File size: 2,912 Bytes
5b0cbb5 |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 |
---
license: mit
---
# Quantum Electronic Integrals
This dataset contains quantum interaction integrals between randomly sampled pairs/quadruples of Gaussian-Type Orbitals (GTOs).
The targets were computed in julia using [GaussianBasis.jl](https://github.com/FermiQC/GaussianBasis.jl).
## Loading data from python
See [qml/data/integrals.py](https://github.com/aklipf/qml).
Loading a mono-electronic integral dataset should be as simple as:
```py
from qml.data import MonoIntegral
I_2_1 = MonoIntegral.h5read("integrals/mono_20k/mono_2_1.h5")
```
The `MonoIntegral` class inherits its `h5read` method from the `TensorDict` mixin.
Each dataset contains its corresponding `TensorDict` dataclass, reading data from any
compatible HDF5 storage (containing enough keys).
# Mono-Electronic Integrals
See [mono_20k](https://huggingface.co/datasets/qml/integrals/tree/main/mono_20k)
and [mono_100k](https://huggingface.co/datasets/qml/integrals/tree/main/mono_100k)
for 2-electron integrals.
Each HDF5 file encodes an object of type:
```julia
# jqml/Data.jl
""" Object storing 1-electron integrals. """
struct MonoIntegral{T} <: ArrayFields
l :: Vector{Int64}
exp :: Union{SArray, Array{T}}
xyz :: Union{SArray, Array{T}}
overlap :: Array{T}
kinetic :: Array{T}
nuclear :: Array{T}
Z :: Array{Int64}
end
```
Input wave functions (ψ1, ψ2) are primitive, spherical GTO-shells
with unit coefficients, i.e.
ψ(C + r) = rˡ ⋅ Yₗₘ(r/|r|) ⋅ exp(-α |r|²)
where C is `ψ.center`, α is `ψ.exp`, and the magnetic quantum number m
takes all possible values in {-l, ..., l} within each subshell.
### Inputs:
- `xyz` : center of ψ2 (ψ1 is centered at 0)
- `l` : pair of angular momenta (l₁, l₂)
- `exp` : exponents (α₁, α₂)
- `Z` : atomic charges used to compute the nuclear integral.
### Targets:
- `overlap` integrals `S₁₂ = ∫ ψ1 ⋅ ψ2`
- `kinetic` integrals `T₁₂ = 1/2 * ∫ ∇ψ1 ⋅ ∇ψ2`
- `nuclear` attraction integrals
`N₁₂ = ∫ ψ1 ⋅ [(Z₁ / |r|) + (Z₂ / |r - xyz|)] ⋅ ψ2`
### Note:
Mono-electronic integrals are square matrices of shape `D × D` with
D = (2 * l1 + 1) + (2 * l2 + 1)
Indices correspond to increasing values of `m1 ∈ {-l1, …, l1}` first,
then increasing values of `m2 ∈ {-l2, …, l2}`.
# Bi-Electronic Integrals
Batches of 2-electron integrals are returned in the
following sparse format:
```julia
"""Object for storing bi-electronic integrals"""
struct BiIntegral4c{T} <: ArrayFields
l :: Vector{Int64}
exp :: Array{T}
xyz :: Array{T}
ijkl :: Array{Int16}
Bijkl :: Array{Float64}
index :: Vector{Int64}
end
```
The `index` field has the same length as `ijkl` and `Bijkl`, and maps each integral element
to the index of the corresponding input GTOs.
See [bi_200](https://huggingface.co/datasets/qml/integrals/tree/main/bi_200)
|