Abstract
We report on theoretical Auger electron kinetic energy distribution originated from sequential two-step Auger decays of molecular double core-hole (DCH) state, using CH_{4}, NH_{3}, and H_{2}CO molecules as representative examples. For CH_{4} and NH_{3} molecules, the DCH state has an empty 1s inner-shell orbital and its Auger spectrum has two well-separated components. One is originated from the 1st Auger transition from the DCH state to the triply ionized states with one core hole and two valence holes (CVV states) and the other is originated from the 2nd Auger transition from the CVV states to quadruply valence ionized (VVVV) states. Our result on the NH_{3} Auger spectrum is consistent with the experimental spectrum of the DCH Auger decay observed recently [J. H. D. Eland, M. Tashiro, P. Linusson, M. Ehara, K. Ueda, and R. Feifel, Phys. Rev. Lett.105, 213005 (2010)]. In contrast to CH_{4} and NH_{3} molecules, H_{2}CO has four different DCH states with C1s^{−2}, O1s^{−2}, and C1s^{−1}O1s^{−1} (singlet and triplet) configurations, and its Auger spectrum has more complicated structure compared to the Auger spectra of CH_{4} and NH_{3} molecules. In the H_{2}CO Auger spectra, the C1s^{−1}O1s^{−1} DCH → CVV Auger spectrum and the CVV → VVVV Auger spectrum overlap each other, which suggests that isolation of these Auger components may be difficult in experiment. The C1s^{−2} and O1s^{−2} DCH → CVV Auger components are separated from the other components in the H_{2}CO Auger spectra and can be observed in experiment. Two-dimensional Auger spectrum, representing a probability of finding two Auger electrons at specific pair of energies, may be obtained by four-electron coincidence detection technique in experiment. Our calculation shows that this two-dimensional spectrum is useful in understanding contributions of CVV and VVVV states to the Auger decay of molecular DCH states.
We thank E. H. D. Eland for sending us the experimental Auger spectrum of the NH_{3} DCH Auger decays. M.T. also thanks N. Kosugi for discussion on theoretical method. M.E. acknowledges the support from JST-CREST and a Grant-in-Aid for Scientific Research from the JSPS.
I. INTRODUCTION
II. THEORETICAL METHOD
A. Auger intensity
B. Detail of the calculation
III. RESULTS AND DISCUSSION
A. CH_{4}
B. NH_{3}
C. H_{2}CO
D. Discussion
IV. SUMMARY
Key Topics
- Vacancies
- 31.0
- Molecular spectra
- 18.0
- Wave functions
- 18.0
- Ionization
- 8.0
- Kinetic theory
- 5.0
Figures
An example of two-step Auger decays originated from the ss-DCH state of NH_{3}. Thin black arrows represent displacements of electrons during the Auger decays. In the 1st Auger decay, the CVV state with one vacancy in the 3a _{1} orbital and another vacancy in the 1e orbital is produced. Then in the 2nd Auger transition, this CVV state decays to produce the VVVV state with additional vacancies in the 1e and 2a _{1} orbitals.
An example of two-step Auger decays originated from the ss-DCH state of NH_{3}. Thin black arrows represent displacements of electrons during the Auger decays. In the 1st Auger decay, the CVV state with one vacancy in the 3a _{1} orbital and another vacancy in the 1e orbital is produced. Then in the 2nd Auger transition, this CVV state decays to produce the VVVV state with additional vacancies in the 1e and 2a _{1} orbitals.
Calculated intensities of the Auger decays of the CH_{4} C1s^{−2} DCH state (DCH→CVV) and the C1s^{−1} CVV states (CVV→VVVV) as a function of Auger electron kinetic energy. The vertical full lines represent the discrete Auger spectrum obtained by the CASCI wave functions with the frozen orbital approximation. The dashed lines are obtained by convoluting the discrete Auger intensities with Gaussian function having 4.5 eV width.
Calculated intensities of the Auger decays of the CH_{4} C1s^{−2} DCH state (DCH→CVV) and the C1s^{−1} CVV states (CVV→VVVV) as a function of Auger electron kinetic energy. The vertical full lines represent the discrete Auger spectrum obtained by the CASCI wave functions with the frozen orbital approximation. The dashed lines are obtained by convoluting the discrete Auger intensities with Gaussian function having 4.5 eV width.
(Upper panel) 2D intensity of the two-step Auger decays of the CH_{4} C1s^{−2} ss-DCH state, as functions of kinetic energies of the 1st and 2nd Auger electrons. The 1st electrons are emitted by the Auger transition from the C1s^{−2} DCH state to the C1s^{−1} CVV states, and the 2nd electrons are emitted by the transition from the C1s^{−1} CVV states to the VVVV states. This 2D spectrum represents a probability of finding two Auger electrons at specific pair of energies. (Lower panel) 2D Auger intensity as functions of CVV and VVVV binding energies, converted from the 2D spectrum in the upper panel. These intensities were obtained by smoothing calculated discrete Auger intensities as in the convoluted intensities in Fig. 2. Unit of the intensity is arbitrary.
(Upper panel) 2D intensity of the two-step Auger decays of the CH_{4} C1s^{−2} ss-DCH state, as functions of kinetic energies of the 1st and 2nd Auger electrons. The 1st electrons are emitted by the Auger transition from the C1s^{−2} DCH state to the C1s^{−1} CVV states, and the 2nd electrons are emitted by the transition from the C1s^{−1} CVV states to the VVVV states. This 2D spectrum represents a probability of finding two Auger electrons at specific pair of energies. (Lower panel) 2D Auger intensity as functions of CVV and VVVV binding energies, converted from the 2D spectrum in the upper panel. These intensities were obtained by smoothing calculated discrete Auger intensities as in the convoluted intensities in Fig. 2. Unit of the intensity is arbitrary.
Integrated 1D Auger intensities as a function of CVV binding energy (upper panel) and VVVV binding energy (lower panel). These spectra can be obtained by integrating the 2D Auger spectrum in the lower panel of Fig. 3 by VVVV energy (upper panel) or CVV energy (lower panel). The vertical bars represent original theoretical intensities which can be directly obtained from our calculation. The other details are the same as in Fig. 2.
Integrated 1D Auger intensities as a function of CVV binding energy (upper panel) and VVVV binding energy (lower panel). These spectra can be obtained by integrating the 2D Auger spectrum in the lower panel of Fig. 3 by VVVV energy (upper panel) or CVV energy (lower panel). The vertical bars represent original theoretical intensities which can be directly obtained from our calculation. The other details are the same as in Fig. 2.
Calculated and experimental Auger intensities of the NH_{3} core-hole decays as a function of Auger electron kinetic energy. DCH→CVV: the transition from the N1s^{−2} DCH state to the N1s^{−1} CVV states, CVV→VVVV: the transition from the N1s^{−1} CVV states to the VVVV states, SCH→VV: the Auger decay of the N1s^{−1} SCH state. Expt.: experimental Auger spectrum of Eland et al. ^{10} The other details are the same as in Fig. 2.
Calculated and experimental Auger intensities of the NH_{3} core-hole decays as a function of Auger electron kinetic energy. DCH→CVV: the transition from the N1s^{−2} DCH state to the N1s^{−1} CVV states, CVV→VVVV: the transition from the N1s^{−1} CVV states to the VVVV states, SCH→VV: the Auger decay of the N1s^{−1} SCH state. Expt.: experimental Auger spectrum of Eland et al. ^{10} The other details are the same as in Fig. 2.
(Upper panel) 2D intensity of the two-step Auger decays of the NH_{3} N1s^{−2} DCH state, as functions of kinetic energies of the 1st and 2nd Auger electrons. (Lower panel) 2D Auger intensity as functions of CVV and VVVV binding energies converted from the 2D spectrum in the upper panel. The other details are the same as in Fig. 3.
(Upper panel) 2D intensity of the two-step Auger decays of the NH_{3} N1s^{−2} DCH state, as functions of kinetic energies of the 1st and 2nd Auger electrons. (Lower panel) 2D Auger intensity as functions of CVV and VVVV binding energies converted from the 2D spectrum in the upper panel. The other details are the same as in Fig. 3.
Integrated 1D Auger intensities as a function of CVV binding energy (upper panel) and VVVV binding energy (lower panel) obtained by integrating the 2D Auger spectrum in the lower panel of Fig. 6. The other details are the same as in Fig. 4.
Integrated 1D Auger intensities as a function of CVV binding energy (upper panel) and VVVV binding energy (lower panel) obtained by integrating the 2D Auger spectrum in the lower panel of Fig. 6. The other details are the same as in Fig. 4.
(Upper panel) The Auger intensities for the O1s core-hole decays of H_{2}CO molecule, which include the Auger decays of the H_{2}CO O1s^{−2} ss-DCH state, the C1s^{−1}O1s^{−1} ts-DCH states, and the O1s^{−1} CVV states. (Lower panel) The Auger intensities for the C1s core-hole decays of H_{2}CO molecule, which include the Auger decays of the H_{2}CO C1s^{−2} ss-DCH state, the C1s^{−1}O1s^{−1} ts-DCH states, and the C1s^{−1} CVV states. The other details are the same as in Fig. 2.
(Upper panel) The Auger intensities for the O1s core-hole decays of H_{2}CO molecule, which include the Auger decays of the H_{2}CO O1s^{−2} ss-DCH state, the C1s^{−1}O1s^{−1} ts-DCH states, and the O1s^{−1} CVV states. (Lower panel) The Auger intensities for the C1s core-hole decays of H_{2}CO molecule, which include the Auger decays of the H_{2}CO C1s^{−2} ss-DCH state, the C1s^{−1}O1s^{−1} ts-DCH states, and the C1s^{−1} CVV states. The other details are the same as in Fig. 2.
(Upper panel) 2D intensity of the two-step Auger decays of the H_{2}CO C1s^{−2} ss-DCH state as functions of kinetic energies of the 1st and the 2nd Auger electrons. (Lower panel) 2D intensity of the two-step Auger decays of the H_{2}CO O1s^{−2} ss-DCH state, as functions of kinetic energies of the 1st and 2nd Auger electrons. The other details are the same as in Fig. 3.
(Upper panel) 2D intensity of the two-step Auger decays of the H_{2}CO C1s^{−2} ss-DCH state as functions of kinetic energies of the 1st and the 2nd Auger electrons. (Lower panel) 2D intensity of the two-step Auger decays of the H_{2}CO O1s^{−2} ss-DCH state, as functions of kinetic energies of the 1st and 2nd Auger electrons. The other details are the same as in Fig. 3.
(Upper panel) 2D Auger intensity of the H_{2}CO C1s^{−2} ss-DCH decay as functions of CVV and VVVV binding energies, converted from the 2D spectrum in the upper panel of Fig. 9. (Lower panel) 2D Auger intensity of the H_{2}CO O1s^{−2} ss-DCH decay as functions of CVV and VVVV binding energies converted from the 2D spectrum in the lower panel of Fig. 9. The other details are the same as in Fig. 3.
(Upper panel) 2D Auger intensity of the H_{2}CO C1s^{−2} ss-DCH decay as functions of CVV and VVVV binding energies, converted from the 2D spectrum in the upper panel of Fig. 9. (Lower panel) 2D Auger intensity of the H_{2}CO O1s^{−2} ss-DCH decay as functions of CVV and VVVV binding energies converted from the 2D spectrum in the lower panel of Fig. 9. The other details are the same as in Fig. 3.
2D Auger spectra of the two-step Auger decays of the H_{2}CO C1s^{−1}O1s^{−1} ts-DCH states. Panel (a): 2D spectrum with the 1st Auger transitions from the C1s^{−1}O1s^{−1} state to the C1s^{−1} CVV states and the 2nd transitions from the C1s^{−1} CVV states to the VVVV states. Panel (b): 2D spectrum with the 1st Auger transitions from the C1s^{−1}O1s^{−1} state to the O1s^{−1} CVV states and the 2nd transitions from the O1s^{−1} CVV states to the VVVV states. Panel (c): 2D Auger intensity as functions of C1s and O1s Auger electron energies, obtained by adding the intensities of two different Auger decay pathways in the panels (a) and (b).
2D Auger spectra of the two-step Auger decays of the H_{2}CO C1s^{−1}O1s^{−1} ts-DCH states. Panel (a): 2D spectrum with the 1st Auger transitions from the C1s^{−1}O1s^{−1} state to the C1s^{−1} CVV states and the 2nd transitions from the C1s^{−1} CVV states to the VVVV states. Panel (b): 2D spectrum with the 1st Auger transitions from the C1s^{−1}O1s^{−1} state to the O1s^{−1} CVV states and the 2nd transitions from the O1s^{−1} CVV states to the VVVV states. Panel (c): 2D Auger intensity as functions of C1s and O1s Auger electron energies, obtained by adding the intensities of two different Auger decay pathways in the panels (a) and (b).
Tables
Expressions of Auger decay amplitude t for transitions from ss-DCH, singlet ts-DCH and triplet ts-DCH states to CVV state, with assumptions of single configurational wave functions and frozen orbitals. “CVV S = 1/2 (S)” represents doublet CVV state with singlet intermediate spin coupling of valence electrons, and “CVV S = 1/2 (T)” represents doublet CVV state with triplet intermediate spin coupling of valence electrons. v and w refer to orbitals involved in the valence hole creation, c stands for inner-shell orbital involved in the core-hole decay, and k represents continuum orbital of Auger electron.
Expressions of Auger decay amplitude t for transitions from ss-DCH, singlet ts-DCH and triplet ts-DCH states to CVV state, with assumptions of single configurational wave functions and frozen orbitals. “CVV S = 1/2 (S)” represents doublet CVV state with singlet intermediate spin coupling of valence electrons, and “CVV S = 1/2 (T)” represents doublet CVV state with triplet intermediate spin coupling of valence electrons. v and w refer to orbitals involved in the valence hole creation, c stands for inner-shell orbital involved in the core-hole decay, and k represents continuum orbital of Auger electron.
Representative CVV states of CH_{4} molecule. Energy refers to the ionization energy with respect to the neutral ground state of CH_{4}. Intermediate spin means spin coupling in valence electrons, where S and T represent singlet and triplet, respectively.
Representative CVV states of CH_{4} molecule. Energy refers to the ionization energy with respect to the neutral ground state of CH_{4}. Intermediate spin means spin coupling in valence electrons, where S and T represent singlet and triplet, respectively.
Representative CVV states of NH_{3} molecule. The other details are the same as in Table II.
Representative CVV states of NH_{3} molecule. The other details are the same as in Table II.
Low-lying C1s^{−1} CVV states of H_{2}CO molecule. C1s^{−2}, C1s^{−1}O1s^{−1} (S), and C1s^{−1}O1s^{−1} (T) are the initial states of the 1st Auger transitions, and represent the C1s^{−2} ss-DCH state, the singlet and triplet C1s^{−1}O1s^{−1} ts-DCH states, respectively. The other details are the same as in Table II.
Low-lying C1s^{−1} CVV states of H_{2}CO molecule. C1s^{−2}, C1s^{−1}O1s^{−1} (S), and C1s^{−1}O1s^{−1} (T) are the initial states of the 1st Auger transitions, and represent the C1s^{−2} ss-DCH state, the singlet and triplet C1s^{−1}O1s^{−1} ts-DCH states, respectively. The other details are the same as in Table II.
Low-lying O1s^{−1} CVV states of H_{2}CO molecule. The other details are the same as in Table IV.
Low-lying O1s^{−1} CVV states of H_{2}CO molecule. The other details are the same as in Table IV.
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