I know that one can determine which type of bond is present between different atoms in a molecule by analyzing the output of an NBO analysis. Furthermore the second order perturbation theory analysis can provide information about the presence interactions like hyperconjugation. But is there also a way to determine whether there are three-center four-electron bonds, i.e. hypervalency in a molecule by a NBO analysis ?

  • $\begingroup$ Hypervalency is an obsolete model which is superseded by Valence Bond Theory (resonance) and/or Molecular Orbital Theory (multicenter bond). $\endgroup$ Mar 25, 2023 at 1:57

2 Answers 2


It is possible to determine such 3-centre bonds using an NBO analysis.

Here is a sample output of an NBO analysis obtained from this website:

enter image description here

The number of 3C (3-centre) bonds can be seen in the Lewis Structure column.

A really good resource is the NBO 6.0 Manual to read more about such 3-centre bonds.

There is a chapter in the manual called: B.16 3-CENTER, 4-ELECTRON HYPERBOND SEARCH

Additionally for some theory on a quantitative definition of hypervalency, this paper discusses a method to determine hypervalency using various charge models, one of which is NBO analysis.

  • $\begingroup$ Thanks for your answer ! So if there are only zeros in the Lewis structure column it does mean that there are no 3-center bonds present in the system ? $\endgroup$
    – C_Swann22
    Mar 10, 2023 at 15:28
  • $\begingroup$ Also, the manual says that the hyperbond search is done by default but when carrying out an NBO analysis on my compound there is no output corresponding to the hyperbond search. Is there an additional keyword I have to add ? I can not find anything about this in the manual. $\endgroup$
    – C_Swann22
    Mar 10, 2023 at 16:01
  • $\begingroup$ I am not an expert in this , from what I can understand in the manual, if there were no 3-c output for your compound then there are no 3-c present.I quote from the manual "If the initial 1c/2c search leaves unassigned NL-density exceeding the current occupancy threshold, the NBO search automatically extends to 3-center NBOs." $\endgroup$ Mar 10, 2023 at 17:50
  • $\begingroup$ The more relevant and probably more interesting chapter in the NBO manual (version 7 can be accessed on the website freely) is the one about Natural Resonance Theory. $\endgroup$ Mar 25, 2023 at 2:05

So I have found out that by default the NBO version implemented in GAUSSIAN 16 searches for 1c and 2c bonds but not for 3c bonds. One has to activate it by adding an NBO input at the end of the GAUSSIAN input file. An example looks like this:

# B3LYP/def2tzvp pop=nboread

nbo 3c bond analysis

0 1
A x1 y1 z1
B x2 y2 z2
C x3 y3 z3


Using this input causes the program to also search for three-center bonds.

  • $\begingroup$ Please do not use this. NBO 3.1 is really old and known to have bugs in implementation and theory. There have been significant advances in this field, too. $\endgroup$ Mar 25, 2023 at 1:54

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