Relativistic and electron correlation effects for molecules of heavy elements: Ab initio fully relativistic coupled‐cluster calculations for PbH<sub>4</sub>
Bibliographic record
Abstract
Abstract Ab initio fully relativistic all‐electron Dirac–Fock (DF) and nonrelativistic (NR) Hartree–Fock (HF) limit self‐consistent field (SCF) benchmark molecular calculations are reported for the tetrahedral (T d ) PbH 4 at various Pb–H bond distances. Our fully relativistic Dirac–Fock and nonrelativistic HF calculations predict for a PbH 4 bond distance of 1.75 and 1.82 Å, respectively. Both our DF and NR HF limit SCF calculations predict the ground state of PbH 4 (T d ) to be bound, with the predicted atomization energy ( A e ) of 7.20 and 8.63 eV, respectively. There are antibinding effects due to relativity of ∼1.4 eV to the predicted atomization energy ( A e ) of PbH 4 . Our relativistic four‐component coupled‐cluster singles and doubles (RCCSD) calculations, which correlate 50 electrons and include 302 active molecular spinors with energies up to ∼46 a.u. in the active space predict the relativistic second‐order Møller‐Plesset (RMP2), RCCSD and RCCSD (T) (RCCSD plus the triple excitation correction included perturbationally) correlation energies as −1.271, −1.161, and −1.186 hartree, respectively. The contribution of the RMP2, RCCSD, and RCCSD (T) electron correlation energies toward the atomization energy of PbH 4 as predicted by our above‐mentioned CC calculation is 3.78, 4.22, and 4.30 eV, respectively. We predict the NR and relativistic MP2, CCSD, and CCSD (T) atomization energies ( A e ) for PbH 4 at the optimized PbH bond distances as 12.72, 12.90, 1.77 and 10.98, 11.42, and 11.50 eV, respectively. With the inclusion of both the electron correlation and effects of relativity, we predict the atomization energy for PbH 4 to be ∼10–11 eV. This should encourage experimentalists to devise new synthetic methods to prepare plumbane, so that its chemical and physical properties can be investigated as in the case of its lighter congeners. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".