Local coordination and conformation in polyether electrolytes: Geometries of M-triglyme complexes (M = Li, Na, K, Mg and Ca) from ab-initio molecular orbital calculations

SOUD STATE ELSEVIER

Solid State Ionics 86-88

IONKS

(1996) 297-302

Local coordination and conformation in polyether electrolytes: geometries of M-triglyme complexes (A4= Li, Na, K, Mg and Ca) from ab-initio molecular orbital calculations Patrik Johansson”, Institute

Shridhar P. Gejji, Jijrgen Tegenfeldt,

Jan Lindgren*

of Chemistry, Uppsala University, Box 531, S-75121 Uppsala, Sweden

Abstract We have performed ab-initio calculations on I:1 complexes of triglyme (triethylene glycol dimethyl ether) with different metal ions. Several stable tetradentate complexes have been found for each cation. The energy difference between the least stable and the most stable conformations ranges from 18 Id/mole for the Na’ complex to 9 kJ/mole for the Mg” complex. The considerable number of complexes obtained reflects the great flexibility of the oligomer chain. Keywords: Polyether electrolytes; Triglyme

complex;

Ab-initio

molecular

1. Introduction Solid polymer electrolytes containing poly ethylene oxide (PEO) are of great interest in a variety of applications such as high energy density batteries, fuel cells and electrochromic devices. A development of the pure polymer-based electrolytes is represented by polymer gel electrolytes prepared from a radiation polymerizable monomer, forming a polymer network in which a low molecular weight solvent and a salt are incorporated. In these systems both the polymer and the solvent may contain PEO oligomer segments. The coordination of metal ions to the ether oxygens of the polyethers and the chain conformations are of great importance for many of the properties of the electrolytes. In particular, the

*Corresponding

author.

0167-2738/96/$15.00 Copyright PII SO167-2738(96)00129-4

01996

orbital calculations

conduction mechanism of these electrolytes involves conformational transformations and associated transitions between different metal to polyether coordinations. In this context the available stable or metastable geometries are of interest as well as the energetics of transitions between such geometries. Experimental information on the geometry of small PEO oligomer complexes with metal ions has been obtained earlier from a large number of crystal structure determinations by diffraction [l-7]. Motivated by the need to get additional data, including energies, on these geometries and on other possible equilibrium geometries in the polymer electrolytes, we have initiated a series of model calculations on small PEO oligomers coordinated to metal ions [8]. In the present work we have extended these calculations to include ab-initio molecular orbital calculations on 1: 1 complexes of M-triethylene glycol dimethyl eEher (triglyme) for M = Li, Na, K, Mg and Ca.

Elsevier Science B.V. All rights reserved

298

2. Calculational

P. Johansson

rt al. I Solid State Ionics 86-88

method

Ab-initio Hartree-Fock (HF) self-consistent held molecular orbital calculations have been performed using the GAMESS program [9]. The basis set used has been 3-21 G* for al! calculations. Suitable starting geometries have been selected on the basis of earlier discussions by Dale [lo] and experimental structure determinations of metal ionPEO oligomer complexes. In the following we will describe the different conformations of PEO oligomers with respect to the bond sequence O-C-C-O. As an example, a typical conformer of triglyme having three such units can be defined in our terminology as aG+g’-aG+a-g’G+a. Here, a refers to an anti (or truns) arrangement around a single bond, G+(g ’ ) to a gauche arrangement and G (g-) to a gauche arrangement in the opposite direction with respect to G+ (8’). Upper-case and lower-case letters are used to identify C-C and C-O dihedral angles, respectively. In a previous ab-initio molecular orbital calculation for Li+-diglyme [8] two different, stable complexes were found. The diglyme in the two complexes had the conformations aG-a aGfa and aG+a g+G+a, referred to as structure 1 and 2 and representing two prototype structures. In both of these prototype structures a sequence of three ether oxygen atoms is suitably arranged for coordination to a metal ion. The sequence g’G+a found in structure 2 gives rise to a sharp bend referred to as a “genuine comer” [lo]. Structure 1 can be considered as a fragment of a crown ether with alternating aG_a and aGCa conformations. Practically all experimentally determined conformers in a complex of a metal ion and a short PEO oligomer [l-7] contain different combinations of structure 1 and structure 2 sequences. Consequently we have used this observation in selecting starting geometries for the metal ion-triglyme complexes. By combining the prototype structure 1 and 2 sequences in a systematic way we have arrived at the following five possible conformers: Tl = aG+g+ aG+a g+G’a, T2 = aG-a aG+g+ aG+a, T3 = aG-a aGCa g’G+a, T4= aGfa aG a aGfa and T5 = aG+a g+G+a g+G+a. All of these five conformers were used as starting geometries in the ab-initio calculations.

(1996) 297-302

3. Results and discussion 3.1. Triglyme complexes with the monovalent cations Li l, Na + and K + Selected geometry parameters and energies of the minimum energy structures obtained, Tl-T5, are presented in Tables 1, 2 and 3. For Li’ the complex with conformational sequence Tl, having a point group symmetry C,, is the global minimum energy structure. The three other local minimum energy structures obtained have energies which differ at most by 9 kJ/mole from that of the Tl structure. Quite different geometrical arrangements of the ether oxygens around Li+ are found for the four cases. The Tl complex can be described as having a distorted tetrahedral arrangement (Fig. l), whereas the T4 complex has a distorted square planar arrangement (Fig. 2). The other two types, T2 and T3, are very similar, having the cations approximately in the same plane as three of the oxygen atoms and the fourth oxygen atom out of the plane, as shown for K+-triglyme (Fig. 3). For the Na+ and K’ complexes the T4 conformation results in a distorted square planar coordination geometry, as in the case of Li+. However for Na+ and K+ the coordination is still more distorted with an enlarged 01-M-04 angle due to increasing cation radii. The T5 conformation provides the least stable complexes for both Naf and Kf and could not be obtained for the other cations, although observed experimentally for Sr*+ [l]. These T5 structures place all oxygen atoms on one side of the cation as shown for NaC-triglyme (Fig. 4) i.e., a roughly square pyramidal coordination with the cation at the apex. The dihedral angle Gt averaged over all conformations is 50” for Li+ and increases to 57” for Na+ and 62” for K+. This is probably due to decreasing Coulomb interaction in the series Li’, Na+ and K+. The corresponding angle in the pure oligomer is -75” [ll]. 3.2. Triglyme complexes Mg’+ and CaZf

with the divalent cations

Selected geometry parameters and energies of the minimum energy structures obtained, Tl-T4, are

1.946 1.933 1.951 1.941 1.943 82.2 157.1 119.6 80.4 146.4 82.7 -164.4 -42.4 - 164.4 166.9 40.5 117.4 178.9 44.9 148.1 42.6

1.936 1.946 1.946 1.936 1.941 84.6 138.6 128.5 82.0 138.7 84.5 160.8 43.2 102.4 175.9 46.6 176.1 102.4 43.2 160.9 44.3

2.320 2.296 2.296 2.320 2.308 72.0 131.4 155.2 69.2 131.8 71.9 154.5 49.0 111.0 169.6 46.9 168.9 111.5 48.8 154.6 48.2

Ca 1.923 I.890 I .977 1.885 1.919 84.6 165.0 110.0 83.9 137.7 84.9 - 177.8 -49. I ~ 177.6 - 175.8 49.4 91.4 - 165.8 52.4 162. I 50.3

1.868 1.916 1.916 1.868 1.892 88.5 129.1 131.0 86.4 129.1 88.5 171.5 46.7 84.7 -164.8 56.3 -164.5 85.1 46.9 171.4 50.0

Mg Mg

complexes

Li

of the M-triglyme

Li

Tl-T4 T2

for the structures

Tl

parameters

Bond lengths (r) in A and bond angles (a, d) in degrees.

r(M-01) r(M-02) r(M-03) r(M-04) z%r(M-0) 2 a(Ol-M-02) a(Ol-M-03) a(Ol-M-04) a(02-M-03) a(02-M-04) a(03-M-04) d(Cl-Ol-C2-C3) d(Ol-C2-C3-02) d(C2-C3-02-C4) d (C3-OZ-CCCS) d(O2-C4-C5-03) d(C4-C5-03-C6) d(C5-03-C6-C7) d( 03-C6-C7-04) d(C6-C7-04-C&3) SGk 2

Table 1 Selected geometry

2.312 2.306 2.295 2.320 2.308 71.5 140.8 146.7 69.3 139.2 71.1 - 147.7 -50.5 -171.7 171.7 44.0 138.5 153.6 47.5 146.4 47.3

Ca I.878 1.911 1.931 I .886 I.902 87.2 149.7 119.3 85.7 130.8 87.0 - 160.6 -50.7 162.8 ~ 162.6 54.5 - 168.1 81.4 45.7 173.0 50.3

Li

T3

I.935 1.951 1.948 1.942 1.944 83.8 153.6 120.5 81.7 141.9 83.8 -146.6 -45.9 170.7 - 172.8 45.2 - 179.1 102.4 42.8 161.0 44.6

Mg 2.312 2.306 2.295 2.320 2.308 71.7 140.2 145.5 69.4 131.6 71.8 - 143.5 -50.9 - 175.4 173.9 47.2 168.7 109.3 48.9 154.7 49.0

Ca

112.2

I.930 1.948 1.947 1.930 1.939 83.3 164.6 81.3 164.5 83.2 - 178.4 49.2 178.8 169.6 -52.6 169.7 178.4 49.2 - 177.9 50.3

Li

T4

I .942 1.953 1.953 1.942 1.948 82.9 158.0 116.3 80.9 158.0 82.9 147.7 45.5 -173.8 177.5 -43.6 177.7 - 173.8 45.4 147.4 44.8

Mg

2.314 2.302 2.304 2.313 2.308 71.5 140.8 147.6 69.5 140.7 71.6 147.1 50.4 172.4 -171.2 -46.9 - 172.0 173.8 50.6 145.8 49.0

Ca

P. Johansson et al. I Solid State tonics 86-88

300 Table 2 Selected geometry

parameters

for the structures

TI

r(M-01)

Tl-T5

of the M-triglyme

T2

(1996) 297-302

complexes

T3

T4

T5

Na

K

Na

K

Na

K

Na

K

Na

K

2.198 2.207 2.201 2.198 2.203 78.0 123.2 155.2 76.1 123.0 78.0 168.6 53.9 81 8 -171.6 61.6 -171.3 81.9 54.1 168.7 56.5

2.662 2.621 2.622 2.662 2.642 51.3 117.1 155.0 64.1 109.6 65.2 167.2 58.5 81.0 177.9 64.8 178.3 81.0 58.5 167.2 60.6

2.204 2.206 2.230 2.196 2.209 50.3 125.8 144.9 75.6 136.0 76.5 - 167.7 -57.0 - 179.8 - 174.1 55.0 88.4 -178.1 59.8 165.1 57.3

2.647 2.638 2.634 2.646 2.641 64.3 128.8 142.5 64.6 117.8 64.7 ~ 165.3 -62.0 - 169.2 - 178.8 59.9 82.3 171.4 64.1 165.8 62.0

2.191 2.205 2.211 2.202 2.202 17.1 146.0 136.1 15.7 128.1 77.5 -161.1 ~58.0 174.3 - 168.0 60.3 -176.1 81.2 53.0 167.3 57.1

2.641 2.639 2.614 2.662 2.639 64.8 127.7 149.8 64.1 112.1 65.2 -161.4 -63.0 - 174.3 - 177.4 64.5 173.9 80.7 57.9 165.5 61.8

2.196 2.213 2.213 2.195 2.204 76.8 149.5 133.1 75.0 149.3 76.7 164.9 58.3 - 176.0 171.8 -58.5 171.9 - 176.0 58.3 164.8 58.4

2646 2.628 2.634 2.641 2.637 64.9 128.8 166.4 64.2 128.4 64.8 163.5 63.4 174.1 - 178.3 -64.0 - 179.3 175.1 63.3 162.1 63.6

2.206 2.224 2.227 2.209 2.217 76.2 146.1 108.6 75.6 129.2 76.0 174.9 60.0 174.6 88.6 55.8 - 178.0 79.8 50.8 170.2 55.5

2.647 2.635 2.627 2.657 2.642 64.9 120.2 104.6 64.4 107.7 64.4 169.8 65.0 168.0 80.6 58.7 - 178.8 82.2 56.8 170.8 60.2

Bond lengths (r) in a and bond angles (a, d) in degrees

Table 3 Total energy (E) and relative energy (AE) for the structures

Li Na K Mg Ca

E AE E AE E AE E AE E AE

Total energies

Tl -T5 of the M-triglyme

complexes

Tl

T2

T3

T4

-616.835782 0 -770.275561 10.09 - 1205.554533 7.42 -807.672257 8.7 I -1282.609124 12.39

-616.832344 9.03 -770.276048 8.83 - 1205.555201 5.67 -807.672350 8.47 - 1282.611474 6.22

-616.835733 0.13 -770.277115 6.03 - 1205.555616 4.58 -807.673599 5.19 ~ 1282.611468 6.23

-616.832532 8.53 -770.279410 0 - 1205.557360 0 -807.675574 0 -1282.613841 0

in au and relative energies

T5

-770.212528 18.07 - 1205.553427 10.33

in kJ/mole.

presented in Tables 1 and 3. As for Na’ and K+ the distorted square planar structure with conformation T4 provides the lowest energy for both divalent cations. Two varieties of the Tl conformation of the Ca2+ complex was obtained depending on starting geometry. The two varieties are similar except that one large difference of 28” is observed for d(C2-C302-C4): 111” and 139” for the two cases. The latter value was obtained in an attempt to obtain confonna-

tion T5. On the other hand for Lif and Mg2+ similar attempts, starting either from Tl or T5 resulted in Tl conformation with identical geometries. The average G’ dihedral angle shows the same trend as for the alkali metal ions; the smaller Mg2+ gives a value of 44” and Ca2+ a value of 48”. Conformation T4 has been found experimentally to occur in the crystal structure of [Ca(SCN),triglyme] H,O [I]. Although, qualitatively, a similar arrangement (T4 conforrna-

P. Johansson

et al. / Solid State Ionics 86-88

(19%)

297-302

301

Fig. 4. The T5 conformation of Na’-Triglyme.

Fig. I. The Tl conformation of Li’-Triglyme.

tion of the triglyme, approximately square planar coordination of Ca2+ by ether oxygeni) occurs in the experimental case and in our calculations, large differences in the geometrical parameters are observed between our calculated values and the experiment. This is probably due to the presence of two SCN- ions and one water molecule in the coordination sphere of the experimental structure.

4. Concluding

Fig. 2. The T4 conformation of Lit-Triglyme.

remarks

At least four different structures of quite different geometries have been obtained for each one of the M-triglyme complexes with A4 = Li +, Na+, K+, Mg*+ and Ca2+. The structures range from a tetrahedral to a square planar arrangement of the ether oxygens. It is interesting to note that although the various stable or metastable structures obtained for

Fig. 3. The T2 conformation of K’-Triglyme.

302

P. Johansson

et al. I Solid State Ionics 86-88

triglyme complexes are quite different, they can basically be described in terms of the prototype structures of the Li+-diglyme complex (structure 1 and 2). Even using only this basic repertoire of prototype structures, one can envisage that going to longer PEO oligomers would lead to still more structures as well as coordination geometries. Furthermore we note that the energy difference between the least stable and the most stable conformers of the triglyme complexes is quite small (from 18 kJ/mole for Na+ complex to 9 kJ/mole for the Mg*+ complex). This suggests that a large number of the numerous equilibrium coordination geometries that would in principle be possible in a long-chain PEO will also occur with a substantial probability. This has important implications for the transport of ions in long-chain polyether electrolytes, since this transport has been postulated to be highly coupled to conformational transformations of the chains. Such transformations would clearly be strongly assisted by the numerous equilibrium geometries accessible for metal ion polyether complexes in such systems.

Acknowledgments This work was supported

297-302

Science Research Council and the Swedish Research Council for Engineering Sciences.

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