zhao_2011#
S.-F. Zhao, J. Xu, C. Jin, A.-T. Le and C. D. Lin, “Effect of orbital symmetry on the orientation dependence of strong field tunnelling ionization of nonlinear polyatomic molecules”, J. Phys. B: At. Mol. Opt. Phys. 44, 035601 (2011)
Source record · Catalogue · Review register
DOI: 10.1088/0953-4075/44/3/035601
Source kind: theory
Recorded technique: MO-ADK structure parameters of the HOMO of 17 nonlinear polyatomic molecules from Hartree-Fock orbitals, not from a model potential: ‘we calculate molecular wavefunctions at the equilibrium geometry from GAUSSIAN [46] using the Hartree-Fock (HF) method and the augmented quadruple-zeta (AUG-cc-pVQZ) basis set where diffuse orbitals have been included. In the asymptotic region, to obtain the C_lm coefficients, we fitted each molecular orbital wavefunction to the form of equations (1) and (2). The typical range of r used in the fitting is from 5 to 10 au for small molecules and from 8 to 20 au for larger molecules’ (p. 3; ref. 46 is GAUSSIAN 03, revision B.04). The geometry: ‘Using the Gaussian code [46], we first locate the equilibrium positions of all the atoms in the molecule’ (p. 3), tabulated as the x, y, z coordinates of Table 2 (p. 9), which also fix the molecular frame; the method and basis of the geometry optimisation are not stated separately. kappa in the fit: ‘In the fitting of the C_lm coefficients, we use the calculated binding energy from the GAUSSIAN code to calculate kappa in equation (2)’ (p. 3; that energy is not printed). The rates: Tong et al. 2002’s MO-ADK (ref. 33) for nonlinear molecules, Eqs. (3)-(10), with the experimental ionisation energy: ‘in using equation (10) to calculate the ionization rates, we always use experimental ionization energy’ (p. 3).
Materials in structured entries: CH4, SF6
Dataset quantities: ionization_energy, tunnelling_structure_coefficient
Contents: 33 datasets; 0 formulas.
Curation notes#
Journal pages 1 to 10 = PDF pages 2 to 11 (PDF page 1 is the publisher’s cover sheet). Title, all five authors (Song-Feng Zhao, Junliang Xu, Cheng Jin, Anh-Thu Le, C D Lin), journal, volume 44, article 035601, year 2011 and DOI checked on the first page of the article (PDF p. 2) on 2026-09-28. The text calls the two tables of the appendix ‘table A.1’ and ‘table A.2’; they are printed with the captions ‘Table 1’ (pp. 7-8) and ‘Table 2’ (p. 9), the names used here. The library’s status is VALIDATED; its review warns of an unmatched figure on PDF p. 7 and an unmapped glyph on PDF p. 3 (in the sentence ‘Atomic units are used throughout this paper’; no number is touched).
EXTRACTED, for CH4 and SF6. Table 1 (p. 7, tbl_6768a1c91416) lists 17 molecules: C2H4, C6H6, H3+, H2O, SO2, N2O4, NH3, CH4, C2H6, C3H8, CH3Cl, and on its continuation (p. 8, tbl_4df3e935bc02) butane, isobutane, CH2Cl2, CHCl3, CCl4 and SF6. Taken: CH4’s ‘experimental vertical’ ionisation energy (12.60 eV) and the C_lm of its three degenerate HOMOs, printed ‘1t_2(HOMO1)’, ‘1t_2(HOMO2)’ and ‘1t_2(HOMO3)’. The library’s cells print the orbitals ‘1b_2(HOMO1)’ etc.; the image and the page read 1t_2, the T2 orbital of a tetrahedral molecule. The label is not a data value; the script checks the library’s string and the record gives the printed one. The library’s cells carry each orbital’s label one row above its values for HOMO1 (on the row of the headers C_{1+-1} ...) and on the row of its values for HOMO2 and HOMO3; the page puts each label on its row of values. The script relies on the positions it checks.
SF6: READ ON THE PAGE, by J. C. Travers’s exception to ‘extracted, not typed’ (2026-09-28, TC-684). The library’s cells of the continuation (tbl_4df3e935bc02) are not a rendering of the page, which prints the table rotated by 90 degrees: six text columns merge headers and values, the SF6 ionisation energy (15.69 eV on the page) is lost (’-’), the orbitals are printed ‘2t_1(HOMO3)’ (CCl4’s label; the page prints 1t_1g(HOMO1), 1t_1g(HOMO2), 1t_1g(HOMO3)), CCl4’s coefficients (+-4.02i, -2.51i, +-0.54 ...) are put on SF6’s rows, the upper and lower signs are all printed ‘+-’, and the columns C_{6+-3}, C_{6+-5}, C_{8+-1}, C_{8+-3}, C_{10+-4}, C_{10+-8} of SF6 are missing; no structural fix recovers the table from them. SF6’s 24 cells and its energy were read on the library’s table image turned upright (2026-09-28) and are written in the extraction script as the page prints them (SF6_PAGE). Evidence, which the script checks: (1) the library’s table is still the reading the exception was made for (a re-extraction fails the script, and SF6 is then taken from the new cells); (2) 11 of the 24 cells are also among the library’s cells with the same header and magnitude (their signs there are all ‘+-’); (3) the three degenerate orbitals, which are rotations of one another, have the same sum of |C_lm|^2 over m for each l to the table’s rounding: l = 4, 145.5 in all three; l = 6, 3.24, 3.24 and 3.28; l = 8, 0.356, 0.356 and 0.354 (l = 10 is printed for HOMO3 only, 0.001). On the page SF6’s coefficients have l = 4, 6, 8 (HOMO1, HOMO2: m = +-1, +-3, +-5, +-7) and l = 4, 6, 8, 10 (HOMO3: m = +-4, +-8). The other 15 molecules are not curated materials and were not checked; the library’s cells of several of them differ from the image (SO2’s second line of coefficients stands on N2O4’s row, for one).
CHECKED on 2026-09-28: every CH4 cell (the headers C_{1+-1} ... C_{4+-2}, the 20 coefficients, the upper and lower signs, the ‘i’, the ionisation energy) against the library’s table image and against the page rendered at 400 and 800 dpi, and against the PDF’s own text layer. The library’s cells agree with the page in 18 of the 20 coefficients and in the energy (the minus sign is printed as a hyphen, ‘-’, the upper-minus sign as ‘\mp’ and the upper-plus as ‘\pm’). Two paired signs are misread by the library, ‘\pm’ where the page prints the upper-minus sign: HOMO1’s C_{3+-1}, printed ‘-+0.13’, and HOMO3’s C_{4+-2}, printed ‘-+0.11i’. The script restores the page’s signs (a structural fix of the extraction, not an erratum: the paper is not in error). The library’s paired signs are unreliable elsewhere in the table too (C3H8’s row, for one), which the curated rows do not touch.
THE COEFFICIENTS (p. 2). Eq. (1): Psi(r) = sum_lm F_lm(r) Y_lm(r^), ‘with m the magnetic quantum number along the molecular axis, and Y_lm(r^) are the spherical harmonics’; Eq. (2): F_lm(r -> inf) ~ C_lm r^(Z_c/kappa - 1) e^(-kappa r), ‘where Z_c and C_lm are the effective Coulomb charge and the structure parameters of the molecule, respectively. Here kappa = sqrt(2 I_p), where I_p is the ionization potential’. Eq. (3): Y_lm ~ Q(l, m) sin^|m| theta_e / (2^|m| |m|!) e^(i m chi_e) / sqrt(2 pi), Eq. (4): Q(l, m) = (-1)^((m + |m|)/2) sqrt((2l + 1)(l + |m|)!/(2(l - |m|)!)); the sign of Q is that of spherical harmonics with the Condon-Shortley phase. Eqs. (6), (8): B(m’) = sum_lm C_lm D^l_{m’,m}(R) Q(l, m’), and the rate Eq. (10) sums |B(m’)|^2: the C_lm enter as complex amplitudes. The normalisation of the orbital before the fit is not stated. The paper’s text says nothing about the complex values or the paired signs of Table 1.
THE SIGN CONVENTION. Table 1 prints the coefficients of +m and -m in one column, C_{l+-m}, with a paired sign (’-+2.23’, ‘+-0.17’, ‘-+0.80i’) or none (‘0.80i’, ‘-0.04i’, ‘3.16’). The paper does not state how the pair is to be read. Taken here: the upper sign belongs to +m, the lower to -m (so ‘-+2.23’ under C_{1+-1} is C_{1,+1} = -2.23 and C_{1,-1} = +2.23), and a value without a paired sign is the same for +m and -m. This is an assumption, recorded as such. It is consistent with the geometry of Table 2 (computed 2026-09-28 with Condon-Shortley Y_lm): with it, HOMO1’s l = 1 and l = 2 terms are proportional to x and to +yz, HOMO2’s to y and +xz, HOMO3’s to z and +xy; the hydrogen atoms at (+,+,+), (+,-,-) have x > 0 and yz > 0, those at (+,+,+), (-,+,-) have y > 0 and xz > 0, those at (+,+,+), (-,-,+) have z > 0 and xy > 0, so an orbital bonding with them (C 2p in phase with the H 1s) has the l = 2 admixture of that sign. Evaluated at the four hydrogen directions, the l = 1 and l = 2 parts of sum_lm C_lm Y_lm are +-0.89 and +-0.41 with the same sign at every hydrogen, for each orbital; with the opposite reading (+m and -m exchanged) they have opposite signs at every hydrogen (computed 2026-09-28; the angular functions are real in both readings, so reality does not decide). The reading also makes the three orbitals the same function rotated: C_10 = 3.16 against sqrt(2) x 2.23 = 3.15, and the l = 2 weight of each orbital is 2 x 0.80^2 = 1.28.
THE DATASETS. One per orbital and signed m, the rows the partial waves l, the value the real part of C_lm and the column imaginary the imaginary part (‘0.80i’ is value 0 and imaginary 0.80; ‘-2.23’ is value -2.23 and imaginary 0). The printed column keeps the library’s header cell and value cell. HOMO1 and HOMO2 have m = +-1 (l = 1 to 4) and m = +-3 (l = 3, 4); HOMO3 has m = 0 (l = 1, 3) and m = +-2 (l = 2, 4). A partial wave not printed is not a value (it may be below the precision of the table).
THE DEGENERATE ORBITALS. ‘The degenerate HOMOs are denoted by HOMO1, HOMO2 and HOMO3’ (caption of Table 1). How their rates are to be combined is not stated: for C2H6 (two degenerate HOMOs) the paper shows the density and the rate of each orbital separately (Fig. 4), and it shows no result for CH4. Summing the three orbitals’ rates, each for one electron, is the usual reading; it is not this paper’s. The sums of |C_lm|^2 over m of each orbital are 11.34 (HOMO1, HOMO2) and 11.38 (HOMO3) (computed 2026-09-28 from the printed values).
THE IONISATION ENERGY. ‘The C_lm coefficients, together with the known experimental vertical ionization energy of the HOMO, are listed in table A.1’ (p. 3); no reference is given. CH4’s 12.60 eV is near the adiabatic threshold, not the vertical energy: berkowitz_1987’s photoionisation onset is 12.61 eV, and the 1t2 band’s maxima are at 13.6, 14.4 and 15.0 eV (heilbronner_1977, bieri_1977; the band is Jahn-Teller split). kind is recorded as the paper says, vertical; a user of the rates should know that the value is about 1 eV below the band maximum.
ACCURACY, as the paper states it. ‘Due to the complexity of nonlinear polyatomic molecules, clearly the accuracy of the data provided here cannot be easily checked until further study’ (p. 2). ‘The wavefunctions for the HOMO orbitals in this work have been calculated from GAUSSIAN [46] using the basis set described in section 2. These wavefunctions are not accurate in the asymptotic region, even if many more diffuse orbitals are added in the basis set. The result is that the C_lm coefficients may not be highly accurate’ (p. 6). ‘Still, the results (figure 2 of [34]) show that the alignment dependence remains nearly the same even after more accurate C_lm coefficients are used, despite that the tunnelling rates can be changed somewhat. Thus we are optimistic that the coefficients tabulated here are sufficient to provide a first-order estimate of strong field ionization of nonlinear polyatomic molecules’ (p. 6; ref. 34 is zhao_2010). Only the HOMO is treated, at the equilibrium geometry; inner orbitals ‘are expected to contribute to tunnelling ionization, especially for angles where tunnelling from the HOMO is small’ (p. 5). No uncertainty of any C_lm is given.
COMPARISONS in the paper (none for CH4): the H2O MO-ADK ionisation probability against theta at chi = 0 agrees ‘well’ with the TDVFD calculation of ref. 28 (Fig. 3, 800 nm, 5e13 W/cm2, 20-cycle sine-squared pulse), no numbers given; for H3+ ‘direct comparison of this calculation with the experiment is not possible at this time’ (p. 4). The rates and densities of Figs. 1-6 are ‘normalized to 1.0 at the peak’ (p. 3).
THE FRAME for CH4 (Table 2, p. 9, in angstrom; checked on the page image): C (0, 0, 0); H (0.627447, 0.627447, 0.627447), (-0.627447, -0.627447, 0.627447), (-0.627447, 0.627447, -0.627447), (0.627447, -0.627447, -0.627447). The z axis is an S4 axis, bisecting two HCH angles; C-H = 1.0868 A (computed). SF6: S at the origin, F at +-1.589634 A on each axis (z a C4 axis).
NOT STATED: the fit range for CH4 (5-10 au ‘for small molecules’); the HF binding energy used for kappa; Z_c (the ‘effective Coulomb charge’, 1 for a neutral molecule in ref. 33); the normalisation of the orbital; the reading of the paired signs; how the degenerate orbitals combine; the source of the experimental ionisation energies; any uncertainty.
FIGURES (not digitised): Figs. 1-6, the asymptotic densities, orbitals and orientation-dependent rates of H3+, H2O (with Fig. 3, the TDVFD comparison), C2H6, butane, isobutane, CH2Cl2, CHCl3 and CCl4.
Recorded bibliographic identity status: VALIDATED. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
zhao_2011/table1_ip_CH4#
{
"id": "table1_ip_CH4",
"material": "CH4",
"file": "CH4/zhao_2011__table1_ip_CH4.csv",
"table": "tbl_6768a1c91416",
"quantity": "ionization_energy",
"unit": "eV",
"abscissa": "none",
"use": "check",
"parameters": {
"kind": "vertical",
"orbital": "1t2 (the three degenerate HOMOs)"
}
}
Table 1, ‘I_p (eV)’, ‘the experimental vertical ionization energies’ (caption); no reference is given. Kind as the caption says; the value is near the adiabatic threshold (berkowitz_1987, 12.61 eV), about 1 eV below the vertical maxima of the 1t2 band (heilbronner_1977: 13.6, 14.4, 15.0 eV); see the record’s notes.
zhao_2011/table1_CH4_homo1_mp1#
{
"id": "table1_CH4_homo1_mp1",
"material": "CH4",
"file": "CH4/zhao_2011__table1_CH4_homo1_mp1.csv",
"table": "tbl_6768a1c91416",
"quantity": "tunnelling_structure_coefficient",
"abscissa": "label",
"columns": {
"imaginary": "1"
},
"use": "check",
"parameters": {
"model": "moadk",
"orbital": "1t2 HOMO1",
"m": 1,
"degenerate_orbitals": 3,
"normalisation": "Zhao et al. 2011 Eqs. (1)-(4), p. 2: Psi(r) = sum_lm F_lm(r) Y_lm(r^), F_lm(r -> inf) ~ C_lm r^(Z_c/kappa - 1) exp(-kappa r), Z_c the effective Coulomb charge, kappa = sqrt(2 I_p) with the GAUSSIAN HF binding energy in the fit (p. 3), atomic units; Y_lm with the Condon-Shortley phase (the sign of Q(l, m), Eq. (4)); C_lm complex (value the real part, column imaginary the imaginary part); the printed C_{l+-m} = -+a read as C_{l,+m} = -a, C_{l,-m} = +a (the upper sign for +m; not stated by the paper, see the record's notes); orbital normalisation not stated",
"frame": "the molecular frame (x, y, z) of Table 2 (p. 9): C at the origin, H at (0.627447, 0.627447, 0.627447), (-0.627447, -0.627447, 0.627447), (-0.627447, 0.627447, -0.627447), (0.627447, -0.627447, -0.627447) angstrom; 'm the magnetic quantum number along the molecular axis' (p. 2), here z, an S4 axis"
}
}
Table 1, CH4, 1t_2(HOMO1), m = +1: C_{1+-1} ‘-+2.23’, C_{2+-1} ‘0.80i’, C_{3+-1} ‘-+0.13’, C_{4+-1} ‘-0.04i’, the upper sign (the record’s reading). value: the real part; imaginary: the imaginary part.
zhao_2011/table1_CH4_homo1_mm1#
{
"id": "table1_CH4_homo1_mm1",
"material": "CH4",
"file": "CH4/zhao_2011__table1_CH4_homo1_mm1.csv",
"table": "tbl_6768a1c91416",
"quantity": "tunnelling_structure_coefficient",
"abscissa": "label",
"columns": {
"imaginary": "1"
},
"use": "check",
"parameters": {
"model": "moadk",
"orbital": "1t2 HOMO1",
"m": -1,
"degenerate_orbitals": 3,
"normalisation": "Zhao et al. 2011 Eqs. (1)-(4), p. 2: Psi(r) = sum_lm F_lm(r) Y_lm(r^), F_lm(r -> inf) ~ C_lm r^(Z_c/kappa - 1) exp(-kappa r), Z_c the effective Coulomb charge, kappa = sqrt(2 I_p) with the GAUSSIAN HF binding energy in the fit (p. 3), atomic units; Y_lm with the Condon-Shortley phase (the sign of Q(l, m), Eq. (4)); C_lm complex (value the real part, column imaginary the imaginary part); the printed C_{l+-m} = -+a read as C_{l,+m} = -a, C_{l,-m} = +a (the upper sign for +m; not stated by the paper, see the record's notes); orbital normalisation not stated",
"frame": "the molecular frame (x, y, z) of Table 2 (p. 9): C at the origin, H at (0.627447, 0.627447, 0.627447), (-0.627447, -0.627447, 0.627447), (-0.627447, 0.627447, -0.627447), (0.627447, -0.627447, -0.627447) angstrom; 'm the magnetic quantum number along the molecular axis' (p. 2), here z, an S4 axis"
}
}
Table 1, CH4, 1t_2(HOMO1), m = -1: C_{1+-1} ‘-+2.23’, C_{2+-1} ‘0.80i’, C_{3+-1} ‘-+0.13’, C_{4+-1} ‘-0.04i’, the lower sign (the record’s reading). value: the real part; imaginary: the imaginary part.
zhao_2011/table1_CH4_homo1_mp3#
{
"id": "table1_CH4_homo1_mp3",
"material": "CH4",
"file": "CH4/zhao_2011__table1_CH4_homo1_mp3.csv",
"table": "tbl_6768a1c91416",
"quantity": "tunnelling_structure_coefficient",
"abscissa": "label",
"columns": {
"imaginary": "1"
},
"use": "check",
"parameters": {
"model": "moadk",
"orbital": "1t2 HOMO1",
"m": 3,
"degenerate_orbitals": 3,
"normalisation": "Zhao et al. 2011 Eqs. (1)-(4), p. 2: Psi(r) = sum_lm F_lm(r) Y_lm(r^), F_lm(r -> inf) ~ C_lm r^(Z_c/kappa - 1) exp(-kappa r), Z_c the effective Coulomb charge, kappa = sqrt(2 I_p) with the GAUSSIAN HF binding energy in the fit (p. 3), atomic units; Y_lm with the Condon-Shortley phase (the sign of Q(l, m), Eq. (4)); C_lm complex (value the real part, column imaginary the imaginary part); the printed C_{l+-m} = -+a read as C_{l,+m} = -a, C_{l,-m} = +a (the upper sign for +m; not stated by the paper, see the record's notes); orbital normalisation not stated",
"frame": "the molecular frame (x, y, z) of Table 2 (p. 9): C at the origin, H at (0.627447, 0.627447, 0.627447), (-0.627447, -0.627447, 0.627447), (-0.627447, 0.627447, -0.627447), (0.627447, -0.627447, -0.627447) angstrom; 'm the magnetic quantum number along the molecular axis' (p. 2), here z, an S4 axis"
}
}
Table 1, CH4, 1t_2(HOMO1), m = +3: C_{3+-3} ‘+-0.17’, C_{4+-3} ‘0.10i’, the upper sign (the record’s reading). value: the real part; imaginary: the imaginary part.
zhao_2011/table1_CH4_homo1_mm3#
{
"id": "table1_CH4_homo1_mm3",
"material": "CH4",
"file": "CH4/zhao_2011__table1_CH4_homo1_mm3.csv",
"table": "tbl_6768a1c91416",
"quantity": "tunnelling_structure_coefficient",
"abscissa": "label",
"columns": {
"imaginary": "1"
},
"use": "check",
"parameters": {
"model": "moadk",
"orbital": "1t2 HOMO1",
"m": -3,
"degenerate_orbitals": 3,
"normalisation": "Zhao et al. 2011 Eqs. (1)-(4), p. 2: Psi(r) = sum_lm F_lm(r) Y_lm(r^), F_lm(r -> inf) ~ C_lm r^(Z_c/kappa - 1) exp(-kappa r), Z_c the effective Coulomb charge, kappa = sqrt(2 I_p) with the GAUSSIAN HF binding energy in the fit (p. 3), atomic units; Y_lm with the Condon-Shortley phase (the sign of Q(l, m), Eq. (4)); C_lm complex (value the real part, column imaginary the imaginary part); the printed C_{l+-m} = -+a read as C_{l,+m} = -a, C_{l,-m} = +a (the upper sign for +m; not stated by the paper, see the record's notes); orbital normalisation not stated",
"frame": "the molecular frame (x, y, z) of Table 2 (p. 9): C at the origin, H at (0.627447, 0.627447, 0.627447), (-0.627447, -0.627447, 0.627447), (-0.627447, 0.627447, -0.627447), (0.627447, -0.627447, -0.627447) angstrom; 'm the magnetic quantum number along the molecular axis' (p. 2), here z, an S4 axis"
}
}
Table 1, CH4, 1t_2(HOMO1), m = -3: C_{3+-3} ‘+-0.17’, C_{4+-3} ‘0.10i’, the lower sign (the record’s reading). value: the real part; imaginary: the imaginary part.
zhao_2011/table1_CH4_homo2_mp1#
{
"id": "table1_CH4_homo2_mp1",
"material": "CH4",
"file": "CH4/zhao_2011__table1_CH4_homo2_mp1.csv",
"table": "tbl_6768a1c91416",
"quantity": "tunnelling_structure_coefficient",
"abscissa": "label",
"columns": {
"imaginary": "1"
},
"use": "check",
"parameters": {
"model": "moadk",
"orbital": "1t2 HOMO2",
"m": 1,
"degenerate_orbitals": 3,
"normalisation": "Zhao et al. 2011 Eqs. (1)-(4), p. 2: Psi(r) = sum_lm F_lm(r) Y_lm(r^), F_lm(r -> inf) ~ C_lm r^(Z_c/kappa - 1) exp(-kappa r), Z_c the effective Coulomb charge, kappa = sqrt(2 I_p) with the GAUSSIAN HF binding energy in the fit (p. 3), atomic units; Y_lm with the Condon-Shortley phase (the sign of Q(l, m), Eq. (4)); C_lm complex (value the real part, column imaginary the imaginary part); the printed C_{l+-m} = -+a read as C_{l,+m} = -a, C_{l,-m} = +a (the upper sign for +m; not stated by the paper, see the record's notes); orbital normalisation not stated",
"frame": "the molecular frame (x, y, z) of Table 2 (p. 9): C at the origin, H at (0.627447, 0.627447, 0.627447), (-0.627447, -0.627447, 0.627447), (-0.627447, 0.627447, -0.627447), (0.627447, -0.627447, -0.627447) angstrom; 'm the magnetic quantum number along the molecular axis' (p. 2), here z, an S4 axis"
}
}
Table 1, CH4, 1t_2(HOMO2), m = +1: C_{1+-1} ‘2.23i’, C_{2+-1} ‘-+0.80’, C_{3+-1} ‘0.13i’, C_{4+-1} ‘+-0.04’, the upper sign (the record’s reading). value: the real part; imaginary: the imaginary part.
zhao_2011/table1_CH4_homo2_mm1#
{
"id": "table1_CH4_homo2_mm1",
"material": "CH4",
"file": "CH4/zhao_2011__table1_CH4_homo2_mm1.csv",
"table": "tbl_6768a1c91416",
"quantity": "tunnelling_structure_coefficient",
"abscissa": "label",
"columns": {
"imaginary": "1"
},
"use": "check",
"parameters": {
"model": "moadk",
"orbital": "1t2 HOMO2",
"m": -1,
"degenerate_orbitals": 3,
"normalisation": "Zhao et al. 2011 Eqs. (1)-(4), p. 2: Psi(r) = sum_lm F_lm(r) Y_lm(r^), F_lm(r -> inf) ~ C_lm r^(Z_c/kappa - 1) exp(-kappa r), Z_c the effective Coulomb charge, kappa = sqrt(2 I_p) with the GAUSSIAN HF binding energy in the fit (p. 3), atomic units; Y_lm with the Condon-Shortley phase (the sign of Q(l, m), Eq. (4)); C_lm complex (value the real part, column imaginary the imaginary part); the printed C_{l+-m} = -+a read as C_{l,+m} = -a, C_{l,-m} = +a (the upper sign for +m; not stated by the paper, see the record's notes); orbital normalisation not stated",
"frame": "the molecular frame (x, y, z) of Table 2 (p. 9): C at the origin, H at (0.627447, 0.627447, 0.627447), (-0.627447, -0.627447, 0.627447), (-0.627447, 0.627447, -0.627447), (0.627447, -0.627447, -0.627447) angstrom; 'm the magnetic quantum number along the molecular axis' (p. 2), here z, an S4 axis"
}
}
Table 1, CH4, 1t_2(HOMO2), m = -1: C_{1+-1} ‘2.23i’, C_{2+-1} ‘-+0.80’, C_{3+-1} ‘0.13i’, C_{4+-1} ‘+-0.04’, the lower sign (the record’s reading). value: the real part; imaginary: the imaginary part.
zhao_2011/table1_CH4_homo2_mp3#
{
"id": "table1_CH4_homo2_mp3",
"material": "CH4",
"file": "CH4/zhao_2011__table1_CH4_homo2_mp3.csv",
"table": "tbl_6768a1c91416",
"quantity": "tunnelling_structure_coefficient",
"abscissa": "label",
"columns": {
"imaginary": "1"
},
"use": "check",
"parameters": {
"model": "moadk",
"orbital": "1t2 HOMO2",
"m": 3,
"degenerate_orbitals": 3,
"normalisation": "Zhao et al. 2011 Eqs. (1)-(4), p. 2: Psi(r) = sum_lm F_lm(r) Y_lm(r^), F_lm(r -> inf) ~ C_lm r^(Z_c/kappa - 1) exp(-kappa r), Z_c the effective Coulomb charge, kappa = sqrt(2 I_p) with the GAUSSIAN HF binding energy in the fit (p. 3), atomic units; Y_lm with the Condon-Shortley phase (the sign of Q(l, m), Eq. (4)); C_lm complex (value the real part, column imaginary the imaginary part); the printed C_{l+-m} = -+a read as C_{l,+m} = -a, C_{l,-m} = +a (the upper sign for +m; not stated by the paper, see the record's notes); orbital normalisation not stated",
"frame": "the molecular frame (x, y, z) of Table 2 (p. 9): C at the origin, H at (0.627447, 0.627447, 0.627447), (-0.627447, -0.627447, 0.627447), (-0.627447, 0.627447, -0.627447), (0.627447, -0.627447, -0.627447) angstrom; 'm the magnetic quantum number along the molecular axis' (p. 2), here z, an S4 axis"
}
}
Table 1, CH4, 1t_2(HOMO2), m = +3: C_{3+-3} ‘0.17i’, C_{4+-3} ‘+-0.10’, the upper sign (the record’s reading). value: the real part; imaginary: the imaginary part.
zhao_2011/table1_CH4_homo2_mm3#
{
"id": "table1_CH4_homo2_mm3",
"material": "CH4",
"file": "CH4/zhao_2011__table1_CH4_homo2_mm3.csv",
"table": "tbl_6768a1c91416",
"quantity": "tunnelling_structure_coefficient",
"abscissa": "label",
"columns": {
"imaginary": "1"
},
"use": "check",
"parameters": {
"model": "moadk",
"orbital": "1t2 HOMO2",
"m": -3,
"degenerate_orbitals": 3,
"normalisation": "Zhao et al. 2011 Eqs. (1)-(4), p. 2: Psi(r) = sum_lm F_lm(r) Y_lm(r^), F_lm(r -> inf) ~ C_lm r^(Z_c/kappa - 1) exp(-kappa r), Z_c the effective Coulomb charge, kappa = sqrt(2 I_p) with the GAUSSIAN HF binding energy in the fit (p. 3), atomic units; Y_lm with the Condon-Shortley phase (the sign of Q(l, m), Eq. (4)); C_lm complex (value the real part, column imaginary the imaginary part); the printed C_{l+-m} = -+a read as C_{l,+m} = -a, C_{l,-m} = +a (the upper sign for +m; not stated by the paper, see the record's notes); orbital normalisation not stated",
"frame": "the molecular frame (x, y, z) of Table 2 (p. 9): C at the origin, H at (0.627447, 0.627447, 0.627447), (-0.627447, -0.627447, 0.627447), (-0.627447, 0.627447, -0.627447), (0.627447, -0.627447, -0.627447) angstrom; 'm the magnetic quantum number along the molecular axis' (p. 2), here z, an S4 axis"
}
}
Table 1, CH4, 1t_2(HOMO2), m = -3: C_{3+-3} ‘0.17i’, C_{4+-3} ‘+-0.10’, the lower sign (the record’s reading). value: the real part; imaginary: the imaginary part.
zhao_2011/table1_CH4_homo3_m0#
{
"id": "table1_CH4_homo3_m0",
"material": "CH4",
"file": "CH4/zhao_2011__table1_CH4_homo3_m0.csv",
"table": "tbl_6768a1c91416",
"quantity": "tunnelling_structure_coefficient",
"abscissa": "label",
"columns": {
"imaginary": "1"
},
"use": "check",
"parameters": {
"model": "moadk",
"orbital": "1t2 HOMO3",
"m": 0,
"degenerate_orbitals": 3,
"normalisation": "Zhao et al. 2011 Eqs. (1)-(4), p. 2: Psi(r) = sum_lm F_lm(r) Y_lm(r^), F_lm(r -> inf) ~ C_lm r^(Z_c/kappa - 1) exp(-kappa r), Z_c the effective Coulomb charge, kappa = sqrt(2 I_p) with the GAUSSIAN HF binding energy in the fit (p. 3), atomic units; Y_lm with the Condon-Shortley phase (the sign of Q(l, m), Eq. (4)); C_lm complex (value the real part, column imaginary the imaginary part); the printed C_{l+-m} = -+a read as C_{l,+m} = -a, C_{l,-m} = +a (the upper sign for +m; not stated by the paper, see the record's notes); orbital normalisation not stated",
"frame": "the molecular frame (x, y, z) of Table 2 (p. 9): C at the origin, H at (0.627447, 0.627447, 0.627447), (-0.627447, -0.627447, 0.627447), (-0.627447, 0.627447, -0.627447), (0.627447, -0.627447, -0.627447) angstrom; 'm the magnetic quantum number along the molecular axis' (p. 2), here z, an S4 axis"
}
}
Table 1, CH4, 1t_2(HOMO3), m = 0: C_{10} ‘3.16’, C_{30} ‘-0.30’. value: the real part; imaginary: the imaginary part.
zhao_2011/table1_CH4_homo3_mp2#
{
"id": "table1_CH4_homo3_mp2",
"material": "CH4",
"file": "CH4/zhao_2011__table1_CH4_homo3_mp2.csv",
"table": "tbl_6768a1c91416",
"quantity": "tunnelling_structure_coefficient",
"abscissa": "label",
"columns": {
"imaginary": "1"
},
"use": "check",
"parameters": {
"model": "moadk",
"orbital": "1t2 HOMO3",
"m": 2,
"degenerate_orbitals": 3,
"normalisation": "Zhao et al. 2011 Eqs. (1)-(4), p. 2: Psi(r) = sum_lm F_lm(r) Y_lm(r^), F_lm(r -> inf) ~ C_lm r^(Z_c/kappa - 1) exp(-kappa r), Z_c the effective Coulomb charge, kappa = sqrt(2 I_p) with the GAUSSIAN HF binding energy in the fit (p. 3), atomic units; Y_lm with the Condon-Shortley phase (the sign of Q(l, m), Eq. (4)); C_lm complex (value the real part, column imaginary the imaginary part); the printed C_{l+-m} = -+a read as C_{l,+m} = -a, C_{l,-m} = +a (the upper sign for +m; not stated by the paper, see the record's notes); orbital normalisation not stated",
"frame": "the molecular frame (x, y, z) of Table 2 (p. 9): C at the origin, H at (0.627447, 0.627447, 0.627447), (-0.627447, -0.627447, 0.627447), (-0.627447, 0.627447, -0.627447), (0.627447, -0.627447, -0.627447) angstrom; 'm the magnetic quantum number along the molecular axis' (p. 2), here z, an S4 axis"
}
}
Table 1, CH4, 1t_2(HOMO3), m = +2: C_{2+-2} ‘-+0.80i’, C_{4+-2} ‘-+0.11i’, the upper sign (the record’s reading). value: the real part; imaginary: the imaginary part.
zhao_2011/table1_CH4_homo3_mm2#
{
"id": "table1_CH4_homo3_mm2",
"material": "CH4",
"file": "CH4/zhao_2011__table1_CH4_homo3_mm2.csv",
"table": "tbl_6768a1c91416",
"quantity": "tunnelling_structure_coefficient",
"abscissa": "label",
"columns": {
"imaginary": "1"
},
"use": "check",
"parameters": {
"model": "moadk",
"orbital": "1t2 HOMO3",
"m": -2,
"degenerate_orbitals": 3,
"normalisation": "Zhao et al. 2011 Eqs. (1)-(4), p. 2: Psi(r) = sum_lm F_lm(r) Y_lm(r^), F_lm(r -> inf) ~ C_lm r^(Z_c/kappa - 1) exp(-kappa r), Z_c the effective Coulomb charge, kappa = sqrt(2 I_p) with the GAUSSIAN HF binding energy in the fit (p. 3), atomic units; Y_lm with the Condon-Shortley phase (the sign of Q(l, m), Eq. (4)); C_lm complex (value the real part, column imaginary the imaginary part); the printed C_{l+-m} = -+a read as C_{l,+m} = -a, C_{l,-m} = +a (the upper sign for +m; not stated by the paper, see the record's notes); orbital normalisation not stated",
"frame": "the molecular frame (x, y, z) of Table 2 (p. 9): C at the origin, H at (0.627447, 0.627447, 0.627447), (-0.627447, -0.627447, 0.627447), (-0.627447, 0.627447, -0.627447), (0.627447, -0.627447, -0.627447) angstrom; 'm the magnetic quantum number along the molecular axis' (p. 2), here z, an S4 axis"
}
}
Table 1, CH4, 1t_2(HOMO3), m = -2: C_{2+-2} ‘-+0.80i’, C_{4+-2} ‘-+0.11i’, the lower sign (the record’s reading). value: the real part; imaginary: the imaginary part.
zhao_2011/table1_ip_SF6#
{
"id": "table1_ip_SF6",
"material": "SF6",
"file": "SF6/zhao_2011__table1_ip_SF6.csv",
"table": "tbl_4df3e935bc02",
"quantity": "ionization_energy",
"unit": "eV",
"abscissa": "none",
"use": "check",
"parameters": {
"kind": "vertical",
"orbital": "1t1g (the three degenerate HOMOs)"
}
}
Table 1 (continued, p. 8), ‘I_p (eV)’, ‘the experimental vertical ionization energies’ (caption); no reference is given. READ ON THE PAGE, not from the library’s cells, which lose it (J. C. Travers’s exception, TC-684; see the record’s notes). 15.69 eV is the first band maximum of SF6 (potts_1970’s 15.69 eV, which that paper assigns to 3t1u; Zhao et al. label the HOMO 1t1g).
zhao_2011/table1_SF6_homo1_mm7#
{
"id": "table1_SF6_homo1_mm7",
"material": "SF6",
"file": "SF6/zhao_2011__table1_SF6_homo1_mm7.csv",
"table": "tbl_4df3e935bc02",
"quantity": "tunnelling_structure_coefficient",
"abscissa": "label",
"columns": {
"imaginary": "1"
},
"use": "check",
"parameters": {
"model": "moadk",
"orbital": "1t1g HOMO1",
"m": -7,
"degenerate_orbitals": 3,
"normalisation": "Zhao et al. 2011 Eqs. (1)-(4), p. 2: Psi(r) = sum_lm F_lm(r) Y_lm(r^), F_lm(r -> inf) ~ C_lm r^(Z_c/kappa - 1) exp(-kappa r), Z_c the effective Coulomb charge, kappa = sqrt(2 I_p) with the GAUSSIAN HF binding energy in the fit (p. 3), atomic units; Y_lm with the Condon-Shortley phase (the sign of Q(l, m), Eq. (4)); C_lm complex (value the real part, column imaginary the imaginary part); the printed C_{l+-m} = -+a read as C_{l,+m} = -a, C_{l,-m} = +a (the upper sign for +m; not stated by the paper, see the record's notes); orbital normalisation not stated",
"frame": "the molecular frame (x, y, z) of Table 2 (p. 9): S at the origin, F at +-1.589634 angstrom on each axis; 'm the magnetic quantum number along the molecular axis' (p. 2), here z, a C4 axis"
}
}
Table 1 (continued, p. 8), SF6, 1t_1g(HOMO1), m = -7: C_{8+-7} ‘+-0.10’, the lower sign (the record’s reading). READ ON THE PAGE, not from the library’s cells (J. C. Travers’s exception, TC-684; see the record’s notes). value: the real part; imaginary: the imaginary part.
zhao_2011/table1_SF6_homo1_mm5#
{
"id": "table1_SF6_homo1_mm5",
"material": "SF6",
"file": "SF6/zhao_2011__table1_SF6_homo1_mm5.csv",
"table": "tbl_4df3e935bc02",
"quantity": "tunnelling_structure_coefficient",
"abscissa": "label",
"columns": {
"imaginary": "1"
},
"use": "check",
"parameters": {
"model": "moadk",
"orbital": "1t1g HOMO1",
"m": -5,
"degenerate_orbitals": 3,
"normalisation": "Zhao et al. 2011 Eqs. (1)-(4), p. 2: Psi(r) = sum_lm F_lm(r) Y_lm(r^), F_lm(r -> inf) ~ C_lm r^(Z_c/kappa - 1) exp(-kappa r), Z_c the effective Coulomb charge, kappa = sqrt(2 I_p) with the GAUSSIAN HF binding energy in the fit (p. 3), atomic units; Y_lm with the Condon-Shortley phase (the sign of Q(l, m), Eq. (4)); C_lm complex (value the real part, column imaginary the imaginary part); the printed C_{l+-m} = -+a read as C_{l,+m} = -a, C_{l,-m} = +a (the upper sign for +m; not stated by the paper, see the record's notes); orbital normalisation not stated",
"frame": "the molecular frame (x, y, z) of Table 2 (p. 9): S at the origin, F at +-1.589634 angstrom on each axis; 'm the magnetic quantum number along the molecular axis' (p. 2), here z, a C4 axis"
}
}
Table 1 (continued, p. 8), SF6, 1t_1g(HOMO1), m = -5: C_{6+-5} ‘+-0.75’, C_{8+-5} ‘-+0.12’, the lower sign (the record’s reading). READ ON THE PAGE, not from the library’s cells (J. C. Travers’s exception, TC-684; see the record’s notes). value: the real part; imaginary: the imaginary part.
zhao_2011/table1_SF6_homo1_mm3#
{
"id": "table1_SF6_homo1_mm3",
"material": "SF6",
"file": "SF6/zhao_2011__table1_SF6_homo1_mm3.csv",
"table": "tbl_4df3e935bc02",
"quantity": "tunnelling_structure_coefficient",
"abscissa": "label",
"columns": {
"imaginary": "1"
},
"use": "check",
"parameters": {
"model": "moadk",
"orbital": "1t1g HOMO1",
"m": -3,
"degenerate_orbitals": 3,
"normalisation": "Zhao et al. 2011 Eqs. (1)-(4), p. 2: Psi(r) = sum_lm F_lm(r) Y_lm(r^), F_lm(r -> inf) ~ C_lm r^(Z_c/kappa - 1) exp(-kappa r), Z_c the effective Coulomb charge, kappa = sqrt(2 I_p) with the GAUSSIAN HF binding energy in the fit (p. 3), atomic units; Y_lm with the Condon-Shortley phase (the sign of Q(l, m), Eq. (4)); C_lm complex (value the real part, column imaginary the imaginary part); the printed C_{l+-m} = -+a read as C_{l,+m} = -a, C_{l,-m} = +a (the upper sign for +m; not stated by the paper, see the record's notes); orbital normalisation not stated",
"frame": "the molecular frame (x, y, z) of Table 2 (p. 9): S at the origin, F at +-1.589634 angstrom on each axis; 'm the magnetic quantum number along the molecular axis' (p. 2), here z, a C4 axis"
}
}
Table 1 (continued, p. 8), SF6, 1t_1g(HOMO1), m = -3: C_{4+-3} ‘+-3.01’, C_{6+-3} ‘-+0.87’, C_{8+-3} ‘+-0.13’, the lower sign (the record’s reading). READ ON THE PAGE, not from the library’s cells (J. C. Travers’s exception, TC-684; see the record’s notes). value: the real part; imaginary: the imaginary part.
zhao_2011/table1_SF6_homo1_mm1#
{
"id": "table1_SF6_homo1_mm1",
"material": "SF6",
"file": "SF6/zhao_2011__table1_SF6_homo1_mm1.csv",
"table": "tbl_4df3e935bc02",
"quantity": "tunnelling_structure_coefficient",
"abscissa": "label",
"columns": {
"imaginary": "1"
},
"use": "check",
"parameters": {
"model": "moadk",
"orbital": "1t1g HOMO1",
"m": -1,
"degenerate_orbitals": 3,
"normalisation": "Zhao et al. 2011 Eqs. (1)-(4), p. 2: Psi(r) = sum_lm F_lm(r) Y_lm(r^), F_lm(r -> inf) ~ C_lm r^(Z_c/kappa - 1) exp(-kappa r), Z_c the effective Coulomb charge, kappa = sqrt(2 I_p) with the GAUSSIAN HF binding energy in the fit (p. 3), atomic units; Y_lm with the Condon-Shortley phase (the sign of Q(l, m), Eq. (4)); C_lm complex (value the real part, column imaginary the imaginary part); the printed C_{l+-m} = -+a read as C_{l,+m} = -a, C_{l,-m} = +a (the upper sign for +m; not stated by the paper, see the record's notes); orbital normalisation not stated",
"frame": "the molecular frame (x, y, z) of Table 2 (p. 9): S at the origin, F at +-1.589634 angstrom on each axis; 'm the magnetic quantum number along the molecular axis' (p. 2), here z, a C4 axis"
}
}
Table 1 (continued, p. 8), SF6, 1t_1g(HOMO1), m = -1: C_{4+-1} ‘-+7.98’, C_{6+-1} ‘-+0.55’, C_{8+-1} ‘-+0.37’, the lower sign (the record’s reading). READ ON THE PAGE, not from the library’s cells (J. C. Travers’s exception, TC-684; see the record’s notes). value: the real part; imaginary: the imaginary part.
zhao_2011/table1_SF6_homo1_mp1#
{
"id": "table1_SF6_homo1_mp1",
"material": "SF6",
"file": "SF6/zhao_2011__table1_SF6_homo1_mp1.csv",
"table": "tbl_4df3e935bc02",
"quantity": "tunnelling_structure_coefficient",
"abscissa": "label",
"columns": {
"imaginary": "1"
},
"use": "check",
"parameters": {
"model": "moadk",
"orbital": "1t1g HOMO1",
"m": 1,
"degenerate_orbitals": 3,
"normalisation": "Zhao et al. 2011 Eqs. (1)-(4), p. 2: Psi(r) = sum_lm F_lm(r) Y_lm(r^), F_lm(r -> inf) ~ C_lm r^(Z_c/kappa - 1) exp(-kappa r), Z_c the effective Coulomb charge, kappa = sqrt(2 I_p) with the GAUSSIAN HF binding energy in the fit (p. 3), atomic units; Y_lm with the Condon-Shortley phase (the sign of Q(l, m), Eq. (4)); C_lm complex (value the real part, column imaginary the imaginary part); the printed C_{l+-m} = -+a read as C_{l,+m} = -a, C_{l,-m} = +a (the upper sign for +m; not stated by the paper, see the record's notes); orbital normalisation not stated",
"frame": "the molecular frame (x, y, z) of Table 2 (p. 9): S at the origin, F at +-1.589634 angstrom on each axis; 'm the magnetic quantum number along the molecular axis' (p. 2), here z, a C4 axis"
}
}
Table 1 (continued, p. 8), SF6, 1t_1g(HOMO1), m = +1: C_{4+-1} ‘-+7.98’, C_{6+-1} ‘-+0.55’, C_{8+-1} ‘-+0.37’, the upper sign (the record’s reading). READ ON THE PAGE, not from the library’s cells (J. C. Travers’s exception, TC-684; see the record’s notes). value: the real part; imaginary: the imaginary part.
zhao_2011/table1_SF6_homo1_mp3#
{
"id": "table1_SF6_homo1_mp3",
"material": "SF6",
"file": "SF6/zhao_2011__table1_SF6_homo1_mp3.csv",
"table": "tbl_4df3e935bc02",
"quantity": "tunnelling_structure_coefficient",
"abscissa": "label",
"columns": {
"imaginary": "1"
},
"use": "check",
"parameters": {
"model": "moadk",
"orbital": "1t1g HOMO1",
"m": 3,
"degenerate_orbitals": 3,
"normalisation": "Zhao et al. 2011 Eqs. (1)-(4), p. 2: Psi(r) = sum_lm F_lm(r) Y_lm(r^), F_lm(r -> inf) ~ C_lm r^(Z_c/kappa - 1) exp(-kappa r), Z_c the effective Coulomb charge, kappa = sqrt(2 I_p) with the GAUSSIAN HF binding energy in the fit (p. 3), atomic units; Y_lm with the Condon-Shortley phase (the sign of Q(l, m), Eq. (4)); C_lm complex (value the real part, column imaginary the imaginary part); the printed C_{l+-m} = -+a read as C_{l,+m} = -a, C_{l,-m} = +a (the upper sign for +m; not stated by the paper, see the record's notes); orbital normalisation not stated",
"frame": "the molecular frame (x, y, z) of Table 2 (p. 9): S at the origin, F at +-1.589634 angstrom on each axis; 'm the magnetic quantum number along the molecular axis' (p. 2), here z, a C4 axis"
}
}
Table 1 (continued, p. 8), SF6, 1t_1g(HOMO1), m = +3: C_{4+-3} ‘+-3.01’, C_{6+-3} ‘-+0.87’, C_{8+-3} ‘+-0.13’, the upper sign (the record’s reading). READ ON THE PAGE, not from the library’s cells (J. C. Travers’s exception, TC-684; see the record’s notes). value: the real part; imaginary: the imaginary part.
zhao_2011/table1_SF6_homo1_mp5#
{
"id": "table1_SF6_homo1_mp5",
"material": "SF6",
"file": "SF6/zhao_2011__table1_SF6_homo1_mp5.csv",
"table": "tbl_4df3e935bc02",
"quantity": "tunnelling_structure_coefficient",
"abscissa": "label",
"columns": {
"imaginary": "1"
},
"use": "check",
"parameters": {
"model": "moadk",
"orbital": "1t1g HOMO1",
"m": 5,
"degenerate_orbitals": 3,
"normalisation": "Zhao et al. 2011 Eqs. (1)-(4), p. 2: Psi(r) = sum_lm F_lm(r) Y_lm(r^), F_lm(r -> inf) ~ C_lm r^(Z_c/kappa - 1) exp(-kappa r), Z_c the effective Coulomb charge, kappa = sqrt(2 I_p) with the GAUSSIAN HF binding energy in the fit (p. 3), atomic units; Y_lm with the Condon-Shortley phase (the sign of Q(l, m), Eq. (4)); C_lm complex (value the real part, column imaginary the imaginary part); the printed C_{l+-m} = -+a read as C_{l,+m} = -a, C_{l,-m} = +a (the upper sign for +m; not stated by the paper, see the record's notes); orbital normalisation not stated",
"frame": "the molecular frame (x, y, z) of Table 2 (p. 9): S at the origin, F at +-1.589634 angstrom on each axis; 'm the magnetic quantum number along the molecular axis' (p. 2), here z, a C4 axis"
}
}
Table 1 (continued, p. 8), SF6, 1t_1g(HOMO1), m = +5: C_{6+-5} ‘+-0.75’, C_{8+-5} ‘-+0.12’, the upper sign (the record’s reading). READ ON THE PAGE, not from the library’s cells (J. C. Travers’s exception, TC-684; see the record’s notes). value: the real part; imaginary: the imaginary part.
zhao_2011/table1_SF6_homo1_mp7#
{
"id": "table1_SF6_homo1_mp7",
"material": "SF6",
"file": "SF6/zhao_2011__table1_SF6_homo1_mp7.csv",
"table": "tbl_4df3e935bc02",
"quantity": "tunnelling_structure_coefficient",
"abscissa": "label",
"columns": {
"imaginary": "1"
},
"use": "check",
"parameters": {
"model": "moadk",
"orbital": "1t1g HOMO1",
"m": 7,
"degenerate_orbitals": 3,
"normalisation": "Zhao et al. 2011 Eqs. (1)-(4), p. 2: Psi(r) = sum_lm F_lm(r) Y_lm(r^), F_lm(r -> inf) ~ C_lm r^(Z_c/kappa - 1) exp(-kappa r), Z_c the effective Coulomb charge, kappa = sqrt(2 I_p) with the GAUSSIAN HF binding energy in the fit (p. 3), atomic units; Y_lm with the Condon-Shortley phase (the sign of Q(l, m), Eq. (4)); C_lm complex (value the real part, column imaginary the imaginary part); the printed C_{l+-m} = -+a read as C_{l,+m} = -a, C_{l,-m} = +a (the upper sign for +m; not stated by the paper, see the record's notes); orbital normalisation not stated",
"frame": "the molecular frame (x, y, z) of Table 2 (p. 9): S at the origin, F at +-1.589634 angstrom on each axis; 'm the magnetic quantum number along the molecular axis' (p. 2), here z, a C4 axis"
}
}
Table 1 (continued, p. 8), SF6, 1t_1g(HOMO1), m = +7: C_{8+-7} ‘+-0.10’, the upper sign (the record’s reading). READ ON THE PAGE, not from the library’s cells (J. C. Travers’s exception, TC-684; see the record’s notes). value: the real part; imaginary: the imaginary part.
zhao_2011/table1_SF6_homo2_mm7#
{
"id": "table1_SF6_homo2_mm7",
"material": "SF6",
"file": "SF6/zhao_2011__table1_SF6_homo2_mm7.csv",
"table": "tbl_4df3e935bc02",
"quantity": "tunnelling_structure_coefficient",
"abscissa": "label",
"columns": {
"imaginary": "1"
},
"use": "check",
"parameters": {
"model": "moadk",
"orbital": "1t1g HOMO2",
"m": -7,
"degenerate_orbitals": 3,
"normalisation": "Zhao et al. 2011 Eqs. (1)-(4), p. 2: Psi(r) = sum_lm F_lm(r) Y_lm(r^), F_lm(r -> inf) ~ C_lm r^(Z_c/kappa - 1) exp(-kappa r), Z_c the effective Coulomb charge, kappa = sqrt(2 I_p) with the GAUSSIAN HF binding energy in the fit (p. 3), atomic units; Y_lm with the Condon-Shortley phase (the sign of Q(l, m), Eq. (4)); C_lm complex (value the real part, column imaginary the imaginary part); the printed C_{l+-m} = -+a read as C_{l,+m} = -a, C_{l,-m} = +a (the upper sign for +m; not stated by the paper, see the record's notes); orbital normalisation not stated",
"frame": "the molecular frame (x, y, z) of Table 2 (p. 9): S at the origin, F at +-1.589634 angstrom on each axis; 'm the magnetic quantum number along the molecular axis' (p. 2), here z, a C4 axis"
}
}
Table 1 (continued, p. 8), SF6, 1t_1g(HOMO2), m = -7: C_{8+-7} ‘0.10i’, the lower sign (the record’s reading). READ ON THE PAGE, not from the library’s cells (J. C. Travers’s exception, TC-684; see the record’s notes). value: the real part; imaginary: the imaginary part.
zhao_2011/table1_SF6_homo2_mm5#
{
"id": "table1_SF6_homo2_mm5",
"material": "SF6",
"file": "SF6/zhao_2011__table1_SF6_homo2_mm5.csv",
"table": "tbl_4df3e935bc02",
"quantity": "tunnelling_structure_coefficient",
"abscissa": "label",
"columns": {
"imaginary": "1"
},
"use": "check",
"parameters": {
"model": "moadk",
"orbital": "1t1g HOMO2",
"m": -5,
"degenerate_orbitals": 3,
"normalisation": "Zhao et al. 2011 Eqs. (1)-(4), p. 2: Psi(r) = sum_lm F_lm(r) Y_lm(r^), F_lm(r -> inf) ~ C_lm r^(Z_c/kappa - 1) exp(-kappa r), Z_c the effective Coulomb charge, kappa = sqrt(2 I_p) with the GAUSSIAN HF binding energy in the fit (p. 3), atomic units; Y_lm with the Condon-Shortley phase (the sign of Q(l, m), Eq. (4)); C_lm complex (value the real part, column imaginary the imaginary part); the printed C_{l+-m} = -+a read as C_{l,+m} = -a, C_{l,-m} = +a (the upper sign for +m; not stated by the paper, see the record's notes); orbital normalisation not stated",
"frame": "the molecular frame (x, y, z) of Table 2 (p. 9): S at the origin, F at +-1.589634 angstrom on each axis; 'm the magnetic quantum number along the molecular axis' (p. 2), here z, a C4 axis"
}
}
Table 1 (continued, p. 8), SF6, 1t_1g(HOMO2), m = -5: C_{6+-5} ‘-0.75i’, C_{8+-5} ‘0.12i’, the lower sign (the record’s reading). READ ON THE PAGE, not from the library’s cells (J. C. Travers’s exception, TC-684; see the record’s notes). value: the real part; imaginary: the imaginary part.
zhao_2011/table1_SF6_homo2_mm3#
{
"id": "table1_SF6_homo2_mm3",
"material": "SF6",
"file": "SF6/zhao_2011__table1_SF6_homo2_mm3.csv",
"table": "tbl_4df3e935bc02",
"quantity": "tunnelling_structure_coefficient",
"abscissa": "label",
"columns": {
"imaginary": "1"
},
"use": "check",
"parameters": {
"model": "moadk",
"orbital": "1t1g HOMO2",
"m": -3,
"degenerate_orbitals": 3,
"normalisation": "Zhao et al. 2011 Eqs. (1)-(4), p. 2: Psi(r) = sum_lm F_lm(r) Y_lm(r^), F_lm(r -> inf) ~ C_lm r^(Z_c/kappa - 1) exp(-kappa r), Z_c the effective Coulomb charge, kappa = sqrt(2 I_p) with the GAUSSIAN HF binding energy in the fit (p. 3), atomic units; Y_lm with the Condon-Shortley phase (the sign of Q(l, m), Eq. (4)); C_lm complex (value the real part, column imaginary the imaginary part); the printed C_{l+-m} = -+a read as C_{l,+m} = -a, C_{l,-m} = +a (the upper sign for +m; not stated by the paper, see the record's notes); orbital normalisation not stated",
"frame": "the molecular frame (x, y, z) of Table 2 (p. 9): S at the origin, F at +-1.589634 angstrom on each axis; 'm the magnetic quantum number along the molecular axis' (p. 2), here z, a C4 axis"
}
}
Table 1 (continued, p. 8), SF6, 1t_1g(HOMO2), m = -3: C_{4+-3} ‘3.01i’, C_{6+-3} ‘-0.87i’, C_{8+-3} ‘0.13i’, the lower sign (the record’s reading). READ ON THE PAGE, not from the library’s cells (J. C. Travers’s exception, TC-684; see the record’s notes). value: the real part; imaginary: the imaginary part.
zhao_2011/table1_SF6_homo2_mm1#
{
"id": "table1_SF6_homo2_mm1",
"material": "SF6",
"file": "SF6/zhao_2011__table1_SF6_homo2_mm1.csv",
"table": "tbl_4df3e935bc02",
"quantity": "tunnelling_structure_coefficient",
"abscissa": "label",
"columns": {
"imaginary": "1"
},
"use": "check",
"parameters": {
"model": "moadk",
"orbital": "1t1g HOMO2",
"m": -1,
"degenerate_orbitals": 3,
"normalisation": "Zhao et al. 2011 Eqs. (1)-(4), p. 2: Psi(r) = sum_lm F_lm(r) Y_lm(r^), F_lm(r -> inf) ~ C_lm r^(Z_c/kappa - 1) exp(-kappa r), Z_c the effective Coulomb charge, kappa = sqrt(2 I_p) with the GAUSSIAN HF binding energy in the fit (p. 3), atomic units; Y_lm with the Condon-Shortley phase (the sign of Q(l, m), Eq. (4)); C_lm complex (value the real part, column imaginary the imaginary part); the printed C_{l+-m} = -+a read as C_{l,+m} = -a, C_{l,-m} = +a (the upper sign for +m; not stated by the paper, see the record's notes); orbital normalisation not stated",
"frame": "the molecular frame (x, y, z) of Table 2 (p. 9): S at the origin, F at +-1.589634 angstrom on each axis; 'm the magnetic quantum number along the molecular axis' (p. 2), here z, a C4 axis"
}
}
Table 1 (continued, p. 8), SF6, 1t_1g(HOMO2), m = -1: C_{4+-1} ‘7.98i’, C_{6+-1} ‘0.55i’, C_{8+-1} ‘0.37i’, the lower sign (the record’s reading). READ ON THE PAGE, not from the library’s cells (J. C. Travers’s exception, TC-684; see the record’s notes). value: the real part; imaginary: the imaginary part.
zhao_2011/table1_SF6_homo2_mp1#
{
"id": "table1_SF6_homo2_mp1",
"material": "SF6",
"file": "SF6/zhao_2011__table1_SF6_homo2_mp1.csv",
"table": "tbl_4df3e935bc02",
"quantity": "tunnelling_structure_coefficient",
"abscissa": "label",
"columns": {
"imaginary": "1"
},
"use": "check",
"parameters": {
"model": "moadk",
"orbital": "1t1g HOMO2",
"m": 1,
"degenerate_orbitals": 3,
"normalisation": "Zhao et al. 2011 Eqs. (1)-(4), p. 2: Psi(r) = sum_lm F_lm(r) Y_lm(r^), F_lm(r -> inf) ~ C_lm r^(Z_c/kappa - 1) exp(-kappa r), Z_c the effective Coulomb charge, kappa = sqrt(2 I_p) with the GAUSSIAN HF binding energy in the fit (p. 3), atomic units; Y_lm with the Condon-Shortley phase (the sign of Q(l, m), Eq. (4)); C_lm complex (value the real part, column imaginary the imaginary part); the printed C_{l+-m} = -+a read as C_{l,+m} = -a, C_{l,-m} = +a (the upper sign for +m; not stated by the paper, see the record's notes); orbital normalisation not stated",
"frame": "the molecular frame (x, y, z) of Table 2 (p. 9): S at the origin, F at +-1.589634 angstrom on each axis; 'm the magnetic quantum number along the molecular axis' (p. 2), here z, a C4 axis"
}
}
Table 1 (continued, p. 8), SF6, 1t_1g(HOMO2), m = +1: C_{4+-1} ‘7.98i’, C_{6+-1} ‘0.55i’, C_{8+-1} ‘0.37i’, the upper sign (the record’s reading). READ ON THE PAGE, not from the library’s cells (J. C. Travers’s exception, TC-684; see the record’s notes). value: the real part; imaginary: the imaginary part.
zhao_2011/table1_SF6_homo2_mp3#
{
"id": "table1_SF6_homo2_mp3",
"material": "SF6",
"file": "SF6/zhao_2011__table1_SF6_homo2_mp3.csv",
"table": "tbl_4df3e935bc02",
"quantity": "tunnelling_structure_coefficient",
"abscissa": "label",
"columns": {
"imaginary": "1"
},
"use": "check",
"parameters": {
"model": "moadk",
"orbital": "1t1g HOMO2",
"m": 3,
"degenerate_orbitals": 3,
"normalisation": "Zhao et al. 2011 Eqs. (1)-(4), p. 2: Psi(r) = sum_lm F_lm(r) Y_lm(r^), F_lm(r -> inf) ~ C_lm r^(Z_c/kappa - 1) exp(-kappa r), Z_c the effective Coulomb charge, kappa = sqrt(2 I_p) with the GAUSSIAN HF binding energy in the fit (p. 3), atomic units; Y_lm with the Condon-Shortley phase (the sign of Q(l, m), Eq. (4)); C_lm complex (value the real part, column imaginary the imaginary part); the printed C_{l+-m} = -+a read as C_{l,+m} = -a, C_{l,-m} = +a (the upper sign for +m; not stated by the paper, see the record's notes); orbital normalisation not stated",
"frame": "the molecular frame (x, y, z) of Table 2 (p. 9): S at the origin, F at +-1.589634 angstrom on each axis; 'm the magnetic quantum number along the molecular axis' (p. 2), here z, a C4 axis"
}
}
Table 1 (continued, p. 8), SF6, 1t_1g(HOMO2), m = +3: C_{4+-3} ‘3.01i’, C_{6+-3} ‘-0.87i’, C_{8+-3} ‘0.13i’, the upper sign (the record’s reading). READ ON THE PAGE, not from the library’s cells (J. C. Travers’s exception, TC-684; see the record’s notes). value: the real part; imaginary: the imaginary part.
zhao_2011/table1_SF6_homo2_mp5#
{
"id": "table1_SF6_homo2_mp5",
"material": "SF6",
"file": "SF6/zhao_2011__table1_SF6_homo2_mp5.csv",
"table": "tbl_4df3e935bc02",
"quantity": "tunnelling_structure_coefficient",
"abscissa": "label",
"columns": {
"imaginary": "1"
},
"use": "check",
"parameters": {
"model": "moadk",
"orbital": "1t1g HOMO2",
"m": 5,
"degenerate_orbitals": 3,
"normalisation": "Zhao et al. 2011 Eqs. (1)-(4), p. 2: Psi(r) = sum_lm F_lm(r) Y_lm(r^), F_lm(r -> inf) ~ C_lm r^(Z_c/kappa - 1) exp(-kappa r), Z_c the effective Coulomb charge, kappa = sqrt(2 I_p) with the GAUSSIAN HF binding energy in the fit (p. 3), atomic units; Y_lm with the Condon-Shortley phase (the sign of Q(l, m), Eq. (4)); C_lm complex (value the real part, column imaginary the imaginary part); the printed C_{l+-m} = -+a read as C_{l,+m} = -a, C_{l,-m} = +a (the upper sign for +m; not stated by the paper, see the record's notes); orbital normalisation not stated",
"frame": "the molecular frame (x, y, z) of Table 2 (p. 9): S at the origin, F at +-1.589634 angstrom on each axis; 'm the magnetic quantum number along the molecular axis' (p. 2), here z, a C4 axis"
}
}
Table 1 (continued, p. 8), SF6, 1t_1g(HOMO2), m = +5: C_{6+-5} ‘-0.75i’, C_{8+-5} ‘0.12i’, the upper sign (the record’s reading). READ ON THE PAGE, not from the library’s cells (J. C. Travers’s exception, TC-684; see the record’s notes). value: the real part; imaginary: the imaginary part.
zhao_2011/table1_SF6_homo2_mp7#
{
"id": "table1_SF6_homo2_mp7",
"material": "SF6",
"file": "SF6/zhao_2011__table1_SF6_homo2_mp7.csv",
"table": "tbl_4df3e935bc02",
"quantity": "tunnelling_structure_coefficient",
"abscissa": "label",
"columns": {
"imaginary": "1"
},
"use": "check",
"parameters": {
"model": "moadk",
"orbital": "1t1g HOMO2",
"m": 7,
"degenerate_orbitals": 3,
"normalisation": "Zhao et al. 2011 Eqs. (1)-(4), p. 2: Psi(r) = sum_lm F_lm(r) Y_lm(r^), F_lm(r -> inf) ~ C_lm r^(Z_c/kappa - 1) exp(-kappa r), Z_c the effective Coulomb charge, kappa = sqrt(2 I_p) with the GAUSSIAN HF binding energy in the fit (p. 3), atomic units; Y_lm with the Condon-Shortley phase (the sign of Q(l, m), Eq. (4)); C_lm complex (value the real part, column imaginary the imaginary part); the printed C_{l+-m} = -+a read as C_{l,+m} = -a, C_{l,-m} = +a (the upper sign for +m; not stated by the paper, see the record's notes); orbital normalisation not stated",
"frame": "the molecular frame (x, y, z) of Table 2 (p. 9): S at the origin, F at +-1.589634 angstrom on each axis; 'm the magnetic quantum number along the molecular axis' (p. 2), here z, a C4 axis"
}
}
Table 1 (continued, p. 8), SF6, 1t_1g(HOMO2), m = +7: C_{8+-7} ‘0.10i’, the upper sign (the record’s reading). READ ON THE PAGE, not from the library’s cells (J. C. Travers’s exception, TC-684; see the record’s notes). value: the real part; imaginary: the imaginary part.
zhao_2011/table1_SF6_homo3_mm8#
{
"id": "table1_SF6_homo3_mm8",
"material": "SF6",
"file": "SF6/zhao_2011__table1_SF6_homo3_mm8.csv",
"table": "tbl_4df3e935bc02",
"quantity": "tunnelling_structure_coefficient",
"abscissa": "label",
"columns": {
"imaginary": "1"
},
"use": "check",
"parameters": {
"model": "moadk",
"orbital": "1t1g HOMO3",
"m": -8,
"degenerate_orbitals": 3,
"normalisation": "Zhao et al. 2011 Eqs. (1)-(4), p. 2: Psi(r) = sum_lm F_lm(r) Y_lm(r^), F_lm(r -> inf) ~ C_lm r^(Z_c/kappa - 1) exp(-kappa r), Z_c the effective Coulomb charge, kappa = sqrt(2 I_p) with the GAUSSIAN HF binding energy in the fit (p. 3), atomic units; Y_lm with the Condon-Shortley phase (the sign of Q(l, m), Eq. (4)); C_lm complex (value the real part, column imaginary the imaginary part); the printed C_{l+-m} = -+a read as C_{l,+m} = -a, C_{l,-m} = +a (the upper sign for +m; not stated by the paper, see the record's notes); orbital normalisation not stated",
"frame": "the molecular frame (x, y, z) of Table 2 (p. 9): S at the origin, F at +-1.589634 angstrom on each axis; 'm the magnetic quantum number along the molecular axis' (p. 2), here z, a C4 axis"
}
}
Table 1 (continued, p. 8), SF6, 1t_1g(HOMO3), m = -8: C_{8+-8} ‘+-0.40i’, C_{10+-8} ‘-+0.02i’, the lower sign (the record’s reading). READ ON THE PAGE, not from the library’s cells (J. C. Travers’s exception, TC-684; see the record’s notes). value: the real part; imaginary: the imaginary part.
zhao_2011/table1_SF6_homo3_mm4#
{
"id": "table1_SF6_homo3_mm4",
"material": "SF6",
"file": "SF6/zhao_2011__table1_SF6_homo3_mm4.csv",
"table": "tbl_4df3e935bc02",
"quantity": "tunnelling_structure_coefficient",
"abscissa": "label",
"columns": {
"imaginary": "1"
},
"use": "check",
"parameters": {
"model": "moadk",
"orbital": "1t1g HOMO3",
"m": -4,
"degenerate_orbitals": 3,
"normalisation": "Zhao et al. 2011 Eqs. (1)-(4), p. 2: Psi(r) = sum_lm F_lm(r) Y_lm(r^), F_lm(r -> inf) ~ C_lm r^(Z_c/kappa - 1) exp(-kappa r), Z_c the effective Coulomb charge, kappa = sqrt(2 I_p) with the GAUSSIAN HF binding energy in the fit (p. 3), atomic units; Y_lm with the Condon-Shortley phase (the sign of Q(l, m), Eq. (4)); C_lm complex (value the real part, column imaginary the imaginary part); the printed C_{l+-m} = -+a read as C_{l,+m} = -a, C_{l,-m} = +a (the upper sign for +m; not stated by the paper, see the record's notes); orbital normalisation not stated",
"frame": "the molecular frame (x, y, z) of Table 2 (p. 9): S at the origin, F at +-1.589634 angstrom on each axis; 'm the magnetic quantum number along the molecular axis' (p. 2), here z, a C4 axis"
}
}
Table 1 (continued, p. 8), SF6, 1t_1g(HOMO3), m = -4: C_{4+-4} ‘+-8.53i’, C_{6+-4} ‘-+1.28i’, C_{8+-4} ‘+-0.13i’, C_{10+-4} ‘-+0.01i’, the lower sign (the record’s reading). READ ON THE PAGE, not from the library’s cells (J. C. Travers’s exception, TC-684; see the record’s notes). value: the real part; imaginary: the imaginary part.
zhao_2011/table1_SF6_homo3_mp4#
{
"id": "table1_SF6_homo3_mp4",
"material": "SF6",
"file": "SF6/zhao_2011__table1_SF6_homo3_mp4.csv",
"table": "tbl_4df3e935bc02",
"quantity": "tunnelling_structure_coefficient",
"abscissa": "label",
"columns": {
"imaginary": "1"
},
"use": "check",
"parameters": {
"model": "moadk",
"orbital": "1t1g HOMO3",
"m": 4,
"degenerate_orbitals": 3,
"normalisation": "Zhao et al. 2011 Eqs. (1)-(4), p. 2: Psi(r) = sum_lm F_lm(r) Y_lm(r^), F_lm(r -> inf) ~ C_lm r^(Z_c/kappa - 1) exp(-kappa r), Z_c the effective Coulomb charge, kappa = sqrt(2 I_p) with the GAUSSIAN HF binding energy in the fit (p. 3), atomic units; Y_lm with the Condon-Shortley phase (the sign of Q(l, m), Eq. (4)); C_lm complex (value the real part, column imaginary the imaginary part); the printed C_{l+-m} = -+a read as C_{l,+m} = -a, C_{l,-m} = +a (the upper sign for +m; not stated by the paper, see the record's notes); orbital normalisation not stated",
"frame": "the molecular frame (x, y, z) of Table 2 (p. 9): S at the origin, F at +-1.589634 angstrom on each axis; 'm the magnetic quantum number along the molecular axis' (p. 2), here z, a C4 axis"
}
}
Table 1 (continued, p. 8), SF6, 1t_1g(HOMO3), m = +4: C_{4+-4} ‘+-8.53i’, C_{6+-4} ‘-+1.28i’, C_{8+-4} ‘+-0.13i’, C_{10+-4} ‘-+0.01i’, the upper sign (the record’s reading). READ ON THE PAGE, not from the library’s cells (J. C. Travers’s exception, TC-684; see the record’s notes). value: the real part; imaginary: the imaginary part.
zhao_2011/table1_SF6_homo3_mp8#
{
"id": "table1_SF6_homo3_mp8",
"material": "SF6",
"file": "SF6/zhao_2011__table1_SF6_homo3_mp8.csv",
"table": "tbl_4df3e935bc02",
"quantity": "tunnelling_structure_coefficient",
"abscissa": "label",
"columns": {
"imaginary": "1"
},
"use": "check",
"parameters": {
"model": "moadk",
"orbital": "1t1g HOMO3",
"m": 8,
"degenerate_orbitals": 3,
"normalisation": "Zhao et al. 2011 Eqs. (1)-(4), p. 2: Psi(r) = sum_lm F_lm(r) Y_lm(r^), F_lm(r -> inf) ~ C_lm r^(Z_c/kappa - 1) exp(-kappa r), Z_c the effective Coulomb charge, kappa = sqrt(2 I_p) with the GAUSSIAN HF binding energy in the fit (p. 3), atomic units; Y_lm with the Condon-Shortley phase (the sign of Q(l, m), Eq. (4)); C_lm complex (value the real part, column imaginary the imaginary part); the printed C_{l+-m} = -+a read as C_{l,+m} = -a, C_{l,-m} = +a (the upper sign for +m; not stated by the paper, see the record's notes); orbital normalisation not stated",
"frame": "the molecular frame (x, y, z) of Table 2 (p. 9): S at the origin, F at +-1.589634 angstrom on each axis; 'm the magnetic quantum number along the molecular axis' (p. 2), here z, a C4 axis"
}
}
Table 1 (continued, p. 8), SF6, 1t_1g(HOMO3), m = +8: C_{8+-8} ‘+-0.40i’, C_{10+-8} ‘-+0.02i’, the upper sign (the record’s reading). READ ON THE PAGE, not from the library’s cells (J. C. Travers’s exception, TC-684; see the record’s notes). value: the real part; imaginary: the imaginary part.
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.