QMC Wavefunction Optimizations¶

We will optimize the Jastrow factor and then the Coupled Cluster (CI) coefficients for both the Ground State (GS) and Excited State (ES).

1. Ground State Optimization¶

Create a directory for the Ground State calculation and link the TREXIO file:

mkdir GS_Calc
cd GS_Calc
ln -s ../COH2_GS.trexio .

Initial Jastrow¶

Create a jastrow.start file suitable for \(COH_2\) (C, O, H atoms):

jastrow_parameter   1
  5  5  0           norda,nordb,nordc
   0.60000000   0.00000000     scalek,a21
   0.00000000   0.00000000  0. 0. 0. 0. (a(iparmj),iparmj=1,nparma) ! e-n C
   0.00000000   0.00000000  0. 0. 0. 0. (a(iparmj),iparmj=1,nparma) ! e-n O
   0.00000000   0.00000000  0. 0. 0. 0. (a(iparmj),iparmj=1,nparma) ! e-n H
   0.50000000   1.00000000  0. 0. 0. 0. (b(iparmj),iparmj=1,nparmb)
 (c(iparmj),iparmj=1,nparmc) ! e-e-n C
 (c(iparmj),iparmj=1,nparmc) ! e-e-n O
 (c(iparmj),iparmj=1,nparmc) ! e-e-n H
end

Prepare a jastrow.der file matching this structure (see previous tutorials).

Optimization Input¶

Create vmc_opt_gs.inp:

%module general
    title           'GS Optimization'
    mode            'vmc_one_mpi1'
%endmodule

load trexio         COH2_GS.trexio
load jastrow        jastrow.start
load jastrow_der    jastrow.der

%module electrons
    nup           6
    nelec         12
%endmodule

%module optwf
    ioptwf        1
    ioptci        0      # Optimize Jastrow first
    ioptjas       1
    ioptorb       0
    method        'sr_n'
    nopt_iter     10
    nblk_max      5000
    ncore         0
    nextorb       600    # Ensure large enough for virtuals
    sr_tau        0.05
    sr_eps        0.01
    sr_adiag      0.01
%endmodule

%module blocking_vmc
    vmc_nstep     20
    vmc_nblk      100
    vmc_nblkeq    1
    vmc_nconf_new 0
%endmodule

Run CHAMP. Save the resulting optimized Jastrow (e.g., cp jastrow_optimal.1.iter10 jastrow_gs.opt).

Optimize CI Coefficients¶

Create a new input or modify the existing one to optimize CI coefficients as well:

    ioptci        1      # Enable CI optimization
    load jastrow  jastrow_gs.opt

Run CHAMP again to get the fully optimized GS wavefunction.

2. Excited State Optimization¶

Create a directory for the Excited State calculation:

cd ..
mkdir ES_Calc
cd ES_Calc
ln -s ../COH2_ES.trexio .

reuse GS Jastrow¶

We can use the optimized Jastrow from the Ground State as a good starting point for the Excited State.

cp ../GS_Calc/jastrow_gs.opt jastrow.start
cp ../GS_Calc/jastrow.der .

ES Optimization Input¶

Create vmc_opt_es.inp. Use the same settings as GS, but load the ES TREXIO file.

load trexio         COH2_ES.trexio
load jastrow        jastrow.start
load jastrow_der    jastrow.der

Run the optimization (Jastrow first, then Jastrow+CI).

3. Calculate Excitation Energy¶

Run DMC calculations for both optimized GS and ES wavefunctions (see Ground State tutorial for DMC setup).

The excitation energy is: $$ \Delta E = E_{\text{DMC}}^{\text{ES}} - E_{\text{DMC}}^{\text{GS}} $$

Compute the error bars using standard error propagation: $$ \delta (\Delta E) = \sqrt{\delta E_{\text{GS}}^2 + \delta E_{\text{ES}}^2} $$