2Σ States Research Articles

Theoretical study of the electronic structure of LiNa and LiNa+ molecules

Adiabatic potential energy, spectroscopic constants, dipole moments, and vibrational levels of the lowest electronic states of the alkali dimer LiNa molecule dissociating into Na (3s, 3p, 4s, 3d, and 4p) + Li (2s, 2p, 3s, and 3p) in 1,3Σ, 1,3Π, and 1,3Δ symmetries are presented. Adiabatic results are also reported for 2Σ, 2Π, and 2Δ electronic states of the molecular ion LiNa+ dissociating into Li (2s, 2p, 3s, and 3p) + Na+ and Li+ + Na(3s, 3p, 4s, 3d, and 4p). We use an ab initio approach involving a non-empirical pseudopotential for the Li (1s2) and Na (1s22s22p6) cores and core valence correlation correction. A very good agreement is obtained for some lowest states of the LiNa and LiNa+ molecules for spectroscopic constants with the available theoretical works. The existence of numerous avoided crossings between electronic states of 2Σ and 2Π symmetries is related to the charge transfer process between the two ionic systems Li+Na and LiNa+.

Theoretical calculation of the low laying electronic states of the molecular ion KH +

Using an ab initio method the potential energy has been calculated for the 25 lowest molecular states of symmetries 2Σ +, 2Π, 2Δ for the molecular ion KH +. The calculation is based on nonempirical pseudopotentials and parameterized ℓ-dependent polarization potentials. Gaussian basis sets have been used for both atoms. The spectroscopic constants for 18 electronic sates have been calculated by fitting the calculated energy values to a polynomial in terms of the internuclear distance R. Through the canonical functions approach the eigenvalue E v, the abscissas of the corresponding turning points ( R min and R max) and the rotational constants B v have been calculated up to 24 vibrational levels for the considered bound states. The comparison of the present results with those available in literature shows a very good agreement.

Extended Hartree–Fock theory of chemical reactions. VIII. Hydroxylation reactions by P450

AbstractWe have investigated the reaction pathways for the primary hydroxylation reaction of trimethylmethane by a high‐valent Fe(IV)O porphyrin π‐cation radical species known as compound I at the B3LYP/CEP‐31G level. The isoelectronic analogy of the Fe(IV)O core of compound I to a molecular oxygen (O2) has been successfully used to clarify the important roles of the singlet excited state of the Fe(IV)O core in the alkane hydroxylation, which has hitherto been neglected. The reaction is initiated by the rate‐determining hydrogen‐atom abstraction from the substrate to give a discrete radical intermediate complex, in accordance with the conventional radical rebound mechanism. Similar to the chemistry of O2, however, one of the singlet excited states, i.e., the diradical component of the 1Δ state of the Fe(IV)O core intercepts the triplet ground state (the 3Σ state) in the region of the transition state for the hydrogen abstraction. Our findings strongly indicate that the exchange polarization or intersystem crossing for the nonradiative transition to the locally singlet state is highly important to enhance the reactivity of compound I. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008

The HeH+ molecular ion in a magnetic field

A detailed study of the low-lying electronic states 1Σ, 3Σ, 3Π, 3Δ of the HeH+ molecular ion in parallel to a magnetic field configuration (when α-particle and proton are situated on the same magnetic line) is carried out for B = 0 − 4.414 × 1013 G in the Born–Oppenheimer approximation. The variational method is employed using a physically adequate trial function. It is shown that for the Σ states the parallel configuration is stable with respect to small deviations. The quantum numbers of the ground state depend on the magnetic field strength. The ground state evolves from the spin-singlet 1Σ state for small magnetic fields B ≲ 0.5 au to the spin-triplet 3Σ (unbound or weakly bound) state for intermediate fields and to the spin-triplet strongly bound 3Π state for B ≳ 15 au. When the HeH+ molecular ion exists, it is stable with respect to dissociation.

A spectroscopic study of the rhodium monoboride molecule

A laser-induced fluorescence spectrum of rhodium monoboride (Rh10B and Rh11B) has been recorded under jet-cooled conditions between 425 and 505 nm at rotational resolution. Two electronic transitions have been identified: a 1Σ–X1Σ system with (0,0) band at 19 985 cm−1 and a 1Π–X1Σ system with (0,0) band at 20 110 cm−1. Both excited states are less strongly bound than the ground state. For the [20.0] 1Σ state of Rh10B/Rh11B, ωe ≈ 682/651 cm−1 and B 0 = 0.533/0.484 cm−1; for the [20.1]1Π state, ΔG 1/2 = 739/710 cm−1 and B 0 = 0.558/0.521 cm−1. Dispersed fluorescence experiments indicate the presence of low-lying electronic levels at 360, 9440 and 10 228 cm−1.

Optical–optical double resonance spectroscopy of YBr and YCl

High resolution optical–optical double resonance (OODR) spectra of YBr and YCl in the spectral region between 338.9 and 371.7 nm have been recorded and analysis. For YBr, the v = 4–6 levels of the J 1 Π state and the v = 1–3 levels of the K 1 Π state were observed via the intermediate C 1Σ state from the X 1Σ state. For YCl, the v = 0–2 levels of the I 1Δ state was reached via the intermediate B 1 Π state from the X 1Σ + state. Rotational and vibrational constants for these electronic states were determined.

Vibrational and rotational excitation within the X 1Σ state of N2 during the pulsed electric discharge and in the afterglow

The time transients of vibrational/rotational excitation up to v = 6 level of the ground electronic state of nitrogen were measured in a positive column during the 1 µs pulsed electric discharges, and in the afterglow. The peak current densities were up to 25 A cm−2 at the gas pressure of 5 Torr. During the active discharge the energy was transferred mainly into vibrational levels, primarily above v = 1, resulting in highly non Boltzmann distribution. The vibrational distribution became Boltzmann-like approximately 80 µs after the discharge pulse and remained of this character until the next pulse. Rapid rotational heating was observed immediately following the cessation of the discharge current. The rotational temperature had risen from about 300 K during the discharge to more than 3000 K within the first 80 µs of the afterglow and returned later to ambient (300 K) in less than 100 µs. Its peak coincided with the time when the redistributed vibrational populations closely resembled the Boltzmann distribution. The vibrational populations could be described by a single temperature (approximately 3000 K) from 100 µs till nearly 1 ms after the discharge. All vibrational bands could be well described by the same rotational temperature at all times. Standard, coherent anti-Stokes Raman spectroscopy was used in all measurements.

Extreme Non‐LTE H2in Comets C/2000 WM1 (LINEAR) and C/2001 A2 (LINEAR)

Rotationally resolved molecular hydrogen transitions originating from excitation of highly excited rovibrational levels of the X 1Σ state have been systematically identified for the first time in the Far Ultraviolet Spectroscopic Explorer (FUSE) observation of comets C/2000 WM1 (LINEAR) and C/2001 A2 (LINEAR). Spectral assignments for the observed lines of H2 and other atomic and molecular species are given. All observed H2 transitions belong to the Lyman (B 1Σ-X 1Σ) and Werner (C 1Πu-X 1Σ) band systems. Solar Lyα fluorescence excitation of highly rovibrationally excited H2 X 1Σ is found to be almost solely responsible for the observed H 2 emission. Resonant excitation of H2 by Lyβ and other solar lines is very limited.

Quantum chemical predictions of vibrational mode analysis of germaformaldehyde and related molecules

Hybrid density functional theory and ab-initio methods have been evaluated as practical tools for calculations of infrared vibrational frequencies and absorption intensities of XGeWZ molecules (where X = O, S, Se; W, Z = H, F, Cl). The theoretical results have been compared with the most current experimental data. It shows that XGeWZ species have two states, namely singlet (1Σ) state and triplet ( 3 Σ) state. We have found that the singlet ( 1 Σ) state of the species is more stable than the triplet ( 3 Σ) state. When different halogens combine to the central Ge atom, the bond length order is Ge-H FGeXF > ClGeXCl (where X = O, S, Se). When element X alters, the bond length order is Ge=O ZWGeZ (X=S)>∠WGeZ (X=Se) (where W, Z = H, F, Cl). The vibrational frequencies and vibrational mode analysis are well agreeing with the optimized geometric results.

Ab initio study of NaRb +: Potential energy curves, spectroscopic constants and atomic polarizabilities

Using an ab initio approach involving a non-empirical pseudopotentials for Na and Rb atoms, the adiabatic potential energy curves of 26 electronic states of NaRb + ionic molecule dissociating up to Na(4p) + Rb + and Na + + Rb(7s) have been investigated. Their molecular spectroscopic constants have been derived and compared with the available theoretical works. Furthermore, the transition dipole moments from X 2Σ + and 2 2Σ + to higher excited states have been determined. Numerous avoided crossings between electronic states of 2Σ + and 2Π symmetries have been localised and analysed. Their existences are related to the charge transfer process between the two ionic systems Na +Rb and NaRb +. The accurate potential energy curves have been exploited to realize a long-range vibrational level spacing analysis using the WKB semi-classical approximation in order to extract the Na and Rb atomic static dipole polarizabilities. A very good agreement between our static dipole polarizabilities and the available experimental and theoretical works has been observed.

A quantum chemical study of the N 2H + + e − → N 2 + H reaction I: The linear dissociation path

A theoretical investigation of the dissociative recombination (DR) of linear N 2 H + ( X 1 Σ g + ) to give N 2 + H has been undertaken because it is of interest for astrochemistry and also because it has been recently studied experimentally. Using state of the art quantum chemical methods, it is shown that the lowest 2Σ repulsive state of N 2H leading to the N 2 and H fragments in their ground electronic states does not cross the curve of the ion nor the one of the lowest N 2H Rydberg state. This lowest 2Σ repulsive state is very low in energy. Its curve passes below the 1Σ N 2H + state and below the lowest bound 2Σ N 2H states. However, it is also shown that there exist higher repulsive 2Σ and 2Δ states of N 2H (the second and third repulsive states) crossing the ion curve. These states will lead to the formation of N 2 in its 3 Σ u + and 3Δ u states. This study, the first of its type, shows that the DR of linear N 2H + should involve the direct mechanism and that it should lead to N 2 in its first excited states. However this process may not be efficient for N 2H + in its ground vibrational state ( v = 0), a state in which it exists in the cold environment of the interstellar medium. For the DR to be efficient for N 2H + in its ground v = 0 vibrational state, bent geometries of the ion might have to be considered.

Theoretical study with rovibrational and electronic transitionmoment calculation of the ion LiCs+

For the molecular ion LiCs+ the potential energy are calculated for the 39 lowest molecular states of symmetries 2Σ+, 2Π, 2Δ, and Ω = 1/2, 3/2, 5/2. Using an ab initio method, the calculation is based on nonempirical pseudopotentials and parameterized [Formula: see text]-dependent polarization potentials. Gaussian basis sets are used for both atoms and spin-orbit effects are taken into account. The spectroscopic constants for 20 states are calculated by fitting the calculated energy values to a polynomial in terms of the internuclear distance r. Through the canonical functions approach, the eigenvalue Ev, the abscissas of the corresponding turning points (rmin and rmax), and the rotational constants Bv are calculated for up to 44 vibrational levels for four bound states. Using the same approach the dipole moment functions, the corresponding matrix elements, and the transition dipole moments are calculated for the bound states (1)2Σ+, (2)2Σ+, and (1)2Π. The comparison of the present results with those available in literature for the ground state shows a very good agreement. Extensive tables of energy values versus internuclear distance are displayed at the following address: http://lasim.univ-lyon1.fr/allouche/licsso.html.PACS Nos.: 31.15.Ar, 31.25.–v, 31.25.Nj

Theoretical investigation on CsLi + and CsNa + ionic molecules

The potential energy curves and the spectroscopic constants of the ionic molecules CsLi + and CsNa + have been determined for the ground and the lowest 2Σ +, 2Π and 2Δ electronic states. Using an ab initio method, the calculation has been performed in a one active electron approach based on a non empirical pseudo-potentials with core valence effects taken into account through parameterized l-dependant polarization potentials. Numerous avoided crossing between electronic states of 2Σ + and 2Π symmetries have been localised and analysed for the both ionic molecules. Their existences are related to the charge transfer process between the two ionic systems Cs +X and CsX + (X = Li, Na). Furthermore, the transition dipole moment from the ground state X 2Σ + and the first excited state 2 2Σ + to higher excited states have been determined for both CsLi + and CsNa + ionic systems. For our best knowledge, there are neither experimental nor theoretical works realised on these ionic molecules.

Ab initio calculation of P, T-odd interaction constant in BaF: a restricted active space configuration interaction approach

A fully relativistic restricted active space (RAS) configuration interaction (CI) approach is employed to compute the P, T-odd interaction constant Wd of the ground 2Σ state of BaF. The present calculation estimates Wd = −0.352 × 1025 Hz/e-cm. We also report the dipole moment μe of the ground state of BaF which is in good agreement with experiment.

Ab initio calculation of P, T-odd effects in YbF molecule

A fully-relativistic restricted active space (RAS) configuration interaction (CI) approach is employed to compute the P, T-odd interaction constant W d of the ground ( 2Σ) state of YbF. A series of increasingly sophisticated CI space yields a best estimate of W d = −1.088 × 10 25 Hz/e-cm. The CI space that yields the best estimate of W d is also used to compute other molecular properties, all of which are found to be in good agreement with experiment.

Theoretical investigation of the molecular structure and transition dipole moments of the NaK + low lying electronic states

The electronic structure and the spectroscopic constants of the low lying electronic states of the NaK + ionic molecule have been determined through using an ab initio approach involving a non-empirical pseudopotential for the Na and K cores and core valence correlation correction. The potential energy of nearly 26 electronic states of 2Σ +, 2Π, and 2Δ symmetries has been calculated up to their dissociation limit Na(4 d) + K + and Na + + K(6 s). Their spectroscopic constants ( R e, D e, T e, ω e, ω e χ e, and B e) are derived and compared with the few available theoretical studies. A good agreement has been found for the ground state and few excited states with previous works. New potential energy curves were presented, for the first time, for the higher excited states. Numerous avoided crossing between electronic states of 2Σ +, 2Π symmetries have been localized and analyzed. Their existences are related to the charge transfer between the two ionic molecules Na +K and NaK +. Furthermore, we have determined the transition dipole moments for several states and analyzed the avoided crossings related to charge transfer between alkaline atoms.

Near infrared spectroscopy of NiF

Four new electronic transitions of NiF, recorded by high-resolution Fourier transform spectroscopy, have been located in the near infrared spectral region. The three new upper electronic states are labeled as [12.5] 2Δ 5/2, [9.9]Ω = 1/2 and [6.3] 2Π 3/2. In addition, the first excited state located at 251 cm −1 above the ground X 2Π 1/2 state has been revisited on the basis of the work carried out by Kopp and Hougen [Can. J. Phys. 45 (1967) 2581–2596], who showed that an Ω = 1/2 state can be described either as a 2Σ state or a 2Π 1/2 state. For NiF, both descriptions of this state have large fine-structure constants with γ = −0.9599 cm −1 for a 2Σ description and p = −0.7399 cm −1 for a 2Π 1/2 description consist with a state of mixed character. If this low-lying state is considered to be a [0.25] 2Π 1/2 state rather than a [0.25] 2Σ state (as proposed up to now), then the experimental pattern of the low-lying electronic states of NiF is similar to those of the related molecules NiH and NiCl.

Adsorption of Water on Reconstructed Rutile TiO2(011)-(2×1): TiO Double Bonds and Surface Reactivity

Recent combined experimental and theoretical studies (Beck et al., Phys. Rev. Lett. 2004, 93, 036104) have provided evidence for Ti=O double-bonded titanyl groups on the reconstructed rutile TiO(2)(011)-(2 x 1) surface. The adsorption of water on the same surface is now investigated to further probe the properties of these groups, as well as to confirm their existence. Ultraviolet photoemission experiments show that water is adsorbed in molecular form at a sample temperature of 110 K. At the same time, the presence of a 3sigma state in the photoemission spectra and work function measurements indicate a significant amount of hydroxyls within the first monolayer of water. At room temperature, scanning tunneling microscopy (STM) suggests that dissociated water is present, and about 30% of the surface active sites are hydroxylated. These findings are well explained by total energy density functional theory calculations and Car-Parrinello molecular dynamics simulations for water adsorption on the titanyl model of TiO(2)(011)-(2 x 1). The theoretical results show that a mixed molecular/dissociative layer is the most stable configuration in the monolayer regime at low temperatures, while complete dissociation takes place at 250 K. The arrangement of the protonated mono-coordinated oxygens in the mixed molecular/dissociated layer is consistent with the observed short-range order of the hydroxyls in the STM images.

Theoretical study of the electronic states and transition dipole moments of the LiK + molecule

The adiabatic potential energy, the spectroscopic constants and the transition dipole moments of the lowest electronic states of the LiK + molecule, dissociating into Li(2 s, 2 p, 3 s, 3 p, 3 d, 4 s, and 4 p) + K + and Li + + K(4 s, 4 p, 5 s, 3 d, 5 p, 4 d, and 6 s), have been investigated. We have used an ab initio approach involving a non-empirical pseudopotential for the Li (1 s 2) and K (1 s 22 s 22 p 63 s 23 p 6) cores and core valence correlation correction. A very good agreement has been obtained for the ground state for the spectroscopic constants with the available theoretical works. The transition dipole moment from X 2Σ, 2 2Σ, 3 2Σ, and 4 2Σ states to higher excited states have been determined. Numerous avoided crossing between electronic states of 2Σ and 2Π symmetries, have been localised and analysed. Their existences are related to the charge transfer process between the two ionic systems Li +K and LiK +.

Ionization of Molecular Hydrogen

A general model, based on a theoretically calculated ionization oscillator strength and an experimentally determined excitation shape function, has been obtained for calculating the molecular hydrogen electron-impact ionization cross section of a transition between any discrete vibrational levels of the neutral X 1Σ state and ionic X 2Σ state. Specifically, the excitation shape function and ionization oscillator strength for transitions from the vi = 0 level of the X 1Σ neutral state to the discrete levels of the X 2Σ ionic state are derived from analyzing several experimental measurements. The derived oscillator strength is found to be consistent with the 1994 photoabsorption measurements of Samson & Haddad and the 1977 theoretical cross sections of Flannery and coworkers. The derived excitation function, along with the oscillator strengths for transitions involving the vi > 0 level calculated from the data of Flannery and coworkers, permits an accurate calculation of the nondissociative cross sections of H2 between any discrete vibrational levels over a wide energy range.