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Jastrow Derivatives

Jastrow derivative files specify which Jastrow parameters should be optimized during wavefunction optimization. This file controls the degrees of freedom in the optimization process by identifying which parameters in the Jastrow factor can vary during energy or variance minimization.

Overview

When optimizing a trial wavefunction, you typically want to optimize only a subset of the Jastrow parameters while keeping others fixed. The Jastrow derivative file (.der file) specifies which parameters are active in the optimization by listing their indices.

Key Concepts

  • Parameter indices: Each Jastrow parameter has an index corresponding to its position in the parameter arrays
  • Selective optimization: Only parameters listed in the derivative file will be optimized
  • Coordinate with Jastrow file: The derivative file must match the structure of the corresponding Jastrow file

File Format

Jastrow derivative parameters are provided in a text file that CHAMP reads during optimization.

Basic Structure

jasderiv
4 4 5 15 15 0 0 nparma,nparmb,nparmc,nparmf
  3 4 5 6 (iwjasa(iparm),iparm=1,nparma)
  3 4 5 6 (iwjasa(iparm),iparm=1,nparma)
2 3 4 5 6 (iwjasb(iparm),iparm=1,nparmb)
3 5 7 8 9         11 13 14 15 16     17 18 20 21 23 (c(iparmj),iparmj=1,nparmc)
3 5 7 8 9         11 13 14 15 16     17 18 20 21 23 (c(iparmj),iparmj=1,nparmc)
end

Format Specification

Line 1: Header 

jasderiv
Identifies this as a Jastrow derivative specification file.

Line 2: Parameter counts 

4 4 5 15 15 0 0 nparma,nparmb,nparmc,nparmf

  • nparma = 4: Number of a parameters to optimize per atom type
  • nparmb = 4: Number of b parameters to optimize
  • nparmc = 15: Number of c parameters to optimize per atom type
  • nparmf = 0: Number of f parameters (typically 0)
  • Additional zeros are placeholders for future parameter types

Lines 3+: Parameter indices

a-parameter indices (electron-nucleus): One line per unique atom type 

  3 4 5 6 (iwjasa(iparm),iparm=1,nparma)
  3 4 5 6 (iwjasa(iparm),iparm=1,nparma)

  • Number of a lines = number of unique atom types
  • Order must match atom type order in Jastrow file
  • Values are 1-indexed positions of parameters to optimize
  • Example: 3 4 5 6 means optimize the 3rd, 4th, 5th, and 6th a parameters
  • First two parameters (indices 1 and 2) are typically fixed at 0.0

b-parameter indices (electron-electron): Single line 

2 3 4 5 6 (iwjasb(iparm),iparm=1,nparmb)

  • Only one b line for entire system
  • Values are 1-indexed positions of parameters to optimize
  • Example: 2 3 4 5 6 means optimize the 2nd through 6th b parameters
  • First parameter (index 1) is often fixed

c-parameter indices (three-body): One line per unique atom type (if nordc > 0) 

3 5 7 8 9         11 13 14 15 16     17 18 20 21 23 (c(iparmj),iparmj=1,nparmc)
3 5 7 8 9         11 13 14 15 16     17 18 20 21 23 (c(iparmj),iparmj=1,nparmc)

  • Number of c lines = number of unique atom types
  • Order must match atom type order in Jastrow file
  • Values are 1-indexed positions of parameters to optimize
  • If no c parameters in Jastrow (nordc = 0), omit these lines

Final line: 

end

Examples

Example 1: Water Molecule - Simple Optimization

Jastrow file (jastrow.jas): 

jastrow_parameter   1
  5  5  0           norda,nordb,nordc
   0.60000000         scalek
   0.00000000   0.00000000  -0.39803661  -0.19727356  -0.04112912   0.08477303 (a for O)
   0.00000000   0.00000000  -0.25378471   0.03693657   0.02169054  -0.00707375 (a for H)
   0.50000000   0.48551602   0.09924779   0.00590014  -0.00626481  -0.00347973 (b)
end

Derivative file (jastrow.der): 

jasderiv
4 5 0 0 nparma,nparmb,nparmc,nparmf
  3 4 5 6 (iwjasa(iparm),iparm=1,nparma)
  3 4 5 6 (iwjasa(iparm),iparm=1,nparma)
2 3 4 5 6 (iwjasb(iparm),iparm=1,nparmb)
end

Explanation:

  • Two atom types (O and H), so two a lines
  • For each atom type: optimize parameters 3-6 (4 parameters)
  • For b parameters: optimize parameters 2-6 (5 parameters)
  • No c parameters since nordc = 0 in Jastrow file
  • First two a parameters and first b parameter remain fixed

Example 2: Water with 3-body Terms

Jastrow file (jastrow.jas):

jastrow_parameter   1
  5  5  5           norda,nordb,nordc
 0.40000  0.00000  scalek a21
 0.00000  0.00000 -0.04730 -0.39690 -0.15944  0.09709 (a(iparmj),iparmj=1,nparma)
 0.00000  0.00000 -0.01800  0.13474 -0.11232  0.00851 (a(iparmj),iparmj=1,nparma)
 0.50000  0.94655  0.14913 -0.13216  0.09053 -0.01728 (b(iparmj),iparmj=1,nparmb)
 1.69203  1.24656 -1.88214  3.91513 -0.74384 -8.64444 -3.45930  7.94537 -0.61759 -7.28154 -3.20830 10.10651  2.84683  3.11254 -1.82060 -4.12168 -2.73375  7.97867  2.63741  0.58993 -3.22734 -3.43777 -0.80525 (c(iparmj),iparmj=1,nparmc)
-0.18440 -2.24997 -1.73422  0.47251  1.54643  6.06904  3.29715  1.00667 -3.97339 -1.90822  2.48432 -1.92995 -5.13868 -1.55965 -3.12079  4.42562  3.87653 -4.16459  0.11133 -3.79462  3.68329  0.66761  1.96643 (c(iparmj),iparmj=1,nparmc)
end

Derivative file (jastrow.der): 

jasderiv
4 4 15 0 nparma,nparmb,nparmc,nparmf
  3 4 5 6 (iwjasa(iparm),iparm=1,nparma)
  3 4 5 6 (iwjasa(iparm),iparm=1,nparma)
2 3 4 5 6 (iwjasb(iparm),iparm=1,nparmb)
3 5 7 8 9         11 13 14 15 16     17 18 20 21 23 (c for O)
3 5 7 8 9         11 13 14 15 16     17 18 20 21 23 (c for H)
end

Explanation:

  • Two atom types (O and H)
  • Optimize 4 a parameters per atom type (indices 3-6)
  • Optimize 5 b parameters (indices 2-6)
  • Optimize 15 c parameters per atom type (non-consecutive indices shown)
  • Some c parameters are not optimized (e.g., indices 1, 2, 4, 6, 10, 12, 19, 22)

Example 3: Selective Optimization Strategy

For staged optimization, you might start with fewer parameters:

Initial stage - optimize only 2-body terms: 

jasderiv
2 3 0 0 nparma,nparmb,nparmc,nparmf
  3 4 (iwjasa for O)
  3 4 (iwjasa for H)
2 3 4 (iwjasb)
end

Later stage - add 1-body terms: 

jasderiv
4 5 0 0 nparma,nparmb,nparmc,nparmf
  3 4 5 6 (iwjasa for O)
  3 4 5 6 (iwjasa for H)
2 3 4 5 6 (iwjasb)
end

Determining Parameter Indices

The parameter indices correspond to positions in the Jastrow parameter arrays:

a-parameters

For norda = 5, there are nparmja = 6 parameters per atom type: 

Index:  1    2    3         4         5         6
Value: 0.0  0.0  -0.39804  -0.19727  -0.04113   0.08477
Typically optimize indices 3-6 (sometimes 4-6 if cusp is pre-set).

b-parameters

For nordb = 5, there are nparmjb = 6 parameters: 

Index:  1    2         3         4         5          6
Value: 0.5  0.48552   0.09925   0.00590  -0.00626   -0.00348
Typically optimize indices 2-6 (index 1 is fixed at 0.5).

c-parameters

For nordc = 5, there are 23 parameters per atom type. The selection depends on which three-body terms are important for your system.

Loading Jastrow Derivatives in CHAMP Input

Specify both the Jastrow file and derivative file:

%module general
    title  'VMC optimization with Jastrow'
    pool   './pool/'
%endmodule

load trexio          $pool/molecule.hdf5
load jastrow         jastrow.jas
load jastrow_der     jastrow.der

%module electrons
    nup    5
    nelec  10
%endmodule

%module optwf
    nopt_iter   10
    method      'linear'
%endmodule

Tips

  • Verify parameter counts match between Jastrow and derivative files
  • Check that all parameter indices are valid (not exceeding array sizes)
  • Start with fewer parameters and gradually increase complexity
  • Monitor optimization progress to ensure parameters are improving the wavefunction
  • Consult Optimization Guide for detailed optimization strategies