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This commit is contained in:
Pierre-Francois Loos 2019-03-20 21:00:05 +01:00
parent ca3a985d50
commit 0405a53fa8
17 changed files with 0 additions and 2706 deletions
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29
src/IntPak/NormCoeff.f90
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@ -1,29 +0,0 @@
function NormCoeff(alpha,a)
implicit none
! Input variables
double precision,intent(in) :: alpha
integer,intent(in) :: a(3)
! local variable
double precision :: pi,dfa(3),dfac
integer :: atot
! Output variable
double precision NormCoeff
pi = 4d0*atan(1d0)
atot = a(1) + a(2) + a(3)
dfa(1) = dfac(2*a(1))/(2d0**a(1)*dfac(a(1)))
dfa(2) = dfac(2*a(2))/(2d0**a(2)*dfac(a(2)))
dfa(3) = dfac(2*a(3))/(2d0**a(3)*dfac(a(3)))
NormCoeff = (2d0*alpha/pi)**(3d0/2d0)*(4d0*alpha)**atot
NormCoeff = NormCoeff/(dfa(1)*dfa(2)*dfa(3))
NormCoeff = sqrt(NormCoeff)
end function NormCoeff

170
src/IntPak/elements.f90
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@ -1,170 +0,0 @@
function element_number(element_name)
implicit none
integer,parameter :: nelement_max = 103
character(len=2),intent(in) :: element_name
integer :: element_number
character(len=2),parameter :: element_list(nelement_max) = &
(/' H', 'He', & ! 2
'Li','Be', ' B',' C',' N',' O',' F','Ne', & ! 10
'Na','Mg', 'Al','Si',' P',' S','Cl','Ar', & ! 18
' K','Ca','Sc','Ti',' V','Cr','Mn','Fe','Co','Ni','Cu','Zn','Ga','Ge','As','Se','Br','Kr', & ! 36
'Rb','Sr',' Y','Zr','Nb','Mo','Tc','Ru','Rh','Pd','Ag','Cd','In','Sn','Sb','Te',' I','Xe', & ! 54
'Cs','Ba', & ! 56
'La','Ce','Pr','Nd','Pm','Sm','Eu','Gd','Tb','Dy','Ho','Er','Tm','Yb', & ! 70
'Lu','Hf','Ta',' W','Re','Os','Ir','Pt','Au','Hg','Tl','Pb','Bi','Po','At','Rn', & ! 86
'Fr','Ra', & ! 88
'Ac','Th','Pa',' U','Np','Pu','Am','Cm','Bk','Cf','Es','Fm','Md','No', & ! 102
'Lr' & ! 103
/)
!=====
integer :: ielement
!=====
ielement=1
do while( ADJUSTL(element_name) /= ADJUSTL(element_list(ielement)) )
if( ielement == nelement_max ) then
write(*,'(a,a)') ' Input symbol ',element_name
write(*,'(a,i3,a)') ' Element symbol is not one of first ',nelement_max,' elements'
write(*,*) '!!! element symbol not understood !!!'
stop
endif
ielement = ielement + 1
enddo
element_number = ielement
end function element_number
function element_core(zval,zatom)
implicit none
double precision,intent(in) :: zval
double precision,intent(in) :: zatom
integer :: element_core
!=====
!
! If zval /= zatom, this is certainly an effective core potential
! and no core states should be frozen.
if( ABS(zval - zatom) > 1d0-3 ) then
element_core = 0
else
if( zval <= 4.00001d0 ) then ! up to Be
element_core = 0
else if( zval <= 12.00001d0 ) then ! up to Mg
element_core = 1
else if( zval <= 30.00001d0 ) then ! up to Ca
element_core = 5
else if( zval <= 48.00001d0 ) then ! up to Sr
element_core = 9
else
write(*,*) '!!! not imlemented in element_core !!!'
stop
endif
endif
end function element_core
function element_covalent_radius(zatom)
! Return covalent radius of an atom
implicit none
include 'parameters.h'
integer,intent(in) :: zatom
double precision :: element_covalent_radius
!
! Data from Cambridge Structural Database
! http://en.wikipedia.org/wiki/Covalent_radius
!
! Values are first given in picometer
! They will be converted in bohr later on
select case(zatom)
case( 1)
element_covalent_radius = 31.
case( 2)
element_covalent_radius = 28.
case( 3)
element_covalent_radius = 128.
case( 4)
element_covalent_radius = 96.
case( 5)
element_covalent_radius = 84.
case( 6)
element_covalent_radius = 73.
case( 7)
element_covalent_radius = 71.
case( 8)
element_covalent_radius = 66.
case( 9)
element_covalent_radius = 57.
case(10) ! Ne.
element_covalent_radius = 58.
case(11)
element_covalent_radius = 166.
case(12)
element_covalent_radius = 141.
case(13)
element_covalent_radius = 121.
case(14)
element_covalent_radius = 111.
case(15)
element_covalent_radius = 107.
case(16)
element_covalent_radius = 105.
case(17)
element_covalent_radius = 102.
case(18) ! Ar.
element_covalent_radius = 106.
case(19)
element_covalent_radius = 203.
case(20)
element_covalent_radius = 176.
case(21)
element_covalent_radius = 170.
case(22)
element_covalent_radius = 160.
case(23)
element_covalent_radius = 153.
case(24)
element_covalent_radius = 139.
case(25)
element_covalent_radius = 145.
case(26)
element_covalent_radius = 145.
case(27)
element_covalent_radius = 140.
case(28)
element_covalent_radius = 124.
case(29)
element_covalent_radius = 132.
case(30)
element_covalent_radius = 122.
case(31)
element_covalent_radius = 120.
case(32)
element_covalent_radius = 119.
case(34)
element_covalent_radius = 120.
case(35)
element_covalent_radius = 120.
case(36) ! Kr.
element_covalent_radius = 116.
case default
write(*,*) '!!! covalent radius not available !!!'
stop
end select
! pm to bohr conversion
element_covalent_radius = element_covalent_radius*pmtoau
end function element_covalent_radius

176
src/IntPak/read_auxiliary_basis.f90
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@ -1,176 +0,0 @@
subroutine read_auxiliary_basis(NAtoms,XYZAtoms,nShell,CenterShell, &
TotAngMomShell,KShell,DShell,ExpShell)
! Read auxiliary basis set information
implicit none
include 'parameters.h'
! Input variables
integer,intent(in) :: NAtoms
double precision,intent(in) :: XYZAtoms(NAtoms,3)
! Local variables
integer :: nShAt,iAt
integer :: i,j,k
character :: shelltype
! Output variables
integer,intent(out) :: nShell
double precision,intent(out) :: CenterShell(maxShell,3)
integer,intent(out) :: TotAngMomShell(maxShell),KShell(maxShell)
double precision,intent(out) :: DShell(maxShell,maxK),ExpShell(maxShell,maxK)
!------------------------------------------------------------------------
! Primary basis set information
!------------------------------------------------------------------------
! Open file with basis set specification
open(unit=2,file='input/basis')
! Read basis information
write(*,'(A28)') 'Gaussian basis set'
write(*,'(A28)') '------------------'
nShell = 0
do i=1,NAtoms
read(2,*) iAt,nShAt
write(*,'(A28,1X,I16)') 'Atom n. ',iAt
write(*,'(A28,1X,I16)') 'number of shells ',nShAt
write(*,'(A28)') '------------------'
! Basis function centers
do j=1,nShAt
nShell = nShell + 1
do k=1,3
CenterShell(nShell,k) = XYZAtoms(iAt,k)
enddo
! Shell type and contraction degree
read(2,*) shelltype,KShell(nShell)
if(shelltype == "S") then
TotAngMomShell(nShell) = 0
write(*,'(A28,1X,I16)') 's-type shell with K = ',KShell(nShell)
elseif(shelltype == "P") then
TotAngMomShell(nShell) = 1
write(*,'(A28,1X,I16)') 'p-type shell with K = ',KShell(nShell)
elseif(shelltype == "D") then
TotAngMomShell(nShell) = 2
write(*,'(A28,1X,I16)') 'd-type shell with K = ',KShell(nShell)
elseif(shelltype == "F") then
TotAngMomShell(nShell) = 3
write(*,'(A28,1X,I16)') 'f-type shell with K = ',KShell(nShell)
elseif(shelltype == "G") then
TotAngMomShell(nShell) = 4
write(*,'(A28,1X,I16)') 'g-type shell with K = ',KShell(nShell)
elseif(shelltype == "H") then
TotAngMomShell(nShell) = 5
write(*,'(A28,1X,I16)') 'h-type shell with K = ',KShell(nShell)
elseif(shelltype == "I") then
TotAngMomShell(nShell) = 6
write(*,'(A28,1X,I16)') 'i-type shell with K = ',KShell(nShell)
endif
! Read exponents and contraction coefficients
write(*,'(A28,1X,A16,A16)') '','Exponents','Contraction'
do k=1,Kshell(nShell)
read(2,*) ExpShell(nShell,k),DShell(nShell,k)
write(*,'(A28,1X,F16.10,F16.10)') '',ExpShell(nShell,k),DShell(nShell,k)
enddo
enddo
write(*,'(A28)') '------------------'
enddo
! Total number of shells
write(*,'(A28,1X,I16)') 'Number of shells in OBS',nShell
write(*,'(A28)') '------------------'
write(*,*)
! Close file with basis set specification
close(unit=2)
!------------------------------------------------------------------------
! Auxiliary basis set information
!------------------------------------------------------------------------
! Open file with auxilairy basis specification
open(unit=3,file='input/auxbasis')
! Read basis information
write(*,'(A28)') 'Auxiliary basis set'
write(*,'(A28)') '-------------------'
do i=1,NAtoms
read(3,*) iAt,nShAt
write(*,'(A28,1X,I16)') 'Atom n. ',iAt
write(*,'(A28,1X,I16)') 'number of shells ',nShAt
write(*,'(A28)') '------------------'
! Basis function centers
do j=1,nShAt
nShell = nShell + 1
do k=1,3
CenterShell(nShell,k) = XYZAtoms(iAt,k)
enddo
! Shell type and contraction degree
read(3,*) shelltype,KShell(nShell)
if(shelltype == "S") then
TotAngMomShell(nShell) = 0
write(*,'(A28,1X,I16)') 's-type shell with K = ',KShell(nShell)
elseif(shelltype == "P") then
TotAngMomShell(nShell) = 1
write(*,'(A28,1X,I16)') 'p-type shell with K = ',KShell(nShell)
elseif(shelltype == "D") then
TotAngMomShell(nShell) = 2
write(*,'(A28,1X,I16)') 'd-type shell with K = ',KShell(nShell)
elseif(shelltype == "F") then
TotAngMomShell(nShell) = 3
write(*,'(A28,1X,I16)') 'f-type shell with K = ',KShell(nShell)
elseif(shelltype == "G") then
TotAngMomShell(nShell) = 4
write(*,'(A28,1X,I16)') 'g-type shell with K = ',KShell(nShell)
elseif(shelltype == "H") then
TotAngMomShell(nShell) = 5
write(*,'(A28,1X,I16)') 'h-type shell with K = ',KShell(nShell)
elseif(shelltype == "I") then
TotAngMomShell(nShell) = 6
write(*,'(A28,1X,I16)') 'i-type shell with K = ',KShell(nShell)
endif
! Read exponents and contraction coefficients
write(*,'(A28,1X,A16,A16)') '','Exponents','Contraction'
do k=1,Kshell(nShell)
read(3,*) ExpShell(nShell,k),DShell(nShell,k)
write(*,'(A28,1X,F16.10,F16.10)') '',ExpShell(nShell,k),DShell(nShell,k)
enddo
enddo
write(*,'(A28)') '------------------'
enddo
! Total number of shells
write(*,'(A28,1X,I16)') 'Number of shells in ABS',nShell
write(*,'(A28)') '------------------'
write(*,*)
! Close file with basis set specification
close(unit=3)
end subroutine read_auxiliary_basis

118
src/IntPak/read_basis.f90
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@ -1,118 +0,0 @@
subroutine read_basis(nNuc,rNuc,nBas,nO,nV,nShell,TotAngMomShell,CenterShell,KShell,DShell,ExpShell)
! Read basis set information
implicit none
include 'parameters.h'
! Input variables
integer,intent(in) :: nNuc,nO
double precision,intent(in) :: rNuc(nNuc,ncart)
! Local variables
integer :: nShAt,iNuc,iShell
integer :: i,j,k
character :: shelltype
! Output variables
integer,intent(out) :: nShell,nBas
double precision,intent(out) :: CenterShell(maxShell,ncart)
integer,intent(out) :: TotAngMomShell(maxShell),KShell(maxShell)
double precision,intent(out) :: DShell(maxShell,maxK),ExpShell(maxShell,maxK)
integer,intent(out) :: nV
!------------------------------------------------------------------------
! Primary basis set information
!------------------------------------------------------------------------
! Open file with basis set specification
open(unit=2,file='input/basis')
! Read basis information
write(*,'(A28)') 'Gaussian basis set'
write(*,'(A28)') '------------------'
nShell = 0
do i=1,nNuc
read(2,*) iNuc,nShAt
write(*,'(A28,1X,I16)') 'Atom n. ',iNuc
write(*,'(A28,1X,I16)') 'number of shells ',nShAt
write(*,'(A28)') '------------------'
! Basis function centers
do j=1,nShAt
nShell = nShell + 1
do k=1,ncart
CenterShell(nShell,k) = rNuc(iNuc,k)
enddo
! Shell type and contraction degree
read(2,*) shelltype,KShell(nShell)
if(shelltype == "S") then
TotAngMomShell(nShell) = 0
write(*,'(A28,1X,I16)') 's-type shell with K = ',KShell(nShell)
elseif(shelltype == "P") then
TotAngMomShell(nShell) = 1
write(*,'(A28,1X,I16)') 'p-type shell with K = ',KShell(nShell)
elseif(shelltype == "D") then
TotAngMomShell(nShell) = 2
write(*,'(A28,1X,I16)') 'd-type shell with K = ',KShell(nShell)
elseif(shelltype == "F") then
TotAngMomShell(nShell) = 3
write(*,'(A28,1X,I16)') 'f-type shell with K = ',KShell(nShell)
elseif(shelltype == "G") then
TotAngMomShell(nShell) = 4
write(*,'(A28,1X,I16)') 'g-type shell with K = ',KShell(nShell)
elseif(shelltype == "H") then
TotAngMomShell(nShell) = 5
write(*,'(A28,1X,I16)') 'h-type shell with K = ',KShell(nShell)
elseif(shelltype == "I") then
TotAngMomShell(nShell) = 6
write(*,'(A28,1X,I16)') 'i-type shell with K = ',KShell(nShell)
endif
! Read exponents and contraction coefficients
write(*,'(A28,1X,A16,A16)') '','Exponents','Contraction'
do k=1,Kshell(nShell)
read(2,*) ExpShell(nShell,k),DShell(nShell,k)
write(*,'(A28,1X,F16.10,F16.10)') '',ExpShell(nShell,k),DShell(nShell,k)
enddo
enddo
write(*,'(A28)') '------------------'
enddo
! Total number of shells
write(*,'(A28,1X,I16)') 'Number of shells',nShell
write(*,'(A28)') '------------------'
write(*,*)
! Close file with basis set specification
close(unit=2)
! Calculate number of basis functions
nBas = 0
do iShell=1,nShell
nBas = nBas + (TotAngMomShell(iShell)*TotAngMomShell(iShell) + 3*TotAngMomShell(iShell) + 2)/2
enddo
write(*,'(A28)') '------------------'
write(*,'(A28,1X,I16)') 'Number of basis functions',NBas
write(*,'(A28)') '------------------'
write(*,*)
! Number of virtual orbitals
nV = nBas - nO
end subroutine read_basis

68
src/IntPak/read_geometry.f90
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@ -1,68 +0,0 @@
subroutine read_geometry(nAt,ZNuc,rA,ENuc)
! Read molecular geometry
implicit none
include 'parameters.h'
! Ouput variables
integer,intent(in) :: nAt
! Local variables
integer :: i,j
double precision :: RAB
character(len=2) :: El
integer,external :: element_number
! Ouput variables
double precision,intent(out) :: ZNuc(NAt),rA(nAt,ncart),ENuc
! Open file with geometry specification
open(unit=1,file='input/molecule')
! Read geometry
read(1,*)
read(1,*)
read(1,*)
do i=1,nAt
read(1,*) El,rA(i,1),rA(i,2),rA(i,3)
ZNuc(i) = element_number(El)
enddo
! Compute nuclear repulsion energy
ENuc = 0
do i=1,nAt-1
do j=i+1,nAt
RAB = (rA(i,1)-rA(j,1))**2 + (rA(i,2)-rA(j,2))**2 + (rA(i,3)-rA(j,3))**2
ENuc = ENuc + ZNuc(i)*ZNuc(j)/sqrt(RAB)
enddo
enddo
! Close file with geometry specification
close(unit=1)
! Print geometry
write(*,'(A28)') '------------------'
write(*,'(A28)') 'Molecular geometry'
write(*,'(A28)') '------------------'
do i=1,NAt
write(*,'(A28,1X,I16)') 'Atom n. ',i
write(*,'(A28,1X,F16.10)') 'Z = ',ZNuc(i)
write(*,'(A28,1X,F16.10,F16.10,F16.10)') 'Atom coordinates:',(rA(i,j),j=1,ncart)
enddo
write(*,*)
write(*,'(A28)') '------------------'
write(*,'(A28,1X,F16.10)') 'Nuclear repulsion energy = ',ENuc
write(*,'(A28)') '------------------'
write(*,*)
end subroutine read_geometry

39
src/IntPak/read_molecule.f90
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@ -1,39 +0,0 @@
subroutine read_molecule(nAt,nEl,nO,nC,nR)
! Read number of atoms nAt and number of electrons nEl
implicit none
include 'parameters.h'
! Input variables
integer,intent(out) :: nAt,nEl,nO,nC,nR
! Open file with geometry specification
open(unit=1,file='input/molecule')
! Read number of atoms and number of electrons
read(1,*)
read(1,*) nAt,nEl,nC,nR
nO = nEl/2
! Print results
write(*,'(A28)') '----------------------'
write(*,'(A28,1X,I16)') 'Number of atoms',nAt
write(*,'(A28)') '----------------------'
write(*,*)
write(*,'(A28)') '----------------------'
write(*,'(A28,1X,I16)') 'Number of electrons',nEl
write(*,'(A28)') '----------------------'
write(*,*)
! Close file with geometry specification
close(unit=1)
end subroutine read_molecule

385
src/IntPak/utils.f90
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@ -1,385 +0,0 @@
!------------------------------------------------------------------------
function KroneckerDelta(i,j) result(delta)
! Kronecker Delta
implicit none
! Input variables
integer,intent(in) :: i,j
! Output variables
integer :: delta
if(i == j) then
delta = 1
else
delta = 0
endif
end function KroneckerDelta
!------------------------------------------------------------------------
subroutine matout(m,n,A)
! Print the MxN array A
implicit none
integer,parameter :: ncol = 5
double precision,parameter :: small = 1d-10
integer,intent(in) :: m,n
double precision,intent(in) :: A(m,n)
double precision :: B(ncol)
integer :: ilower,iupper,num,i,j
do ilower=1,n,ncol
iupper = min(ilower + ncol - 1,n)
num = iupper - ilower + 1
write(*,'(3X,10(7X,I6))') (j,j=ilower,iupper)
do i=1,m
do j=ilower,iupper
B(j-ilower+1) = A(i,j)
enddo
do j=1,num
if(abs(B(j)) < small) B(j) = 0d0
enddo
write(*,'(I7,10F15.8)') i,(B(j),j=1,num)
enddo
enddo
end subroutine matout
!------------------------------------------------------------------------
subroutine CalcTrAB(n,A,B,Tr)
! Calculate the trace of the square matrix A.B
implicit none
! Input variables
integer,intent(in) :: n
double precision,intent(in) :: A(n,n),B(n,n)
! Local variables
integer :: i,j
! Output variables
double precision,intent(out) :: Tr
Tr = 0d0
do i=1,n
do j=1,n
Tr = Tr + A(i,j)*B(j,i)
enddo
enddo
end subroutine CalcTrAB
!------------------------------------------------------------------------
function EpsilonSwitch(i,j) result(delta)
! Epsilon function
implicit none
! Input variables
integer,intent(in) :: i,j
integer :: delta
if(i <= j) then
delta = 1
else
delta = -1
endif
end function EpsilonSwitch
!------------------------------------------------------------------------
function KappaCross(i,j,k) result(kappa)
! kappa(i,j,k) = eps(i,j) delta(i,k) - eps(k,i) delta(i,j)
implicit none
! Input variables
integer,intent(in) :: i,j,k
! Local variables
integer :: EpsilonSwitch,KroneckerDelta
double precision :: kappa
kappa = dble(EpsilonSwitch(i,j)*KroneckerDelta(i,k) - EpsilonSwitch(k,i)*KroneckerDelta(i,j))
end function KappaCross
!------------------------------------------------------------------------
subroutine CalcInv3(a,det)
! Calculate the inverse and the determinant of a 3x3 matrix
implicit none
double precision,intent(inout) :: a(3,3)
double precision, intent(inout) :: det
double precision :: b(3,3)
integer :: i,j
det = a(1,1)*(a(2,2)*a(3,3)-a(2,3)*a(3,2)) &
- a(1,2)*(a(2,1)*a(3,3)-a(2,3)*a(3,1)) &
+ a(1,3)*(a(2,1)*a(3,2)-a(2,2)*a(3,1))
do i=1,3
b(i,1) = a(i,1)
b(i,2) = a(i,2)
b(i,3) = a(i,3)
enddo
a(1,1) = b(2,2)*b(3,3) - b(2,3)*b(3,2)
a(2,1) = b(2,3)*b(3,1) - b(2,1)*b(3,3)
a(3,1) = b(2,1)*b(3,2) - b(2,2)*b(3,1)
a(1,2) = b(1,3)*b(3,2) - b(1,2)*b(3,3)
a(2,2) = b(1,1)*b(3,3) - b(1,3)*b(3,1)
a(3,2) = b(1,2)*b(3,1) - b(1,1)*b(3,2)
a(1,3) = b(1,2)*b(2,3) - b(1,3)*b(2,2)
a(2,3) = b(1,3)*b(2,1) - b(1,1)*b(2,3)
a(3,3) = b(1,1)*b(2,2) - b(1,2)*b(2,1)
do i=1,3
do j=1,3
a(i,j) = a(i,j)/det
enddo
enddo
end subroutine CalcInv3
!------------------------------------------------------------------------
subroutine CalcInv4(a,det)
implicit none
double precision,intent(inout) :: a(4,4)
double precision,intent(inout) :: det
double precision :: b(4,4)
integer :: i,j
det = a(1,1)*(a(2,2)*(a(3,3)*a(4,4)-a(3,4)*a(4,3)) &
-a(2,3)*(a(3,2)*a(4,4)-a(3,4)*a(4,2)) &
+a(2,4)*(a(3,2)*a(4,3)-a(3,3)*a(4,2))) &
- a(1,2)*(a(2,1)*(a(3,3)*a(4,4)-a(3,4)*a(4,3)) &
-a(2,3)*(a(3,1)*a(4,4)-a(3,4)*a(4,1)) &
+a(2,4)*(a(3,1)*a(4,3)-a(3,3)*a(4,1))) &
+ a(1,3)*(a(2,1)*(a(3,2)*a(4,4)-a(3,4)*a(4,2)) &
-a(2,2)*(a(3,1)*a(4,4)-a(3,4)*a(4,1)) &
+a(2,4)*(a(3,1)*a(4,2)-a(3,2)*a(4,1))) &
- a(1,4)*(a(2,1)*(a(3,2)*a(4,3)-a(3,3)*a(4,2)) &
-a(2,2)*(a(3,1)*a(4,3)-a(3,3)*a(4,1)) &
+a(2,3)*(a(3,1)*a(4,2)-a(3,2)*a(4,1)))
do i=1,4
b(1,i) = a(1,i)
b(2,i) = a(2,i)
b(3,i) = a(3,i)
b(4,i) = a(4,i)
enddo
a(1,1) = b(2,2)*(b(3,3)*b(4,4)-b(3,4)*b(4,3))-b(2,3)*(b(3,2)*b(4,4)-b(3,4)*b(4,2))+b(2,4)*(b(3,2)*b(4,3)-b(3,3)*b(4,2))
a(2,1) = -b(2,1)*(b(3,3)*b(4,4)-b(3,4)*b(4,3))+b(2,3)*(b(3,1)*b(4,4)-b(3,4)*b(4,1))-b(2,4)*(b(3,1)*b(4,3)-b(3,3)*b(4,1))
a(3,1) = b(2,1)*(b(3,2)*b(4,4)-b(3,4)*b(4,2))-b(2,2)*(b(3,1)*b(4,4)-b(3,4)*b(4,1))+b(2,4)*(b(3,1)*b(4,2)-b(3,2)*b(4,1))
a(4,1) = -b(2,1)*(b(3,2)*b(4,3)-b(3,3)*b(4,2))+b(2,2)*(b(3,1)*b(4,3)-b(3,3)*b(4,1))-b(2,3)*(b(3,1)*b(4,2)-b(3,2)*b(4,1))
a(1,2) = -b(1,2)*(b(3,3)*b(4,4)-b(3,4)*b(4,3))+b(1,3)*(b(3,2)*b(4,4)-b(3,4)*b(4,2))-b(1,4)*(b(3,2)*b(4,3)-b(3,3)*b(4,2))
a(2,2) = b(1,1)*(b(3,3)*b(4,4)-b(3,4)*b(4,3))-b(1,3)*(b(3,1)*b(4,4)-b(3,4)*b(4,1))+b(1,4)*(b(3,1)*b(4,3)-b(3,3)*b(4,1))
a(3,2) = -b(1,1)*(b(3,2)*b(4,4)-b(3,4)*b(4,2))+b(1,2)*(b(3,1)*b(4,4)-b(3,4)*b(4,1))-b(1,4)*(b(3,1)*b(4,2)-b(3,2)*b(4,1))
a(4,2) = b(1,1)*(b(3,2)*b(4,3)-b(3,3)*b(4,2))-b(1,2)*(b(3,1)*b(4,3)-b(3,3)*b(4,1))+b(1,3)*(b(3,1)*b(4,2)-b(3,2)*b(4,1))
a(1,3) = b(1,2)*(b(2,3)*b(4,4)-b(2,4)*b(4,3))-b(1,3)*(b(2,2)*b(4,4)-b(2,4)*b(4,2))+b(1,4)*(b(2,2)*b(4,3)-b(2,3)*b(4,2))
a(2,3) = -b(1,1)*(b(2,3)*b(4,4)-b(2,4)*b(4,3))+b(1,3)*(b(2,1)*b(4,4)-b(2,4)*b(4,1))-b(1,4)*(b(2,1)*b(4,3)-b(2,3)*b(4,1))
a(3,3) = b(1,1)*(b(2,2)*b(4,4)-b(2,4)*b(4,2))-b(1,2)*(b(2,1)*b(4,4)-b(2,4)*b(4,1))+b(1,4)*(b(2,1)*b(4,2)-b(2,2)*b(4,1))
a(4,3) = -b(1,1)*(b(2,2)*b(4,3)-b(2,3)*b(4,2))+b(1,2)*(b(2,1)*b(4,3)-b(2,3)*b(4,1))-b(1,3)*(b(2,1)*b(4,2)-b(2,2)*b(4,1))
a(1,4) = -b(1,2)*(b(2,3)*b(3,4)-b(2,4)*b(3,3))+b(1,3)*(b(2,2)*b(3,4)-b(2,4)*b(3,2))-b(1,4)*(b(2,2)*b(3,3)-b(2,3)*b(3,2))
a(2,4) = b(1,1)*(b(2,3)*b(3,4)-b(2,4)*b(3,3))-b(1,3)*(b(2,1)*b(3,4)-b(2,4)*b(3,1))+b(1,4)*(b(2,1)*b(3,3)-b(2,3)*b(3,1))
a(3,4) = -b(1,1)*(b(2,2)*b(3,4)-b(2,4)*b(3,2))+b(1,2)*(b(2,1)*b(3,4)-b(2,4)*b(3,1))-b(1,4)*(b(2,1)*b(3,2)-b(2,2)*b(3,1))
a(4,4) = b(1,1)*(b(2,2)*b(3,3)-b(2,3)*b(3,2))-b(1,2)*(b(2,1)*b(3,3)-b(2,3)*b(3,1))+b(1,3)*(b(2,1)*b(3,2)-b(2,2)*b(3,1))
do i=1,4
do j=1,4
a(i,j) = a(i,j)/det
enddo
enddo
end subroutine CalcInv4
!double precision function binom(i,j)
! implicit none
! integer,intent(in) :: i,j
! double precision :: logfact
! integer, save :: ifirst
! double precision, save :: memo(0:15,0:15)
! integer :: k,l
! if (ifirst == 0) then
! ifirst = 1
! do k=0,15
! do l=0,15
! memo(k,l) = dexp( logfact(k)-logfact(l)-logfact(k-l) )
! enddo
! enddo
! endif
! if ( (i<=15).and.(j<=15) ) then
! binom = memo(i,j)
! else
! binom = dexp( logfact(i)-logfact(j)-logfact(i-j) )
! endif
!end
!
!double precision function fact(n)
! implicit none
! integer :: n
! double precision, save :: memo(1:100)
! integer, save :: memomax = 1
!
! if (n<=memomax) then
! if (n<2) then
! fact = 1.d0
! else
! fact = memo(n)
! endif
! return
! endif
!
! integer :: i
! memo(1) = 1.d0
! do i=memomax+1,min(n,100)
! memo(i) = memo(i-1)*dble(i)
! enddo
! memomax = min(n,100)
! double precision :: logfact
! fact = dexp(logfact(n))
!end function
!
!double precision function logfact(n)
! implicit none
! integer :: n
! double precision, save :: memo(1:100)
! integer, save :: memomax = 1
!
! if (n<=memomax) then
! if (n<2) then
! logfact = 0.d0
! else
! logfact = memo(n)
! endif
! return
! endif
!
! integer :: i
! memo(1) = 0.d0
! do i=memomax+1,min(n,100)
! memo(i) = memo(i-1)+dlog(dble(i))
! enddo
! memomax = min(n,100)
! logfact = memo(memomax)
! do i=101,n
! logfact += dlog(dble(i))
! enddo
!end function
!
!double precision function dble_fact(n)
! implicit none
! integer :: n
! double precision :: dble_fact_even, dble_fact_odd
!
! dble_fact = 1.d0
!
! if(n.lt.0) return
!
! if(iand(n,1).eq.0)then
! dble_fact = dble_fact_even(n)
! else
! dble_fact= dble_fact_odd(n)
! endif
!
!end function
!
!double precision function dble_fact_even(n) result(fact2)
! implicit none
! integer :: n,k
! double precision, save :: memo(0:100)
! integer, save :: memomax = 0
! double precision :: prod
!
!
! if (n <= memomax) then
! if (n < 2) then
! fact2 = 1.d0
! else
! fact2 = memo(n)
! endif
! return
! endif
!
! integer :: i
! memo(0)=1.d0
! memo(1)=1.d0
! do i=memomax+2,min(n,100),2
! memo(i) = memo(i-2)* dble(i)
! enddo
! memomax = min(n,100)
! fact2 = memo(memomax)
!
! if (n > 100) then
! double precision :: dble_logfact
! fact2 = dexp(dble_logfact(n))
! endif
!
!end function
!
!double precision function dble_fact_odd(n) result(fact2)
! implicit none
! integer :: n
! double precision, save :: memo(1:100)
! integer, save :: memomax = 1
!
! if (n<=memomax) then
! if (n<3) then
! fact2 = 1.d0
! else
! fact2 = memo(n)
! endif
! return
! endif
!
! integer :: i
! memo(1) = 1.d0
! do i=memomax+2,min(n,99),2
! memo(i) = memo(i-2)* dble(i)
! enddo
! memomax = min(n,99)
! fact2 = memo(memomax)
!
! if (n > 99) then
! double precision :: dble_logfact
! fact2 = dexp(dble_logfact(n))
! endif
!
!end function

29
src/QuAcK/NormCoeff.f90
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@ -1,29 +0,0 @@
function NormCoeff(alpha,a)
implicit none
! Input variables
double precision,intent(in) :: alpha
integer,intent(in) :: a(3)
! local variable
double precision :: pi,dfa(3),dfac
integer :: atot
! Output variable
double precision NormCoeff
pi = 4d0*atan(1d0)
atot = a(1) + a(2) + a(3)
dfa(1) = dfac(2*a(1))/(2d0**a(1)*dfac(a(1)))
dfa(2) = dfac(2*a(2))/(2d0**a(2)*dfac(a(2)))
dfa(3) = dfac(2*a(3))/(2d0**a(3)*dfac(a(3)))
NormCoeff = (2d0*alpha/pi)**(3d0/2d0)*(4d0*alpha)**atot
NormCoeff = NormCoeff/(dfa(1)*dfa(2)*dfa(3))
NormCoeff = sqrt(NormCoeff)
end function NormCoeff

170
src/QuAcK/elements.f90
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@ -1,170 +0,0 @@
function element_number(element_name)
implicit none
integer,parameter :: nelement_max = 103
character(len=2),intent(in) :: element_name
integer :: element_number
character(len=2),parameter :: element_list(nelement_max) = &
(/' H', 'He', & ! 2
'Li','Be', ' B',' C',' N',' O',' F','Ne', & ! 10
'Na','Mg', 'Al','Si',' P',' S','Cl','Ar', & ! 18
' K','Ca','Sc','Ti',' V','Cr','Mn','Fe','Co','Ni','Cu','Zn','Ga','Ge','As','Se','Br','Kr', & ! 36
'Rb','Sr',' Y','Zr','Nb','Mo','Tc','Ru','Rh','Pd','Ag','Cd','In','Sn','Sb','Te',' I','Xe', & ! 54
'Cs','Ba', & ! 56
'La','Ce','Pr','Nd','Pm','Sm','Eu','Gd','Tb','Dy','Ho','Er','Tm','Yb', & ! 70
'Lu','Hf','Ta',' W','Re','Os','Ir','Pt','Au','Hg','Tl','Pb','Bi','Po','At','Rn', & ! 86
'Fr','Ra', & ! 88
'Ac','Th','Pa',' U','Np','Pu','Am','Cm','Bk','Cf','Es','Fm','Md','No', & ! 102
'Lr' & ! 103
/)
!=====
integer :: ielement
!=====
ielement=1
do while( ADJUSTL(element_name) /= ADJUSTL(element_list(ielement)) )
if( ielement == nelement_max ) then
write(*,'(a,a)') ' Input symbol ',element_name
write(*,'(a,i3,a)') ' Element symbol is not one of first ',nelement_max,' elements'
write(*,*) '!!! element symbol not understood !!!'
stop
endif
ielement = ielement + 1
enddo
element_number = ielement
end function element_number
function element_core(zval,zatom)
implicit none
double precision,intent(in) :: zval
double precision,intent(in) :: zatom
integer :: element_core
!=====
!
! If zval /= zatom, this is certainly an effective core potential
! and no core states should be frozen.
if( ABS(zval - zatom) > 1d0-3 ) then
element_core = 0
else
if( zval <= 4.00001d0 ) then ! up to Be
element_core = 0
else if( zval <= 12.00001d0 ) then ! up to Mg
element_core = 1
else if( zval <= 30.00001d0 ) then ! up to Ca
element_core = 5
else if( zval <= 48.00001d0 ) then ! up to Sr
element_core = 9
else
write(*,*) '!!! not imlemented in element_core !!!'
stop
endif
endif
end function element_core
function element_covalent_radius(zatom)
! Return covalent radius of an atom
implicit none
include 'parameters.h'
integer,intent(in) :: zatom
double precision :: element_covalent_radius
!
! Data from Cambridge Structural Database
! http://en.wikipedia.org/wiki/Covalent_radius
!
! Values are first given in picometer
! They will be converted in bohr later on
select case(zatom)
case( 1)
element_covalent_radius = 31.
case( 2)
element_covalent_radius = 28.
case( 3)
element_covalent_radius = 128.
case( 4)
element_covalent_radius = 96.
case( 5)
element_covalent_radius = 84.
case( 6)
element_covalent_radius = 73.
case( 7)
element_covalent_radius = 71.
case( 8)
element_covalent_radius = 66.
case( 9)
element_covalent_radius = 57.
case(10) ! Ne.
element_covalent_radius = 58.
case(11)
element_covalent_radius = 166.
case(12)
element_covalent_radius = 141.
case(13)
element_covalent_radius = 121.
case(14)
element_covalent_radius = 111.
case(15)
element_covalent_radius = 107.
case(16)
element_covalent_radius = 105.
case(17)
element_covalent_radius = 102.
case(18) ! Ar.
element_covalent_radius = 106.
case(19)
element_covalent_radius = 203.
case(20)
element_covalent_radius = 176.
case(21)
element_covalent_radius = 170.
case(22)
element_covalent_radius = 160.
case(23)
element_covalent_radius = 153.
case(24)
element_covalent_radius = 139.
case(25)
element_covalent_radius = 145.
case(26)
element_covalent_radius = 145.
case(27)
element_covalent_radius = 140.
case(28)
element_covalent_radius = 124.
case(29)
element_covalent_radius = 132.
case(30)
element_covalent_radius = 122.
case(31)
element_covalent_radius = 120.
case(32)
element_covalent_radius = 119.
case(34)
element_covalent_radius = 120.
case(35)
element_covalent_radius = 120.
case(36) ! Kr.
element_covalent_radius = 116.
case default
write(*,*) '!!! covalent radius not available !!!'
stop
end select
! pm to bohr conversion
element_covalent_radius = element_covalent_radius*pmtoau
end function element_covalent_radius

118
src/QuAcK/read_basis.f90
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@ -1,118 +0,0 @@
subroutine read_basis(nAt,rAt,nBas,nO,nV,nShell,TotAngMomShell,CenterShell,KShell,DShell,ExpShell)
! Read basis set information
implicit none
include 'parameters.h'
! Input variables
integer,intent(in) :: nAt,nO
double precision,intent(in) :: rAt(nAt,ncart)
! Local variables
integer :: nShAt,iAt,iShell
integer :: i,j,k
character :: shelltype
! Output variables
integer,intent(out) :: nShell,nBas
double precision,intent(out) :: CenterShell(maxShell,ncart)
integer,intent(out) :: TotAngMomShell(maxShell),KShell(maxShell)
double precision,intent(out) :: DShell(maxShell,maxK),ExpShell(maxShell,maxK)
integer,intent(out) :: nV
!------------------------------------------------------------------------
! Primary basis set information
!------------------------------------------------------------------------
! Open file with basis set specification
open(unit=2,file='input/basis')
! Read basis information
write(*,'(A28)') 'Gaussian basis set'
write(*,'(A28)') '------------------'
nShell = 0
do i=1,nAt
read(2,*) iAt,nShAt
write(*,'(A28,1X,I16)') 'Atom n. ',iAt
write(*,'(A28,1X,I16)') 'number of shells ',nShAt
write(*,'(A28)') '------------------'
! Basis function centers
do j=1,nShAt
nShell = nShell + 1
do k=1,ncart
CenterShell(nShell,k) = rAt(iAt,k)
enddo
! Shell type and contraction degree
read(2,*) shelltype,KShell(nShell)
if(shelltype == "S") then
TotAngMomShell(nShell) = 0
write(*,'(A28,1X,I16)') 's-type shell with K = ',KShell(nShell)
elseif(shelltype == "P") then
TotAngMomShell(nShell) = 1
write(*,'(A28,1X,I16)') 'p-type shell with K = ',KShell(nShell)
elseif(shelltype == "D") then
TotAngMomShell(nShell) = 2
write(*,'(A28,1X,I16)') 'd-type shell with K = ',KShell(nShell)
elseif(shelltype == "F") then
TotAngMomShell(nShell) = 3
write(*,'(A28,1X,I16)') 'f-type shell with K = ',KShell(nShell)
elseif(shelltype == "G") then
TotAngMomShell(nShell) = 4
write(*,'(A28,1X,I16)') 'g-type shell with K = ',KShell(nShell)
elseif(shelltype == "H") then
TotAngMomShell(nShell) = 5
write(*,'(A28,1X,I16)') 'h-type shell with K = ',KShell(nShell)
elseif(shelltype == "I") then
TotAngMomShell(nShell) = 6
write(*,'(A28,1X,I16)') 'i-type shell with K = ',KShell(nShell)
endif
! Read exponents and contraction coefficients
write(*,'(A28,1X,A16,A16)') '','Exponents','Contraction'
do k=1,Kshell(nShell)
read(2,*) ExpShell(nShell,k),DShell(nShell,k)
write(*,'(A28,1X,F16.10,F16.10)') '',ExpShell(nShell,k),DShell(nShell,k)
enddo
enddo
write(*,'(A28)') '------------------'
enddo
! Total number of shells
write(*,'(A28,1X,I16)') 'Number of shells',nShell
write(*,'(A28)') '------------------'
write(*,*)
! Close file with basis set specification
close(unit=2)
! Calculate number of basis functions
nBas = 0
do iShell=1,nShell
nBas = nBas + (TotAngMomShell(iShell)*TotAngMomShell(iShell) + 3*TotAngMomShell(iShell) + 2)/2
enddo
write(*,'(A28)') '------------------'
write(*,'(A28,1X,I16)') 'Number of basis functions',NBas
write(*,'(A28)') '------------------'
write(*,*)
! Number of virtual orbitals
nV = nBas - nO
end subroutine read_basis

68
src/QuAcK/read_geometry.f90
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@ -1,68 +0,0 @@
subroutine read_geometry(nNuc,ZNuc,rNuc,ENuc)
! Read molecular geometry
implicit none
include 'parameters.h'
! Ouput variables
integer,intent(in) :: nNuc
! Local variables
integer :: i,j
double precision :: RAB
character(len=2) :: El
integer,external :: element_number
! Ouput variables
double precision,intent(out) :: ZNuc(nNuc),rNuc(nNuc,ncart),ENuc
! Open file with geometry specification
open(unit=1,file='input/molecule')
! Read geometry
read(1,*)
read(1,*)
read(1,*)
do i=1,nNuc
read(1,*) El,rNuc(i,1),rNuc(i,2),rNuc(i,3)
ZNuc(i) = element_number(El)
enddo
! Compute nuclear repulsion energy
ENuc = 0
do i=1,nNuc-1
do j=i+1,nNuc
RAB = (rNuc(i,1)-rNuc(j,1))**2 + (rNuc(i,2)-rNuc(j,2))**2 + (rNuc(i,3)-rNuc(j,3))**2
ENuc = ENuc + ZNuc(i)*ZNuc(j)/sqrt(RAB)
enddo
enddo
! Close file with geometry specification
close(unit=1)
! Print geometry
write(*,'(A28)') '------------------'
write(*,'(A28)') 'Molecular geometry'
write(*,'(A28)') '------------------'
do i=1,nNuc
write(*,'(A28,1X,I16)') 'Atom n. ',i
write(*,'(A28,1X,F16.10)') 'Z = ',ZNuc(i)
write(*,'(A28,1X,F16.10,F16.10,F16.10)') 'Atom coordinates:',(rNuc(i,j),j=1,ncart)
enddo
write(*,*)
write(*,'(A28)') '------------------'
write(*,'(A28,1X,F16.10)') 'Nuclear repulsion energy = ',ENuc
write(*,'(A28)') '------------------'
write(*,*)
end subroutine read_geometry

119
src/QuAcK/read_integrals.f90
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@ -1,119 +0,0 @@
subroutine read_integrals(nBas,S,T,V,Hc,G)
! Read one- and two-electron integrals from files
implicit none
! Input variables
integer,intent(in) :: nBas
! Local variables
logical :: debug
integer :: mu,nu,la,si
double precision :: Ov,Kin,Nuc,ERI
double precision :: scale
! Output variables
double precision,intent(out) :: S(nBas,nBas),T(nBas,nBas),V(nBas,nBas),Hc(nBas,nBas),G(nBas,nBas,nBas,nBas)
! Open file with integrals
debug = .false.
scale = 1d0
open(unit=8 ,file='int/Ov.dat')
open(unit=9 ,file='int/Kin.dat')
open(unit=10,file='int/Nuc.dat')
open(unit=11,file='int/ERI.dat')
! Read overlap integrals
S = 0d0
do
read(8,*,end=8) mu,nu,Ov
S(mu,nu) = Ov
enddo
8 close(unit=8)
! Read kinetic integrals
T = 0d0
do
read(9,*,end=9) mu,nu,Kin
T(mu,nu) = Kin/scale**2
enddo
9 close(unit=9)
! Read nuclear integrals
V = 0d0
do
read(10,*,end=10) mu,nu,Nuc
V(mu,nu) = Nuc
enddo
10 close(unit=10)
! Define core Hamiltonian
Hc = T + V
! Read nuclear integrals
G = 0d0
do
read(11,*,end=11) mu,nu,la,si,ERI
ERI = ERI/scale
! <12|34>
G(mu,nu,la,si) = ERI
! <32|14>
G(la,nu,mu,si) = ERI
! <14|32>
G(mu,si,la,nu) = ERI
! <34|12>
G(la,si,mu,nu) = ERI
! <41|23>
G(si,mu,nu,la) = ERI
! <23|41>
G(nu,la,si,mu) = ERI
! <21|43>
G(nu,mu,si,la) = ERI
! <43|21>
G(si,la,nu,mu) = ERI
enddo
11 close(unit=11)
! Print results
if(debug) then
write(*,'(A28)') '----------------------'
write(*,'(A28)') 'Overlap integrals'
write(*,'(A28)') '----------------------'
call matout(nBas,nBas,S)
write(*,*)
write(*,'(A28)') '----------------------'
write(*,'(A28)') 'Kinetic integrals'
write(*,'(A28)') '----------------------'
call matout(nBas,nBas,T)
write(*,*)
write(*,'(A28)') '----------------------'
write(*,'(A28)') 'Nuclear integrals'
write(*,'(A28)') '----------------------'
call matout(nBas,nBas,V)
write(*,*)
write(*,'(A28)') '----------------------'
write(*,'(A28)') 'Electron repulsion integrals'
write(*,'(A28)') '----------------------'
do la=1,nBas
do si=1,nBas
call matout(nBas,nBas,G(1,1,la,si))
enddo
enddo
write(*,*)
endif
end subroutine read_integrals

64
src/QuAcK/read_molecule.f90
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@ -1,64 +0,0 @@
subroutine read_molecule(nNuc,nEl,nO,nC,nR)
! Read number of atoms and number of electrons
implicit none
include 'parameters.h'
! Input variables
integer,intent(out) :: nNuc
integer,intent(out) :: nEl(nspin)
integer,intent(out) :: nO(nspin)
integer,intent(out) :: nC(nspin)
integer,intent(out) :: nR(nspin)
! Local variables
integer :: nCore
integer :: nRyd
! Open file with geometry specification
open(unit=1,file='input/molecule')
! Read number of atoms and number of electrons
read(1,*)
read(1,*) nNuc,nEl(1),nEl(2),nCore,nRyd
if(mod(nCore,2) /= 0 .or. mod(nRyd,2) /= 0) then
print*, 'The number of core and Rydberg electrons must be even!'
stop
end if
nO(:) = nEl(:)
nC(:) = nCore/2
nR(:) = nRyd/2
! Print results
write(*,'(A28)') '----------------------'
write(*,'(A28,1X,I16)') 'Number of atoms',nNuc
write(*,'(A28)') '----------------------'
write(*,*)
write(*,'(A28)') '----------------------'
write(*,'(A28,1X,I16)') 'Number of spin-up electrons',nEl(1)
write(*,'(A28,1X,I16)') 'Number of spin-down electrons',nEl(2)
write(*,'(A28,1X,I16)') ' Total number of electrons',sum(nEl(:))
write(*,'(A28)') '----------------------'
write(*,*)
write(*,'(A28)') '----------------------'
write(*,'(A28,1X,I16)') 'Number of core electrons',sum(nC(:))
write(*,'(A28,1X,I16)') 'Number of Rydberg electrons',sum(nR(:))
write(*,'(A28)') '----------------------'
write(*,*)
! Close file with geometry specification
close(unit=1)
end subroutine read_molecule

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!------------------------------------------------------------------------
function Kronecker_delta(i,j) result(delta)
! Kronecker Delta
implicit none
! Input variables
integer,intent(in) :: i,j
! Output variables
double precision :: delta
if(i == j) then
delta = 1d0
else
delta = 0d0
endif
end function Kronecker_delta
!------------------------------------------------------------------------
subroutine matout(m,n,A)
! Print the MxN array A
implicit none
integer,parameter :: ncol = 5
double precision,parameter :: small = 1d-10
integer,intent(in) :: m,n
double precision,intent(in) :: A(m,n)
double precision :: B(ncol)
integer :: ilower,iupper,num,i,j
do ilower=1,n,ncol
iupper = min(ilower + ncol - 1,n)
num = iupper - ilower + 1
write(*,'(3X,10(9X,I6))') (j,j=ilower,iupper)
do i=1,m
do j=ilower,iupper
B(j-ilower+1) = A(i,j)
enddo
do j=1,num
if(abs(B(j)) < small) B(j) = 0d0
enddo
write(*,'(I7,10F15.8)') i,(B(j),j=1,num)
enddo
enddo
end subroutine matout
!------------------------------------------------------------------------
subroutine trace_vector(n,v,Tr)
! Calculate the trace of the vector v of length n
!!! Please use the intrinsic fortran sum() !!!
implicit none
! Input variables
integer,intent(in) :: n
double precision,intent(in) :: v(n)
! Local variables
integer :: i
! Output variables
double precision,intent(out) :: Tr
Tr = 0d0
do i=1,n
Tr = Tr + v(i)
enddo
end subroutine trace_vector
!------------------------------------------------------------------------
function trace_matrix(n,A) result(Tr)
! Calculate the trace of the square matrix A
implicit none
! Input variables
integer,intent(in) :: n
double precision,intent(in) :: A(n,n)
! Local variables
integer :: i
! Output variables
double precision :: Tr
Tr = 0d0
do i=1,n
Tr = Tr + A(i,i)
enddo
end function trace_matrix
!------------------------------------------------------------------------
subroutine compute_error(nData,Mean,Var,Error)
! Calculate the statistical error
implicit none
! Input variables
double precision,intent(in) :: nData,Mean(3)
! Output variables
double precision,intent(out) :: Error(3)
double precision,intent(inout):: Var(3)
Error = sqrt((Var-Mean**2/nData)/nData/(nData-1d0))
end subroutine compute_error
!------------------------------------------------------------------------
subroutine identity_matrix(N,A)
! Set the matrix A to the identity matrix
implicit none
! Input variables
integer,intent(in) :: N
! Local viaruabkes
integer :: i
! Output variables
double precision,intent(out) :: A(N,N)
A = 0d0
do i=1,N
A(i,i) = 1d0
enddo
end subroutine identity_matrix
!------------------------------------------------------------------------
subroutine prepend(N,M,A,b)
! Prepend the vector b of size N into the matrix A of size NxM
implicit none
! Input variables
integer,intent(in) :: N,M
double precision,intent(in) :: b(N)
! Local viaruabkes
integer :: i,j
! Output variables
double precision,intent(out) :: A(N,M)
! print*,'b in append'
! call matout(N,1,b)
do i=1,N
do j=M-1,1,-1
A(i,j+1) = A(i,j)
enddo
A(i,1) = b(i)
enddo
end subroutine prepend
!------------------------------------------------------------------------
subroutine append(N,M,A,b)
! Append the vector b of size N into the matrix A of size NxM
implicit none
! Input variables
integer,intent(in) :: N,M
double precision,intent(in) :: b(N)
! Local viaruabkes
integer :: i,j
! Output variables
double precision,intent(out) :: A(N,M)
do i=1,N
do j=2,M
A(i,j-1) = A(i,j)
enddo
A(i,M) = b(i)
enddo
end subroutine append
!------------------------------------------------------------------------
subroutine AtDA(N,A,D,B)
! Perform B = At.D.A where A is a NxN matrix and D is a diagonal matrix given
! as a vector of length N
implicit none
! Input variables
integer,intent(in) :: N
double precision,intent(in) :: A(N,N),D(N)
! Local viaruabkes
integer :: i,j,k
! Output variables
double precision,intent(out) :: B(N,N)
B = 0d0
do i=1,N
do j=1,N
do k=1,N
B(i,k) = B(i,k) + A(j,i)*D(j)*A(j,k)
enddo
enddo
enddo
end subroutine AtDA
!------------------------------------------------------------------------
subroutine ADAt(N,A,D,B)
! Perform B = A.D.At where A is a NxN matrix and D is a diagonal matrix given
! as a vector of length N
implicit none
! Input variables
integer,intent(in) :: N
double precision,intent(in) :: A(N,N),D(N)
! Local viaruabkes
integer :: i,j,k
! Output variables
double precision,intent(out) :: B(N,N)
B = 0d0
do i=1,N
do j=1,N
do k=1,N
B(i,k) = B(i,k) + A(i,j)*D(j)*A(k,j)
enddo
enddo
enddo
end subroutine ADAt
!------------------------------------------------------------------------
subroutine DA(N,D,A)
! Perform A <- D.A where A is a NxN matrix and D is a diagonal matrix given
! as a vector of length N
implicit none
integer,intent(in) :: N
integer :: i,j,k
double precision,intent(in) :: D(N)
double precision,intent(inout):: A(N,N)
do i=1,N
do j=1,N
A(i,j) = D(i)*A(i,j)
enddo
enddo
end subroutine DA
!------------------------------------------------------------------------
subroutine AD(N,A,D)
! Perform A <- A.D where A is a NxN matrix and D is a diagonal matrix given
! as a vector of length N
implicit none
integer,intent(in) :: N
integer :: i,j,k
double precision,intent(in) :: D(N)
double precision,intent(inout):: A(N,N)
do i=1,N
do j=1,N
A(i,j) = A(i,j)*D(j)
enddo
enddo
end subroutine AD
!------------------------------------------------------------------------
subroutine print_warning(message)
! Print warning
implicit none
character(len=*),intent(in) :: message
write(*,*) message
end subroutine print_warning

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!subroutine eigenvalues_non_symmetric_matrix(N,A,e)
!
!! Diagonalize a square matrix
!
! implicit none
!
!! Input variables
!
! integer,intent(in) :: N
! double precision,intent(inout):: A(N,N)
! double precision,intent(out) :: e(N)
!
!! Local variables
!
! integer :: lwork,info
! double precision,allocatable :: work(:)
!
!! Memory allocation
!
! allocate(eRe(N),eIm(N),work(3*N))
! lwork = size(work)
!
! call DGEEV('N','N',N,A,N, eRe, eIm, 0d0,1, VR,LDVR, WORK, LWORK, INFO )
!
! if(info /= 0) then
! print*,'Problem in diagonalize_matrix (dseev)!!'
! stop
! endif
!
!end subroutine eigenvalues_non_symmetric_matrix
subroutine diagonalize_matrix(N,A,e)
! Diagonalize a square matrix
implicit none
! Input variables
integer,intent(in) :: N
double precision,intent(inout):: A(N,N)
double precision,intent(out) :: e(N)
! Local variables
integer :: lwork,info
double precision,allocatable :: work(:)
! Memory allocation
allocate(work(3*N))
lwork = size(work)
call dsyev('V','U',N,A,N,e,work,lwork,info)
if(info /= 0) then
print*,'Problem in diagonalize_matrix (dsyev)!!'
endif
end subroutine diagonalize_matrix
subroutine svd(N,A,U,D,Vt)
! Compute A = U.D.Vt
! Dimension of A is NxN
implicit none
integer, intent(in) :: N
double precision,intent(in) :: A(N,N)
double precision,intent(out) :: U(N,N)
double precision,intent(out) :: Vt(N,N)
double precision,intent(out) :: D(N)
double precision,allocatable :: work(:)
integer :: info,lwork
double precision,allocatable :: scr(:,:)
allocate (scr(N,N))
scr(:,:) = A(:,:)
! Find optimal size for temporary arrays
allocate(work(1))
lwork = -1
call dgesvd('A','A',N,N,scr,N,D,U,N,Vt,N,work,lwork,info)
lwork = int(work(1))
deallocate(work)
allocate(work(lwork))
call dgesvd('A','A',N,N,scr,N,D,U,N,Vt,N,work,lwork,info)
deallocate(work,scr)
if (info /= 0) then
print *, info, ': SVD failed'
stop
endif
end
subroutine inverse_matrix(N,A,B)
! Returns the inverse of the square matrix A in B
implicit none
integer,intent(in) :: N
double precision, intent(in) :: A(N,N)
double precision, intent(out) :: B(N,N)
integer :: info,lwork
integer, allocatable :: ipiv(:)
double precision,allocatable :: work(:)
allocate (ipiv(N),work(N*N))
lwork = size(work)
B(1:N,1:N) = A(1:N,1:N)
call dgetrf(N,N,B,N,ipiv,info)
if (info /= 0) then
print*,info
stop 'error in inverse (dgetrf)!!'
endif
call dgetri(N,B,N,ipiv,work,lwork,info)
if (info /= 0) then
print *, info
stop 'error in inverse (dgetri)!!'
endif
deallocate(ipiv,work)
end subroutine inverse_matrix
subroutine linear_solve(N,A,b,x,rcond)
! Solve the linear system A.x = b where A is a NxN matrix
! and x and x are vectors of size N
implicit none
integer,intent(in) :: N
double precision,intent(in) :: A(N,N),b(N),rcond
double precision,intent(out) :: x(N)
integer :: info,lwork
double precision :: ferr,berr
integer,allocatable :: ipiv(:),iwork(:)
double precision,allocatable :: AF(:,:),work(:)
lwork = 3*N
allocate(AF(N,N),ipiv(N),work(lwork),iwork(N))
call dsysvx('N','U',N,1,A,N,AF,N,ipiv,b,N,x,N,rcond,ferr,berr,work,lwork,iwork,info)
! if (info /= 0) then
! print *, info
! stop 'error in linear_solve (dsysvx)!!'
! endif
end subroutine linear_solve
subroutine easy_linear_solve(N,A,b,x)
! Solve the linear system A.x = b where A is a NxN matrix
! and x and x are vectors of size N
implicit none
integer,intent(in) :: N
double precision,intent(in) :: A(N,N),b(N)
double precision,intent(out) :: x(N)
integer :: info,lwork
integer,allocatable :: ipiv(:)
double precision,allocatable :: work(:)
allocate(ipiv(N),work(N*N))
lwork = size(work)
x = b
call dsysv('U',N,1,A,N,ipiv,x,N,work,lwork,info)
if (info /= 0) then
print *, info
stop 'error in linear_solve (dsysv)!!'
endif
end subroutine easy_linear_solve

400
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!------------------------------------------------------------------------
function Kronecker_delta(i,j) result(delta)
! Kronecker Delta
implicit none
! Input variables
integer,intent(in) :: i,j
! Output variables
double precision :: delta
if(i == j) then
delta = 1d0
else
delta = 0d0
endif
end function Kronecker_delta
!------------------------------------------------------------------------
subroutine matout(m,n,A)
! Print the MxN array A
implicit none
integer,parameter :: ncol = 5
double precision,parameter :: small = 1d-10
integer,intent(in) :: m,n
double precision,intent(in) :: A(m,n)
double precision :: B(ncol)
integer :: ilower,iupper,num,i,j
do ilower=1,n,ncol
iupper = min(ilower + ncol - 1,n)
num = iupper - ilower + 1
write(*,'(3X,10(9X,I6))') (j,j=ilower,iupper)
do i=1,m
do j=ilower,iupper
B(j-ilower+1) = A(i,j)
enddo
do j=1,num
if(abs(B(j)) < small) B(j) = 0d0
enddo
write(*,'(I7,10F15.8)') i,(B(j),j=1,num)
enddo
enddo
end subroutine matout
!------------------------------------------------------------------------
subroutine trace_vector(n,v,Tr)
! Calculate the trace of the vector v of length n
!!! Please use the intrinsic fortran sum() !!!
implicit none
! Input variables
integer,intent(in) :: n
double precision,intent(in) :: v(n)
! Local variables
integer :: i
! Output variables
double precision,intent(out) :: Tr
Tr = 0d0
do i=1,n
Tr = Tr + v(i)
enddo
end subroutine trace_vector
!------------------------------------------------------------------------
function trace_matrix(n,A) result(Tr)
! Calculate the trace of the square matrix A
implicit none
! Input variables
integer,intent(in) :: n
double precision,intent(in) :: A(n,n)
! Local variables
integer :: i
! Output variables
double precision :: Tr
Tr = 0d0
do i=1,n
Tr = Tr + A(i,i)
enddo
end function trace_matrix
!------------------------------------------------------------------------
subroutine compute_error(nData,Mean,Var,Error)
! Calculate the statistical error
implicit none
! Input variables
double precision,intent(in) :: nData,Mean(3)
! Output variables
double precision,intent(out) :: Error(3)
double precision,intent(inout):: Var(3)
Error = sqrt((Var-Mean**2/nData)/nData/(nData-1d0))
end subroutine compute_error
!------------------------------------------------------------------------
subroutine identity_matrix(N,A)
! Set the matrix A to the identity matrix
implicit none
! Input variables
integer,intent(in) :: N
! Local viaruabkes
integer :: i
! Output variables
double precision,intent(out) :: A(N,N)
A = 0d0
do i=1,N
A(i,i) = 1d0
enddo
end subroutine identity_matrix
!------------------------------------------------------------------------
subroutine prepend(N,M,A,b)
! Prepend the vector b of size N into the matrix A of size NxM
implicit none
! Input variables
integer,intent(in) :: N,M
double precision,intent(in) :: b(N)
! Local viaruabkes
integer :: i,j
! Output variables
double precision,intent(out) :: A(N,M)
! print*,'b in append'
! call matout(N,1,b)
do i=1,N
do j=M-1,1,-1
A(i,j+1) = A(i,j)
enddo
A(i,1) = b(i)
enddo
end subroutine prepend
!------------------------------------------------------------------------
subroutine append(N,M,A,b)
! Append the vector b of size N into the matrix A of size NxM
implicit none
! Input variables
integer,intent(in) :: N,M
double precision,intent(in) :: b(N)
! Local viaruabkes
integer :: i,j
! Output variables
double precision,intent(out) :: A(N,M)
do i=1,N
do j=2,M
A(i,j-1) = A(i,j)
enddo
A(i,M) = b(i)
enddo
end subroutine append
!------------------------------------------------------------------------
subroutine AtDA(N,A,D,B)
! Perform B = At.D.A where A is a NxN matrix and D is a diagonal matrix given
! as a vector of length N
implicit none
! Input variables
integer,intent(in) :: N
double precision,intent(in) :: A(N,N),D(N)
! Local viaruabkes
integer :: i,j,k
! Output variables
double precision,intent(out) :: B(N,N)
B = 0d0
do i=1,N
do j=1,N
do k=1,N
B(i,k) = B(i,k) + A(j,i)*D(j)*A(j,k)
enddo
enddo
enddo
end subroutine AtDA
!------------------------------------------------------------------------
subroutine ADAt(N,A,D,B)
! Perform B = A.D.At where A is a NxN matrix and D is a diagonal matrix given
! as a vector of length N
implicit none
! Input variables
integer,intent(in) :: N
double precision,intent(in) :: A(N,N),D(N)
! Local viaruabkes
integer :: i,j,k
! Output variables
double precision,intent(out) :: B(N,N)
B = 0d0
do i=1,N
do j=1,N
do k=1,N
B(i,k) = B(i,k) + A(i,j)*D(j)*A(k,j)
enddo
enddo
enddo
end subroutine ADAt
!------------------------------------------------------------------------
subroutine DA(N,D,A)
! Perform A <- D.A where A is a NxN matrix and D is a diagonal matrix given
! as a vector of length N
implicit none
integer,intent(in) :: N
integer :: i,j,k
double precision,intent(in) :: D(N)
double precision,intent(inout):: A(N,N)
do i=1,N
do j=1,N
A(i,j) = D(i)*A(i,j)
enddo
enddo
end subroutine DA
!------------------------------------------------------------------------
subroutine AD(N,A,D)
! Perform A <- A.D where A is a NxN matrix and D is a diagonal matrix given
! as a vector of length N
implicit none
integer,intent(in) :: N
integer :: i,j,k
double precision,intent(in) :: D(N)
double precision,intent(inout):: A(N,N)
do i=1,N
do j=1,N
A(i,j) = A(i,j)*D(j)
enddo
enddo
end subroutine AD
!------------------------------------------------------------------------
subroutine print_warning(message)
! Print warning
implicit none
character(len=*),intent(in) :: message
write(*,*) message
end subroutine print_warning
!------------------------------------------------------------------------
recursive function fac(n) result(fact)
implicit none
integer :: fact
integer, intent(in) :: n
if (n == 0) then
fact = 1
else
fact = n * fac(n-1)
end if
end function fac
!------------------------------------------------------------------------
function dfac(n) result(fact)
implicit none
double precision :: fact
integer, intent(in) :: n
integer :: fac
fact = dble(fac(n))
end function dfac
!------------------------------------------------------------------------
function NormCoeff(alpha,a)
! Compute normalization coefficients for cartesian gaussians
implicit none
! Input variables
double precision,intent(in) :: alpha
integer,intent(in) :: a(3)
! local variable
double precision :: pi,dfa(3),dfac
integer :: atot
! Output variable
double precision NormCoeff
pi = 4d0*atan(1d0)
atot = a(1) + a(2) + a(3)
dfa(1) = dfac(2*a(1))/(2d0**a(1)*dfac(a(1)))
dfa(2) = dfac(2*a(2))/(2d0**a(2)*dfac(a(2)))
dfa(3) = dfac(2*a(3))/(2d0**a(3)*dfac(a(3)))
NormCoeff = (2d0*alpha/pi)**(3d0/2d0)*(4d0*alpha)**atot
NormCoeff = NormCoeff/(dfa(1)*dfa(2)*dfa(3))
NormCoeff = sqrt(NormCoeff)
end function NormCoeff

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!subroutine eigenvalues_non_symmetric_matrix(N,A,e)
!
!! Diagonalize a square matrix
!
! implicit none
!
!! Input variables
!
! integer,intent(in) :: N
! double precision,intent(inout):: A(N,N)
! double precision,intent(out) :: e(N)
!
!! Local variables
!
! integer :: lwork,info
! double precision,allocatable :: work(:)
!
!! Memory allocation
!
! allocate(eRe(N),eIm(N),work(3*N))
! lwork = size(work)
!
! call DGEEV('N','N',N,A,N, eRe, eIm, 0d0,1, VR,LDVR, WORK, LWORK, INFO )
!
! if(info /= 0) then
! print*,'Problem in diagonalize_matrix (dseev)!!'
! stop
! endif
!
!end subroutine eigenvalues_non_symmetric_matrix
subroutine diagonalize_matrix(N,A,e)
! Diagonalize a square matrix
implicit none
! Input variables
integer,intent(in) :: N
double precision,intent(inout):: A(N,N)
double precision,intent(out) :: e(N)
! Local variables
integer :: lwork,info
double precision,allocatable :: work(:)
! Memory allocation
allocate(work(3*N))
lwork = size(work)
call dsyev('V','U',N,A,N,e,work,lwork,info)
if(info /= 0) then
print*,'Problem in diagonalize_matrix (dsyev)!!'
endif
end subroutine diagonalize_matrix
subroutine svd(N,A,U,D,Vt)
! Compute A = U.D.Vt
! Dimension of A is NxN
implicit none
integer, intent(in) :: N
double precision,intent(in) :: A(N,N)
double precision,intent(out) :: U(N,N)
double precision,intent(out) :: Vt(N,N)
double precision,intent(out) :: D(N)
double precision,allocatable :: work(:)
integer :: info,lwork
double precision,allocatable :: scr(:,:)
allocate (scr(N,N))
scr(:,:) = A(:,:)
! Find optimal size for temporary arrays
allocate(work(1))
lwork = -1
call dgesvd('A','A',N,N,scr,N,D,U,N,Vt,N,work,lwork,info)
lwork = int(work(1))
deallocate(work)
allocate(work(lwork))
call dgesvd('A','A',N,N,scr,N,D,U,N,Vt,N,work,lwork,info)
deallocate(work,scr)
if (info /= 0) then
print *, info, ': SVD failed'
stop
endif
end
subroutine inverse_matrix(N,A,B)
! Returns the inverse of the square matrix A in B
implicit none
integer,intent(in) :: N
double precision, intent(in) :: A(N,N)
double precision, intent(out) :: B(N,N)
integer :: info,lwork
integer, allocatable :: ipiv(:)
double precision,allocatable :: work(:)
allocate (ipiv(N),work(N*N))
lwork = size(work)
B(1:N,1:N) = A(1:N,1:N)
call dgetrf(N,N,B,N,ipiv,info)
if (info /= 0) then
print*,info
stop 'error in inverse (dgetrf)!!'
endif
call dgetri(N,B,N,ipiv,work,lwork,info)
if (info /= 0) then
print *, info
stop 'error in inverse (dgetri)!!'
endif
deallocate(ipiv,work)
end subroutine inverse_matrix
subroutine linear_solve(N,A,b,x,rcond)
! Solve the linear system A.x = b where A is a NxN matrix
! and x and x are vectors of size N
implicit none
integer,intent(in) :: N
double precision,intent(in) :: A(N,N),b(N),rcond
double precision,intent(out) :: x(N)
integer :: info,lwork
double precision :: ferr,berr
integer,allocatable :: ipiv(:),iwork(:)
double precision,allocatable :: AF(:,:),work(:)
lwork = 3*N
allocate(AF(N,N),ipiv(N),work(lwork),iwork(N))
call dsysvx('N','U',N,1,A,N,AF,N,ipiv,b,N,x,N,rcond,ferr,berr,work,lwork,iwork,info)
! if (info /= 0) then
! print *, info
! stop 'error in linear_solve (dsysvx)!!'
! endif
end subroutine linear_solve
subroutine easy_linear_solve(N,A,b,x)
! Solve the linear system A.x = b where A is a NxN matrix
! and x and x are vectors of size N
implicit none
integer,intent(in) :: N
double precision,intent(in) :: A(N,N),b(N)
double precision,intent(out) :: x(N)
integer :: info,lwork
integer,allocatable :: ipiv(:)
double precision,allocatable :: work(:)
allocate(ipiv(N),work(N*N))
lwork = size(work)
x = b
call dsysv('U',N,1,A,N,ipiv,x,N,work,lwork,info)
if (info /= 0) then
print *, info
stop 'error in linear_solve (dsysv)!!'
endif
end subroutine easy_linear_solve