Topological study of chemical bonds under pressure: solid hydrogen

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Topological study of chemical bonds under pressure:

solid hydrogen

Vanessa Riffet, Vanessa Labet, Julia Contreras-García

To cite this version:

Vanessa Riffet, Vanessa Labet, Julia Contreras-García. Topological study of chemical bonds under pressure: solid hydrogen. Joint AIRAPT-25 & EHPRG-53 - International Conference on High Pressure Science and Technology, Aug 2015, Madrid, Spain. �hal-02262295�

P63/m s

Topological study of chemical bonds under pressure:

solid hydrogen

Vanessa Riffet ^a ; Vanessa Labet ^b ; Julia Contreras-García ^a

a

Laboratoire de Chimie Théorique, Université Pierre et Marie Curie and CNRS, F-75005 Paris, France. E-mail : vanessa.riffet@lct.jussieu.fr

b

Laboratoire MONARIS, Université Pierre et Marie Curie and CNRS, F-75005 Paris, France.

Introduction

H

₂

is the simplest molecule and as any molecular solid, hydrogen is expected to polymerize under pressure. The comprehension of the mechanism by which this polymerization occurs is the main motivation for the work presented here. For that, we used a topological approach to reveal the process of polymerization using the NCI topological tool.[1] The current best plausible structural candidates for hydrogen under pressure were investigated theoretically in Refs [2,3].

Theoretical background

3H ₂ molecular model

Conclusion

Best candidates

➢ 3H

₂

molecules confined in a ring

➢ imposed D

_3h

symmetry

➢ the d distance adjusted to model the effect of pressure

➢ Wigner-seitz radius and d relationship: 2πd = 6(2r

_s

a

₀

)

➢ molecular motif contained in C2/c and Cmca-12

2.47 1.48

1.09 0.94

0.88 0.74

75 100 125 150 175 200 225 250

-0,30 -0,25 -0,20 -0,15 -0,10 -0,05 0,00 0,05 0,10 0,15

0,74 0,94 1,14 1,34 1,54 1,74 1,94 2,14 2,34 d (pm)

sign(λ 2)ρ(a.u.)

r_s

To have a better understanding of this chemical bond transformation, we decided to computationally study the following molecular model:

H H

H

H H

H

d

r_H-H

1 1

3 2 23 #2

A B

A B C D A

B A

A B A

an ABA stacking an ABCD stacking monoatomic phase

P6

₃

/m

C2/c Cmca-12 Cmca

I4

₁

/amd

The pressure range (GPa) of stability

P6₃/m: 0 < P < 105 C2/c: 105 < P < 270

Cmca-12: 270 < P < 385 Cmca: 385 < P < 490

I4₁/amd: 490 < P

Dipolar attraction for r

_s

≥ 1.58:

➢ only weak vdW interactions (ρ = 0 to 0.006 a.u.)

➢ V(λ

₂

< 0) increase and reach its maxima at r

_s

= 1.58

➢ this is correlated with the strengthening of the vdW interactions

Repulsion for 1.58 < r

_s

< 0.88:

➢ the intermolecular interactions strengthen and the covalent bonds become weaker under pressure.

➢ V(λ

₂

< 0) decreases which is correlated with the fact that the vdW interactions progressively transform into covalent bonds.

➢ V(λ

₂

> 0) continues to increase up to r

_s

= 0.99 and then decreases

Complete polymerization for r

_s

≤ 0.88:

➢ the NCI peaks 1 and 2 are superposed

➢ the interactions 1 and 2 become equivalent

➢ the model system has polymerized

➢ In dense hydrogen; each H

₂

molecule or hydrogen interacts mainly with the nearest neighbors

➢ Our analyses focuses on the solid phases using the first coordination spheres of each non-equivalent hydrogen.

-0.281

-0.263

-0.281 -0.126

-0.117 -0.111

0.061

Cmca-12, 350 GPa*

-0.189

I4

₁

/amd, 750 GPa**

-0,30 -0,25 -0,20 -0,15 -0,10 -0,05 0,00 0,05 0,10 0,15 0,20

1 10

100 1000

10000

sign(λ 2)ρ(a.u)

P (GPa)

van der Waals interactions

covalent bond

0 [ ] Dipolar attraction Repulsion

Complete polymerization

I4₁/amd C2/c P6₃/m

Cmca-12Cmca

s(ρ) = ^|𝛻ρ|

2(3π

²

)

1 3

ρ

4 3

The NCI analysis is based on the electron density and its derivatives:

Plot 2D

NCI isosurfaces

low density:

non-covalent interactions high density:

covalent bond

λ₂ > 0

repulsive contributions λ₂ < 0

attractive contributions

sign(λ₂)ρ ~ 0 vdW

r_s = 1.88

V

_NCI

= ׬ _Ω

𝑁𝐶𝐼

𝑑 Ԧ𝑟 Integration

volume of the

isosurface NCI region

#1 #2

#1

#2

polymerization

➢ similar to profile of the 3H

₂

molecular model.

➢ possibility of delimiting this profile in three regions already identified in the section « 3H

₂

molecular model ». For this, the equalization index values correlating r

_s

(3H

₂

) and P can be used (results not shown here).

➢ H

₂

solid phases and the polymerization process can be understood thanks to the 3H

₂

molecular model.

➢ Three transition regimes were highlighted: dipolar attraction, repulsion and complete polymerization.

Evolution of sign(λ

₂

)ρ values of NCI peaks Volume integrations within the NCI region

➢ The polymerization process starts in the repulsive region.

➢ The NCI topological tool is therefore a very useful tool for the analysis of bonding transformation.

[1] J. Am. Chem. Soc. 132, 6498 (2010). [2] Nature Physics 3, 473 (2007). [3] Phys. Rev. Lett. 106, 165302 (2011).

0 10 20 30 40 50 60

0,90 1,10 1,30 1,50 1,70 1,90 2,10 2,30 2,50

V (a.u)

r_s

Série1 Série2 Série3

λ₂ < 0 λ₂ > 0 Total Repulsion Dipolar attraction

*s(ρ) = 0.2 a.u. ;

color scale: -0.2 < sign(λ₂)ρ < 0.05 a.u.

**s(ρ) = 0.1 a.u. ;

color scale: -0.2 < sign(λ₂)ρ < 0.2 a.u.

ring repulsion intermolecular bond

#1 covalent bond

-0.293

-0.293 -0.043

-0.045 -0.293

-0.293

-0.285

-0.281 -0.281

-0.103

-0.099 -0.099

0.050

C2/c, 250 GPa*

P6

₃

/m, 100 GPa*

-0.267

-0.135

Cmca, 490 GPa*