Computational Inorganic Chemistry: Hunt Research Goup, Imperial College London

NBO Analysis

Now you are going to optimise a molecule of NH₃ for practice and then we are going to carry out an NBO analysis on it.

Practice at optimising

create a molecule of NH₃
use the 6-31G(d,p) basis (exactly the same basis set as we used for the higher level BH₃ calculation). Because this molecule is so small we can in-fact go straight to the high level basis set (if your molecule has more than 4-5 atoms this is NOT recommended).
then carry out a frequency analysis to ensure you have a minimum.
finally carry out the population analysis
Link to your completed 6-31G(d,p) NH₃ optimisation, frequency and MO analysis files in your wiki, you will loose marks if these files are not present. Be sure to summarize the details of the calculation, such as basis set and method, also show on your wiki that the optimisation is converged, that the low frequencies are low and that there are no negative frequencies.

NBO analysis of NH₃

Now we are going to carry out a "Natural Bond Orbital Analysis", both inside gaussview and in the log file from gaussian.

open the .log file from your population analysis, it is important that we use the .log file for the NBO (and the .chk for the MOs!). Goto the results tab and select charge distribution:
on the panel that appears select NBO as the type and color the atoms by charge. Important: you must select the NBO charge distribution not the default Mulliken (which is a poor method for computing charge). Many students have forgen this and they have reported the wrong charges. Bright green indicates highly positive charge and bright red highly negative charge. As expected the nitrogen atom which is electronegative is highly negatively charged.
Include an image of the charge distribution in your wiki. Make sure you identify the charge range in your wiki, otherwise we would not know the charge limits associated with the bright green or bright red colours, it could be -0.01 to +0.01 or -1.0 to +1.0, thus this information is vital.
Now deselect the "colour atoms by charge" option, and select the "show numbers" option, indicated by "2."
What are the specific NBO charges for the nitrogen and hydrogen atoms? Include this information in your wiki
The NBO analysis gives much more information than the "atomic charges", however gaussview only provides a graphical interface for viewing specific information, it is not sophisticated enough to deal with the NBO analysis. Thus we have to go into the "guts" of the .log file ourselves. Goto the results tab and select "view file", scroll down until you find the start of the NBO analysis, everything after this heading is the NBO analysis:

******************************Gaussian NBO Version 3.1******************************
             N A T U R A L   A T O M I C   O R B I T A L   A N D
          N A T U R A L   B O N D   O R B I T A L   A N A L Y S I S
 ******************************Gaussian NBO Version 3.1******************************

The NBO analysis can tell us many interesting things, but I will only pick out a few to think about in more detail.

Scroll down until you find the "Summary of Natural Population Analysis:". The numbers under the "Natural Charge" heading are exactly those we just studied using gaussview:

Summary of Natural Population Analysis:

                                       Natural Population
                Natural  -----------------------------------------------
    Atom  No    Charge         Core      Valence    Rydberg      Total
 -----------------------------------------------------------------------
      N    1   -1.12515      1.99982     6.11104    0.01429     8.12515
      H    2    0.37505      0.00000     0.62250    0.00246     0.62495
      H    3    0.37505      0.00000     0.62250    0.00246     0.62495
      H    4    0.37505      0.00000     0.62249    0.00246     0.62495
 =======================================================================
   * Total *    0.00000      1.99982     7.97852    0.02166    10.00000

Then keep scrolling down until you find the section with the headding "Bond orbital/ Coefficients/ Hybrids" this describes the bonding in the compound:

      (Occupancy)   Bond orbital/ Coefficients/ Hybrids
 ---------------------------------------------------------------------------------
     1. (1.99909) BD ( 1) N   1 - H   2
                ( 68.83%)   0.8297* N   1 s( 24.87%)p 3.02( 75.05%)d 0.00(  0.09%)
                                           -0.0001 -0.4986 -0.0059  0.0000 -0.2910
                                            0.0052  0.8155  0.0277  0.0000  0.0000
                                            0.0281  0.0000  0.0000  0.0032  0.0082
                ( 31.17%)   0.5583* H   2 s( 99.91%)p 0.00(  0.09%)
                                           -0.9996  0.0000  0.0072 -0.0289  0.0000
     2. (1.99909) BD ( 1) N   1 - H   3
                ( 68.83%)   0.8297* N   1 s( 24.86%)p 3.02( 75.05%)d 0.00(  0.09%)
                                            0.0001  0.4986  0.0059  0.0000  0.2910
                                           -0.0052  0.4077  0.0138  0.7062  0.0240
                                            0.0140  0.0243  0.0076  0.0033  0.0031
                ( 31.17%)   0.5583* H   3 s( 99.91%)p 0.00(  0.09%)
                                            0.9996  0.0000 -0.0072 -0.0145 -0.0250
     3. (1.99909) BD ( 1) N   1 - H   4
                ( 68.83%)   0.8297* N   1 s( 24.87%)p 3.02( 75.05%)d 0.00(  0.09%)
                                            0.0001  0.4986  0.0059  0.0000  0.2909
                                           -0.0052  0.4077  0.0138 -0.7062 -0.0239
                                            0.0140 -0.0243 -0.0076  0.0033  0.0031
                ( 31.17%)   0.5583* H   4 s( 99.91%)p 0.00(  0.09%)
                                            0.9996  0.0000 -0.0072 -0.0145  0.0250
     4. (1.99982) CR ( 1) N   1           s(100.00%)
                                            1.0000 -0.0002  0.0000  0.0000  0.0000
                                            0.0000  0.0000  0.0000  0.0000  0.0000
                                            0.0000  0.0000  0.0000  0.0000  0.0000
     5. (1.99721) LP ( 1) N   1           s( 25.38%)p 2.94( 74.52%)d 0.00(  0.10%)
                                            0.0001  0.5036 -0.0120  0.0000 -0.8618
                                            0.0505  0.0000  0.0000  0.0000  0.0000
                                            0.0000  0.0000  0.0000 -0.0269  0.0155

The NBO analysis partitions the electron density of the whole molecule out into atomic like orbitals, which are then used to form 2e-2c bonds, key information about these bonds is printed above.
For example the first bond (BD) is between nitrogen (atom 1) and hydrogen (atom 2) and 69% of the bond is contributed from the N orbitals which have a hybridisation of 25%s+75%p, while 31% of the bond comes from the H orbital which is 100%s.
Thus the N has formed 4 essentially sp³ hybrid orbitals which each interact with the sAO of one hydrogen atom. The last orbital shown (Orbital 5) is the nitrogen lone pair (LP) 25% s abd 75% p orbital. This is formally occupied so it has an occupation close to 2.00 (actually 1.997)
Orbital 4 is the core (CR) 1sAO of nitrogen.

Continue down to see a section "Second Order Perturbation Theory Analysis of Fock Matrix in NBO Basis" this section outlines the interactions between the various MOs (ie mixing). Normally these are interactions from bonding NBOs into non-bonding or antibonding orbitals. It does not contain much information for NH₃ but is important for other molecules. If any of the values in the E(2) column are greater than 20 kcal/mol they are of interest.
```
Second Order Perturbation Theory Analysis of Fock Matrix in NBO Basis

     Threshold for printing:    .50 kcal/mol
                                                    E(2)  E(j)-E(i) F(i,j)
Donor NBO (i)           Acceptor NBO (j)         kcal/mol   a.u.    a.u.
===========================================================================
```

The final section is headed "Natural Bond Orbital (Summary)", in this section are recorded the energy and population or occupation of the N-H bonds, and the nitrogen lone pair N(LP):

 Natural Bond Orbitals (Summary):

                                                            Principal Delocalizations
           NBO                        Occupancy    Energy   (geminal,vicinal,remote)
 ====================================================================================
 Molecular unit  1  (H3N)
     1. BD (   1) N   1 - H   2          1.99909    -0.60417
     2. BD (   1) N   1 - H   3          1.99909    -0.60417
     3. BD (   1) N   1 - H   4          1.99909    -0.60416
     4. CR (   1) N   1                  1.99982   -14.16768
     5. LP (   1) N   1                  1.99721    -0.31756

All the N-H bonds are at the same energy, the lone pair is higher in energy. Look at the energy of the core orbital, -14.2 au, while the energy of the valence orbitals is between -1.0 and 0.0 au. This is why we leave the core orbitals off an MO diagram, they are very deep in energy compared to the valence orbitals.
Thus the NBO analysis takes a delocalised MO picture and turns it back into the "organic chemists" picture of 2e-2c bonding. If you want to find out more about the NBO analysis (this is OPTIONAL) go to the NBO web-site The information can be quite technical, but the beginners tutorial provides a good starting point.
When you are ready close the gaussview text window move onto the next step

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NBO Analysis

Practice at optimising

NBO analysis of NH3

NBO analysis of NH₃