Table 1 Comparison between SHDMC (20K determinant active space) and Selected CI.

From: Multireference diffusion Monte Carlo reaches 2D materials

Method

Total Energy (Ha)

Abs. Error (mHa)

No. Dets

sCI-NO-5Z \(E_\textrm{var}\)

-11.193464

6.2(1)

\(14.6\times 10^6\)

sCI-NO-5Z extrap.

-11.194027

5.6(1)

\(\infty\)

SHDMC-TM-QZ

-11.19446(6)

5.2(1)

8994

SHDMC-LA-QZ

-11.19481(6)

4.8(1)

8994

sCI-NO-6Z \(E_\textrm{var}\)

-11.194964

4.6(1)

\(3.5\times 10^6\)

sCI-NO-6Z extrap.

-11.196381

3.2(1)

\(\infty\)

sCI (CBS)

-11.1996(1)

0.0(1)

\(\infty\)

SHDMC extrap.

-11.2013(6)

-1.3(7)

\(\infty\)

  1. Comparison between total energies (in units of Hartrees), obtained from SHDMC with T-moves (SHDMC-TM-QZ) and with the locality approximation (SHDMC-LA-QZ), sCI total energies (sCI-NO-5Z and sCI-NO-6Z), and sCI +rPT2 (sCI-NO-5Z extrap. and sCI-NO-6Z extrap.) The sCI-NO-5Z extrap. and sCI-NO-6Z extrap. energies are obtained by extrapolating to the infinite determinant limit (where the rPT2 correction to the energy approaches to zero). The SHDMC-TM-QZ and SHDMC-LA-QZ total energies are the average local energies (with statistical re-blocking) obtained in the limit of timestep = 0 \(\textrm{Ha}^{-1}\), using the converged SHDMC wavefunction as the trial wavefunction. The errors in the SHDMC-TM-QZ and SHDMC-LA-QZ total energies are the statistical errors in the estimate of the average local energy (DMC total energy). The absolute errors in the total energies (in units of millihartrees) are given as the difference between any of the given total energy values and the sCI (CBS) total energy. The total energy obtained from extrapolating SHDMC results to the infinite determinant limit (SHDMC extrap.) is compared to the selected CI energy obtained from extrapolating to the complete basis set limit (sCI (CBS)). The number of determinants, with a nonzero weight, used to construct each multideterminant wavefunction is provided in the column labeled No. Dets. Both the SHDMC-TM-QZ and SHDMC-LA-QZ wavefunctions were obtained using a 20,000 determinant active space.