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66 lines
2.1 KiB
Org Mode
66 lines
2.1 KiB
Org Mode
* Rotation matrix in a subspace to rotation matrix in the full space
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Usually, we are using a list of MOs, for exemple the active ones. When
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we compute a rotation matrix to rotate the MOs, we just compute a
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rotation matrix for these MOs in order to reduce the size of the
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matrix which has to be computed. Since the computation of a rotation
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matrix scale in $O(N^3)$ with $N$ the number of MOs, it's better to
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reuce the number of MOs involved.
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After that we replace the rotation matrix in the full space by
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building the elements of the rotation matrix in the full space from
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the elements of the rotation matrix in the subspace and adding some 0
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on the extradiagonal elements and some 1 on the diagonal elements,
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for the MOs that are not involved in the rotation.
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Provided:
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| mo_num | integer | Number of MOs |
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Input:
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| m | integer | Size of tmp_list, m <= mo_num |
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| tmp_list(m) | integer | List of MOs |
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| tmp_R(m,m) | double precision | Rotation matrix in the space of |
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| | | the MOs containing by tmp_list |
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Output:
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| R(mo_num,mo_num | double precision | Rotation matrix in the space |
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| | | of all the MOs |
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Internal:
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| i,j | integer | indexes in the full space |
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| tmp_i,tmp_j | integer | indexes in the subspace |
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#+BEGIN_SRC f90 :comments org :tangle sub_to_full_rotation_matrix.irp.f
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subroutine sub_to_full_rotation_matrix(m,tmp_list,tmp_R,R)
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BEGIN_DOC
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! Compute the full rotation matrix from a smaller one
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END_DOC
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implicit none
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! in
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integer, intent(in) :: m, tmp_list(m)
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double precision, intent(in) :: tmp_R(m,m)
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! out
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double precision, intent(out) :: R(mo_num,mo_num)
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! internal
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integer :: i,j,tmp_i,tmp_j
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! tmp_R to R, subspace to full space
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R = 0d0
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do i = 1, mo_num
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R(i,i) = 1d0 ! 1 on the diagonal because it is a rotation matrix, 1 = nothing change for the corresponding orbital
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enddo
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do tmp_j = 1, m
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j = tmp_list(tmp_j)
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do tmp_i = 1, m
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i = tmp_list(tmp_i)
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R(i,j) = tmp_R(tmp_i,tmp_j)
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enddo
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enddo
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end
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#+END_SRC
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