ElectronSpinDynamics

Schulten-Wolynes and Semiclassical electronic spin dynamics implemented by Julia.

DifferentialEquations.jl is used for ensemble semiclassical simulation.

Installation

1. Install Julia

See julialang.org for installation instructions. I personally recommend using Juliaup to install Julia.

2. Clone the repository

git clone https://github.com/KenHino/ElectronSpinDynamics.jl.git
cd ElectronSpinDynamics.jl

3. Install the package

julia --project=. -e 'using Pkg; Pkg.instantiate()'

4. Run the tests

julia --project=. -e 'using Pkg; Pkg.test("ElectronSpinDynamics")'

5. Examples

cd example
julia --project=.. --threads 4 tutorial.jl

6. (optional) You can perform simulation without input file. See function such SC and SW.

7. (optional) The results are exported in HDF format. You can access the data by Python (needless to say, Julia as well).

# Access results by Python
import h5py
f = h5py.File('example/SC/results.h5', 'r')
B005_SC_Tp = f['B=0.05']['T+'][:]
B005_SC_T0 = f['B=0.05']['T0'][:]
B005_SC_S = f['B=0.05']['S'][:]
B005_SC_Tm = f['B=0.05']['T-'][:]
B005_SC_time = f['B=0.05']['time_ns'][:]

Input file is example/input.ini.

Input file

Hamiltonian

• J: Exchange coupling constant in mT (divided by absolute value of γe)
• D: D tensor in mT
• kS: Singlet rate constant in μs-1
• kT: Triplet rate constant in μs-1
• I: Multiplicity of the nuclei (not quantum numbers) when I=3, nucleus is nitrogen, when I=2, nucleus is hydrogen. other nuclei are not supported yet.
• An: Nuclear hyperfine coupling constants in mT (asymmetric is not supported yet)
• out: Output folder
• B: Magnetic field in mT
• simulation_time: Simulation time in ns (not μs)
• dt: Time step in ns
• N_samples: Number of samples

Caution: The other parameters are not used currently! But for compatibility, I left them here.

[system variables]
J = 0.224
D = -0.2533333333333333 -0.0 -0.0 -0.0 -0.2533333333333333 -0.0 -0.0 -0.0 +0.5066666666666666
kS = 1.0
kT = 1.0
[electron 1]
g = 2.0023193
I = 3 2 2 2 2 2 2 2 2 2 3
N_I = 1 1 1 1 1 1 1 1 1 1 1
A1 = 0.5141406139911681 0.0 0.0 0.0 0.5141406139911681 0.0 0.0 0.0 0.5141406139911681
A2 = -0.13706792618414612 -0.0 -0.0 -0.0 -0.13706792618414612 -0.0 -0.0 -0.0 -0.13706792618414612
A3 = -0.13706792618414612 -0.0 -0.0 -0.0 -0.13706792618414612 -0.0 -0.0 -0.0 -0.13706792618414612
A4 = -0.13706792618414612 -0.0 -0.0 -0.0 -0.13706792618414612 -0.0 -0.0 -0.0 -0.13706792618414612
A5 = -0.44033852832217035 -0.0 -0.0 -0.0 -0.44033852832217035 -0.0 -0.0 -0.0 -0.44033852832217035
A6 = 0.4546400686867858 0.0 0.0 0.0 0.4546400686867858 0.0 0.0 0.0 0.4546400686867858
A7 = 0.4546400686867858 0.0 0.0 0.0 0.4546400686867858 0.0 0.0 0.0 0.4546400686867858
A8 = 0.4546400686867858 0.0 0.0 0.0 0.4546400686867858 0.0 0.0 0.0 0.4546400686867858
A9 = 0.4262605982027767 0.0 0.0 0.0 0.4262605982027767 0.0 0.0 0.0 0.4262605982027767
A10 = 0.4233203613613487 0.0 0.0 0.0 0.4233203613613487 0.0 0.0 0.0 0.4233203613613487
A11 = 0.1784350286060594 0.0 0.0 0.0 0.1784350286060594 0.0 0.0 0.0 0.1784350286060594
[electron 2]
g = 2.0023193
I = 2 3 3 2 2 2 2
N_I = 1 1 1 1 1 1 1
A1 = 1.6045 0.0 0.0 0.0 1.6045 0.0 0.0 0.0 1.6045
A2 = 0.32156666666666667 0.0 0.0 0.0 0.32156666666666667 0.0 0.0 0.0 0.32156666666666667
A3 = 0.1465 0.0 0.0 0.0 0.1465 0.0 0.0 0.0 0.1465
A4 = -0.278 -0.0 -0.0 -0.0 -0.278 -0.0 -0.0 -0.0 -0.278
A5 = -0.3634 -0.0 -0.0 -0.0 -0.3634 -0.0 -0.0 -0.0 -0.3634
A6 = -0.4879 -0.0 -0.0 -0.0 -0.4879 -0.0 -0.0 -0.0 -0.4879
A7 = -0.5983 -0.0 -0.0 -0.0 -0.5983 -0.0 -0.0 -0.0 -0.5983
[simulation parameters]
simulation_type = SW
output_folder = out
seed = 42 99
B = 0.05
initial_state = singlet
simulation_time = 201.0
dt = 1.0
N_krylov = 7
integrator_tolerance = 1e-08
N_samples = 1000000

References

• SW theory: Schulten, Klaus, and Peter G. Wolynes. "Semiclassical description of electron spin motion in radicals including the effect of electron hopping." The Journal of Chemical Physics 68.7 (1978): 3292-3297.
• SC theory:
  • w/o D and J: Manolopoulos, David E., and P. J. Hore. "An improved semiclassical theory of radical pair recombination reactions." The Journal of chemical physics 139.12 (2013).
  • with kS != kT: Lewis, Alan M., David E. Manolopoulos, and P. J. Hore. "Asymmetric recombination and electron spin relaxation in the semiclassical theory of radical pair reactions." The Journal of Chemical Physics 141.4 (2014).
  • with D and J: Fay, Thomas P., et al. "How quantum is radical pair magnetoreception?." Faraday discussions 221 (2020): 77-91.