yuen_2023#
C. H. Yuen, P. Modak, Y. Song, S.-F. Zhao and C. D. Lin, “Modeling the sequential dissociative double ionization of O2 by ultrashort intense infrared laser pulses”, Phys. Rev. A 107, 013112 (2023)
Source record · Catalogue · Review register
DOI: 10.1103/PhysRevA.107.013112
Source kind: theory
Recorded technique: The density-matrix model of sequential double ionisation (DM-SDI; Yuen and Lin 2022, yuen_2022) extended to O2, Eqs. (1): MO-ADK rates (Tong et al. 2002) from O2 to the O2+ X 2Pi_g, a 4Pi_u and b 4Sigma_g- states and from these to eight O2^2+ states (Table II); the a and b states coupled by the field, and, new here, couplings between the dication states (Table IV); fixed nuclei at R = 1.21 angstrom, isotropic alignment average, KER spectra convolved with Gaussians of 0.4 eV resolution. Where one orbital leads to several dication states of one configuration (states 1-3, states 4-5), one effective binding energy is used, the multiplicity-weighted mean of the state energies (E_b = dE1/2 + dE2/4 + dE3/4; dE4/3 + 2 dE5/3), with rate weights (p. 3). Electronic structure: SA-CASSCF/CASPT2 with the ANO-L basis in OpenMolcas at R = 1.21 angstrom, 1sigma_g and 1sigma_u frozen, active space 2sigma_g, 2sigma_u, 3sigma_g, 1pi_u, 1pi_g and 3sigma_u; SA3-CASSCF(11,8) for the O2+ a-b dipole, SA8- and SA6-CASSCF(10,8)/CASPT2 for the triplet and singlet O2^2+ states. Structure parameters by the method of Zhao et al. 2010 (zhao_2010).
Materials in structured entries: O2, O2+, O2++
Dataset quantities: ionization_energy, ionization_model_parameter, kinetic_energy_release, transition_dipole_moment, tunnelling_structure_coefficient
Contents: 19 datasets; 0 formulas.
Curation notes#
Journal pages 013112-1 to -10 = PDF pages 1-10; the library copy is the version of record. Identity checked on PDF p. 1 (C. H. Yuen, P. Modak, Yan Song, Song-Feng Zhao and C. D. Lin; received 19 October 2022, published 24 January 2023) on 2026-10-09. The register entry is TC-956.
THE PULSE OF THE MODEL (p. 4): ‘a linearly polarized Gaussian laser pulse with peak intensity at 1.2 x 10^15 W/cm2, central wavelength of 800 nm, and pulse duration of 8 fs’ (Fig. 2, against Voss et al. 2004 and Wu et al. 2010, the latter’s spectrum shifted by 0.8 eV; Wu et al. used 780 nm, 1e15 W/cm^2). The pulse form is that of yuen_2022 (the duration an intensity FWHM). Also 564 and 1675 nm (Fig. 7), aligned and antialigned distributions (Fig. 8), intensities around 12 x 10^14 W/cm^2 and a volume average (Figs. 9-10). ‘the ratios between the peaks could vary by about +-20% when the peak intensities vary also by +-20%’ (p. 8).
TABLE I (p. 2): taken. I_p ‘Experimental vertical ionization potential ... to the O2+ states [36]’ (Baltzer et al. 1992): 12.3, 16.7 and 18.2 eV, the same as zhao_2010’s Table IV (also Baltzer et al.); a copy, not fitted beside it. The C_lm are captioned ‘structure parameters of the O2 orbitals for MO-ADK tunnel ionization rates [37]’ (ref. 37 = Zhao et al. 2010) but are not zhao_2010’s printed values (TC-956): HOMO 1pi_g {0.69, 0.06} against zhao_2010’s {0.52, 0.03} (Table III) and zhao_2017’s {0.64, 0.04}; 1pi_u {1.86, 0.36, 0.02} against {2.04, 0.33, 0.01}; 3sigma_g {3.49, 2.06, 0.25} against {3.05, 1.59, 0.08} (Table V). The ratios differ by orbital and by l, so it is not a change of normalisation. They are recorded as this paper’s (use = check).
TABLE II (p. 2): taken. Calculated vertical I_p to the O2^2+ states with two valence holes; ‘The zero of energy is set to be the zero-point energy of O2’, and ‘The calculated energies were systematically shifted such that the B 3Pi_g state has I_p = 43.46 eV’ (the value of Bao et al.’s fit of the O2 normal Auger spectrum, p. 4); states 1 and 2 agree with Bao et al.’s 43.05 and 44.2 eV (p. 4). ‘The indexes are arranged according to the KER, which are obtained by subtracting the I_p by the dissociation limit’: I_p - KER is 35.68 eV for O+(4S) + O+(2D) and 32.35 eV for O+(4S) + O+(4S) (checked by the script); the limits’ energies are not printed, so no dissociation_energy dataset is made. Fig. 1’s caption: ‘dissociation limits of states 2 and 4-7 are different from Table II since these states dissociate through spin-orbit interactions with other states’; Table II’s limit is the one each state reaches. The parent O2+ states of each row are in the printed cells.
TABLE III (p. 3): taken. ‘Effective binding energies of the spin-up orbitals of the X state and its structure parameters, assuming the remaining electron in the 1pi_g orbital is spin down’; the same C_lm ‘were also used for ionization from the a and b states, as well as for the spin-down orbitals’ (p. 3). The binding energies are model inputs (multiplicity-weighted means), so ionization_model_parameter, not ionization_energy.
TABLE IV (p. 4): taken, material O2++ (registered in TC-954). Calculated transition dipoles (au) between O2^2+ states, all along x (perpendicular to the axis): W 3Delta_u - B 3Pi_g, B 3Sigma_u- - B 3Pi_g, A 3Sigma_u+ - B 3Pi_g, 1 1Sigma_u- - 1 1Pi_g (‘the dipole moment between W 3Delta_u and B 3Pi_g is double counted since both states are doubly degenerate’).
TEXT VALUES (taken as points): the O2+ a-b transition dipole, ‘0.29 x atomic units’ (SA3-CASSCF(11,8)/CASPT2, p. 4, agreeing ‘with the result from Ref. [35]’, Marian et al. 1982), with the calculated a-b excitation energy 1.42 eV against the experimental 1.5 eV; the quintet states 1 5Sigma_g+ and 1 5Pi_u at 45.5 and 46.9 eV (SA3-CASSCF(10,8) /CASPT2) with KER 13.2 and 11.2 eV to O+(4S) + O+(4S) and O+(4S) + O+(2D) (p. 5); footnote 41 (p. 10): ‘The binding energies for the 1pi_g orbital of the a and b state are 26.2 and 25.3 eV. Their structure parameters C_lm are {1.83, 0.23} and {1.72, 0.24}’. Not taken: the two lowest 2Pi_u states of O2+, 5.56 and 6.98 eV above X (p. 4, unreachable by tunnelling, no state energy needed by any model here).
FIGURES (not digitised; all vector drawings): Fig. 3, the populations of the O2^2+ states 0-7 left by the 800 nm, 8 fs, 1.2e15 W/cm^2 pulse with the KER spectrum; Fig. 9, the angle-averaged yield of states 0-3 and 6 against peak intensity; Fig. 7, the yields at 800, 564 and 1675 nm; Figs. 2, 4-6, 8, 10, KER spectra. Fig. 1 (potential curves) from Refs. 25 and 34.
Recorded bibliographic identity status: VALIDATED. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
yuen_2023/table1_ip#
{
"id": "table1_ip",
"material": "O2",
"file": "O2/yuen_2023__table1_ip_O2.csv",
"table": "tbl_8972394235c5",
"quantity": "ionization_energy",
"unit": "eV",
"abscissa": "label",
"use": "reproduced",
"reproduced_from": [
"P. Baltzer, B. Wannberg, L. Karlsson, M. Carlsson Gothe and M. Larsson, Phys. Rev. A 45, 4374 (1992)"
],
"parameters": {
"kind": "vertical",
"initial_state": "O2 X 3Sigma_g-",
"final_state": "the O2+ state of the row"
}
}
Table I, ‘I_p (eV)’: ‘Experimental vertical ionization potential’ of O2 to the O2+ X, a and b states (rows), the hole in the configuration column. Equal to zhao_2010’s table4_expt_O2 (the same reference); never fitted beside it.
yuen_2023/table1_cl_x#
{
"id": "table1_cl_x",
"material": "O2",
"file": "O2/yuen_2023__table1_cl_x_O2.csv",
"table": "tbl_8972394235c5",
"quantity": "tunnelling_structure_coefficient",
"abscissa": "label",
"use": "check",
"parameters": {
"model": "moadk",
"orbital": "HOMO 1pi_g",
"m": 1,
"normalisation": "as Zhao et al. 2010 (zhao_2010, Eqs. (19)-(20)), the method the paper cites; the paper prints no definition"
}
}
Table I, X 2Pi_g row: C_lm of the O2 HOMO (rows l = 2, 4). Captioned with ref. 37 (Zhao et al. 2010) but not zhao_2010’s printed {0.52, 0.03} nor zhao_2017’s {0.64, 0.04} (TC-956). R = 1.21 angstrom (p. 2).
yuen_2023/table1_cl_a#
{
"id": "table1_cl_a",
"material": "O2",
"file": "O2/yuen_2023__table1_cl_a_O2.csv",
"table": "tbl_8972394235c5",
"quantity": "tunnelling_structure_coefficient",
"abscissa": "label",
"use": "check",
"parameters": {
"model": "moadk",
"orbital": "HOMO-1 1pi_u",
"m": 1,
"normalisation": "as Zhao et al. 2010 (zhao_2010, Eqs. (19)-(20)), the method the paper cites; the paper prints no definition"
}
}
Table I, a 4Pi_u row: C_lm of the O2 HOMO-1 (rows l = 1, 3, 5). zhao_2010’s Table V prints {2.04, 0.33, 0.01} (TC-956). R = 1.21 angstrom.
yuen_2023/table1_cl_b#
{
"id": "table1_cl_b",
"material": "O2",
"file": "O2/yuen_2023__table1_cl_b_O2.csv",
"table": "tbl_8972394235c5",
"quantity": "tunnelling_structure_coefficient",
"abscissa": "label",
"use": "check",
"parameters": {
"model": "moadk",
"orbital": "HOMO-2 3sigma_g",
"m": 0,
"normalisation": "as Zhao et al. 2010 (zhao_2010, Eqs. (19)-(20)), the method the paper cites; the paper prints no definition"
}
}
Table I, b 4Sigma_g- row: C_lm of the O2 HOMO-2 (rows l = 0, 2, 4). zhao_2010’s Table V prints {3.05, 1.59, 0.08} (TC-956). R = 1.21 angstrom.
yuen_2023/table2_ip#
{
"id": "table2_ip",
"material": "O2",
"file": "O2/yuen_2023__table2_ip_O2.csv",
"table": "tbl_4676ff61cd02",
"quantity": "ionization_energy",
"unit": "eV",
"abscissa": "label",
"use": "check",
"parameters": {
"kind": "vertical",
"initial_state": "O2 X 3Sigma_g- (v = 0)",
"final_state": "the O2^2+ state of the row"
}
}
Table II, ‘I_p (eV)’: calculated (CASPT2) vertical double-ionisation energy of O2 to each O2^2+ state (rows: the table’s index 0-7, x the state; the configuration, limit, KER and parents in the printed cells), from the zero-point level of O2 at R = 1.21 angstrom, shifted as a whole so that state 6 (B 3Pi_g) is 43.46 eV, Bao et al.’s fitted Auger value. So only the spacings are this calculation’s. No uncertainty is stated.
yuen_2023/table2_ker_4s2d#
{
"id": "table2_ker_4s2d",
"material": "O2",
"file": "O2/yuen_2023__table2_ker_4s2d_O2.csv",
"table": "tbl_4676ff61cd02",
"quantity": "kinetic_energy_release",
"unit": "eV",
"abscissa": "label",
"use": "check",
"parameters": {
"channel": "O2 -> O2^2+ (the state of the row) -> O+(4S) + O+(2D)",
"kind": "calculated",
"state": "the O2^2+ state of the row"
}
}
Table II, ‘KER (eV)’ of states 1, 2, 4 and 5 (rows: the table’s index), limit O+(4S) + O+(2D): I_p less the limit, 35.68 eV above the zero-point level of O2 as implied by every row. States 2, 4 and 5 reach this limit through spin-orbit coupling to other states (Fig. 1 caption). The KER of a dication channel is filed under the neutral, O2, with the dication state in the channel (TC-954).
yuen_2023/table2_ker_4s4s#
{
"id": "table2_ker_4s4s",
"material": "O2",
"file": "O2/yuen_2023__table2_ker_4s4s_O2.csv",
"table": "tbl_4676ff61cd02",
"quantity": "kinetic_energy_release",
"unit": "eV",
"abscissa": "label",
"use": "check",
"parameters": {
"channel": "O2 -> O2^2+ (the state of the row) -> O+(4S) + O+(4S)",
"kind": "calculated",
"state": "the O2^2+ state of the row"
}
}
Table II, ‘KER (eV)’ of states 3, 6 and 7, limit O+(4S) + O+(4S): I_p less 32.35 eV. States 6 and 7 reach it through spin-orbit coupling (Fig. 1 caption). As table2_ker_4s2d otherwise.
yuen_2023/table3_eb#
{
"id": "table3_eb",
"material": "O2+",
"file": "O2+/yuen_2023__table3_eb_O2+.csv",
"table": "tbl_4b5f5b8c6a36",
"quantity": "ionization_model_parameter",
"unit": "eV",
"abscissa": "label",
"use": "check",
"parameters": {
"model": "moadk (DM-SDI, effective binding energy)",
"parameter": "E_b"
}
}
Table III, ‘I_p (eV)’: the effective binding energies of the spin-up 1pi_g, 1pi_u and 3sigma_g orbitals of O2+ X 2Pi_g (rows), the multiplicity-weighted means of the energies of the dication states each orbital leads to (p. 3), used in the MO-ADK rates of the second ionisation. Not ionisation energies of O2+ to any one state.
yuen_2023/table3_cl_1pig#
{
"id": "table3_cl_1pig",
"material": "O2+",
"file": "O2+/yuen_2023__table3_cl_1pig_O2+.csv",
"table": "tbl_4b5f5b8c6a36",
"quantity": "tunnelling_structure_coefficient",
"abscissa": "label",
"use": "check",
"parameters": {
"model": "moadk",
"orbital": "O2+ X 2Pi_g, spin-up 1pi_g",
"m": 1,
"normalisation": "as Zhao et al. 2010 (zhao_2010, Eqs. (19)-(20)), the method the paper cites, with the ion's asymptotic charge; the paper prints no definition"
}
}
Table III: C_lm of the spin-up 1pi_g orbital of O2+ X 2Pi_g (rows l = 2, 4), the remaining 1pi_g electron spin down, at R = 1.21 angstrom; obtained ‘using the method in Ref. [37]’ (Zhao et al. 2010). Larger than the neutral’s (table1_cl_x): 1.63 against 0.69 for l = 2.
yuen_2023/table3_cl_1piu#
{
"id": "table3_cl_1piu",
"material": "O2+",
"file": "O2+/yuen_2023__table3_cl_1piu_O2+.csv",
"table": "tbl_4b5f5b8c6a36",
"quantity": "tunnelling_structure_coefficient",
"abscissa": "label",
"use": "check",
"parameters": {
"model": "moadk",
"orbital": "O2+ X 2Pi_g, spin-up 1pi_u",
"m": 1,
"normalisation": "as Zhao et al. 2010 (zhao_2010, Eqs. (19)-(20)), the method the paper cites, with the ion's asymptotic charge; the paper prints no definition"
}
}
Table III: C_lm of the spin-up 1pi_u orbital of O2+ X 2Pi_g (rows l = 1, 3, 5). As table3_cl_1pig otherwise.
yuen_2023/table3_cl_3sigmag#
{
"id": "table3_cl_3sigmag",
"material": "O2+",
"file": "O2+/yuen_2023__table3_cl_3sigmag_O2+.csv",
"table": "tbl_4b5f5b8c6a36",
"quantity": "tunnelling_structure_coefficient",
"abscissa": "label",
"use": "check",
"parameters": {
"model": "moadk",
"orbital": "O2+ X 2Pi_g, spin-up 3sigma_g",
"m": 0,
"normalisation": "as Zhao et al. 2010 (zhao_2010, Eqs. (19)-(20)), the method the paper cites, with the ion's asymptotic charge; the paper prints no definition"
}
}
Table III: C_lm of the spin-up 3sigma_g orbital of O2+ X 2Pi_g (rows l = 0, 2, 4). As table3_cl_1pig otherwise.
yuen_2023/note41_eb#
{
"id": "note41_eb",
"material": "O2+",
"table": "text",
"quantity": "ionization_model_parameter",
"unit": "eV",
"abscissa": "label",
"use": "check",
"parameters": {
"model": "moadk (DM-SDI, effective binding energy)",
"parameter": "E_b"
}
}
2 inline points in the source record.
Footnote 41 (reference list, p. 10): ‘The binding energies for the 1pi_g orbital of the a and b state are 26.2 and 25.3 eV’; used only to test the effect of orbital relaxation after excitation, which changes the KER peak ratios by less than 5 % (p. 6).
yuen_2023/note41_cl_a#
{
"id": "note41_cl_a",
"material": "O2+",
"table": "text",
"quantity": "tunnelling_structure_coefficient",
"abscissa": "label",
"use": "check",
"parameters": {
"model": "moadk",
"orbital": "O2+ a 4Pi_u, 1pi_g",
"m": 1,
"normalisation": "as Zhao et al. 2010 (zhao_2010, Eqs. (19)-(20)), the method the paper cites, with the ion's asymptotic charge; the paper prints no definition"
}
}
2 inline points in the source record.
Footnote 41 (p. 10): C_lm {1.83, 0.23} of the 1pi_g orbital of O2+ a 4Pi_u (cf. Table III), obtained by changing only the occupation numbers (p. 6). l = 2, 4 as Table III’s 1pi_g.
yuen_2023/note41_cl_b#
{
"id": "note41_cl_b",
"material": "O2+",
"table": "text",
"quantity": "tunnelling_structure_coefficient",
"abscissa": "label",
"use": "check",
"parameters": {
"model": "moadk",
"orbital": "O2+ b 4Sigma_g-, 1pi_g",
"m": 1,
"normalisation": "as Zhao et al. 2010 (zhao_2010, Eqs. (19)-(20)), the method the paper cites, with the ion's asymptotic charge; the paper prints no definition"
}
}
2 inline points in the source record.
Footnote 41 (p. 10): C_lm {1.72, 0.24} of the 1pi_g orbital of O2+ b 4Sigma_g-. As note41_cl_a otherwise.
yuen_2023/text_dipole_ab#
{
"id": "text_dipole_ab",
"material": "O2+",
"table": "text",
"quantity": "transition_dipole_moment",
"unit": "au",
"abscissa": "label",
"use": "check",
"parameters": {
"states": "a 4Pi_u - b 4Sigma_g-",
"component": "perpendicular (x)",
"geometry": "R = 1.21 angstrom"
}
}
1 inline points in the source record.
p. 4: ‘The transition dipole moment between these two states is found to be 0.29 x atomic units (a.u.)’, SA3-CASSCF(11,8)/CASPT2 at R = 1.21 angstrom; ‘we used the d_x component to represent the transition from both Pi_+- states to a Sigma state’.
yuen_2023/text_ip_quintet#
{
"id": "text_ip_quintet",
"material": "O2",
"table": "text",
"quantity": "ionization_energy",
"unit": "eV",
"abscissa": "label",
"use": "check",
"parameters": {
"kind": "vertical",
"initial_state": "O2 X 3Sigma_g- (v = 0)",
"final_state": "the O2^2+ state of the row"
}
}
2 inline points in the source record.
p. 5: ‘from our SA3-CASSCF(10,8)/CASPT2 calculations for the quintet states, the 1 5Sigma_g+ and 1 5Pi_u states have vertical ionization potentials of 45.5 and 46.9 eV’, from O2, presumably with Table II’s shift (not stated). Not in the model.
yuen_2023/text_ker_quintet_4s4s#
{
"id": "text_ker_quintet_4s4s",
"material": "O2",
"table": "text",
"quantity": "kinetic_energy_release",
"unit": "eV",
"abscissa": "label",
"use": "check",
"parameters": {
"channel": "O2 -> O2^2+ (1 5Sigma_g+) -> O+(4S) + O+(4S)",
"kind": "calculated",
"state": "1 5Sigma_g+"
}
}
1 inline points in the source record.
p. 5: the KER of the 1 5Sigma_g+ state, 13.2 eV (its I_p 45.5 eV less the 4S + 4S limit; 45.5 - 32.35 = 13.15).
yuen_2023/text_ker_quintet_4s2d#
{
"id": "text_ker_quintet_4s2d",
"material": "O2",
"table": "text",
"quantity": "kinetic_energy_release",
"unit": "eV",
"abscissa": "label",
"use": "check",
"parameters": {
"channel": "O2 -> O2^2+ (1 5Pi_u) -> O+(4S) + O+(2D)",
"kind": "calculated",
"state": "1 5Pi_u"
}
}
1 inline points in the source record.
p. 5: the KER of the 1 5Pi_u state, 11.2 eV (46.9 eV less the 4S + 2D limit; 46.9 - 35.68 = 11.22).
yuen_2023/table4_dipole#
{
"id": "table4_dipole",
"material": "O2++",
"file": "O2++/yuen_2023__table4_dipole_O2++.csv",
"table": "tbl_c2f42888899a",
"quantity": "transition_dipole_moment",
"unit": "au",
"abscissa": "label",
"use": "check",
"parameters": {
"states": "the pair of O2^2+ states of the row",
"component": "perpendicular (x)",
"geometry": "R = 1.21 angstrom"
}
}
Table IV: the calculated transition dipoles between O2^2+ states (rows: the pair; Table II’s states 1, 2, 3 and 4 with 6 and 7), SA8-/SA6-CASSCF(10,8)/CASPT2 at R = 1.21 angstrom, each printed with x-hat. The caption: ‘the dipole moment between W 3Delta_u and B 3Pi_g is double counted since both states are doubly degenerate’, so the W-B row is the value the model uses, not a single-component matrix element. No uncertainty stated.
Formulas#
No formulas are recorded.
Corrections#
No dataset errata are recorded in this source record.
Formula corrections, where recorded, appear with their formulas above. Curation notes may also discuss corrections or unresolved interpretation. Consult the review register for the checks and decisions.