awasthi_2008 ============ M\. Awasthi, Y\. V\. Vanne, A\. Saenz, A\. Castro and P\. Decleva, "Single\-active\-electron approximation for describing molecules in ultrashort laser pulses and its application to molecular hydrogen", Phys\. Rev\. A 77, 063403 \(2008\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1103/PhysRevA\.77\.063403 `__ **Source kind:** theory **Recorded technique:** Single\-active\-electron time\-dependent Schrodinger equation \(SAE\-TDSE\) for H2 at fixed R = 1\.40 a0, the active electron's Kohn\-Sham or Hartree\-Fock Hamiltonian in a B\-spline and STO basis \(ADF\), with several exchange\-correlation potentials \(HF, LDA, TSLDA, LB94\), compared with full two\-electron CI\-TDSE and a pseudo\-SAE CI, and with the MO\-ADK and molecular strong\-field approximations; linear polarisation parallel to the axis, cos^2 pulses\. **Materials in structured entries:** H2 **Dataset quantities:** ionization\_energy, tunnelling\_structure\_coefficient **Contents:** 13 datasets; 0 formulas. Curation notes -------------- PDF pages 1\-17, page n = journal page 063403\-n\. Authors checked on the first page\. EXTRACTED\. Table I \(p\. 6\)\: for H2 at R = 1\.4 a0, the vertical ionisation potential of each method \(HF, LB94, TSLDA, LDA, SAE\-CI, CI\: this work; HF \[6\] Kjeldsen et al\. and 'X alpha \[17\]' Tong et al\. 2002\: reproduced\) and, for the independent\-particle models, C\_0, C\_2, C\_4 with m = 0 \('In the present case of H2 only the values for m = 0 are required', p\. 6\)\. The coefficients are defined by Eq\. \(19\), p\. 4\: phi\(r\) ~ sum\_l C\_l r^\(nu \- 1\) e^\(\-kappa r\) Y\_l0, nu = Z/kappa, kappa = sqrt\(2 I\_p\)\: Tong et al\.'s normalisation\. The paper states no numerical accuracy for them beyond 'expected to be numerically accurate' \(p\. 11\), and warns that 'the obtained coefficients depend quite strongly on the model and the numerical quality of the electronic\-structure calculation' \(p\. 11\)\: the HF and LB94 C\_0 differ by a factor of 2, which the different I\_p largely compensate in the MO\-ADK yields \(Fig\. 9, p\. 11\)\. FINDINGS\. \(1\) The 'X alpha \[17\]' row quotes Tong et al\.'s coefficients correctly but its I\_p as 15\.70 eV, which is Tong's F2 value; Tong's hydrogen row has 15\.47 \(see ip\_xalpha\_tong, excluded\)\. \(2\) zhao\_2010's Table III reprints the LB94 row rounded as its reference \[30\]\. EQUIVALENT ELECTRONS \(bearing on solprop's occupancy factor, TC\-439\)\: 'An intrinsic problem of the SAE is the question how equivalent electrons should be treated\. In the present example of H2 there are evidently two equivalent electrons that could be ionized \(within the SAE model\) independently of each other\. Therefore it appears natural to scale the SAE yields by a factor of 2' \(p\. 7\); with the factor the HF and LB94 SAE yields agree very well with the CI yield up to about 2 x 10^14 W/cm^2 at 800 nm, and overestimate it above \(Fig\. 4\); 'at least for H2 and 800 nm wavelength the SAE results should be multiplied with a factor of 2 for ionization yields below 10%' \(p\. 7\), while the unscaled SAE agrees with CI above about 20 % yield\. The MO\-ADK comparison of Fig\. 9 notes that an earlier agreement at 10^14 W/cm^2 'ignores the factor of 2 for the two equivalent electrons' \(p\. 12\)\. The rates themselves \(the SAE and MO\-ADK results of Table I's parameters\) are per active electron\. FIGURES \(not digitised; all H2 at R = 1\.4 a0, polarisation parallel to the axis\)\: Fig\. 1 ionisation yield against photon energy, 2 x 10^12 W/cm^2, 15 fs; Figs\. 2\-8 yields against peak intensity at 800 nm \(12 cycles, about 32 fs\), 400 nm and 266 nm for CI, SAE\-CI and SAE\-TDSE \(HF, LB94, LDA, TSLDA\), and excitation yields; Fig\. 9 MO\-ADK yields with the Table I parameters \(800 nm\); Fig\. 10 molecular SFA in velocity and length gauge\. **Recorded bibliographic identity status:** VALIDATED. This concerns identification of the source; it does not establish the scientific correctness of its contents. Datasets -------- awasthi\_2008/ip\_hf ~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "ip_hf", "material": "H2", "file": "H2/awasthi_2008__ip_hf.csv", "table": "tbl_4bbfbf50c79d", "quantity": "ionization_energy", "unit": "eV", "abscissa": "none", "use": "check", "parameters": { "kind": "vertical", "method": "HF", "internuclear_distance_bohr": 1.4 } } Table I, row HF\: Hartree\-Fock, the Hartree \(static\) potential of the HF 1 sigma\_g orbital \(this work, B\-spline/STO SAE code\)\. 'the vertical ionization potentials I\_p \(at the equilibrium distance R = 1\.40 a0 at which all calculations in this work were performed\)' \(p\. 6\)\. awasthi\_2008/cl\_hf ~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "cl_hf", "material": "H2", "file": "H2/awasthi_2008__cl_hf.csv", "table": "tbl_4bbfbf50c79d", "quantity": "tunnelling_structure_coefficient", "abscissa": "label", "use": "check", "parameters": { "model": "moadk", "orbital": "HOMO 1 sigma_g", "m": 0, "normalisation": "Awasthi et al. 2008 Eq. (19), p. 4: phi(r) ~ sum_l C_l r^(nu - 1) exp(-kappa r) Y_l0(r^) for large r, nu = Z/kappa, kappa = sqrt(2 I_p), atomic units, one-centre expansion (Tong et al. 2002's convention)", "method": "HF", "internuclear_distance_bohr": 1.4 } } Table I, row HF\: C\_0, C\_2, C\_4 \(m = 0\) fitted to the asymptotic tail of the HF HOMO at R = 1\.4 a0; 'in the present approach the long\-range asymptotic tail of the highest occupied molecular orbital \(HOMO\) should be accurately described by the long\-range B\-spline expansion, so that the C\_l coefficients extracted are expected to be numerically accurate' \(p\. 11\)\. No C\_l for LDA, whose asymptotic HOMO is too wrong to fit \(p\. 6\)\. awasthi\_2008/ip\_lb94 ~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "ip_lb94", "material": "H2", "file": "H2/awasthi_2008__ip_lb94.csv", "table": "tbl_4bbfbf50c79d", "quantity": "ionization_energy", "unit": "eV", "abscissa": "none", "use": "check", "parameters": { "kind": "vertical", "method": "LB94", "internuclear_distance_bohr": 1.4 } } Table I, row LB94\: density\-functional SAE potential with the van Leeuwen\-Baerends 1994 functional \(this work\)\. 'the vertical ionization potentials I\_p \(at the equilibrium distance R = 1\.40 a0 at which all calculations in this work were performed\)' \(p\. 6\)\. awasthi\_2008/cl\_lb94 ~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "cl_lb94", "material": "H2", "file": "H2/awasthi_2008__cl_lb94.csv", "table": "tbl_4bbfbf50c79d", "quantity": "tunnelling_structure_coefficient", "abscissa": "label", "use": "check", "parameters": { "model": "moadk", "orbital": "HOMO 1 sigma_g", "m": 0, "normalisation": "Awasthi et al. 2008 Eq. (19), p. 4: phi(r) ~ sum_l C_l r^(nu - 1) exp(-kappa r) Y_l0(r^) for large r, nu = Z/kappa, kappa = sqrt(2 I_p), atomic units, one-centre expansion (Tong et al. 2002's convention)", "method": "LB94", "internuclear_distance_bohr": 1.4 } } Table I, row LB94\: C\_0, C\_2, C\_4 \(m = 0\) fitted to the asymptotic tail of the LB94 HOMO at R = 1\.4 a0; 'in the present approach the long\-range asymptotic tail of the highest occupied molecular orbital \(HOMO\) should be accurately described by the long\-range B\-spline expansion, so that the C\_l coefficients extracted are expected to be numerically accurate' \(p\. 11\)\. No C\_l for LDA, whose asymptotic HOMO is too wrong to fit \(p\. 6\)\. zhao\_2010 reprints this row rounded \(1\.15, 0\.067, 0\.001\) as its reference \[30\]\. awasthi\_2008/ip\_tslda ~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "ip_tslda", "material": "H2", "file": "H2/awasthi_2008__ip_tslda.csv", "table": "tbl_4bbfbf50c79d", "quantity": "ionization_energy", "unit": "eV", "abscissa": "none", "use": "check", "parameters": { "kind": "vertical", "method": "TSLDA", "internuclear_distance_bohr": 1.4 } } Table I, row TSLDA\: transition\-state LDA \(Slater's transition state, half an electron removed\) \(this work\)\. 'the vertical ionization potentials I\_p \(at the equilibrium distance R = 1\.40 a0 at which all calculations in this work were performed\)' \(p\. 6\)\. awasthi\_2008/cl\_tslda ~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "cl_tslda", "material": "H2", "file": "H2/awasthi_2008__cl_tslda.csv", "table": "tbl_4bbfbf50c79d", "quantity": "tunnelling_structure_coefficient", "abscissa": "label", "use": "check", "parameters": { "model": "moadk", "orbital": "HOMO 1 sigma_g", "m": 0, "normalisation": "Awasthi et al. 2008 Eq. (19), p. 4: phi(r) ~ sum_l C_l r^(nu - 1) exp(-kappa r) Y_l0(r^) for large r, nu = Z/kappa, kappa = sqrt(2 I_p), atomic units, one-centre expansion (Tong et al. 2002's convention)", "method": "TSLDA", "internuclear_distance_bohr": 1.4 } } Table I, row TSLDA\: C\_0, C\_2, C\_4 \(m = 0\) fitted to the asymptotic tail of the TSLDA HOMO at R = 1\.4 a0; 'in the present approach the long\-range asymptotic tail of the highest occupied molecular orbital \(HOMO\) should be accurately described by the long\-range B\-spline expansion, so that the C\_l coefficients extracted are expected to be numerically accurate' \(p\. 11\)\. No C\_l for LDA, whose asymptotic HOMO is too wrong to fit \(p\. 6\)\. awasthi\_2008/ip\_lda ~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "ip_lda", "material": "H2", "file": "H2/awasthi_2008__ip_lda.csv", "table": "tbl_4bbfbf50c79d", "quantity": "ionization_energy", "unit": "eV", "abscissa": "none", "use": "check", "parameters": { "kind": "vertical", "method": "LDA", "internuclear_distance_bohr": 1.4 } } Table I, row LDA\: ground\-state LDA \(VWN\) \(this work\)\. 'the vertical ionization potentials I\_p \(at the equilibrium distance R = 1\.40 a0 at which all calculations in this work were performed\)' \(p\. 6\)\. awasthi\_2008/ip\_sae\_ci ~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "ip_sae_ci", "material": "H2", "file": "H2/awasthi_2008__ip_sae_ci.csv", "table": "tbl_4bbfbf50c79d", "quantity": "ionization_energy", "unit": "eV", "abscissa": "none", "use": "check", "parameters": { "kind": "vertical", "method": "SAE-CI", "internuclear_distance_bohr": 1.4 } } Table I, row SAE\-CI\: pseudo\-SAE configuration interaction\: configurations with one electron in the lowest sigma\_g orbital of H2\+ \(this work, ~4200 configurations\)\. 'the vertical ionization potentials I\_p \(at the equilibrium distance R = 1\.40 a0 at which all calculations in this work were performed\)' \(p\. 6\)\. awasthi\_2008/ip\_ci ~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "ip_ci", "material": "H2", "file": "H2/awasthi_2008__ip_ci.csv", "table": "tbl_4bbfbf50c79d", "quantity": "ionization_energy", "unit": "eV", "abscissa": "none", "use": "check", "parameters": { "kind": "vertical", "method": "CI", "internuclear_distance_bohr": 1.4 } } Table I, row CI\: full two\-electron configuration interaction \(this work, ~6000 configurations\)\. 'the vertical ionization potentials I\_p \(at the equilibrium distance R = 1\.40 a0 at which all calculations in this work were performed\)' \(p\. 6\)\. awasthi\_2008/ip\_hf\_kjeldsen ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "ip_hf_kjeldsen", "material": "H2", "file": "H2/awasthi_2008__ip_hf_kjeldsen.csv", "table": "tbl_4bbfbf50c79d", "quantity": "ionization_energy", "unit": "eV", "abscissa": "none", "use": "reproduced", "reproduced_from": [ "T. K. Kjeldsen, C. Z. Bisgaard, L. B. Madsen and H. Stapelfeldt, Phys. Rev. A 71, 013418 (2005)" ], "parameters": { "kind": "not stated", "method": "HF [6]", "internuclear_distance_bohr": 1.4 } } Table I, row 'HF \[6\]'\: the numerical Hartree\-Fock value of Kjeldsen et al\. \(ref\. 6\), a literature value 'used previously for MO\-ADK and MO\-SFA\-LG calculations' \(p\. 6\)\. The text calls this work's rows vertical; the kind of the quoted value is not stated\. awasthi\_2008/cl\_hf\_kjeldsen ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "cl_hf_kjeldsen", "material": "H2", "file": "H2/awasthi_2008__cl_hf_kjeldsen.csv", "table": "tbl_4bbfbf50c79d", "quantity": "tunnelling_structure_coefficient", "abscissa": "label", "use": "reproduced", "reproduced_from": [ "T. K. Kjeldsen, C. Z. Bisgaard, L. B. Madsen and H. Stapelfeldt, Phys. Rev. A 71, 013418 (2005)" ], "parameters": { "model": "moadk", "orbital": "HOMO 1 sigma_g", "m": 0, "normalisation": "Awasthi et al. 2008 Eq. (19), p. 4: phi(r) ~ sum_l C_l r^(nu - 1) exp(-kappa r) Y_l0(r^) for large r, nu = Z/kappa, kappa = sqrt(2 I_p), atomic units, one-centre expansion (Tong et al. 2002's convention)", "method": "HF [6]", "internuclear_distance_bohr": 1.4 } } Table I, row 'HF \[6\]'\: C\_0, C\_2 of Kjeldsen et al\.'s numerical Hartree\-Fock orbital \(no C\_4 printed\); 'the HF parameters found in the present approach are quite similar' \(p\. 6\)\. awasthi\_2008/ip\_xalpha\_tong ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "ip_xalpha_tong", "material": "H2", "file": "H2/awasthi_2008__ip_xalpha_tong.csv", "table": "tbl_4bbfbf50c79d", "quantity": "ionization_energy", "unit": "eV", "abscissa": "none", "use": "excluded", "reproduced_from": [ "tong_2002" ], "parameters": { "kind": "not stated", "method": "X alpha [17]" } } Table I, row 'X alpha \[17\]' \(Tong et al\. 2002, the multiple\-scattering X\-alpha calculation\)\: I\_p printed 15\.70, which is not Tong's hydrogen value \(tong\_2002 Table I\: 'D\_2' 15\.47 eV\) but Tong's F2 value \(15\.70\)\: a misquotation\. Excluded; kept as printed\. awasthi\_2008/cl\_xalpha\_tong ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "cl_xalpha_tong", "material": "H2", "file": "H2/awasthi_2008__cl_xalpha_tong.csv", "table": "tbl_4bbfbf50c79d", "quantity": "tunnelling_structure_coefficient", "abscissa": "label", "use": "reproduced", "reproduced_from": [ "tong_2002" ], "parameters": { "model": "moadk", "orbital": "HOMO 1 sigma_g", "m": 0, "normalisation": "Tong et al. 2002 Eqs. (1)-(2): Psi^m = sum_l C_l F_l(r) Y_lm, F_l(r -> inf) ~ r^(Z_c/kappa - 1) exp(-kappa r), kappa = sqrt(2 I_p), atomic units", "method": "X alpha [17]" } } Table I, row 'X alpha \[17\]'\: Tong et al\.'s C\_0, C\_2, C\_4 for the hydrogen row \(printed 'D\_2' there\), 2\.51, 0\.06, 0\.00 as in tong\_2002\. 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.