c------------------------------------------------------
      double precision function HNose(ek,s,e,pi,Q,t_bath,dimen)
      implicit none
      double precision ek,s,e,pi,Q,t_bath,Rb
      integer dimen
      Rb=0.001986d0
      HNose=ek+e+pi**2/(2*Q)+dimen*Rb*t_bath*log(s)
c      print '(6f15.5,i5,a2,2f15.5)',ek,s,e,pi,Q,t_bath,dimen,"--",
c     &      pi**2/(2*Q),dimen*Rb*t_bath*log(s)
      return
      end
c-----------------------------------------------------------------
      double precision function HNose_nh(eki,e)
      implicit real*8 (a-h,o-z)
      include 'DIMENSIONS'
      include 'COMMON.MD'
      HNose_nh=eki+e+dimen*Rb*t_bath*xlogs(1)+qmass(1)*vlogs(1)**2/2
      do i=2,nnos
        HNose_nh=HNose_nh+qmass(i)*vlogs(i)**2/2+Rb*t_bath*xlogs(i)
      enddo
c      write(4,'(5e15.5)') 
c     &       vlogs(1),xlogs(1),HNose,eki,e
      return
      end
c-----------------------------------------------------------------
      SUBROUTINE NHCINT(akin,scale,wdti,wdti2,wdti4,wdti8)
      implicit real*8 (a-h,o-z)
      include 'DIMENSIONS'
      include 'COMMON.MD'
      double precision akin,gnkt,dt,aa,gkt,scale
      double precision wdti(maxyosh),wdti2(maxyosh),
     &                 wdti4(maxyosh),wdti8(maxyosh)
      integer i,iresn,iyosh,inos,nnos1

      dt=d_time
      nnos1=nnos+1
      GKT = Rb*t_bath
      GNKT = dimen*GKT
      akin=akin*2

      
C THIS ROUTINE DOES THE NOSE-HOOVER PART OF THE
C INTEGRATION FROM t=0 TO t=DT/2
C GET THE TOTAL KINETIC ENERGY
      SCALE = 1.D0
c      CALL GETKINP(MASS,VX,VY,VZ,AKIN)
C UPDATE THE FORCES
      GLOGS(1) = (AKIN - GNKT)/QMASS(1)
C START THE MULTIPLE TIME STEP PROCEDURE
      DO IRESN = 1,NRESN
       DO IYOSH = 1,NYOSH
C UPDATE THE THERMOSTAT VELOCITIES
        VLOGS(NNOS) = VLOGS(NNOS) + GLOGS(NNOS)*WDTI4(IYOSH)
        DO INOS = 1,NNOS-1
         AA = EXP(-WDTI8(IYOSH)*VLOGS(NNOS1-INOS) )
         VLOGS(NNOS-INOS) = VLOGS(NNOS-INOS)*AA*AA
     &          + WDTI4(IYOSH)*GLOGS(NNOS-INOS)*AA
        ENDDO
C UPDATE THE PARTICLE VELOCITIES
        AA = EXP(-WDTI2(IYOSH)*VLOGS(1) )
        SCALE = SCALE*AA
C UPDATE THE FORCES
        GLOGS(1) = (SCALE*SCALE*AKIN - GNKT)/QMASS(1)
C UPDATE THE THERMOSTAT POSITIONS
        DO INOS = 1,NNOS
         XLOGS(INOS) = XLOGS(INOS) + VLOGS(INOS)*WDTI2(IYOSH)
        ENDDO
C UPDATE THE THERMOSTAT VELOCITIES
        DO INOS = 1,NNOS-1
         AA = EXP(-WDTI8(IYOSH)*VLOGS(INOS+1) )
         VLOGS(INOS) = VLOGS(INOS)*AA*AA
     &      + WDTI4(IYOSH)*GLOGS(INOS)*AA
         GLOGS(INOS+1) = (QMASS(INOS)*VLOGS(INOS)*VLOGS(INOS)
     &      -GKT)/QMASS(INOS+1)
        ENDDO
        VLOGS(NNOS) = VLOGS(NNOS) + GLOGS(NNOS)*WDTI4(IYOSH)
       ENDDO
      ENDDO
C UPDATE THE PARTICLE VELOCITIES
c outside of this subroutine
c      DO I = 1,N
c       VX(I) = VX(I)*SCALE
c       VY(I) = VY(I)*SCALE
c       VZ(I) = VZ(I)*SCALE
c      ENDDO
      RETURN
      END
c-----------------------------------------------------------------
      subroutine tnp1_respa_i_step1
c Applying Nose-Poincare algorithm - step 1 to coordinates
c JPSJ 70 75 (2001) S. Nose
c
c d_t is not updated here
c
      implicit real*8 (a-h,o-z)
      include 'DIMENSIONS'
      include 'COMMON.CONTROL'
      include 'COMMON.VAR'
      include 'COMMON.MD'
      include 'COMMON.CHAIN'
      include 'COMMON.DERIV'
      include 'COMMON.GEO'
      include 'COMMON.LOCAL'
      include 'COMMON.INTERACT'
      include 'COMMON.IOUNITS'
      include 'COMMON.NAMES'
      double precision adt,adt2,tmp
        
      tmp=1+pi_np/(2*Q_np)*0.5*d_time
      s12_np=s_np*tmp**2
      pistar=pi_np/tmp
      s12_dt=d_time/s12_np
      d_time_s12=d_time*0.5*s12_np

      do j=1,3
        d_t_new(j,0)=d_t_old(j,0)+d_a_old(j,0)*d_time_s12
        dc(j,0)=dc_old(j,0)+d_t_new(j,0)*s12_dt
      enddo
      do i=nnt,nct-1	
        do j=1,3    
          d_t_new(j,i)=d_t_old(j,i)+d_a_old(j,i)*d_time_s12
          dc(j,i)=dc_old(j,i)+d_t_new(j,i)*s12_dt
        enddo
      enddo
      do i=nnt,nct
        if (itype(i).ne.10) then
          inres=i+nres
          do j=1,3    
           d_t_new(j,inres)=d_t_old(j,inres)+d_a_old(j,inres)*d_time_s12
           dc(j,inres)=dc_old(j,inres)+d_t_new(j,inres)*s12_dt
          enddo
        endif      
      enddo 
      return
      end
c---------------------------------------------------------------------
      subroutine tnp1_respa_i_step2
c  Step 2 of the velocity Verlet algorithm: update velocities
      implicit real*8 (a-h,o-z)
      include 'DIMENSIONS'
      include 'COMMON.CONTROL'
      include 'COMMON.VAR'
      include 'COMMON.MD'
      include 'COMMON.CHAIN'
      include 'COMMON.DERIV'
      include 'COMMON.GEO'
      include 'COMMON.LOCAL'
      include 'COMMON.INTERACT'
      include 'COMMON.IOUNITS'
      include 'COMMON.NAMES'

      double precision d_time_s12

      do i=0,2*nres
       do j=1,3
        d_t(j,i)=d_t_new(j,i)
       enddo
      enddo

      call kinetic(EK)
      EK=EK/s12_np**2

      d_time_s12=0.5d0*s12_np*d_time

      do j=1,3
        d_t(j,0)=d_t_new(j,0)+d_a(j,0)*d_time_s12
      enddo
      do i=nnt,nct-1
        do j=1,3
          d_t(j,i)=d_t_new(j,i)+d_a(j,i)*d_time_s12
        enddo
      enddo
      do i=nnt,nct
        if (itype(i).ne.10) then
          inres=i+nres
          do j=1,3
            d_t(j,inres)=d_t_new(j,inres)+d_a(j,inres)*d_time_s12
          enddo
        endif
      enddo 

      pistar=pistar+(EK-0.5*(E_old+potE)
     &       -dimen*Rb*t_bath*log(s12_np)+Csplit-dimen*Rb*t_bath)*d_time
      tmp=1+pistar/(2*Q_np)*0.5*d_time
      s_np=s12_np*tmp**2
      pi_np=pistar/tmp

      return
      end
c-------------------------------------------------------

      subroutine tnp1_step1
c Applying Nose-Poincare algorithm - step 1 to coordinates
c JPSJ 70 75 (2001) S. Nose
c
c d_t is not updated here
c
      implicit real*8 (a-h,o-z)
      include 'DIMENSIONS'
      include 'COMMON.CONTROL'
      include 'COMMON.VAR'
      include 'COMMON.MD'
      include 'COMMON.CHAIN'
      include 'COMMON.DERIV'
      include 'COMMON.GEO'
      include 'COMMON.LOCAL'
      include 'COMMON.INTERACT'
      include 'COMMON.IOUNITS'
      include 'COMMON.NAMES'
      double precision adt,adt2,tmp
        
      tmp=1+pi_np/(2*Q_np)*0.5*d_time
      s12_np=s_np*tmp**2
      pistar=pi_np/tmp
      s12_dt=d_time/s12_np
      d_time_s12=d_time*0.5*s12_np

      do j=1,3
        d_t_new(j,0)=d_t_old(j,0)+d_a_old(j,0)*d_time_s12
        dc(j,0)=dc_old(j,0)+d_t_new(j,0)*s12_dt
      enddo
      do i=nnt,nct-1	
        do j=1,3    
          d_t_new(j,i)=d_t_old(j,i)+d_a_old(j,i)*d_time_s12
          dc(j,i)=dc_old(j,i)+d_t_new(j,i)*s12_dt
        enddo
      enddo
      do i=nnt,nct
        if (itype(i).ne.10) then
          inres=i+nres
          do j=1,3    
           d_t_new(j,inres)=d_t_old(j,inres)+d_a_old(j,inres)*d_time_s12
           dc(j,inres)=dc_old(j,inres)+d_t_new(j,inres)*s12_dt
          enddo
        endif      
      enddo 
      return
      end
c---------------------------------------------------------------------
      subroutine tnp1_step2
c  Step 2 of the velocity Verlet algorithm: update velocities
      implicit real*8 (a-h,o-z)
      include 'DIMENSIONS'
      include 'COMMON.CONTROL'
      include 'COMMON.VAR'
      include 'COMMON.MD'
      include 'COMMON.CHAIN'
      include 'COMMON.DERIV'
      include 'COMMON.GEO'
      include 'COMMON.LOCAL'
      include 'COMMON.INTERACT'
      include 'COMMON.IOUNITS'
      include 'COMMON.NAMES'

      double precision d_time_s12

      do i=0,2*nres
       do j=1,3
        d_t(j,i)=d_t_new(j,i)
       enddo
      enddo

      call kinetic(EK)
      EK=EK/s12_np**2

      d_time_s12=0.5d0*s12_np*d_time

      do j=1,3
        d_t(j,0)=d_t_new(j,0)+d_a(j,0)*d_time_s12
      enddo
      do i=nnt,nct-1
        do j=1,3
          d_t(j,i)=d_t_new(j,i)+d_a(j,i)*d_time_s12
        enddo
      enddo
      do i=nnt,nct
        if (itype(i).ne.10) then
          inres=i+nres
          do j=1,3
            d_t(j,inres)=d_t_new(j,inres)+d_a(j,inres)*d_time_s12
          enddo
        endif
      enddo 

cd      write(iout,*) 'pistar',pistar,EK,E_old,potE,s12_np
      pistar=pistar+(EK-0.5*(E_old+potE)
     &       -dimen*Rb*t_bath*log(s12_np)+H0-dimen*Rb*t_bath)*d_time
      tmp=1+pistar/(2*Q_np)*0.5*d_time
      s_np=s12_np*tmp**2
      pi_np=pistar/tmp

      return
      end

c-----------------------------------------------------------------
      subroutine tnp_respa_i_step1
c Applying Nose-Poincare algorithm - step 1 to coordinates
c J.Comput.Phys. 151 114 (1999) S.D.Bond B.J.Leimkuhler B.B.Laird
c
c d_t is not updated here, it is destroyed
c
      implicit real*8 (a-h,o-z)
      include 'DIMENSIONS'
      include 'COMMON.CONTROL'
      include 'COMMON.VAR'
      include 'COMMON.MD'
      include 'COMMON.CHAIN'
      include 'COMMON.DERIV'
      include 'COMMON.GEO'
      include 'COMMON.LOCAL'
      include 'COMMON.INTERACT'
      include 'COMMON.IOUNITS'
      include 'COMMON.NAMES'
      double precision C_np,d_time_s,tmp,d_time_ss

      d_time_s=d_time*0.5*s_np        
ct2      d_time_s=d_time*0.5*s12_np

      do j=1,3
        d_t_new(j,0)=d_t_old(j,0)+d_a_old(j,0)*d_time_s
      enddo
      do i=nnt,nct-1	
        do j=1,3    
          d_t_new(j,i)=d_t_old(j,i)+d_a_old(j,i)*d_time_s
        enddo
      enddo
      do i=nnt,nct
        if (itype(i).ne.10) then
          inres=i+nres
          do j=1,3    
           d_t_new(j,inres)=d_t_old(j,inres)+d_a_old(j,inres)*d_time_s
          enddo
        endif      
      enddo 

      do i=0,2*nres
       do j=1,3
        d_t(j,i)=d_t_new(j,i)
       enddo
      enddo

      call kinetic(EK)
      EK=EK/s_np**2

      C_np=0.5*d_time*(dimen*Rb*t_bath*(1.0+log(s_np))-EK+potE-Csplit)
     &                     -pi_np

      pistar=-2.0*C_np/(1.0+sqrt(1.0-C_np*d_time/Q_np))
      tmp=0.5*d_time*pistar/Q_np
      s12_np=s_np*(1.0+tmp)/(1.0-tmp)

      d_time_ss=0.5*d_time*(1.0/s12_np+1.0/s_np)
ct2      d_time_ss=d_time/s12_np
c      d_time_ss=0.5*d_time*(1.0/sold_np+1.0/s_np) 

      do j=1,3
        dc(j,0)=dc_old(j,0)+d_t_new(j,0)*d_time_ss
      enddo
      do i=nnt,nct-1	
        do j=1,3    
          dc(j,i)=dc_old(j,i)+d_t_new(j,i)*d_time_ss
        enddo
      enddo
      do i=nnt,nct
        if (itype(i).ne.10) then
          inres=i+nres
          do j=1,3    
           dc(j,inres)=dc_old(j,inres)+d_t_new(j,inres)*d_time_ss
          enddo
        endif      
      enddo 

      return
      end
c---------------------------------------------------------------------

      subroutine tnp_respa_i_step2
c  Step 2 of the velocity Verlet algorithm: update velocities
      implicit real*8 (a-h,o-z)
      include 'DIMENSIONS'
      include 'COMMON.CONTROL'
      include 'COMMON.VAR'
      include 'COMMON.MD'
      include 'COMMON.CHAIN'
      include 'COMMON.DERIV'
      include 'COMMON.GEO'
      include 'COMMON.LOCAL'
      include 'COMMON.INTERACT'
      include 'COMMON.IOUNITS'
      include 'COMMON.NAMES'

      double precision d_time_s

      EK=EK*(s_np/s12_np)**2
      HNose1=Hnose(EK,s12_np,potE,pistar,Q_np,t_bath,dimen)
      pi_np=pistar+0.5*d_time*(2*EK-dimen*Rb*t_bath
     &                              -HNose1+Csplit)         

cr      print '(a,5f)','i_step2',EK,potE,HNose1,pi_np,E_long
      d_time_s=d_time*0.5*s12_np
c      d_time_s=d_time*0.5*s_np

      do j=1,3
        d_t(j,0)=d_t_new(j,0)+d_a(j,0)*d_time_s
      enddo
      do i=nnt,nct-1
        do j=1,3
          d_t(j,i)=d_t_new(j,i)+d_a(j,i)*d_time_s
        enddo
      enddo
      do i=nnt,nct
        if (itype(i).ne.10) then
          inres=i+nres
          do j=1,3
            d_t(j,inres)=d_t_new(j,inres)+d_a(j,inres)*d_time_s
          enddo
        endif
      enddo 

      s_np=s12_np

      return
      end
c-----------------------------------------------------------------
      subroutine tnp_respa_step1
c Applying Nose-Poincare algorithm - step 1 to vel for RESPA
c J.Comput.Phys. 151 114 (1999) S.D.Bond B.J.Leimkuhler B.B.Laird
c
c d_t is not updated here, it is destroyed
c
      implicit real*8 (a-h,o-z)
      include 'DIMENSIONS'
      include 'COMMON.CONTROL'
      include 'COMMON.VAR'
      include 'COMMON.MD'
      include 'COMMON.CHAIN'
      include 'COMMON.DERIV'
      include 'COMMON.GEO'
      include 'COMMON.LOCAL'
      include 'COMMON.INTERACT'
      include 'COMMON.IOUNITS'
      include 'COMMON.NAMES'
      double precision C_np,d_time_s,tmp,d_time_ss
      double precision energia(0:n_ene)

      d_time_s=d_time*0.5*s_np        

      do j=1,3
        d_t_old(j,0)=d_t_old(j,0)+d_a(j,0)*d_time_s
      enddo
      do i=nnt,nct-1	
        do j=1,3    
          d_t_old(j,i)=d_t_old(j,i)+d_a(j,i)*d_time_s
        enddo
      enddo
      do i=nnt,nct
        if (itype(i).ne.10) then
          inres=i+nres
          do j=1,3    
           d_t_old(j,inres)=d_t_old(j,inres)+d_a(j,inres)*d_time_s
          enddo
        endif      
      enddo 


c      C_np=0.5*d_time*(dimen*Rb*t_bath*(1.0+log(s_np))-EK+potE-H0)
c     &                     -pi_np
c
c      pistar=-2.0*C_np/(1.0+sqrt(1.0-C_np*d_time/Q_np))
c      tmp=0.5*d_time*pistar/Q_np
c      s12_np=s_np*(1.0+tmp)/(1.0-tmp)
c      write(iout,*) 'tnp_respa_step1',s_np,s12_np,EK,potE,C_np,pistar,tmp

ct1      pi_np=pistar
c      sold_np=s_np
c      s_np=s12_np

c-------------------------------------
c test of reviewer's comment
       pi_np=pi_np-0.5*d_time*(E_long+Csplit-H0)
cr       print '(a,3f)','1 pi_np,s_np',pi_np,s_np,E_long
c-------------------------------------

      return
      end
c---------------------------------------------------------------------
      subroutine tnp_respa_step2
c  Step 2 of the velocity Verlet algorithm: update velocities for RESPA
      implicit real*8 (a-h,o-z)
      include 'DIMENSIONS'
      include 'COMMON.CONTROL'
      include 'COMMON.VAR'
      include 'COMMON.MD'
      include 'COMMON.CHAIN'
      include 'COMMON.DERIV'
      include 'COMMON.GEO'
      include 'COMMON.LOCAL'
      include 'COMMON.INTERACT'
      include 'COMMON.IOUNITS'
      include 'COMMON.NAMES'

      double precision d_time_s

ct1      s12_np=s_np
ct2      pistar=pi_np

ct      call kinetic(EK)
ct      HNose1=Hnose(EK,s12_np,potE,pistar,Q_np,t_bath,dimen)
ct      pi_np=pistar+0.5*d_time*(2*EK-dimen*Rb*t_bath)
ct     &                              -0.5*d_time*(HNose1-H0)         

c-------------------------------------
c test of reviewer's comment
      pi_np=pi_np-0.5*d_time*(E_long+Csplit-H0)
cr      print '(a,3f)','2 pi_np,s_np',pi_np,s_np,E_long
c-------------------------------------
      d_time_s=d_time*0.5*s_np

      do j=1,3
        d_t_old(j,0)=d_t_old(j,0)+d_a(j,0)*d_time_s
      enddo
      do i=nnt,nct-1
        do j=1,3
          d_t_old(j,i)=d_t_old(j,i)+d_a(j,i)*d_time_s
        enddo
      enddo
      do i=nnt,nct
        if (itype(i).ne.10) then
          inres=i+nres
          do j=1,3
            d_t_old(j,inres)=d_t_old(j,inres)+d_a(j,inres)*d_time_s
          enddo
        endif
      enddo 

cd      s_np=s12_np

      return
      end
c---------------------------------------------------------------------
      subroutine tnp_step1
c Applying Nose-Poincare algorithm - step 1 to coordinates
c J.Comput.Phys. 151 114 (1999) S.D.Bond B.J.Leimkuhler B.B.Laird
c
c d_t is not updated here, it is destroyed
c
      implicit real*8 (a-h,o-z)
      include 'DIMENSIONS'
      include 'COMMON.CONTROL'
      include 'COMMON.VAR'
      include 'COMMON.MD'
      include 'COMMON.CHAIN'
      include 'COMMON.DERIV'
      include 'COMMON.GEO'
      include 'COMMON.LOCAL'
      include 'COMMON.INTERACT'
      include 'COMMON.IOUNITS'
      include 'COMMON.NAMES'
      double precision C_np,d_time_s,tmp,d_time_ss

      d_time_s=d_time*0.5*s_np        

      do j=1,3
        d_t_new(j,0)=d_t_old(j,0)+d_a_old(j,0)*d_time_s
      enddo
      do i=nnt,nct-1	
        do j=1,3    
          d_t_new(j,i)=d_t_old(j,i)+d_a_old(j,i)*d_time_s
        enddo
      enddo
      do i=nnt,nct
        if (itype(i).ne.10) then
          inres=i+nres
          do j=1,3    
           d_t_new(j,inres)=d_t_old(j,inres)+d_a_old(j,inres)*d_time_s
          enddo
        endif      
      enddo 

      do i=0,2*nres
       do j=1,3
        d_t(j,i)=d_t_new(j,i)
       enddo
      enddo

      call kinetic(EK)
      EK=EK/s_np**2

      C_np=0.5*d_time*(dimen*Rb*t_bath*(1.0+log(s_np))-EK+potE-H0)
     &                     -pi_np

      pistar=-2.0*C_np/(1.0+sqrt(1.0-C_np*d_time/Q_np))
      tmp=0.5*d_time*pistar/Q_np
      s12_np=s_np*(1.0+tmp)/(1.0-tmp)
c      write(iout,*) 'tnp_step1',s_np,s12_np,EK,potE,C_np,pistar,tmp

      d_time_ss=0.5*d_time*(1.0/s12_np+1.0/s_np)

      do j=1,3
        dc(j,0)=dc_old(j,0)+d_t_new(j,0)*d_time_ss
      enddo
      do i=nnt,nct-1	
        do j=1,3    
          dc(j,i)=dc_old(j,i)+d_t_new(j,i)*d_time_ss
        enddo
      enddo
      do i=nnt,nct
        if (itype(i).ne.10) then
          inres=i+nres
          do j=1,3    
           dc(j,inres)=dc_old(j,inres)+d_t_new(j,inres)*d_time_ss
          enddo
        endif      
      enddo 

      return
      end
c-----------------------------------------------------------------
      subroutine tnp_step2
c  Step 2 of the velocity Verlet algorithm: update velocities
      implicit real*8 (a-h,o-z)
      include 'DIMENSIONS'
      include 'COMMON.CONTROL'
      include 'COMMON.VAR'
      include 'COMMON.MD'
      include 'COMMON.CHAIN'
      include 'COMMON.DERIV'
      include 'COMMON.GEO'
      include 'COMMON.LOCAL'
      include 'COMMON.INTERACT'
      include 'COMMON.IOUNITS'
      include 'COMMON.NAMES'

      double precision d_time_s

      EK=EK*(s_np/s12_np)**2
      HNose1=Hnose(EK,s12_np,potE,pistar,Q_np,t_bath,dimen)
      pi_np=pistar+0.5*d_time*(2*EK-dimen*Rb*t_bath)
     &                              -0.5*d_time*(HNose1-H0)         

cd      write(iout,'(a,4f)') 'mmm',EK,potE,HNose1,pi_np
      d_time_s=d_time*0.5*s12_np

      do j=1,3
        d_t(j,0)=d_t_new(j,0)+d_a(j,0)*d_time_s
      enddo
      do i=nnt,nct-1
        do j=1,3
          d_t(j,i)=d_t_new(j,i)+d_a(j,i)*d_time_s
        enddo
      enddo
      do i=nnt,nct
        if (itype(i).ne.10) then
          inres=i+nres
          do j=1,3
            d_t(j,inres)=d_t_new(j,inres)+d_a(j,inres)*d_time_s
          enddo
        endif
      enddo 

      s_np=s12_np

      return
      end