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|
!
! Copyright (C) 2009 D. Forrer and M. Pavone
! This file is distributed under the terms of the
! GNU General Public License. See the file `License'
! in the root directory of the present distribution,
! or http://www.gnu.org/copyleft/gpl.txt .
!
! Z=55-86 contributed by Martin Andersson (2011)
!------------------------------------------------------------------------------
!
MODULE london_module
!
! Module for Dispersion Correction
! [ V. Barone et al. J. Comp. Chem., 30, 934 (2009) ]
! [ S. Grimme, J. Comp. Chem., 27, 1787 (2006) ].
!
USE kinds , ONLY : DP
!
IMPLICIT NONE
!
SAVE
!
!
REAL ( DP ) , ALLOCATABLE , PRIVATE :: C6_i ( : ) , &
R_vdw ( : ) , &
C6_ij ( : , : ) , &
R_sum ( : , : ) , &
r ( : , : ) , &
dist2 ( : )
!
! C6_i ( ntyp ) : atomic C6 coefficient of each atom type
! R_vdw ( ntyp ) : Van der Waals Radii of each atom type
! C6_ij ( ntyp , ntyp ) : C6 coefficients of each atom type pair: sqrt ( C6i * C6j )
! R_sum ( ntyp , ntyp ) : sum of VdW radii
! r ( 3 , mxr ) : ordered distance vectors
! dist2 ( mxr ) : ordered distances
!
REAL ( DP ) , PUBLIC :: scal6 , lon_rcut
!
! scal6 : global scaling factor
! lon_rcut : public cut-off radius
!
INTEGER , PRIVATE :: mxr
!
! max number of r ( see rgen)
!
REAL ( DP ) , PRIVATE :: r_cut , beta = 20.0_DP
!
! beta : damping function parameter
! r_cut : cut-off radius in alat units
!
CONTAINS
!
!---------------------------------------------------------------------------
! Initialize parameters
!---------------------------------------------------------------------------
!
SUBROUTINE init_london ( )
!
! extract parameters from database and compute C6_ij and R_sum(i,j)
!
USE ions_base , ONLY : ntyp => nsp, &
atom_label => atm
!
USE cell_base , ONLY : alat, omega
!
USE io_global, ONLY : ionode, ionode_id, stdout
!
#if defined __MPI
USE mp, ONLY : mp_bcast
USE mp_images, ONLY : intra_image_comm
#endif
!
IMPLICIT NONE
!
INTEGER, PARAMETER :: maxZ = 86
REAL (DP) :: vdw_coeffs(2,maxZ)
!
! vdw C6 and radii for the first 86 atoms for the DFTD2 method
! Data from the DFT-D2 section of the dftd3.f file found on S.Grimme's home page:
! http://www.thch.uni-bonn.de/tc/index.php?section=downloads&subsection=DFT-D3
! See also S. Grimme, J. Comp. Chem., 27, 1787 (2006)
! First column: C6, converted to Ry*Bohr^6 units
! (in the paper: J*nm^6/mol, conversion factor: 1 J*nm^6/mol = 34.69 Ry*Bohr^6)
! Second column: radii, in Bohr (in the paper they are in A)
!
DATA vdw_coeffs / &
4.857, 1.892,&
2.775, 1.912,&
55.853, 1.559,&
55.853, 2.661,&
108.584, 2.806,&
60.710, 2.744,&
42.670, 2.640,&
24.284, 2.536,&
26.018, 2.432,&
21.855, 2.349,&
198.087, 2.162,&
198.087, 2.578,&
374.319, 3.097,&
320.200, 3.243,&
271.980, 3.222,&
193.230, 3.180,&
175.885, 3.097,&
159.927, 3.014,&
374.666, 2.806,&
374.666, 2.785,&
374.666, 2.952,&
374.666, 2.952,&
374.666, 2.952,&
374.666, 2.952,&
374.666, 2.952,&
374.666, 2.952,&
374.666, 2.952,&
374.666, 2.952,&
374.666, 2.952,&
374.666, 2.952,&
589.405, 3.118,&
593.221, 3.264,&
567.896, 3.326,&
438.498, 3.347,&
432.600, 3.305,&
416.642, 3.264,&
855.833, 3.076,&
855.833, 3.035,&
855.833, 3.097,&
855.833, 3.097,&
855.833, 3.097,&
855.833, 3.097,&
855.833, 3.097,&
855.833, 3.097,&
855.833, 3.097,&
855.833, 3.097,&
855.833, 3.097,&
855.833, 3.097,&
1294.678, 3.160,&
1342.899, 3.409,&
1333.532, 3.555,&
1101.101, 3.575,&
1092.775, 3.575,&
1040.391, 3.555,&
10937.246, 3.405,&
7874.678, 3.330,&
6114.381, 3.251,&
4880.348, 3.313,&
4880.348, 3.313,&
4880.348, 3.313,&
4880.348, 3.313,&
4880.348, 3.313,&
4880.348, 3.313,&
4880.348, 3.313,&
4880.348, 3.313,&
4880.348, 3.313,&
4880.348, 3.313,&
4880.348, 3.313,&
4880.348, 3.313,&
4880.348, 3.313,&
4880.348, 3.313,&
3646.454, 3.378,&
2818.308, 3.349,&
2818.308, 3.349,&
2818.308, 3.349,&
2818.308, 3.349,&
2818.308, 3.349,&
2818.308, 3.349,&
2818.308, 3.349,&
1990.022, 3.322,&
1986.206, 3.752,&
2191.161, 3.673,&
2204.274, 3.586,&
1917.830, 3.789,&
1983.327, 3.762,&
1964.906, 3.636/
!
INTEGER :: ilab , ata , atb , i
! local : counter of atom type
! ata , atb : counters of C6_ij matrix
! counter
INTEGER, EXTERNAL :: atomic_number
!!
REAL ( DP ) :: R_0, C_0, e_cut , sls
! local : buffers
!
! here we allocate parameters
!
ALLOCATE ( C6_ij ( ntyp , ntyp ) , &
R_sum ( ntyp , ntyp ) )
!
IF ( ionode ) THEN
!
! and some buffers on ionode
!
ALLOCATE ( C6_i ( ntyp ) , &
R_vdw ( ntyp ) )
!
! here we initialize parameters to unphysical values
!
C6_i ( : ) = -1.d0
R_vdw ( : ) = -1.d0
C6_ij ( : , : ) = -1.d0
R_sum ( : , : ) = -1.d0
!
DO ilab = 1 , ntyp
!
i = atomic_number ( atom_label ( ilab ) )
IF ( i > 0 .AND. i < 87 ) THEN
C6_i ( ilab ) = vdw_coeffs(1,i)
R_vdw ( ilab ) = vdw_coeffs(2,i)
ELSE
CALL errore ( ' init_london ' ,&
'atom ' // atom_label(ilab) //' not found ' , ilab )
END IF
!
END DO
!
! are there all the parameters we need?
!
DO ilab = 1 , ntyp
!
IF ( ( C6_i ( ilab ) < 0.d0 ) .or. &
( R_vdw ( ilab ) < 0.d0 ) ) THEN
!
CALL errore ( ' init_london ' ,&
' one or more parameters not found ' , 4 )
!
END IF
!
END DO
!
! ...here we store C6_ij parameters of each pair of atom types
! into a square matrix C6_ij = sqrt ( C6_i * C6_j )
!
DO atb = 1 , ntyp
!
DO ata = 1 , ntyp
!
C6_ij ( ata , atb ) = sqrt ( C6_i ( ata ) * C6_i ( atb ) )
!
R_sum ( ata , atb ) = R_vdw ( ata ) + R_vdw ( atb )
!
END DO
!
END DO
!
WRITE ( stdout ,'( /, 5X, "-------------------------------------" , &
& /, 5X, "Parameters for Dispersion Correction:" , &
& /, 5X, "-------------------------------------" , &
& /, 5X, " atom VdW radius C_6 " , / )' )
DO ata = 1 , ntyp
!
WRITE (stdout , '( 8X, A3 , 6X , F7.3 , 6X , F9.3 )' ) &
atom_label ( ata ) , R_vdw ( ata ) , C6_i ( ata )
!
END DO
!
! ... atomic parameters are deallocated
!
DEALLOCATE ( C6_i , R_vdw )
!
! ... cutoff radius in alat units
!
r_cut = lon_rcut / alat
!
! ... define a gross maximum bound of the mxr size
!
mxr = 1 + INT ( ( 2 * ( lon_rcut + alat ) ) ** 3 / omega )
!
END IF
!
#if defined __MPI
! broadcast data to all processors
!
CALL mp_bcast ( C6_ij, ionode_id, intra_image_comm )
CALL mp_bcast ( R_sum, ionode_id, intra_image_comm )
CALL mp_bcast ( r_cut, ionode_id, intra_image_comm )
CALL mp_bcast ( mxr , ionode_id, intra_image_comm )
!
#endif
!
ALLOCATE ( r ( 3 , mxr ) , dist2 ( mxr ) )
!
RETURN
!
END SUBROUTINE init_london
!
!---------------------------------------------------------------------------
! Compute dispersion energy
!---------------------------------------------------------------------------
!
FUNCTION energy_london ( alat , nat , ityp , at , bg , tau )
!
! here we compute the dispersion contribution to the total energy
!
! E = - ( C_6^ij / R_ij ** 6 ) * f_damp ( R_ij ) * scal6
!
! where f_damp is the damping function:
!
! f_damp ( R_ij ) = [ 1 + exp ( -beta ( R_ij / (R_i^0+R_j^0) - 1 )) ] ** (-1)
!
! and scal6 is a global scaling factor
!
#if defined __MPI
USE mp_images, ONLY : me_image , nproc_image, intra_image_comm
USE mp, ONLY : mp_sum
#endif
!
IMPLICIT NONE
!
INTEGER :: ata , atb , nrm , nr
! locals :
! ata , atb : atom counters
! nrm : actual number of vectors computed by rgen
! nr : counter
!
INTEGER :: first , last , resto , divid
! locals : parallelization stuff
!
INTEGER , INTENT ( IN ) :: nat , ityp ( nat )
! input:
! nat : number of atoms
! itype : type of each atom
!
REAL ( DP ) :: dist , f_damp , energy_london , dtau ( 3 ) , dist6
! locals:
! dist : distance R_ij between the current pair of atoms
! f_damp : damping function
! energy_london : the dispersion energy
! dtau : output of rgen ( not used )
! dist6 : distance**6
!
REAL ( DP ) , INTENT ( IN ) :: alat , tau (3, nat) , &
at ( 3 , 3 ) , bg ( 3 , 3 )
! input :
! alat : the cell parameter
! tau : atomic positions in alat units
! at : direct lattice vectors
! bg : reciprocal lattice vectors
!
energy_london = 0.d0
!
#if defined __MPI
!
! parallelization: divide atoms across processors of this image
! (different images have different atomic positions)
!
resto = MOD ( nat , nproc_image )
divid = nat / nproc_image
!
IF ( me_image + 1 <= resto ) THEN
!
first = ( divid + 1 ) * me_image + 1
last = ( divid + 1 ) * ( me_image + 1 )
!
ELSE
!
first = ( ( divid + 1 ) * resto ) + ( divid ) * ( me_image-resto ) + 1
last = ( divid + 1 ) * resto + ( divid ) * ( me_image - resto + 1 )
!
END IF
!
#else
!
first = 1
last = nat
#endif
!
! ... the dispersion energy
!
DO ata = first , last
!
DO atb = 1 , nat
!
dtau ( : ) = tau ( : , ata ) - tau ( : , atb )
!
CALL rgen ( dtau, r_cut, mxr, at, bg, r, dist2, nrm )
!
!$omp parallel do private(nr,dist,dist6,f_damp) default(shared), reduction(-:energy_london)
DO nr = 1 , nrm
!
dist = alat * sqrt ( dist2 ( nr ) )
dist6 = dist ** 6
!
f_damp = 1.d0 / ( 1.d0 + &
exp ( -beta * ( dist / ( R_sum ( ityp (atb) , ityp (ata) ) ) - 1 )))
!
energy_london = energy_london - &
( C6_ij ( ityp ( atb ) , ityp ( ata ) ) / dist6 ) * &
f_damp
!
END DO
!$omp end parallel do
!
END DO
!
END DO
!
energy_london = scal6 * 0.5d0 * energy_london
!
#if defined (__MPI)
CALL mp_sum ( energy_london , intra_image_comm )
#endif
!
RETURN
!
END FUNCTION energy_london
!
!---------------------------------------------------------------------------
! Compute dispersion forces acting on atoms
!---------------------------------------------------------------------------
!
FUNCTION force_london ( alat , nat , ityp , at , bg , tau )
!
!
#if defined __MPI
USE mp_images, ONLY : me_image , nproc_image , intra_image_comm
USE mp, ONLY : mp_sum
#endif
!
IMPLICIT NONE
!
INTEGER :: ata , atb , nrm , nr , ipol
! locals :
! ata , atb : atom counters
! nrm : actual number of vectors computed by rgen
! nr : counter on neighbours shells
! ipol : counter on coords
!
INTEGER :: first , last , resto, divid
! locals :
! first : lower bound on processor
! last : upper
!
INTEGER , INTENT ( IN ) :: nat , ityp ( nat )
! input:
! nat : number of atoms
! ityp : type of each atom
!
REAL ( DP ) :: dist , f_damp , dtau ( 3 ) , force_london ( 3 , nat ) , &
dist6 , dist7 , exparg , expval , par , fac , add
! locals :
! dist : distance R_ij between the current pair of atoms
! f_damp : damping function
! dtau : \vec R_ij
! force_london : dispersion forces
! dist6 : dist**6
! dist7 : dist**7
! ... and some buffers
!
REAL ( DP ) , INTENT ( IN ) :: alat , tau (3, nat) , &
at ( 3 , 3 ) , bg ( 3 , 3 )
! input:
! alat : the cell parameter
! tau : atomic positions in alat units
! at : direct lattice vectors
! bg : reciprocal lattice vectors
!
!
force_london ( : , : ) = 0.d0
!
#if defined __MPI
!
! parallelization: divide atoms across processors of this image
! (different images have different atomic positions)
!
resto = MOD ( nat , nproc_image )
divid = nat / nproc_image
!
IF ( me_image + 1 <= resto ) THEN
!
first = ( divid + 1 ) * me_image + 1
last = ( divid + 1 ) * ( me_image + 1 )
!
ELSE
!
first = ( ( divid + 1 ) * resto ) + ( divid ) * ( me_image-resto ) + 1
last = ( divid + 1 ) * resto + ( divid ) * ( me_image - resto + 1 )
!
END IF
!
#else
!
first = 1
last = nat
#endif
!
! ... the dispersion forces
!
DO ata = first , last
!
DO atb = 1 , nat
!
IF ( ata /= atb ) THEN
!
dtau ( : ) = tau ( : , ata ) - tau ( : , atb )
!
! generate neighbours shells
!
CALL rgen ( dtau, r_cut, mxr, at, bg, r, dist2, nrm )
!
! compute forces
!
par = beta / ( R_sum ( ityp ( atb ) , ityp ( ata ) ) )
!
!$omp parallel do private(nr,dist,dist6,dist7,exparg,expval,fac,add,ipol) default(shared), reduction(+:force_london)
DO nr = 1 , nrm
!
dist = alat * sqrt ( dist2 ( nr ) )
dist6 = dist ** 6
dist7 = dist6 * dist
!
exparg = - beta * ( dist / ( R_sum ( ityp(atb) , ityp(ata) ) ) - 1 )
expval = exp ( exparg )
!
fac = C6_ij ( ityp ( atb ) , ityp ( ata ) ) / dist6
add = 6.d0 / dist
!
DO ipol = 1 , 3
!
force_london ( ipol , ata ) = force_london ( ipol , ata ) + &
( scal6 / ( 1 + expval ) * fac * &
( - par * expval / ( 1.d0 + expval ) + add ) * &
r ( ipol , nr ) * alat / dist )
!
END DO
!
END DO
!$omp end parallel do
!
END IF
!
END DO
!
END DO
!
#if defined (__MPI)
CALL mp_sum ( force_london , intra_image_comm )
#endif
!
RETURN
!
END FUNCTION force_london
!
!
!---------------------------------------------------------------------------
! Compute dispersion contribution to the stress tensor
!---------------------------------------------------------------------------
!
FUNCTION stres_london ( alat , nat , ityp , at , bg , tau , omega )
!
!
#if defined __MPI
USE mp_images, ONLY : me_image , nproc_image , intra_image_comm
USE mp, ONLY : mp_sum
#endif
!
IMPLICIT NONE
!
INTEGER :: ata , atb , nrm , nr , ipol , lpol , spol
! locals :
! ata , atb : atom counters
! nrm : actual number of vectors computed by rgen
! nr : counter on neighbours shells
! xpol : coords counters ipol lpol spol
!
INTEGER :: first , last , resto, divid
! locals : parallelization
!
INTEGER , INTENT ( IN ) :: nat , ityp ( nat )
! input:
! nat : number of atoms
! ityp : type of each atom
!
REAL ( DP ) :: dist , f_damp , dtau ( 3 ) , stres_london ( 3 , 3 ) , &
dist6 , dist7 , exparg , expval , par , fac , add
! locals:
! dist : distance R_ij of current pair of atoms
! f_damp : damping function
! dtau : \vec R_ij
! stres_london : dispersion contribution to stress tensor
! dist6 : dist**6
! dist7 : dist**7
! and some buffers
!
REAL ( DP ) , INTENT ( IN ) :: alat , tau (3, nat) , omega , &
at ( 3 , 3 ) , bg ( 3 , 3 )
! input :
! alat : the cell parameter
! tau : atomic positions in alat units
! omega : unit cell volume
! at : direct lattice vectors
! bg : reciprocal lattice vectors
!
!
!
stres_london ( : , : ) = 0.d0
!
first=0
last=0
!
#if defined __MPI
!
! parallelization: divide atoms across processors of this image
! (different images have different atomic positions)
!
resto = MOD ( nat , nproc_image )
divid = nat / nproc_image
!
IF ( me_image + 1 <= resto ) THEN
!
first = ( divid + 1 ) * me_image + 1
last = ( divid + 1 ) * ( me_image + 1 )
!
ELSE
!
first = ( ( divid + 1 ) * resto ) + ( divid ) * ( me_image-resto ) + 1
last = ( divid + 1 ) * resto + ( divid ) * ( me_image - resto + 1 )
!
END IF
!
#else
!
first = 1
last = nat
#endif
!
! ... the dispersion stress tensor
!
DO ata = first , last
!
DO atb = 1 , nat
!
dtau ( : ) = tau ( : , ata ) - tau ( : , atb )
!
! generate neighbours shells
!
CALL rgen ( dtau, r_cut, mxr, at, bg, r, dist2, nrm )
!
! compute stress
!
par = beta / ( R_sum ( ityp ( atb ) , ityp ( ata ) ) )
!
DO nr = 1 , nrm
!
dist = alat * sqrt ( dist2 ( nr ) )
dist6 = dist ** 6
dist7 = dist6 * dist
!
exparg = - beta * ( dist / ( R_sum ( ityp ( atb ) , ityp ( ata ) ) ) - 1 )
!
expval = exp ( exparg )
!
fac = C6_ij ( ityp ( atb ) , ityp ( ata ) ) / dist6
!
add = 6.d0 / dist
!
DO ipol = 1 , 3
!
DO lpol = 1 , ipol
!
stres_london ( lpol , ipol ) = stres_london ( lpol , ipol ) + &
( scal6 / ( 1 + expval ) * fac * &
( - par * expval / ( 1.d0 + expval ) + add ) * &
r ( ipol , nr ) * alat / dist ) * &
r ( lpol , nr ) * alat
!
END DO
!
END DO
!
END DO
!
END DO
!
END DO
!
DO ipol = 1 , 3
!
DO lpol = ipol + 1 , 3
!
stres_london ( lpol , ipol ) = stres_london ( ipol , lpol )
!
END DO
!
END DO
!
stres_london ( : , : ) = - stres_london ( : , : ) / ( 2.d0 * omega )
!
#if defined (__MPI)
CALL mp_sum ( stres_london , intra_image_comm )
#endif
!
RETURN
!
END FUNCTION stres_london
!
!---------------------------------------------------------------------------
! clean memory
!---------------------------------------------------------------------------
!
SUBROUTINE dealloca_london
!
IMPLICIT NONE
!
IF ( ALLOCATED ( C6_i ) ) DEALLOCATE ( C6_i )
IF ( ALLOCATED ( R_vdw ) ) DEALLOCATE ( R_vdw )
IF ( ALLOCATED ( C6_ij ) ) DEALLOCATE ( C6_ij )
IF ( ALLOCATED ( R_sum ) ) DEALLOCATE ( R_sum )
IF ( ALLOCATED ( r ) ) DEALLOCATE ( r )
IF ( ALLOCATED ( dist2 ) ) DEALLOCATE ( dist2 )
!
RETURN
!
END SUBROUTINE dealloca_london
!
END MODULE london_module
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