GFN2-xTB geometry optimization of complexes with Z>86, specifically closed-shell Rn-like ions Fr(I),Ra(II),Ac(III),Th(IV)

[skattejag]

Hi,

I'm interested in determining the optimized geometries of a series of metal complexes with closed-shell Rn[Z=86]-like ions, for example Fr(I),Ra(II),Ac(III) and Th(IV). As the electronic structure of the latter metal ions should be similar to Rn, and the primary contributor to the chemistry should be determined by the charge/ionic radii of the alkaline earth metal.

The aim is to rapidly determine potential conformer candidates in an approximate way via GFN2-xTB/CREST, for evaluation with subsequent DFT modelling with relativistic treatment - using the Gaussian/ORCA electronic structure package.

Using Ra(II)H2O as an example (although much more complex ligands with many donor atoms will be considered):
I would like to know if either/both of the two approaches outlined below is valid, in an approximate way, or if any other changes need to be applied, or if another approach will yield more reasonable results:

1)
Executing xtb --chrg 2 --uhf 0 --gfn 2 --vparam param_gfn2-xtb_mod.txt --norestart Ra_water.xyz > Ra_water.out,
and adding an entry for Ra[Z=88] by using either Ba[Z=56] or Rn[Z=86] as a template, or by extrapolating the known parameters for elements Ca < Sr < Ba to estimate parameters for Ra.
Ba[Z=56]'s parameter entry:

$Z=56 Wed Apr 18 09:11:51 CEST 2018 
 ao=6s6p5d                        
 lev=   -5.900000   -2.133395   -1.514900
 exp=    1.528102    0.991572    1.500000
 GAM=    0.245937
 GAM3=    2.069097
 KCNS=    0.352001
 KCNP=   -0.926576
 KCND=    0.147995
 DPOL=   -0.260000
 QPOL=    0.015000
 REPA=    0.716259
 REPB=   46.984607
 POLYS=  -14.036589
 POLYP=   18.774072
 POLYD=   11.389672
 LPARP=   22.247532
 LPARD=   -2.300000
$end

Example for additional parameter entry in "param_gfn2-xtb_mod.txt": Ra [Z=88] using Rn[Z=86] as a template, modifying 'Z' and 'ao' :

$Z=88 Mon Apr 23 23:25:34 CEST 2018 
 ao=7s7p6d                        
 lev=  -21.000000  -10.496406   -1.415056
 exp=    3.109394    2.541934    1.790000
 GAM=    0.303400
 GAM3=    0.097834
 KCNS=   -0.001712
 KCNP=   -0.005280
 KCND=   -3.206020
 DPOL=   -0.167597
 QPOL=   -0.111556
 REPA=    0.965577
 REPB=  128.133580
 POLYS=  -35.245372
 POLYP=  -11.989735
 POLYD=   21.167024
 LPARP=   -0.302388
 LPARD=   -2.300000
$end

Alternatively, if approach (1) cannot be implemented or will not yield reasonable results.

2)
Do not add parameters in "param_gfn2-xtb_mod.txt" instead a) create an artificial Ra(II) ion using Rn[Z=86] which is constrained/frozen with a positive point charge placed at the Rn coordinate (eg. origin) with a corresponding formal charge (eg. +2 for Ra(II))
Executing xtb --chrg 0 --uhf 0 --gfn 2 --input embed.input --norestart Ra_water.xyz > Ra_water.out,

embed.input :

$fix
   elements: Rn
$end

$embedding
   input=embed_charge.pc
$end

embed_charge.pc :

2
  2.0    0.00000000000000    0.00000000000000    0.00000000000000  
 -2.0   999.00000000000000    999.00000000000000   999.00000000000000   

The above formal charges cancel out, however the charge -2 is located far away from the atoms of the complex and should therefore not affect the resultant optimized geometry, whereas the +2 formal charge is located at the metal center and will therefore result in a reasonable approximation of the Ra(II) ion. Also, should the chemical hardness be set to some large value, eg. 99?

Or b) could Rb(I) (effective ionic radius = 1.52 A) perhaps be used instead somehow, since it has a similar effective ionic radius to Ra, i.e. 1.48(8)?

Although the minimized geometries are the main point of interest, may the relative energies obtained be relied upon for selecting a subset for determination of minimum-energy conformer candidates, in the gas and/or solution phase (water, alpb), for subsequent DFT optimization?

I would greatly appreciate any assistance.

Kind regards
Cameron