jagau_2016#
T.-C. Jagau, “Investigating tunnel and above-barrier ionization using complex-scaled coupled-cluster theory”, J. Chem. Phys. 145, 204115 (2016)
Source record · Catalogue · Review register
DOI: 10.1063/1.4967961
Source kind: theory
Recorded technique: Static-field ionisation rates from complex-scaled quantum chemistry in Gaussian basis sets (Q-Chem): the Hamiltonian with the static field F is complex scaled, and the ground state becomes a resonance of energy E_res = E - i Gamma/2 (Eq. (4), p. 3); Gamma is the ionisation rate. Levels of theory: complex-scaled Hartree-Fock (cs-HF), second-order perturbation theory (cs-MP2) and coupled cluster with singles and doubles (cs-CCSD), which for helium is full configuration interaction (cs-FCI). ‘In the cs-MP2 and cs-CCSD calculations, all electrons were always included in the correlation treatment’ (p. 6). Basis sets: aug-cc-pVQZ+3s3p3d3f for He, aug-cc-pCVQZ+3s3p3d3f for Ne and Ar (p. 6), the added diffuse functions even-tempered with a factor of 2.0 (ref. 94). The resonance energy is taken at the scaling angle of the stationary point of the trajectory E(theta), after the correction of Eq. (12) for the imaginary part that the field-free energy acquires in a finite basis (pp. 5-6). Non-relativistic: the ion has one threshold.
Materials in structured entries: Ar, He, Ne
Dataset quantities: ionization_rate
Contents: 9 datasets; 0 formulas.
Curation notes#
Pages are the article’s pdf pages (pdf page 1 is the publisher’s cover) and, for the supplementary material, its own pdf pages (‘SM p.’). The supplement is in the library as supplement_01 of the paper’s directory; the tables named by the datasets are under its tables/.
WHAT IS TAKEN. The rates Gamma (au) against the field F (au) of Tables S3 (He, SM p. 6), S4 (Ne, SM p. 7) and S5 (Ar, SM p. 7), at the three levels of theory: nine datasets. Every cell of the three tables was checked against the table images (2026-09-28): they agree. ‘See supplementary material for numerical values corresponding to Figures 3-8’ (p. 13): the tables are the numbers of Figs. 3, 6 and 7. A dash is printed where no value was obtained (HF for He at 0.10 au, for Ne at 0.08 au and for Ar at 0.05 au; MP2 for Ne at 0.08 au) and is skipped. Rates are wavelength_nm = inf, polarization = static.
WHAT THE RATES COUNT. The width of the N-electron ground state: the total rate of single ionisation of the atom, all electrons and all channels together, not a per-orbital rate. To compare with a one-electron rate, the latter is to be multiplied by the number of electrons that ionise (optmat’s effective number of electrons, TC-658).
ACCURACY (quoted; no uncertainty is given for any tabulated value). Conclusions (p. 13): ‘strong-field ionization rates from complex-scaled CCSD calculations are in excellent agreement with reference data if appropriate Gaussian basis sets are used. Only for ionization rates below ca. 10^-6 a.u., the current approach becomes impractical as more and more diffuse basis functions are required’. Basis set, from hydrogen and helium (p. 6): ‘Ionization rates are more sensitive towards the basis set than Stark shifts’; for helium ‘aug-cc-pVQZ+6s6p6d6f matches reference data obtained with cs-FCI in a Hylleraas basis set [Scrinzi et al. 1999] and from a time-dependent approach [Parker et al. 2009] within 1%-2%, whereas aug-cc-pVTZ+6s6p6d values deviate by ~5%’; ‘limiting the diffuse part of the basis set to 3 instead of 6 s, p, d, and f functions hardly makes an impact on the ionization rate’. The correction of Eq. (12) (p. 6): ‘the computation of ionization rates below ~10^-3 a.u. is often impossible without applying Eq. (12)’; at F = 0.2 au for He it ‘amounts to 5%’ and at 0.3 au ‘it is below 1%’. Table S2 (SM p. 5; not taken) shows what this means at low field for helium: at F = 0.10 au the basis of Table S3 gives 0.00000232 and the one with six diffuse functions 0.00000348, against 0.00000288 (Scrinzi et al.) and 0.00000294 (Parker et al.); at 0.12 au 0.00003234 and 0.00003144 against 0.0000362 and 0.00003683; at 0.14 au and from 0.20 to 0.50 au the basis of Table S3 is within 2.5 % of Scrinzi et al., and 8 % and 6 % above them at 0.16 and 0.18 au. No such comparison of basis sets is given for Ne or Ar. For Ne and Ar (p. 10): ‘good agreement is obtained for both Ne and Ar between CCSD ionization rates and values from the haCC approach’ (majety_2015, whose Ne and Ar rates are in a figure only).
DOUBT. The low-field rates of Ne and Ar are not smooth in F: the CCSD rate of Ne rises by 3.8 from 0.10 to 0.11 au and by 2.1 from 0.11 to 0.12 au, where optmat’s default model gives 3.0 and 2.5 (computed 2026-09-28); the CCSD rate of Ar at 0.05 au, 0.00004270, is 3.7 times the haCC(4) rate read from majety_2015’s Fig. 1. These are rates of 1e-5 au and below, near the limit of 1e-6 au that the paper states, and optmat’s comparison gives them no weight below 0.14 au (Ne) and 0.07 au (Ar) (TC-669). The values are as printed; nothing is corrected.
NOT TAKEN. The Stark shifts of the same tables (no quantity holds them; they are in the files’ printed cells). Table S1 (H) and Table S2 (He, four basis sets, with the rates of Scrinzi et al. 1999 and Parker et al. 2009 reproduced): a study of basis sets, quoted above. Tables S6-S8 (Li, Be, C: not optmat’s gases). Tables S9-S14 (dipole and second moments).
Recorded bibliographic identity status: VALIDATED. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
jagau_2016/tableS3_hf_He#
{
"id": "tableS3_hf_He",
"material": "He",
"file": "He/jagau_2016__tableS3_hf_He.csv",
"table": "tbl_835beff31b7f",
"quantity": "ionization_rate",
"unit": "au",
"abscissa": "field",
"abscissa_unit": "au",
"use": "check",
"parameters": {
"wavelength_nm": Infinity,
"polarization": "static",
"method": "cs-HF/aug-cc-pVQZ+3s3p3d3f"
}
}
Table S3 (SM p. 6), column Gamma, cs-HF, basis aug-cc-pVQZ+3s3p3d3f: complex-scaled Hartree-Fock: no electron correlation. A step of the paper’s study of correlation, not a reference. Rate of the atom (the width Gamma of the complex-scaled ground state, E_res = E - i Gamma/2), au, against F in au, 0.10 to 0.50 au. No value at 0.10 au (a dash). No uncertainty is stated.
jagau_2016/tableS3_mp2_He#
{
"id": "tableS3_mp2_He",
"material": "He",
"file": "He/jagau_2016__tableS3_mp2_He.csv",
"table": "tbl_835beff31b7f",
"quantity": "ionization_rate",
"unit": "au",
"abscissa": "field",
"abscissa_unit": "au",
"use": "check",
"parameters": {
"wavelength_nm": Infinity,
"polarization": "static",
"method": "cs-MP2/aug-cc-pVQZ+3s3p3d3f"
}
}
Table S3 (SM p. 6), column Gamma, cs-MP2, basis aug-cc-pVQZ+3s3p3d3f: complex-scaled second-order perturbation theory. ‘MP2 overestimates the correlation contribution at all field strengths’ (p. 10, of Ne and Ar). A step of the paper’s study of correlation, not a reference. Rate of the atom (the width Gamma of the complex-scaled ground state, E_res = E - i Gamma/2), au, against F in au, 0.10 to 0.50 au. No uncertainty is stated.
jagau_2016/tableS3_fci_He#
{
"id": "tableS3_fci_He",
"material": "He",
"file": "He/jagau_2016__tableS3_fci_He.csv",
"table": "tbl_835beff31b7f",
"quantity": "ionization_rate",
"unit": "au",
"abscissa": "field",
"abscissa_unit": "au",
"use": "primary",
"parameters": {
"wavelength_nm": Infinity,
"polarization": "static",
"method": "cs-FCI/aug-cc-pVQZ+3s3p3d3f"
}
}
Table S3 (SM p. 6), column Gamma, cs-FCI, basis aug-cc-pVQZ+3s3p3d3f: complex-scaled full configuration interaction (‘For He, CCSD is equivalent to FCI’, p. 7): exact in the basis. In this basis the rate is within 2.5 % of Scrinzi et al.’s (1999) at 0.14 au and from 0.20 to 0.50 au, 8 % and 6 % above it at 0.16 and 0.18 au, and 19 % and 11 % below it at 0.10 and 0.12 au (Table S2; see the record’s notes). Rate of the atom (the width Gamma of the complex-scaled ground state, E_res = E - i Gamma/2), au, against F in au, 0.10 to 0.50 au. No uncertainty is stated.
jagau_2016/tableS4_hf_Ne#
{
"id": "tableS4_hf_Ne",
"material": "Ne",
"file": "Ne/jagau_2016__tableS4_hf_Ne.csv",
"table": "tbl_bdfc58139762",
"quantity": "ionization_rate",
"unit": "au",
"abscissa": "field",
"abscissa_unit": "au",
"use": "check",
"parameters": {
"wavelength_nm": Infinity,
"polarization": "static",
"method": "cs-HF/aug-cc-pCVQZ+3s3p3d3f"
}
}
Table S4 (SM p. 7), column Gamma, cs-HF, basis aug-cc-pCVQZ+3s3p3d3f: complex-scaled Hartree-Fock: no electron correlation. A step of the paper’s study of correlation, not a reference. Rate of the atom (the width Gamma of the complex-scaled ground state, E_res = E - i Gamma/2), au, against F in au, 0.08 to 0.24 au. No value at 0.08 au (a dash). No uncertainty is stated.
jagau_2016/tableS4_mp2_Ne#
{
"id": "tableS4_mp2_Ne",
"material": "Ne",
"file": "Ne/jagau_2016__tableS4_mp2_Ne.csv",
"table": "tbl_bdfc58139762",
"quantity": "ionization_rate",
"unit": "au",
"abscissa": "field",
"abscissa_unit": "au",
"use": "check",
"parameters": {
"wavelength_nm": Infinity,
"polarization": "static",
"method": "cs-MP2/aug-cc-pCVQZ+3s3p3d3f"
}
}
Table S4 (SM p. 7), column Gamma, cs-MP2, basis aug-cc-pCVQZ+3s3p3d3f: complex-scaled second-order perturbation theory. ‘MP2 overestimates the correlation contribution at all field strengths’ (p. 10, of Ne and Ar). A step of the paper’s study of correlation, not a reference. Rate of the atom (the width Gamma of the complex-scaled ground state, E_res = E - i Gamma/2), au, against F in au, 0.08 to 0.24 au. No value at 0.08 au (a dash). No uncertainty is stated.
jagau_2016/tableS4_ccsd_Ne#
{
"id": "tableS4_ccsd_Ne",
"material": "Ne",
"file": "Ne/jagau_2016__tableS4_ccsd_Ne.csv",
"table": "tbl_bdfc58139762",
"quantity": "ionization_rate",
"unit": "au",
"abscissa": "field",
"abscissa_unit": "au",
"use": "primary",
"parameters": {
"wavelength_nm": Infinity,
"polarization": "static",
"method": "cs-CCSD/aug-cc-pCVQZ+3s3p3d3f"
}
}
Table S4 (SM p. 7), column Gamma, cs-CCSD, basis aug-cc-pCVQZ+3s3p3d3f: complex-scaled coupled cluster with singles and doubles, all electrons correlated: the paper’s result for the atom. Not smooth in F below 0.14 au (see the record’s notes, DOUBT). Rate of the atom (the width Gamma of the complex-scaled ground state, E_res = E - i Gamma/2), au, against F in au, 0.08 to 0.24 au. No uncertainty is stated.
jagau_2016/tableS5_hf_Ar#
{
"id": "tableS5_hf_Ar",
"material": "Ar",
"file": "Ar/jagau_2016__tableS5_hf_Ar.csv",
"table": "tbl_e8cea2aae6b7",
"quantity": "ionization_rate",
"unit": "au",
"abscissa": "field",
"abscissa_unit": "au",
"use": "check",
"parameters": {
"wavelength_nm": Infinity,
"polarization": "static",
"method": "cs-HF/aug-cc-pCVQZ+3s3p3d3f"
}
}
Table S5 (SM p. 7), column Gamma, cs-HF, basis aug-cc-pCVQZ+3s3p3d3f: complex-scaled Hartree-Fock: no electron correlation. A step of the paper’s study of correlation, not a reference. Rate of the atom (the width Gamma of the complex-scaled ground state, E_res = E - i Gamma/2), au, against F in au, 0.05 to 0.20 au. No value at 0.05 au (a dash). No uncertainty is stated.
jagau_2016/tableS5_mp2_Ar#
{
"id": "tableS5_mp2_Ar",
"material": "Ar",
"file": "Ar/jagau_2016__tableS5_mp2_Ar.csv",
"table": "tbl_e8cea2aae6b7",
"quantity": "ionization_rate",
"unit": "au",
"abscissa": "field",
"abscissa_unit": "au",
"use": "check",
"parameters": {
"wavelength_nm": Infinity,
"polarization": "static",
"method": "cs-MP2/aug-cc-pCVQZ+3s3p3d3f"
}
}
Table S5 (SM p. 7), column Gamma, cs-MP2, basis aug-cc-pCVQZ+3s3p3d3f: complex-scaled second-order perturbation theory. ‘MP2 overestimates the correlation contribution at all field strengths’ (p. 10, of Ne and Ar). A step of the paper’s study of correlation, not a reference. Rate of the atom (the width Gamma of the complex-scaled ground state, E_res = E - i Gamma/2), au, against F in au, 0.05 to 0.20 au. No uncertainty is stated.
jagau_2016/tableS5_ccsd_Ar#
{
"id": "tableS5_ccsd_Ar",
"material": "Ar",
"file": "Ar/jagau_2016__tableS5_ccsd_Ar.csv",
"table": "tbl_e8cea2aae6b7",
"quantity": "ionization_rate",
"unit": "au",
"abscissa": "field",
"abscissa_unit": "au",
"use": "primary",
"parameters": {
"wavelength_nm": Infinity,
"polarization": "static",
"method": "cs-CCSD/aug-cc-pCVQZ+3s3p3d3f"
}
}
Table S5 (SM p. 7), column Gamma, cs-CCSD, basis aug-cc-pCVQZ+3s3p3d3f: complex-scaled coupled cluster with singles and doubles, all electrons correlated: the paper’s result for the atom. The value at 0.05 au is 3.7 times majety_2015’s haCC(4) rate read from its figure (see the record’s notes, DOUBT). Rate of the atom (the width Gamma of the complex-scaled ground state, E_res = E - i Gamma/2), au, against F in au, 0.05 to 0.20 au. No uncertainty is stated.
Formulas#
No formulas are recorded.
Corrections#
No dataset errata are recorded in this source record.
Formula corrections, where recorded, appear with their formulas above. Curation notes may also discuss corrections or unresolved interpretation. Consult the review register for the checks and decisions.