yuen_2022 ========= C\. H\. Yuen and C\. D\. Lin, "Density\-matrix approach for sequential dissociative double ionization of molecules", Phys\. Rev\. A 106, 023120 \(2022\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1103/PhysRevA\.106\.023120 `__ **Source kind:** theory **Recorded technique:** Density\-matrix model of sequential double ionisation \(DM\-SDI\), Eqs\. \(1\)\: the neutral, the cation and the dication are separate open systems\. The neutral population decays by rate equations into the N2\+ X 2Sigma\_g\+, A 2Pi\_u and B 2Sigma\_u\+ states \(ionisation of the HOMO 3sigma\_g, HOMO\-1 1pi\_u and HOMO\-2 2sigma\_u\); the three cation states are coupled by the field through the von Neumann equation with a source term; the cation states ionise by rate equations into the eleven N2^2\+ states with two valence holes \(Table I\), which are not coupled to each other\. All rates are MO\-ADK \(Tong et al\. 2002\), with the structure parameters of N2 from Zhao et al\. 2010 \(zhao\_2010\) for the neutral and the same parameters for the cation's orbitals; the second ionisation energy is Table I's I\_p minus the cation state's ionisation energy\. Nuclei fixed at the neutral's equilibrium, R = 1\.09 angstrom \(p\. 3\); no coherence between charge states or between states populated by tunnelling\. Solved by the classic Runge\-Kutta method, averaged over isotropic alignment \(Eq\. 2\) and convolved with a Gaussian of sigma = 0\.28 eV for the KER spectrum \(Eq\. 3\)\. **Materials in structured entries:** N2, N2\+ **Dataset quantities:** ionization\_energy, kinetic\_energy\_release, transition\_dipole\_moment **Contents:** 6 datasets; 0 formulas. Curation notes -------------- The library holds the accepted manuscript \(CHORUS, 11 PDF pages; dated 23 August 2022, published 31 August 2022\); pages are cited as PDF pages\. Identity checked on PDF pp\. 1\-2 \(C\. H\. Yuen and C\. D\. Lin, J\. R\. Macdonald Laboratory, Kansas State University\) on 2026\-10\-09\. The register entry is TC\-955\. THE PULSE OF THE MODEL \(p\. 4\)\: E\(t\) = E0 exp\(\-2 ln 2 t^2 / Gamma^2\) cos\(omega t\), Gamma the intensity FWHM, fixed at 8 fs throughout \('a longer pulse would allow the nuclei to move appreciably'\); linear polarisation in the xz plane, the molecular axis along z\. Main results \(Figs\. 2, 3, 6\-8\)\: 800 nm, 1\.2e15 W/cm^2 peak, to compare with Voss et al\. 2004 \(800 nm, 8 fs, 1\.2e15 W/cm^2\)\. Fig\. 4 also 391 and 918 nm; Fig\. 5 the intensity dependence; Fig\. 7 a Gaussian\-beam volume average \(Eq\. 4\)\. 'the ratio between the 1st to 2nd peak in the spectrum changes by at most 2% and 1% for different pulse durations \(5 \- 8 fs\) and carrier\-envelop phases \(0 \- pi\)' \(p\. 7\)\. TABLE I \(p\. 5\)\: taken\. I\_p 'taken from Bhattacharya et al \[28\]' \(J\. Phys\. Chem\. A 125, 7778 \(2021\)\), measured from the neutral N2 ground state \('Vertical ionization energy to the N2^2\+ states'\); limits 'taken from Iwayama et al \[25\]' \(J\. Chem\. Phys\. 145, 034305 \(2016\)\), those of states 10 and 11 'identified from the PEC' of ref\. 28; KER the model's\. The limits are named, not given as energies\: I\_p \- KER is 38\.96 eV for every 3P \+ 3P row and 42\.76 eV for both 1D \+ 1D rows \(checked by the script\), so no dissociation\_energy dataset is made\. State 10 is printed 'm\.s\. / N\+\(1D\) \+ N\+\(1D\)' with a KER of 7\.81 eV; it is put with the 1D \+ 1D limit\. The text names the KER peaks of the spectrum\: 6\.77 eV \(mostly state 5\), 7\.58 eV \(states 6\-8\), 10\.16 eV \(state 9\) \(p\. 6\)\. TEXT VALUES \(taken as points\)\: the 'experimental ionization energy of 15\.58, 16\.93, and 18\.75 eV for HOMO, HOMO\-1, and HOMO\-2' \(p\. 4\), no reference given; the dipole couplings of the cation, 'd\_x = 0\.25 a0 \[29\]' between X and A and 'd\_z = 0\.75 a0 \[30\]' between X and B \(p\. 3; refs\. 29\-30 Langhoff, Bauschlicher and Partridge 1987, Langhoff and Bauschlicher 1988\)\. Also on p\. 4, not taken \(they are Table I's differences\)\: 'The ionization energy to state 6 from the A and from the B state are then 29\.49 and 27\.67 eV' = 46\.42 \- 16\.93 and 46\.42 \- 18\.75\. THE STRUCTURE PARAMETERS are not printed\: the paper uses zhao\_2010's for N2 and the same for the cation\. NO COUPLINGS BETWEEN DICATION STATES in this model; Jia et al\. 2024 \(jia\_2024\) add them and the vibrational spread of R\. FIGURES \(not digitised; vector drawings except Fig\. 1\)\: Fig\. 2 bottom, the angle\-averaged yields of the dissociative N2^2\+ states 5\-11 with and without the cation couplings \(800 nm, 8 fs, 1\.2e15 W/cm^2\), the populations of the dication left by the pulse; Fig\. 5, the angle\-averaged yield of states 1\-9 against peak intensity; Fig\. 3, the X, A, B populations against time at 45 degrees; Figs\. 2 top, 4, 6\-8, KER spectra \(wavelength, volume and alignment\)\. Fig\. 1 \(potential curves, from ref\. 28\) is a raster image\. **Recorded bibliographic identity status:** VALIDATED. This concerns identification of the source; it does not establish the scientific correctness of its contents. Datasets -------- yuen\_2022/table1\_ip ~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table1_ip", "material": "N2", "file": "N2/yuen_2022__table1_ip_N2.csv", "table": "tbl_076ba83089ee", "quantity": "ionization_energy", "unit": "eV", "abscissa": "label", "use": "reproduced", "reproduced_from": [ "D. Bhattacharya, K. R. Shamasundar and A. Emmanouilidou, J. Phys. Chem. A 125, 7778 (2021)" ], "parameters": { "kind": "vertical", "initial_state": "N2 X 1Sigma_g+", "final_state": "the N2^2+ state of the row" } } Table I, 'I\_p \(eV\)'\: the vertical double\-ionisation energy from the neutral ground state to each N2^2\+ state with two valence holes, at the neutral's equilibrium geometry \(R = 1\.09 angstrom, p\. 3\); rows are the table's index \(states 1\-11, used throughout the paper\), x the state; the configuration is in the printed cells\. States 1\-4 are metastable\. No uncertainty is stated\. yuen\_2022/table1\_ker\_3p3p ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table1_ker_3p3p", "material": "N2", "file": "N2/yuen_2022__table1_ker_3p3p_N2.csv", "table": "tbl_076ba83089ee", "quantity": "kinetic_energy_release", "unit": "eV", "abscissa": "label", "use": "check", "parameters": { "channel": "N2 -> N2^2+ (the state of the row) -> N+(3P) + N+(3P)", "kind": "calculated", "state": "the N2^2+ state of the row" } } Table I, 'KER \(eV\)' of states 5\-9 \(rows\: the table's index\), which dissociate to N\+\(3P\) \+ N\+\(3P\) \(limit from Iwayama et al\. 2016\)\. The KER is the model's\: I\_p of the row less the limit, 38\.96 eV above the neutral as implied by every row \(the limit's energy is not printed\)\. Vertical at R = 1\.09 angstrom; the KER of a dication channel is filed under the neutral, N2, with the dication state in the channel \(TC\-954\)\. yuen\_2022/table1\_ker\_1d1d ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table1_ker_1d1d", "material": "N2", "file": "N2/yuen_2022__table1_ker_1d1d_N2.csv", "table": "tbl_076ba83089ee", "quantity": "kinetic_energy_release", "unit": "eV", "abscissa": "label", "use": "check", "parameters": { "channel": "N2 -> N2^2+ (the state of the row) -> N+(1D) + N+(1D)", "kind": "calculated", "state": "the N2^2+ state of the row" } } Table I, 'KER \(eV\)' of states 10 \(printed 'm\.s\. / N\+\(1D\) \+ N\+\(1D\)'\) and 11, whose limit N\+\(1D\) \+ N\+\(1D\) was 'identified from the PEC from Ref\. \[28\]'\. I\_p less KER is 42\.76 eV for both\. As table1\_ker\_3p3p otherwise\. yuen\_2022/text\_ip ~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "text_ip", "material": "N2", "table": "text", "quantity": "ionization_energy", "unit": "eV", "abscissa": "label", "use": "check", "parameters": { "kind": "not stated", "initial_state": "N2 X 1Sigma_g+", "final_state": "the N2+ state of the row" } } 3 inline points in the source record. p\. 4\: 'experimental ionization energy of 15\.58, 16\.93, and 18\.75 eV for HOMO, HOMO\-1, and HOMO\-2 were used' for the first ionisation, with no reference and no statement of vertical or adiabatic; the inputs of the model's MO\-ADK rates to the X, A and B states\. zhao\_2010's Table IV prints 15\.6, 17\.2 and 18\.7 eV as the experimental vertical values for the same orbitals\. yuen\_2022/text\_dipole\_xa ~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "text_dipole_xa", "material": "N2+", "table": "text", "quantity": "transition_dipole_moment", "unit": "au", "abscissa": "label", "use": "reproduced", "reproduced_from": [ "S. R. Langhoff, C. W. Bauschlicher Jr. and H. Partridge, J. Chem. Phys. 87, 4716 (1987)" ], "parameters": { "states": "X 2Sigma_g+ - A 2Pi_u", "component": "perpendicular (x)", "geometry": "the neutral's equilibrium, R = 1.09 angstrom" } } 1 inline points in the source record. p\. 3\: 'The X and A state \.\.\. are coupled by a dipole moment of d\_x = 0\.25 a0 \[29\]'; the model's coupling at the neutral's equilibrium geometry\. jia\_2024's Table III \(the same reference\) gives 0\.271 at R = 2\.00 a0 and 0\.262 at 2\.10 a0, so about 0\.265 at 1\.09 angstrom \(2\.06 a0\)\. yuen\_2022/text\_dipole\_xb ~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "text_dipole_xb", "material": "N2+", "table": "text", "quantity": "transition_dipole_moment", "unit": "au", "abscissa": "label", "use": "reproduced", "reproduced_from": [ "S. R. Langhoff and C. W. Bauschlicher Jr., J. Chem. Phys. 88, 329 (1988)" ], "parameters": { "states": "X 2Sigma_g+ - B 2Sigma_u+", "component": "parallel (z)", "geometry": "the neutral's equilibrium, R = 1.09 angstrom" } } 1 inline points in the source record. p\. 3\: 'the X and B state are coupled by a dipole moment of \.\.\. d\_z = 0\.75 a0 \[30\]'; the model's coupling at the neutral's equilibrium geometry\. jia\_2024's Table III \(the same reference\) gives 0\.764 at R = 2\.00 a0 and 0\.729 at 2\.10 a0, so about 0\.74 at 1\.09 angstrom \(2\.06 a0\)\. 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 :doc:`review register ` for the checks and decisions.