28.8 Examples

Examples: Closed-shell ground-state calculations for $N_2$ (results from one MPI process):

nn_fciqmc.com

This yields

RESULTS FOR STATE 1.1
=====================

 Current reference energy                            -104.125525474439
 Projected correlation energy                          -0.200494452975
 Estimated error in Projected correlation energy        0.000267794947
 Shift correlation energy                              -0.200119481250
 Estimated error in shift correlation energy            0.003568889015

 Projected and shift energy estimates agree within errorbars: EDiff =      0.00037497

 Total projected energy        -104.32601993 +/-    0.267795E-03
 Total shift energy            -104.32564496 +/-    0.356889E-02
 !FCIQMC STATE 1.1 ENERGY            -104.326019927414
 !FCIQMC STATE 1.1 FCIQMC_ERR           0.000267794947

To redo the error analysis, we can run again in the same directory, with the input line changed to include fciqmc,reblockshift=1200,reblockproje=1200, set to approximate equilibrated iterations, which returns

RESULTS FOR STATE 1.1
=====================

 Current reference energy                            -104.125525474439
 Projected correlation energy                          -0.200551071781
 Estimated error in Projected correlation energy        0.000257264982
 Shift correlation energy                              -0.198657872098
 Estimated error in shift correlation energy            0.003792051242

 Projected and shift energy estimates agree within errorbars: EDiff =      0.00189320

 Total projected energy        -104.32607655 +/-    0.257265E-03
 Total shift energy            -104.32418335 +/-    0.379205E-02
 !FCIQMC STATE 1.1 ENERGY            -104.326076546221
 !FCIQMC STATE 1.1 FCIQMC_ERR           0.000257264982

High spin UHF calculations on atomic Nitrogen, including core correlation, and comparison to FCI (one MPI process):

n_uhf_fciqmc.com

This returns

RESULTS FOR STATE 1.8
=====================

 Current reference energy                             -54.391114562126
 Projected correlation energy                          -0.089063298446
 Estimated error in Projected correlation energy        0.000031993101
 Shift correlation energy                              -0.088986058082
 Estimated error in shift correlation energy            0.000239973111

 Projected and shift energy estimates agree within errorbars: EDiff =      0.00007724

 Total projected energy         -54.48017786 +/-    0.319931E-04
 Total shift energy             -54.48010062 +/-    0.239973E-03
 !FCIQMC STATE 1.8 ENERGY             -54.480177860572
 !FCIQMC STATE 1.8 FCIQMC_ERR           0.000031993101

RESULTS FOR STATE 1.8
=====================

 Correlation energy                    -0.089000492121
 !FCI STATE 1.8 Energy                -54.480115054246

Excited spin state calculations of Be$_2$ using the SPIN option. With spin=odd set, it will converge to the lowest odd $S$ spin state (one MPI process):

be2_highspin_fciqmc.com

This returns

RESULTS FOR STATE 1.1
=====================

 Current reference energy                             -28.418109510728
 Projected correlation energy                          -0.145376051508
 Estimated error in Projected correlation energy        0.000214957903
 Shift correlation energy                              -0.145621476634
 Estimated error in shift correlation energy            0.000167618454

 Projected and shift energy estimates agree within errorbars: EDiff =      0.00024543

 Total projected energy         -28.56348556 +/-    0.214958E-03
 Total shift energy             -28.56373099 +/-    0.167618E-03
 !FCIQMC STATE 1.1 ENERGY             -28.563730987362
 !FCIQMC STATE 1.1 FCIQMC_ERR           0.000167618454

which agrees with the fifth state (no symmetry) obtained with FCI:

RESULTS FOR STATE 5.1
=====================

 !FCI STATE 5.1 Energy                -28.563629184909



molpro@molpro.net 2018-10-21