarily responsible for the highly intense shoulder found in this region of the B₂H₆ spectrum. The other strong feature with essentially continuous absorption peaking at 9.3 eV is suggested to result from superposition of several Rydberg-type transitions in the generally broad absorption pattern expected for the ¹(π,π^*) species at significantly higher vertical excitation energy. Quite good agreement is obtained between calculation and experiment for all of the six lowest IPs of diborane and also for the locations of the ¹(n, π^*) and ¹(σ, π^*) transitions previously assigned to the two weak features observed at 6.8 and 8.3 eV in this spectrum.     

A theoretical study of the electronic spectrum of CCl2

Ab into configuration interaction calculations for some low-lying electronic states of the dichlorocarbene radical (CCl₂) have been carried out. The UV absorption band at 330 nm (3.76 eV) obtained by the pulse radiolysis experiment is confirmed and assigned to the ¹A₁ – ¹B₁ transition. The calculated transition energy amounts to 318.4 nm (3.90 eV). The first triplet state (³B₁) is found to lie 0.83 eV above the ¹A₁ ground state.     

CEPA calculations on open-shell molecules

Ab initio calculations at SCF and CEPA levels using large Gaussian basis sets have been performed for the two lowest electronic states,X ² Σ⁺ andA ² Π, of HeAr⁺. Spin-orbit coupling (SOC) effects have been added using a semiempirical treatment. The resulting potential curves for the three statesX,A ₁, andA ₂ have been used to evaluate molecular constants such as vibrational intervals ΔG(v + 1/2) and rotational constantsB _v as well as — by means of a Dunham expansion — equilibrium constants such asR _e , ω _e ,B _e etc. Comparison with the experimental data from UV emission spectroscopy shows that the calculated potential curves are slightly too shallow and have too large equilibrium distances:D _e = 242 cm^?1 andR _e = 2.66 Å compared to the experimental values of 262 cm^?1 and 2.585 Å, respectively, for theX ²Σ⁺ ground state. However, the ab initio calculations yield more bound vibrational levels than observed experimentally and allow for a more complete Dunham analysis, in particular for theA ₂ state. The experimental value of 154 cm^?1 for the dissociation energyD _e of this state is certainly too low; our best estimate is 180±5 cm^?1. For theA ₁ state our calculations are predictions since this state has not yet been observed experimentally.