A fast and precise DFT wavelet code

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A fast and precise DFT wavelet code
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Introduction to O(N) BigDFT

The purpose of this lesson is to introduce linear-scaling BigDFT and explain how to do to basic calculations. Make sure you have read the relevant papers in articles describing BigDFT before beginning. As discussed on the "Input variables" page, we require a coordinate file posinp.xyz and an input.yaml file.

Methanol

"visualisation methanol"

We begin with the example of methanol, using the coordinates in methanol.xyz :

6 angstroem 
free 
C       -0.047131    0.664389    0.000000 
O       -0.047131   -0.758551    0.000000 
H       -1.092995    0.969785    0.000000 
H        0.878534   -1.048458    0.000000 
H        0.437145    1.080376    0.891772 
H        0.437145    1.080376   -0.891772

We will first run a cubic-scaling calculation as a point of reference, using the file methanol_cubic.yaml:

 dft:
   hgrids: 0.4
   rmult: [5.0, 7.0]
   ixc: LDA (ABINIT)
   disablesym: Yes

Copy methanol_cubic.yaml to methanol.yaml and run BigDFT using

./bigdft methanol | tee methanol_cubic.out

We will use this output as a reference for the energy, forces and KS eigenvalues.

We now proceed to running the first O(N) calculations. We begin by running a calculation using the diagonalization approach, for which the parameters are defined in the file methanol_linear.yaml:

 dft:
   hgrids: 0.4
   rmult: [5.0, 7.0]
   ixc: LDA (ABINIT)
   inputpsiid: linear
   disablesym: Yes
 perf:
   store_index: Yes
   check_sumrho: 1
   check_overlap: 1
   check_matrix_compression: No
   experimental_mode: Yes
   calculate_KS_residue: No
   correction_co_contra: Yes
   hamapp_radius_incr: 6
   mixing_after_inputguess: 1
   kappa_conv: 0.1
 lin_general:
   hybrid: Yes
   nit: 50
   rpnrm_cv: 1.0E-012
   taylor_order: 1020
   max_inversion_error: 5.0e-8
   output_mat: 1
   charge_multipoles: 11
 lin_basis:
   nit: 8
   idsx: 8
   alpha_diis: 0.5
   alpha_sd: 0.5
   nstep_prec: 6
   fix_basis: 1.0e-12
   correction_orthoconstraint: 0
   gnrm_ig: 1.e-1
   gnrm_cv: 2.0e-3
   min_gnrm_for_dynamic: 4.0e-3
 lin_kernel:
   nit: 6
   nstep: 2
   idsx: 6
   idsx_coeff: 2
   alphamix: 0.3
   linear_method: DIAG
 lin_basis_params:
   C:
     nbasis: 4
     ao_confinement: -1.0
     confinement: -1.0
     rloc: 5.5
     rloc_kernel: 9.0
     rloc_kernel_foe: 10.0
   O:
     nbasis: 4
     ao_confinement: -1.0
     confinement: -1.0
     rloc: 5.5
     rloc_kernel: 9.0
     rloc_kernel_foe: 10.0
   H:
     nbasis: 1
     ao_confinement: -1.0
     confinement: -1.0
     rloc: 5.0
     rloc_kernel: 9.0
     rloc_kernel_foe: 10.0

By copying methanol_linear.yaml to methanol.yaml we can then run BigDFT in the same way as the cubic version. A reasonable value for the number of MPI tasks cores is about one fifth of the total number of support functions. This can be increased (with a negative impact on the efficiency) up to a maximum of one support function/MPI.

We can easily rerun with FOE by modifying the following variable:

linear_method: FOE

or with direct minimization by modifying:

linear_method: DIRMIN
alphamix: 1.0

For large systems the diagonalization test will be much more expensive, but for a system of this size all three methods take a similar amount of time. Run with all three and compare the outputs. You should notice that all three converge in roughly 12 iterations of the outer loop to a final energy of -24.021 Ha (grep for delta out if you want to see an overview of the outer loop convergence - see below for more information on the output file), compared to -24.028 Ha for the cubic-scaling code. FOE gives a slightly higher final energy, but the differences are within the expected error for the given basis and convergence parameters.

You may also have noticed that for FOE there are no KS eigenvalues printed, while for direct minimization they are only written at the beginning where the input guess orbitals are printed, compared to diagonalization where they are printed at each kernel iteration. Why is this? Well for FOE we aren't calculating the KS states, while for direct minimization we are calculating an arbitrary linear combination of the eigenstates, so in each case we don't have access to the eigenvalues. If you do want the eigenvalues, we can still use FOE or direct minimization, we simply have to perform a diagonalization at the end of the calculation. Add the line

 subspace_diag: Yes 

to the end of the lin_general section and rerun. You will see that there is an additional kernel update at the end of the calculation and the eigenvalues are now printed (note that the occupancies given here are incorrect). Comparing to the diagonalization calculation there are some small differences, these are expected to be bigger than the difference in the total energy, but in both cases this difference will decrease if the convergence thresholds are modified. Note that only the occupied and low energy unoccupied states are expected to be accurate, as the support functions are optimized to minimize the occupied states. If the unoccupied states are required, a small number can be explicitly included in the minimization procedure using the direct minimization approach.

Exercise: Run the above inputs with increasing localization radii. What's the closest you can get to the cubic-scaling energy? Compare also the forces and KS eigenvalues.

Input profiles

Sometimes we want to use a consistent set of values for most parameters, and only want to modify a few. In this case we can import a profile, which already defines a set of common values. This is achieved by simply adding a line like the following to the input file:

 import: linear 

This imports all the information from the profile, and we can then add or overwrite those values if we choose to. The input file for the direct minimization approach then becomes methanol_linear_profile.yaml:

 import: linear
 dft:
   hgrids: 0.4
   rmult: [5.0, 7.0]
   ixc: LDA (ABINIT)
 perf:
   store_index: Yes
 lin_general:
   rpnrm_cv: 1.0E-012
   subspace_diag: Yes
 lin_kernel:
   nstep: 2
   idsx_coeff: 2
   alphamix: 1.0
   linear_method: DIRMIN
 lin_basis_params:
   C:
     nbasis: 4
     ao_confinement: -1.0
     confinement: -1.0
     rloc: 5.5
     rloc_kernel_foe: 10.0
   O:
     nbasis: 4
     ao_confinement: -1.0
     confinement: -1.0
     rloc: 5.5
     rloc_kernel_foe: 10.0
   H:
     nbasis: 1
     ao_confinement: -1.0
     confinement: -1.0
     rloc: 5.0
     rloc_kernel_foe: 10.0

As you can see, this is much shorter than the original input file given above and it also becomes quicker to determine which are the important parameters for this calculation. Currently available profiles can be found in the file bigdft/src/input_variables_definition.yaml where you can also find information about the input parameters.

Exercise: Verify that methanol_linear_profile.yaml gives the same output as running without a profile.

The output file

Much of the BigDFT output is identical to the cubic-scaling version (e.g. the forces, the noise, the stress tensor etc.). The following are some notable exceptions:

fnrm: The gradient of the support functions, which should reach the convergence threshold specified by gnrm_cv. If this value is chosen too small, the code has some tools to detect it and might already exit sooner (if min_gnrm_for_dynamic is reached).

delta: The mean change of the density between two iterations of the kernel optimization. This value should converge to the specified threshold rpnrm_cv.

delta out: The mean change of the density between two outer loop iterations (support function and kernel optimization). This value should converge to the specified threshold rpnrm_cv and is the final stop criterion.

max dev from unity: Gives the maximal deviation of the overlap matrix from the identity. This value should never become larger than about 0.1-0.2. If it does, this indicates that the chosen cutoff radii are too small.

max/mean error: Gives the error of the various matrix powers (inversion, square root etc.). This value should not increase too much and stay of the order of 1.0e−8 . If the error becomes too large, depending on the selected method for calculating the matrices, the code will try to increase the precision of the matrix inversions. If this still does not help, you will see the warning “Taylor order reached maximum”. In such a case you should try to increase the cutoff radii or change the method used.

check boundary values: Gives the weight of the support functions which is located on the boundary of the localization regions. This value should not become much larger than 1.0e-2 and is also an indicator that the localization radii might need to be increased.



Spin polarized calculations

In this section we briefly want to have a look at spin polarized calculations. In this case, the number of up and down spins is different, and we thus need two sets of support functions and kernels (one for the up and one for the down part). Obviously this makes the calculations heavier.

As example we use O_2. Use the following posinp.xyz

2 angstroem
free
O 0.0 0.0 0.0    2
O 0.0 0.0 1.208  0

and the following input.yaml:

import: linear
dft:
  nspin: 2
  mpol: 2
lin_general:
  charge_multipoles: 0
lin_basis_params:
  O:
    nbasis: 9
ig_occupation:
  O:
    2s: [1.0, 1.0]
    2p:
    - 1.0
    - 1.0
    - 1.0
    - 1/3
    - 1/3
    - 1/3
    3d: 0.0

We start the run with a polarization of 2. Can you see in the output that this is as well the polarization that we get in the end?

Now let's see what happens if we run a closed shell (i.e. not spin polarized) calculation. Can you modify the input.yaml in such a way as to run a closed shell calculation? If you have troubles you can find the solution here: O2.yaml

Run this closed shell calculation and compare the final result for the energy with the one from the spin polarized case. Which one is lower?


Metallic systems

THIS TUTORIAL MUST BE REWORKED!!!

The linear version performs best for system with a finite HOMO-LUMO gap. Nevertheless we can also treat metallic systems.

As simple example we take one single copper atom. Create a xyz file with a Cu atom at the position (0.0,0.0,0.0). Then copy the following to your input.yaml and launch the calculation:

import: linear
lin_general:
  subspace_diag: yes
perf:
  foe_gap: yes
lin_kernel:
  nit: 6
  alphamix: 0.1
lin_basis_params:
  ao_confinement: -1.0
  confinement: -1.0
  rloc_kernel: 10.0
  rloc_kernel_foe: 12.0
  Cu: {nbasis: 9, rloc: 7.0}
ig_occupation:
  Cu:
    3d: 10.0
    4s: 1.0
    4p: 0.0
chess:
  foe:
    fscale: 5.e-3

You can already see in the first few iterations that the code has convergence problems. For metallic systems this can be an indication that the mixing parameters is chosen too large ("charge sloshing"). Can you try to change the mixing parameter to a smaller value in order to avoid this problem? Hint 1: The corresponding input variable is already contained in the input.yaml file. Hint 2: If you reduce the mixing factor it is also recommendable to increase the number of iterations in the mixing loop.

If you don't find parameters which work, you can find here a solution:Cu.yaml

Troubleshooting

The default values used by BigDFT are usually quite stable. Nevertheless, this run shall illustrate some typical problems that could arise.

For this test we will use a small silicon cluster. Copy the following to a file posinp.xyz

4 angstroem
free
Si        0.000   1.280   0.000
Si        0.000   0.000  -2.047
Si        0.000   0.000   2.047
Si        0.000  -1.280   0.000

In the file input.yaml we simply take the default values:

import: linear

Run this calculation. You will note that it takes more iteration to converge than for the other systems ran so far.

It turns out that for Silicon you often need to include support functions with a d character. That is, instead of the standard setup with 4 (1 s-like, 3 p-like) you now need 9 support functions. Can you modify the input.yaml file in such a way as to use 9 basis support functions per atom, where the additional 5 have d character?

Hint: you need to modify the fields lin_basis_params and ig_occupation.

You can find the solution here: Si4.yaml

Post-processing

Some tips for post-processing. Note you must have specified the printing of the support function matrices in the sparse format!

For the post-processing go into the data directory that has been created.

multipole analysis :

The following performs an atomic multipole analysis, based on the matrices calculated during the run.

bigdft-tool \
    -a multipole-analysis \
    --mpirun='' \
    --overlap_file=overlap_sparse.txt \
    --kernel_file=density_kernel_sparse.txt  \
    --kernel_matmul_file=density_kernel_sparse_matmul.txt \
    --hamiltonian_file=hamiltonian_sparse.txt \
    --metadata_file=sparsematrix_metadata.dat \
    --multipole_matrix_0_0=mpmat_0_0.txt \
    --multipole_matrix_1_0=mpmat_1_-1.txt \
    --multipole_matrix_1_1=mpmat_1_0.txt \
    --multipole_matrix_1_2=mpmat_1_1.txt \
    --multipole_matrix_2_0=mpmat_2_-2.txt \
    --multipole_matrix_2_1=mpmat_2_-1.txt \
    --multipole_matrix_2_2=mpmat_2_0.txt \
    --multipole_matrix_2_3=mpmat_2_1.txt \
    --multipole_matrix_2_4=mpmat_2_2.txt


pdos :

This generates a gnuplot file PDoS.gp ready to be plotted (you only have to adjust the colors and label according to your needs). To do so you first have to diagonalize the Hamiltonian:

bigdft-tool \
    -a solve-eigensystem \
    --mpirun='' \
    --matrix_format='serial_text' \
    --metadata_file=sparsematrix_metadata.dat \
    --overlap_file=overlap_sparse.txt \
    --hamiltonian_file=hamiltonian_sparse.txt \
    --coeff_file=coeffs.txt

This will write the eigenvectors in the file coeffs.txt.

Now you can calculate the partial density of states:


bigdft-tool \
    -a pdos \
    --mpirun='' \
    --matrix_format='serial_text' \
    --metadata_file=sparsematrix_metadata.dat \
    --overlap_file=overlap_sparse.txt \
    --hamiltonian_file=hamiltonian_sparse.txt \
    --coeff_file=coeffs.txt \
    --pdos_file=pdos.dat

The file pdos.dat indicates which pdos shall be calculated. For the example of methanol you can use the following one:

4     # number of pdos
# C
C 1   # for the first pdos, take support function number 1 of the carbon atoms
C 2   # ... plus also number 2
C 3   # ... plus also number 3
C 4   # ... plus also number 4
# O
O 1   # for the second pdos, take support function number 1 of the oxygen atoms
O 2   # ... plus also number 2
O 3   # ... plus also number 3
O 4   # ... plus also number 4
# H
H 1   # for the third pdos, take support function number 1 of the hydrogen atoms
# total
C 1   # For the total dos, take all support functions
C 2   # 
C 3   # 
C 4   # 
O 1   # 
O 2   # 
O 3   # 
O 4   # 
H 1   # 

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