Long-range interaction between 1s and 2s or 2p hydrogen atoms

Long-range interaction energy between two hydrogen atoms has been computed in the second order of the perturbation theory. All states of the system arising when one of the atoms is in the 1s and the other in the 2s or 2p state have been considered. The energy represented by a series expansion in inverse powers of the internuclear distance, R, has been computed up to the terms in R^?8. The results are believed to give reliable interaction energies for R > 15 a.u. Accurate interaction energy for two ground-state hydrogen atoms has also been obtained up to the terms in R^?10. Results for the B′ ¹∑ state are employed to discuss the experimental ground-state dissociation energy of H₂, D₂, and HD. For H₂ all values of the dissociation energy obtained from various experimental absorption limits, by using the computed potential energy curve to separate off the effect of rotation, are shown to be satisfactorily consistent. The resulting total energy of H₂ is, however, higher than the most accurate theoretical value.     

Effect of the exchange integral K2s2p on the 2p-orbitals of the 1P and 3P states of the beryllium isoelectronic sequence arising from the configuration (1s)2(2s)(2p)

The ¹P and ³P states arising from the configuration (1s)²(2s)(2p) of the Be isoelectronic sequence are investigated. In the single configuration approximation, the energies of the two states are expressed as E⁰ + K_2s2p and E⁰ - K_2s2p, respectively. K_2s2p is the exchange integral between the 2s and 2p electrons and E⁰ is the energy of a model in which K_2s2p is deleted. First we calculate the 2s- and 2p-orbitals in this model. Second, by taking account of K_2s2p in this model, effects of this term on the 2p-orbitals in the ^1,3P states are investigated. In this manner, an explanation is given for the following facts which are obtained from a minimal Slater-type orbital set; (1) for Be and B⁺, the 2p-orbital of the ¹P state is broader than that of the ³P state; (2) for C²⁺, the extension of the 2p-orbital in the two states is almost the same; (3) for O⁴⁺ and Ne⁶⁺, in contrast to Be and B⁺, the 2p-orbital of the ¹P state is tighter than that of the ³P state.     

Lifetimes of the 4s4p 3 P 1 and 4s3d 1 D 2 states of Ca I

The lifetimes of the 4s4p ³ P ₁ and 4s3d ¹ D ₂ metastable states of Ca have been studied using the time-of-flight technique. Two kinds of observations were performed. First, the exponential decay of the fluorescence, using a (continuous) dc discharge for excitation and then the velocity distribution of the radiating atoms, using a pulsed discharge, were measured. From the combined results of these measurements the lifetimes were derived. The lifetimes of the 4s4p ³ P ₁ and 4s3d ¹ D ₂ states of Ca are determined to be 0.57±0.03 ms and 1.5±0.4 ms, respectively.     

Systematic determination of the Slater-Condon parameters of atoms and ions with 1s 2 2s m 2p n configurations

Semiempirical values of the Slater parameters F ²(2p,2p) and G ¹(2s, 2p) have been determined for the atoms and ions with the electron configurations 1s ²2s ^m2p ⁿ from the experimental atomic energy levels. Particular attention has been paid to get the values of the parameters to be used for semiempirical calculations on molecular electronic structure. The calculation has also yielded E _av's, the average energies of configurations of these atoms. Evaluation of the semiempirical or effective value of F ⁰ from E of an appropriate electron-transfer reaction, based on the idea presented by Anno [15], is also referred to in the present paper. The semiempirical values of the Slater parameters as well as those of E's and E _av's show almost linear dependence upon atomic number Z through isoelectronic series. From the overall tendency of the correlation lines, it is pointed out that the assignment of atomic energy levels of Na⁵⁺ (1s ²2p ⁴) must be wrong.

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Zusammenfassung Semiempirische Werte der Slater-Parameter F ²(2p,2p) und G ¹(2s, 2p) wurden für die Atome und Ionen mit der Elektronenkonfiguration 1s ²2s ^m2p ⁿ aus den experimentellen atomaren Energietermen bestimmt. Insbesondere wurden die Parameter bestimmt, die für semiempirische Berechnungen der Elektronenstruktur von Molekülen benötigt werden. Die Berechnung ergibt weiterhin Werte von E _av, der Durchschnittsenergie der Konfigurationen der genannten Atome. Die vorliegende Arbeit geht auch auf die Bestimmung des semiempirischen bzw. effektiven Wertes von F ⁰ aus E einer geeigneten Elektronenübertragungsreaktion ein, die auf die Arbeit von Anno [15] zurückgeht. Die semiempirischen Werte der Slater-Parameter sowie der E und E _av zeigen annähernd lineare Abhängigkeit von der Atomnummer Z innerhalb isoelektronischer Reihen. Aus dem Gesamtverhalten der genannten Kurven wird geschlossen, da die Zuordnung der atomaren Energieterme von Na⁵⁺(1s ²2p ⁴) falsch sein dürfte.

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Résumé Détermination à partir des niveaux d'énergie atomiques expérimentaux des valeurs semi-empiriques des paramètres de Slater F ²(2p, 2p) et G ¹(2s, 2p) pour les atomes et les ions ayant les configurations 1s ²2s ^m2p ⁿ. On a fait particulièrement attention d'obtenir les valeurs des paramètres à utiliser pour des calculs moléculaires semi-empiriques. Le calcul a aussi fourni les énergies moyennes des configurations de ces atomes. On évoque aussi le calcul de la valeur semi-empirique ou effective de F ⁰ à partir du E d'une réaction appropriée de transfert électronique, selon une idée de Anno [15]. Les valeurs semiempiriques des paramètres de Slater, ainsi que celles des E et E _moy, montrent une dépendance presque linéaire au nombre atomique Z à travers les séries isoélectroniques. A partir des tendances générales des lignes de corrélation, on remarque que l'attribution des niveaux d'énergie atomiques de Na⁵⁺(1s ²2p ⁴) doit être fausse.

     

Valence orbital ionization potentials of 1s 22s m2p n atoms and ions

The 2s and 2p valence orbital ionization potentials (VOIP) are determined systematically for atoms and ions with configurations 1s ²2s ^m2p ⁿ , using the Anno-Teruya values of the average energies of the configurations. All the cases with possible values of m and n, in conformity with the Pauli principle, are treated. The 2s or 2p VOIP of a particular ion with the configuration of this type is almost independent of the electron configuration. The VOIP's of an isoelectronic series are fitted to a quadratic equation in terms of atomic number Z: VOIP=A ₀+A ₁ Z+A ₂ Z ², by a least-squares method. There are remarkable regularities among A ₀'s, A ₁'s or A ₂'s, for different isoelectronic series, which may be explained by Slater's simple expression for the total energy of an atom (or ion) with the idea of screening effect due to inner electrons. Various screening constants have been determined from the analysis of such regularities.

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Zusammenfassung Unter Benutzung der Anno-Teruya-Werte für die durchschnittliche Energie der Konfigurationen werden systematisch für Atome und Ionen der Konfiguration 1^{s 2}2s ^m 2p ⁿ die 2s- und 2p-VOIP's bestimmt. Alle FÄlle mit den nach dem Pauli-Prinzip möglichen Werten für m und n werden behandelt. Das 2s- oder 2p-VOIP eines besonderen Ions ist beinahe unabhÄngig von der Elektronenkonfiguration. Nach der Methode der kleinsten quadratischen Abweichung werden die VOIP's einer isoelektronischen Serie mit Hilfe einer in Z (Z=Kernladungszahl) quadratischen Gleichung bestimmt: VOIP=A ₀ +A ₁ Z+A ₂ Z ². Die Koeffizienten A ₀,A₁ und A ₂ zeigen untereinander für verschiedene isoelektronische Serien bemerkenswerte RegelmÄ\igkeiten, die mit der einfachen Slaterformel für die Gesamtenergie eines Atoms oder Ions als Abschirmeffekte der inneren Elektronen erklÄrt werden können. Durch die Untersuchung dieser RegelmÄ\igkeiten konnten verschiedene Abschirmkonstanten bestimmt werden.

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Résumé Les potentiels d'ionisation des orbitales de valence (VOIP) 2s et 2p sont systématiquement déterminés pour les atomes et les ions de configuration 1s ²2s ^m2p ⁿ, en utilisant les valeurs de Anno-Teruya pour les énergies moyennes des configurations. Tous les cas possibles d'après le principe de Pauli sont traités. Le VOIP 2s ou 2p d'un ion donné avec une configuration de ce type est presque indépendant de la configuration électronique. Une relation quadratique en fonction du numéro atomique Z est ajustée pour les VOIP d'une série isoélectronique par la méthode des moindres carrés: VOIP=A ₀+A ₁ Z +A ₂ Z ². Des régularités remarquables se manifestent pour A ₀, A ₁, A ₂ dans différentes séries isoélectroniques; ceci peut Être expliqué à l'aide des expressions simples de Slater pour l'énergie totale d'un atome (ou d'un ion) avec l'idée d'un effet d'écran d aux électrons internes. Différentes constantes d'écran ont été déterminées par l'analyse de ces régularités.

     

Behaviour of the 3p 511s’ [1/2]1 level of Argon I in a strong magnetic field

The properties of the autoionizing 3p ⁵11s’ [1/2]₁ Argon I level have been experimentally studied in the presence of a strong magnetic field (2.14-2.22 T). Quasi- Landau type oscillations have been observed in the width and position of the 3p ⁵-4p[1/2]₀ -3p ⁵11s’ [1/2]₁ exciting transition. The results provide an additional support for earlier observations of Lemoigne et al. [7]. No evidence for similar oscillations in magnetic field dependence of the Fano q parameter was observed.     

The spin-allowed and spin-forbidden 5s 2 1 S 0-5s5p 1 P 1,3 P 1 transitions in strontium isoelectronic sequence

Relativistic multiconfiguration Dirac-Fock (MCDF) transition energies and oscillator strengths are determined for both the spin-allowed 5s ^{2 1} S ₀-5s5p ¹ P ₁ and the spin-forbidden 5s ^{2 1} S ₀-5s5p ³ P ₁ transitions in the strontium isoelectronic sequence. The modest relativistic configuration mixing to represent intravalence correlation is combined with a polarization model to account for valence-core electron correlations. The multiconfiguration Dirac-Fock calculations are performed in an average level scheme; however for neutral strontium and singly ionized yttrium a thorough comparison of the average and the optimal level schemes is presented. The average level scheme, though less accurate for the neutral end of the sequence, avoids the convergence problems encountered for highly ionized systems, where the 5s 5p ³ P ₁,¹ P ₁ states are raised owing to the collapse of the 4d _{3/2, 5/2} spin-orbitals in the isoelectronic sequence and, thus, allows us to extend our study to multiple charged ions (throughW ³⁶⁺). Since for such systems there is practically no difference between the results of the average and the optimal level versions of MCDF calculations, we believe that our average level predictions of ionization energies and oscillator strengths for states with total angular numberJ=0 andJ=1 are of comparable quality to those that could be obtained with an optimal level scheme.This study was supported by the Pedagogical Academy of Kraków Statutory Activity Grant No BS-29/91     

Photoionization of the 2s, 2p and 3s subshells of Mg+

We present calculations of total and partial photoionisation cross sections for the 2s, 2p and 3s subshells of Mg⁺ from their ionisation thresholds up to a photon energy of 220 eV. Photoelectron angular distribution parameters are also calculated for the 2p subshell. Oscillator strengths are given for discrete structure, and calculated energy levels compared with experimental values. The significance of electron correlations and two electron excitation for this atomic ion is discussed.     

Precision measurement of the energy of the 4d 9 5s 2 2 D 5/2 metastable level in Ag I

The energy of the 4d ⁹ 5s ^{2 2} D _5/2 metastable level in Ag I, which is the upper level of the very narrow 5s ² S _1/2 – 4d ⁹ 5s ^{2 2} D _5/2 two-photon transition at 661.2 nm, has been determined from precision measurements of the wavelengths of the 206.1 nm (5s ² S _1/2 – 6p ² P ₃ ^2/0 ) and 547.5 nm (4d ⁹ 5s ^{2 2} D _5/2 – 6p ² P ₃ ^2/0 ) lines emitted from a hollow-cathode discharge. The measured energy of the 4d ⁹ 5s ^{2 2} D _5/2 level, 30 242.286(7) cm^–1, is combined with the known hyperfine splittings and the estimated¹⁰⁷Ag-¹⁰⁹Ag isotope shift to obtain accurate absolute frequencies for the hyperfine components of the 661.2 nm transition. These results should help in the detection of the narrow 661.2 nm two-photon transition, which has been proposed as a new optical frequency standard.     

Angular distributions of photoelectrons in resonantly enhanced multiphoto ionization via the 7s[1 1/2]0 1 and 8s[1 1/2]0 1 states of Xe

Photoelectron angular distributions have been measured for the three-photon resonant one-photon ionization, (3+1), of Xe via the 7s[1 1/2]⁰ ₁ and 8s[1 1/2]⁰ ₁ states. The results are in good agreement with the theoretical predictions of Tang and Lambropoulos [13] for the 8s[1 1/2]⁰ ₁, but not for the 7s[1 1/2]⁰ ₁ state. Furthermore, the results are compared to those which have been obtained by Blazewicz et al. [1] for the three-photon resonant two-photon ionization, (3+2), of Xe via the 6s[1 1/2]⁰ ₁ state.     

Quantal close-coupling calculation of the cross sections for the j 1 m 1 → j 2 m 2 transitions in the 4p 2P and 3d 2D excited states of Ca+ induced by collisions with helium

Cross sections for the j ₁ m ₁ → j ₂ m ₂ transitions in the resonance 4p ²P and metastable 3d ²D states of the singly charged calcium ion induced by collisions with the ground-state He atom have been calculated using the quantal close-coupling method. The calculations are based on the earlier obtained Ca⁺-He pseudopotential SCF potential energy curves. The calculated cross sections are discussed in the energy range from threshold to 1.5 eV. Satisfactory agreement with other theoretical results has been found for the 4p ²P state. However, relatively large discrepancy between theory and available experimental data still exists for both the Ca⁺ states.     

Calculation of the photo-electrons angular distribution asymmetry parameter β2p near the (3s3p)1 P resonance of He*

Near the (3s3p)¹ P resonance of He, we have calculated the photoelectrons angular distribution asymmetry parameter β_2p in the diagonalization approximation. Using the measured value of β _n=2 near the (3s3p)¹ P level obtained by Lindle et al. in the resonance photo-ionization of He to He^?(n=2), we have estimated the ratioR=σ_2p /σ_2s of the partial 2p photo-ionization cross section to the partial 2s photo-ionization cross section. Our calculation supports the result that in the resonance region, the formation of ions in the 2p level dominates over the 2s level. This is in good agreement with the experimental and most of the theoretical results reported to date.     

1/Z perturbation theory for calculation of line strengths in the neon isoelectronic sequence

The line strengths of 2–2 and 3–3 transitions (2s²2p⁵3s–2s²2p⁵3p–2s²2p⁵3d, 2s2s2p⁶3s–2s2p⁶3p-2s2p⁶3d, 2s²2p⁵3l-2s2p⁶3l) have been calculated for the Ne isoelectronic sequence (Z = 14 ÷ 100). The calculation has been carried out in intermediate coupling. Relativistic corrections have been included through the Breit operator. Perturbation theory in 1/Z has been used to account for electronic interactions.     

A relativistic CI study on OIII: wavefunctions,excitation energies and transition probabilities

The relativistic CI method is used to determine N-electron wavefunctions for the 1s ² 2s ² 2p ² (³ P ₀,³ P ₂,¹ D ₂), 1s ² 2p ^{4 3} P ₂ even levels, and the 1s ²2s2p ³ (³ D ₁,³ P ₁,³ S ₁,¹ P ₁), 1s ²2s ²2p3s (³ P ₁ and¹ P ₁), 1s ²2s ²2p3d (³ D ₁,³ P ₁,¹ P ₁)J=1 OIII levels. Excitation energies and emission probabilities between these levels are reported in the electric dipole approximation, both for the Coulomb and the Babushkin gauges.ns, p,np,nd- andnd (n17) numerical basis functions have been used for the construction of CSF's entering the CI expansion for the ASF's of these levels. Radiative matrix elements of the type calculated here within the framework of the relativistic CI method, may be used in laser assisted spectroscopic studies of atoms and ions.     

Scaled AMO calculations on the hydrogen molecule. III. The 1s2s 3∑ state

The potential energy curve for the 1s2s ³∑ state of the hydrogen molecule is calculated in a scaled version of the AMO approximation. Deviations from a simple potential curve occur. The agreement with experimental data is found to be better for the present state than for the 1sσ2pσ ¹∑ state studied in a previous paper.     

Isentropic Compressibility Changes of Mixing for 1,3-Dioxolane or 1,4-Dioxane + Water + Propanol Ternary Mixtures

Speed of sound data, u_ijk, of 1,3-dioxolane or 1,4-dioxane(i) + water(j) + propan-1-ol or propan-2-ol(k) ternary mixtures and their sub-binary mixtures, u_ij, of 1,3-dioxolane or 1,4-dioxane(i) + water or propan-1-ol or propan-2-ol(j) and water(i) + propan-1-ol or propan-2-ol(j) mixtures have been measured over the entire composition range at 308.15 K. Isentropic compressibility changes of mixing, (κ_s^E)_ij and (κ_s^E) _ijk, for the binary and ternary mixtures have been determined by employing the observed speeds of sound data and densities (calculated from their molar excess volumes data). The (κ_s^E) _ij and (κ_s^E) _ijk values have also been predicated by the graph theoretical approach and the Flory theory. It has been observed that (κ_s^E) _ij and (κ_s^E) _ijk predicted by the graph theoretical approach compare well with their corresponding experimental values.     

Application of the extended method of calculation for atoms and ions having the electronic configurations 1s22s22pN

The atoms and ions in the electronic configurations 1s²2s²2p^N (N = 2, 3, 4, 5, 6) are examined. N hydrogen-like radial orbitals for 2p electrons were used. The calculated energies of the 2p shell are compared with those of the ordinary method and with experimental results. The intermultiplet separation ratios are considered as well.     

Laser and radiofrequency spectroscopy of the 5d 4 6s 6 D multiplet in Ta I

The hyperfine structure (hfs) of¹⁸¹Ta has been investigated using laser radio-frequency double resonance and high resolution laser spectroscopy on collimated atomic beams. The magnetic dipole and electric quadrupole hyperfine structure coupling constants of the 5d ^{4 6} s 6D _{3/2, 5/2, 7/2, 9/2} metastable states have been determined using radio-frequency spectroscopy. In the 5d ⁴ 6s ⁶ D _1/2 metastable state and the excited 5d ³ 6s 6p ⁴ D _3/2,⁶ D _{5/2, 9/2} as well as the unidentified 28 182.6 cm^–1 and 30 021.2 cm^–1 states, hfs constants have been obtained from high resolution laser spectroscopy. A radio-frequency converter has been developed in order to reach the frequency region 2.7–10 GHz.     

Excess Isentropic Compressibilities for 1,3-Dioxolane or 1,4-Dioxane <Emphasis Type="Italic">+</Emphasis> Water <Emphasis Type="Italic">+</Emphasis> Formamide or N,N-Dimethylformamide Ternary Mixtures at 308.15 K

Speeds of sound, u_ijk, of 1,3-dioxolane or 1,4-dioxane (i) + water (j) + formamide or dimethylformamide (k) ternary mixtures and of their binary subsystems, u_ij, of 1,3-dioxolane or 1,4-dioxane (i) + formamide or dimethylformamide (j), and water (i) + formamide or dimethylformamide (j) have been measured over the entire composition range at 308.15 K. The experimental data have been used to evaluate the excess isentropic compressibilities of binary (κ_s^E)_ij and ternary (κ_s^E)_ijk mixtures using their densities calculated from molar excess volume data. The Moelwyn-Huggins concept [M. L. Huggins, Polymer 12, 389 (1971)] of interaction between the surfaces of components of a binary mixture has been employed to evaluate the excess isentropic compressibilities (using the concept of connectivity parameter of third degree of a molecule, ³ξ, which in turn depends on its topology) of binary mixtures, and this method has been extended to predict excess compressibilities of ternary mixtures. Values of (κ_s^E)_ij and (κ_s^E)_ijk have also been calculated by the Flory theory. It was observed that (κ_s^E)_ij and (κ_s^E)_ijk predicted by the Moelwyn-Huggins approach compare well with calculated and experimental values.     

Theoretical studies of organometallic compounds. III. Structures and bond energies of FeCHn and FeCH (n = 1, 2, 3)

The geometries and dissociation energies for the Fe? C and C? H bonds of FeCH_n and FeCH (n = 1, 2, 3) have been calculated by ab initio quantum mechanical methods using different effective core potential models and Møller–Plesset perturbation theory. The HW3 ECP model, which has a configuration [core] (n?1)s², (n?1)p⁶, (n?1)d¹, (n)s^m for the transition metals, is clearly superior to the larger core LANL1DZ ECP model with the configuration [core] (n?1)d¹, (n)s^m. The Fe? C bond energies calculated at correlated levels using the HW3 ECP are in much better agreement with experiment than the LANL1DZ results. This effect is mainly due to the higher number of correlated electrons rather than the inclusion of the outermost core electrons in the Hartree–Fock calculation. At the PMP4/HW3TZ/6-31G(d)//MP2/HW3TZ/6-31G(d) level, the theoretically predicted Fe? C bond energies for FeCH are in the range of 80% of the experimental values and have nearly the same accuracy as all-electron calculations using large valence basis sets and the MCPF method for the correlation energy. © 1992 by John Wiley & Sons, Inc.