Comparison of Some Structural Parameters of the Model Systems nM+[CrX6]3- and 3M+[CrX6]3- + 18MCl (M–Na, K, Cs; X–F, Cl; n=1–6)
Authors: Kuznetsov Sergey A. , Kremenetsky Vyacheslav G. 
Published: February 2020

Previously (1-2), the possibility of qualitative evaluation of the charge transfer activation energies was studied in small model systems such as nM+[AX6]3-, where M–Na, K, Cs; A–Cr, Nb; X–Cl, F; n=1– n
lim (n
lim is the limiting number of outer-sphere cations bound to a complex). At a following stage, it is planned to pass to the analysis of the extended model systems which contain in addition 18 molecules МХ. The final goal of this research is quantum-chemical modeling of charge transfer in the molten salts.
The aim of this work is comparison of some structural characteristics of the small (I) and the extended (II) systems containing chromium complex [CrF6] or [CrCl6].
Quantum-chemical calculations were carried out at the DFT/B3LYP theory level with utilization of the Stuttgart/Cologne groups' quasi-relativistic ECP basis. Earlier calculations were made in the non-relativistic all-electron basis for Na-, K-systems only. Comparison of these calculations allows verifying the results obtained in the Stuttgart basis for Na-, K-systems.
Cesium-containing systems are needed for the decision of the further tasks related to simulation of electrochemical charge transfer. For this reason quasi-relativistic basis set was implemented in the given work.
The following parameters were considered:
energy of formation of the cationic outersphere shell E
os and compositions of the most stable particles in systems I and of their analogues in the systems II, the interaction energies of outersphere shells (M+)
n
with [CrX6] complex E
int(M
n
-com) and with the rest of the model systems II
E
int(M
n
-rest), the interaction energy of the fragments {(M+)
n
[CrX6]} with the rest of the systems II
E
int(p). Note, in systems II the outersphere cations are ranked in ascending series of the (Cr-M) distances (r), that is, with an increase in the number n the distance r(Cr-M(n)) increases, too.
The E
os dependences of the number of cations n always have a minimum at some intermediate n
min value (i.e. n
min < n
lim). The existence of the minimum is mainly caused by an increase in the repulsion between outersphere M+ cations as their number increases. The composition of the system I at point n
min is the most stable. The composition of the most stable fragments in systems II coincides with or is close to the composition of the most stable species in appropriate systems I. That is, in considered model systems, the ligand composition of the electrolyte does not significantly affect the composition of the stable complex particles of chromium.
Although the second coordination sphere of chromium in systems II contains about 7–10 M+ cations, the energy minimum corresponds to n
min = 4 or 5 only. It means that at quantum-chemical and thermodynamic estimations of parameters of electrochemical charge transfer in molten salts it is reasonable to consider compositions with n=n
lim as a single particle and the rest of system as a background.
If we denote such fragments as [CrX6], (M+)
n
and the rest of system II by characters A, B, C, respectively, then the first energy E
int(M
n
-com) corresponds to equation A+B=AB. The second energy, that is, E
int(M
n
-rest), characterizes the equation B+C=BC.
As follows from our results for systems II, in the range n = 1-6, the energy of interaction of the cationic shell (M+)
n
with the complex E
int(M
n
-com) is larger than with the outer environment (rest of system) in all model systems except for Cs3CrF6+18CsF system where it is satisfied in the range of n = 1-5. The difference between these energies, i.e.
ΔE = E
int(M
n
-rest) – E
int(M
n
-com) (1)
corresponds to equilibrium (AB)+C=A+(BC). These results are consistent with the conclusions based on calculations of the E
os values.
The E
int(p) energy of interaction of the {(M+)
n
[CrX6]} fragment with the outer environment (the rest of the system II) as a function of the outersphere cations number were calculated from the following equation

E
int(p) = Es
– Ep
– Er
. (2)
Here the symbols Es
, Ep
and Er
denote energies of the entire model system, its fragment {(M+)
n
[CrX6]} and the rest of system II, respectively. This function has a maximum (minimal magnitude of the E
int(p) energy in absolute value) at n = 3. Thus, the composition of the fragment {(M+)
n
[CrX6]} at which its interaction with the environment is minimal (n = 3) is close to the most stable compositions (n = 4, 5).

References:
1. S.A. Kuznetsov, V.G. Kremenetsky, A.V. Popova, O.V. Kremenetskaya, V.T. Kalinnikov, Dokl.
Phys. Chem.
2009, 428 (2), 209.
2. V. G. Kremenetsky, O. V. Kremenetskaya, S. A. Kuznetsov, V. T. Kalinnikov, Dokl. Phys. Chem.
2011, 437 (2) 75.