Keyword CONFIGURE

This keyword controls the atomic configuration. Therefore it is applicable only to calculations for single atoms.
Options:

	MAX=$<$Integer$>$		Maximum number of SCF cycles for which the configuration is used. By default it is used for all SCF cycles.
	OCCUPY		The (fractional) occupation of the specified atomic configuration is given explicitly in the subsequent input.

Description:
The orbital configuration is defined in the first line of the keyword body of CONFIGURE. In the case of OKS and ROKS calculations (see 4.5.1), two lines, the first for the $\alpha$-orbital configuration and the second for the $\beta$-orbital configuration, are required. If spherical orbitals (see 4.5.2) are to be used, one integer for $s$, three for $p$, five for $d$, etc. must be specified. Empty shells (see 4.3.1 for the definition of a shell) can be omitted. In deMon2k spherical orbitals are defined over real spherical harmonic Gaussians [162] as (without normalization):

$$\phi_{lm}({\bf r}) = r^l \, e^{- \alpha r^2} \, S_l^m(\vartheta, \phi)%$$ (9)

The $S_l^m$ denote real spherical harmonics that are constructed from complex spherical harmonics by [163]:

$$S_l^m = \phantom{-} {1 \over {\sqrt{2}}} \, \left ( \, Y_l^m + Y_l^{-m} \, \right )$$ (10)

$$S_l^{-m} = -{i \over {\sqrt{2}}} \, \left ( \, Y_l^m - Y_l^{-m} \, \right )$$ (11)

It should be noted that the $S_l^m$ are not eigenfunctions of the $\hat{l}_z$ operator and, therefore, $m$ is not a good quantum number for these orbitals.

The ordering of the integer numbers in the configuration line follows the $l$ (shell) and $m$ index of the real spherical harmonics:

$$s p d \ldots$$ Shell

$$l 1 2 \ldots$$ 0

$$m \ldots$$ 0 -1 0 1 -2 -1 0 1 2

$$s p_y p_z p_x d_{xy} d_{yz} d_{z^2} d_{xz} d_{x^2-y^2} \ldots$$ Orbital

As an example the open-shell (OKS or ROKS) triplet ground state configuration of the carbon atom, $1s^2 \> 2s^2 \> 2p^2$, can be defined in the keyword block of CONFIGURE as:

 
 2 1 1 0
 2 0 0 0

The first line defines the $\alpha$-orbital configuration with two electrons in the most stable $s$-orbitals ($1s$ and $2s$) and one electron each in the most stable $p_y$ ($m = -1$) and $p_z$ ($m = 0$) $\alpha$-orbital ($2p_y$ and $2p_z$). The second line assigns two electrons to the two most stable $\beta$ $s$-orbitals. Unspecified shells (here $d$ and higher) are not considered. If Cartesian orbitals are used, only the number of electrons in the $s$, $p$, $d$, etc. shells needs to be specified. Thus, for Cartesian orbitals the foregoing configuration definition changes to:

 
 2 2
 2 0

Because of the $p$-orbital degeneracy, the chosen Cartesian configuration has to be stabilized during the SCF procedure (see 4.4.5 or 4.5.7). The calculation of the triplet carbon ground state with spherical and Cartesian orbitals using CONFIGURE is described by the examples and in the deMon2k Tutorial, respectively.

To access excited atomic states or to use fractional occupation numbers, the option OCCUPY must be used. In this case, an explicit definition of the orbital occupation is expected after the orbital configuration line(s). In the case of spherical atomic orbitals an input line describing the occupation of each real spherical harmonic orbital type is needed. The occupation numbers can be given as real or integer values. To describe the excited triplet state of carbon, $1s^2 \> 2s^1 \> 2p^2 \> 3s^1$, for example, the following keyword body of CONFIGURE, using the option OCCUPY, is needed.

 
 3 1 1 0
 2 0 0 0
 1 0 1
 1
 1
 1 1

Here, the 3 in the first configuration line indicates that the three lowest $s$-type $\alpha$-orbitals will be occupied (note that this number does not represent the number of electrons in these orbitals). The 1 1 0 in the first line indicates that the $p_y$ and $p_z$ $\alpha$-orbitals will be occupied (we assume the default spherical orbitals with the order given above). The second line gives the $\beta$ configuration. Here, only the two lowest $\beta$ $s$ orbitals will be occupied. Occupation patterns begin in the third line, which, for the three lowest $s$-type $\alpha$ orbitals in this example is ( 1 0 1 ). This scheme has the lowest $\alpha$ $s$-orbital occupied with 1 electron, the next one empty, and the third one again occupied with 1 electron. Therefore, a hole in the $\alpha$ $s$-orbital occupation is produced. The next two occupation lines assign 1 electron to the $p_y$ and 1 to the $p_z$ $\alpha$-orbital. The last occupation has the two lowest $\beta$ $s$-orbitals occupied with 1 electron each. Please also note that zero (0) entries in the configuration line(s) do not have corresponding occupation lines. Example on page of the deMon2k Tutorial describes the calculation of the excited $1s^2 \> 2s^1 \> 2p^2 \> 3s^1$ carbon triplet state.

As already mentioned, the OCCUPY option may also be used to generate fractional occupations, e.g. for the calculation of spherical atoms. In the case of the triplet carbon ground state, the following CONFIGURE keyword body produces a spherical atom.

 
 2 1 1 1
 2 0 0 0
 1 1
 0.6666
 0.6666
 0.6666
 1 1

The first configuration line describes the occupation of two $\alpha$ $s$-orbitals and of all three $p$-orbitals. According to the specified occupation (third line), the two $s$-orbitals are occupied by one electron each. The three $\alpha$ $p$-orbitals are occupied uniformly by $2/3$ of an electron each (0.6666 in lines 4, 5, and 6). Finally, the $\beta$ $s$-orbital occupation is given by the last line. (See Example on page of the tutorial for the discussion of the corresponding output).

Because the Kohn-Sham method is a single-determinant approach, atomic states are approximated by a single configuration (see however [164] for a multi-determinantal approach). This can be done as in spatially unrestricted Hartree-Fock calculations [165]. For $s$ and $p$ occupations, all possible configurations yield the correct spatial symmetry. However, for $d$ occupations this is not the case and care must be taken with the occupation scheme. Correct spatial symmetry uniquely defines the orbital occupancies for $d^2$, $d^3$, $d^5$, $d^7$ and $d^8$. The other $d$ occupations are selected to maximize the absolute angular momentum (this choice is arbitrary because $m$ is no longer a good quantum number). Thus, the following $d$ configurations must be used:

$$d^1(^2D) (d_{xy})^1$$ :

$$d^2(^3F) (d_{z^2})^1 \, (d_{x^2-y^2})^1$$ :

$$d^3(^4F) (d_{xy})^1 \, (d_{xz})^1 \, (d_{yz})^1$$ :

$$d^4(^5D) (d_{z^2})^1 \, (d_{xy})^1 \, (d_{xz})^1 \, (d_{yz})^1$$ :

$$d^5(^6S) (d_{z^2})^1 \, (d_{x^2-y^2})^1 \, (d_{xy})^1 \, (d_{xz})^1 \, (d_{yz})^1$$ :

$$d^6(^5D) (d_{z^2})^1 \, (d_{x^2-y^2})^1 \, (d_{xy})^2 \, (d_{xz})^1 \, (d_{yz})^1$$ :

$$d^7(^4F) (d_{z^2})^2 \, (d_{x^2-y^2})^2 \, (d_{xy})^1 \, (d_{xz})^1 \, (d_{yz})^1$$ :

$$d^8(^3F) (d_{z^2})^1 \, (d_{x^2-y^2})^1 \, (d_{xy})^2 \, (d_{xz})^2 \, (d_{yz})^2$$ :

$$d^9(^2D) (d_{z^2})^2 \, (d_{x^2-y^2})^2 \, (d_{xy})^1 \, (d_{xz})^2 \, (d_{yz})^2$$ :