Configuration strings

Configurations are stored in the database using an unambiguous notation which should be familiar to most users. A configuration consists of a space-delimited list of sub-shells in standard order each having the form, , where is the sub-shell (standard order: 1s, 2s, 2p, 3s, ...) and is the occupation number. Note that the shorthand notation of omitting when unity is not used, e.g. 2s1 not 2s. Configuration strings obey the rules:

• all closed sub-shells starting with 1s and ending just prior to the first open (or last) sub-shell are not part of the configuration string,
• the first open sub-shell is always displayed even if it is empty (), and
• all empty sub-shells beyond the first open sub-shell are not displayed.

Some examples:

• 1s$^2$ 2s$^2$ 2p$^3$ becomes 2p3,
• 1s$^2$ 2s 2p$^4$ becomes 2s1 2p4,
• 1s$^2$ 2s 2p$^5$ becomes 2s0 2p5, and
• 1s 2s$^2$ 2p$^4$ becomes 1s1 2s2 2p4.

Using a list of occupation numbers as the configuration label was considered and ultimately rejected due to the impracticality of storing Rydberg levels. Consider the configuration, 1s 200p; whereas only 13 characters are needed to store this configuration in the form described above, nearly 40000 characters are required if using a list of occupation numbers.

To get the number of electrons of a configuration takes two steps; first you need to calculate the number of electrons in the core and then add up the occupation numbers of the visible sub-shells. To get the number of electrons in the core, , take the principal quantum number, $n$, and the orbital angular momentum, of the first open sub-shell and apply the following expression:

(E.1)

For a configuration of 4p5 5s2 5p1 we have and . The above expression yields and the total occupation of the visible sub-shells is 8 so this configuration has 38 electrons.