backflow transformation for N2

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Fan_Wang
Posts: 13
Joined: Fri Aug 15, 2014 8:55 am

backflow transformation for N2

Post by Fan_Wang »

With single-determinant SJ wavefunction, error in atomization energy for N2 is about 5 Kcal/mol using LDA orbitals according to JCTC, 8, 2255 (2012). I got similar results with CASINO. I am wondering whether this error could be reduced with backflow transformation. Unfortunately, I could not get reasonable result when optimizing parameters for N2. (It seems OK with N). The initial Jastrow factors are from emin optimization without bf transformation. When I set "Apply no-curl constraint" to zero, results with emin optimization will have very large variance, much larger than that without bf transformation. When this parameter is set to 1, it seems to me the backflow transformation does not work at all ( the parameters in bf part are smaller than 1E-5 and the resulting energy does not change at all.) Is there anything wrong with my setting for bf part or input?

in correlation.data file:

Code: Select all

START BACKFLOW
 Title
 AE Nitrogen
 Truncation order
   3
 START ETA TERM
 Expansion order
   8
 Spin dep (0->uu=dd=ud; 1->uu=dd/=ud; 2->uu/=dd/=ud)
   1
 Cut-off radii ;      Optimizable (0=NO; 1=YES; 2=YES BUT NO SPIN-DEP)
  0.831243458551654                1       ! L_1
 Parameter ;          Optimizable (0=NO; 1=YES)
 END ETA TERM
 START MU TERM
 Number of sets
   1
 START SET 1
 Number of atoms in set
   2
 Labels of the atoms in this set
    1   2
 Type of e-N cusp conditions (0->PP/cuspless AE; 1->AE with cusp)
   1
 Expansion order
   6
 Spin dep (0->u=d; 1->u/=d)
   0
 Cutoff (a.u.)     ;  Optimizable (0=NO; 1=YES)
   3.68216019293890                1
 Parameter values  ;  Optimizable (0=NO; 1=YES)
 END SET 1
 END MU TERM
 START PHI TERM
 Number of sets
   1
 START SET 1
 Number of atoms in set
   2
 Labels of the atoms in this set
    1    2
 Type of e-N cusp conditions (0=PP; 1=AE)
   1
 Apply no-curl constraint (0=NO; 1=YES)
   0
 Electron-nucleus expansion order N_eN
   3
 Electron-electron expansion order N_ee
   3
 Spin dep (0->uu=dd=ud; 1->uu=dd/=ud; 2->uu/=dd/=ud)
   0
 Cutoff (a.u.)     ;  Optimizable (0=NO; 1=YES)
   3.59996205053959                1
 Parameter values  ;  Optimizable (0=NO; 1=YES)
 END SET 1
 END PHI TERM
 END BACKFLOW
in input file:

Code: Select all

vmc_equil_nstep   : 5000           #*! Number of equilibration steps (Integer)
vmc_nstep         : 2000000        #*! Number of steps (Integer)
vmc_nblock        : 10             #*! Number of checkpoints (Integer)
vmc_nconfig_write : 20000          #*! Number of configs to write (Integer)

opt_method        : emin           #*! Opt method (varmin/madmin/emin/...)
opt_cycles        : 10             #*! Number of optimization cycles (Integer)
opt_jastrow       : T              #*! Optimize Jastrow factor (Boolean)
opt_det_coeff     : F              #*! Optimize determinant coeffs (Boolean)
opt_backflow      : T              #*! Optimize backflow parameters (Boolean)
opt_orbitals      : F              #*! Optimize orbital parameters (Boolean)
Mike Towler
Posts: 239
Joined: Thu May 30, 2013 11:03 pm
Location: Florence
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Re: backflow transformation for N2

Post by Mike Towler »

Hi Fan,

Can you post the entire input and output files (you'll need to gzip them for them to be accepted as attachments).

In the meantime:

I can't see anything obviously wrong with the correlation.data file or the few lines of input you selected. Can you confirm this really is an all-electron calculation with cusp corrections activated, as stated in the backflow data file?

Possibly you're not using enough configurations to optimize the Jastrow and backflow parameters simultaneously. What happens if you use more configurations (e.g. 100000 rather than 20000) and if you simplify things a bit e.g. set the backflow cutoff radii to their defaults and make them non-optimizable, reduce the two expansion orders in the backflow phi term to 2 instead of 3, and turn off simultaneous optimization of the Jastrow factor (opt_jastrow=F, opt_backflow=T).

I would keep the 'Apply no-curl constraint' thing as zero.

If that works, then once you have a Jastrow and a simple backflow function with optimized parameters you can attempt more complex optimizations.

Cheers,
Mike
Fan_Wang
Posts: 13
Joined: Fri Aug 15, 2014 8:55 am

Re: backflow transformation for N2

Post by Fan_Wang »

Dear Mike,

Thank you for your reply. I will try your suggestions first. Previous results are attached with this post. In emin.1, no-curl constraint to zero and large variance shows up. In emin.2, it is set to 1 and the results does not change at all. Parameters in correlation.data for Jastrow part are from emin optimization without backflow transformation.

best regards,

Fan
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