! ! Copyright (C) 2003-2010 Quantum ESPRESSO group ! 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 . ! ! Last edition: ! Date: April 30, 2010 ! Author: Eyvaz Isaev ! Department of Physics, Chemistry and Biology (IFM), Linkoping University, Sweden ! ! a) Input: Add lattice parameters units: au or Ang ! b) Output: More info printed out ! c) Output: Additional output file with E+PV ! PROGRAM ev ! ! fit of E(v) to an equation of state (EOS) ! ! Input data file format for cubic systems: ! a0(1) Etot(1) ! ... ! a0(n) Etot(n) ! Input data file format for hexagonal systems: ! V0(1) Etot(1) ! ... ! V0(n) Etot(n) ! where V0(i) = sqrt(3)/2 * a^2 * c is the unit-cell volume ! Etot(i)= min Etot(c) for the given volume V0(i) ! V0, a0, etot in atomic (Rydberg) units ; bulk modulus in kbar ! ! Output data file format for cubic systems: ! a0(1) Etot(1) Efit(1) Pfit(1) Etot(1)-Efit(1) ! ... ! a0(n) Etot(n) Efit(n) Pfit(n) Etot(n)-Efit(n) ! Output data file format for hexagonal systems: ! V0(1) Etot(1) Efit(1) Pfit(1) Etot(1)-Efit(1) ! ... ! V0(n) Etot(n) Efit(n) Pfit(n) Etot(n)-Efit(n) ! ! where Efit is the fitted value from the EOS ! Pfit is the corresponding pressure from the EOS ! USE kinds, only: DP USE constants, only: bohr_radius_angs, ry_kbar IMPLICIT NONE INTEGER nmaxpar, nmaxpt, nseek, nmin, npar,npt,istat PARAMETER(nmaxpar=4, nmaxpt=100, nseek=10000, nmin=4) CHARACTER bravais*3, au_unit*3, filin*256 REAL(DP) par(nmaxpar), deltapar(nmaxpar), parmin(nmaxpar), & parmax(nmaxpar), v0(nmaxpt), etot(nmaxpt), efit(nmaxpt), & fac, emin, chisq, a LOGICAL :: convert_to_au ! ! PRINT '(5x,''Lattice parameter or Volume are in '', & & ''(au, Ang) > '',$)' READ '(a)', au_unit convert_to_au = au_unit.eq.'Ang' .or. au_unit.eq.'ANG' .or. & au_unit.eq.'ang' IF (convert_to_au) PRINT '(5x,"Assuming Angstrom")' PRINT '(5x,''Enter type of bravais lattice '', & & ''(fcc, bcc, sc, hex) > '',$)' READ '(a)',bravais ! IF(bravais.EQ.'fcc'.OR.bravais.EQ.'FCC') THEN fac = 0.25d0 ELSE IF(bravais.EQ.'bcc'.OR.bravais.EQ.'BCC') THEN fac = 0.50d0 ELSE IF(bravais.EQ.'sc'.OR.bravais.EQ.'SC') THEN fac = 1.0d0 ELSE IF(bravais.EQ.'hex'.OR.bravais.EQ.'HEX') THEN fac = SQRT(3d0)/2d0 ELSE PRINT '(5x,''ev: unexpected lattice '',a3)', bravais STOP ENDIF ! PRINT '(5x,''Enter type of equation of state :''/& &5x,''1=birch1, 2=birch2, 3=keane, 4=murnaghan > '',$)' READ *,istat IF(istat.EQ.1 .OR. istat.EQ.4) THEN npar=3 ELSE IF(istat.EQ.2 .OR. istat.EQ.3) THEN npar=4 ELSE PRINT '(5x,''Unexpected eq. of state '',i2)', istat STOP END IF PRINT '(5x,''Input file > '',$)' READ '(a)',filin OPEN(unit=2,file=filin,status='old',form='formatted') 10 CONTINUE emin=1d10 DO npt=1,nmaxpt IF (bravais.EQ.'hex'.OR.bravais.EQ.'HEX') THEN READ(2,*,err=10,END=20) v0(npt), etot(npt) IF (convert_to_au) v0(npt)=v0(npt)/bohr_radius_angs**3 ELSE READ(2,*,err=10,END=20) a, etot(npt) IF (convert_to_au) a = a/bohr_radius_angs v0 (npt) = fac*a**3 END IF IF(etot(npt).LT.emin) THEN par(1) = v0(npt) emin = etot(npt) END IF ENDDO npt = nmaxpt+1 20 npt = npt-1 ! ! par(1) = V, Volume of the unit cell in (a.u.^3) ! par(2) = B, Bulk Modulus (in KBar) ! par(3) = dB/dP (adimensional) ! par(4) = d^2B/dP^2 (in KBar^(-1), used only by 2nd order formulae) ! par(2) = 500.0d0 par(3) = 5.0d0 par(4) = -0.01d0 ! parmin(1) = 0.0d0 parmin(2) = 0.0d0 parmin(3) = 1.0d0 parmin(4) = -1.0d0 ! parmax(1) = 100000.d0 parmax(2) = 100000.d0 parmax(3) = 15.0d0 parmax(4) = 0.0d0 ! deltapar(1) = 0.1d0 deltapar(2) = 100.d0 deltapar(3) = 1.0d0 deltapar(4) = 0.01d0 ! CALL find_minimum & (npar,par,deltapar,parmin,parmax,nseek,nmin,chisq) ! CALL write_results & (npt,bravais,fac,v0,etot,efit,istat,par,npar,emin,chisq) ! STOP CONTAINS ! !----------------------------------------------------------------------- SUBROUTINE eqstate(npar,par,chisq) !----------------------------------------------------------------------- ! IMPLICIT NONE INTEGER nmaxpt, npar, i PARAMETER( nmaxpt=100 ) REAL(DP) par(npar), k0, dk0, d2k0, c0, c1, x, vol0, ddk, chisq ! vol0 = par(1) k0 = par(2)/ry_kbar ! converts k0 to Ry atomic units... dk0 = par(3) d2k0 = par(4)*ry_kbar ! and d2k0/dp2 to (Ry a.u.)^(-1) ! IF(istat.EQ.1.OR.istat.EQ.2) THEN IF(istat.EQ.1) THEN c0 = 0.0d0 ELSE c0 = ( 9.d0*k0*d2k0 + 9.d0*dk0**2-63.d0*dk0+143.d0 )/48.d0 ENDIF c1 = 3.d0*(dk0-4.d0)/8.d0 DO i=1,npt x = vol0/v0(i) efit(i) = 9.d0*k0*vol0*( (-0.5d0+c1-c0)*x**(2.d0/3.d0)/2.d0 & +( 0.50-2.d0*c1+3.d0*c0)*x**(4.d0/3.d0)/4.d0 & +( c1-3.d0*c0)*x**(6.d0/3.d0)/6.d0 & +( c0)*x**(8.d0/3.d0)/8.d0 & -(-1.d0/8.d0+c1/6.d0-c0/8.d0) ) ENDDO ELSE IF(istat.EQ.3) THEN ddk = dk0 + k0*d2k0/dk0 ELSE ddk = dk0 ENDIF DO i=1,npt efit(i) = - k0*dk0/ddk*vol0/(ddk-1.d0) & + v0(i)*k0*dk0/ddk**2*( (vol0/v0(i))**ddk/(ddk-1.d0)+1.d0) & - k0*(dk0-ddk)/ddk*( v0(i)*LOG(vol0/v0(i)) + v0(i)-vol0 ) ENDDO ENDIF ! ! emin = equilibrium energy obtained by minimizing chi**2 ! emin = 0.0d0 DO i = 1,npt emin = emin + etot(i)-efit(i) ENDDO emin = emin/npt ! chisq = 0.0d0 DO i = 1,npt efit(i) = efit(i)+emin chisq = chisq + (etot(i)-efit(i))**2 ENDDO chisq = chisq/npt ! RETURN END SUBROUTINE eqstate ! !----------------------------------------------------------------------- SUBROUTINE write_results & (npt,bravais,fac,v0,etot,efit,istat,par,npar,emin,chisq) !----------------------------------------------------------------------- ! IMPLICIT NONE INTEGER npt, istat, npar, i, iun, ios CHARACTER filout*256, bravais*3 REAL(DP) v0(npt), etot(npt), efit(npt), par(npar), emin, chisq, fac REAL(DP) p(npt), epv(npt) 10 CONTINUE PRINT '(5x,''Output file > '',$)' READ '(a)',filout IF(filout.NE.' ') THEN iun=8 OPEN(unit=iun,file=filout,form='formatted',status='new', & iostat=ios) IF (ios.NE.0) THEN PRINT '(5x,''Cannot open, try again! '')' go to 10 END IF ELSE iun=6 END IF IF(istat.EQ.1) THEN WRITE(iun,'(''# equation of state: '', & &''birch 1st order. chisq = '',d10.4)') chisq ELSE IF(istat.EQ.2) THEN WRITE(iun,'(''# equation of state: '', & &''birch 2nd order. chisq = '',d10.4)') chisq ELSE IF(istat.EQ.3) THEN WRITE(iun,'(''# equation of state: '', & &''keane. chisq = '',d10.4)') chisq ELSE IF(istat.EQ.4) THEN WRITE(iun,'(''# equation of state: '', & &''murnaghan. chisq = '',d10.4)') chisq END IF IF(istat.EQ.1 .OR. istat.EQ.4) par(4) = 0.0d0 IF(istat.EQ.1 .OR. istat.EQ.2) THEN DO i=1,npt p(i)=birch(v0(i)/par(1),par(2),par(3),par(4)) END DO ELSE DO i=1,npt p(i)=keane(v0(i)/par(1),par(2),par(3),par(4)) END DO END IF do i=1,npt epv(i) = etot(i) + p(i)*v0(i) / ry_kbar enddo IF(bravais.NE.'hex'.AND.bravais.NE.'HEX') THEN WRITE(iun,'(''# a0 ='',f6.2,'' a.u., k0 ='',i5,'' kbar, dk0 ='', & &f6.2,'' d2k0 ='',f7.3,'' emin ='',f11.5)') & (par(1)/fac)**(1d0/3d0), INT(par(2)), par(3), par(4), emin WRITE(iun,'(''# a0 ='',f7.3,'' Ang, k0 ='', f6.1,'' GPa, V0 = '',f7.3,'' (a.u.)^3, V0 ='', & &f7.3,'' A^3 '',/)') & (par(1)/fac)**(1d0/3d0)*bohr_radius_angs, par(2)/10, par(1), & & par(1)*bohr_radius_angs**3 write(iun,'(73("#"))') write(iun,'("# Lat.Par", 5x, "E_calc", 8x, "E_fit", 7x, & & "E_diff", 4x, "Pressure", 6x, "Enthalpy")') write(iun,'("# Ang", 11x, "Ry", 11x, "Ry", 12x, & & "Ry", 8x, "GPa", 11x, "Ry")') write(iun,'(73("#"))') WRITE(iun,'(f7.3,2x,f12.5, 2x,f12.5, f12.5, 3x, f8.2, 3x,f12.5)') & & ( (v0(i)/fac)**(1d0/3d0)*bohr_radius_angs, etot(i), efit(i), & & etot(i)-efit(i), p(i), epv(i), i=1,npt ) ELSE WRITE(iun,'(''# V0 ='',f8.2,'' a.u.^3, k0 ='',i5,'' kbar, dk0 ='', & & f6.2,'' d2k0 ='',f7.3,'' emin ='',f11.5)') & & par(1), INT(par(2)), par(3), par(4), emin WRITE(iun,'("# V0 =",f8.2," Ang^3, k0 =",f6.1," GPa"/)') & & par(1)*bohr_radius_angs**3, par(2)/10 write(iun,'(74("#"))') write(iun,'("# Vol.", 8x, "E_calc", 8x, "E_fit", 7x, & & "E_diff", 4x, "Pressure", 6x, "Enthalpy")') write(iun,'("# Ang^3", 9x, "Ry", 11x, "Ry", 12x, & & "Ry", 8x, "GPa", 11x, "Ry")') write(iun,'(74("#"))') WRITE(iun,'(f8.2,2x,f12.5, 2x,f12.5, f12.5, 3x, f8.2, 3x,f12.5)') & ( v0(i)*bohr_radius_angs**3, etot(i), efit(i), & etot(i)-efit(i), p(i), epv(i), i=1,npt ) END IF IF(filout.NE.' ') CLOSE(unit=iun) RETURN END SUBROUTINE write_results ! !----------------------------------------------------------------------- SUBROUTINE find_minimum & (npar,par,deltapar,parmin,parmax,nseek,nmin,chisq) !----------------------------------------------------------------------- ! ! Very Stupid Minimization ! USE random_numbers, ONLY : randy IMPLICIT NONE INTEGER maxpar, nseek, npar, nmin, n,j,i PARAMETER (maxpar=4) REAL(DP) par(npar), deltapar(npar), parmin(npar), parmax(npar), & parnew(maxpar), chisq, chinew, bidon ! ! various initializations ! chisq = 1.0d30 chinew= 1.0d30 CALL eqstate(npar,par,chisq) DO j = 1,nmin DO i = 1,nseek DO n = 1,npar 10 parnew(n) = par(n) + (0.5d0 - randy())*deltapar(n) IF(parnew(n).GT.parmax(n) .OR. parnew(n).LT.parmin(n)) & go to 10 ENDDO ! CALL eqstate(npar,parnew,chinew) ! IF(chinew.LT.chisq) THEN DO n = 1,npar par(n) = parnew(n) ENDDO chisq = chinew ENDIF ENDDO DO n = 1,npar deltapar(n) = deltapar(n)/10.d0 ENDDO ENDDO ! CALL eqstate(npar,par,chisq) ! RETURN END SUBROUTINE find_minimum ! FUNCTION birch(x,k0,dk0,d2k0) ! IMPLICIT NONE REAL(DP) birch, x, k0,dk0, d2k0 REAL(DP) c0, c1 IF(d2k0.NE.0.d0) THEN c0 = (9.d0*k0*d2k0 + 9.d0*dk0**2 - 63.d0*dk0 + 143.d0 )/48.d0 ELSE c0 = 0.0d0 ENDIF c1 = 3.d0*(dk0-4.d0)/8.d0 birch = 3.d0*k0*( (-0.5d0+ c1- c0)*x**( -5.d0/3.d0) & +( 0.5d0-2.d0*c1+3.0d0*c0)*x**( -7.d0/3.d0) & +( c1-3*c0)*x**( -9.0d0/3d0) & +( c0)*x**(-11.0d0/3d0) ) RETURN END FUNCTION birch ! FUNCTION keane(x,k0,dk0,d2k0) ! IMPLICIT NONE REAL(DP) keane, x, k0, dk0, d2k0, ddk ddk = dk0 + k0*d2k0/dk0 keane = k0*dk0/ddk**2*( x**(-ddk) - 1d0 ) + (dk0-ddk)/ddk*LOG(x) RETURN END FUNCTION keane END PROGRAM ev