ELECTRONIC SUPPLEMENTARY INFORMATION AUG. 23, 2021 Potential energy surface for high-energy N + N2 collisions Zoltan Varga and Donald G. Truhlar Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, USA CONTENTS OpenMolcas example-1 input file Geometry file for the OpenMolcas example 1 OpenMolcas example-2 input file Geometry file for the OpenMolcas example 2 Geometry and energy data set of the N3(4A") surface Fortran 90 potential energy subroutine of the N3(4A") surface ******OpenMolcas example-1 input file &GATEWAY Coord=N3_4app.xyz Basis=maug-cc-pVQZ Group=X EndofInput &SEWARD &RASSCF Spin=4 Lumorb Symmetry=2 CIRoot= 2 2; 1 2; 9 1 Inactive=6 0 Ras2=6 3 Nactel= 9 &CASPT2 Frozen= 6 0 MULT= 1 1 IPEA= 0.0 SHIF= 0.0 IMAG= 0.1 MAXITER= 40 ******Geometry file for the OpenMolcas example 1 3 Angstrom N 0.00000 0.00000 .350 N 0.00000 0.00000 -.350 N 0.00000 .86603 -.49998 ******OpenMolcas example-2 input file &GATEWAY Coord=N3_4app.xyz Basis=maug-cc-pVQZ Group=X EndofInput &SEWARD &RASSCF Spin=4 Lumorb Symmetry=2 CIRoot= 2 2; 1 2; 9 1 Inactive=6 0 Ras2=6 3 Nactel= 9 &CASPT2 Frozen= 6 0 MULT= 1 1 IPEA= 0.0 SHIF= 0.0 IMAG= 0.1 MAXITER= 40 ******Geometry file for the OpenMolcas example 2 3 Angstrom N 0.00000 0.00000 .350 N 0.00000 0.00000 -.350 N 0.00000 .86603 -.49998 ******Geometry and energy data set of the N3(4A") surface Data points of N3(4App) surface *** Ref. energy is N2(1Sigmag+) + N(4S) CASPT2/SA(2)-CASSCF(9,9)/maug-cc-pVQZ *** Format of the dataset: 1. # of the point, DE_total (in kcal/mol) 2. N1= x1, y1, z1 (in Ang) 3. N2= x2, y2, z2 (in Ang) 4. N3= x3, y3, z3 (in Ang) *** Conversion factors: 1 hartree = 627.509474 kcal/mol 1 bohr = 0.52917721092 angstrom 1 hartree/bohr = 1185.82105 kcal mol^-1 angstrom^-1 *** *** *** *** *** 1 0.00000000 0.00000000 0.00000000 0.00000000 1.09610000 0.00000000 0.00000000 0.54823247 19.99322490 0.00000000 2 787.59512000 0.00000000 0.00000000 0.00000000 0.70000000 0.00000000 0.00000000 0.35000000 5.00000498 0.00000000 3 326.33572000 0.00000000 0.00000000 0.00000000 0.80000000 0.00000000 0.00000000 0.40000000 4.99999550 0.00000000 4 108.13051000 0.00000000 0.00000000 0.00000000 0.90000000 0.00000000 0.00000000 0.45000000 5.00000084 0.00000000 5 19.92102000 0.00000000 0.00000000 0.00000000 1.00000000 0.00000000 0.00000000 0.50000000 5.00000220 0.00000000 6 0.00602000 0.00000000 0.00000000 0.00000000 1.10000000 0.00000000 0.00000000 0.55000000 5.00000096 0.00000000 7 14.32377000 0.00000000 0.00000000 0.00000000 1.20000000 0.00000000 0.00000000 0.60000000 4.99999867 0.00000000 8 43.90002000 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0.05953000 0.00000000 0.00000000 0.00000000 1.09600000 0.00000000 0.00000000 0.85294118 3.48665832 0.00000000 7171 0.03568000 0.00000000 0.00000000 0.00000000 1.09600000 0.00000000 0.00000000 0.85729342 3.53647299 0.00000000 7172 0.01676000 0.00000000 0.00000000 0.00000000 1.09600000 0.00000000 0.00000000 0.86164923 3.58628116 0.00000000 7173 0.00185000 0.00000000 0.00000000 0.00000000 1.09600000 0.00000000 0.00000000 0.86600947 3.63609357 0.00000000 7174 -0.00976000 0.00000000 0.00000000 0.00000000 1.09600000 0.00000000 0.00000000 0.87037327 3.68590076 0.00000000 ******Fortran 90 potential energy subroutine of the N3(4A") surface !********************************************************************** ! System: N3 ! Functional form: permutation-invariant polynomials ! Common name: N3 4App (quartet A" state) ! Number of derivatives: 1 ! Number of bodies: 3 ! Number of electronic surfaces: 1 ! Interface: Section-2 ! ! Reference: Z. Varga and D. G. Truhlar, to be published in PCCP ! ! Notes: -Mixed-exponential-Gaussian (MEG) ! variables are applied ! -Diatomic potential contains ! dispersion correction ! ! Input: X(3),Y(3),Z(3) in unit of bohr ! Output: E in unit of hartree ! Output: dEdX(3),dEdY(3),dEdZ(3) hartree/bohr !********************************************************************** module N3_4App_MB_PIP_MEG1 implicit none private public :: pot, ev2gm2 ! Conversion factors ! Cconv: bohr to Angstrom ! 1 bohr = 0.52917721092 angstrom ! Econv: kcal/mol to hartree ! 1 kcal/mol = 0.159360144 * 10^-2 hartree ! Gconv: kcal/(mol*Angstrom) to hartree/bohr ! 1 kcal mol^-1 angstrom^-1 = 0.843297564 * 10^-3 hartree/bohr double precision,parameter :: Cconv = 0.52917721092d0 double precision,parameter :: Econv = 0.159360144d-2 double precision,parameter :: Gconv = 0.843297564d-3 ! Common variables ! R(3): Interatomic bond distance ! rMs(6) Array to store base terms ! rM(0:7) Array to store monomials ! P(0:66) Array to store polynomials ! B(1:56) Array to store basis functions ! dMsdR(3,3): The derivative of base terms w.r.t. R ! dMdR(3,8): The derivative of monomials w.r.t. R ! dPdR(3,67): The derivative of basis functions w.r.t. R ! dVdR(3): The derivative of V w.r.t. R ! dRdX(3,9): The derivative of R w.r.t. X ! dBdR(3,56) The derivative of B w.r.t. R double precision :: R(3) double precision :: rMs(3),rM(0:7),P(0:66),B(56) double precision :: dMsdR(3,3),dMdR(3,0:7),dPdR(3,0:66) double precision :: dVdR(3),dRdX(3,9),dBdR(3,56) ! Nonlinear parameters: ! a(in Ang) ! ab (in Ang^2) ! ra (in Ang) ! and rb (in Ang) double precision,parameter :: a = 1.280d0 double precision,parameter :: ab = 2.100d0 double precision,parameter :: ra = 1.098d0 double precision,parameter :: rb = 1.098d0 ! Reference energy of infinitely separated N2 + N in hartree (taken ! from CASPT2 calculations) double precision,parameter :: Eref = -163.65202806 ! For N2 + N2 framework total diss. energy is 2*228.4 kcal/mol double precision,parameter :: totdiss = 456.8d0 ! Linear parameters optimized by the weighted-least square fitting double precision,parameter :: C(56) = (/ & -0.350120274856D+03 & , 0.281093379749D+03 & , 0.504222011875D+04 & , 0.774595390008D+04 & , -0.153977000048D+05 & , -0.341980773453D+05 & , 0.421291716912D+05 & , -0.118457148928D+06 & , 0.485872504516D+05 & , 0.126542076928D+06 & , 0.479715536807D+05 & , -0.430825904195D+05 & , 0.351123766345D+06 & , -0.393715206114D+05 & , -0.124625021693D+06 & , -0.263800314496D+06 & , -0.839917151081D+04 & , 0.153566935802D+05 & , -0.167551509503D+05 & , -0.510531730539D+06 & , 0.642719554456D+05 & , 0.176493066952D+06 & , 0.325900189079D+06 & , -0.808274097880D+05 & , 0.929658499777D+05 & , 0.922980021155D+05 & , -0.522086545864D+05 & , 0.470098466709D+06 & , -0.704531576918D+05 & , -0.569186006731D+05 & , -0.133918206304D+06 & , -0.241532954576D+06 & , -0.767179058281D+06 & , 0.322616894753D+06 & , -0.179596800582D+06 & , -0.428279161417D+06 & , -0.701871514181D+05 & , 0.167945612096D+06 & , -0.281749185916D+06 & , 0.490556308761D+05 & , 0.959017744649D+04 & , 0.518488791569D+05 & , 0.101035720167D+06 & , 0.842133667245D+05 & , 0.656068569063D+05 & , -0.184873054675D+06 & , 0.391252917892D+05 & , 0.263542187638D+06 & , 0.209985542260D+05 & , -0.891093615300D+05 & , 0.789434896598D+05 & , -0.247967448188D+05 & , -0.242734300770D+04 & , 0.154198371772D+04 & , -0.744339642914D+04 & , -0.185997161122D+05 & /) contains subroutine pot(X,Y,Z,E,dEdX,dEdY,dEdZ) !********************************************************************** ! Local variables used in the O3 PES subroutine ! input coordinate matrix: X(9)in Ang ! o1: X(1),X(2),X(3) ! O2: X(4),X(5),X(6) ! O3: X(7),X(8),X(9) ! input flag: igrad igrad=0 energy-only calculation ! igrad=1 energy + gradient ! output potential energy: v in kcal/mol ! output gradient: dVdX in kcal/(mol*Ang) !********************************************************************** double precision,intent(out) :: E double precision V double precision,intent(in) :: X(3),Y(3),Z(3) double precision,intent(out) :: dEdX(3),dEdY(3),dEdZ(3) double precision Xcart(9) double precision dVdX(9) integer i ! Convert to local variables do i=1,3 Xcart(3*i-2)=X(i)*Cconv Xcart(3*i-1)=Y(i)*Cconv Xcart(3*i)=Z(i)*Cconv enddo call n3pes(Xcart,v,dVdX,1) ! Convert local output to the ones ANT wants E = v*Econv + Eref do i=1,3 dEdX(i)=dVdX(3*i-2)*Gconv dEdY(i)=dVdX(3*i-1)*Gconv dEdZ(i)=dVdX(3*i)*Gconv enddo end subroutine pot subroutine n3pes(X,v,dVdX,igrad) !********************************************************************** ! Subroutine to calculate the potential energy V and gradient dVdX ! for given Cartesian coordinates X(9) ! R: Interatomic bond distance (3) ! V: Calculated potential energy ! dVdX: The derivative of V w.r.t. X, dim(9) ! dVdR: The derivative of V w.r.t. R, dim(3) ! dPdR: The derivative of basis functions w.r.t. R ! dim(3*67) ! dMdR: The derivative of monomials w.r.t. R ! dim(3*8) ! dRdX: The derivative of R w.r.t. X, dim(3*9) !********************************************************************** integer i,igrad,j,nob,k double precision V double precision dVdX(9),X(9) ! Read Cartesian coordinate from input file call coord_convt(X) if (igrad .le. 1) then ! Call subroutine Evv to evaluate potential energy V call evv(V) if (igrad .eq. 1) then ! Call EvdVdX to evaluate the derivatives of V w.r.t. X call evdvdx(X,dVdX) endif else write (*,*) 'Only igrad = 0, 1 is allowed!' endif end subroutine n3pes subroutine coord_convt(X) !********************************************************************** ! Program to calculate the six interatomic distance ! by reading XYZ coordinate !********************************************************************** integer i double precision X(9) !********************************************************************** ! Now, calculate the inter-atomic distance ! r1 = r(O1O2) ! r2 = r(O1O3) ! r3 = r(O2O3) !********************************************************************** R(1)=Sqrt((X(4)-X(1))**2 + (X(5)-X(2))**2 + (X(6)-X(3))**2) R(2)=Sqrt((X(7)-X(1))**2 + (X(8)-X(2))**2 + (X(9)-X(3))**2) R(3)=Sqrt((X(4)-X(7))**2 + (X(5)-X(8))**2 + (X(6)-X(9))**2) return end subroutine coord_convt subroutine EvV(V) !********************************************************************** ! Subroutine to evaluate V for given R ! V(R) = C*P ! C: Coefficients, stored in 'dim.inc' ! P: Basis functions evaluated for given R ! rMs: rMs(3), six mixed exponential-Gaussian terms (MEG) ! a: Nonlinear parameters in Morse terms(Angstrom) ! ab: Nonlinear parameters in Gauss terms(Angstrom^2) ! re: Equilibrium bond length(Angstrom) ! nop: number of points ! nom: number of monomials ! nob: number of basis functions(polynomials) ! rM(0:7): Array to store monomials ! P(0:66): Array to store polynomials ! B(1:56): Array to store basis functions !********************************************************************** integer i,j,k double precision dist,dv2dr,V,V2 double precision Vpf,dVpfdR(3) ! Calculate the six MEG terms for each point call evmorse ! Calculate the monomials for each point by using six MEG terms call evmono ! Calculate the polynomials (basis functions) by using monomials call evpoly ! Calculate the basis functions by removing unconnected and 2-body terms call evbas ! Initialized v to be totdiss v=totdiss ! Evaluate 2-body interactions do i=1,3 dist=r(i) call ev2gm2(dist,v2,dv2dr,1,0) v=v+v2 enddo !! D3 dispersion correction is called inside the ev2gm2 !! ! Add D3 dispersion correction ! call d3disp(r,disp,dispdr,0) ! v=v+disp ! Evaluate V by taken the product of C and Basis function array do i=1,56 v=v + c(i)*b(i) enddo ! Add a patch function to get the D3h structure call patchfunc(Vpf,dVpfdR,0) v=v - Vpf ! Write(*,9999) V ! 9999 Format('The potential energy is ',F20.14,' kcal/mol') return end subroutine EvV subroutine EvdVdX(X,dVdX) !********************************************************************** ! Subroutine to evaluate dRdX for given R and X ! R: R(3), 3 bond lengths ! X: X(9), 9 Cartesian coordinates ! rM(0:7): Array to store monomials ! P(0:66): Array to store polynomials ! dVdX: dVdX(9), derivatives of V w.r.t. Cartesian coordinates ! dVdR: dVdR(3), derivatives of V w.r.t. 3 bond lengths ! dRdX: dRdX(3,9), derivatives of R(3) w.r.t. 9 ! Cartesian coordinates !********************************************************************** integer i,j double precision dVdX(9),X(9) ! Initialize dVdX do i=1,9 dVdX(i)=0.0d0 enddo ! Call EvdVdR to evaluate dVdR(3) Call evdvdr ! Call EvdRdX to evaluate dRdX(3,9) Call evdrdx(X) ! Calculate dVdX by using chain rule: dV/dXi=(dV/dRj)*(dRj/dXi), ! j = 1 to 3 do i=1,9 do j=1,3 dVdX(i)=dVdX(i) + dVdR(j)*dRdX(j,i) enddo enddo ! write(*,*) 'The 9 dVdX are:' ! Write(*,9999) (dVdX(i),i=1,9) ! 9999 Format(1x,3F15.8) return end subroutine EvdVdX subroutine EvMorse !********************************************************************** ! mixed exponential-Gaussian terms = exp(-(r-ra)/a-(r-rb)^2/ab) ! ra: reference bond length ! rb: reference bond length ! a: nonlinear parameter, unit Anstrom ! ab: nonlinear parameter, unit Anstrom^2 !********************************************************************** integer i do i=1,3 rms(i)=Exp(-(r(i)-ra)/a-((r(i)-rb)**2.0d0)/ab) enddo end subroutine EvMorse subroutine EvMono !********************************************************************** ! The subroutine reads six MEG variables(X) and calculates the ! monomials(M) that do not have usable decomposition. ! For A4 with max. degree 10, the number of monomials is nom. !********************************************************************** rm(0) = 1.0d0 rm(1) = rms(3) rm(2) = rms(2) rm(3) = rms(1) rm(4) = rm(1)*rm(2) rm(5) = rm(1)*rm(3) rm(6) = rm(2)*rm(3) rm(7) = rm(1)*rm(6) return end subroutine EvMono subroutine EvPoly !********************************************************************** ! The subroutine reads monomials(m) and calculates the ! permutation invariant polynomials(p) ! For A4 with max. degree 10, the number of polynomials is nob. !********************************************************************** p( 0) = rm(0) p( 1) = rm(1) + rm(2) + rm(3) p( 2) = rm(4) + rm(5) + rm(6) p( 3) = p( 1)*p( 1) - p( 2) - p( 2) p( 4) = rm(7) p( 5) = p( 1)*p( 2) - p( 4) - p( 4) - p( 4) p( 6) = p( 1)*p( 3) - p( 5) p( 7) = p( 1)*p( 4) p( 8) = p( 2)*p( 2) - p( 7) - p( 7) p( 9) = p( 2)*p( 3) - p( 7) p(10) = p( 1)*p( 6) - p( 9) p(11) = p( 2)*p( 4) p(12) = p( 3)*p( 4) p(13) = p( 1)*p( 8) - p(11) p(14) = p( 2)*p( 6) - p(12) p(15) = p( 1)*p(10) - p(14) p(16) = p( 4)*p( 4) p(17) = p( 4)*p( 5) p(18) = p( 4)*p( 6) p(19) = p( 2)*p( 8) - p(17) p(20) = p( 1)*p(13) - p(17) - p(19) - p(19) p(21) = p( 2)*p(10) - p(18) p(22) = p( 1)*p(15) - p(21) p(23) = p( 1)*p(16) p(24) = p( 4)*p( 8) p(25) = p( 3)*p(11) - p(23) p(26) = p( 4)*p(10) p(27) = p( 1)*p(19) - p(24) p(28) = p( 6)*p( 8) - p(23) p(29) = p( 2)*p(15) - p(26) p(30) = p( 1)*p(22) - p(29) p(31) = p( 2)*p(16) p(32) = p( 3)*p(16) p(33) = p( 1)*p(24) - p(31) p(34) = p( 4)*p(14) p(35) = p( 4)*p(15) p(36) = p( 2)*p(19) - p(33) p(37) = p( 3)*p(19) - p(31) p(38) = p( 8)*p(10) - p(32) p(39) = p( 2)*p(22) - p(35) p(40) = p( 1)*p(30) - p(39) p(41) = p( 4)*p(16) p(42) = p( 4)*p(17) p(43) = p( 4)*p(19) p(44) = p( 6)*p(16) p(45) = p( 4)*p(20) p(46) = p( 4)*p(21) p(47) = p( 4)*p(22) p(48) = p( 1)*p(36) - p(43) p(49) = p( 1)*p(37) - p(45) - p(48) p(50) = p( 8)*p(15) - p(44) p(51) = p( 2)*p(30) - p(47) p(52) = p( 1)*p(40) - p(51) p(53) = p( 1)*p(41) p(54) = p( 4)*p(24) p(55) = p( 3)*p(31) - p(53) p(56) = p( 1)*p(43) - p(54) p(57) = p(10)*p(16) p(58) = p( 4)*p(28) p(59) = p( 4)*p(29) p(60) = p( 4)*p(30) p(61) = p( 2)*p(36) - p(56) p(62) = p( 3)*p(36) - p(54) p(63) = p(10)*p(19) - p(53) p(64) = p( 8)*p(22) - p(57) p(65) = p( 2)*p(40) - p(60) p(66) = p( 1)*p(52) - p(65) return end subroutine EvPoly subroutine evbas !********************************************************************** ! The subroutine eliminate the 2-body terms in Bowman's approach !********************************************************************** integer i double precision b1(67) ! Pass P(0:66) to BM1(1:67) do i=1,67 b1(i)=p(i-1) enddo ! Remove unconnected terms and 2-body terms and pass to B(1:430) b(1)=b1(3) do i=2,3 b(i)=b1(i+3) enddo do i=4,6 b(i)=b1(i+4) enddo do i=7,10 b(i)=b1(i+5) enddo do i=11,16 b(i)=b1(i+6) enddo do i=17,23 b(i)=b1(i+7) enddo do i=24,32 b(i)=b1(i+8) enddo do i=33,43 b(i)=b1(i+9) enddo do i=44,56 b(i)=b1(i+10) enddo return end subroutine evbas subroutine ev2gm2(r,v,grad,imol,igrad) !********************************************************************** ! ! Compute the diatomic potential of ground-state N2 (singlet) ! ! Input: r interatomic distance in Angstrom ! imol 1 - stands for N2 for N4 PES ! igrad 1 - gradient is calculated ! 0 - gradient is not calculated ! Output: V potential in kcal/mol ! grad gradient (kcal/mol)/Angstrom ! !********************************************************************** implicit none integer,intent(in) :: imol, igrad double precision :: r double precision :: v, grad double precision :: re, de, as(0:6) double precision :: y, fy, u double precision :: dfdy,rr,dydr,dfdr integer :: k ! Dispersion variables double precision :: dist(1),disp,dispdr(1) ! Modified parameters for D3(BJ) re=1.098d0 de= 224.9157d0 ! 228.4d0 as(0) = 2.7599278840949d0 ! 2.71405774451d0 as(1) = 0.2318898277373d0 ! 1.32757649829d-1 as(2) = 0.1908422945648d0 ! 2.66756890408d-1 as(3) = -0.2727504034613d0 ! 1.95350725241d-1 as(4) = -0.5345112219335d0 !-4.08663480982d-1 as(5) = 1.0857331617073d0 ! 3.92451705557d-1 as(6) = 1.6339897930305d0 ! 1.13006674877d0 v=0.d0 y=(r*r*r*r - re*re*re*re)/(r*r*r*r + re*re*re*re) fy = as(0) + as(1)*y + as(2)*y*y + as(3)*y*y*y + as(4)*y*y*y*y & + as(5)*y*y*y*y*y + as(6)*y*y*y*y*y*y u=exp(-fy*(r-re)) v=de*(1.0d0-u)*(1.0d0-u)-de ! Add D3 dispersion correction dist(1)=r call d3disp(dist,disp,dispdr,0,imol) v=v+disp ! Compute the gradient if needed if (igrad.eq.1) then grad=0.d0 dfdy = as(1) + 2.0d0*as(2)*y + 3.0d0*as(3)*y*y & + 4.0d0*as(4)*y*y*y + 5.0d0*as(5)*y*y*y*y & + 6.0d0*as(6)*y*y*y*y*y rr = r*r*r*r + re*re*re*re dydr = 8.0d0*r*r*r*re*re*re*re/(rr*rr) dfdr = dfdy*dydr grad = 2.0d0*de*(1-u)*u*(dfdr*(r-re)+fy) ! Add analytical gradient of D3 dispersion correction call d3disp(dist,disp,dispdr,1,imol) grad= grad + dispdr(1) endif return end subroutine ev2gm2 subroutine patchfunc(Vpf,dVpfdR,igrad) !********************************************************************** ! A patch function to correct the barrier between 2A1 and 2B1 ! minima of the doublet surface !********************************************************************** integer igrad integer i,j double precision Vpf double precision tmp1,tmp2,tmp3 double precision tmp(3,3) double precision dVpfdR(3) double precision rfx,afx,v0,b,b2 double precision a(3),aa(3) v0 = 17.0d0 ! in kcal/mol b = 3.4d0 ! in Ang^-1 b2 = 6.8d0 ! in rad^-1 ! rfx is the bond length of D3h geometry rfx = 1.532d0 ! in Ang ! afx is 60 deg afx = 1.047197551d0 ! in rad aa(1)= (( r(1)**2 - r(2)**2 - r(3)**2 )/(-2.0d0*r(2)*r(3))) aa(2)= (( r(2)**2 - r(1)**2 - r(3)**2 )/(-2.0d0*r(1)*r(3))) aa(3)= (( r(3)**2 - r(1)**2 - r(2)**2 )/(-2.0d0*r(1)*r(2))) do i=1,3 if(aa(i).gt.(1.0d0-1.0d-10)) then aa(i)=(1.0d0-1.0d-10) else if (aa(i).lt.-(1.0d0-1.0d-10)) then aa(i)=-(1.0d0-1.0d-10) endif enddo a(1)= acos(aa(1)) a(2)= acos(aa(2)) a(3)= acos(aa(3)) tmp1=-(b*(r(1)-rfx))**2 -(b*(r(2)-rfx))**2 -(b2*(a(3)-afx))**2 tmp2=-(b*(r(1)-rfx))**2 -(b*(r(3)-rfx))**2 -(b2*(a(2)-afx))**2 tmp3=-(b*(r(2)-rfx))**2 -(b*(r(3)-rfx))**2 -(b2*(a(1)-afx))**2 Vpf = v0*( Exp(tmp1) + Exp(tmp2) + Exp(tmp3) ) if (igrad .eq. 1) then tmp=0.0d0 tmp(1,1) = 2.0d0*b2**2*(1.0d0/r(2)-cos(a(3))/r(1))*(a(3)-afx) tmp(1,1) = tmp(1,1)/sqrt(1.0d0-(cos(a(3)))**2) tmp(1,1) = tmp(1,1) -2.0d0*b**2*(r(1)-rfx) tmp(1,2) = 2.0d0*b2**2*(1.0d0/r(3)-cos(a(2))/r(1))*(a(2)-afx) tmp(1,2) = tmp(1,2)/sqrt(1.0d0-(cos(a(2)))**2) tmp(1,2) = tmp(1,2) -2.0d0*b**2*(r(1)-rfx) tmp(1,3) = -(2.0d0*b2**2*r(1)*(a(1)-afx)) tmp(1,3) = tmp(1,3)/(r(2)*r(3)*sqrt(1.0d0-(cos(a(1)))**2)) tmp(2,1) = 2.0d0*b2**2*(1.0d0/r(1)-cos(a(3))/r(2))*(a(3)-afx) tmp(2,1) = tmp(2,1)/sqrt(1.0d0-(cos(a(3)))**2) tmp(2,1) = tmp(2,1) -2.0d0*b**2*(r(2)-rfx) tmp(2,2) = -(2.0d0*b2**2*r(2)*(a(2)-afx)) tmp(2,2) = tmp(2,2)/(r(1)*r(3)*sqrt(1.0d0-(cos(a(2)))**2)) tmp(2,3) = 2.0d0*b2**2*(1.0d0/r(3)-cos(a(1))/r(2))*(a(1)-afx) tmp(2,3) = tmp(2,3)/sqrt(1.0d0-(cos(a(1)))**2) tmp(2,3) = tmp(2,3) -2.0d0*b**2*(r(2)-rfx) tmp(3,1) = -(2.0d0*b2**2*r(3)*(a(3)-afx)) tmp(3,1) = tmp(3,1)/(r(1)*r(2)*sqrt(1.0d0-(cos(a(3)))**2)) tmp(3,2) = 2.0d0*b2**2*(1.0d0/r(1)-cos(a(2))/r(3))*(a(2)-afx) tmp(3,2) = tmp(3,2)/sqrt(1.0d0-(cos(a(2)))**2) tmp(3,2) = tmp(3,2) -2.0d0*b**2*(r(3)-rfx) tmp(3,3) = 2.0d0*b2**2*(1.0d0/r(2)-cos(a(1))/r(3))*(a(1)-afx) tmp(3,3) = tmp(3,3)/sqrt(1.0d0-(cos(a(1)))**2) tmp(3,3) = tmp(3,3) -2.0d0*b**2*(r(3)-rfx) do i=1,3 do j=1,3 if(abs(tmp(i,j)).gt.10d20) then if(tmp(i,j).gt.10d20) then tmp(i,j)=10d10 else if (tmp(i,j).lt.-10d20) then tmp(i,j)=-10d10 endif endif if(isnan(tmp(i,j))) then tmp(i,j) = 0.0d0 endif enddo enddo dVpfdR(1) = v0*(tmp(1,1)*Exp(tmp1) + tmp(1,2)*Exp(tmp2) + & tmp(1,3)*Exp(tmp3)) dVpfdR(2) = v0*(tmp(2,1)*Exp(tmp1) + tmp(2,2)*Exp(tmp2) + & tmp(2,3)*Exp(tmp3)) dVpfdR(3) = v0*(tmp(3,1)*Exp(tmp1) + tmp(3,2)*Exp(tmp2) + & tmp(3,3)*Exp(tmp3)) ! do i=1,3 ! if(isnan(dVpfdR(i))) then ! dVpfdR(i) = 0.0d0 ! endif ! enddo ! write(*,*) "dVpfdR(1) ",dVpfdR(1) ! write(*,*) "dVpfdR(2) ",dVpfdR(2) ! write(*,*) "dVpfdR(3) ",dVpfdR(3) endif end subroutine patchfunc subroutine EvdVdR !********************************************************************** ! Subroutine to evaluate dVdR for given R ! dVdR = dV2dR + C*dBdR ! C: Coefficients, stored in 'dim.inc' ! P: Basis functions evaluated for given R ! M: Monomials evaluated for given R ! dV2dR: Gradient of 2-body interactions ! dMsdR: dMsdR(3,3), 3 MEG terms w.r.t. 3 bond length ! dMdR: dMdR(3,nom), nom monomials w.r.t.3 bond length ! dPdR: dPdR(3,nob), nop polynomial basis functions ! w.r.t. 3 bond length ! nom: number of monomials ! nob: number of basis functions(polynomials) ! M(nom): Array to store monomials ! P(nob): Array to store polynomials !********************************************************************** integer i,j double precision dist,v2,dv2dr double precision Vpf,dVpfdR(3) ! Initialize dVdR(3) do i=1,3 dVdR(i)=0.0d0 enddo ! Add dV2dR(i) to dVdR do i=1,3 dist=R(i) call ev2gm2(dist,v2,dv2dr,1,1) dVdR(i)=dv2dr enddo !! D3 dispersion correction is called inside the ev2gm2 !! ! Add numerical gradient of D3 dispersion correction ! do i=1,3 ! call d3disp(R,disp,dispdr,1) ! dVdR(i)= dVdR(i) + dispdr(i) ! enddo ! Calculate dMEG/dr(3,3) for given R(3) call evdmsdr ! Calculate the monomials for each point by using six MEG terms call evdmdr ! Calculate the polynomials by using monomials call evdpdr ! Remove 2-body interactions and unconnected terms from polynomials call evdbdr ! Evaluate dVdR(3) by taken the product of C(j) and dPdR(i,j) do i=1,3 do j=1,56 dVdR(i)=dVdR(i) + c(j)*dBdR(i,j) enddo enddo ! Subtract the derivative of patch function to get the D3h correction call patchfunc(Vpf,dVpfdR,1) do i=1,3 dVdR(i) = dVdR(i) - dVpfdR(i) enddo return end subroutine EvdVdR subroutine EvdRdX(X) !********************************************************************** ! Subroutine to evaluate dRdX for given R and X ! R: R(3), 3 bond lengths ! X: X(9), 9 Cartesian coordinates ! ! dMdR: dMdR(3,nom), nom monomials w.r.t.3 bond length ! dPdR: dPdR(3,nob), nop polynomial basis functions ! w.r.t. 3 bond length ! M(nom): Array to store monomials ! P(nob): Array to store polynomials !********************************************************************** integer i,j double precision X(9) ! Initialize dRdX(3,9) do i=1,3 do j=1,9 dRdX(i,j)=0.0d0 enddo enddo ! Start to calculate the non-zero dRdX ! dr1dx dRdX(1,1)=(x(1)-x(4))/r(1) dRdX(1,2)=(x(2)-x(5))/r(1) dRdX(1,3)=(x(3)-x(6))/r(1) dRdX(1,4)=-dRdX(1,1) dRdX(1,5)=-dRdX(1,2) dRdX(1,6)=-dRdX(1,3) ! dr2dx dRdX(2,1)=(x(1)-x(7))/r(2) dRdX(2,2)=(x(2)-x(8))/r(2) dRdX(2,3)=(x(3)-x(9))/r(2) dRdX(2,7)=-dRdX(2,1) dRdX(2,8)=-dRdX(2,2) dRdX(2,9)=-dRdX(2,3) ! dr3dx dRdX(3,4)=(x(4)-x(7))/r(3) dRdX(3,5)=(x(5)-x(8))/r(3) dRdX(3,6)=(x(6)-x(9))/r(3) dRdX(3,7)=-dRdX(3,4) dRdX(3,8)=-dRdX(3,5) dRdX(3,9)=-dRdX(3,6) ! Finish the calculation of non-zero dRdX return end subroutine EvdRdX subroutine EvdMsdR !********************************************************************** ! Subroutine to evaluate the derivatives of MEG term X ! w.r.t. interatomic distance R(3) ! dmsdR: Local variables, dirm(3,3) ! a: Nonlinear pamameter(Angstrom) ! ab: Nonlinear pamameter(Angstrom^2) ! ra: reference bond length(Angstrom) ! rb: reference bond length(Angstrom) !********************************************************************** integer i,j ! Initialize dmsdr do i=1,3 do j=1,3 dmsdr(i,j)=0.0d0 enddo enddo ! MEG term dmsdr = exp(-(r-re)/a-(r-re)^2/ab) ! dmsdr(i,j)=0 i!=j do i=1,3 dmsdr(i,i)=(-2.0d0*(r(i)-rb)/ab-1/a) & * Exp(-(r(i)-ra)/a-((r(i)-rb)**2.0d0)/ab) enddo return end subroutine EvdMsdR subroutine EvdMdR !********************************************************************** ! The subroutine reads M(nom) and dMSdR(3,3) and calculates the ! dMdR(3,nom) that do not have usable decomposition. ! For A4 with max. degree 10, the number of monomials is nom. !********************************************************************** integer i do i=1,3 dmdr(i,0) = 0.0d0 dmdr(i,1) = dmsdr(i,3) dmdr(i,2) = dmsdr(i,2) dmdr(i,3) = dmsdr(i,1) dmdr(i,4) = dmdr(i,1)*rm(2) + rm(1)*dmdr(i,2) dmdr(i,5) = dmdr(i,1)*rm(3) + rm(1)*dmdr(i,3) dmdr(i,6) = dmdr(i,2)*rm(3) + rm(2)*dmdr(i,3) dmdr(i,7) = dmdr(i,1)*rm(6) + rm(1)*dmdr(i,6) enddo return end subroutine EvdMdR subroutine EvdPdr !********************************************************************** ! The subroutine reads monomials(m) and calculates the ! permutation invariant polynomials(p) ! For A4 with max. degree 10, the number of polynomials is nob. !********************************************************************** integer i do i=1,3 dpdr(i, 0) = dmdr(i,0) dpdr(i, 1) = dmdr(i,1) + dmdr(i,2) + dmdr(i,3) dpdr(i, 2) = dmdr(i,4) + dmdr(i,5) + dmdr(i,6) dpdr(i, 3) = dpdr(i, 1)*p( 1) + p( 1)*dpdr(i, 1) - dpdr(i, 2) & - dpdr(i, 2) dpdr(i, 4) = dmdr(i,7) dpdr(i, 5) = dpdr(i, 1)*p( 2) + p( 1)*dpdr(i, 2) - dpdr(i, 4) & - dpdr(i, 4) - dpdr(i, 4) dpdr(i, 6) = dpdr(i, 1)*p( 3) + p( 1)*dpdr(i, 3) - dpdr(i, 5) dpdr(i, 7) = dpdr(i, 1)*p( 4) + p( 1)*dpdr(i, 4) dpdr(i, 8) = dpdr(i, 2)*p( 2) + p( 2)*dpdr(i, 2) - dpdr(i, 7) & - dpdr(i, 7) dpdr(i, 9) = dpdr(i, 2)*p( 3) + p( 2)*dpdr(i, 3) - dpdr(i, 7) dpdr(i,10) = dpdr(i, 1)*p( 6) + p( 1)*dpdr(i, 6) - dpdr(i, 9) dpdr(i,11) = dpdr(i, 2)*p( 4) + p( 2)*dpdr(i, 4) dpdr(i,12) = dpdr(i, 3)*p( 4) + p( 3)*dpdr(i, 4) dpdr(i,13) = dpdr(i, 1)*p( 8) + p( 1)*dpdr(i, 8) - dpdr(i,11) dpdr(i,14) = dpdr(i, 2)*p( 6) + p( 2)*dpdr(i, 6) - dpdr(i,12) dpdr(i,15) = dpdr(i, 1)*p(10) + p( 1)*dpdr(i,10) - dpdr(i,14) dpdr(i,16) = dpdr(i, 4)*p( 4) + p( 4)*dpdr(i, 4) dpdr(i,17) = dpdr(i, 4)*p( 5) + p( 4)*dpdr(i, 5) dpdr(i,18) = dpdr(i, 4)*p( 6) + p( 4)*dpdr(i, 6) dpdr(i,19) = dpdr(i, 2)*p( 8) + p( 2)*dpdr(i, 8) - dpdr(i,17) dpdr(i,20) = dpdr(i, 1)*p(13) + p( 1)*dpdr(i,13) - dpdr(i,17) & - dpdr(i,19) - dpdr(i,19) dpdr(i,21) = dpdr(i, 2)*p(10) + p( 2)*dpdr(i,10) - dpdr(i,18) dpdr(i,22) = dpdr(i, 1)*p(15) + p( 1)*dpdr(i,15) - dpdr(i,21) dpdr(i,23) = dpdr(i, 1)*p(16) + p( 1)*dpdr(i,16) dpdr(i,24) = dpdr(i, 4)*p( 8) + p( 4)*dpdr(i, 8) dpdr(i,25) = dpdr(i, 3)*p(11) + p( 3)*dpdr(i,11) - dpdr(i,23) dpdr(i,26) = dpdr(i, 4)*p(10) + p( 4)*dpdr(i,10) dpdr(i,27) = dpdr(i, 1)*p(19) + p( 1)*dpdr(i,19) - dpdr(i,24) dpdr(i,28) = dpdr(i, 6)*p( 8) + p( 6)*dpdr(i, 8) - dpdr(i,23) dpdr(i,29) = dpdr(i, 2)*p(15) + p( 2)*dpdr(i,15) - dpdr(i,26) dpdr(i,30) = dpdr(i, 1)*p(22) + p( 1)*dpdr(i,22) - dpdr(i,29) dpdr(i,31) = dpdr(i, 2)*p(16) + p( 2)*dpdr(i,16) dpdr(i,32) = dpdr(i, 3)*p(16) + p( 3)*dpdr(i,16) dpdr(i,33) = dpdr(i, 1)*p(24) + p( 1)*dpdr(i,24) - dpdr(i,31) dpdr(i,34) = dpdr(i, 4)*p(14) + p( 4)*dpdr(i,14) dpdr(i,35) = dpdr(i, 4)*p(15) + p( 4)*dpdr(i,15) dpdr(i,36) = dpdr(i, 2)*p(19) + p( 2)*dpdr(i,19) - dpdr(i,33) dpdr(i,37) = dpdr(i, 3)*p(19) + p( 3)*dpdr(i,19) - dpdr(i,31) dpdr(i,38) = dpdr(i, 8)*p(10) + p( 8)*dpdr(i,10) - dpdr(i,32) dpdr(i,39) = dpdr(i, 2)*p(22) + p( 2)*dpdr(i,22) - dpdr(i,35) dpdr(i,40) = dpdr(i, 1)*p(30) + p( 1)*dpdr(i,30) - dpdr(i,39) dpdr(i,41) = dpdr(i, 4)*p(16) + p( 4)*dpdr(i,16) dpdr(i,42) = dpdr(i, 4)*p(17) + p( 4)*dpdr(i,17) dpdr(i,43) = dpdr(i, 4)*p(19) + p( 4)*dpdr(i,19) dpdr(i,44) = dpdr(i, 6)*p(16) + p( 6)*dpdr(i,16) dpdr(i,45) = dpdr(i, 4)*p(20) + p( 4)*dpdr(i,20) dpdr(i,46) = dpdr(i, 4)*p(21) + p( 4)*dpdr(i,21) dpdr(i,47) = dpdr(i, 4)*p(22) + p( 4)*dpdr(i,22) dpdr(i,48) = dpdr(i, 1)*p(36) + p( 1)*dpdr(i,36) - dpdr(i,43) dpdr(i,49) = dpdr(i, 1)*p(37) + p( 1)*dpdr(i,37) - dpdr(i,45) & - dpdr(i,48) dpdr(i,50) = dpdr(i, 8)*p(15) + p( 8)*dpdr(i,15) - dpdr(i,44) dpdr(i,51) = dpdr(i, 2)*p(30) + p( 2)*dpdr(i,30) - dpdr(i,47) dpdr(i,52) = dpdr(i, 1)*p(40) + p( 1)*dpdr(i,40) - dpdr(i,51) dpdr(i,53) = dpdr(i, 1)*p(41) + p( 1)*dpdr(i,41) dpdr(i,54) = dpdr(i, 4)*p(24) + p( 4)*dpdr(i,24) dpdr(i,55) = dpdr(i, 3)*p(31) + p( 3)*dpdr(i,31) - dpdr(i,53) dpdr(i,56) = dpdr(i, 1)*p(43) + p( 1)*dpdr(i,43) - dpdr(i,54) dpdr(i,57) = dpdr(i,10)*p(16) + p(10)*dpdr(i,16) dpdr(i,58) = dpdr(i, 4)*p(28) + p( 4)*dpdr(i,28) dpdr(i,59) = dpdr(i, 4)*p(29) + p( 4)*dpdr(i,29) dpdr(i,60) = dpdr(i, 4)*p(30) + p( 4)*dpdr(i,30) dpdr(i,61) = dpdr(i, 2)*p(36) + p( 2)*dpdr(i,36) - dpdr(i,56) dpdr(i,62) = dpdr(i, 3)*p(36) + p( 3)*dpdr(i,36) - dpdr(i,54) dpdr(i,63) = dpdr(i,10)*p(19) + p(10)*dpdr(i,19) - dpdr(i,53) dpdr(i,64) = dpdr(i, 8)*p(22) + p( 8)*dpdr(i,22) - dpdr(i,57) dpdr(i,65) = dpdr(i, 2)*p(40) + p( 2)*dpdr(i,40) - dpdr(i,60) dpdr(i,66) = dpdr(i, 1)*p(52) + p( 1)*dpdr(i,52) - dpdr(i,65) enddo return end subroutine EvdPdR subroutine evdbdr !********************************************************************** ! The subroutine eliminate the 2-body terms in Bowman's approach !********************************************************************** integer i,j double precision db1dr(3,67) ! Pass P(3,0:66) to BM1(3,1:67) do j=1,3 do i=1,67 db1dr(j,i)=dpdr(j,i-1) enddo enddo ! Remove unconnected terms and 2-body terms and pass to B(1:56) do j=1,3 dbdr(j,1)=db1dr(j,3) do i=2,3 dbdr(j,i)=db1dr(j,i+3) enddo do i=4,6 dbdr(j,i)=db1dr(j,i+4) enddo do i=7,10 dbdr(j,i)=db1dr(j,i+5) enddo do i=11,16 dbdr(j,i)=db1dr(j,i+6) enddo do i=17,23 dbdr(j,i)=db1dr(j,i+7) enddo do i=24,32 dbdr(j,i)=db1dr(j,i+8) enddo do i=33,43 dbdr(j,i)=db1dr(j,i+9) enddo do i=44,56 dbdr(j,i)=db1dr(j,i+10) enddo enddo return end subroutine evdbdr subroutine d3disp(dist,disp,dispdr,igrad,imol) !********************************************************************** ! Dispersion correction based on Grimme's D3(BJ) calculation for ! diatomic pairs ! ! Several subroutines of DFTD3 V3.1 Rev 1 by Grimme were merged into ! subroutine edisp and they have been heavily modified to calculate ! only dispersion energy corrections that are needed. ! ! S. Grimme, J. Antony, S. Ehrlich and H. Krieg ! J. Chem. Phys, 132 (2010), 154104 ! and ! S. Grimme, S. Ehrlich and L. Goerigk, J. Comput. Chem, 32 (2011), ! 1456-1465 ! ! The C6 values are fixed. ! !********************************************************************** double precision cn(2),s6,s8,rs6,rs8 double precision dist(1), e6(1), e8(1), disp, dispdr(1), c6(2) double precision e6dr(1),e8dr(1) integer iz(2), mxc(94), i, j, igrad double precision c6ab(94,94,5,5,3) double precision r2r4(94) double precision autoang,autokcal integer imol autoang =0.52917726d0 autokcal=627.509541d0 ! Generalized parameters for BJ damping from P. Verma, B. Wang, ! L. E. Fernandez, and D. G. Truhlar, J. Phys. Chem. A 121, 2855 (2017) s6= 1.0d0 s8= 2.0d0 rs6= 0.5299d0 rs8= 2.20d0 do i=1,1 dist(i)=dist(i)/autoang enddo if (imol.eq.1) then ! iz for N2 system iz(1)=7 iz(2)=7 ! C6 for N2 system c6(1)=19.7d0 c6(2)=19.7d0 else ! currently imol = 1 is used stop endif ! Calculate dispersion correction call edisp(94,5,2,dist,iz,mxc, & rs6,rs8,e6,e8,e6dr,e8dr,c6,0) disp = 0.0d0 do i=1,1 disp =disp + (-s6*e6(i)-s8*e8(i))*autokcal enddo if (igrad .eq. 1) then call edisp(94,5,2,dist,iz,mxc, & rs6,rs8,e6,e8,e6dr,e8dr,c6,1) dispdr(:) = 0.0d0 do i=1,1 dispdr(i) =dispdr(i) + (-s6*e6dr(i)-s8*e8dr(i))*autokcal/autoang enddo endif do i=1,1 dist(i)=dist(i)*autoang enddo end subroutine d3disp !********************************************************************** ! compute energy !********************************************************************** subroutine edisp(max_elem,maxc,n,dist,iz,mxc, & rs6,rs8,e6,e8,e6dr,e8dr,c6a,igrad) integer n,iz(2),max_elem,maxc,mxc(max_elem) double precision dist(1),r2r4(max_elem),r0ab(max_elem,max_elem) double precision rs6,rs8,rcov(max_elem) double precision c6ab(max_elem,max_elem,maxc,maxc,3) double precision e6(1), e8(1), c6a(2), e6dr(1), e8dr(1) integer iat,jat,igrad double precision r,tmp,c6,c8,a1,a2 double precision damp6,damp8 double precision cn(n) double precision r2ab(n*n),cc6ab(n*n),dmp(n*n) integer step e6(:) =0.0d0 e8(:) =0.0d0 e6dr(:) =0.0d0 e8dr(:) =0.0d0 a1=rs6 a2=rs8 ! r2r4 =sqrt(0.5*r2r4(i)*dfloat(i)**0.5 ) with i=elementnumber ! the large number of digits is just to keep the results consistent ! with older versions. They should not imply any higher accuracy than ! the old values r2r4(1:94)=(/ & 2.00734898d0, 1.56637132d0, 5.01986934d0, 3.85379032d0, & 3.64446594d0, 3.10492822d0, 2.71175247d0, 2.59361680d0, & 2.38825250d0, 2.21522516d0, 6.58585536d0, 5.46295967d0, & 5.65216669d0, 4.88284902d0, 4.29727576d0, 4.04108902d0, & 3.72932356d0, 3.44677275d0, 7.97762753d0, 7.07623947d0, & 6.60844053d0, 6.28791364d0, 6.07728703d0, 5.54643096d0, & 5.80491167d0, 5.58415602d0, 5.41374528d0, 5.28497229d0, & 5.22592821d0, 5.09817141d0, 6.12149689d0, 5.54083734d0, & 5.06696878d0, 4.87005108d0, 4.59089647d0, 4.31176304d0, & 9.55461698d0, 8.67396077d0, 7.97210197d0, 7.43439917d0, & 6.58711862d0, 6.19536215d0, 6.01517290d0, 5.81623410d0, & 5.65710424d0, 5.52640661d0, 5.44263305d0, 5.58285373d0, & 7.02081898d0, 6.46815523d0, 5.98089120d0, 5.81686657d0, & 5.53321815d0, 5.25477007d0, 11.02204549d0, 0.15679528d0, & 9.35167836d0, 9.06926079d0, 8.97241155d0, 8.90092807d0, & 8.85984840d0, 8.81736827d0, 8.79317710d0, 7.89969626d0, & 8.80588454d0, 8.42439218d0, 8.54289262d0, 8.47583370d0, & 8.45090888d0, 8.47339339d0, 7.83525634d0, 8.20702843d0, & 7.70559063d0, 7.32755997d0, 7.03887381d0, 6.68978720d0, & 6.05450052d0, 5.88752022d0, 5.70661499d0, 5.78450695d0, & 7.79780729d0, 7.26443867d0, 6.78151984d0, 6.67883169d0, & 6.39024318d0, 6.09527958d0, 11.79156076d0, 11.10997644d0, & 9.51377795d0, 8.67197068d0, 8.77140725d0, 8.65402716d0, & 8.53923501d0, 8.85024712d0 /) ! these new data are scaled with k2=4./3. and converted to a_0 ! via autoang=0.52917726d0 rcov(1:94)=(/ & 0.80628308d0, 1.15903197d0, 3.02356173d0, 2.36845659d0, & 1.94011865d0, 1.88972601d0, 1.78894056d0, 1.58736983d0, & 1.61256616d0, 1.68815527d0, 3.52748848d0, 3.14954334d0, & 2.84718717d0, 2.62041997d0, 2.77159820d0, 2.57002732d0, & 2.49443835d0, 2.41884923d0, 4.43455700d0, 3.88023730d0, & 3.35111422d0, 3.07395437d0, 3.04875805d0, 2.77159820d0, & 2.69600923d0, 2.62041997d0, 2.51963467d0, 2.49443835d0, & 2.54483100d0, 2.74640188d0, 2.82199085d0, 2.74640188d0, & 2.89757982d0, 2.77159820d0, 2.87238349d0, 2.94797246d0, & 4.76210950d0, 4.20778980d0, 3.70386304d0, 3.50229216d0, & 3.32591790d0, 3.12434702d0, 2.89757982d0, 2.84718717d0, & 2.84718717d0, 2.72120556d0, 2.89757982d0, 3.09915070d0, & 3.22513231d0, 3.17473967d0, 3.17473967d0, 3.09915070d0, & 3.32591790d0, 3.30072128d0, 5.26603625d0, 4.43455700d0, & 4.08180818d0, 3.70386304d0, 3.98102289d0, 3.95582657d0, & 3.93062995d0, 3.90543362d0, 3.80464833d0, 3.82984466d0, & 3.80464833d0, 3.77945201d0, 3.75425569d0, 3.75425569d0, & 3.72905937d0, 3.85504098d0, 3.67866672d0, 3.45189952d0, & 3.30072128d0, 3.09915070d0, 2.97316878d0, 2.92277614d0, & 2.79679452d0, 2.82199085d0, 2.84718717d0, 3.32591790d0, & 3.27552496d0, 3.27552496d0, 3.42670319d0, 3.30072128d0, & 3.47709584d0, 3.57788113d0, 5.06446567d0, 4.56053862d0, & 4.20778980d0, 3.98102289d0, 3.82984466d0, 3.85504098d0, & 3.88023730d0, 3.90543362d0 /) ! DFT-D3 step=0 do iat=1,n-1 do jat=iat+1,n step=step+1 r=dist(step) c6=c6a(step) ! r2r4 stored in main as sqrt c8 =3.0d0*c6*r2r4(iz(iat))*r2r4(iz(jat)) ! energy for BJ damping tmp=sqrt(c8/c6) e6(step)= c6/(r**6+(a1*tmp+a2)**6) e8(step)= c8/(r**8+(a1*tmp+a2)**8) ! calculate gradients if (igrad .eq. 1) then ! grad for BJ damping e6dr(step)=c6*(-6*r**5)/(r**6+(a1*tmp+a2)**6)**2 e8dr(step)=c8*(-8*r**7)/(r**8+(a1*tmp+a2)**8)**2 endif enddo enddo end subroutine edisp end module N3_4App_MB_PIP_MEG1