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Orbital Numbering In The Output

There are many places in the output where information about the wavefunction is written, especially in terms of the molecular orbitals that are used in the reference wavefunction. In addition, there are some input options where orbital numbering is required. Unfortunately, there is more than one way that orbitals are indexed in the output (as well as the input). While not optimal, this reflects various convenient schemes for coding, and will not be changed in the immediate future. This section of the manual provides a guide for interpreting the outputting of orbital indices.

The most common scheme in the code is one in which orbitals are numbered as follows. Orbital numbers 1-n are the n occupied orbitals used in the calculation, and orbitals n+1 through N are the virtual orbitals. Within each of these orbital subsets, the orbitals are ordered by symmetry species, and within that construct by the ordering of energy (lowest to highest). That is:

Orbital NumbersInterpretation
1 thru n1Occupied orbitals of symmetry 1
n1+1 thru n1+n2Occupied orbitals of symmetry 2
......
n+1 thru n+N1Virtual orbitals of symmetry 1
......

A table which, quite explicitly, provides the mapping between the SCF (or other single-determinant) orbitals and their numbers as used in the post-SCF codes (coupled-cluster and MBPT energy evaluations, associated gradient calculations and EOM-CC calculations) appears just after the SCF executes, and during the process of the transformation of two-electron integrals from the atomic to the molecular orbitals basis sets. It looks something like this:


  Index      Eigenvalue    Symmetry    Index      Eigenvalue    Symmetry

     1       -20.5528864        1        13         3.8425967        1 
     2        -1.3350747        1        14         1.1996751        2 
     3        -0.5700203        1        15         1.6604890        2 
     4        -0.4935002        2        16         3.2913604        2 
     5        -0.6912694        3        17         0.2554905        3 
     6         0.1839348        1        18         0.7768297        3 
     7         0.8581087        1        19         1.2561528        3 
     8         1.1660212        1        20         1.9409157        3 
     9         1.4241265        1        21         2.4312166        3 
    10         1.8638805        1        22         4.1523172        3 
    11         2.4777109        1        23         1.4821853        4 
    12         3.5090481        1        24         3.3235555        4 

where you might note the correspondence between this scheme and that discussed above. Thus, in the section of the output where the largest amplitudes from the CCSD calculation are printed, such as:

   Largest T2 amplitudes for spin case AB:
       _       _                 _       _                 _       _
   i   j   a   b             i   j   a   b             i   j   a   b


[ 4 4 14 14]-0.04719 [ 3 3 8 8]-0.03196 [ 5 5 18 18]-0.03030
[ 4 3 14 8] 0.02886 [ 3 4 8 14] 0.02886 [ 5 5 17 17]-0.02715
[ 5 4 19 14] 0.02342 [ 4 5 14 19] 0.02342 [ 5 4 17 14]-0.02330
[ 4 5 14 17]-0.02330 [ 5 5 7 7]-0.02280 [ 3 3 18 18]-0.02190
[ 5 5 19 19]-0.02169 [ 5 3 17 8] 0.01874 [ 3 5 8 17] 0.01874
-----------------------------------------------------------------------------
Norm of T2AB vector ( 2459 symmetry allowed elements): 0.1947459830.
-----------------------------------------------------------------------------

from which we see that the largest amplitude corresponds to a double excitation from the occupied orbital of symmetry to the lowest virtual orbital of symmetry 2.

Note that in UHF calculations, you must be careful to discriminate between alpha and beta orbitals. In such calculations, you will see two different lists of orbitals right after the SCF calculation:


                         * Spin case alpha *

  Index      Eigenvalue    Symmetry    Index      Eigenvalue    Symmetry

     1       -11.3167060        1        19         3.3452450        1
     2       -11.2569049        1        20        23.6887911        1
     3        -1.0430284        1        21        24.4813631        1
     4        -0.7314635        1        22         0.1665982        2
     5        -0.6058037        1        23         0.4482190        2
     6        -0.4488829        2        24         0.6153313        2
     7        -0.4488829        3        25         1.3236087        2
     8         0.2490546        1        26         1.8075384        2
     9         0.3463969        1        27         2.6096370        2
    10         0.4536009        1        28         0.1665982        3
    11         0.6184240        1        29         0.4482190        3
    12         0.9669227        1        30         0.6153313        3
    13         1.0772308        1        31         1.3236087        3
    14         1.4316622        1        32         1.8075384        3
    15         1.4606961        1        33         2.6096370        3
    16         1.8802091        1        34         1.4606961        4
    17         2.1470292        1        35         1.8802091        4
    18         2.5650050        1


                         * Spin case beta *

  Index      Eigenvalue    Symmetry    Index      Eigenvalue    Symmetry

     1       -11.2801010        1        19         3.3477578        1
     2       -11.2558306        1        20        23.7158973        1
     3        -1.0109162        1        21        24.4890464        1
     4        -0.7135602        1        22         0.2043852        2
     5        -0.4226688        2        23         0.4551253        2
     6        -0.4226688        3        24         0.6363880        2
     7         0.0370763        1        25         1.3406480        2
     8         0.2494724        1        26         1.8608878        2
     9         0.3773488        1        27         2.6257682        2
    10         0.4736252        1        28         0.2043852        3
    11         0.6638077        1        29         0.4551253        3
    12         1.0141228        1        30         0.6363880        3
    13         1.1240509        1        31         1.3406480        3
    14         1.4732550        1        32         1.8608878        3
    15         1.4751578        1        33         2.6257682        3
    16         1.8980859        1        34         1.4751578        4
    17         2.1879023        1        35         1.8980859        4
    18         2.5963531        1

and you need to use the appropriate spin when determining the identity of an amplitude or an orbital.

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