! ! 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 . ! !------------------------------------------------------------------------------ ! 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 __PARA USE mp, ONLY : mp_bcast #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 taken from the DFTD2 sections of the dftd3.f file found on S.Grimmes home page for the DFTD3 method ! http://toc.uni-muenster.de/DFTD3/index.html 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 , 8X , F7.3 )' ) & 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 = INT ( ( 2 * ( lon_rcut + alat ) ) ** 3 / omega ) ! END IF ! #if defined __PARA ! broadcast data to all processors ! CALL mp_bcast ( C6_ij, ionode_id ) CALL mp_bcast ( R_sum, ionode_id ) CALL mp_bcast ( r_cut, ionode_id ) CALL mp_bcast ( mxr , ionode_id ) ! #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 __PARA USE mp_global, ONLY : me_image , nproc_image, intra_image_comm USE mp, ONLY : mp_sum #endif ! IMPLICIT NONE ! !INTEGER , PARAMETER :: mxr = 500000 ! local: max number of r ( see rgen ) ! 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 __PARA ! ! 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 ) ! 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 ! END DO ! END DO ! energy_london = scal6 * 0.5d0 * energy_london ! ! #if defined (__PARA) 999 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 __PARA USE mp_global, ONLY : me_image , nproc_image , intra_image_comm USE mp, ONLY : mp_sum #endif ! IMPLICIT NONE ! !INTEGER , PARAMETER :: mxr = 500000 ! local: max number of r ( see rgen ) ! 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 __PARA ! ! 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 ) ) ) ! 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 ! END IF ! END DO ! END DO ! #if defined (__PARA) 999 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 __PARA USE mp_global, ONLY : me_image , nproc_image , intra_image_comm USE mp, ONLY : mp_sum #endif ! IMPLICIT NONE ! !INTEGER , PARAMETER :: mxr = 500000 ! local: max number of r ( see rgen ) ! 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 __PARA ! ! 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 (__PARA) 999 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