Green's function calculation of ionization energies of Ca (Z=20), Kr (Z=36), Sr (Z=38) and Yb (Z=70)

The Ca 3s, Kr 4s, Sr 4s and Yb 5s atomic ionization spectra are calculated using the one-particle Green's function method within the framework of Random phase approximation with exchange. Pronounced final ionic correlation effects are found for these levels. The relative intensity of the main ionic state is reduced considerably byns ^?1?np ^?2 nd super Coster Kronig process. The ionization energy of the main ionic state is shifted as much as ～4 eV from the relativistic Hartree-Fock ΔSCF ionization energy byns ^?1?np ^?2 nd super Coster-Kronig process. The existence of strongnp ^?2 nd ² S satellite is predicted for these levels.     

The triplet state of magnesiumporphin · ethanol in an n-octane crystal studied by microwave induced changes in the fluorescence intensity

The zero-field splitting of the triplet state of magnesiumporphin solvated by ethanol is represented by D = 0.035 cm^?1 and |E| = 0.010 cm^?1. The decay rates of the upper two spin components both are found to be about 20 s^?1, while that of the bottom component (where the spin lies in the molecular plane) is about 2 s^?1.     

Singlet exciton interactions in crystalline naphthalene

The decay of prompt fluorescence in crystalline naphthalene at 300 K, excited by a picosecond 266 nm pulse, has been studied as a function of excitation intensity. Experimental decay curves can be fitted only when the exponential distribution in depth of excitation and the radial (gaussian) intensity profile of the excitation are both taken into account. From an analysis of the decay at early time (?5 ns) a best fit value of the singlet—singlet annihilation rate constant is found γ_SS = (4 ± 1) × 10^?10 cm³ s^?1. If the reaction is diffusion-limited, this rate implies an average singlet diffusivity D_S = (2 ± 1) × 10^?4 cm² s^?1.     

Quantum chemical ab initio calculations for excited states of F IV

Quantum chemical ab initio calculations have been performed for the ground state and for several excited states of the F³⁺ ion (F IV). Three levels of accuracy have been used: Frozen-core SCF calculations (FRC-SCF) to determine orbital energies ε _nl and quantum defects δ _l for excited Rydberg orbitalsnl; frozen-core SCF followed by CI calculations (FRC-CI) which account for multiplet splittings and configuration mixings, and multi-configuration coupled-electron-pair approximation (MC-CEPA) calculations which include dynamic correlation effects. The accuracy of the calculated excitation energies is in the order of 5000 cm^?1 at the FRC-CI level and in the order of 500 cm^?1 at the MC-CEPA level. This latter error amounts to about 0.1% for excitation energies in the range of 400000 to 600000 cm^?1. The MC-CEPA calculations have been performed for 17 experimentally known states and for 14 experimentally unknown states, in particular for the configurations 2s2p ² (² D)3s, 2s 2p ²(² S)3s, 2s ² 2p 4p, and 2s ² 2p 5p.     

A laser flash photolysis/IR diode laser absorption study of the reaction of chlorine atoms with selected alkanes

A high‐resolution IR diode laser in conjunction with a Herriot multiple reflection flow‐cell has been used to directly determine the rate coefficients for simple alkanes with Cl atoms at room temperature (298 K). The following results were obtained: k(Cl + n‐butane) = (1.91 ± 0.10) × 10^?10 cm³ molecule^?1 s^?1, k(Cl + n‐pentane) = (2.46 ± 0.12) × 10^?10 cm³ molecule^?1 s^?1, k(Cl + iso‐pentane) = (1.94 ± 0.10) × 10^?10 cm³ molecule^?1 s^?1, k(Cl + neopentane) = (1.01 ± 0.05) × 10^?10 cm³ molecule^?1 s^?1, k(Cl + n‐hexane) = (3.44 ± 0.17) × 10^?10 cm³ molecule^?1 s^?1 where the error limits are ±1σ. These values have been used in conjunction with our own previous measurements on Cl + ethane and literature values on Cl + propane and Cl + iso‐butane to generate a structure activity relationship (SAR) for Cl atom abstraction reactions based on direct measurements. The resulting best fit parameters are k_p = (2.61 ± 0.12) × 10^?11 cm³ molecule^?1 s^?1, k_s = (8.40 ± 0.60) × 10^?11 cm³ molecule^?1 s^?1, k_t = (5.90 ± 0.30) × 10^?11 cm³ molecule^?1 s^?1, with f( ? CH₂^? ) = f (? CH₂^? ) = f (?C?) = f = 0.85 ± 0.06. Tests were carried out to investigate the potential interference from production of excited state HCl(v = 1) in the Cl + alkane reactions. There is some evidence for HCl(v = 1) production in the reaction of Cl with shape n‐hexane. © 2001 John Wiley & Sons, Inc. Int J Chem Kinet 34: 86–94, 2002     

Bemerkung zur Rayleigh-Schrödinger-Störungstheorie

The time-independent Hamiltonians ? ₀ and ?=? ₀ + V have a discrete spectrum, eigenvalues, and eigenvectors E _s ^(o) , ¦s〉^(o) resp. E _s, ¦s〉. If the RS perturbation theory can be applied here then an operator \(\mathfrak{p}\) with the property $$\left| s \right\rangle ^{(n + 1)} = \frac{1}{{n + 1}}\mathfrak{p}\left| s \right\rangle ^{(n)} , E_s^{(n + 1)} = \frac{1}{{n + 1}}\mathfrak{p}E_s^{(n)} $$ exists where ¦s〉⁽ⁿ⁾ and E _s ⁽ⁿ⁾ denote the n-th order corrections of perturbation theory if E _s ^(o) is nondegenerate. In the case of degeneracy the operation \(\mathfrak{p}\) remains defined and can always be used todetermine perturbation corrections of quantum mechanical expressions which are invariant in zerothorder under transformations of the basis in degenerate subspaces of ? ₀. The equations $$\left| s \right\rangle = \sum\limits_n^{0,\infty } {\left| s \right\rangle ^{(n)} = e^\mathfrak{p} \left| s \right\rangle ^{(0)} } , E_s = \sum\limits_n^{0,\infty } {E_s^{(n)} } = e^\mathfrak{p} E_s^{(0)} $$ correspond to a basis transformation where nondegenerate eigenvectors ¦s∝> ^(o) and eigenvalues E _s ^(o) of ? ₀ transform into eigenvectors ¦s∝> and eigenvalues E _s of ?. Examples show the usefulness of this formulation.     

Relativistic molecular orbital theory of zero-field splittings in triplets

A method of calculating matrix elements of 1/r₁₂ in a basis of Dirac scattered-wave (DSW) orbitals is outlined. In the limit c → ∞, this method reduces to that described by Cook and Karplus for non-relativistic orbitals. For triplet states that can be described by a single configuration with two unpaired electrons, the relativistic exchange integrals give not only the singlet—triplet splittings (as in non-relativistic theory), but also the spin—orbit contributions to the triplet zero-field splittings. Results are reported for the ³ (n → π*) excited state of γ-thiopyrone (4H-pyran-4-thione), which has a very large value of D (calc. ?31 cm^?1, exp. ?24 to ?28 cm^?1).     

Polyene spectroscopy: Vibronic evidence for a forbidden transition in DECA-2,4,6,8-tetraene

The dimethylpolyene deca-2,4,6,8-tetraene was studied by absorption, fluorescence excitation and fluorescence spectroscopy in glasses at 77 K and in n-alkane crystals at 4.2 K. A strong transition to a ¹B_u excited state is observed with an origin at 32400 cm^?1 in isopentane at 77 K and at 31280 cm^?1 in n-undecane at 4.2 K. A weak transition to a ¹A_g excited state is observed with an origin at 28738 cm^?1 in the n-undecane matrix. The radiative fluorescence lifetime is 500 ns. In undecane the transition from the ground state to the ¹A_g excited state exhibits a classic Herzberg—Teller vibronic pattern indicating a symmetry forbidden transition.     

Two-dimensional fully numerical solutions of molecular dirac equations. Results for ground singlet states of H2 and HeH+

Two-dimensional fully numerical solutions of the Dirac-Fock problem are reported for the singlet ground states of He, H₂ and HeH⁺. The relativistic total energy R = 1.4 au for H₂ is -1.13364396 au and the relativistic correction is 1.439 × 10^?5 au.     

Hyperfine structure in the configuration 4f 115d6s 2 of Er I

Hyperfine constants of low lying levels of the configuration 4f ¹¹5d6s ² in Er I have been measured for the only stable odd isotope,¹⁶⁷Er, using high resolution laseratomic-beam spectroscopy. Hyperfine parameters were evaluated from the experimental data using the effective tensor operator formalism. For this purpose eigenfunctions have been determined from an analysis of the fine structure energies of Er I as well as from ab initio multiconfiguration Dirac-Fock calculations. With the latter method also ab initio hyperfine constants for the levels investigated were evaluated. A comparison of calculated fine structure energies, Landég _J -factors and hyperfine constants with the experimental data allowed a test of the reliability of the fine structure and multiconfiguration Dirac-Fock wavefunctions. Effective nuclear electric quadrupole moments for¹⁶⁷Er have been determined from the experimental hyperfine constants using both calculated relativistic electronic radial integrals and hyperfine parameters for the 4f and 5d electrons in the configuration 4f ¹¹5d6s ² in Er I. From a comparison with the nuclear quadrupole moment measured in the mesic atom Sternheimer shielding factors are calculated. Configuration-interaction contributions to the radial integrals 〈r ^?3〉 _nl ⁰¹ of the 4f and 5d electrons have been determined.     

Collisional de-excitation of the metastableD-states of Ba+ by He,Ne, N2 and H2

The rate constants 〈σ · υ〉 for collisional de-excitation of the metastable 5D states of Ba⁺ ions have been determined in an ion trap experiment. TheD-states are selectively populated by pulsed laser excitation of the 6P _1/2 or 6P _3/2 state and the decay at different background pressures is monitored by the change in fluorescence intensity of the excited ions. From the pressure dependence of the decay constants we calculate the de-excitation rate constants for different collision partners, averaged over the velocity distribution of the trapped ion cloud. For He, Ne, H₂ and N₂ we obtain in the c.m. energy range of 0.1–0.5 eV: 〈σ·υ〉 (He)=3.0±0.2·10^?13cm³/s, 〈σ·υ〉 (Ne)=5.1±0.4·10^?13cm³/s, 〈σ·υ〉 (H₂)=3.7±0.3·10^?11cm³/s, 〈σ·υ〉 (N₂)=4.4±0.3·10^?11cm³/s. The results can be understood qualitatively by a consideration of the ion-atom and ion-molecules interaction potential.     

The relaxation of HCl(ν = 1) and DCl(ν = 1) by O atoms between 196 and 400 K

The rates of relaxation of HCl(ν = 1) and DCl(ν = 1) by atomic oxygen have been determined between 196 and 400 K using the laser induced vibrational fluorescence method. The values of the rate constants, κ_1,H and κ_1,D, can be matched quite well by Arrhenius expressions: κ_1,H = 6.2 × 10^?12 exp (?1.0₅ kcal mole^?1/RT) cm³ molecule^?1 s^?1 and κ_1,D = 2.9 × 10^?12 exp (?0.5 kcal mole^?1/RT) cm³ molecule^?1 s^?1. The most likely explanation of the absolute and relative magnitudes of these rate constants appears to be that relaxation occurs as a result of non-adiabatic vibronic transitions during collisions.     

M?ssbauer spectroscopy for heavy elements: a relativistic benchmark study of mercury

The electrostatic contribution to the M?ssbauer isomer shift of mercury for the series HgF _n (n?=?1,?2,?4) with respect to the neutral atom has been investigated in the framework of four- and two-component relativistic theory. Replacing the integration of the electron density over the nuclear volume by the contact density (that is, the electron density at the nucleus) leads to a 10% overestimation of the isomer shift. The systematic nature of this error suggests that it can be incorporated into a correction factor, thus justifying the use of the contact density for the calculation of the M?ssbauer isomer shift. The performance of a large selection of density functionals for the calculation of contact densities has been assessed by comparing with finite-field four-component relativistic coupled-cluster with single and double and perturbative triple excitations [CCSD(T)] calculations. For the absolute contact density of the mercury atom, the Density Functional Theory (DFT) calculations are in error by about 0.5%, a result that must be judged against the observation that the change in contact density along the series HgF _n (n?=?1,?2,?4), relevant for the isomer shift, is on the order of 50?ppm with respect to absolute densities. Contrary to previous studies of the ⁵⁷Fe isomer shift (F Neese, Inorg Chim Acta 332:181, 2002), for mercury, DFT is not able to reproduce the trends in the isomer shift provided by reference data, in our case CCSD(T) calculations, notably the non-monotonous decrease in the contact density along the series HgF _n (n?=?1,?2,?4). Projection analysis shows the expected reduction of the 6s _1/2 population at the mercury center with an increasing number of ligands, but also brings into light an opposing effect, namely the increasing polarization of the 6s _1/2 orbital due to increasing effective charge of the mercury atom, which explains the non-monotonous behavior of the contact density along the series. The same analysis shows increasing covalent contributions to bonding along the series with the effective charge of the mercury atom reaching a maximum of around +2 for HgF₄ at the DFT level, far from the formal charge +4 suggested by the oxidation state of this recently observed species. Whereas the geometries for the linear HgF₂ and square-planar HgF₄ molecules were taken from previous computational studies, we optimized the equilibrium distance of HgF at the four-component Fock-space CCSD/aug-cc-pVQZ level, giving spectroscopic constants r _e = 2.007 ? and ?? _e = 513.5?cm^?1.     

Energy transfer in collisions of Ar(3P0,2 metastable atoms with H(2S) atoms. I. Total rate constant and mechanism

The Ar(4s,³P₂) + H(1S,²S) reaction, which gives excited H(n=2) atoms, has been studied. The room temperature rate constant for Lyman-α (2p-1s) excitation was measured as 2.4 × 10^?10 cm³ mol^?1 s^?1. The method was based upon comparison of the Lyman-α emission intensity with the Kr resonance emission intensity produced from Ar(³P₂) + Kr, which has a known rate constant. The H atom excitation, which has a large energy defect of 1.3 eV, is discussed in terms of a curve crossing mechanism.     

Reactions of CFBr studied by laser-induced fluorescence

Laser-induced fluorescence has been used to study reactions of CFBr radicals in a discharge-flow system. Arrhenius expressions of (1.9 ± 0.6) ξ 10^?12 exp(?762± 92/T) and (1.4 ± 0.3) ξ 10^?12 exp(?533 ± 62/T) cm³ molecule ^?1s^?1 for their reactions with Cl₂ and Br₂ respectively. Upper limits were obtained for the rate of reaction of CFBr with O₂ and F₂CCFBr.     

Temperature dependence of the hole mobility in the alpha phase of 9,10-dichloroanthracene

The mobility of holes in the alpha of 9,10-dichloroanthracene is isotropic with a value of 300 K of 3.8 ± 0.2 cm² V^?1 s^?1 and a temperature dependence given by T^?n where n = 2.4.     

Experimental study of triplet exciton diffusion in diphenyl and benzophenone crystals

Biphenyl crystals to which have been added to 10^?2 mole/mole of benzophenone and a various concentration of naphthalene, excited by radiation absorbed only by benzophenone molecules give naphthalene phosphorescence. This emission is interpreted as a consequence of energy migration from benzophenone molecules to the naphthalene molecules through the triplet exciton band of biphenyl. From the study, at 120 K, of the intensity of the naphthalene phosphorescence dependence on concentrations, a coefficient of diffusion of triplet excitons of biphenyl is measured (D ≈ 10^?6 cm² s^?1). Analogous kinetics applied to binary mixed crystals, naphthalene-benzophenone, give a coefficient of diffusion of triplet excitions for benzophenone (D ≈ 10^?7 cm² s^?1).     

Relativistic corrections to alkali atomg-factors

Relativistic and Breit corrections tog-factors in ground states of alkali atoms, obtained by using a four component non-perturbative formalism and single determinantal wavefunctions constructed from central field Dirac-Fock four-component orbitals, are reported. The results enable a clear assessment on the magnitude of relativistic effects on alkali-atomg-factors. Deviations of our results from experiment further provide estimates on the effect of electron correlation on alkali atomg-factors.     

Kinetics and mechanism of atmospheric reactions of partially fluorinated alcohols

Gas-phase reactions typical of the Earth’s atmosphere have been studied for a number of partially fluorinated alcohols (PFAs). The rate constants of the reactions of CF₃CH₂OH, CH₂FCH₂OH, and CHF₂CH₂OH with fluorine atoms have been determined by the relative measurement method. The rate constant for CF₃CH₂OH has been measured in the temperature range 258–358 K (k = (3.4 ± 2.0) × 10¹³exp(?E/RT) cm³ mol^?1 s^?1, where E = ?(1.5 ± 1.3) kJ/mol). The rate constants for CH₂FCH₂OH and CHF₂CH₂OH have been determined at room temperature to be (8.3 ± 2.9) × 10¹³ (T = 295 K) and (6.4 ± 0.6) × 10¹³ (T = 296 K) cm³ mol^?1 s^?1, respectively. The rate constants of the reactions between dioxygen and primary radicals resulting from PFA + F reactions have been determined by the relative measurement method. The reaction between O₂ and the radicals of the general formula C₂H₂F₃O (CF₃CH₂? and CF₃?HOH) have been investigated in the temperature range 258–358 K to obtain k = (3.8 ± 2.0) × 10⁸exp(?E/RT) cm³ mol^?1 s^?1, where E = ?(10.2 ± 1.5) kJ/mol. For the reaction between O₂ and the radicals of the general formula C₂H₄FO (? HFCH₂O, CH₂F?HOH, and CH₂FCH₂?) at T = 258–358 K, k = (1.3 ± 0.6) × 10¹¹exp(?E/RT) cm³ mol^?1 s^?1, where E = ?(5.3 ± 1.4) kJ/mol. The rate constant of the reaction between O₂ and the radicals with the general formula C₂H₃F₂O (?F₂CH₂O, CHF₂?HOH, and CHF₂CH₂?) at T = 300 K is k = 1.32 × 10¹¹ cm³ mol^?1 s^?1. For the reaction between NO and the primary radicals with the general formula C₂H₂F₃O (CF₃CH₂? and CF₃?HOH), which result from the reaction CF₃CH₂OH + F, the rate constant at 298 K is k = 9.7 × 10⁹ cm³ mol^?1 s^?1. The experiments were carried out in a flow reactor, and the reaction mixture was analyzed mass-spectrometrically. A mechanism based on the results of our studies and on the literature data has been suggested for the atmospheric degradation of PFAs.     

Absolute rate constants for the reaction of O(3P) aroms with n-butane and NO(M  Ar) over the temperature range 298–439 K

Absolute rate constants for the reaction of O(³P) atoms with n-butane (k₂) and NO(M  Ar)(k₃) have been determined over the temperature range 298–439 K using a flash photolysis-NO₂ chemiluminescence technique. The Arrhenius expressions obtained were k₂ = 2.5 × 10^?11exp[-(4170 ± 300)/RT] cm³ molecule^?1 s^?1, k₃ = 1.46 × 10^?32 exp[940 ± 200)/ RT] cm⁶ molecule^?2 s^?1, with rate constants at room temperature of k₂ = (2.2 ± 0.4) × 10^?14 cm³ molecule^?1 s^?1 and k₃ = (7.04 ± 0.70)×10^?32 cm⁶ molecule^?2 s^?1. These rate constants are compared and discussed with literature values.