## Natural Population Analysis

Link 607 of Gaussian contains version 3.1 of the NBO program by F. Weinhold and coworkers. Using formaldehyde (CH2O, C2v symmetry) at the HF/STO-3G level as an example, the calculation of NPA charges only involves calculation of the natural atomic orbitals and summation over all NAOs of a given atom to obtain the Natural Charges for each of the atoms. The corresponding input file is:

 ```#P HF/STO-3G scf=tight pop=npa HF/STO-3G//HF/STO-3G sp formaldehyde 0 1 C1 O2 1 r2 H3 1 r3 2 a3 H4 1 r3 2 a3 3 180.0 r2=1.21672286 r3=1.10137241 a3=122.73666566 ```

The following output is obtaind using this input:

```
******************************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******************************
/RESON  / : Allow strongly delocalized NBO set

Analyzing the SCF density

Job title: test21f HF/STO-3G opt formaldehyde scf=conventional

Storage needed:       510 in NPA (   2000000 available)

NATURAL POPULATIONS:  Natural atomic orbital occupancies

NAO Atom No lang   Type(AO)    Occupancy      Energy
---------------------------------------------------------
1    C  1  s      Cor( 1s)     2.00000     -11.05947
2    C  1  s      Val( 2s)     1.08461      -0.26145
3    C  1  px     Val( 2p)     0.90165      -0.04494
4    C  1  py     Val( 2p)     0.99304       0.07032
5    C  1  pz     Val( 2p)     0.85379       0.14739

6    O  2  s      Cor( 1s)     1.99999     -20.15602
7    O  2  s      Val( 2s)     1.79982      -1.09031
8    O  2  px     Val( 2p)     1.09835      -0.11626
9    O  2  py     Val( 2p)     1.91857      -0.38126
10    O  2  pz     Val( 2p)     1.37055      -0.15404

11    H  3  s      Val( 1s)     0.98982       0.02250

12    H  4  s      Val( 1s)     0.98982       0.02250
```
``` Summary of Natural Population Analysis:

Natural Population
Natural   -----------------------------------------------
Atom No    Charge        Core      Valence    Rydberg      Total
-----------------------------------------------------------------------
C  1    0.16692      2.00000     3.83308    0.00000     5.83308
O  2   -0.18728      1.99999     6.18729    0.00000     8.18728
H  3    0.01018      0.00000     0.98982    0.00000     0.98982
H  4    0.01018      0.00000     0.98982    0.00000     0.98982
=======================================================================
* Total *  0.00000      3.99999    12.00001    0.00000    16.00000

Natural Population
--------------------------------------------------------
Core                       3.99999 ( 99.9997% of   4)
Valence                   12.00001 (100.0001% of  12)
Natural Minimal Basis     16.00000 (100.0000% of  16)
Natural Rydberg Basis      0.00000 (  0.0000% of  16)
--------------------------------------------------------

Atom No         Natural Electron Configuration
----------------------------------------------------------------------------
C  1      [core]2s( 1.08)2p( 2.75)
O  2      [core]2s( 1.80)2p( 4.39)
H  3            1s( 0.99)
H  4            1s( 0.99)
```

A full online-manual for the NBO program explaining some of the underlying concepts and all additional keywords can be found here.

The Weinhold group also offers updated versions of the NBO program. The corresponding web page also contains substantial additional information on the concept of NBO and NPA.

A detailed overview of the performance of the NPA method in describing the charge distribution in water can be found in: F. Martin, H. Zipse, J. Comp. Chem. 2005, 26, 97 - 105. A copy of the pdf file is available here.

```last changes: 01.04.2008, AS