Extended tight binding studies of theinitial reaction between ethylenecarbonate and lithium

Uppsala University

Chemistry

Degree Project C 1KB010

Extended tight binding studies of the initial reaction between ethylene

carbonate and lithium

Author:

Johan Erkers

Supervisors:

Jolla Kullgren Peter Broqvist

July 17, 2020

Abstract

The initial reaction between ethylene carbonate(EC) and pristine lithium was studied using the density functional tight binding method GFN1-xTB. The GFN1-xTB simulations showed a thermodynami- cally favourable reaction for the bond-breaking of the C-O bond, with a change of Gibbs free energy of -1.37 eV. An evaluation of the GFN1- xTB methods fitness for systems containing lithium and EC was also performed. The study showed that the GFN1-xTB may not be well suited for systems containing lithium and EC. Several possible sec- ondary reaction products for the bond-broken EC was observed. Some of the reaction products that were observed were lithium ethylene di- carbonate (LEDC), lithium carbonate (Li ₂ CO ₃ ) and ethylene (C ₂ H ₄ ).

The effects of charge on lithium EC was studied. It was shown that

uncharged complexes had a smaller bond angle and binding distance

compered to the positively charged complexes this was true for com-

plexes with up to three coordinated EC molecules.

Contents

1 Introduction 3

2 Theory 5

2.1 Density functional theory . . . . 5

2.2 Density functional tight binding . . . . 8

2.3 GFN1-xTB . . . . 10

3 Method 11 4 Results and Discussion 11 4.1 Evaluation of GFN1-xTB . . . . 12

4.2 Ethylene carbonate complexes . . . . 16

4.3 Initial reaction . . . . 18

4.4 Formation of lithium ethylene dicarbonate . . . . 19

4.5 Other secondary reactions . . . . 21

5 Conclusion 25

6 References 26

1 Introduction

The use of lithium-based batteries permeates our society today from use in mobile devices and computers to use in the automotive industry. Therefore it is important to study the functions of these batteries. There are two forms of lithium based batteries that are of interest to many studies. These are lithium-ion and lithium metal batteries. The reason lithium is used is due to the high specific energy density of ≈ 250 ^{W h} _kg for lithium-ion batteries and

≈ 440 ^{W h} _kg lithium metal, as well as the electrochemical potential of –3.04 V versus the standard hydrogen electrode(SHE), which is the lowest of all the elements. [1, 2, 3] The low electrochemical potential of metallic lithium makes it a highly reactive element. The high reactivity of lithium can cause dendrite formation in the electrolyte of the battery which in turn causes a drop in capacity as well as cause safety concerns as the dendrite formation might short circuit the battery and ignite the electrolyte.

Lithium-based batteries form a passivizing layer at the electrodes that pre- vents further reactions, this layer is called the solid electrolyte interphase(SEI).

The formation and stability of the SEI is of great importance to the func- tionality of the battery. The formation of the SEI accrues when the battery power is cycled, causing the lithium and electrolyte to react and form organic and inorganic compounds at the interface.[4] Therefore it is of interest to in- vestigate interactions between the electrolytes and lithium and to control the process of the interactions.

There have been several studies on the degradation of electrolytes used in

lithium batteries.[5, 6, 7, 8, 9, 10, 11] Methods that have been used are Fourier

transformed infrared spectroscopy(FTIR)[5, 6, 10] and X-ray photoelectron

spectroscopy(XPS)[4, 12]. Several reaction products have been identified

such as lithium ethylene dicarbonate(LEDC), lithium carbonat(Li ₂ CO ₃ ),

RCOOLi, ROCO ₂ Li, (ROCO ₂ Li) ₂ and RCO ₂ Li.[10, 12] Gas chromatography

(GC) has been used to identify gases that are formed when the reaction be-

tween the electrolytes and lithium has taken place. These gases are CO ₂ ,

CO, CH ₄ , C ₂ H ₄ , C ₂ H ₆ and more.[10] Several studies have been done using

computational methods to evaluate the formation of the SEI for various elec-

trolytes by the use of density functional theory (DFT), ab initio molecular

dynamics (AIMD) and molecular dynamics(MD) methods.[6, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23]

Ethylene carbonate (EC) is a widely used chemical as an electrolyte in lithium batteries due to its favourable dielectric constant and viscosity. It also haves the ability to form a stable SEI. Therefore, it is of intrest to decipher the reactions of EC that leads to the formation of the SEI. Figure 2 shows a description of what the different parts of the EC molecule will be named in this report.

Figure 1: Figure of EC molecule with different labels to differentiate the atoms position in the molecule. The red spheres are oxygen the dark grey carbon and white ones hydrogen.

The aim of this project is by the use of simulations to identify the possible

initial reaction between pristine lithium and EC as well as identifying the

reaction products. It is also of interest to investigate the effects that the

reaction products will have on the continued reaction. The density functional

tight binding (DFTB) GFN1-xTB model was also evaluated by comparing

the optimised geometries and energies with experiments and other theoretical

studies. The evaluations was done to investigate the possible application of

the GFN1-xTB model to other systems such as polymer electrolyte batteries

and lithium metal batteries.

2 Theory

This part will be dedicated to the theory of the methods that will be used to simulate the formation of the SEI. The methods that will be discussed in this section are density functional theory (DFT), density functional tight binding (DFTB) and the tight-tinding quantum chemical method labelled as Geometry, Frequency, Noncovalent, eXtended Tight-Binding (GFN1-xTB).

The theory part will not be exhaustive but rather simplified so as to give a overview of the methods and to shed light on what separates these methods from one another.

2.1 Density functional theory

The foundation of density functional theory is found in the Hohenberg- Kohn theorem.[24] Lets begin by considering a system of N interacting elec- trons(spin 1/2-particles) under the influence of an external potential ˆ v _ext (r).

The Hamiltonian ˆ H for such a system can be found in equation 1.

H = ˆ ˆ T + ˆ V _ext + ˆ W (1)

T in equation 1 is the kinetic energy operator. ˆ

T = − ˆ 1 2

N

X

i=1

∇ ² _i (2)

The ˆ V _ext term is an operator of the external potential ˆ v _ext (r).

V ˆ _ext =

N

X

i=1

ˆ

v _ext (r _i ) (3)

The term ˆ W represents the operator the of particle-particle interaction.

W = 1/2 ˆ

N

X

i,j=1;i6=j

w(r _i , r _j ) (4)

If the eigenstates of the Hamiltonian ˆ H are defined to be |Ψi then these can be used to define the Schr¨ odinger equation 5

H |Ψi = E |Ψi ˆ (5)

Let’s consider the ground state function |Ψ ₌ i from which we can define the electronic density of the ground state from the electronic density ˆ n(r) 6

n ₀ (r) = hΨ ₀ |ˆ n(r)|Ψ ₀ i (6) n ₀ (r) is a functional(a function of other functions) of ˆ v _ext (r). If it can be proven that ˆ v ext (r) is a unique functional n 0 (r) then an effective computa- tional method can be devised to solve quantum mechanical problems. The proof is of the form reductio ad absurdum.[24] Let’s begin by assuming that there exists another external potential ˆ v ⁰ _ext (r) with a ground state function Ψ ⁰ ₀ that has the same ground electronic density n ₀ (r). With the exception of the trivial case ˆ v ⁰ _ext (r) − ˆ v _ext (r) = constant. Ψ cannot be equal to Ψ ⁰ because they satisfy different Schr¨ odinger equations.[24, 25, 26, 27] For the two potential ˆ v _ext ⁰ (r) and ˆ v _ext (r) we define the Hamiltonians( ˆ H and ˆ H ⁰ ) and ground state energies(E and E’).

From equation 1 it is clear that ˆ H ⁰ = ˆ H + ˆ V ⁰ − ˆ V From the properties of the ground-state the following assumption is made:[24]

E ₀ ⁰ = hΨ ⁰ ₀ | ˆ H ⁰ |Ψ ⁰ ₀ i < hΨ ₀ | ˆ H ⁰ |Ψ ₀ i (7) From this we get the following equation:

E ₀ ⁰ < E ₀ + Z

d ³ r n ₀ (r)[ˆ v _ext ⁰ (r) − ˆ v _ext (r)] (8) But the the primed and unprimed quantities can be interchanged giving the following equation:

E ₀ < E ₀ ⁰ + Z

d ³ r n ₀ (r)[ˆ v _ext (r) − ˆ v _ext ⁰ (r)] (9) Adding equation 8 to 9 we get the following contradiction:

E ₀ + E ₀ ⁰ < E ₀ ⁰ + E ₀ (10)

This proves that n ₀ (r) is a unique functional of ˆ v _ext (r). Because we have proven that n ₀ (r) is a unique functional of ˆ v _ext (r) we can use the variational principle to minimise the energy by the following equation:

∂

∂n(r) [E(n − µ(

Z

d ² r n(r) − N ))] (11) E[n ₀ (r)] < E[n ⁰ ₀ (r)] ⇐⇒ E ₀ = min(E[n]) (12) But in order to make an effective energy minimisation we must first find a way to construct a system that separates the particle interactions. This is done by the Kohn-Sham scheme.[24, 25, 26, 27] The Kohn-Sham scheme functions by introducing a system of non-interacting particles, but in order to have an accurate description of energy an exchange and correlation term needs to be introduced. This yields the following definition of the total energy:

E[n] = T [n] + E H [n] + E ext [n] + E XC [n] + E II [n] (13) Where T is the kinetic energy contribution for a non-interacting system, E _ext is the energy of the external field, E _XC is the exchange-correlation term, E _H is the hartree energy contribution and the E II is the energy contribution of ion-ion interactions. The hartree term describes the interaction between the particle and the electron density n.[24, 25, 26, 27] The E _XC term can be described as:

E _XC = (T _i − T ) + (E _ee − E _H ) (14) Where E ee is the energy of the electron-electron interaction. T i is the kinetic energy term for a system of interacting particles. From equation 13 we get the following Hamiltonian:

H = − 1

2 ∇ + V ext + V H + V XC (15)

The exchange-correlation energy E XC contains the energy contribution from

the system of interacting particles. The construction and formation of E _XC

and the functional of the exchange-correlation (V _XC ) is not clear and there-

fore there exists many ways of calculating it. This leads to several different

ways of describing the exchange-correlation functional V _XC .

2.2 Density functional tight binding

The density functional tight binding (DFTB) method is derived from DFT eq 13 but for the case of a small change in the electron density ∂n(r):

E[∂n] ≈ X

a

f _a hΨ _a | ˆ H[n ₀ ]|Ψ _a i

+ 1 2

Z Z 0

( ∂ ² E _XC [n ₀ ]

∂n∂n ⁰ + 1

|r − r ⁰ | )∂n∂n ⁰ − 1 2

Z

V _H [n ₀ ](r)n ₀ (r) + E _XC [n ₀ ] + E _II −

Z

V _XC [n ₀ ](r)n ₀ (r)

(16) The first term of equation 16 is the representation of the electronic band structure:

E _BS = X

a

f _a hΨ _a | ˆ H[n ₀ ]|Ψ _a i (17) Where ˆ H represents the the Hamiltonian in equation 15 but for the ground state electron density and without any charge transfer. The second term in equation 16 represents the term of charge fluctuation, primarily from Coulomb interaction but also from the exchange-correlation contribution.[27]

E _CF [∂n] = 1 2

Z Z 0

( ∂ ² E _XC [n ₀ ]

∂n∂n ⁰ + 1

|r − r ⁰ | )∂n∂n ⁰ (18) The last terms of the equation represent the so called repulsive energy of the system:

E _rep = − 1 2

Z

V _H [n ₀ ](r)n ₀ (r) + E _XC [n ₀ ] + E _II − Z

V _XC [n ₀ ](r)n ₀ (r) (19) Equation 16 can now be written as:

E[∂n] = E _BS + E _CF [∂n] + E _rep (20)

The energy terms can be simplified more in order to reduce the calculation

cost. The repulsive term E _rep can be simplified as a function of the atom

pair interaction based only on the elements and their distances.[27] So for each atom pairs IJ we define a repulsive function V _rep ^IJ (R) such that:

E _rep = X

I<J

V _rep ^IJ (R _IJ ) (21)

The atomic pair repulsive function V _rep ^IJ (R) can be calculated theoretically which yield specific parameters for the atom-atom interaction.[27] The charge fluctuation term E _CF can be simplified as this:

E _CF = 1 2

X

IJ

γ _IJ (R _IJ )δq _i δq _j (22) Where δq represents the extra electron population which can be expressed as a function of the electron density n(r) and where γ _IJ is the following function:

γ _IJ =

( U _I , I = J

erf (C

,R

)

R

, I 6= J (23)

Where U _I is the Hubbard parameter for the atom which is related to the elec- tron affinity and the the ionization energy of the atom. The function C _IJ is a function related to the charge distribution which is approximated by a spher- ical symmetric charge distribution, usually a Gaussian type distribution.[27]

For the band-structure contribution E _BS this is done by introducing tight- binding of the electrons meaning the electrons are tightly bound to their atoms and molecules. Tight-binding also means that local minimum basis can be used to construct the basis functions:

Ψ _a (r) = X

µ

C _{µ µ} ^a (r)φ (24)

The minimality of the basis function means that they are represented by one radial function for each angulur momentum state implying that there is one radial function for the s-shell, three for the p-shell and so on. This is usually done by the use of spherical harmonics.[27] This yields a function for E _BS

E _BS = X

a

f _a X

µv

c ^a _µ ^∗ c ^a _v H _µv ⁰ (25) Where the term H _µv ⁰ is:

H _µv ⁰ = hρ _µ | H ⁰ |ρ _v i (26)

The elements of the matrix H _µv ⁰ can be treated just as numbers which makes

it simpler. In eq 28,26 µ and v represents atomic orbitals.

2.3 GFN1-xTB

Geometry, Frequency, Noncovalent, eXtended TB(GFN1-xTB) is a method based on DFTB methodology but certain parts have been modified such that the number of atom-pair specific parameters are reduced. The atom- atom specific parameters are often replaced by element specific parameters.

The GFN1-xTB method is adapted for all elements up to Radon(Z=86) and it is also well adapted for all types of elements.[28] The expression for the total energy in the GFN1-xTB method is described by the following equation:

E = E _el + E _rep + E _disp + E _XB (27) From the expression an electronic(el) part can be found as well as a repul- sion(rep) part, a dispersion(disp) part and a halogen binding(XB) term.[28]

The electronic part can be described by the expression:

E _el = X

i

n _i hΨ _i |H ₀ |Ψ _i i+ 1 2

X

A,B

X

l(A)

X

l

(B)

p ^A _l p ^B _l

γ _AB,ll

+ 1 3

X

3

Γ _A q _A ³ −T _el S _el (28)

Where Ψ _i represents the valence molecular orbits(MOs) with the occupa- tional number n _i . The MOs are expressed as a linear combination of atom- centred orbitals(LACO) and are approximated with Slater-type

orbitals(STOs)[28] in the following expression:

Ψ _i =

N

X

µ

c _µi φ _i (ξ, ST O − mG) (29)

N AO represents the total number of atomic orbitals(AOs).The ξ term is a element specific parameter and c is just a scaling term. The H ₀ term rep- resents the zero-order Hamiltonian for the system. The second term in the expression is summed over the the atoms A and B as well as their cor- responding shells l and l ⁰ . The part p ^X _l is the charge distribution over the orbital shells with angular momentum l on atom X. The γ _AB,ll

term is the Mataga−Nishimoto−Ohno−Klopman formula which depends on the distance between the atoms as well as the chemical hardness and a global parameter that is fitted from other models such as DFT. q _a is the Mulliken charge of atom A and Γ a is the charge derivative of the Hubbard parameter.

The T _el S _el term describes the electronic free energy. T _el is the electronic free

energy that is a adjustable parameter. S _el is the overlap matrix of the atomic

orbitals.[28] The dispersion energy is similar to another DFTB method. The repulsive energy term takes the form of a pairwise potential of the form:

E _rep = X

AB

Z _A ^{ef f} Z _B ^{ef f}

R _AB e ^−(α

^α

^)1/2(R

^)k

(30) Where k _f is a global parameter, α is a element-specific parameter and Z ^eff is the effective nuclear charge which is fitted. The Halogen-bonding(XB) was fitted using a pairwise Lennard-Jones potential which contains several global parameters.[28]

3 Method

All calculations were made in the software Amsterdam modelling suite (AMS) made by software for chemicals and materials (SCM).[29] The systems were constructed by building the EC molecule and then placing Li at several dif- ferent positions around the EC molecule. Once the Li and EC molecules were placed the system was geometry optimised and then vibrations anal- yses were performed. Some manual stretching of bonds was performed to initiate some reactions. The Computer used for the simulations was a lap- top with a processor with 2 cores(intel(r) core(tm) i5-3230m cpu @ 2.60ghz 2.60ghz).

4 Results and Discussion

The initial part of this section will be dedicated to the evaluation of the GFN1-xTB to better understand the capabilities and limitations of the GFN1- xTB method. In the evaluation, information regarding complex formation is presented and then compared to results acquired in other studies. In or- der to investigate the the complexes further, a comparison is made between +1 charged and uncharged complexes. The report then continues with lay- ing out the results for the initial reaction between lithium and EC and how these reaction products may react further. The polarity of the EC molecule can be approximated from the electronegativity of the atoms, this shows a dipole-moment with direction from the Cx atom to the Ox atom.

General sources of error for this studies are related to the circumstances

of the simulations. One problem was that the simulations were carried out in gas-phase which is not ideal as the lithium batteries are usually liquid- phase with viscosity and solvation effects that are not taken into account. In future studies the simulations should be performed in a liquid-phase as this would increase the relevance of the study.

4.1 Evaluation of GFN1-xTB

From previous studies is has been shown that the most likely amount of EC in the solvation shell was 4.[30, 31] The data in table 1 shows the calculated binding distances for EC at various conditions, calculated by geometry op- timisation. The binding distance appears to be reasonable when compared to previous studies and experiments.[15, 18, 32] Compared to the previous studies the calculated binding distances are shorter. This may be due to the fact that the EC is calculated to be planar see tables ,3,6, while in the other studies the ethylene carbonate is non-planar and puckered. The dif- ference may also be due to the fact that ab initio and DFT methods were used in those studies whereas this study is based on DFTB methodology which is a method that dose not describe systems as rigorously as those methods.[15, 18, 32, 33] Calculation time comparison between DFT method RPBE-D3-ADZP and GFN1-xTB was done by geometry optimisation of EC the total elapsed time was 223.99 min for RPBE-D3-ADZP and 12.38 min for GFN1-xTB. The GFN1-xTB study showed that a full geometry optimi- sation of a system of 453 atoms took 14 min on 4 CPUs. Compared to the DFT method PBEh-3c which took 20 min for one optimisation step with 16 CPUs.[28] The experimental data(exp) for EC was taken from Masia et al.

[15]

Figure 2: Figure of EC molecule with different labels to differentiate the atoms position in the molecule and a bonding angel. The red spheres are oxygen the dark grey carbon and white ones hydrogen.

Table 1: Binding distance between the parts in the [Li(EC) _n ] ⁺ .

EC(calc) EC(exp) [Li(EC)] ⁺ [Li(EC) ₂ ] ⁺ [Li(EC) ₃ ] ⁺ [Li(EC) ₄ ] ⁺ Li-Ox - - 1.620 ˚ A 1.704 ˚ A 1.770 ˚ A 1.843-1.846 ˚ A Ox-Cx 1.184 ˚ A 1.203 ˚ A 1.224 ˚ A 1.212 ˚ A 1.263 ˚ A 1.194 ˚ A Cx-Os 1.350 ˚ A 1.342 ˚ A 1.309 ˚ A 1.318 ˚ A 1.327 ˚ A 1.334 ˚ A Os-Ch 1.412 ˚ A 1.457 ˚ A 1.430 ˚ A 1.426 ˚ A 1.422 ˚ A 1.419 ˚ A Ch-h 1.096 ˚ A 1.522 ˚ A 1.094 ˚ A 1.094 ˚ A 1.095 ˚ A 1.095 ˚ A Ch-Ch 1.543 ˚ A 1.091 ˚ A 1.542 ˚ A 1.542 ˚ A 1.542 ˚ A 1.545 ˚ A

Table 2: Binding angels in [Li(EC) n ] ⁺ complexes.

EC(calc) EC(exp) [Li(EC)] ⁺ [Li(EC) ₂ ] ⁺ [Li(EC) ₃ ] ⁺ [Li(EC) ₄ ] ⁺

Li-Ox-Cx - - 179.9 179.9 177.9 176.1

Ox-Cx-Os 125.1 124.17 123.4 123.8 124.2 124.5

Os-Cx-Os 109.8 111.67 113.1 112.3 111.7 111.1

Table 2 shows the bond angle calculated for EC by geometry optimisation.

The bond angle is similar to data acquired in a previous study with the exception for the case of a complex with four coordinated ECs. The bond angle Li-Ox-Cx shows that the introduction of the lithium ion to EC does not bend any binding in the EC molecules.

Table 3: Dihedral angel in [Li(EC) _n ] ⁺ complexes.

EC(calc) EC(exp) [Li(EC)] ⁺ [Li(EC) ₂ ] ⁺ [Li(EC) ₃ ] ⁺ [Li(EC) ₄ ] ⁺

Ox-Cx-Os-Ch 180.0 - 180.0 180.0 179.8 176.1

Cx-Os-Ch-Ch 0.0 21.25 0.0 0.0 0.5 0.2

Os-Ch-Ch-Os 0.0 -24.80 0.0 0.0 0.5 0.3

Os-Cx-Os-Ch 0.0 -8.73 0.0 0.0 0.2 0.2

Ox-Cx-Os-Os 180.0 171.27 180.0 180.0 180.0 179.9

The data presented in table 3 shows the dihedral angle of EC as a part of a

complex as well as when it is not a part of a complex. The data was acquired

by geometry optimisation. The dihedral angle of the complex indicates that

it is planar for every system. This seems to be problematic even though

this is in line with some theoretical studies.[32, 34] Even though there are

studies showing the possibilities of EC taking a planar conformation, it is

contradicted by experimental studies as well as other theoretical studies that

have been done.[15, 33, 35, 36, 37]

Figure 3: Various complexes of ethylene carbonate and lithium with one positive charge and from one to four EC molecules coordinated to the lithium.

The red spheres represent oxygen, dark grey carbon, white hydrogen and light grey lithium.

From figure 3 it is clear that the ethylene carbonate complexes for the com- plexes with 1-3 EC molecules form planar complexes, which is consistent with other studies.[15, 33] The exception is the complex with four EC that forms a tetrahedral complex, which is also consistent with previous studies.[15, 33]

It seems that the GFN1-xTB method may not be a optimal method to study

the complex formation of EC molecules. This may be due to electron corre-

lation not being well adapted for this method. One should also keep in mind

that the method used in this project is a DFTB method which is adapted for

larger systems compared to the ab initio hartree-fock selfconsistent field(HF-

SCF) and DFT methods used in earlier projects meaning it will probably be

less accurate than more computationally demanding methods. GFN1-xTB is

though capable of analysing larger systems compared to other methods and

that it is well adapted for all types of elements. [15, 28, 33, 34, 36]

4.2 Ethylene carbonate complexes

Further studies were done on the ethylene complex formation because it was also of interest to investigate if the charge of the complex had any impact on the form of the complex. From table 4 it becomes clear that the bind- ing distance of the binding Li-Ox decreases for the complexes with up to 3 ECs coordinated, which is reasonable as the charge difference between the lithium and the EC molecules will be larger. The Ox-Cx and Cx-Os bonds in the uncharged complex show an increase in binding distance compared to those in the charged complexes. The longer binding distance is a result of the Li atom having a stronger pull on the parts of the ECs closer to the lithium atom stretching the Ox-Cx and Cx-Os bindings. Due to the fact that GFN1-xTB uses general parameters for atoms rather then atom-pair specific parameters like other DFTB method could be problematic because some specific information on interactions may be lost.[28]

Table 4: Binding distance between the parts in the [Li(EC) n ] complexes.

[Li(EC) _n ] [Li(EC) ₂ ] [Li(EC) ₃ ] [Li(EC) ₄ ] Li-Ox 1.599 ˚ A 1.663-1.684 ˚ A 1.760-1.771 ˚ A 1.834-1.869 ˚ A Ox-Cx 1.303 ˚ A 1.253 ˚ A 1.224 ˚ A 1.208 ˚ A Cx-Os 1.407 ˚ A 1.380 ˚ A 1.368 ˚ A 1.368 ˚ A Os-Ch 1.404 ˚ A 1.407 ˚ A 1.407 ˚ A 1.407 ˚ A Ch-h 1.099 ˚ A 1.097 ˚ A 1.098 ˚ A 1.098 ˚ A Ch-Ch 1.546 ˚ A 1.547 ˚ A 1.546 ˚ A 1.546 ˚ A

Table 5: Binding angels in [Li(EC) _n ] complexes.

[Li(EC) _n ] [Li(EC) ₂ ] [Li(EC) ₃ ] [Li(EC) ₄ ]

Li-Ox-Cx 163.1 177.1 178.1 172.5

Ox-Cx-Os 116.7 123.7 124.7 124.9

Os-Cx-Os 108.2 111.1 110.5 110.1

Table 5 shows the bond angle of the uncharged complexes from which we can

see that the charge does effect the bond angle. The uncharged Li[EC] has a

smaller bond angle for the Li-Ox-Cx angel. This may be due to lithium being

more attracted to the Os oxygens of the EC as the addition of an electron

may cause a change in local charge density. But the Li-Ox-Cx bond angle for complexes with more ECs in them seems to be almost unaffected by the charge increase. This is most likely due to the extra electron being dispersed among all EC molecules and therefore mitigating its effect on each individual EC molecule.

Table 6: Dihedral angel in [Li(EC) _n ] complexes.

[Li(EC) n ] [Li(EC) 2 ] [Li(EC) 3 ] [Li(EC) 4 ] Ox-Cx-Os-Ch 140.2 161.5 180.6 182.3

Cx-Os-Ch-Ch 3.6 0.9 0.7 0.1

Os-Ch-Ch-Os 0.5 2.9 0.7 0.5

Os-Cx-Os-Ch 6.3 4.9 0.1 1.0

Ox-Cx-Os-Os 226.1 202.0 181.0 177.0

The dihedral angles of the Li[EC] _n complexes in table 6 show that although

there is some difference between the charged and uncharged complexes, all

the ECs tend towards a planar structure which is similar to that of the

charged complexes. The most significant difference is the bond angle on the

Li[EC] and Li[EC] ₂ structures. The bending probably occurs due to a more

favourable binding for the lithium with some of the oxygen.

Figure 4: Various uncharged complexes of ethylene carbonate and lithium with one to four EC molecules coordinated to the lithium

From figure 4 one can see that the Li[EC] ₂ and Li[EC] ₃ form planar complexes like the charged complexes do, see figure 3. The Li[EC] ₄ complex forms a tetrahedral structure which is also like the ones observed in the charged complexes.

4.3 Initial reaction

The initial reaction between a Li atom and a EC molecule can take many

forms. The reaction pathway that seems to be the most suggested is seen in

figure 5.[16, 19, 20, 38]

(a)

− I

→

(b)

− II →

(c)

Figure 5: Suggested initial reaction between pristine lithium and ethylene carbonate

The systems were calculated using the GFN1-xTB with geometry optimi- sation as well as frequency analysis. The calculated Gibbs free energy (G) of the system was: (a):-622.19 eV, (b):-623.10 eV and (c):-623.56 eV. This results in a total change in Gibbs free energy of −1.37 eV. This shows that the reaction is thermodynamically favourable. For the reaction steps I and II we have a change in Gibbs free energy of I:−0.91 eV and for II:−0.45 eV. In the study by Wang et al[19], it was found that the change in Gibbs free energy was -1.40 eV for the formation of (c) which is comparable to the change in Gibbs free energy acquired in this study. It is to be noted that the starting configurations in this study differ from theirs.[22] Even though Cx-Os bond breaking has been suggested in other studies no such reaction was successfully made in this study. The reaction barrier for the reactions I and II has been estimated to be low. [38]

4.4 Formation of lithium ethylene dicarbonate

The formation of lithium ethylene dicarbonate (LEDC) is suggested to occur

when the product (c) from figure 5 reacts with another (c) molecule. From

the calculations performed with the two (c) molecules through geometry

optimisation, the complex that was formed can be seen in figure 6.

Figure 6: Lithium ethylene dicarbonate with an ethylene(C ₂ H ₄ ) molecule

The Gibbs free energy that was calculated for this system was -1250.59 eV.

The Gibbs free energy of an individual (c) molecule is -623.56 eV, so the Gibbs

free energy of two are −1247.12 eV. This means that the change in Gibbs

free energy is −3.47 eV. This means that the reaction is thermodynamically

favourable. The thermodynamical favourablity of the reaction is in line with

the fact that LEDC has been deemed to be one of the primary precursors for

SEI formation. The formation of C ₂ H ₄ is also in line with what experimental

studies have shown.[5, 6, 10, 13, 17]

Figure 7: Lithium ethylene dicarbonate with an ethylene(C ₂ H ₄ ) molecule

Figure 6 does not represent the only possible conformation of LEDC. During the project another conformation of LEDC was discovered that has a lower Gibbs free energy then that shown in figure 6. This conformation can be seen in figure 7. The Gibbs free energy for that system was calculated to be - 1252.05 eV this suggests a change of Gibbs free energy from two (c) molecules to be −4.93 eV. The reason that the calculations did not converge to a single form of LEDC might be due to the system having several local minima and an energy gradient that differs depending on the starting positions of the molecules involved in the reaction. This might also be due to the GFN1- xTB method allowing other conformations that might not be allowed in other methods or because GFN1-xTB describes the system poorly.

4.5 Other secondary reactions

Throughout this study several other reaction products have been found. The

system to be discussed is the system that can be seen in figure 8.

Figure 8: Lithium carbonate(Li ₂ O ₃ ) with a ethylene(C ₂ H ₄ ) molecule and ethylene carbonate

As can be seen in figure 8 there is a formation of lithium carbonate as well

as an ethylene carbonate molecule that has been reformed and a ethylene

molecule. The Gibbs free energy for the system was calculated to be -1250.98

eV and the change in Gibbs free energy −3.86 eV. Because the formation of

both Li ₂ CO ₃ and C ₂ H ₄ is well documented, it makes this reaction pathway

probable.[10, 5, 6] The reaction is also termodynamicly favourable, which

suggests that formation of these reaction products is probable.

Figure 9: A system of hydrogen carbonate and a broken ethylene carbonate with a additional hydrogen group ethyne(C ₂ H ₂ ) molecule

Figure 9 shows the formation of an ethyne(C ₂ H ₂ ) molecule as well as a

molecule that is similar to the one in (c) which has an additional hydro-

gen. The Gibbs free energy for the system was calculated to be -1251.22 eV

and the change in Gibbs free energy −4.10 eV. Also this system is thermo-

dynamically favourable. The problem with this system is that the formation

of ethyne is not well documented. This can be due to the calculations of the

model resulting in a unlikely system or it could be that the reaction barrier

for this system is high, meaning the formation rate of these product would

be low.[10] Another hypothesis would be that the ethyne reacts quickly so

that it is not detected.

Figure 10: System of carbon and oxide formed with Li atoms formed from a reaction of two opened ethylene carbonate

Figure 10 shows a reaction product that seems to consist of an EC with a molecule (c) having attached itself to the Cx carbon. The Gibbs free energy for this system was calculated to be -1250.21 eV and the change in Gibbs free energy −3.10 eV, which shows the system is thermodynamically favourable.

Based on prior studies this seems to be a possible reaction product. [5, 6,

10]

5 Conclusion

The purpose of this project has been to identify the initial reaction between lithium and ethylene carbonate and the reaction products from the reactions.

A plausible initial reaction pathway between lithium and ethylene carbon-

ate has been identified. It was also found that the reaction pathways were

thermodynamically favourable. Some plausible reaction products have been

identified for the reaction of the initial reaction products and the formation

of these products were found to be thermodynamically favourable. The re-

action products that have been suggested are LEDC, C ₂ H ₄ and Li ₂ CO ₃ . The

GFN1-xTB method was evaluated and compared to previous studies. It was

shown that the GFN1-xTB method was not well adapted for the system it

was tested for, but there are modifications to the method which could effect

the results. It has also been shown that altering the charge of a complex of

lithium coordinated with EC has some effects such as changes in the bond

angle and binding distance. The change in Gibbs free energy for all reactions

has were rather high.

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