Non-adiabatic Coupling

In Hefei-NAMD non-adiabatic coupling (NAC) is defined as the derivative of wavefunctions

\begin{equation} \mathbf{D}_{jk} = \mel{\phi_j}{\dv{t}}{\phi_k} \end{equation}

where $\phi$ is the Kohn-Sham (KS) orbitals calculated by VASP.

To simulate photo-excitations process, momentum matrix element $\mathbf{P}_{jk} = \mel{j}{\mathbf{p}}{k}$ is needed to calculate the light-matter interaction (LMI) term

\begin{equation} \mathcal{H}_{jk}^{\mathrm{LMI}} = -e \frac{\mathbf{A}}{m_e} \mel{j}{\mathbf{p}}{k} \end{equation}

in which $\mathbf{p}$ is the momentum opeartor, and $\mathbf{A}$ is the vector potential of external field.

NOTE: namd_lmi is capable of calculating both $\mathbf{D}_{jk}$ and $\mathbf{P}_{jk}$.

Help message

$ namd_lmi nac
Calculate non-adiabatic coupling (NAC) including `<j| d/dt |k>` and momentum matrix `<i| p |j>`

Usage: namd_lmi nac [OPTIONS]

Options:
  -n, --nthreads <NTHREADS>
          Number of threads for parallel calculation.

          If 0 is set, it will fall back to the number of logic CPU cores of you machine.

          [default: 0]

  -c, --config <CONFIG>
          Config file name.

          Aliases: "cfg", "conf".

          [default: nac_config.toml]

      --generate <GENERATE>
          Generate auxiliary files for the calculation and analysis.

          The calculation will not run if this flag is set.

          Alias: "gen"

          Possible values:
          - config-template:      Generate config template for NAC calculation. Aliases: "config", "cfg", "conf"
          - postprocess-template: Generate post-process scripts for NAC analysis. Aliases: "post-process", "postprocess", "pp"

  -h, --help
          Print help (see a summary with '-h')

Procedures

Generate a configuration template.

$ namd_lmi nac --generate conf
2024-11-19 20:26:10 [ INFO] Global logger initialized with targets being stderr and "./globalrun.log"
2024-11-19 20:26:10 [ INFO] Writing `01_nac_config_template.toml ...`
2024-11-19 20:26:10 [ INFO] Time used: 1.351249ms

where the 01_nac_config_template.toml reads

		 rundir = "../run"
		ikpoint = 1
		 brange = [0, 0]
			nsw = 2000
		 ndigit = 4
		  potim = 1
	temperature = 0
phasecorrection = true
	   nacfname = "NAC.h5"

Modify the configuration according to your AIMD parameters.

If you are familiar with the original Hefei-NAMD procedure, the parameters in 01_nac_config_template.toml is not hard to understand:
- rundir string: AIMD directory where thousands of SCF with WAVECARs lies within.
- ikpoint integer: Which K point to choose, the index counts from 1. For now, you can only choose one K point is selectable to calculate NAC and momentum matrix elements.
- brange [integer, integer]: Selected band range for calculation. [100, 120] will select band from 100 to 120 to do the calculation, 21 bands in total.
- nsw integer: Number of steps in AIMD. If there are 2000 steps in your run/, this field should be 2000.
- ndigit integer: Number of digits for the index of each step. If the directories in your run/ are 00001 ... 02000, this field should be 5.
- potim float: Time step of the AIMD, consistent with the POTIM in INCAR during NVE.
- temperature float: Temperature of the MD, consistent with the TEEND in INCAR during NVT.
- phasecorrection bool: Do phase correction for the KS orbitals or not. Should be either true or false. Usually this term is essential for the photo-excitation process.
- nacfname string: Output file name.
NOTE: The string fields must be surrounded with quotation mark "".

Do the coupling calculation.

This process is quite simple

$ namd_lmi nac -c 01_nac_config_template.toml
2024-11-19 21:06:20 [ INFO] Global logger initialized with targets being stderr and "./globalrun.log"
2024-11-19 21:06:20 [ INFO]
+----------------------------------------------------------------------+
|                                                                      |
|    _   _            __  __  _____           _       __  __  _____    |
|   | \ | |    /\    |  \/  ||  __ \         | |     |  \/  ||_   _|   |
|   |  \| |   /  \   | \  / || |  | | ______ | |     | \  / |  | |     |
|   | . ` |  / /\ \  | |\/| || |  | ||______|| |     | |\/| |  | |     |
|   | |\  | / ____ \ | |  | || |__| |        | |____ | |  | | _| |_    |
|   |_| \_|/_/    \_\|_|  |_||_____/         |______||_|  |_||_____|   |
|                                                                      |
+----------------------------------------------------------------------+

Welcome to use namd!
    current version:    0.1.0
    git hash:           d659586
    author(s):          Ionizing
    host:               x86_64-unknown-linux-gnu
    built time:         2024-11-19 15:34:05 +08:00

2024-11-19 21:06:20 [ INFO] Running with 0 threads.
2024-11-19 21:06:20 [ INFO] Got NAC config:
####         NAMD-lmi config for Non-Adiabatic Coupling (NAC) calculation       ####
####    YOU NEED TO CHANGE THE PARAMETERS IN THE FOLLOWING TO FIT YOU SYSTEM    ####

               rundir = "../../aimd/static_ncl_40/run/"
              ikpoint = 1
               brange = [213, 220]
                  nsw = 2000
               ndigit = 4
                potim = 1
          temperature = 300
      phasecorrection = true
             nacfname = "NAC.h5"

2024-11-19 21:06:20 [ INFO] No pre-calculated NAC available, start calculating from scratch in "../../aimd/static_ncl_40/run/"/.../WAVECARs ...
2024-11-19 21:06:20 [ INFO]  Calculating couplings between "../../aimd/static_ncl_40/run/0001" and "../../aimd/static_ncl_40/run/0002" ..., remains:   1999
2024-11-19 21:06:20 [ INFO]  Calculating couplings between "../../aimd/static_ncl_40/run/0312" and "../../aimd/static_ncl_40/run/0313" ..., remains:   1998
2024-11-19 21:06:20 [ INFO]  Calculating couplings between "../../aimd/static_ncl_40/run/1000" and "../../aimd/static_ncl_40/run/1001" ..., remains:   1997
2024-11-19 21:06:20 [ INFO]  Calculating couplings between "../../aimd/static_ncl_40/run/0218" and "../../aimd/static_ncl_40/run/0219" ..., remains:   1996
2024-11-19 21:06:20 [ INFO]  Calculating couplings between "../../aimd/static_ncl_40/run/0078" and "../../aimd/static_ncl_40/run/0079" ..., remains:   1995
2024-11-19 21:06:20 [ INFO]  Calculating couplings between "../../aimd/static_ncl_40/run/0132" and "../../aimd/static_ncl_40/run/0133" ..., remains:   1994
...
2024-11-19 21:08:31 [ INFO]  Calculating couplings between "../../aimd/static_ncl_40/run/1370" and "../../aimd/static_ncl_40/run/1371" ..., remains:      5
2024-11-19 21:08:31 [ INFO]  Calculating couplings between "../../aimd/static_ncl_40/run/1358" and "../../aimd/static_ncl_40/run/1359" ..., remains:      4
2024-11-19 21:08:31 [ INFO]  Calculating couplings between "../../aimd/static_ncl_40/run/1216" and "../../aimd/static_ncl_40/run/1217" ..., remains:      3
2024-11-19 21:08:31 [ INFO]  Calculating couplings between "../../aimd/static_ncl_40/run/1217" and "../../aimd/static_ncl_40/run/1218" ..., remains:      2
2024-11-19 21:08:31 [ INFO]  Calculating couplings between "../../aimd/static_ncl_40/run/1215" and "../../aimd/static_ncl_40/run/1216" ..., remains:      1
2024-11-19 21:08:32 [ INFO] Time used: 72.490979406s

namd_lmi nac uses rayon to utilize multi-threaded parallelism and you can specify the number of threads used by this command via -n/--nthreads. For example namd_lmi -c 01_nac_config_template.toml -n 32 uses 32 threads to calculate the couplings.

Visualize couplings

Run namd_lmi nac --generate pp to get a Python script to visualize the produced NAC.h5

$ namd_lmi nac --generate pp
2024-11-19 21:14:22 [ INFO] Global logger initialized with targets being stderr and "./globalrun.log"
2024-11-19 21:14:22 [ INFO] Writing `nac_plot.py` ...
2024-11-19 21:14:22 [ INFO] Time used: 1.241002ms 

$ python3 ./nac_plot.py
Writing nac_bands.png
Writing nac_nac.png

And the produced .pngs should look like

You can modify nac_plot.py to visualize whatever you want.

Data fields of `NAC.h5`

$ h5dump -H NAC.h5
HDF5 "NAC.h5" {
GROUP "/" {
   DATASET "brange" {
      DATATYPE  H5T_ARRAY { [2] H5T_STD_U64LE }
      DATASPACE  SCALAR
   }
   DATASET "efermi" {
      DATATYPE  H5T_IEEE_F64LE
      DATASPACE  SCALAR
   }
   DATASET "eigs" {
      DATATYPE  H5T_IEEE_F64LE
      DATASPACE  SIMPLE { ( 1999, 1, 8 ) / ( 1999, 1, 8 ) }
   }
   DATASET "ikpoint" {
      DATATYPE  H5T_STD_U64LE
      DATASPACE  SCALAR
   }
   DATASET "nbands" {
      DATATYPE  H5T_STD_U64LE
      DATASPACE  SCALAR
   }
   DATASET "nbrange" {
      DATATYPE  H5T_STD_U64LE
      DATASPACE  SCALAR
   }
   DATASET "ndigit" {
      DATATYPE  H5T_STD_U64LE
      DATASPACE  SCALAR
   }
   DATASET "nspin" {
      DATATYPE  H5T_STD_U64LE
      DATASPACE  SCALAR
   }
   DATASET "nsw" {
      DATATYPE  H5T_STD_U64LE
      DATASPACE  SCALAR
   }
   DATASET "olaps_i" {
      DATATYPE  H5T_IEEE_F64LE
      DATASPACE  SIMPLE { ( 1999, 1, 8, 8 ) / ( 1999, 1, 8, 8 ) }
   }
   DATASET "olaps_r" {
      DATATYPE  H5T_IEEE_F64LE
      DATASPACE  SIMPLE { ( 1999, 1, 8, 8 ) / ( 1999, 1, 8, 8 ) }
   }
   DATASET "phasecorrection" {
      DATATYPE  H5T_ENUM {
         H5T_STD_I8LE;
         "FALSE"            0;
         "TRUE"             1;
      }
      DATASPACE  SCALAR
   }
   DATASET "pij_i" {
      DATATYPE  H5T_IEEE_F64LE
      DATASPACE  SIMPLE { ( 1999, 1, 3, 8, 8 ) / ( 1999, 1, 3, 8, 8 ) }
   }
   DATASET "pij_r" {
      DATATYPE  H5T_IEEE_F64LE
      DATASPACE  SIMPLE { ( 1999, 1, 3, 8, 8 ) / ( 1999, 1, 3, 8, 8 ) }
   }
   DATASET "potim" {
      DATATYPE  H5T_IEEE_F64LE
      DATASPACE  SCALAR
   }
   DATASET "proj" {             // This part is cropped from PROCARs
      DATATYPE  H5T_IEEE_F64LE
      DATASPACE  SIMPLE { ( 1999, 4, 8, 36, 9 ) / ( 1999, 4, 8, 36, 9 ) }
   }
   DATASET "temperature" {
      DATATYPE  H5T_IEEE_F64LE
      DATASPACE  SCALAR
   }
}
}

NAMD-LMI Manual

Non-adiabatic Coupling

Help message

Procedures

Data fields of NAC.h5

Data fields of `NAC.h5`