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X2C (Scalar Relativistic)

For molecules containing heavy elements, scalar-relativistic effects on the core electrons become significant and propagate into valence properties such as bond lengths and energetics. TeraChem captures these effects with the spin-free exact two-component (SFX2C-1e) method,12 which folds the relativistic kinematics into a modified one-electron (core) Hamiltonian.

SFX2C-1e is a scalar (spin-free) treatment: it includes the mass–velocity and Darwin-type scalar-relativistic corrections but not spin–orbit coupling. Because it only modifies the one-electron Hamiltonian, it composes with the ordinary SCF — both Hartree–Fock and DFT — and with analytic gradients,3 at negligible extra cost relative to the underlying SCF.

Spin–orbit coupling is separate

The relativistic keyword provides scalar relativity only. Spin–orbit coupling is a distinct feature handled by the configuration-interaction methods (see CASSCF and Excited States).

The relativistic keyword

Scalar-relativistic treatment is selected with a single keyword, which also offers two atomic approximations that reduce the cost of constructing the X2C transformation for large systems:

Value Method Description
non (default) Non-relativistic Ordinary non-relativistic one-electron Hamiltonian
sfx2c1e SFX2C-1e Full molecular spin-free exact two-component, one-electron variant
ax1e SFX2C-1e + atomic X The decoupling (X) matrix is built from atomic blocks rather than the full molecular matrix — cheaper, with minimal loss of accuracy
axr1e SFX2C-1e + atomic X and R As ax1e, and additionally approximating the renormalization (R / picture-change) matrix from atomic blocks

The atomic approximations (ax1e, axr1e) exploit the fact that the relativistic decoupling is dominated by the atomic core regions, so the X (and R) matrices can be assembled atom-by-atom. This makes the relativistic step scale favorably for large molecules while closely reproducing the full sfx2c1e result.4

Quick start

Add a single line to an otherwise standard SCF input:

relativistic   sfx2c1e

Example: SFX2C-1e Hartree–Fock gradient

A spin-free X2C Hartree–Fock gradient on Ne₂. Tight thresholds and double precision are advisable for relativistic calculations:

x2c_hf_gradient.in
coordinates    ne2.xyz
basis          cc-pvdz
method         hf
charge         0
spinmult       1
run            gradient

relativistic   sfx2c1e
guess          hcore
precision      double
threall        1e-20
convthre       1.0e-10
purify         no
end

Switching relativistic to ax1e or axr1e requests the atomic approximations; everything else in the input is unchanged.

Notes

  • The default is non-relativistic; relativity is off unless relativistic is set (non turns it off explicitly).
  • SFX2C-1e is scalar/spin-free only — no spin–orbit coupling.
  • It applies to the SCF one-electron Hamiltonian, so it works with both HF and DFT, for energies and analytic gradients.
  • X2C accuracy depends on the basis set in the core region; use a basis suitable for relativistic calculations for the heavy elements of interest.

Summary of keywords

Keyword Values Default Description
relativistic non, sfx2c1e, ax1e, axr1e non Scalar-relativistic treatment of the one-electron Hamiltonian

References

  1. K. G. Dyall, Interfacing relativistic and nonrelativistic methods. I. Normalized elimination of the small component, J. Chem. Phys. 106, 9618 (1997). ↩

  2. W. Liu and D. Peng, Exact two-component Hamiltonians revisited, J. Chem. Phys. 131, 031104 (2009). ↩

  3. L. Cheng and J. Gauss, Analytic energy gradients for the spin-free exact two-component theory using an exact block diagonalization for the one-electron Dirac Hamiltonian, J. Chem. Phys. 135, 084114 (2011). ↩

  4. D. Peng and M. Reiher, Local relativistic exact decoupling, J. Chem. Phys. 136, 244108 (2012). ↩