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Integral Lists

The following section describes the contents of the MOINTS, GAMLAM, MOABCD, SECDER and DERINT files, which are used to store two-electron integrals and various other quantities.

PART I. Lists used in standard calculation types (single point energy, first and second derivative calculations)


   J      I           Quantity           Storage Mode  
                                          ALL ; FOR 
                                               EACH

 1-NIRREP  5          <AB|IJ>             A,I ; B,J (NOT ANTISYMMETRIZED)
 1-NIRREP  6          <ab|ij>             a,i ; b,j (NOT ANTISYMMETRIZED)

 1-NIRREP 11          <IJ||KL>            I<J ; K<L                    ***
 1-NIRREP 12          <ij||kl>            i<j ; k<l                    ***
 1-NIRREP 13          <Ij||Kl>            I,j ; K,l                   

 1-NIRREP  7          <IJ||KA>            I<J ; K,A
 1-NIRREP  8          <ij||ka>            i<j ; k,a                     ***
 1-NIRREP  9          <Ij|Ak>             I,j ; A,k                     ***
 1-NIRREP 10          <Ij|Ka>             I,j ; K,a

 1-NIRREP 14          <AB||IJ>            A<B ; I<J
 1-NIRREP 15          <ab||ij>            a<b ; i<j                     ***
 1-NIRREP 16          <Ab|Ij>             A,b ; I,j
 1-NIRREP 17          <Ab|Ij> = <bI|jA>   b,j ; A,I                     ***
 1-NIRREP 18          <Ab|Ij> = <Aj|Ib>   A,I ; b,j
 1-NIRREP 19          <AB||IJ>            A,I ; B,J 
 1-NIRREP 20          <ab||ij>            a,i ; b,j                     ***
 1-NIRREP 21          <Ab|Ij> = <Aj|Ib>   A,j ; b,I
 1-NIRREP 22          <Ab|Ij> = <bI|Aj>   b,I ; A,j                     ***

 1-NIRREP 23          <IA||JB>            B,I ; A,J
 1-NIRREP 24          <ia||jb>            b,i ; a,j                     ***

 lists 23 and 24 are resorted in UHF calculations in the module xcphf
 (see corresponding comment on JOBARC record ST2324)

 1-NIRREP 23 (resorted)                   B,J ; A,I
 1-NIRREP 24 (resorted)                   b,j ; a,i

 1-NIRREP 25          <iA|jB> = <iB|jA>   B,i ; A,j
 1-NIRREP 26          <aI|bJ>             b,I ; a,J                     ***

 1-NIRREP 27          <AB||CI>            A<B ; C,I
 1-NIRREP 28          <ab||ci>            a<b ; c,i                     ***
 1-NIRREP 29          <Ab|Ic>             A,b ; I,c                     ***
 1-NIRREP 30          <Ab|Ci>             A,b ; C,i

 1-NIRREP 34         T2(IJ,AB)            A,J ; B,I
 1-NIRREP 35         T2(ij,ab)            a,j ; b,i                     ***
 1-NIRREP 36         T2(Ij,Ab)            b,j ; A,I                     ***
 1-NIRREP 37         T2(Ij,Ab)            A,I ; b,j
 1-NIRREP 38         T2(Ij,Ab)            b,I ; A,j                     ***
 1-NIRREP 39         T2(Ij,Ab)            A,j ; b,I

 1-NIRREP 40         T2(IJ,AB) (increment)A,J ; B,I      (rings)        ***
 1-NIRREP 41         T2(ij,ab) (increment)a,j ; b,i      (rings)        *** 
 1-NIRREP 42         T2(Ij,Ab) (increment)A,I ; b,j      (rings)
 1-NIRREP 43         T2(Ij,Ab) (increment)A,j ; b,I      (rings)

 1-NIRREP 44         T2(IJ,AB)            A<B ; I<J
 1-NIRREP 45         T2(ij,ab)            a<b ; i<j                     ***
 1-NIRREP 46         T2(Ij,Ab)            A,b ; I,j

     (In MBPT(3) and MBPT(4) calculations, lists 44-46 contain after vcc
      in all cases the first-order amplitudes T2[1](IJ,AB))  

 1-NIRREP 48         D(IJ,AB)             A<B ; I<J
 1-NIRREP 49         D(ij,ab)             a<b ; i<j                     ***
 1-NIRREP 50         D(Ij,Ab)             A,b ; I,j      

 1-NIRREP 51         W(MN,IJ) intermed.   M<N ; I<J                     ***
 1-NIRREP 52         W(mn,ij) intermed.   m<n ; i<j                     ***
 1-NIRREP 53         W(Mn,Ij) intermed.   M,n ; I,j

 1-NIRREP 54         W(MB,EJ) intermed.   E,M ; B,J                    (***)    
 1-NIRREP 55         W(mb,ej) intermed.   e,m ; b,j                     ***
 1-NIRREP 56         W(Mb,Ej) intermed.   E,M ; b,j              
 1-NIRREP 57         W(mB,eJ) intermed.   e,m ; B,J                     ***
 1-NIRREP 58         W(mB,Ej) intermed.   E,m ; B,j              
 1-NIRREP 59         W(Mb,eJ) intermed.   e,M ; b,J                     ***

 Note that for MBPT(4) and CC gradient calculations, list 54 to
 59 are overwritten by the so-called H intermediates. However,
 for MBPT(4) and CC second derivative calculations, list 54 to 
 59 are preserved and H is written to lists 254 to 259

 1-NIRREP 254        H(MB,EJ intermed.  (L indices, T indices) 
 1-NIRREP 255
 1-NIRREP 256
 1-NIRREP 257
 1-NIRREP 258
 1-NIRREP 259

 1-NIRREP 61         T2(IJ,AB) increment  A<B ; I<J                     ***
                     L2(IJ,AB) increment  A<B ; I<J in Lambda iterations ***
                     T2(IJ,AB)[3]         A<B ; I<J  iterative         ROHF
 1-NIRREP 62         T2(ij,ab) increment  a<b ; i<j                     ***
                     L2(ij,ab) increment  a<b ; i<j in Lambda iterations ***
                     T2(ij,ab)[3]         a<b ; i<j  iterative         ROHF
 1-NIRREP 63         T2(Ij,Ab) increment  A,b ; I,j
                     L2(Ij,Ab) increment  A,b ; I,j in Lambda iterations 
                     T2(Ij,Ab)[3]         A,b ; I,j  iterative         ROHF

      (In MBPT(3) calculations, lists 61-63 contain after vcc the
       total T2 amplitudes, i.e. the sum of first and second-order 
       amplitudes, in MBPT(4) derivative calculations, lists 61-63
       contain parts of the third-order amplitudes)

 1-NIRREP 64         Reciprocal D(IJ,AB)  A<B ; I<J
  9       64         Reciprocal D(I,A)      A,I   
 1-NIRREP 65         Reciprocal D(ij,ab)  a<b ; i<j                     ***
  9       65         Reciprocal D(i,a)      a,i                         ***
 1-NIRREP 66         Reciprocal D(Ij,Ab)  A,b ; I,j 

 (old 1-3      70-89      Reserved for RLE Jacobi iterates)

 1,2      70        reserved for DIIS in unperturbed calculations

 1-NIRREP 74
 1-NIRREP 75
 1-NIRREP 76         scratch lists in DT1RING in ECC
 1-NIRREP 77
 1-NIRREP 78
 1-NIRREP 79

  for localized MBPT methods

 1-NIRREP 80           R(AB,IJ)                A<B ; I<J                ***
 1-NIRREP 81           R(ab,ij)                a<b ; i<j                ***
 1-NIRREP 82           R(Ab,Ij)                A,b ; I,j

 1-NIRREP 83
 1-NIRREP 84
 1-NIRREP 85
 1-NIRREP 86           T(Am,Ij)                A,m ; I,j 

  1      90          T1AA                    A,I                     
  2      90          T1BB                    a,i                        ***
  3      90          T1AA AND L1AA INCREM    A,I
  4      90          T1BB AND L1BB INCREM    a,i                        ***
  5      90          AB MO OVERLAP MATRIX    I,j  (o-o)                 ***
  6      90          AB MO OVERLAP MATRIX    A,j  (v-o)                 ***
  7      90          AB MO OVERLAP MATRIX    I,b  (o-v)                 ***
  8      90          AB MO OVERLAP MATRIX    A,b  (v-v)                 ***
  9      90          T1AA[2]; iterative      A,I                       ROHF
 10      90          T1BB[2]; iterative      a,i                       ROHF

  1      91          F(M*,I) intermed.       M,I
  2      91          F(m*,i) intermed.       m,i                        ***
  3      91          f(M*,I) (fock matrix)   M,I  (only non-HF methods)
  4      91          f(m*,i) (fock matrix)   m,i  (only non-HF methods) ***

  3,91 and 4,91 are also used in case of localized orbitals for the 
  off-diagonal fock matrix elements

  1      92          F(E,A*) intermed.       E,A
  2      92          F(e,a*) intermed.       e,a                        ***
  3      92          f(E*,A) (fock matrix)   E,A  (only non-HF methods)
  4      92          f(e*,a) (fock matrix)   e,a  (only non-HF methods) ***

  3,92 and 4,92 are also used in case of localized orbitals for the 
  off-diagonal fock matrix elements

  1      93          F(A,I*) intermed.       A,I
  2      93          F(a,i*) intermed.       a,i                        ***
  3      93          f(A*,I) (fock matrix)   A,I  (only non-HF methods)
  4      93          f(a*,i) (fock matrix)   a,i  (only non-HF methods) ***

  intermediates in CCSDT-3 calculations  (???)

 1-NIRREP 94         T2(IJ,AB)[2] iterative  A<B ; I<J                 ROHF
 1-NIRREP 95         T2(ij,ab)[2] iterative  a<b ; i<j                 ROHF
 1-NIRREP 96         T2(Ij,Ab)[2] iterative  A,b ; I,j                 ROHF


 1-NIRREP 98         T2(Ij,Ab) cumulative    A,b ; I,j  (MBPT S^2)     ROHF

 1        99          parts of F(a,e) intermediates 
 2        99

Derivatives of one-electron integrals in AO basis:

 1-NIRREP 100        h(mu*,nu)^chi         ipert ; mu >= nu    **
 for PROP=1,2,RESP:
  1-NIRREP 100      efg(mu*,nu)            ipert ; mu >= mu

 1-NIRREP 101        S(mu*,nu)^chi         ipert ; mu >= nu    
 1-NIRREP 102        f(mu*,nu^(chi) (alpha)ipert ; mu >= nu    
 1-NIRREP 103        f(mu*,nu^(chi) (beta) ipert ; mu >= nu              ***
 1-3      104        dipole(mu*,nu)        ixyz  ; mu >= nu
 4-9      104        quadrupole(mu*,nu)    ipert ; mu >= nu
 1-NIRREP 105        A^(chi)*DREL  (alpha)ipert ; mu >= nu    **
 1-NIRREP 106        A^(chi)*DREL  (beta) ipert ; mu >= nu    **        ***

  ** correlated second derivative calculations only 

H_bar elements in CC gradient and EOM-CC calculations:

 1-NIRREP 107        G(IJ,KA)             I<J ; K,A                     ***
                     W(IJ,KA)             I<J ; K,A in VLAMCC/LCC       ***
 1-NIRREP 108        G(ij,ka)             i<j ; k,a                     ***
                     W(ij,ka)             i<j ; k,a in VLAMCC/LCC       ***
 1-NIRREP 109        G(Ij,Ak)             I,j ; A,k                     ***
                     W(Ij,Ak)             I,j ; A,k in VLAMCC/LCC       ***
 1-NIRREP 110        G(Ij,Ka)             I,j ; K,a   
                     W(Ij,Ka)             I,j ; K,a in VLAMCC/LCC

 1-NIRREP 111        G(IJ,KL)             I<J ; K<L                     ***
 1-NIRREP 112        G(ij,kl)             i<j ; k<l                     ***
 1-NIRREP 113        G(Ij,Kl)             I,j ; K,l

 1-NIRREP 114        G(IJ,AB)             A<B ; I<J
 1-NIRREP 115        G(ij,ab)             a<b ; i<j                     ***
 1-NIRREP 116        G(Ij,Ab)             A,b ; I,j
 1-NIRREP 117        G(bI,jA)             b,j ; A,I                     ***
   resorted in VDENS to                   b,I ; A,j   equiv. to 20      ***
 1-NIRREP 118        G(Aj,Ib)             A,I ; b,j
   resorted in VDENS to                   A,j ; b,I   equiv. to 21
 1-NIRREP 123        G(IA,JB)             B,I ; A,J
   resorted in VDENS to                   B,J ; A,I                   
 1-NIRREP 124        G(ia,jb)             b,i ; a,j                     ***
   resorted in VDENS to                   b,j ; a,i                     ***
 1-NIRREP 125        G(iA,jB)             B,i ; A,j
   resorted in VDENS to                   B,j ; A,i
 1-NIRREP 126        G(Ia,Jb)             b,I ; a,J                     ***
   resorted in VDENS to                   b,J ; a,I                     ***

 1-NIRREP 127        G(AB,CI)             A<B ; C,I                     ***
                     W(AB,CI)             A<B ; C,I in VLAMCC/LCC       ***
 1-NIRREP 128        G(ab,ci)             a<b ; c,i                     ***
                     W(ab,ci)             a<b ; c,i in VLAMCC/LCC       ***
 1-NIRREP 129        G(Ab,Ic)             A,b ; I,c                     ***
                     W(Ab,Ic)             A,b ; I,c in VLAMCC/LCC       ***
 1-NIRREP 130        G(Ab,Ci)             A,b ; C,i
                     W(Ab,Ci)             A,b ; C,i in VLAMCC/LCC

 1-NIRREP 131        G(AB,CD)             A<B ; C<D                     ***
 1-NIRREP 132        G(ab,cd)             a<b ; c<d                     ***
 1-NIRREP 133        G(Ab,Cd)             A,b ; C,d

 1-NIRREP 134        L2(IJ,AB)            A,J ; B,I
 1-NIRREP 135        L2(ij,ab)            a,j ; b,i                     ***
 1-NIRREP 136        L2(Ij,Ab)            b,j ; A,I                     ***
 1-NIRREP 137        L2(Ij,Ab)            A,I ; b,j
 1-NIRREP 138        L2(Ij,Ab)            b,I ; A,j                     ***
 1-NIRREP 139        L2(Ij,Ab)            A,j ; b,I

 (Note that for MBPT(4), lists 134-139 contain the resorted second-order
  amplitudes (note that these are the pure second-order amplitudes and
  that these lists do not contain contributions due to the first-order
  amplitudes)

 Lists 140 to 143 are used in ANTI in case of a direct calculation of 
 G(ab,cd) only. Those lists are not available in other modules.

 1        140       T1(A,I)                A,I
 2        140       T1(a,i)                a,i                          ***
 1-NIRREP 141       T2(AB,IJ)              A<B;I<J                      ***
 1-NIRREP 142       T2(ab,ij)              a<b;i<j                      ***
 1-NIRREP 143       T2(Ab,Ij)              A,b;I,j 

 1-NIRREP 144        L2(IJ,AB)            A<B ; I<J
 1-NIRREP 145        L2(ij,ab)            a<b ; i<j                     ***
 1-NIRREP 146        L2(Ij,Ab)            A,b ; I,j

 1-NIRREP 151  V(IJ,MN) (MN from T, IJ from L)   M<N ; I<J              ***
 1-NIRREP 152        V(ij,MN)             m<n ; i<j                     ***
 1-NIRREP 153        V(Ij,MN)             M,n ; I,j

 1-NIRREP 156        A^(chi)*D (I,J)
 1-NIRREP 157        A^(chi)*D (i,j)                                    ***
 1-NIRREP 158        A^(chi)*D (A,I)
 1-NIRREP 159        A^(chi)*D (a,i)                                    ***

Relaxed density matrix (correlation correction only):

 1        160        D(I,J)               occ.-occ. block of relaxed
                                          density matrix (alpha)
 2        160        D(i,j)               occ.-occ. block of relaxed
                                          density matrix (beta)        ***
 3        160        D(A,B)               virt.-virt. block of relaxed
                                          density matrix (alpha)
 4        160        D(a,b)               virt.-virt. block of relaxed
                                          density matrix (beta)         ***
 5        160        D(A,I)               occ.-virt. block of relaxed
                                          density matrix (alpha)
 6        160        D(a,i)               occ.-virt. block of relaxed
                                          density matrix (beta)         ***
 7        160        D(A,I)               occ.-virt. block of unrelaxed
                                          density matrix (alpha)
 8        160        D(a,i)               occ.-virt. block of unrelaxed
                                          density matrix (beta)         ***

Intermediate matrix I(p,q) (correlation correction only):

 1        161        I(I,J)               occ.-occ. block of intermediate
                                          matrix (alpha)
 2        161        I(i,j)               occ.-occ. block of intermediate
                                          matrix (beta)                 ***
 3        161        I(A,B)               virt.-virt. block of intermediate
                                          matrix (alpha)
 4        161        I(a,b)               virt.-virt. block of intermediate
                                          matrix (beta)                 ***
 5        161        I(A,I)               virt.-occ. block of intermediate
                                          matrix (alpha)
 6        161        I(a,i)               virt.-occ. block of intermediate
                                          matrix (beta)                 ***

Gamma-intermediates created in the triple code for CCSD(T), ...

 1-NIRREP 162        G^trip(IJ,KA)         I<J ; K,A                    ***
 1-NIRREP 163        G^trip(ij,ka)         i<j ; k,a                    ***
 1-NIRREP 164        G^trip(Ij,Ak)         I,j ; A,k                    ***
 1-NIRREP 165        G^trip(Ij,Ka)         I,j ; K,a                 
 1-NIRREP 166        G^trip(AB,CI)         A<B ; C,I                    ***
 1-NIRREP 167        G^trip(ab,ci)         a<b ; c,i                    ***
 1-NIRREP 168        G^trip(Ab,Ic)         A,b ; I,c                    ***
 1-NIRREP 169        G^trip(Ab,Ci)         A,b ; C,i

 also used for CCSDT in ECC as T3*W Intermediates

 also used for CCSDT-1b and higher in ECC/LCC as T3*W contribution to Hbar

 also used for CCSDT-2 and higher in ECC/LCC as gamma intermediates

Derivatives of Overlap and Fock matrices and CPHF coefficients in MO basis:

 1-NIRREP 170        S(I*,J)^chi
 1-NIRREP 171        S(i*,j)^chi                                         ***

 Note that list 170 and 171 contain for ``perturbed canonical'' as wel
 as ``perturbed localized'' orbitals after module xcphf the CPHF
 coefficients U(I*,J) and U(i*,j), respectively.

 1-NIRREP 172        S(A*,B)^chi
 1-NIRREP 173        S(a*,b)^chi                                         ***
 1-NIRREP 174        S(A*,I)^chi
 1-NIRREP 175        S(a*,i)^chi                                         ***
 1-NIRREP 176        F(I*,J)^chi
 1-NIRREP 177        F(i*,j)^chi                                         ***
 1-NIRREP 178        F(A*,B)^chi
 1-NIRREP 179        F(a*,b)^chi                                         ***
 1-NIRREP 180        F(A*,I)^chi
 1-NIRREP 181        F(a*,i)^chi                                         ***

 Note that in CC/MBPT second derivative calculations, lists 176 to 179 
 (for ROHF also lists 180 to 181) contain the total derivatives of the
 fock matrices.

 1-NIRREP 182        U(A*,I)^chi
 1-NIRREP 183        U(a*,i)^chi                                         ***
 1-NIRREP 184        additional lists used in CPHF (RHF and UHF)  
 1-NIRREP 185        additional lists used in CPHF (UHF only)            ***

 Lists 184 and 185 contain Fock matrix derivative contributions without U(a,i)
 contribution for the occupied-occupied block.

 For the calculation of magnetic properties (conventional approach, in
 particular magnetazibilities) or electrical properties using xsdcc
 lists 186 to 188 contain    

 1-NIRREP 186        h(I*,J)^chi
 1-NIRREP 187        h(i*,j)^chi                                         ***
 1-NIRREP 188        h(A*,B)^chi
 1-NIRREP 189        h(a*,b)^chi                                         ***

 The derivatives h(A,I)^chi and h(a,i)^chi can be found on lists 180 and
 181. The reason behind that strategy is that for particular second derivative
 calculations we need h(P,Q)^chi and h(p,q)^chi, with the AOs independent
 of chi. While lists 176 to 179 are used to hold the total derivatives of
 the fock matrices including the orbital contributions, there is no such
 term within the virtual-occupied block (compare Brillouin's theorem) and
 186 to 189 hold the corresponding derivatives without the orbital con-
 tributions. 

 This applies only for magnetazibilities and polarizabilities calculations, 
 for chemical shifts, the two kind perturbations are different and the orbital
 term is never calculated for chi equals the nuclear magnetic moment perturba-
 tions.

 Note also that in case of the perturbed lists, the asterisks mark the 
 indices which represent complex conjugate orbitals. While this is of
 no importance for real perturbations, the accompanied sign change has
 to be taken into account for imaginary perturbations.

  1     190          L1AA                    A,I                     
  2     190          L1BB                    a,i                        ***

  1     191      G(MI) intermed. (M from T, I from L)    M,I
  2     191      G(mi) intermed.             m,i                        ***

  1     192      G(A,E) intermed. (E from T, A from L)   E,A 
  2     192      G(a,e) intermed.            e,a                        ***

 1-NIRREP 193      f(I,J)^chi
 1-NIRREP 194      f(i,j)^chi
 1-NIRREP 195      f(A,B)^chi
 1-NIRREP 196      f(a,b)^chi
 1-NIRREP 197      f(A,I)^chi
 1-NIRREP 198      f(a,i)^chi

 1-NIRREP 207         W(IA,JK)
 1-NIRREP 208         W(ia,jk)
 1-NIRREP 209         W(Ai,Jk)
 1-NIRREP 210         W(Ia,Jk)

 1-NIRREP 214         X(IJ,AB)
 1-NIRREP 215         X(ij,ab)
 1-NIRREP 216         X(Ij,Ab)

 Lists 211 to 213 are only used in SDQ-MBPT(4) second derivative
 calculations to save X(IJ,AB). IN SDQ-MBPT(4) gradient calculations,
 X(IJ,AB) is stored on lists 111 to 113 and then overwritten in
 GAMMA1 with the total two-particle density G(IJ,AB).

 1-NIRREP 227         W(AB,CI)
 1-NIRREP 228         W(ab,ci)
 1-NIRREP 229         W(Ab,Ic)
 1-NIRREP 230         W(Ab,Ci)

 1-NIRREP 231         <AB||CD>            A<B ; C<D                     ***
                      W(AB,CD)            A<B ; C<D DURING VLAMCC       ***
 1-NIRREP 232         <ab||cd>            a<b ; c<d                     ***
                      W(ab,cd)            a<b ; c<d DURING VLAMCC       ***
 1-NIRREP 233         <Ab|Cd>             A,b ; C,d  
                      <Ab|Cd>             A<=b; C,d single point RHF         
                      W(Ab,Cd)            A,b ; C,d DURING VLAMCC      

 1-NIRREP 244         dT(MUNU,IJ)/dx
 1-NIRREP 245         dT(munu,ij)/dx
 1-NIRREP 246         dT(MUnu,Ij)/dx

 1-NIRREP 254         H(MB,EJ) intermed.   E,M ; B,J              
 1-NIRREP 255         H(mb,ej) intermed.   e,m ; b,j                     ***
 1-NIRREP 256         H(Mb,Ej) intermed.   E,M ; b,j              
 1-NIRREP 257         H(mB,eJ) intermed.   e,m ; B,J                     ***
 1-NIRREP 258         H(mB,Ej) intermed.   E,m ; B,j              
 1-NIRREP 259         H(Mb,eJ) intermed.   e,M ; b,J                     ***

 1-NIRREP 261         dZ(MUNU,IJ)/dx       MU<NU;I<J                     ***
 1-NIRREP 262         dZ(munu,ij)/dx       mu<nu;i<j                     ***
 1-NIRREP 263         dZ(MUnu,Ij)/dx       Mu,nu;Ij

 Note that lists 244-246 and 261 to 263 are only used in AO based calculations
 (vcc and lambda:
 (sdcc:

 Note that lists 254 to 259 are only used for MBPT(4) and
 CC second derivative calculations.

 T3*W CONTRIBUTION IN CCSDT SECOND DERIVATIVES

 1-NIRREP 273
 1-NIRREP 274
 1-NIRREP 275
 1-NIRREP 276
 1-NIRREP 277
 1-NIRREP 278
 1-NIRREP 279
 1-NIRREP 280

 1-NIRREP 283
 1-NIRREP 284
 1-NIRREP 285
 1-NIRREP 286
 1-NIRREP 287
 1-NIRREP 288
 1-NIRREP 289
 1-NIRREP 290

 Note that lists 254 to 259 are resorted for GAMMA5 and GAMMA6
 as well as DGAMMA5 and DGAMMA6

 1-NIRREP 293
 1-NIRREP 294
 1-NIRREP 295
 1-NIRREP 296
 1-NIRREP 297
 1-NIRREP 298
 1-NIRREP 299
 1-NIRREP 300

Some additional lists are used in MBPT(2) second derivative calculations. These are:

 1-NIRREP 314       d<IJ||AB>/dx         A<B ; I<J,IPERT                *** 
 1-NIRREP 315       d<ij||ab>/dx         a<b ; i<j,IPERT                ***
 1-NIRREP 316       d<Ij||Ab>/dx         A,b ; I,j,IPERT

In analytic gradient calculations, the direct access files are reinitialized and restructured by the modules XANTI and XBCKTRN, which process and transform the two-particle reduced density matrix. These programs use the MOINTS and GAMLAM files in the following way

a) Lists used by ANTI


left right quantity symmetry storage index index type


   1     1-NSYM       G(PQ,rs)   AAAA      P<Q ; r<s                 
   2     1-NSYM       G(PQ,rs)   AABB      P<Q ; r<s                
   3     1-NSYM       G(PQ,rs)   ABAB      P,Q ; r,s               
   4     1-NSYM       G(PQ,rs)   ABCD      P,Q ; r,s              
   1    51-50+NSYM    G(pq,RS)   AAAA      p<q ; R<S                  ***
   2    51-50+NSYM    G(pq,RS)   AABB      p<q ; R<S                  ***
   3    51-50+NSYM    G(pq,RS)   ABAB      p,q ; R,S                  ***
   4    51-50+NSYM    G(pq,RS)   ABCD      p,q ; R,S                  ***
   6     1-NSYM       G(PQ,RS)   AAAA      P<Q ; R<S                  ***
   7     1-NSYM       G(PQ,RS)   AABB      P<Q ; R<S                  ***
   8     1-NSYM       G(PQ,RS)   ABAB      P,Q ; R,S                  ***
   9     1-NSYM       G(PQ,RS)   ABCD      P,Q ; R,S                  ***
   6    51-50+NSYM    G(pq,rs)   AAAA      p<q ; r<s                  ***
   7    51-50+NSYM    G(pq,rs)   AABB      p<q ; r<s                  ***
   8    51-50+NSYM    G(pq,rs)   ABAB      p,q ; r,s                  ***
   9    51-50+NSYM    G(pq,rs)   ABCD      p,q ; r,s                  ***

b) Lists used in BCKTRN and ABACUS

   1     1-NSYM       G(mu,nu,sigma,rho)  AAAA    mu < nu ; sigma < rho
   2     1-NSYM       G(mu,nu,sigma,rho)  AABB    mu < nu ; sigma < rho 
   3     1-NSYM       G(mu,nu,sigma,rho)  ABAB    mu,nu ; sigma,rho
   4     1-NSYM       G(mu,nu,sigma,rho)  ABCD    mu,nu ; sigma,rho       

In the above, the number of possible sublists defined by the right index of the list depends upon the symmetry type. Obviously, there are NIRREP different sublists for symmetry type 1 : 1,1,1,1;

 ....; NIRREP,NIRREP,NIRREP,NIRREP. For the second symmetry

type, there are NIRREP*(NIRREP-1)/2 different sublists, namely those for each possible pair of irreps with A < B (A faster running than B). We have thus 1,1,2,2; 1,1,3,3; 2,2,3,3; .... NIRREP-1,NIRREP-1,NIRREP, NIRREP. The symmetry type ABAB involves also NIRREP*(NIRREP-1)/2 sublists. They are however given in such a way that the main loop is over IRREP(AB), and the second, faster loop over B with A faster than B and IRREP(A) < IRREP(B). The fourth symmetry type, ABCD, is by far the most complicated. The main loop runs first over IRREP(CD)=IRREP(AB) with a subloop over IRREP(C) and IRREP(D) in such a way that C is faster than D and IRREP(C) < IRREP(D). For a given CD (note again IRREP(AB) = IRREP(CD)), the fastest loops runs over all possible combinations of IRREP(A) and IRREP(B) with A faster than B, IRREP(A) < IRREP(B) and also (IRREP(A), IRREP(B)) > IRREP(C),IRREP(D). The loop structure is set up for example in a very clear way in the routine GAMSRT which might be consulted for further questions regarding the set up of the loops and dealing with the AO-two-particle density matrix.

PART II. Extra lists used in excitation energy calculations


   J      I           Quantity           Storage Mode  
                                          ALL ; FOR 
                                               EACH

 1-NIRREP 434         C(IJ,AB)           A,J ; B,I  [INCREMENT]         ***
 1-NIRREP 435         C(ij,ab)           a,j ; b,i  [INCREMENT]         ***
 1-NIRREP 436         C(Ij,Ab)           b,j ; A,I  [INCREMENT]         ***
 1-NIRREP 437         C(Ij,Ab)           A,I ; b,j  [INCREMENT]   
 1-NIRREP 438         C(Ij,Ab)           b,I ; A,j  [INCREMENT]         ***
 1-NIRREP 439         C(Ij,Ab)           A,j ; b,I  [INCREMENT]
 1-NIRREP 444         C(AB,IJ)           A<B ; I<J                      ***
 1-NIRREP 445         C(ab,ij)           a<b ; i<j                      ***
 1-NIRREP 446         C(Ab,Ij)           A,b ; I,j
 1-NIRREP 448         D(IJ,AB)           A<B ; I<J
 1-NIRREP 449         D(ij,ab)           a<b ; i<j                      ***
 1-NIRREP 450         D(Ij,Ab)           A,b ; I,j      
 1-NIRREP 461         C(AB,IJ)           A<B ; I<J  [INCREMENT]         ***
 1-NIRREP 462         C(ab,ij)           a<b ; i<j  [INCREMENT]         ***
 1-NIRREP 463         C(Ab,Ij)           A,b ; I,j  [INCREMENT]
 1-NRECS  470      C vectors (one/record)                 
 1-NRECS  471      HC vectors (one/record)                 
 1        472      Converged right C vector (on one record)
 2        472      Converged left C vector (on one record)
 1        490         C1(AI)             AI  ;       
 2        490         C1(ai)             ai  ;       
 3        490         C1(AI)             AI  ;      [INCREMENT]         
 4        490         C1(ai)             ai  ;      [INCREMENT]         ***
 1        491          X(IJ)             IJ  ; 
 2        491          X(ij)             ij  ;                          ***
 1        492          X(AB)             AB  ;
 2        492          X(ab)             ab  ;                          ***
 1        493          X(AI)             AB  ;
 2        493          X(ai)             ab  ;                          ***
 1-NIRREP  94          TDA eigenvectors (one/record)                   
 1-NIRREP  95          TDA eigenvalues (one/record)                   

PART IIIa. Extra lists used in EOMIP calculations

  H(ai,bj) = -L(mi,b)*r(mj,a)
  H2( i,aj) = L(im,e)*T(jm,ea)

During the calculation of the final state density matrices, the right and left-hand vectors are stored as follows

                       RIGHT              LEFT

Converged vector 461-464 444-447 Resorted vector 454-459 434-439 singles 490;3,4 490;1,2

lists 461-464 ho


   J      I           Quantity           Storage Mode  
                                          ALL ; FOR 
                                               EACH

 1-NIRREP  54         H(AI,BJ)           A,J ; B,I            
 1-NIRREP  55         H(ai,bj)           a,j ; b,i
 1-NIRREP  56         H(Ai,bJ)           A,J ; b,i
 1-NIRREP  57         H(aI,Bj)           a,j ; B,I
 1-NIRREP  58         H(Ai,Bj)           A,j ; B,i
 1-NIRREP  59         H(aI,bJ)           a,J ; b,I

 1        190      ZETA(AI)                 AI 
 2        190      ZETA(ai)                 ai             *** 
 1-NIRREP  61      ZETA(AB,IJ)           A<B ; I<J         ***
 1-NIRREP  62      ZETA(ab,ij)           a<b ; i<j         ***
 1-NIRREP  63      ZETA(Ab,Ij)           A,b ; I,j     

 3         90        XI(AI)                 AI  
 4         90        XI(ai)                 ai             ***
 1-NIRREP 144        XI(AB,IJ)           A<B ; I<J         ***
 1-NIRREP 145        XI(ab,ij)           a<b ; i<j         ***
 1-NIRREP 146        XI(Ab,Ij)           A,b ; I,j

 1        160         D(IJ)                 IJ
 2        160         D(ij)                 ij
 3        160         D(AB)                 AB
 4        160         D(ab)                 ab
 5        160         D(AI)                 AI
 6        160         D(ai)                 ai

    used in CALCXIEA for H-intermediate

 1-NIRREP 174         H(AI,BJ)           A,J ; B,I            
 1-NIRREP 175         H(ai,bj)           a,j ; b,i
 1-NIRREP 176         H(Ai,bJ)           A,J ; b,i
 1-NIRREP 177         H(aI,Bj)           a,j ; B,I
 1-NIRREP 178         H(Ai,Bj)           A,j ; B,i
 1-NIRREP 179         H(aI,bJ)           a,J ; b,I


 3        190      R2*L1 => D(AI)           AI 
 4        190      R2*L1 => D(ai)           ai

 1        193      Y(A,I) = R2*L1           AI
 2        193      Y(a,i) = R2*L1           ai              ***

 1-NIRREP 414        H2( I,AJ)             I ; A,J
 1-NIRREP 415        H2( i,aj)             i ; a,j
 1-NIRREP 416        H2( I,aj)             I ; a,j
 1-NIRREP 417        H2( i,AJ)             i ; A,J
 1-NIRREP 418        H2( i,Aj)             i ; A,j
 1-NIRREP 419        H2( I,aJ)             I ; a,J
 1-NIRREP 444         C(IJ,A )           I<J ; A
 1-NIRREP 445         C(ij,a )           i<j ; a
 1-NIRREP 446         C(Ij,A )           I,j ; A
 1-NIRREP 447         C(iJ,a )           J,i ; a
 1-NIRREP 461         C(IJ,A )           I<J ; A [increment]
 1-NIRREP 462         C(ij,a )           i<j ; a [increment]
 1-NIRREP 463         C(Ij,A )           I,j ; A [increment]
 1-NIRREP 464         C(iJ,a )           J,i ; a [increment]
 1-NIRREP 434         C(IJ,A )             J ; A,I
 1-NIRREP 435         C(ij,a )             j ; a,i
 1-NIRREP 436         C(Ij,A )             j ; A,I
 1-NIRREP 437         C(iJ,a )             J ; a,i
 1-NIRREP 438         C(Ij,A )             I ; A,j
 1-NIRREP 439         C(iJ,a )             i ; a,J
 1-NIRREP 454         X(IJ,A )             J ; A,I
 1-NIRREP 455         X(ij,a )             j ; a,i
 1-NIRREP 456         X(Ij,A )             j ; A,I
 1-NIRREP 457         X(iJ,a )             J ; a,i
 1-NIRREP 458         X(Ij,A )             I ; A,j
 1-NIRREP 459         X(iJ,a )             i ; a,J

 1-ISIDE  470                              extrapolation vectors
 1-ISIDE  471                              extrapolation vectors
 1-ISIDE  472          

 1        490         C(I)                 I
 2        490         C(i)                 i
 3        490         C(I)                 I [increment]
 4        490         C(i)                 i [increment]
 1        495         L2*R2 -> FDA         A
 2        495         L2*R2 -> FDA         a
 3        495         L2*T2 -> FDA         A
 4        495         L2*T2 -> FDA         a

PART IIIb. Extra lists used in EOMEA calculations

   H(ai,bj)  =  -L(i,be)*r(j,ae)
   H2(a,bi)  = L(m,ea)*T(im,eb)

During the calculation of the final state density matrices, the right and left-hand vectors are stored as follows

                       RIGHT              LEFT

Converged vector 461-464 444-446 Resorted vector 454-459 434-439 singles 494;3,4 494;1,2

lists 461-464 ho


   J      I           Quantity           Storage Mode  
                                          ALL ; FOR 
                                               EACH

 1-NIRREP  54         H(AI,BJ)           A,J ; B,I            
 1-NIRREP  55         H(ai,bj)           a,j ; b,i
 1-NIRREP  56         H(Ai,bJ)           A,J ; b,i
 1-NIRREP  57         H(aI,Bj)           a,j ; B,I
 1-NIRREP  58         H(Ai,Bj)           A,j ; B,i
 1-NIRREP  59         H(aI,bJ)           a,J ; b,I
 1-NIRREP  61      ZETA(AB,IJ)           A<B ; I<J
 1-NIRREP  62      ZETA(ab,ij)           a<b ; i<j
 1-NIRREP  63      ZETA(Ab,Ij)           A,b ; I,j
 3         90        XI(AI)                 AI  
 4         90        XI(ai)                 ai
 3         91         G(M,N) = L2*R2        MN
 4         91         G(m,n) = L2*R2        mn                ***
 3         92         G(E,F) = R2*L2        EF 
 4         92         G(e,f) = R2*L2        ef                ***
 1-NIRREP 144        XI(AB,IJ)           A<B ; I<J
 1-NIRREP 145        XI(ab,ij)           a<b ; i<j
 1-NIRREP 146        XI(Ab,Ij)           A,b ; I,j
 1        160         D(IJ)                 IJ
 2        160         D(ij)                 ij
 3        160         D(AB)                 AB
 4        160         D(ab)                 ab
 5        160         D(AI)                 AI
 6        160         D(ai)                 ai
 1        190      ZETA(AI)                 AI 
 2        190      ZETA(ai)                 ai 
 3        190      R2*L1 => D(AI)           AI 
 4        190      R2*L1 => D(ai)           ai 
 1        193      Y(A,I) = R2*L1           AI
 2        193      Y(a,i) = R2*L1           ai              ***
 1-NIRREP 414        H2( I,AJ)             I ; A,J
 1-NIRREP 415        H2( i,aj)             i ; a,j
 1-NIRREP 416        H2( I,aj)             I ; a,j
 1-NIRREP 417        H2( i,AJ)             i ; A,J
 1-NIRREP 418        H2( i,Aj)             i ; A,j
 1-NIRREP 419        H2( I,aJ)             I ; a,J

 1-NIRREP 444         C(AB,I )           A<B ; I                   ****
 1-NIRREP 445         C(ab,i )           a<b ; i                   ****
 1-NIRREP 446         C(Ab,I )           A,b ; I                   **** 
 1-NIRREP 447         C(bA,i )           A,b ; i

 1-NIRREP 461         C(AB,I )           A<B ; I [increment]
 1-NIRREP 462         C(ab,i )           a<b ; i [increment]
 1-NIRREP 463         C(Ab,I )           A,b ; I [increment]
 1-NIRREP 464         C(bA,i )           A,b ; i [increment]

 1-NIRREP 434         C(AB,I )             B ; I,A                 ****
 1-NIRREP 435         C(ab,i )             b ; i,a                 ****
 1-NIRREP 436         C(Ab,I )             b ; I,A                 ****
 1-NIRREP 437         C(bA,i )             A ; i,b
 1-NIRREP 438         C(Ab,I )             A ; I,b                 ****
 1-NIRREP 439         C(bA,i )             b ; i,A

 1-NIRREP 454         X(ab,i )             A ; B,I
 1-NIRREP 455         X(ab,i )             a ; b,i
 1-NIRREP 456         X(Ab,I )             e ; B,I
 1-NIRREP 457         X(bA,i )             E ; b,i
 1-NIRREP 458         X(Ab,I )             E ; b,I 
 1-NIRREP 459         X(bA,i )             e ; B,i

 1-ISIDE  470                              extrapolation vectors
 1-ISIDE  471                              extrapolation vectors
 1-ISIDE  472          

 1        494         C(A)                 A
 2        494         C(a)                 a
 3        494         C(A)                 I [increment]
 4        494         C(a)                 i [increment]
 1        495         R2*LAMBDA2    -> FDA I 
 2        495         r2*lamnba2    -> FDA i
 3        495         L2*T2         -> FDA I 
 4        495         l2*t2         -> FDA i
 5        495         R2*INTEGRALS  -> FDA I 
 6        495         r2*integrals  -> FDA i

PART IV. extra lists used in CC/MBPT second derivative calculations


   J      I           Quantity           Storage Mode  
                                          ALL ; FOR 
                                               EACH

 1-NIRREP 311        d<i*j*||kl>/dx         I<J ; K<L                    ***
 1-NIRREP 312        d<I*J*||KL>/dx         i<j ; k<l                    ***
 1-NIRREP 313        d<I*j*|Kl>/dx          I,j ; K,l

 1-NIRREP 307        d<I*J*||KA>/dx         I<J ; K,A                    ***
 1-NIRREP 308        d<i*j*||ka>/dx         i<j ; k,a                    ***
 1-NIRREP 309        d<I*j*|Ak>/dx          I,j ; A,k                    ***
 1-NIRREP 310        d<I*j*|Ka>/dx          I,j ; K,a

 1-NIRREP 314        d<A*B*||IJ>/dx         A<B ; I<J                    ***
 1-NIRREP 315        d<a*b*||ij>/dx         a<b ; i<j                    ***
 1-NIRREP 316        d<A*b*|Ij>/dx          A,b ; I,j
 1-NIRREP 317        d<I*b*|Aj>/dx          b,j ; A,I
 1-NIRREP 318        d<A*j*|Ib>/dx          A,I ; b,j
 1-NIRREP 319        d<a*J*||iB>/dx
 1-NIRREP 320        d<ab||ij>/dx
 1-NIRREP 321        d<A*j*|Ib>/dx          A,j ; b,I
 1-NIRREP 322        d<Ab|Ij>/dx

 1-NIRREP 323        d<I*A*||JB>/dx         A,I , B,J                         ***
 1-NIRREP 323        d<I*A*||JB>/dx         A,J , B,I  (in dvcc after st2324) ***  
 1-NIRREP 324        d<i*a*||jb>/dx         a,i , b,j                         ***
 1-NIRREP 324        d<i*a*||jb>/dx         a,j , b,i  (in dvcc after st2324) ***
 1-NIRREP 325        d<i*A*|jB>/dx          A,i ; B,j
 1-NIRREP 325        d<i*A*|jB>/dx          A,j ; B,i (in dvcc after res25)
 1-NIRREP 326        d<a*I*|bJ>/dx          a,I ; b,j                       ***
 1-NIRREP 326        d<a*I*|bJ>/dx          a,J ; b,I (in dvcc after res25) ***

 1-NIRREP 327        d<A*B*||CI>/dx         A<B ; C,I                       ***
 1-NIRREP 328        d<a*b*||ci>/dx         a<b ; c,i                       ***
 1-NIRREP 329        d<A*b*|Ic>/dx          A,b ; I,c                       ***
 1-NIRREP 330        d<A*b*|Ci>/dx          A,b ; C,i

 1-NIRREP 331       d<A*B*||CD>/dx
 1-NIRREP 332       d<a*b*||cd>/dx
 1-NIRREP 333       d<A*b*|Cd>/dx

 1-NIRREP 337       d<A*b*||Ij>/dx          b,j ; A,I  (only for imaginary perturbations) ***
 1-NIRREP 338       d<A*b*||Ij>/dx          A,I ; b,j  (only for imaginary perturbations)
 1-NIRREP 339       d<A*B*||IJ>/dx          A,I ; B,J  (only for imaginary perturbations) ***
 1-NIRREP 340       d<a*b*||ij>/dx          a,i ; b,j  (only for imaginary perturbations) ***
 1-NIRREP 341       d<A*b*||Ij>/dx          A,j ; b,I  (only for imaginary perturbations)
 1-NIRREP 342       d<A*b*||Ij>/dx          b,I , A,j  (only for imaginary perturbations) ***

 the following lists are only required for CCSDT-1b and higher:

 1-NIRREP 342       dW(IJ,kA)/dx            I,J ; K,A       ***
 1-NIRREP 343       dW(ij,ka)/dx            i,j ; k,a       ***
 1-NIRREP 344       dW(Ij,Ak)/dx            I,j ; A,k       ***
 1-NIRREP 345       dW(Ij,Ka)/dx            I,j ; K,a       

 1-NIRREP 346       dW(AB,CI)/dx            A,B ; C,I       ***
 1-NIRREP 347       dW(ab,ci)/dx            a,b ; c,i       ***
 1-NIRREP 348       dW(Ab,Ic)/dx            A,b ; I,c       ***
 1-NIRREP 349       dW(Ab,Ci)/dx            A,b ; C,i       

 general intermediate lists (not needed for MBPT(2) AND MBPT(3)):

 1-NIRREP 351       dW(M*N*,IJ)/dx          M<N ; I<J                     ***
 1-NIRREP 352       dW(m*n*,ij)/dx          m<n ; i<j                     ***
 1-NIRREP 353       dW(M*n*,Ij)/dx          M,n ; I,j
 1-NIRREP 354       dW(MB,E*J*)/dx          E,M ; B,J                     ***
 1-NIRREP 355       dW(mb,e*j*)/dx          e,m ; b,j                     ***
 1-NIRREP 356       dW(Mb,E*j*)/dx          E,M ; b,j
 1-NIRREP 357       dW(mB,e*J*)/dx          e,m ; B,J                     ***
 1-NIRREP 358       dW(mB,E*j*)/dx          E,m ; B,j
 1-NIRREP 359       dW(Mb,e*J*)/dx          e,M ; b,J                     ***

 Note that lists 354 to 358 contain first the so-called tilde intermediates
 and only after solution of the perturbed CC equations the full Hbar elements
 corresponding to this intermediate type. Also, take care of the proper
 sign in case of imaginary perturbations.

 1-NIRREP 364      dH(MB,EJ)/dx intermed.  E,M ; B,J              
 1-NIRREP 365      dH(mb,ej)/dx intermed.  e,m ; b,j                     ***
 1-NIRREP 366      dH(Mb,Ej)/dx intermed.  E,M ; b,j              
 1-NIRREP 367      dH(mB,eJ)/dx intermed.  e,m ; B,J                     ***
 1-NIRREP 368      dH(mB,Ej)/dx intermed.  E,m ; B,j              
 1-NIRREP 369      dH(Mb,eJ)/dx intermed.  e,M ; b,J                     ***

 Note that lists 364 to 369 contain the derivatives of 
 the H intermediates used in MBPT(4) and CC second derivative
 calculations.

 1-NIRREP 374      dWtildetilde(MB,EJ)/dx intermed.  E,M ; B,J     
 1-NIRREP 375      dWtildetilde(mb,ej)/dx intermed.  e,m ; b,j              ***
 1-NIRREP 376      dWtildetilde(Mb,Ej)/dx intermed.  E,M ; b,j      
 1-NIRREP 377      dWtildetilde(mB,eJ)/dx intermed.  e,m ; B,J              ***
 1-NIRREP 378      dWtildetilde(mB,Ej)/dx intermed.  E,m ; B,j        
 1-NIRREP 379      dWtildetilde(Mb,eJ)/dx intermed.  e,M ; b,J              ***

 Lists 374 to 375 are used in the construction of the derivatives
 of W(ab,ci) and W(ia,mn) in CCSD second derivatives

 1-NIRREP 381
 1-NIRREP 382
 1-NIRREP 383

 1-NIRREP 384
 1-NIRREP 385
 1-NIRREP 386

 1-NIRREP 391
 1-NIRREP 392
 1-NIRREP 393

 1-NIRREP 394
 1-NIRREP 395
 1-NIRREP 396

 Lists 381 to 386 are used for the AO based algorithm in SDCC
 Lists 391 to 396 are used for the AO based algorithm in SDCC

 1-NIRREP 411       d G(IJ,K*L*)/dx           I<J ; K<L                     ***
 1-NIRREP 412       d G(ij,k*l*)/dx           i<j ; k<l                     ***
 1-NIRREP 413       d G(Ij,K*l*)/dx           I,j ; K,l

 1-NIRREP 407       d G(IJ,K*A*)/dx           I<J ; K,A                     ***
 1-NIRREP 408       d G(ij,k*a*)/dx           i<j ; k,a                     ***
 1-NIRREP 409       d G(Ij,A*k*)/dx           I,j ; A,k                     ***
 1-NIRREP 410       d G(Ij,K*a*)/dx           I,j ; K,a   

 Note that in SDQ-MBPT(4) second derivative calculations, lists 413 to 
 416 contain first the dX(IJ,AB)/dx contribution to G(IJ,AB) which
 is used in DDENSOO and DDENSVV to construct the total one-particle
 density matrix derivative and later overwritten with dG(IJ,AB)/dx.

 1-NIRREP 414       d G(IJ,A*B*)/dx             A<B ; I<J              ***
 1-NIRREP 415       d G(ij,a*b*)/dx             a<b ; i<j              ***
 1-NIRREP 416       d G(Ij,A*b*)/dx             A,b ; I,j 

 1-NIRREP 417       d G(iA,bJ)/dx             b,j ; A,I                ***
   resorted in SDCC  to                       b,I ; A,j                ***
 1-NIRREP 418       d G(Ia,Bj)/dx             B,J ; a,i
   resorted in SDCC to                        B,i ; a,J
 1-NIRREP 423       d G(IA,JB)/dx             B,I ; A,J
   resorted in SDCC to                        B,J ; A,I                   
 1-NIRREP 424       d G(ia,jb)/dx             b,i ; a,j                 ***
   resorted in SDCC to                        b,j ; a,i                 ***
 1-NIRREP 425       d G(iA,jB)/dx             B,i ; A,j
   resorted in SDCC to                        B,j ; A,i
 1-NIRREP 426       d G(Ia,Jb)/dx             b,I ; a,J                 ***
   resorted in SDCC to                        b,J ; a,I                 ***

 1-NIRREP 427       d G(AB,C*I*)/dx           A<B ; C,I                 ***
 1-NIRREP 428       d G(ab,c*i*)/dx           a<b ; c,i                 ***
 1-NIRREP 429       d G(Ab,I*c*)/dx           A,b ; I,c                 ***
 1-NIRREP 430       d G(Ab,C*i*)/dx           A,b ; C,i

 1-NIRREP 431       d G(AB,C*D*)/dx
 1-NIRREP 432       d G(ab,c*d*)/dx
 1-NIRREP 433       d G(Ab,C*d*)/dx

 1-NIRREP 434       dT2(IJ,A*B*)/dx
 1-NIRREP 435       dT2(ij,a*b*)/dx
 1-NIRREP 436       dT2(Ij,A*b*)/dx
 1-NIRREP 437       dT2(Ij,A*b*)/dx
 1-NIRREP 438       dT2(Ij,A*b*)/dx
 1-NIRREP 439       dT2(Ij,A*b*)/dx

  (Note that in MBPT(3) and MBPT(4) calculations, these list always 
   contain only the resorted first-order T2 amplitudes)

 1-NIRREP 440       dT2(IJ,A*B*)/dx increment
 1-NIRREP 441       dT2(ij,a*b*)/dx increment 
 1-NIRREP 442       dT2(Ij,A*b*)/dx increment
 1-NIRREP 443       dT2(Ij,A*b*)/dx increment

 1-NIRREP 444       dT2(IJ,A*B*)/dx           A<B ; I<J                ***
 1-NIRREP 445       dT2(ij,a*b*)/dx           a<b ; i<j                ***
 1-NIRREP 446       dT2(Ij,A*b*)/dx           A,b ; I,j            

 (Note that lists 444 to 446 contain in MBPT(3) and MBPT(4) second
  derivative calculations the derivatives of the first-order amplitudes
  only)

 1-NIRREP 448      D(IJ,AB) (total symmetry IRREPX)    A<B ; I<j    ***
 1-NIRREP 449      D(ij,ab) (total symmetry IRREPX)    a<b ; i<j    ***
 1-NIRREP 450      D(Ij,Ab) (total symmetry IRREPX)    A,b ; I,j

        9 448      D(I,A)   (total symmetry IRREPX)     A  ,  I
        9 449      D(i,a)   (total symmetry IRREPX)     a  ,  i     ****

 Note that for SDQ-MBPT(4) calculations, lists 451-453 contain

 1-NIRREP 451       dV(M*N*,IJ)/dx                     M<N ; I<J    ***
 1-NIRREP 452       dV(m*n*,ij)/dx                     m<n ; i<j    ***
 1-NIRREP 453       dV(M*n*,Ij)/dx                     M,n ; I,j

 Note that for CC calculations, lists 451-453 contain

 1-NIRREP 451       dV(I*J*,MN)/dx                     M<N ; I<J    ***
 1-NIRREP 452       dV(i*j*,MN)/dx                     m<n ; i<j    ***
 1-NIRREP 453       dV(I*j*,MN)/dx                     M,n ; I,j

 For a detailed definition of these quantities in the various
 parts of the code, see the comments in the source text and
 consults the theory of CC second derivatives

 1-NIRREP 454       dT2(IJ,A*B*)/dx            
 1-NIRREP 455       dT2(ij,a*b*)/dx
 1-NIRREP 456       dT2(Ij,A*b*)/dx
 1-NIRREP 457       dT2(Ij,A*b*)/dx
 1-NIRREP 458       dT2(Ij,A*b*)/dx
 1-NIRREP 459       dT2(Ij,A*b*)/dx

 (Only used for MBPT(4) second derivative calculations, lists 454 to 459
  contain resorted second-order amplitudes)

 1-NIRREP 461      dT2(IJ,A*B*)/dx increment          A<B ; I<J     ***
 1-NIRREP 462      dT2(ij,a*b*)/dx increment          a<b ; i<j     ***
 1-NIRREP 463      dT2(Ij,A*b*)/dx increment          A,b ; I,j

 (Note that lists 461 to 463 contain in MBPT(3) and MBPT(4) second derivative
  calculations the derivatives of the full T2 amplitudes, i.e., the
  derivatives of the sum of first- and second-order amplitudes)
  For CC calculation, 461 to 463 contain the increments during the CC
  or Lambda iterations)

          470      Vectors used for DIIS extrapolation

 1-NIRREP 471      dT2(IJ,A*B*)/dx                    A<B ; I<J     ***
 1-NIRREP 472      dT2(ij,a*b*)/dx                    a<b ; i<j     ***
 1-NIRREP 473      dT2(Ij,A*b*)/dx                    A,b ; I,j 

 (Only used in MBPT(4) calculations, contain derivatives of the sum
  of (partial) third-order T2 amplitudes)

 (Note that for CC calculations, lists 471 to 473 contain the constant
  term for the doubles equations)

 1-NIRREP 474      dL2(I*J*,AB)/dx                    A<B ; I<J     ***
 1-NIRREP 475      dL2(i*j*,ab)/dx                    a<b ; i<j     ***
 1-NIRREP 476      dL2(I*j*,Ab)/dx                    A,b ; I,j 

  for localized MBPT methods

 1-NIRREP 480      dR(A*B*,IJ)/dx                     A<B ; I<J     ***
 1-NIRREP 481      dR(a*b*,ij)/dx                     a<b ; i<j     ***
 1-NIRREP 482      dR(A*b*,Ij)/dx                     A,b ; I,j

 1-NIRREP 484       dL2(I*J*,AB)/dx
 1-NIRREP 485       dL2(i*j*,ab)/dx
 1-NIRREP 486       dL2(I*j*,Ab)/dx
 1-NIRREP 487       dL2(I*j*,Ab)/dx
 1-NIRREP 488       dL2(I*j*,Ab)/dx
 1-NIRREP 489       dL2(I*j*,Ab)/dx

 1        490     dT1(I,A*)/dx
 2        490     dT1(i,a*)/dx
 3        490     dT1(I,A*)/dx (CC iterations) or dL1(I*,A)/dx increment
 4        490     dT1(I,A*)/dx (CC iterations) or dL1(i*,a)/dx increment

 5        490     Z(A*,I) (CC iterations) or Z(I*,A) (Lambda iterations)
 6        490     Z(a*,i) (CC iterations) or Z(i*,a) (Lambda iterations)

 7        490     dL(I,A*)/dx  
 8        490     dL(i,a*)/dx

 9        490

10 490

 1        491     dF(M*I)/dx intermed.         M,I
 2        491     dF(m*i)/dx intermed.         m,i                        ***

 1        492     dF(EA*)/dx intermed.         E,A
 2        492     dF(ea*)/dx intermed.         e,a                        ***

 1        493     dF(AI)/dx intermed.         A,I
 2        493     dF(ai)/dx intermed.         a,i                        ***

Note that the lists 491 - 493 contain after solution of the perturbed CC equations the derivatives of the one-particle part of Hbar. During the solution of the perturbed CC equations, these lists contain the F^chi derivatives as required for the perturbed CC equations (for a definition of these intermediates, see the appropriate literature)

 1        494     dG(M*I)/dx intermed.         M,I          
 2        494     dG(m*i)/dx intermed.         m,i                        *** 

 1        495     dG(EA*)/dx intermed.         E,A          
 2        495     dG(EA*)/dx intermed.         e,a                        ***

 1        498     dI(V,O)/dx                   A,I
 2        498     dI(V,0)/dx                   a,i                        ***

Lists 498 are used in AO based calculations to store some intermediate quantities (AO based contribution of dI(V,O)/dx

Note that the exact definition of dG/dx might be different in different parts of the code. Please consult the detailed description of the source code. The same applies also to lists 451 to 453 which holds the derivatives of the V(mn,ij) intermediates.

Note that the asterisks mark in case of the pertrbed lists those indices which represent complex conjuagte orbitals. While this is of no relevance for real perturbations, this is important in calculations with imaginary perturbations, e.g. NMR chemical shift calculations.

Note that the one-particle density matrix elements are stored for imaginary perturbations as dD(i,j*)/dx, dD(a,b*)/dx, and dD(a,i*)/dx.

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CFOUR is partially supported by the U.S. National Science Foundation.