Dear Kris Harris,

Negative SFO contributions:
see ADFUsersGuide Chapter 3.2, paragraph about SFO populations
http://www.scm.com/Doc/Doc2005.01/ADF/ADFUsersGuide/page228.html
In the section that prints the SFO populations of (selected) MOs you may
occasionally find, for some SFOs in some MOs, /negative/ SFO
contributions. This may seem unphysical and hence suspicious, but it is
'only' a result of the Mulliken-type analysis method that underlies the
computation of the SFO contributions. See the section below that
discusses the output file. Likewise for larger-than-100% contributions:
don't worry too much, these numbers may be correct (mathematically,
given the Mulliken population formulas).

Some explanation how to read the ADF output:
Example H2, DZ basis, symmetry nosym.

In the create run the an atomic DFT calculation of H is performed.
In this case it calculates the 1s and 2s orbital in the basis of two
Slater type functions.
The 1s orbital on H_1 is a linear combination of Slater type functions
on H_1,
this combination is not printed in the output.
The 2s orbital on H_1 is also a linear combination of Slater type
functions on H_1.
The 1s orbital and 2s orbital on H_1 are orthogonal.
The two Slater type functions on H_1 are not orthogonal.

What you need from the ADF output:

 =======
 S F O s *** (Symmetrized Fragment Orbitals) ***
 =======

 SFOs are linear combinations of (valence) Fragment Orbitals (FOs), such that the SFOs transform as the
 irreducible representations of the (molecular) symmetry group. Each SFO is therefore characterized by
 an irrep of the molecule and by a few (or only one) generating FOs.
 The SFOs constitute a symmetry-adapted basis for the Fock matrix. The MO eigenvector coefficients in
 this basis provide a direct interpretation of the MOs in terms of Frontier Orbital Theory.

 The SFOs are combined with auxiliary Core Functions (CFs) to ensure orthogonalization on the (frozen)
 Core Orbitals (COs). The Core-orthogonalized SFOs (CSFOs) constitute the true Fock basis.

                                       === A ===
 Nr. of SFOs : 4
 Cartesian basis functions that participate in this irrep (total number = 4) :
      1 2 3 4

    SFO (index Fragment Generating Expansion in Fragment Orbitals
  indx incl.CFs) Occup Orb.Energy FragmentType Coeff. Orbital on Fragment
 --------------------------------------------------------------------------------------
     1 1 1.000 -0.235 au H 1.00 1 S 1
                        ( -6.383 eV)
     2 2 -- 0.403 au H 1.00 2 S 1
                        ( 10.959 eV)
     3 3 1.000 -0.235 au H 1.00 1 S 2
                        ( -6.383 eV)
     4 4 -- 0.403 au H 1.00 2 S 2
                        ( 10.959 eV)

 
                                             *************************
                                             * SFO MO coefficients *
                                             *************************
                                 

                                       === A ===
 MOs expanded in CFs+SFOs
 ========================

 The SFOs have been characterized in an earlier part of output.
 To deduce the bonding / antibonding nature of SFO combinations in an MO, consider the products
 of the coefficients AND THE OVERLAP between the SFOs (may be NEGATIVE). The SFO overlap matrix
 is printed later, in the SFO Populations section.
 
 (The CF coefficients are not printed)

 MOs : 1 2 3 4
 occup: 2.00 0.00 0.00 0.00
 CF+SFO
     1 0.5314 2.0005 0.0438 -0.7413
     2 -0.1208 0.5788 0.5612 -1.3303
     3 0.5314 -2.0005 0.0438 0.7413
     4 -0.1208 -0.5788 0.5612 1.3303

 ====== SFO Overlap Matrix (valence part only)

 column 1 2 3 4
 row
    1 1.00000000000000E+00
    2 6.19881407834534E-17 1.00000000000000E+00
    3 7.88803816794494E-01 2.15135333633690E-01 1.00000000000000E+00
    4 2.15135333633690E-01 5.43305094130786E-01 1.32798155323502E-16 1.00000000000000E+00

The section 'MOs expanded in CFs+SFOs' gives the coefficients and
relative signs.
Thus orbital 1 is +0.5314 times 1s orbital on H_1 -0.1208 times 2s
orbital on H_1
+0.5314 times 1s orbital on H_2 -0.1208 times 2s orbital on H_2
This is in fact a sigma.g orbital.

The 1s orbital and 2s orbital on H_1 are orthogonal, see also the: SFO
Overlap Matrix.
However, orbitals on H_1 do not have to be orthogonal to orbitals on H_2.
Therefore the sum of squares of coefficients do not have to be 1.

If you would have performed this calculation with symmetry, the SFOs
(Symmetrized Fragment Orbitals)
are:

                                       === SIGMA.g ===
 Nr. of SFOs : 2
 Cartesian basis functions that participate in this irrep (total number = 4) :
      1 3 2 4

    SFO (index Fragment Generating Expansion in Fragment Orbitals
  indx incl.CFs) Occup Orb.Energy FragmentType Coeff. Orbital on Fragment
 --------------------------------------------------------------------------------------
     1 1 1.000 -0.235 au H 0.71 1 S 1
                        ( -6.383 eV) 0.71 1 S 2
     2 2 -- 0.403 au H 0.71 2 S 1
                        ( 10.959 eV) 0.71 2 S 2

                                       === SIGMA.u ===
 Nr. of SFOs : 2
 Cartesian basis functions that participate in this irrep (total number = 4) :
      1 3 2 4

    SFO (index Fragment Generating Expansion in Fragment Orbitals
  indx incl.CFs) Occup Orb.Energy FragmentType Coeff. Orbital on Fragment
 --------------------------------------------------------------------------------------
     1 1 1.000 -0.235 au H 0.71 1 S 1
                        ( -6.383 eV) -0.71 1 S 2
     2 2 -- 0.403 au H 0.71 2 S 1
                        ( 10.959 eV) -0.71 2 S 2

In this case you can already see how the orbitals are symmetry adapted,
by looking at the signs.

 MOs expanded in CFs+SFOs
 ========================

 The SFOs have been characterized in an earlier part of output.
 To deduce the bonding / antibonding nature of SFO combinations in an MO, consider the products
 of the coefficients AND THE OVERLAP between the SFOs (may be NEGATIVE). The SFO overlap matrix
 is printed later, in the SFO Populations section.
 
 (The CF coefficients are not printed)

 MOs : 1 2
 occup: 2.00 0.00
 CF+SFO
     1 0.7515 0.0619
     2 -0.1708 0.7936

                                       === SIGMA.u ===
 MOs expanded in CFs+SFOs
 ========================

 MOs : 1 2
 occup: 0.00 0.00
 CF+SFO
     1 2.8292 1.0483
     2 0.8186 1.8814

Orbital 1 of sigma.g is
0.7515 times SFO 1 of sigma.g symmetry -0.1708 times SFO 2 of sigma.g
symmetry,
which is equal to
+0.7515 times (0.71 times 1s orbital on H_1 + 0.71 times 1s orbital on H_2)
-0.1708 times (0.71 times 2s orbital on H_1 + 0.71 times 2s orbital on H_2),
which is equal to
+0.5314 times 1s orbital on H_1 -0.1208 times 2s orbital on H_1
+0.5314 times 1s orbital on H_2 -0.1208 times 2s orbital on H_2

Best regards,
Erik van Lenthe
SCM

You wrote:

> I want to paste some ADF output as part of my question, and I can't
> ever seem to get emails to format themselves properly because of
> unfortunate word-wrapping, so I've just attached my question as a text
> file which should be readable if it's opened in a window that is wide
> enough.
>
>
> thanks for any comments/suggestions
>
> Kris Harris,
> SSNMR Laboratory
> University of Alberta
> Supervisor: R.E. Wasylishen
>
> kjharris_at_sdf.lonestar.org
> SDF Public Access UNIX System - http://sdf.lonestar.org
>
>------------------------------------------------------------------------
>
>First a disclaimer - I think this may be a uninformed question, so I
>apologize in advance
>
>What I would like to be able to do is understand fully the ADF output
>molecular orbitals in terms of the contributing bonding atomic orbitals,
>i.e. for H2 molecule, see that the MOs for a minimal basis set are:
>psi1 = c( |1sa> + |1sb>)
>psi2 = c( |1sa> - |1sb>)
>
>I have two questions remaining before I can really answer this question
>from the output.
>
>1. Can I determine the relative signs of the added in basis orbitals?
>If I run H2, I get in the section "List of all MOs, ..."
>
>
> -7.161 2.00 1 A 50.00% 1 S -3.376 1.00 1 H
> 50.00% 1 S -3.376 1.00 2 H
> 2.472 0.00 2 A 50.00% 1 S -3.376 1.00 2 H
> 50.00% 1 S -3.376 1.00 1 H
>
>So, this is what I expect from above, except that the I've lost the negative sign on the
>LUMO orbitals, but I supposed that this was part of the design to not imply too much info.,
>because with non s-type orbitals we have shape as well as phase, and we would need to worry
>about the location of the orbitals to see if the overlap is constructive or destructive.
>
>but, if I now run this with a double-zeta basis set, the output becomes:
>
> -9.087 2.00 1 A 50.68% 1 S -6.666 1.00 2 H
> 50.68% 1 S -6.666 1.00 1 H
> -1.928 0.00 2 A 55.88% 1 S -6.666 1.00 1 H
> 55.88% 1 S -6.666 1.00 2 H
> -5.88% 2 S 10.542 0.00 2 H
> -5.88% 2 S 10.542 0.00 1 H
>
>so we now have negative contributions.
>
>I guess then, question one is what is the significance of the negative percentage SFO
>contribution when it doesn't show the sign of the orbital that is added in for the
>linear combination? And this also brings up, how can I determine the antibonding/bonding nature of
>the linear combination of atomic orbitals? From the output section "SFO overlap matrix", I can
>tell if a linear combination is bonding/antibonding, but I need to know the signs of each
>SFO in the final MO.
>
>
>2. I would also like to be able to be able to deconstruct the SFOs in terms of the basis functions.
>For example in the above DZ calculation, I see from the output of the create job that I have
>two orbitals of 1s symmetry from the section "Orbital Energies, per ..."
>
> Occup E (au) E (eV) Diff (eV) with prev. cycle
> ----- -------------------- ------ --------------------------
> S
> 1 1.000 -0.24495278897385E+00 -6.666 3.69E-09
> 2 0.000 0.38741497816209E+00 10.542
>
>so it seems that the two basis 1s functions have formed two linear combinations which are of course
>of s-type symmetry. My question is what the coefficients of each of the two basis functions in the
>orbitals is. The point is that I would like to know in the output of the actual density calculation
>what the SFOs that contribute to an MO look like, e.g. for the DZ calculation of H2 above, the output
>shows -5.8% of the LUMO from the create run, so I would like to know what exactly this means in terms
>of the basis functions.
>
>btw, this is where we run into my ignorance, because I'm not sure where the orthogonality of the
>HOMO/LUMO of the create run arises - if we just have 1s slater functions which have no nodes and
>are spherically symmetric, how is the overlap zero? Is the create-run LUMO formed something like:
>1s(basis fn 1) - 1s(basis fn 2) to provide a sort of 2s function and yield the zero overlap?
>and in larger calculations, are the e.g. 3s basis functions which have no nodes combined to make
>an SFO which does?
>
>Anyway, just struggling to make sure I'm actually understanding what I'm doing from the ground up,
>I'd appreciate help for the first two questions about the format of the output (how to deconstruct
>MOs in terms of the linear combination of SFOs including signs, and the similiar problem with
>SFOs and basis functions). The last paragraph of questions is really just a signpost for my ignorance,
>but I'm not a computational chemist, so I hope that excuses me enough for someone to provide a
>useful comment or reference.
>
>
>
>
Received on 2005-11-03 12:24:49