zhao_2010#

S.-F. Zhao, C. Jin, A.-T. Le, T. F. Jiang and C. D. Lin, “Determination of structure parameters in strong-field tunneling ionization theory of molecules”, Phys. Rev. A 81, 033423 (2010)

Source record · Catalogue · Review register

DOI: 10.1103/PhysRevA.81.033423

Source kind: theory

Recorded technique: Single-active-electron model potentials for linear molecules from density functional theory, exchange-only LDA plus the van Leeuwen-Baerends (LB) gradient correction (alpha = 1.0, beta = 0.05, Eqs. (1)-(12)), built from GAMESS or GAUSSIAN Hartree-Fock orbitals and iterated once so that the potential has the right -1/r tail (p. 3, Fig. 1); the one-electron Schrodinger equation solved in a one-centre expansion (l_max = 40) with B-splines (Eqs. (13)-(18)); the asymptotic radial functions fitted to Eq. (20) for the MO-ADK coefficients C_lm.

Materials in structured entries: Ar, CO, CO2, H2, H2+, He, Kr, N2, Ne, O2, Xe

Dataset quantities: ionization_energy, tunnelling_structure_coefficient

Contents: 56 datasets; 0 formulas.

Curation notes#

Journal pages 033423-1 to -11 = PDF pages 1-11. Authors checked on the first page. solprop’s default MO-ADK parameters (moadk_zhao2010, for ‘D2/H2’, N2 and O2) are this paper’s Table III.

THE ERRATUM. Phys. Rev. A 82, 049903(E) (2010) (zhao_2010_erratum, one page, image checked) corrects two things only: ‘In Table V, the C_2m of the HOMO-1 (1 pi) of CO molecule should be 0.014’ (printed 0.14; applied here as an erratum of table5_homo1_CO), and ‘In Table VI, the binding energies of 2p pi_g and 2p pi_u of H2+ should be 0.2267 and 0.4288, respectively’ (printed the other way round; Table VI is in these notes only, corrected below). Nothing else changes: Tables I-IV, Table III’s C_lm of every molecule (so solprop’s H2, D2, N2 and O2 rows), and Table V’s other rows stand as printed. solprop’s statement that the erratum ‘leaves these neutral rows unchanged’ is confirmed.

EXTRACTED. Table I (p. 4): rare-gas ionisation energies (au), this work’s LDA + LB orbital energies, Banerjee and Harbola’s (ref. 26) for He, Ne, Ar, and the experimental values (Emsley, ref. 27). Table II (p. 4): R (angstrom), the LDA + LB HOMO energy and the ‘experimental vertical ionization potentials’ (eV) of H2+, the hydrogen molecule (printed ‘D_2/H_2’), N2, O2, CO and CO2. Table III (p. 4): the newly fitted C_lm and the earlier values the table reprints ([9] = tong_2002, [30] = awasthi_2008, [17] = Le et al. 2007), one dataset per molecule and row. Table IV (p. 6): HOMO, HOMO-1 and HOMO-2 binding energies (N2, O2, CO2; HOMO and HOMO-1 for CO): LDA + LB, LB-alpha (refs. 29 and 6) and experimental vertical (refs. 43-45). Table V (p. 6): C_l of HOMO-1 and HOMO-2 of N2, O2, CO2 and of HOMO-1 of CO (the HOMO rows repeat Table III, checked by the script). Not curated, not taken: F2, S2, NO, SO, C2H2, HF, HCl, HCN. Every C_l file carries Table II’s R as the column internuclear_distance.

THE COEFFICIENTS (p. 3). Eq. (19): psi_n^(m)(r) = sum_l F_lm(r) Y_lm(theta, phi); ‘In the MO-ADK theory, the radial functions in the asymptotic region are fitted to the following form’, Eq. (20): F_lm(r) = C_lm r^((Z_c/kappa) - 1) e^(-kappa r), ‘where Z_c is the asymptotic charge and kappa = sqrt(2 I_p), I_p is the ionization energy’ (Tong et al. 2002’s convention). m: ‘For sigma orbital, m = 0 and pi orbital, m = 1’ (Table V caption). The fitting range of r is not stated anywhere in the paper, nor an accuracy of the coefficients. Which I_p enters kappa in the fit is not stated either; for the rates the paper says ‘we always use experimental binding energy’ (p. 4) and ‘one should always use the experimental vertical ionization energy since the tunneling ionization rate depends exponentially on the ionization potential’ (p. 4).

THE RATES. The alignment-dependent rates are Tong et al.’s analytic formula (tong_2002, its Eqs. (7)-(10)) with these C_lm, per orbital; ‘probabilities in Fig. 2 from MO-ADK include ionization from the HOMO only’ (p. 5), while TDDFT shows inner orbitals contributing. For a heteronuclear molecule the static rate differs for the two orientations AB and BA along the field, and ‘MO-ADK-S’ averages theta and pi - theta (p. 7). CO: the on-axis ratio (2.32 + 1.62)/(2.32 - 1.62) = 5.6 gives a rate ratio of 32 (p. 6). H2 parallel:perpendicular rate ratio 1.45 with the new coefficients, 1.15 with the old (p. 9).

THE IONISATION ENERGIES. Table I’s experimental and Table II’s I_p columns are the values used for the rates. Table II’s I_p agree digit for digit (and with R) with tong_2002’s Table I for all ten molecules the two share, and are reproduced from it (the identity is this record’s inference: Table II cites no source). The caption calls them ‘experimental vertical’, but tong_2002’s text says its Table I values for D2 and O2 are about 0.88 and 0.33 eV below the vertical energies it used; kind is recorded as the caption says. Table IV’s experimental O2 HOMO energy (12.3 eV, Baltzer et al.) differs from Table II’s 12.03. CO2’s 13.78 eV (Table II) and 13.8 (Table IV) are not in tong_2002.

THE HYDROGEN ROW is printed ‘D_2/H_2’ in Tables II and III and is used for H2 in the figures (Fig. 2(e), Fig. 6(c), Staudte et al.’s H2 data). Recorded as H2; the fixed- nuclei orbital at a given R does not depend on the nuclear masses, and solprop uses the row for H2 and D2 alike (TC-439). The reprinted Tong row [9] was printed ‘D_2’ by Tong.

TABLE VI (p. 10, notes only): H2+ at R = 2.0-4.0 a.u.: binding energies (au) ‘Present’ and ‘Exact’ and C_l of the 1s sigma_g, 1s sigma_u, 2p pi_g and 2p pi_u states. The 1s sigma_g ground state at R = 2.0 (equilibrium): 1.1025 and 1.1026 hartree, C_0m, C_2m, C_4m = 4.52, 0.62, 0.03, identical to Table III’s H2+ row (checked by the script), which is the dataset. The other rows are excited states or stretched geometries: 1s sigma_g at R = 2.5, 3.0, 3.5, 4.0: 0.9937/0.9938, 0.9107/0.9109, 0.8463/0.8466, 0.7958/0.7961 hartree; C_0m 4.25, 4.10, 4.00, 3.96; C_2m 0.81, 1.04, 1.31, 1.60; C_4m 0.05, 0.08, 0.12, 0.19. 1s sigma_u at R = 2.0: 0.6674/0.6675, C_1m 1.89, C_3m 0.08, C_5m 0.00; 2p pi_g at 2.0: 0.4288/0.4288, C_2m 0.11, C_4m 0.002; 2p pi_u at 2.0: 0.2267/0.2267, C_1m 0.90, C_3m 0.02 (the library merges two coefficients per cell; read on the image). The 2p pi_g and 2p pi_u binding energies above are as printed; the erratum (zhao_2010_erratum) swaps them: 2p pi_g 0.2267, 2p pi_u 0.4288 (the bonding pi_u state is the more deeply bound). The table image also prints 1s sigma_u at R = 2.5, 3.0, 3.5, 4.0 (0.6920/0.6921, 0.7012/0.7014, 0.7009/0.7012, 0.6952/0.6956; C_1m 2.18, 2.48, 2.79, 3.13; C_3m 0.15, 0.25, 0.37, 0.53; C_5m 0.00, 0.01, 0.02, 0.04), untouched by the erratum.

FIGURES (not digitised): Fig. 1 effective charges of Ne and CO2; Fig. 2 normalised alignment dependence for N2, O2 (1e14 W/cm^2), F2, H2+ (5e14), H2 (2.3e14), C2H2 against TDDFT and TDSE; Fig. 3 HOMO, HOMO-1, HOMO-2 rates against angle for N2 (1.5e14), O2 (1.3e14), CO2 (1.1e14), C2H2; Fig. 4 CO (4e14) and HCl; Fig. 5 CO2 against Spanner and Patchkovskii and Smirnova et al.; Fig. 6 against the measurements of Pavicic et al. (N2, O2; linear), Staudte et al. (H2) and Akagi et al. (HCl; circular); Figs. 7-8 H2+.

Recorded bibliographic identity status: VALIDATED. This concerns identification of the source; it does not establish the scientific correctness of its contents.

Datasets#

zhao_2010/table1_ldalb_He#

{
  "id": "table1_ldalb_He",
  "material": "He",
  "file": "He/zhao_2010__table1_ldalb_He.csv",
  "table": "tbl_fba864ad07cc",
  "quantity": "ionization_energy",
  "unit": "hartree",
  "abscissa": "none",
  "use": "check",
  "parameters": {
    "kind": "adiabatic"
  }
}

Table I, ‘LDA + LB (a.u.)’: the binding energy of the outer orbital in this paper’s exchange-only LDA + LB single-active-electron potential (alpha = 1.0, beta = 0.05, Eq. (9)); ‘the present one-electron model is still not sufficiently accurate for predicting the binding energy’ (p. 4). For an atom the adiabatic and vertical energies coincide.

zhao_2010/table1_banerjee_He#

{
  "id": "table1_banerjee_He",
  "material": "He",
  "file": "He/zhao_2010__table1_banerjee_He.csv",
  "table": "tbl_fba864ad07cc",
  "quantity": "ionization_energy",
  "unit": "hartree",
  "abscissa": "none",
  "use": "reproduced",
  "reproduced_from": [
    "A. Banerjee and M. K. Harbola, Phys. Rev. A 60, 3599 (1999)"
  ],
  "parameters": {
    "kind": "adiabatic"
  }
}

Table I, LDA + LB column, second value marked b (ref. 26), ‘the same approximate exchange potential’ (p. 4). For an atom the adiabatic and vertical energies coincide.

zhao_2010/table1_expt_He#

{
  "id": "table1_expt_He",
  "material": "He",
  "file": "He/zhao_2010__table1_expt_He.csv",
  "table": "tbl_fba864ad07cc",
  "quantity": "ionization_energy",
  "unit": "hartree",
  "abscissa": "none",
  "use": "reproduced",
  "reproduced_from": [
    "J. Emsley, The Elements (Clarendon Press, Oxford, 1998)"
  ],
  "parameters": {
    "kind": "adiabatic"
  }
}

Table I, ‘I_p (a.u.)’, experimental, mark a (ref. 27, Emsley’s The Elements); the first ionisation energy, to the ion’s ground state (adiabatic and vertical coincide for an atom).

zhao_2010/table1_ldalb_Ne#

{
  "id": "table1_ldalb_Ne",
  "material": "Ne",
  "file": "Ne/zhao_2010__table1_ldalb_Ne.csv",
  "table": "tbl_fba864ad07cc",
  "quantity": "ionization_energy",
  "unit": "hartree",
  "abscissa": "none",
  "use": "check",
  "parameters": {
    "kind": "adiabatic"
  }
}

zhao_2010/table1_banerjee_Ne#

{
  "id": "table1_banerjee_Ne",
  "material": "Ne",
  "file": "Ne/zhao_2010__table1_banerjee_Ne.csv",
  "table": "tbl_fba864ad07cc",
  "quantity": "ionization_energy",
  "unit": "hartree",
  "abscissa": "none",
  "use": "reproduced",
  "reproduced_from": [
    "A. Banerjee and M. K. Harbola, Phys. Rev. A 60, 3599 (1999)"
  ],
  "parameters": {
    "kind": "adiabatic"
  }
}

Table I, LDA + LB column, second value marked b (ref. 26), ‘the same approximate exchange potential’ (p. 4). For an atom the adiabatic and vertical energies coincide.

zhao_2010/table1_expt_Ne#

{
  "id": "table1_expt_Ne",
  "material": "Ne",
  "file": "Ne/zhao_2010__table1_expt_Ne.csv",
  "table": "tbl_fba864ad07cc",
  "quantity": "ionization_energy",
  "unit": "hartree",
  "abscissa": "none",
  "use": "reproduced",
  "reproduced_from": [
    "J. Emsley, The Elements (Clarendon Press, Oxford, 1998)"
  ],
  "parameters": {
    "kind": "adiabatic"
  }
}

Table I, ‘I_p (a.u.)’, experimental, mark a (ref. 27, Emsley’s The Elements); the first ionisation energy, to the ion’s ground state (adiabatic and vertical coincide for an atom).

zhao_2010/table1_ldalb_Ar#

{
  "id": "table1_ldalb_Ar",
  "material": "Ar",
  "file": "Ar/zhao_2010__table1_ldalb_Ar.csv",
  "table": "tbl_fba864ad07cc",
  "quantity": "ionization_energy",
  "unit": "hartree",
  "abscissa": "none",
  "use": "check",
  "parameters": {
    "kind": "adiabatic"
  }
}

zhao_2010/table1_banerjee_Ar#

{
  "id": "table1_banerjee_Ar",
  "material": "Ar",
  "file": "Ar/zhao_2010__table1_banerjee_Ar.csv",
  "table": "tbl_fba864ad07cc",
  "quantity": "ionization_energy",
  "unit": "hartree",
  "abscissa": "none",
  "use": "reproduced",
  "reproduced_from": [
    "A. Banerjee and M. K. Harbola, Phys. Rev. A 60, 3599 (1999)"
  ],
  "parameters": {
    "kind": "adiabatic"
  }
}

Table I, LDA + LB column, second value marked b (ref. 26), ‘the same approximate exchange potential’ (p. 4). For an atom the adiabatic and vertical energies coincide.

zhao_2010/table1_expt_Ar#

{
  "id": "table1_expt_Ar",
  "material": "Ar",
  "file": "Ar/zhao_2010__table1_expt_Ar.csv",
  "table": "tbl_fba864ad07cc",
  "quantity": "ionization_energy",
  "unit": "hartree",
  "abscissa": "none",
  "use": "reproduced",
  "reproduced_from": [
    "J. Emsley, The Elements (Clarendon Press, Oxford, 1998)"
  ],
  "parameters": {
    "kind": "adiabatic"
  }
}

Table I, ‘I_p (a.u.)’, experimental, mark a (ref. 27, Emsley’s The Elements); the first ionisation energy, to the ion’s ground state (adiabatic and vertical coincide for an atom).

zhao_2010/table1_ldalb_Kr#

{
  "id": "table1_ldalb_Kr",
  "material": "Kr",
  "file": "Kr/zhao_2010__table1_ldalb_Kr.csv",
  "table": "tbl_fba864ad07cc",
  "quantity": "ionization_energy",
  "unit": "hartree",
  "abscissa": "none",
  "use": "check",
  "parameters": {
    "kind": "adiabatic"
  }
}

zhao_2010/table1_expt_Kr#

{
  "id": "table1_expt_Kr",
  "material": "Kr",
  "file": "Kr/zhao_2010__table1_expt_Kr.csv",
  "table": "tbl_fba864ad07cc",
  "quantity": "ionization_energy",
  "unit": "hartree",
  "abscissa": "none",
  "use": "reproduced",
  "reproduced_from": [
    "J. Emsley, The Elements (Clarendon Press, Oxford, 1998)"
  ],
  "parameters": {
    "kind": "adiabatic"
  }
}

Table I, ‘I_p (a.u.)’, experimental, mark a (ref. 27, Emsley’s The Elements); the first ionisation energy, to the ion’s ground state (adiabatic and vertical coincide for an atom).

zhao_2010/table1_ldalb_Xe#

{
  "id": "table1_ldalb_Xe",
  "material": "Xe",
  "file": "Xe/zhao_2010__table1_ldalb_Xe.csv",
  "table": "tbl_fba864ad07cc",
  "quantity": "ionization_energy",
  "unit": "hartree",
  "abscissa": "none",
  "use": "check",
  "parameters": {
    "kind": "adiabatic"
  }
}

zhao_2010/table1_expt_Xe#

{
  "id": "table1_expt_Xe",
  "material": "Xe",
  "file": "Xe/zhao_2010__table1_expt_Xe.csv",
  "table": "tbl_fba864ad07cc",
  "quantity": "ionization_energy",
  "unit": "hartree",
  "abscissa": "none",
  "use": "reproduced",
  "reproduced_from": [
    "J. Emsley, The Elements (Clarendon Press, Oxford, 1998)"
  ],
  "parameters": {
    "kind": "adiabatic"
  }
}

Table I, ‘I_p (a.u.)’, experimental, mark a (ref. 27, Emsley’s The Elements); the first ionisation energy, to the ion’s ground state (adiabatic and vertical coincide for an atom).

zhao_2010/table2_ldalb_H2+#

{
  "id": "table2_ldalb_H2+",
  "material": "H2+",
  "file": "H2+/zhao_2010__table2_ldalb_H2+.csv",
  "table": "tbl_b4bf810303ee",
  "quantity": "ionization_energy",
  "unit": "eV",
  "abscissa": "none",
  "use": "check",
  "parameters": {
    "kind": "not stated",
    "orbital": "1s sigma_g"
  }
}

Table II, ‘LDA + LB (eV)’: the HOMO binding energy of this paper’s exchange-only LDA + LB potential at the fixed internuclear distance of the table; kind not stated.

zhao_2010/table2_ip_H2+#

{
  "id": "table2_ip_H2+",
  "material": "H2+",
  "file": "H2+/zhao_2010__table2_ip_H2+.csv",
  "table": "tbl_b4bf810303ee",
  "quantity": "ionization_energy",
  "unit": "eV",
  "abscissa": "none",
  "use": "reproduced",
  "reproduced_from": [
    "tong_2002"
  ],
  "parameters": {
    "kind": "vertical",
    "orbital": "1s sigma_g"
  }
}

Table II, ‘I_p (eV)’, captioned ‘experimental vertical ionization potentials’ without a reference; digit-identical (with R) to tong_2002 Table I, whose text says its values are not the vertical energies (see the record’s notes). Kind as the caption says.

zhao_2010/table2_ldalb_H2#

{
  "id": "table2_ldalb_H2",
  "material": "H2",
  "file": "H2/zhao_2010__table2_ldalb_H2.csv",
  "table": "tbl_b4bf810303ee",
  "quantity": "ionization_energy",
  "unit": "eV",
  "abscissa": "none",
  "use": "check",
  "parameters": {
    "kind": "not stated",
    "orbital": "HOMO 1 sigma_g"
  }
}

Table II, ‘LDA + LB (eV)’: the HOMO binding energy of this paper’s exchange-only LDA + LB potential at the fixed internuclear distance of the table; kind not stated. The row is printed ‘D_2/H_2’ (recorded as H2; see the record’s notes).

zhao_2010/table2_ip_H2#

{
  "id": "table2_ip_H2",
  "material": "H2",
  "file": "H2/zhao_2010__table2_ip_H2.csv",
  "table": "tbl_b4bf810303ee",
  "quantity": "ionization_energy",
  "unit": "eV",
  "abscissa": "none",
  "use": "reproduced",
  "reproduced_from": [
    "tong_2002"
  ],
  "parameters": {
    "kind": "vertical",
    "orbital": "HOMO 1 sigma_g"
  }
}

zhao_2010/table2_ldalb_N2#

{
  "id": "table2_ldalb_N2",
  "material": "N2",
  "file": "N2/zhao_2010__table2_ldalb_N2.csv",
  "table": "tbl_b4bf810303ee",
  "quantity": "ionization_energy",
  "unit": "eV",
  "abscissa": "none",
  "use": "check",
  "parameters": {
    "kind": "not stated",
    "orbital": "HOMO 3 sigma_g"
  }
}

Table II, ‘LDA + LB (eV)’: the HOMO binding energy of this paper’s exchange-only LDA + LB potential at the fixed internuclear distance of the table; kind not stated.

zhao_2010/table2_ip_N2#

{
  "id": "table2_ip_N2",
  "material": "N2",
  "file": "N2/zhao_2010__table2_ip_N2.csv",
  "table": "tbl_b4bf810303ee",
  "quantity": "ionization_energy",
  "unit": "eV",
  "abscissa": "none",
  "use": "reproduced",
  "reproduced_from": [
    "tong_2002"
  ],
  "parameters": {
    "kind": "vertical",
    "orbital": "HOMO 3 sigma_g"
  }
}

zhao_2010/table2_ldalb_O2#

{
  "id": "table2_ldalb_O2",
  "material": "O2",
  "file": "O2/zhao_2010__table2_ldalb_O2.csv",
  "table": "tbl_b4bf810303ee",
  "quantity": "ionization_energy",
  "unit": "eV",
  "abscissa": "none",
  "use": "check",
  "parameters": {
    "kind": "not stated",
    "orbital": "HOMO 1 pi_g"
  }
}

Table II, ‘LDA + LB (eV)’: the HOMO binding energy of this paper’s exchange-only LDA + LB potential at the fixed internuclear distance of the table; kind not stated.

zhao_2010/table2_ip_O2#

{
  "id": "table2_ip_O2",
  "material": "O2",
  "file": "O2/zhao_2010__table2_ip_O2.csv",
  "table": "tbl_b4bf810303ee",
  "quantity": "ionization_energy",
  "unit": "eV",
  "abscissa": "none",
  "use": "reproduced",
  "reproduced_from": [
    "tong_2002"
  ],
  "parameters": {
    "kind": "vertical",
    "orbital": "HOMO 1 pi_g"
  }
}

zhao_2010/table2_ldalb_CO#

{
  "id": "table2_ldalb_CO",
  "material": "CO",
  "file": "CO/zhao_2010__table2_ldalb_CO.csv",
  "table": "tbl_b4bf810303ee",
  "quantity": "ionization_energy",
  "unit": "eV",
  "abscissa": "none",
  "use": "check",
  "parameters": {
    "kind": "not stated",
    "orbital": "HOMO 5 sigma"
  }
}

Table II, ‘LDA + LB (eV)’: the HOMO binding energy of this paper’s exchange-only LDA + LB potential at the fixed internuclear distance of the table; kind not stated.

zhao_2010/table2_ip_CO#

{
  "id": "table2_ip_CO",
  "material": "CO",
  "file": "CO/zhao_2010__table2_ip_CO.csv",
  "table": "tbl_b4bf810303ee",
  "quantity": "ionization_energy",
  "unit": "eV",
  "abscissa": "none",
  "use": "reproduced",
  "reproduced_from": [
    "tong_2002"
  ],
  "parameters": {
    "kind": "vertical",
    "orbital": "HOMO 5 sigma"
  }
}

zhao_2010/table2_ldalb_CO2#

{
  "id": "table2_ldalb_CO2",
  "material": "CO2",
  "file": "CO2/zhao_2010__table2_ldalb_CO2.csv",
  "table": "tbl_b4bf810303ee",
  "quantity": "ionization_energy",
  "unit": "eV",
  "abscissa": "none",
  "use": "check",
  "parameters": {
    "kind": "not stated",
    "orbital": "HOMO 1 pi_g"
  }
}

Table II, ‘LDA + LB (eV)’: the HOMO binding energy of this paper’s exchange-only LDA + LB potential at the fixed internuclear distance of the table; kind not stated.

zhao_2010/table2_ip_CO2#

{
  "id": "table2_ip_CO2",
  "material": "CO2",
  "file": "CO2/zhao_2010__table2_ip_CO2.csv",
  "table": "tbl_b4bf810303ee",
  "quantity": "ionization_energy",
  "unit": "eV",
  "abscissa": "none",
  "use": "check",
  "parameters": {
    "kind": "vertical",
    "orbital": "HOMO 1 pi_g"
  }
}

Table II, ‘I_p (eV)’, ‘experimental vertical ionization potentials’ (caption); no reference is given (not in tong_2002).

zhao_2010/table3_H2+#

{
  "id": "table3_H2+",
  "material": "H2+",
  "file": "H2+/zhao_2010__table3_H2+.csv",
  "table": "tbl_7f5181e18a32",
  "quantity": "tunnelling_structure_coefficient",
  "abscissa": "label",
  "columns": {
    "internuclear_distance": "angstrom"
  },
  "use": "check",
  "parameters": {
    "model": "moadk",
    "orbital": "1s sigma_g",
    "m": 0,
    "normalisation": "Zhao et al. 2010 Eqs. (19)-(20), p. 3 (Tong et al. 2002's convention): psi^(m)(r) = sum_l F_lm(r) Y_lm(theta, phi), F_lm(r) = C_lm r^(Z_c/kappa - 1) exp(-kappa r) in the asymptotic region, Z_c the asymptotic charge, kappa = sqrt(2 I_p), atomic units; one-centre expansion, m along the molecular axis"
  }
}

Table III, H2+ (sigma_g), this work: the 1s sigma_g ground state at R = 2.0 a0 (Table VI’s first row repeats it). The internuclear_distance column is Table II’s R.

zhao_2010/table3_tong_H2+#

{
  "id": "table3_tong_H2+",
  "material": "H2+",
  "file": "H2+/zhao_2010__table3_tong_H2+.csv",
  "table": "tbl_7f5181e18a32",
  "quantity": "tunnelling_structure_coefficient",
  "abscissa": "label",
  "columns": {
    "internuclear_distance": "angstrom"
  },
  "use": "reproduced",
  "reproduced_from": [
    "tong_2002"
  ],
  "parameters": {
    "model": "moadk",
    "orbital": "1s sigma_g",
    "m": 0,
    "normalisation": "Tong et al. 2002 Eqs. (1)-(2): Psi^m = sum_l C_l F_l(r) Y_lm, F_l(r -> inf) ~ r^(Z_c/kappa - 1) exp(-kappa r), kappa = sqrt(2 I_p), atomic units"
  }
}

Table III, H_2^+ row marked [9] (Tong et al. 2002, Table I; the printed values agree with tong_2002). internuclear_distance: Table II’s R.

zhao_2010/table3_H2#

{
  "id": "table3_H2",
  "material": "H2",
  "file": "H2/zhao_2010__table3_H2.csv",
  "table": "tbl_7f5181e18a32",
  "quantity": "tunnelling_structure_coefficient",
  "abscissa": "label",
  "columns": {
    "internuclear_distance": "angstrom"
  },
  "use": "check",
  "parameters": {
    "model": "moadk",
    "orbital": "HOMO 1 sigma_g",
    "m": 0,
    "normalisation": "Zhao et al. 2010 Eqs. (19)-(20), p. 3 (Tong et al. 2002's convention): psi^(m)(r) = sum_l F_lm(r) Y_lm(theta, phi), F_lm(r) = C_lm r^(Z_c/kappa - 1) exp(-kappa r) in the asymptotic region, Z_c the asymptotic charge, kappa = sqrt(2 I_p), atomic units; one-centre expansion, m along the molecular axis"
  }
}

Table III, ‘D_2/H_2 (sigma_g)’, this work (recorded as H2; the same fixed-nuclei orbital serves D2). solprop’s moadk_zhao2010 for H2 and D2 is this row. The internuclear_distance column is Table II’s R.

zhao_2010/table3_tong_H2#

{
  "id": "table3_tong_H2",
  "material": "H2",
  "file": "H2/zhao_2010__table3_tong_H2.csv",
  "table": "tbl_7f5181e18a32",
  "quantity": "tunnelling_structure_coefficient",
  "abscissa": "label",
  "columns": {
    "internuclear_distance": "angstrom"
  },
  "use": "reproduced",
  "reproduced_from": [
    "tong_2002"
  ],
  "parameters": {
    "model": "moadk",
    "orbital": "HOMO 1 sigma_g",
    "m": 0,
    "normalisation": "Tong et al. 2002 Eqs. (1)-(2): Psi^m = sum_l C_l F_l(r) Y_lm, F_l(r -> inf) ~ r^(Z_c/kappa - 1) exp(-kappa r), kappa = sqrt(2 I_p), atomic units"
  }
}

Table III, D_2/H_2 row marked [9] (Tong et al. 2002, Table I; the printed values agree with tong_2002). Tong prints the row as ‘D_2’. internuclear_distance: Table II’s R.

zhao_2010/table3_awasthi_H2#

{
  "id": "table3_awasthi_H2",
  "material": "H2",
  "file": "H2/zhao_2010__table3_awasthi_H2.csv",
  "table": "tbl_7f5181e18a32",
  "quantity": "tunnelling_structure_coefficient",
  "abscissa": "label",
  "columns": {
    "internuclear_distance": "angstrom"
  },
  "use": "reproduced",
  "reproduced_from": [
    "awasthi_2008"
  ],
  "parameters": {
    "model": "moadk",
    "orbital": "HOMO 1 sigma_g",
    "m": 0,
    "normalisation": "Awasthi et al. 2008 Eq. (19): phi(r) ~ sum_l C_l r^(nu - 1) exp(-kappa r) Y_l0(r^), nu = Z/kappa, kappa = sqrt(2 I_p), atomic units"
  }
}

Table III, ‘D_2/H_2’ row marked [30] (Awasthi et al. 2008): awasthi_2008’s LB94 row (1.146, 0.0666, 0.0008 at R = 1.4 a0) rounded to 1.15, 0.067, 0.001. internuclear_distance: Table II’s R (0.742 A; Awasthi’s 1.4 a0 is 0.741 A).

zhao_2010/table3_N2#

{
  "id": "table3_N2",
  "material": "N2",
  "file": "N2/zhao_2010__table3_N2.csv",
  "table": "tbl_7f5181e18a32",
  "quantity": "tunnelling_structure_coefficient",
  "abscissa": "label",
  "columns": {
    "internuclear_distance": "angstrom"
  },
  "use": "check",
  "parameters": {
    "model": "moadk",
    "orbital": "HOMO 3 sigma_g",
    "m": 0,
    "normalisation": "Zhao et al. 2010 Eqs. (19)-(20), p. 3 (Tong et al. 2002's convention): psi^(m)(r) = sum_l F_lm(r) Y_lm(theta, phi), F_lm(r) = C_lm r^(Z_c/kappa - 1) exp(-kappa r) in the asymptotic region, Z_c the asymptotic charge, kappa = sqrt(2 I_p), atomic units; one-centre expansion, m along the molecular axis"
  }
}

Table III, N2 (sigma_g), this work = Table V’s 3 sigma_g (HOMO). solprop’s moadk_zhao2010 for N2 is this row. The internuclear_distance column is Table II’s R.

zhao_2010/table3_tong_N2#

{
  "id": "table3_tong_N2",
  "material": "N2",
  "file": "N2/zhao_2010__table3_tong_N2.csv",
  "table": "tbl_7f5181e18a32",
  "quantity": "tunnelling_structure_coefficient",
  "abscissa": "label",
  "columns": {
    "internuclear_distance": "angstrom"
  },
  "use": "reproduced",
  "reproduced_from": [
    "tong_2002"
  ],
  "parameters": {
    "model": "moadk",
    "orbital": "HOMO 3 sigma_g",
    "m": 0,
    "normalisation": "Tong et al. 2002 Eqs. (1)-(2): Psi^m = sum_l C_l F_l(r) Y_lm, F_l(r -> inf) ~ r^(Z_c/kappa - 1) exp(-kappa r), kappa = sqrt(2 I_p), atomic units"
  }
}

Table III, N_2 row marked [9] (Tong et al. 2002, Table I; the printed values agree with tong_2002). internuclear_distance: Table II’s R.

zhao_2010/table3_O2#

{
  "id": "table3_O2",
  "material": "O2",
  "file": "O2/zhao_2010__table3_O2.csv",
  "table": "tbl_7f5181e18a32",
  "quantity": "tunnelling_structure_coefficient",
  "abscissa": "label",
  "columns": {
    "internuclear_distance": "angstrom"
  },
  "use": "check",
  "parameters": {
    "model": "moadk",
    "orbital": "HOMO 1 pi_g",
    "m": 1,
    "normalisation": "Zhao et al. 2010 Eqs. (19)-(20), p. 3 (Tong et al. 2002's convention): psi^(m)(r) = sum_l F_lm(r) Y_lm(theta, phi), F_lm(r) = C_lm r^(Z_c/kappa - 1) exp(-kappa r) in the asymptotic region, Z_c the asymptotic charge, kappa = sqrt(2 I_p), atomic units; one-centre expansion, m along the molecular axis"
  }
}

Table III, O2 (pi_g), this work: C_2m and C_4m (no s wave) = Table V’s 1 pi_g (HOMO). solprop’s moadk_zhao2010 for O2 is this row. The internuclear_distance column is Table II’s R.

zhao_2010/table3_tong_O2#

{
  "id": "table3_tong_O2",
  "material": "O2",
  "file": "O2/zhao_2010__table3_tong_O2.csv",
  "table": "tbl_7f5181e18a32",
  "quantity": "tunnelling_structure_coefficient",
  "abscissa": "label",
  "columns": {
    "internuclear_distance": "angstrom"
  },
  "use": "reproduced",
  "reproduced_from": [
    "tong_2002"
  ],
  "parameters": {
    "model": "moadk",
    "orbital": "HOMO 1 pi_g",
    "m": 1,
    "normalisation": "Tong et al. 2002 Eqs. (1)-(2): Psi^m = sum_l C_l F_l(r) Y_lm, F_l(r -> inf) ~ r^(Z_c/kappa - 1) exp(-kappa r), kappa = sqrt(2 I_p), atomic units"
  }
}

Table III, O_2 row marked [9] (Tong et al. 2002, Table I; the printed values agree with tong_2002). internuclear_distance: Table II’s R.

zhao_2010/table3_CO#

{
  "id": "table3_CO",
  "material": "CO",
  "file": "CO/zhao_2010__table3_CO.csv",
  "table": "tbl_7f5181e18a32",
  "quantity": "tunnelling_structure_coefficient",
  "abscissa": "label",
  "columns": {
    "internuclear_distance": "angstrom"
  },
  "use": "check",
  "parameters": {
    "model": "moadk",
    "orbital": "HOMO 5 sigma",
    "m": 0,
    "normalisation": "Zhao et al. 2010 Eqs. (19)-(20), p. 3 (Tong et al. 2002's convention): psi^(m)(r) = sum_l F_lm(r) Y_lm(theta, phi), F_lm(r) = C_lm r^(Z_c/kappa - 1) exp(-kappa r) in the asymptotic region, Z_c the asymptotic charge, kappa = sqrt(2 I_p), atomic units; one-centre expansion, m along the molecular axis"
  }
}

Table III, CO (sigma), this work: C_0m ... C_4m (the fifth value, C_4m = 0.05, is lost from Table V’s CO row in the library but kept here). The internuclear_distance column is Table II’s R.

zhao_2010/table3_tong_CO#

{
  "id": "table3_tong_CO",
  "material": "CO",
  "file": "CO/zhao_2010__table3_tong_CO.csv",
  "table": "tbl_7f5181e18a32",
  "quantity": "tunnelling_structure_coefficient",
  "abscissa": "label",
  "columns": {
    "internuclear_distance": "angstrom"
  },
  "use": "reproduced",
  "reproduced_from": [
    "tong_2002"
  ],
  "parameters": {
    "model": "moadk",
    "orbital": "HOMO 5 sigma",
    "m": 0,
    "normalisation": "Tong et al. 2002 Eqs. (1)-(2): Psi^m = sum_l C_l F_l(r) Y_lm, F_l(r -> inf) ~ r^(Z_c/kappa - 1) exp(-kappa r), kappa = sqrt(2 I_p), atomic units"
  }
}

Table III, CO row marked [9] (Tong et al. 2002, Table I; the printed values agree with tong_2002). Tong’s Table I prints no l = 4 for CO; Zhao’s reprint adds C_4m = 0.00. internuclear_distance: Table II’s R.

zhao_2010/table3_CO2#

{
  "id": "table3_CO2",
  "material": "CO2",
  "file": "CO2/zhao_2010__table3_CO2.csv",
  "table": "tbl_7f5181e18a32",
  "quantity": "tunnelling_structure_coefficient",
  "abscissa": "label",
  "columns": {
    "internuclear_distance": "angstrom"
  },
  "use": "check",
  "parameters": {
    "model": "moadk",
    "orbital": "HOMO 1 pi_g",
    "m": 1,
    "normalisation": "Zhao et al. 2010 Eqs. (19)-(20), p. 3 (Tong et al. 2002's convention): psi^(m)(r) = sum_l F_lm(r) Y_lm(theta, phi), F_lm(r) = C_lm r^(Z_c/kappa - 1) exp(-kappa r) in the asymptotic region, Z_c the asymptotic charge, kappa = sqrt(2 I_p), atomic units; one-centre expansion, m along the molecular axis"
  }
}

Table III, CO2 (pi_g), this work: C_2m, C_4m, C_6m = Table V’s 1 pi_g (HOMO). The internuclear_distance column is Table II’s R.

zhao_2010/table3_le_CO2#

{
  "id": "table3_le_CO2",
  "material": "CO2",
  "file": "CO2/zhao_2010__table3_le_CO2.csv",
  "table": "tbl_7f5181e18a32",
  "quantity": "tunnelling_structure_coefficient",
  "abscissa": "label",
  "columns": {
    "internuclear_distance": "angstrom"
  },
  "use": "reproduced",
  "reproduced_from": [
    "A.-T. Le, X. M. Tong and C. D. Lin, J. Mod. Opt. 54, 967 (2007)"
  ],
  "parameters": {
    "model": "moadk",
    "orbital": "HOMO 1 pi_g",
    "m": 1,
    "normalisation": "Zhao et al. 2010 Eqs. (19)-(20), p. 3 (Tong et al. 2002's convention): psi^(m)(r) = sum_l F_lm(r) Y_lm(theta, phi), F_lm(r) = C_lm r^(Z_c/kappa - 1) exp(-kappa r) in the asymptotic region, Z_c the asymptotic charge, kappa = sqrt(2 I_p), atomic units; one-centre expansion, m along the molecular axis"
  }
}

Table III, CO2 row marked [17] (Le, Tong and Lin 2007): the earlier coefficients from Gaussian-basis orbitals, which the text calls inaccurate for CO2 (p. 9, ref. 19). internuclear_distance: Table II’s R.

zhao_2010/table4_ldalb_N2#

{
  "id": "table4_ldalb_N2",
  "material": "N2",
  "file": "N2/zhao_2010__table4_ldalb_N2.csv",
  "table": "tbl_2bc9b27f5a3b",
  "quantity": "ionization_energy",
  "unit": "eV",
  "abscissa": "label",
  "use": "check",
  "parameters": {
    "kind": "not stated"
  }
}

Table IV, ‘LDA + LB’: binding energies of the HOMO, HOMO-1 and HOMO-2 orbitals (rows, labelled by the orbital) in this paper’s model; kind not stated.

zhao_2010/table4_lbalpha_N2#

{
  "id": "table4_lbalpha_N2",
  "material": "N2",
  "file": "N2/zhao_2010__table4_lbalpha_N2.csv",
  "table": "tbl_2bc9b27f5a3b",
  "quantity": "ionization_energy",
  "unit": "eV",
  "abscissa": "label",
  "use": "reproduced",
  "reproduced_from": [
    "D. A. Telnov and Shih I. Chu, Phys. Rev. A 79, 041401(R) (2009)"
  ],
  "parameters": {
    "kind": "not stated"
  }
}

Table IV, ‘LB alpha’ column, mark a (ref. 29): binding energies of the HOMO, HOMO-1 and HOMO-2 orbitals in the LB-alpha model; kind not stated.

zhao_2010/table4_expt_N2#

{
  "id": "table4_expt_N2",
  "material": "N2",
  "file": "N2/zhao_2010__table4_expt_N2.csv",
  "table": "tbl_2bc9b27f5a3b",
  "quantity": "ionization_energy",
  "unit": "eV",
  "abscissa": "label",
  "use": "reproduced",
  "reproduced_from": [
    "A. Lofthus and P. H. Krupenie, J. Phys. Chem. Ref. Data 6, 113 (1977)"
  ],
  "parameters": {
    "kind": "vertical"
  }
}

Table IV, ‘I_p’, ‘experimental vertical ionization potential’ (caption), mark b (ref. 43); rows labelled by the orbital ionised (the ionic states are not named).

zhao_2010/table4_ldalb_O2#

{
  "id": "table4_ldalb_O2",
  "material": "O2",
  "file": "O2/zhao_2010__table4_ldalb_O2.csv",
  "table": "tbl_2bc9b27f5a3b",
  "quantity": "ionization_energy",
  "unit": "eV",
  "abscissa": "label",
  "use": "check",
  "parameters": {
    "kind": "not stated"
  }
}

Table IV, ‘LDA + LB’: binding energies of the HOMO, HOMO-1 and HOMO-2 orbitals (rows, labelled by the orbital) in this paper’s model; kind not stated.

zhao_2010/table4_lbalpha_O2#

{
  "id": "table4_lbalpha_O2",
  "material": "O2",
  "file": "O2/zhao_2010__table4_lbalpha_O2.csv",
  "table": "tbl_2bc9b27f5a3b",
  "quantity": "ionization_energy",
  "unit": "eV",
  "abscissa": "label",
  "use": "reproduced",
  "reproduced_from": [
    "D. A. Telnov and Shih I. Chu, Phys. Rev. A 79, 041401(R) (2009)"
  ],
  "parameters": {
    "kind": "not stated"
  }
}

Table IV, ‘LB alpha’ column, mark a (ref. 29): binding energies of the HOMO, HOMO-1 and HOMO-2 orbitals in the LB-alpha model; kind not stated.

zhao_2010/table4_expt_O2#

{
  "id": "table4_expt_O2",
  "material": "O2",
  "file": "O2/zhao_2010__table4_expt_O2.csv",
  "table": "tbl_2bc9b27f5a3b",
  "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"
  }
}

Table IV, ‘I_p’, ‘experimental vertical ionization potential’ (caption), mark c (ref. 44); rows labelled by the orbital ionised (the ionic states are not named).

zhao_2010/table4_ldalb_CO2#

{
  "id": "table4_ldalb_CO2",
  "material": "CO2",
  "file": "CO2/zhao_2010__table4_ldalb_CO2.csv",
  "table": "tbl_2bc9b27f5a3b",
  "quantity": "ionization_energy",
  "unit": "eV",
  "abscissa": "label",
  "use": "check",
  "parameters": {
    "kind": "not stated"
  }
}

Table IV, ‘LDA + LB’: binding energies of the HOMO, HOMO-1 and HOMO-2 orbitals (rows, labelled by the orbital) in this paper’s model; kind not stated.

zhao_2010/table4_lbalpha_CO2#

{
  "id": "table4_lbalpha_CO2",
  "material": "CO2",
  "file": "CO2/zhao_2010__table4_lbalpha_CO2.csv",
  "table": "tbl_2bc9b27f5a3b",
  "quantity": "ionization_energy",
  "unit": "eV",
  "abscissa": "label",
  "use": "reproduced",
  "reproduced_from": [
    "S. K. Son and Shih I. Chu, Phys. Rev. A 80, 011403(R) (2009)"
  ],
  "parameters": {
    "kind": "not stated"
  }
}

Table IV, ‘LB alpha’ column, mark d (ref. 6; the note is lost from the library’s text and was read on the page): binding energies of the HOMO, HOMO-1 and HOMO-2 orbitals in the LB-alpha model; kind not stated.

zhao_2010/table4_expt_CO2#

{
  "id": "table4_expt_CO2",
  "material": "CO2",
  "file": "CO2/zhao_2010__table4_expt_CO2.csv",
  "table": "tbl_2bc9b27f5a3b",
  "quantity": "ionization_energy",
  "unit": "eV",
  "abscissa": "label",
  "use": "reproduced",
  "reproduced_from": [
    "D. W. Turner et al., Molecular Photoelectron Spectroscopy (Wiley Interscience, London, 1970)"
  ],
  "parameters": {
    "kind": "vertical"
  }
}

Table IV, ‘I_p’, ‘experimental vertical ionization potential’ (caption), mark e (ref. 45); rows labelled by the orbital ionised (the ionic states are not named).

zhao_2010/table4_ldalb_CO#

{
  "id": "table4_ldalb_CO",
  "material": "CO",
  "file": "CO/zhao_2010__table4_ldalb_CO.csv",
  "table": "tbl_2bc9b27f5a3b",
  "quantity": "ionization_energy",
  "unit": "eV",
  "abscissa": "label",
  "use": "check",
  "parameters": {
    "kind": "not stated"
  }
}

Table IV, ‘LDA + LB’: binding energies of the HOMO and HOMO-1 orbitals (rows, labelled by the orbital) in this paper’s model; kind not stated.

zhao_2010/table4_expt_CO#

{
  "id": "table4_expt_CO",
  "material": "CO",
  "file": "CO/zhao_2010__table4_expt_CO.csv",
  "table": "tbl_2bc9b27f5a3b",
  "quantity": "ionization_energy",
  "unit": "eV",
  "abscissa": "label",
  "use": "reproduced",
  "reproduced_from": [
    "D. W. Turner et al., Molecular Photoelectron Spectroscopy (Wiley Interscience, London, 1970)"
  ],
  "parameters": {
    "kind": "vertical"
  }
}

Table IV, ‘I_p’, ‘experimental vertical ionization potential’ (caption), mark e (ref. 45); rows labelled by the orbital ionised (the ionic states are not named).

zhao_2010/table5_homo1_N2#

{
  "id": "table5_homo1_N2",
  "material": "N2",
  "file": "N2/zhao_2010__table5_homo1_N2.csv",
  "table": "tbl_825e661a911b",
  "quantity": "tunnelling_structure_coefficient",
  "abscissa": "label",
  "columns": {
    "internuclear_distance": "angstrom"
  },
  "use": "check",
  "parameters": {
    "model": "moadk",
    "orbital": "HOMO-1 1 pi_u",
    "m": 1,
    "normalisation": "Zhao et al. 2010 Eqs. (19)-(20), p. 3 (Tong et al. 2002's convention): psi^(m)(r) = sum_l F_lm(r) Y_lm(theta, phi), F_lm(r) = C_lm r^(Z_c/kappa - 1) exp(-kappa r) in the asymptotic region, Z_c the asymptotic charge, kappa = sqrt(2 I_p), atomic units; one-centre expansion, m along the molecular axis"
  }
}

Table V, 1 pi_u (HOMO-1); m = 1 per the caption (‘For sigma orbital, m = 0 and pi orbital, m = 1’). The binding energy for the rate is the experimental one of Table IV (p. 6). internuclear_distance: Table II’s R.

zhao_2010/table5_homo2_N2#

{
  "id": "table5_homo2_N2",
  "material": "N2",
  "file": "N2/zhao_2010__table5_homo2_N2.csv",
  "table": "tbl_825e661a911b",
  "quantity": "tunnelling_structure_coefficient",
  "abscissa": "label",
  "columns": {
    "internuclear_distance": "angstrom"
  },
  "use": "check",
  "parameters": {
    "model": "moadk",
    "orbital": "HOMO-2 2 sigma_u",
    "m": 0,
    "normalisation": "Zhao et al. 2010 Eqs. (19)-(20), p. 3 (Tong et al. 2002's convention): psi^(m)(r) = sum_l F_lm(r) Y_lm(theta, phi), F_lm(r) = C_lm r^(Z_c/kappa - 1) exp(-kappa r) in the asymptotic region, Z_c the asymptotic charge, kappa = sqrt(2 I_p), atomic units; one-centre expansion, m along the molecular axis"
  }
}

Table V, 2 sigma_u (HOMO-2); m = 0 per the caption (‘For sigma orbital, m = 0 and pi orbital, m = 1’). The binding energy for the rate is the experimental one of Table IV (p. 6). internuclear_distance: Table II’s R.

zhao_2010/table5_homo1_O2#

{
  "id": "table5_homo1_O2",
  "material": "O2",
  "file": "O2/zhao_2010__table5_homo1_O2.csv",
  "table": "tbl_825e661a911b",
  "quantity": "tunnelling_structure_coefficient",
  "abscissa": "label",
  "columns": {
    "internuclear_distance": "angstrom"
  },
  "use": "check",
  "parameters": {
    "model": "moadk",
    "orbital": "HOMO-1 1 pi_u",
    "m": 1,
    "normalisation": "Zhao et al. 2010 Eqs. (19)-(20), p. 3 (Tong et al. 2002's convention): psi^(m)(r) = sum_l F_lm(r) Y_lm(theta, phi), F_lm(r) = C_lm r^(Z_c/kappa - 1) exp(-kappa r) in the asymptotic region, Z_c the asymptotic charge, kappa = sqrt(2 I_p), atomic units; one-centre expansion, m along the molecular axis"
  }
}

zhao_2010/table5_homo2_O2#

{
  "id": "table5_homo2_O2",
  "material": "O2",
  "file": "O2/zhao_2010__table5_homo2_O2.csv",
  "table": "tbl_825e661a911b",
  "quantity": "tunnelling_structure_coefficient",
  "abscissa": "label",
  "columns": {
    "internuclear_distance": "angstrom"
  },
  "use": "check",
  "parameters": {
    "model": "moadk",
    "orbital": "HOMO-2 3 sigma_g",
    "m": 0,
    "normalisation": "Zhao et al. 2010 Eqs. (19)-(20), p. 3 (Tong et al. 2002's convention): psi^(m)(r) = sum_l F_lm(r) Y_lm(theta, phi), F_lm(r) = C_lm r^(Z_c/kappa - 1) exp(-kappa r) in the asymptotic region, Z_c the asymptotic charge, kappa = sqrt(2 I_p), atomic units; one-centre expansion, m along the molecular axis"
  }
}

Table V, 3 sigma_g (HOMO-2); m = 0 per the caption (‘For sigma orbital, m = 0 and pi orbital, m = 1’). The binding energy for the rate is the experimental one of Table IV (p. 6). internuclear_distance: Table II’s R.

zhao_2010/table5_homo1_CO2#

{
  "id": "table5_homo1_CO2",
  "material": "CO2",
  "file": "CO2/zhao_2010__table5_homo1_CO2.csv",
  "table": "tbl_825e661a911b",
  "quantity": "tunnelling_structure_coefficient",
  "abscissa": "label",
  "columns": {
    "internuclear_distance": "angstrom"
  },
  "use": "check",
  "parameters": {
    "model": "moadk",
    "orbital": "HOMO-1 1 pi_u",
    "m": 1,
    "normalisation": "Zhao et al. 2010 Eqs. (19)-(20), p. 3 (Tong et al. 2002's convention): psi^(m)(r) = sum_l F_lm(r) Y_lm(theta, phi), F_lm(r) = C_lm r^(Z_c/kappa - 1) exp(-kappa r) in the asymptotic region, Z_c the asymptotic charge, kappa = sqrt(2 I_p), atomic units; one-centre expansion, m along the molecular axis"
  }
}

zhao_2010/table5_homo2_CO2#

{
  "id": "table5_homo2_CO2",
  "material": "CO2",
  "file": "CO2/zhao_2010__table5_homo2_CO2.csv",
  "table": "tbl_825e661a911b",
  "quantity": "tunnelling_structure_coefficient",
  "abscissa": "label",
  "columns": {
    "internuclear_distance": "angstrom"
  },
  "use": "check",
  "parameters": {
    "model": "moadk",
    "orbital": "HOMO-2 3 sigma_u",
    "m": 0,
    "normalisation": "Zhao et al. 2010 Eqs. (19)-(20), p. 3 (Tong et al. 2002's convention): psi^(m)(r) = sum_l F_lm(r) Y_lm(theta, phi), F_lm(r) = C_lm r^(Z_c/kappa - 1) exp(-kappa r) in the asymptotic region, Z_c the asymptotic charge, kappa = sqrt(2 I_p), atomic units; one-centre expansion, m along the molecular axis"
  }
}

Table V, 3 sigma_u (HOMO-2); m = 0 per the caption (‘For sigma orbital, m = 0 and pi orbital, m = 1’). The binding energy for the rate is the experimental one of Table IV (p. 6). internuclear_distance: Table II’s R.

zhao_2010/table5_homo1_CO#

{
  "id": "table5_homo1_CO",
  "material": "CO",
  "file": "CO/zhao_2010__table5_homo1_CO.csv",
  "table": "tbl_825e661a911b",
  "quantity": "tunnelling_structure_coefficient",
  "abscissa": "label",
  "columns": {
    "internuclear_distance": "angstrom"
  },
  "use": "check",
  "parameters": {
    "model": "moadk",
    "orbital": "HOMO-1 1 pi",
    "m": 1,
    "normalisation": "Zhao et al. 2010 Eqs. (19)-(20), p. 3 (Tong et al. 2002's convention): psi^(m)(r) = sum_l F_lm(r) Y_lm(theta, phi), F_lm(r) = C_lm r^(Z_c/kappa - 1) exp(-kappa r) in the asymptotic region, Z_c the asymptotic charge, kappa = sqrt(2 I_p), atomic units; one-centre expansion, m along the molecular axis"
  }
}

Table V, 1 pi (HOMO-1); m = 1 per the caption (‘For sigma orbital, m = 0 and pi orbital, m = 1’). The binding energy for the rate is the experimental one of Table IV (p. 6). The cells file drops the fifth printed column: C_5m = 0.02 is read from the table image (p. 6) by the script, guarded by the extracted row. C_2m is printed 0.14 and corrected to 0.014 by the authors’ erratum (zhao_2010_erratum; the [[errata]] entry below). internuclear_distance: Table II’s R.

Formulas#

No formulas are recorded.

Corrections#

[
  {
    "dataset": "table5_homo1_CO",
    "row": "2",
    "column": "value",
    "printed": "0.14",
    "corrected": "0.014",
    "reason": "The authors' erratum, Phys. Rev. A 82, 049903(E) (2010): 'In Table V, the C_2m of the HOMO-1 (1 pi) of CO molecule should be 0.014.' A misprint of the paper, not of the extraction.",
    "evidence": "Table V image (tbl_825e661a911b, p. 6) prints 0.14 for C_2m of CO 1 pi (HOMO-1) (checked 2026-09-27); the erratum (zhao_2010_erratum, library Zhao_2010_ErratumDeterminationStructure, p. 1, page image checked) gives 0.014."
  }
]

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.