CCL:G: NBO - Bond Order

[Thomas Manz <thomasamanz(_)gmail.com>]

 Sent to CCL by: Thomas Manz [thomasamanz^^gmail.com]
 Dear Meilani Kurniawati Wibowo,
 I recommend the spin-corrected Mayer bond order in the NAO basis,
 which is accurate and reliable for molecular systems.
 The spin-corrected Mayer bond order is defined by Equation (11) of the
 article I. Mayer, "On Bond Orders and Valences in the Ab Initio
 Quantum Chemical Theory," Int. J. Quant. Chem. Vol. 29, (1986) pp.
 73-84. This equation is reproduced as Equations (44) and (46) of the
 review article I. Mayer, "Bond Order and Valence Indices: A Personal
 Account," J. Comput. Chem. Vol. 28 (2007) pp. 204-221. Mayer applied
 his definition using the basis set (Mulliken analysis) to compute the
 overlap matrix, but this leads to high basis set sensitivity.
 The problem of high basis set sensitivity in Mulliken analysis was
 resolved by Natural Population Analysis which generates Natural Atomic
 Orbitals (NAOs) as described in the article A.E. Reed, R.B. Weinstock,
 and F. Weinhold, "Natural population analysis," J. Chem. Phys. Vol. 83
 (1985) pp. 735-746.
 The spin-corrected Mayer bond order in the NAO basis uses Natural
 Population Analysis to compute the overlap matrices. It can be
 computed as following:
 1) add Pop=NBOread to the route line of the Gaussian input file
 2) add the following line to the bottom of file:
 $NBO BNDIDX RESONANCE $END
 (One blank line should occur before and after this line.)
 3) After the jobs completes, search the Gaussian output file for the
 line "Wiberg bond index matrix in the NAO basis:". Depending on the
 type of job, this line may occur multiple times in the log file, so
 you must be careful to identify the right ones. By default, Gaussian
 performs population analysis on the first and last steps of a geometry
 optimization. You want to use the entry for the last geometry step,
 which will appear near the bottom of the output file. If the geometry
 does not change during the calculation (e.g., single-point or
 frequency calculation), then the population analysis will be performed
 only once (unless you have requested a multi-part job).
 For spin unpolarized systems: The spin-corrected Mayer bond order in
 the NAO basis equals the "Wiberg bond index in the NAO basis" so you
 can just read the corresponding entry from the Gaussian output file.
 (Do not multiply by two.)
 For spin polarized systems: The spin-corrected Mayer bond order in the
 NAO basis = 2*W(alpha) + 2*W(beta), where W(alpha) is the Wiberg bond
 index in the NAO basis for the alpha spin orbitals and W(beta) is the
 Wiberg bond index in the NAO basis for the beta spin orbitals.
 For spin polarized systems NBO analysis is automatically performed three times:
 first for the total density matrix (ignore this part)
 then for the spin up (alpha) density matrix in the section following the lines
 ***************************************************
  *******         Alpha spin orbitals         *******
  ***************************************************
 W(alpha) is the entry under "Wiberg bond index matrix in the NAO
 basis:"
  and finally for the spin down (beta) density matrix in the section
 following the lines
  ***************************************************
  *******         Beta  spin orbitals         *******
  ***************************************************
 W(beta) is the entry under "Wiberg bond index matrix in the NAO
 basis:"
 Example: The O2 molecule. Since the ground state of the O2 molecule is
 a spin triplet, this is a spin polarized calculation. Below is an
 excerpt of lines from the Gaussian output file:
  ***************************************************
  *******         Alpha spin orbitals         *******
  ***************************************************
 (deleted lines)
  Wiberg bond index matrix in the NAO basis:
      Atom    1       2
      ---- ------  ------
    1.  O  0.0000  0.2560
    2.  O  0.2560  0.0000
 (more deleted lines)
  ***************************************************
  *******         Beta  spin orbitals         *******
  ***************************************************
 (deleted lines)
  Wiberg bond index matrix in the NAO basis:
      Atom    1       2
      ---- ------  ------
    1.  O  0.0000  0.7505
    2.  O  0.7505  0.0000
 (more delete lines)
 So, the effective bond order for the O2 molecule is: 2*0.2560 +
 2*0.7505 = 2.013.
 (Note: The Wiberg bond index is symmetric, so you can look for either
 the entry (1,2) or the entry (2,1) to get the terms for the bond
 between atom 1 and atom 2.)
 In my experience, this is one of the most reliable ways to compute
 effective bond orders of molecular systems.
 Sincerely,
 Tom Manz
 On Fri, Mar 22, 2013 at 2:13 AM, Meilani Kurniawati Wibowo
 piano_oz1989() yahoo.co.id <owner-chemistry-.-ccl.net> wrote:
 >
 > Sent to CCL by: "Meilani Kurniawati Wibowo"
 [piano_oz1989_+_yahoo.co.id]
 > Dear all,
 >
 > How to determine the bond order from the Gaussian output file? What keyword
 I
 > have to add to get the value of bond order?
 >
 > Thank you.>
 >