Electronic structure of CmF¶
We want to investigate the structure of the diatomic molecule CmF (Curium Fluoride).
The curium atom¶
The ground state configuration of curium (Cm, Z=96) is \([Rn]5f^76d^17s^2\) (see here for general information and also here), so with two open shells.
The number of microstates generated by this configuration is
We first carry out an average-of-configuration Hartree-Fock calculation of the neutral atom. A problem will be that by default DIRAC will order orbitals according to their energies and assume that inactive (fully occupied) orbitals have lower energies than active (partly occupied) ones. This may not hold true for f elements, where the open \((n-2)f\) orbitals may have lower energy than \((n-1)d\) and \(ns\) orbitals. We shall therefore calculate the atom in two steps:
- We calculate the trivalent cation \(Cm^{3+}\) with electron configuration \([Rn]5f^7\).
- Once we have identified the \(6d\) and \(7s\) orbitals amongst the virtuals we can easily calculate the neutral atom using reordering of orbitals and overlap selection.
We shall next investigate the electronic structure of the diatomic CmF molecule. For ease of analysis we shall impose linear symmetry also in the atomic calculation. We achieve this through the introduction of a ghost center
2
Cm 0.00 0.00 0.00
Cm.GH 0.00 0.00 10.00
The menu file for the trivalent cation then reads
**DIRAC
.WAVE FUNCTION
.ANALYZE
**ANALYZE
.MULPOP
*MULPOP
.VECPOP
1..oo
.LABEL
SHELL
**WAVE FUNCTION
.SCF
*SCF
.CLOSED SHELL
86
.OPEN SHELL
1
7/14
.OPENFAC
1.0
**MOLECULE
*BASIS
.DEFAULT
dyall.cv3z
.SPECIAL
Cm.GH NOBASIS
*END OF
Note that
- we perform Mulliken population on all positive-energy orbitals.
- we use the keyword SHELL to only indicate atomic shell type since we do not need more detailed information
- we specify that the ghost center has no basis.
We run the calculation using:
pam --inp=CmIII --mol=Cm.xyz --put "cf.CmIII=DFCOEF"
(keywords for parallel run omitted). Here is a snippet of the Mulliken population analysis
* Electronic eigenvalue no. 44: -1.4043324007679 (Occupation : f = 0.5000) m_j= -3/2
==========================================================================================
* Gross populations greater than 0.00010
Gross Total | L Cm 1 f Cm 1 _small
-----------------------------------------------------
alpha 0.7141 | 0.7140 0.0001
beta 0.2859 | 0.2856 0.0003
* Electronic eigenvalue no. 45: -1.4043324004783 (Occupation : f = 0.5000) m_j= 1/2
==========================================================================================
* Gross populations greater than 0.00010
Gross Total | L Cm 1 f Cm 1 _small
-----------------------------------------------------
alpha 0.4286 | 0.4284 0.0003
beta 0.5714 | 0.5712 0.0002
* Electronic eigenvalue no. 46: -1.4043323993941 (Occupation : f = 0.5000) m_j= 5/2
==========================================================================================
* Gross populations greater than 0.00010
Gross Total | L Cm 1 f Cm 1 _small
-----------------------------------------------------
alpha 0.1432 | 0.1428 0.0004
beta 0.8568 | 0.8568 0.0000
* Electronic eigenvalue no. 47: -1.3526882033809 (Occupation : f = 0.5000) m_j= 1/2
==========================================================================================
* Gross populations greater than 0.00010
Gross Total | L Cm 1 f Cm 1 _small
-----------------------------------------------------
alpha 0.5714 | 0.5712 0.0002
beta 0.4286 | 0.4284 0.0002
* Electronic eigenvalue no. 48: -1.3526882033217 (Occupation : f = 0.5000) m_j= -3/2
==========================================================================================
* Gross populations greater than 0.00010
Gross Total | L Cm 1 f Cm 1 _small
-----------------------------------------------------
alpha 0.2859 | 0.2856 0.0003
beta 0.7141 | 0.7140 0.0001
* Electronic eigenvalue no. 49: -1.3526882030390 (Occupation : f = 0.5000) m_j= 5/2
==========================================================================================
* Gross populations greater than 0.00010
Gross Total | L Cm 1 f Cm 1 _small
-----------------------------------------------------
alpha 0.8569 | 0.8568 0.0001
beta 0.1431 | 0.1428 0.0003
* Electronic eigenvalue no. 50: -1.3526882019259 (Occupation : f = 0.5000) m_j= -7/2
==========================================================================================
* Gross populations greater than 0.00010
Gross Total | L Cm 1 f Cm 1 _small
-----------------------------------------------------
alpha 0.0004 | 0.0000 0.0004
beta 0.9996 | 0.9996 0.0000
* Electronic eigenvalue no. 51: -0.6877744017943 (Occupation : f = 0.0000) m_j= 1/2
==========================================================================================
* Gross populations greater than 0.00010
Gross Total | L Cm 1 s
--------------------------------------
alpha 1.0000 | 0.9999
beta 0.0000 | 0.0000
* Electronic eigenvalue no. 52: -0.6545606850572 (Occupation : f = 0.0000) m_j= 1/2
==========================================================================================
* Gross populations greater than 0.00010
Gross Total | L Cm 1 d
--------------------------------------
alpha 0.4000 | 0.4000
beta 0.6000 | 0.5999
* Electronic eigenvalue no. 53: -0.6545606849576 (Occupation : f = 0.0000) m_j= -3/2
==========================================================================================
* Gross populations greater than 0.00010
Gross Total | L Cm 1 d
--------------------------------------
alpha 0.7999 | 0.7999
beta 0.2001 | 0.2000
* Electronic eigenvalue no. 54: -0.6380858302106 (Occupation : f = 0.0000) m_j= 1/2
==========================================================================================
* Gross populations greater than 0.00010
Gross Total | L Cm 1 d
--------------------------------------
alpha 0.6000 | 0.6000
beta 0.4000 | 0.4000
* Electronic eigenvalue no. 55: -0.6380858295766 (Occupation : f = 0.0000) m_j= 5/2
==========================================================================================
* Gross populations greater than 0.00010
Gross Total | L Cm 1 d
--------------------------------------
alpha 0.9999 | 0.9999
beta 0.0001 | 0.0000
* Electronic eigenvalue no. 56: -0.6380858288659 (Occupation : f = 0.0000) m_j= -3/2
==========================================================================================
* Gross populations greater than 0.00010
Gross Total | L Cm 1 d
--------------------------------------
alpha 0.2000 | 0.2000
beta 0.8000 | 0.7999
One clearly sees that the fractionally occupied \(5f\) orbitals are followed by first virtual \(7s\), then virtual \(6d\) orbitals. We want to reorder them as \(\left(5f,7s,6d\right)\rightarrow\left(5f,6d,7s\right)\) such that both open shells follow the closed \(7s\) shell in the neutral atom. We therefore set up the input file
**DIRAC
.WAVE FUNCTION
.ANALYZE
**ANALYZE
.MULPOP
**WAVE FUNCTION
.SCF
.REORDER
1..43,51,44..50,52..56
*SCF
.CLOSED SHELL
88
.OPEN SHELL
2
7/14
1/10
.OPENFAC
1.0
.OVLSEL
.NODYNSEL
**MOLECULE
*BASIS
.DEFAULT
dyall.cv3z
.SPECIAL
Cm.GH NOBASIS
*END OF
This assures that the orbitals are correctly ordered when we start the SCF iterations. In order to keep them in the desired order, we invoke overlap selection. We impose non-dynamic overlap selection, which means that orbitals in a given iteration are selected based on their overlap with the initial orbitals.