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lammps/tools/i-pi/drivers/distance.f90
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distance.f90
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! This contains the algorithms needed to calculate the distance between atoms.
!
! Copyright (C) 2013, Joshua More and Michele Ceriotti
!
! Permission is hereby granted, free of charge, to any person obtaining a copy
! of this software and associated documentation files (the "Software"), to deal
! in the Software without restriction, including without limitation the rights
! to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
! copies of the Software, and to permit persons to whom the Software is
! furnished to do so, subject to the following conditions:
! The above copyright notice and this permission notice shall be included in
! all copies or substantial portions of the Software.
! THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
! IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
! FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
! AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
! LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
! OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
! THE SOFTWARE.
!
! Functions:
! vector_separation: Calculates the vector separating two atoms.
! separation: Calculates the square distance between two vectors.
! nearest_neighbours: Generates arrays to calculate the pairs of atoms within
! a certain radius of each other.
MODULE DISTANCE
IMPLICIT NONE
CONTAINS
SUBROUTINE vector_separation(cell_h, cell_ih, ri, rj, rij, r2)
! Calculates the vector separating two atoms.
!
! Note that minimum image convention is used, so only the image of
! atom j that is the shortest distance from atom i is considered.
!
! Also note that while this may not work if the simulation
! box is highly skewed from orthorhombic, as
! in this case it is possible to return a distance less than the
! nearest neighbour distance. However, this will not be of
! importance unless the cut-off radius is more than half the
! width of the shortest face-face distance of the simulation box,
! which should never be the case.
!
! Args:
! cell_h: The simulation box cell vector matrix.
! cell_ih: The inverse of the simulation box cell vector matrix.
! ri: The position vector of atom i.
! rj: The position vector of atom j
! rij: The vector separating atoms i and j.
! r2: The square of the distance between atoms i and j.
DOUBLE PRECISION, DIMENSION(3,3), INTENT(IN) :: cell_h
DOUBLE PRECISION, DIMENSION(3,3), INTENT(IN) :: cell_ih
DOUBLE PRECISION, DIMENSION(3), INTENT(IN) :: ri
DOUBLE PRECISION, DIMENSION(3), INTENT(IN) :: rj
DOUBLE PRECISION, DIMENSION(3), INTENT(OUT) :: rij
DOUBLE PRECISION, INTENT(OUT) :: r2
INTEGER k
DOUBLE PRECISION, DIMENSION(3) :: sij
! The separation in a basis where the simulation box
! is a unit cube.
sij = matmul(cell_ih, ri - rj)
DO k = 1, 3
! Finds the smallest separation of all the images of atom i and j
sij(k) = sij(k) - dnint(sij(k))
ENDDO
rij = matmul(cell_h, sij)
r2 = dot_product(rij,rij)
END SUBROUTINE
SUBROUTINE separation(cell_h, cell_ih, ri, rj, r2)
! Calculates the squared distance between two position vectors.
!
! Note that minimum image convention is used, so only the image of
! atom j that is the shortest distance from atom i is considered.
!
! Also note that while this may not work if the simulation
! box is highly skewed from orthorhombic, as
! in this case it is possible to return a distance less than the
! nearest neighbour distance. However, this will not be of
! importance unless the cut-off radius is more than half the
! width of the shortest face-face distance of the simulation box,
! which should never be the case.
!
! Args:
! cell_h: The simulation box cell vector matrix.
! cell_ih: The inverse of the simulation box cell vector matrix.
! ri: The position vector of atom i.
! rj: The position vector of atom j
! r2: The square of the distance between atoms i and j.
DOUBLE PRECISION, DIMENSION(3,3), INTENT(IN) :: cell_h
DOUBLE PRECISION, DIMENSION(3,3), INTENT(IN) :: cell_ih
DOUBLE PRECISION, DIMENSION(3), INTENT(IN) :: ri
DOUBLE PRECISION, DIMENSION(3), INTENT(IN) :: rj
DOUBLE PRECISION, INTENT(OUT) :: r2
INTEGER k
! The separation in a basis where the simulation box
! is a unit cube.
DOUBLE PRECISION, DIMENSION(3) :: sij
DOUBLE PRECISION, DIMENSION(3) :: rij
sij = matmul(cell_ih, ri - rj)
DO k = 1, 3
! Finds the smallest separation of all the images of atom i and j
sij(k) = sij(k) - dnint(sij(k))
ENDDO
rij = matmul(cell_h, sij)
r2 = dot_product(rij, rij)
END SUBROUTINE
SUBROUTINE nearest_neighbours(rn, natoms, atoms, cell_h, cell_ih, index_list, n_list)
! Creates a list of all the pairs of atoms that are closer together
! than a certain distance.
!
! This takes all the positions, and calculates which ones are
! shorter than the distance rn. This creates two vectors, index_list
! and n_list. index_list(i) gives the last index of n_list that
! corresponds to a neighbour of atom i.
!
!
! Args:
! rn: The nearest neighbour list cut-off parameter. This should
! be larger than the potential cut-off radius.
! natoms: The number of atoms in the system.
! atoms: A vector holding all the atom positions.
! cell_h: The simulation box cell vector matrix.
! cell_ih: The inverse of the simulation box cell vector matrix.
! index_list: A array giving the last index of n_list that
! gives the neighbours of a given atom. Essentially keeps
! track of how many atoms neighbour a given atom.
! n_list: An array giving the indices of the atoms that neighbour
! the atom determined by index_list. Essentially keeps track
! of which atoms neighbour a given atom.
DOUBLE PRECISION, INTENT(IN) :: rn
INTEGER, INTENT(IN) :: natoms
DOUBLE PRECISION, DIMENSION(:,:), INTENT(IN) :: atoms
DOUBLE PRECISION, DIMENSION(3,3), INTENT(IN) :: cell_h
DOUBLE PRECISION, DIMENSION(3,3), INTENT(IN) :: cell_ih
INTEGER, DIMENSION(natoms), INTENT(OUT) :: index_list
INTEGER, DIMENSION(natoms*(natoms-1)/2), INTENT(OUT) :: n_list
INTEGER :: i, j
DOUBLE PRECISION r2
index_list(1) = 0
DO i = 1, natoms - 1
DO j = i + 1, natoms
CALL separation(cell_h, cell_ih, atoms(i,:), atoms(j,:), r2)
IF (r2 < rn*rn) THEN
! We have found an atom that neighbours atom i, so the
! i-th index of index_list is incremented by one, and a new
! entry is added to n_list.
index_list(i) = index_list(i) + 1
n_list(index_list(i)) = j
ENDIF
ENDDO
index_list(i+1) = index_list(i)
ENDDO
END SUBROUTINE
END MODULE
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