As Bader has shown in his ``Theory of Atoms in Molecules'' [13] one can define an atom via the zero-flux surface of the electron density: Looking at the gradient vector field, one finds that the all gradient vector trajectories terminate at only one nucleus each. This allows to define an atomic basin as the space which is crossed by the gradient vector trajectories starting at the corresponding nucleus (cf. 4). The border of such a basin is the zero-flux surface. This type of definition of an atom yields quantum mechanically defined charges of atoms, which are more indicative of properties than e.g. Mulliken charges.
A selection of charges and populations derived by different methods is given in table 7. For the silatrane studied here we find a very positive silicon atom and corresponding negative nitrogen and oxygen atoms. This indicates a strong ionic contribution to the bonding.
Atom | Mull.Pop. | Charge | Low.Pop. | Charge | Bader Pop. | Charge |
1 SI | 12.623108 | 1.376892 | 13.227044 | 0.772956 | 10.65411 | 3.34588 |
2 O | 8.740145 | -0.740145 | 8.451786 | -0.451786 | 9.5138 | -1.5138 |
3 O | 8.732526 | -0.732526 | 8.452240 | -0.452240 | -- | -- |
4 O | 8.767042 | -0.767042 | 8.440570 | -0.440570 | -- | -- |
5 N | 7.793785 | -0.793785 | 7.191056 | -0.191056 | 8.47333 | -1.47333 |
6 C | 6.700731 | -0.700731 | 6.725870 | -0.725870 | -- | -- |
7 C | 5.919583 | 0.080417 | 6.138055 | -0.138055 | -- | -- |