hettema_1992 ============ H\. Hettema, H\. J\. Aa\. Jensen, P\. Jørgensen and J\. Olsen, "Quadratic response functions for a multiconfigurational self\-consistent field wave function", J\. Chem\. Phys\. 97, 1174\-1190 \(1992\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1063/1\.463245 `__ **Source kind:** theory **Recorded technique:** The quadratic response function of a multiconfiguration self\-consistent field \(MCSCF\) state and its residues, implemented \(Secs\. II\-III\); the two\-photon transition moment of the reference state to an excited state from two linear response vectors and the excited state's eigenvector \(Eq\. 47\)\. Sample calculations \(Sec\. IV\)\: H2 at R = 1\.4011 au \(HF and two CAS\), and Ne in the basis of Maroulis and Thakkar \(one extra diffuse s, p, d function for a basis test\) at four levels\: SCF \(HF\), CAS three shell \(2s, 2p, 3s, 3p, 3d\), SD RAS three shell and SD RAS four shell \(all singles and doubles from 2s, 2p into the 3s\-3d or 3s\-4f shells\), the 1s frozen; an estimate from the three by Eq\. \(102\)\. Non\-relativistic, LS coupling\. **Materials in structured entries:** None recorded. **Dataset quantities:** None recorded. **Contents:** 0 datasets; 0 formulas. Curation notes -------------- Journal pp\. 1174\-1190 = PDF pages 2\-18 \(PDF page 1 is the AIP download cover\); journal page = PDF page \+ 1172\. Identity checked on the first page \(PDF p\. 2\: 'J\. Chem\. Phys\. 97 \(2\), 15 July 1992', Hinne Hettema \(Nijmegen\), Hans Jørgen Aa\. Jensen and Poul Jørgensen \(Aarhus\), Jeppe Olsen \(Lund\); received 14 August 1991, accepted 5 March 1992\) on 2026\-10\-08\. Nothing is taken\. The paper's two\-photon numbers are single tensor elements of the transition moment, which no quantity of the vocabulary holds \(two\_photon\_transition\_strength holds the rotational average delta^TP, TC\-872\), and it gives no rotational average, rate constant or cross section\. NEON \(Sec\. IV D, pp\. 1186\-1188; Tables VII, VIII, image checked\)\. Table VII\: 'Two\-photon transition moments of Ne between the 1Se ground state and the first excited state of 1De symmetry\. The A operator is the x dipole operator\. The B operator is the y dipole operator carrying the frequency\. All values are in atomic units\.' Its first row is each method's excitation energy \(HF 0\.738 881, CAS three shell 0\.700 454, SD RAS three shell 0\.706 363 \(0\.706 177 with the diffuse functions\), SD RAS four shell 0\.704 482 au\), the others the element S\_xy at four frequencies of the B photon, 0\.085 625, 0\.171 25, 0\.256 875 and 0\.342 5 au \(a quarter, half, three quarters and all of half the experimental energy 0\.6850 au\), the other photon carrying omega\_f \- omega\_B with the method's omega\_f\. At 0\.3425 au\: HF 2\.9663, CAS three shell 3\.3265, SD RAS three shell 3\.2665 \(3\.2434\), SD RAS four shell 3\.3450\. So S\_xy is the one element of the level's xy component; the F = G = H = 2 average of that component is \(4/15\) S\_xy^2 and the level's \(all five components\) \(4/3\) S\_xy^2 \(sundholm\_1994's notes, TC\-887, TC\-888\)\. CHECKED \(2026\-10\-08, by direct computation\)\. Table VIII \(the contributions at 0\.3425 au\) sums to its totals, which are Table VII's last row \(2\.9663, 3\.3265, 3\.2665, 3\.3450\)\. The text\: 'the contribution from the E\(3\) and S\(3\) terms is only 0\.07 a\.u\.' \(\-0\.0684\); 'about 60%' of the correlation of the excitation energy recovered \(\(0\.738 881 \- 0\.704 482\)/\(0\.738 881 \- 0\.6850\) = 0\.638\); 'at the highest frequency, the correlation contribution is about 10%\-15%' \(3\.3450/2\.9663 = 1\.128\)\. The RPA energy 0\.738 881 au is moccia\_1984's RPA 0\.7389, as the text says\. The text \(p\. 1187\) gives Table VIII's frequency as '0\.3452 a\.u\.', the caption as 0\.3425 a\.u\., Table VII's last row \(the caption and Table VII are consistent; the text's digits are transposed; no value is taken, so no erratum\)\. FINDING\: THE EXTRAPOLATED EXCITATION ENERGY\. Eq\. \(102\) \(Q = SD RAS four \+ \(CAS three \- SD RAS three\) \+ \(1/2\)\(SD RAS four \- SD RAS three\), \+\- the sum of the two differences' magnitudes\) gives from Table VII 0\.697 63 \+\- 0\.006 85 au; the text prints '0\.6936 \+\- 0\.0068 a\.u\.' \(p\. 1187\)\: the uncertainty is reproduced, the value is not \(0\.0040 au lower\)\. hattig\_1998b's Table I prints Ne 1De 'MCSCF' 18\.874 eV \(footnote a, this paper\) = 0\.6936 au, the printed estimate \(0\.697 63 au would be 18\.984 eV\)\. FINDING\: THE QUOTATIONS IN hattig\_1998b \(TC\-887\)\. Its Table IV's SCF 8\.799 for Ne 1De is 2\.9663^2 \(8\.7989\), but at omega\_B = 0\.3425 au and omega\_2 = 0\.738 881 \- 0\.3425 = 0\.3964 au, not the degenerate pair of the column it stands in \(its footnote b computes K 'assuming omega\_1 = omega\_2 = 0\.3425 a\.u\.'\)\. Its MCSCF 11\.289 is no square of a value printed here\: SD RAS four shell 3\.3450^2 = 11\.189, CAS three shell 11\.066, SD RAS three shell 10\.670, and Eq\. \(102\) applied to the 0\.3425 au elements gives 3\.444, squared 11\.86; its K, 0\.0885e\-51 cm4 s, follows 11\.289 \(11\.189 would give 0\.0877e\-51\)\. sqrt\(11\.289\) = 3\.3599 is none of Table VII's twenty cells; also tried \(2026\-10\-09\), none reproduces it\: the extended\-basis SD RAS three shell 3\.2434^2 = 10\.520, Eq\. \(102\) with that value 3\.4789^2 = 12\.10, SD RAS four shell without the E\(3\), S\(3\) term \(3\.1807^2 = 10\.117\), Eq\. \(102\) applied to the squares \(11\.84\)\. Not resolved\: hattig\_1998b cites this paper alone \(its Ref\. 6\) and states no other source\. henriksson\_2005's quotations \(HF 2\.9663 and SD RAS 3\.3450 au at 20\.106 and 19\.170 eV, one photon at 9\.320 eV\) are this paper's \(0\.738 881 and 0\.704 482 au; 0\.3425 au = 9\.320 eV\)\. FINDING\: THE COMPARISON WITH MOCCIA AND RIZZO \(p\. 1187\)\. The text compares Moccia and Rizzo's RPA amplitude 3\.84 \(moccia\_1984, Table 2, at omega\_1 = omega\_2\) with its own SCF S\_xy 2\.9663 and calls the difference large, blaming the basis\. Moccia and Rizzo's M is the zz element of the M = 0 component for parallel linear polarisation \(moccia\_1984's notes\), which is \(2/sqrt 3\) S\_xy\: their 3\.836 is S\_xy = 3\.322, 12 % \(not 29 %\) above 2\.9663, and they used experimental excitation energies for the final level and the lowest 1Po levels \(0\.6850 and 0\.6192 au against RPA 0\.7389 and 0\.6741\), which raises the amplitude\. The basis is not needed to explain most of the difference\. H2 \(Sec\. IV A, Tables II\-IV\)\: the zz element of the X 1Sigma\_g\+ \-\> \(E,F\) 1Sigma\_g\+ two\-photon transition moment at R = 1\.4011 au \(HF, CAS 1, CAS 2\), at seven frequencies, and its sum\-over\-states decomposition; the HF values 'identical to those of Parkinson and Oddershede' \(W\. A\. Parkinson, P\. W\. Sengeløv and J\. Oddershede, Int\. J\. Quant\. Chem\. S24, 487 \(1990\), not in the library\)\. Not taken\: one molecule\-fixed element at one internuclear distance, not a rotationally and vibrationally averaged strength\. NOT TAKEN, out of this curation's scope \(two\-photon\)\: the Ne polarizability and second hyperpolarizability \(Sec\. IV E; Tables IX\-XII\: the ESHG gamma\(\-2w; w, w, 0\) at HF and CAS three shell at Shelton's frequencies, Table X; the estimate 99 \+\- 6 au static and 109 \+\- 7 au at 0\.076 641 au, Table XI; the static polarizability estimate 2\.643 \+\- 0\.049 au, p\. 1189\)\. They belong to the third\-order and dispersion families and have not been checked here\. Tables I and V \(MP2 natural orbital occupations\), VI \(finite\-field convergence\)\. **Recorded bibliographic identity status:** VALIDATED\_WITH\_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents. Datasets -------- No datasets are recorded. 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.