Domain 7 of 10
Heavy Elements and Spin
Scalar relativistic Hamiltonians, effective core potentials, spin-orbit coupling and magnetic resonance properties.
3 Checked3 Partial4 UnverifiedEngine 1.10.12 live
What You Can Compute
Scalar Relativity
Spin-free X2C, checked against Dirac eigenvalues, DKH2 and scalar ZORA.
Effective Core Potentials
Stuttgart sets for Ag, Cd, Au, Hg and Ga, Ge, As, In, Sn, Sb, Pb, Bi (Metz sets unverified) and Wadt-Hay sets for Na to Ar. Energies and orbitals only.
Spin-Orbit and g-Tensor
Singlet-triplet couplings, mean-field SOC and the EPR g-tensor; zero-field splitting, whose spin-orbit part agrees with a printed value; broken-symmetry exchange coupling, electric field gradients with Mossbauer parameters, and paramagnetic NMR (the last three built and not yet run against printed values).
Every Method, with Its Level of Support
Generated from the engine's own capability report (engine 1.10.12), so this list never runs ahead of the code.
Checked reproduces printed values Checked (exact) no printed value exists; checked against exact mathematics or brute force Partial code exists, unchecked parts badged in the app Unverified built, no printed check yet
| Method | Support | Since | Primary Sources |
|---|---|---|---|
| Spin-free X2CExact two-component one-electron Hamiltonian for energies and orbitals. | Checked | 0.9.0 | Kutzelnigg, Liu 2005; Ilias, Saue 2007; Reiher 2006 |
| Scalar ZORAZeroth-order regular approximation by numerical quadrature. | Unverified | 0.9.0 | van Lenthe, Snijders, Baerends 1996 |
| Effective core potentialsStuttgart sets for Ag, Cd, Au, Hg and Ga, Ge, As, In, Sn, Sb, Pb, Bi, and Wadt-Hay sets for Na to Ar. Energy and orbitals only: no ECP gradients, correlated methods or solvation. Printed-value checks: Hartree-Fock ionisation energies of Ag, Cd, Au and Hg agree with Andrae et al. 1990 Table 3 within 0.02 eV (valence basis of the paper; open-shell states unrestricted), and the valence energies of Na, Mg and Ar with Wadt, Hay 1985 Table XVII within 2e-5 Eh. For Al to Cl our unrestricted energies lie at or below the printed values by less than 0.002 Eh, because the open-shell treatment of the paper is not reproduced. The Metz, Stoll, Dolg 2000 sets for Ga, Ge, As, In, Sn, Sb, Pb and Bi are unverified: only the Pb parameters were compared with the printed table; no printed energy is reproduced yet. | Partial | 0.9.0 | Andrae et al. 1990; Metz, Stoll, Dolg 2000; Wadt, Hay 1985 |
| Spin-orbit couplingSinglet-triplet couplings from CIS/TDA or full-response TDHF/TDDFT amplitudes, with the one-electron effective-charge or the mean-field operator, and atomic fine structure. The effective nuclear charges equal those printed in Neese 2001 and Koseki et al. 1995, 1998; spin-orbit integrals are checked against numerical quadrature, state couplings against explicit Slater determinants, and atomic multiplets against exact splitting rules. One printed value is matched: the Cu(II) spin-orbit constant, 848 cm-1 against 845 (Neese 2001 Table VI, with different orbitals). No printed singlet-triplet coupling or fine-structure splitting is reproduced yet. Closed-shell references for state couplings; no solvent, range-separated hybrids, meta-GGA or ECP; no spin-orbit perturbed energies. | Partial | 1.2.2 | Koseki et al. 1995; Koseki et al. 1998; Neese 2001; Hess et al. 1996; de Souza et al. 2019 |
| Mean-field two-electron SOCMean-field one- plus two-electron spin-orbit operator (one-centre or all integrals) for the g-tensor and singlet-triplet couplings. Printed-value checks go through the zero-field splitting and the g-tensor, not through state couplings. All-integral form: the spin-orbit part of the O2 zero-field splitting is 1.62 cm-1 against 1.60 (Neese 2007 Table I, BLYP/def2-TZVPP, bond length 1.2075 A because the paper prints no geometry). One-centre form: for CO+ and H2O+ the two-electron spin-orbit contribution to the g-shift agrees with Malkina et al. 2000 Tables 1 and 2 within about 7 % and its ratio to the one-electron term within 0.02, with a different functional and basis (ours PBE/def2-TZVPP, the paper BP86 with basis BIII): that part is a pattern, not a match. The two large components of the H2O+ g-shift are 9 and 14 % above the printed ones. Singlet-triplet couplings with this operator are compared only with the effective-charge operator, not with printed values. The all-integral form is limited to 150 basis functions. | Checked | 1.3.0 | Hess et al. 1996; Marian 2012; Neese 2007; Malkina et al. 2000 |
| EPR g-tensorRelativistic mass, gauge and spin-orbit contributions for UHF and UKS. Printed-value checks use UKS (PBE, PBE0). Relativistic mass and gauge corrections match printed values within 10 ppm for H2O+ (Lushington, Grein 1997 Table I at the printed geometry; Neese 2001 Table IV) and within 15 ppm for CO+ (Lushington, Grein 1997 Table I); the CO+ gauge correction of Neese 2001 Table III (138 and 30 ppm) is not reproduced (ours 194 and 81). Against Neese 2001 Table I the large components of the total Delta g agree only within about 15 %, with our own geometry and basis because that paper prints no geometries. | Checked | 1.2.2 | Neese 2001; Lushington, Grein 1997 |
| DKH2, SOMF spin-orbit and paramagnetic NMRSecond-order Douglas-Kroll-Hess, spin-orbit coupling with the mean-field operator and paramagnetic NMR shifts from the hyperfine and g tensors. No coupled-perturbed SOC for hybrids; paramagnetic NMR is built and not yet run, for doublets only and without orbital shielding of open shells. | Unverified | 1.5.0 | Reiher 2006; Neese 2007 |
| Zero-field splittingZero-field splitting D and E from the spin-spin and spin-orbit terms, with the mean-field spin-orbit operator and its variants, for UHF and UKS with multiplicity 3 or more; the D tensor is reported in its proper frame with the contributions. Spin-orbit D reproduces Neese 2007 Table I; spin-spin D from the UKS spin density differs from the printed UNO value (UNO not built). The spin-orbit part with exact exchange, meta-GGA, range-separated hybrids, ECPs, relativistic Hamiltonians, correlated methods and solvation are refused; spin-spin needs at most 150 basis functions. | Partial | 1.9.0 | Neese 2007 |
| Exchange coupling from broken symmetryHeisenberg exchange coupling J between two spin fragments from high-spin and broken-symmetry UHF or UKS determinants, by the Yamaguchi, Noodleman and Bencini formulas. Built and not yet run against a printed value. Two fragments only. | Unverified | 1.9.0 | Neese 2009 |
| Electric field gradients and MossbauerElectric field gradient tensors at the nuclei, nuclear quadrupole coupling constants, and 57Fe Mossbauer quadrupole splitting and isomer shift from the SCF electron density, with a published calibration or one you fit. Built and not yet run against a printed value. All-electron RHF, RKS, UHF and UKS densities only. | Unverified | 1.9.0 | Neese 2009; Helgaker et al. 1999 |
Printed Value, Our Value
| Quantity | Source | Printed | Ours | Result |
|---|---|---|---|---|
| CO+ g-Shift Delta g Perp, Ppm | Malkina et al. 2000 | -2458 | -2462; the totals agree by cancellation: our spin-orbit term is 54 ppm more negative (-2402 against -2348) and our gauge correction 51 ppm larger (122 against 71); PBE/def2-TZVPP, the paper BP86 | Pattern |
| H2O+ Gauge Correction, Ppm | Lushington, Grein 1997 Table I | 101, 209, 208 | 100.2, 209.6, 209.1 | Match |
| X2C 1s, One-Electron Ions Z 20 to 100 | Reiher 2006 Table 1 | Dirac eigenvalues | within 1e-8 to 1e-5 | Match |
| Zero-Field Splitting D, Spin-Orbit Part, cm-1 | Neese 2007 Table I, doi 10.1063/1.2772857 | 1.60 | 1.620 (spin-spin: 1.93 from the UKS spin density against the printed 1.60 from UNO; UNO not built) | Match |
| H2O+ Delta g Contributions: Relativistic Mass Correction (RMC) and One-Electron Gauge Correction (GC) | Neese 2001 Table IV, doi 10.1063/1.1419058 | RMC -312; GC(1e) 106, 212, 213 ppm | -309; 100, 209, 210 ppm (PBE with our own geometry and basis; the paper used BP86 and prints no geometry) | Match |
| O2 Zero-Field Splitting D, Spin-Orbit Part, All-Integral Mean-Field Operator, BLYP/def2-TZVPP, cm-1 | Neese 2007 Table I, doi 10.1063/1.2772857 | 1.60 | 1.620 (bond length 1.2075 A; the paper prints no geometry) | Match |
Not Offered Today
- Two- and four-component Dirac methods
- Relativistic gradients and frequencies
- g-tensor with ROHF, meta-GGA or ECPs
- ECP gradients
In the Chemistry Lab
Pick a heavy-element molecule and the engine offers X2C, ZORA or an ECP set in the Level of theory tab; spin-orbit and g-tensor sit under Spectra.
Relativistic and Magnetic Questions
Were ZORA results ever wrong?
Yes. ZORA energies from engines 0.9.0 to 1.0.1 had a doubled kinetic term. Our own ion check found it and 1.1.0 fixed it; older results show a Recompute notice.
How was the g-tensor checked?
CO+ and H2O+ against printed values, term by term: the relativistic mass and gauge corrections of H2O+ agree within 10 ppm. The CO+ total, Delta g perp -2462 ppm against -2458 printed, agrees only by cancellation: our spin-orbit term is 54 ppm more negative and our gauge correction 51 ppm larger than in Malkina et al. 2000.
Which magnetic properties are built but not yet checked?
Exchange coupling J from broken symmetry, electric field gradients with 57Fe Mossbauer splitting and isomer shift, and paramagnetic NMR shifts are listed as Unverified because none has been run against a printed value. Zero-field splitting is Partial: its spin-orbit part agrees with Neese 2007 Table I, and its spin-spin part does not match the printed value yet.
See It on a Molecule of Your Own
Describe a molecule and your question; the assistant drafts the plan and you approve it. Or see it first in a 30 minute demo.