pathak_2020#
H. Pathak, T. Sato and K. L. Ishikawa, “Time-dependent optimized coupled-cluster method for multielectron dynamics. III. A second-order many-body perturbation approximation”, J. Chem. Phys. 153, 034110 (2020)
Source record · Catalogue · Review register
DOI: 10.1063/5.0008789
Source kind: theory
Recorded technique: Time-dependent many-electron calculations of Ar in a laser pulse (Sec. III B, PDF p. 6): TDHF, TD-OMP2 (time-dependent orbital-optimised second-order many-body perturbation theory, introduced here), TD-OCCD (time-dependent optimised coupled-cluster doubles) and TD-CASSCF, with the dipole interaction ‘in the velocity gauge’ (Eq. 28), ‘the 1s2s2p core is kept frozen, and the dynamics of remaining 8 electrons are actively taken into account with 4 (TDHF) or 13 (TD-OMP2, TD-OCCD, and TD-CASSCF) active orbitals’. Within one active space TD-CASSCF is the benchmark (‘TD-CASSCF produces highly accurate results’). Orbitals on a spherical FEDVR basis: l_max = 72 (converged at the TDHF level), 78 finite elements of 23 DVR functions each, 0 < r < R_max = 300, a cos^(1/4) mask switched on at 240; fourth-order exponential Runge-Kutta, 20 000 time steps per optical cycle; ‘The simulations are continued after the end of pulse for further 6000 time steps’ (0.3 cycle). And a single-active-electron (SAE) calculation (Eqs. 30-32): the effective Hamiltonian h_eff = p^2/2 + V_eff(r) with V_eff(r) = -(1/r){1 + A e^(-r) + (Z - 1 - A) e^(-B r)}, ‘with A = 5.4 and B = 3.682 for Ar’ (refs. 65, 66: Muller and Kooiman, Phys. Rev. Lett. 81, 1207 (1998); Schiessl et al., Phys. Rev. A 74, 053412 (2006)), which ‘correctly supports 1s, 2s, 2p, 3s, and 3p bound orbitals, with the 3p orbital energy of -15.82 eV with the present FEDVR basis’; i d|chi>/dt = Q{h_eff + A(t) p_z}|chi> (Eq. 32) ‘starting from the 3p0 orbital’, the projector Q = 1 - sum_j |phi_j><phi_j| over the 1s, 2s, 2p, 3s and 3p+-1 orbitals (each multiplied by the gauge factor e^(-iA(t)z)) keeping chi orthogonal to them. The pulse (Eq. 29): E(t) = E0 sin(omega_0 t) sin^2(pi t / 3T) for 0 <= t <= 3T and zero otherwise, 1200 nm, ‘the period T = 2 pi / omega_0 ~ 4.00 fs, and the peak intensity I0 = E0^2’, 1, 2 and 4 x 10^14 W/cm^2, ‘linearly polarized in the z direction’. The single-ionisation probability (Fig. 2) is ‘evaluated as the probability of finding an electron outside a sphere of 20 a.u. radius’ (p. 7): for the many-electron methods from the reduced density matrices (the defining formula is not printed here); for SAE the paper does not say how (presumably 1 - the norm of chi within 20 a.u.).
Materials in structured entries: Ar
Dataset quantities: ionization_yield
Contents: 5 datasets; 0 formulas.
Curation notes#
PDF page 1 is AIP’s cover page; journal pp. 034110-1 to -9 are PDF pages 2-10, so the journal page is 034110-(PDF page - 1). Identity checked on the first page (PDF p. 2: ‘J. Chem. Phys. 153, 034110 (2020); doi: 10.1063/5.0008789’, Himadri Pathak, Takeshi Sato and Kenichi L. Ishikawa, The University of Tokyo; submitted 25 March 2020, accepted 22 June 2020, published online 16 July 2020) on 2026-10-06.
EXTRACTED (tools/extract/pathak_2020.py). The paper prints no number of the time-dependent calculations and has no supplement: the single-ionisation probabilities are only in Fig. 2 (PDF p. 7, journal 034110-6), a vector drawing (no image on the page), read from the PDF by data rule 8 (TC-699). The library’s figure fig_37c2c1bdbe02 lost panel (a) (1e14 W/cm^2); the PDF has it and the script reads all three panels from the PDF. Each method’s curve is one filled outline (the stroke converted to a polygon of lines and Beziers), coloured as panel (c)’s legend shows (TDHF blue, TD-OMP2 green, TD-OCCD red, TD-CASSCF thick black, SAE black dotted; the legend’s order checked); the line’s centre at a time is the mid-point of the outline’s two crossings of that vertical, the dotted line’s interpolated between its dots’ centres. The curves that overlap on the page (SAE on TDHF in (a); TD-CASSCF and TD-OCCD close in (a) and (b)) are separate objects in the drawing, so each is read on its own. Axes calibrated from the drawing’s own tick marks (inward, on all four edges, the top and right repeating the bottom and left within 0.01 pt): time 0 to 500 au (29.831 pt per 100 au), probability (a) 0 to 0.00075 (1.24e-5 per pt), (b) 0 to 0.03 (4.70e-4 per pt), (c) 0 to 0.4 (5.28e-3 per pt), all linear; the worst tick residuals are below 0.0001 pt (x) and 0.0003, below 0.0001 and 0.0006 pt (y, panels a, b, c).
THE TIMES. The value taken is at the end of the pulse, t = 3T = 496.44 au (T = 2 pi / omega_0 at 1200 nm, 165.48 au; the paper’s ‘~4.00 fs’). Every curve starts at t = 0 (at zero probability, checked at 20 au within 0.05 pt) and ends at 546.08 au = 3.3T (found from the drawing: the solid outlines end half a line width, a projecting cap, beyond the line, at 546.08-546.53 au; the dotted lines’ last dots end within one dot period of it), the 6000 steps after the pulse. The value at the curve’s end is in each point’s printed cell: it differs from that at 3T by +0.02 to +0.36 % (TD-CASSCF at 4e14 W/cm^2, whose line oscillates there, by +0.36 %; between 3T and 3.3T the curves move within a band of 0.02 to 0.83 % of the value).
THE VALUES at 3T (at 3.3T): 1e14 W/cm^2: TDHF 4.487e-4 (4.502e-4), TD-OMP2 9.397e-4 (9.411e-4), TD-OCCD 6.864e-4 (6.88e-4), TD-CASSCF 7.255e-4 (7.264e-4), SAE 4.512e-4 (4.52e-4). 2e14: TDHF 0.02077 (0.02078), TD-OMP2 0.03561 (0.03569), TD-OCCD 0.02953 (0.02957), TD-CASSCF 0.03102 (0.03106), SAE 0.02225 (0.02229). 4e14: TDHF 0.2037 (0.2038), TD-OMP2 0.3995 (0.4), TD-OCCD 0.3044 (0.3053), TD-CASSCF 0.3401 (0.3413), SAE 0.2918 (0.292).
THE CHECKS (the script fails if one is missed), against what the text says of Fig. 2 (p. 7; it prints no number): ‘a systematic overestimation by TD-OMP2 and underestimation by TDHF in comparison to the TD-CASSCF result’ (TD-OMP2 > TD-CASSCF > TDHF in every panel, at 3T and at 3.3T; TD-OMP2 is 1.15-1.30 and TDHF 0.60-0.67 times TD-CASSCF); at the highest intensity ‘the SAE result is as accurate as the TD-OCCD one’ (4e14: SAE 0.858 and TD-OCCD 0.895 times TD-CASSCF; checked within 15 %, TDHF more than 30 % below). The extracted values, mapped back through the calibrations and overlaid on the rendered page, sit on every line at 3T and at its end (inspected 2026-10-06).
DIGITISING UNCERTAINTY: the outline’s centre is fixed to about 0.03 pt (the outline’s vertical width varies by 0.03 pt along the flat tails: 0.80-0.84 pt for the thin lines, 1.20-1.24 pt for TD-CASSCF), with tick residuals below 0.001 pt: 0.05 pt is 0.07 to 0.14 % of the values (36 to 230 pt above the zero tick). 0.5 % is stated, the source stating none. The value depends more on the time it is read at than on the reading: up to 0.9 % between 3T and 3.3T (above).
THE SAE CURVE: ONE ELECTRON OR TWO. The paper does not say how the SAE probability is normalised (whether one 3p0 electron’s probability is doubled, or counted for the six 3p electrons). What it says: SAE describes ‘tunneling the ionization of the single, most weakly bound electron (one of the 3p0 electrons in the present case)’ (p. 6), and one orbital chi is propagated (Eq. 32). The curve is one electron’s: the same potential and pulse run with one electron in tRecX (travers_2026_trecx, part M1(b), the probability outside 20 au at 3T, 5.060e-4, 0.02559, 0.3300) gives 1.12-1.15 times these SAE values (0.892, 0.869, 0.884 of it at 1, 2, 4e14 W/cm^2); twice one electron’s would be about 1.75 times it. The remaining 11-13 % is not explained here (the projector Q of Eq. 32, which forbids chi from the 1s, 2s, 2p, 3s and 3p+-1 orbitals, the FEDVR against tRecX’s discretisation, or the measure; the 3p energies agree, -15.82 eV both). Taken as the paper’s: electrons = ‘one active electron’.
THE PULSE. Eq. (29) is printed on the field, with a sine carrier and the sin^2 envelope spanning 3T foot to foot (its second ‘E(T) = 0 otherwise’ is a slip for E(t)); with it A(3T) = 0. pulse_fs is that total, 3T = 12.008 fs. The abscissa is I0 = E0^2, the caption’s peak intensity; the field’s largest magnitude is 0.9365 E0 (the carrier’s maximum is off the envelope’s peak).
NOT TAKEN: Fig. 1 (the dipole moments), Figs. 3-5 (the harmonic spectra), Table I (BH ground-state energies), Table II (computation times).
Recorded bibliographic identity status: VALIDATED. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
pathak_2020/fig2_tdhf_Ar#
{
"id": "fig2_tdhf_Ar",
"material": "Ar",
"file": "Ar/pathak_2020__fig2_tdhf_Ar.csv",
"table": "fig_37c2c1bdbe02",
"digitised": "vector",
"quantity": "ionization_yield",
"unit": "1",
"abscissa": "intensity",
"abscissa_unit": "W/cm2",
"use": "check",
"uncertainty": {
"relative": 0.005,
"level": "not stated"
},
"parameters": {
"wavelength_nm": 1200,
"pulse_fs": 12.008,
"pulse_fs_definition": "the total, foot-to-foot duration tau of the sin^2 envelope on the field: 3 cycles",
"polarization": "linear",
"pulse_envelope": "sin^2",
"envelope_of": "field",
"cep": "sine carrier",
"cep_definition": "E(t) = E0 sin(omega t) sin^2(pi t / tau), 0 <= t <= tau (Eq. 29)",
"measure": "the probability of finding an electron outside a sphere of R0 = 20 a.u., at t = 3T (from the reduced density matrices)",
"method": "TDHF, velocity gauge, 4 active orbitals (3s, 3p), FEDVR l_max = 72, R_max = 300 au",
"electrons": "eight valence electrons (3s2 3p6) active, the 1s2s2p core frozen"
}
}
Fig. 2(a)-(c), p. 7, TDHF (blue): the single-ionisation probability of Ar, ‘the probability of finding an electron outside a sphere of 20 a.u. radius’, at the end of the pulse, t = 3T, at 1, 2 and 4e14 W/cm^2: 4.487e-4, 0.02077, 0.2037, read from the vector drawing (the record’s notes); the value at the curve’s end, 3.3T, in each printed cell (4.502e-4, 0.02078, 0.2038). 0.62, 0.67, 0.60 times TD-CASSCF. 0.5 %: the digitising (0.07-0.14 %) rounded up; the paper states none (the record’s notes).
pathak_2020/fig2_tdomp2_Ar#
{
"id": "fig2_tdomp2_Ar",
"material": "Ar",
"file": "Ar/pathak_2020__fig2_tdomp2_Ar.csv",
"table": "fig_37c2c1bdbe02",
"digitised": "vector",
"quantity": "ionization_yield",
"unit": "1",
"abscissa": "intensity",
"abscissa_unit": "W/cm2",
"use": "check",
"uncertainty": {
"relative": 0.005,
"level": "not stated"
},
"parameters": {
"wavelength_nm": 1200,
"pulse_fs": 12.008,
"pulse_fs_definition": "the total, foot-to-foot duration tau of the sin^2 envelope on the field: 3 cycles",
"polarization": "linear",
"pulse_envelope": "sin^2",
"envelope_of": "field",
"cep": "sine carrier",
"cep_definition": "E(t) = E0 sin(omega t) sin^2(pi t / tau), 0 <= t <= tau (Eq. 29)",
"measure": "the probability of finding an electron outside a sphere of R0 = 20 a.u., at t = 3T (from the reduced density matrices)",
"method": "TD-OMP2 (time-dependent orbital-optimised second-order perturbation theory), velocity gauge, 13 active orbitals, FEDVR l_max = 72, R_max = 300 au",
"electrons": "all eight valence electrons (3s2 3p6) correlated in 13 orbitals, the 1s2s2p (Ne) core frozen"
}
}
Fig. 2(a)-(c), p. 7, TD-OMP2 (green): the single-ionisation probability of Ar, ‘the probability of finding an electron outside a sphere of 20 a.u. radius’, at the end of the pulse, t = 3T, at 1, 2 and 4e14 W/cm^2: 9.397e-4, 0.03561, 0.3995, read from the vector drawing (the record’s notes); the value at the curve’s end, 3.3T, in each printed cell (9.411e-4, 0.03569, 0.4). The paper’s new method, which ‘systematically’ overestimates: 1.30, 1.15, 1.17 times TD-CASSCF. 0.5 %: the digitising (0.07-0.14 %) rounded up; the paper states none (the record’s notes).
pathak_2020/fig2_tdoccd_Ar#
{
"id": "fig2_tdoccd_Ar",
"material": "Ar",
"file": "Ar/pathak_2020__fig2_tdoccd_Ar.csv",
"table": "fig_37c2c1bdbe02",
"digitised": "vector",
"quantity": "ionization_yield",
"unit": "1",
"abscissa": "intensity",
"abscissa_unit": "W/cm2",
"use": "check",
"uncertainty": {
"relative": 0.005,
"level": "not stated"
},
"parameters": {
"wavelength_nm": 1200,
"pulse_fs": 12.008,
"pulse_fs_definition": "the total, foot-to-foot duration tau of the sin^2 envelope on the field: 3 cycles",
"polarization": "linear",
"pulse_envelope": "sin^2",
"envelope_of": "field",
"cep": "sine carrier",
"cep_definition": "E(t) = E0 sin(omega t) sin^2(pi t / tau), 0 <= t <= tau (Eq. 29)",
"measure": "the probability of finding an electron outside a sphere of R0 = 20 a.u., at t = 3T (from the reduced density matrices)",
"method": "TD-OCCD (time-dependent optimised coupled-cluster doubles), velocity gauge, 13 active orbitals, FEDVR l_max = 72, R_max = 300 au",
"electrons": "all eight valence electrons (3s2 3p6) correlated in 13 orbitals, the 1s2s2p (Ne) core frozen"
}
}
Fig. 2(a)-(c), p. 7, TD-OCCD (red): the single-ionisation probability of Ar, ‘the probability of finding an electron outside a sphere of 20 a.u. radius’, at the end of the pulse, t = 3T, at 1, 2 and 4e14 W/cm^2: 6.864e-4, 0.02953, 0.3044, read from the vector drawing (the record’s notes); the value at the curve’s end, 3.3T, in each printed cell (6.88e-4, 0.02957, 0.3053). 0.95, 0.95, 0.90 times TD-CASSCF. 0.5 %: the digitising (0.07-0.14 %) rounded up; the paper states none (the record’s notes).
pathak_2020/fig2_tdcasscf_Ar#
{
"id": "fig2_tdcasscf_Ar",
"material": "Ar",
"file": "Ar/pathak_2020__fig2_tdcasscf_Ar.csv",
"table": "fig_37c2c1bdbe02",
"digitised": "vector",
"quantity": "ionization_yield",
"unit": "1",
"abscissa": "intensity",
"abscissa_unit": "W/cm2",
"use": "check",
"uncertainty": {
"relative": 0.005,
"level": "not stated"
},
"parameters": {
"wavelength_nm": 1200,
"pulse_fs": 12.008,
"pulse_fs_definition": "the total, foot-to-foot duration tau of the sin^2 envelope on the field: 3 cycles",
"polarization": "linear",
"pulse_envelope": "sin^2",
"envelope_of": "field",
"cep": "sine carrier",
"cep_definition": "E(t) = E0 sin(omega t) sin^2(pi t / tau), 0 <= t <= tau (Eq. 29)",
"measure": "the probability of finding an electron outside a sphere of R0 = 20 a.u., at t = 3T (from the reduced density matrices)",
"method": "TD-CASSCF (time-dependent complete-active-space self-consistent field), velocity gauge, 13 active orbitals, FEDVR l_max = 72, R_max = 300 au",
"electrons": "all eight valence electrons (3s2 3p6) correlated in 13 orbitals, the 1s2s2p (Ne) core frozen"
}
}
Fig. 2(a)-(c), p. 7, TD-CASSCF (thick black): the single-ionisation probability of Ar, ‘the probability of finding an electron outside a sphere of 20 a.u. radius’, at the end of the pulse, t = 3T, at 1, 2 and 4e14 W/cm^2: 7.255e-4, 0.03102, 0.3401, read from the vector drawing (the record’s notes); the value at the curve’s end, 3.3T, in each printed cell (7.264e-4, 0.03106, 0.3413; at 4e14 the line oscillates by 0.8 % after the pulse). The paper’s benchmark within the active space. 0.5 %: the digitising (0.07-0.14 %) rounded up; the paper states none (the record’s notes).
pathak_2020/fig2_sae_Ar#
{
"id": "fig2_sae_Ar",
"material": "Ar",
"file": "Ar/pathak_2020__fig2_sae_Ar.csv",
"table": "fig_37c2c1bdbe02",
"digitised": "vector",
"quantity": "ionization_yield",
"unit": "1",
"abscissa": "intensity",
"abscissa_unit": "W/cm2",
"use": "check",
"uncertainty": {
"relative": 0.005,
"level": "not stated"
},
"parameters": {
"wavelength_nm": 1200,
"pulse_fs": 12.008,
"pulse_fs_definition": "the total, foot-to-foot duration tau of the sin^2 envelope on the field: 3 cycles",
"polarization": "linear",
"pulse_envelope": "sin^2",
"envelope_of": "field",
"cep": "sine carrier",
"cep_definition": "E(t) = E0 sin(omega t) sin^2(pi t / tau), 0 <= t <= tau (Eq. 29)",
"measure": "the probability of finding an electron outside a sphere of R0 = 20 a.u., at t = 3T (how it is computed for SAE is not stated)",
"method": "SAE (Eqs. 30-32): i d|chi>/dt = Q{h_eff + A(t) p_z}|chi>, velocity gauge, Q projecting out 1s, 2s, 2p, 3s and 3p+-1 (with the gauge factor), FEDVR l_max = 72, R_max = 300 au",
"electrons": "one active electron (the paper does not state the normalisation; one electron's, by the comparison in the record's notes)",
"orbital": "3p0",
"m": 0,
"potential": "Muller and Kooiman 1998, Schiessl et al. 2006 (Eq. 31): V = -(1 + A exp(-r) + (Z - 1 - A) exp(-B r))/r, Z = 18, A = 5.4, B = 3.682",
"model_ionization_energy_au": 0.5814
}
}
Fig. 2(a)-(c), p. 7, SAE (black dotted): the single-active-electron probability of Ar, ‘the probability of finding an electron outside a sphere of 20 a.u. radius’, at the end of the pulse, t = 3T, at 1, 2 and 4e14 W/cm^2: 4.512e-4, 0.02225, 0.2918, read from the dots of the vector drawing (the record’s notes); the value at the dotted line’s end (its last dot, 540.8-546.1 au) in each printed cell (4.52e-4, 0.02229, 0.292). One electron’s probability (the record’s notes: not stated by the paper; the same potential and pulse with one electron in tRecX, travers_2026_trecx part M1(b), gives 1.12-1.15 times these). 0.62, 0.72, 0.86 times TD-CASSCF. 0.5 %: the digitising (0.07-0.14 %) rounded up; the paper states none (the record’s notes).
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.