In the format provided by the authors and unedited.

Stable Compound of Helium and Sodium at High Pressure Xiao Dong,1, 2, 3 Artem R. Oganov,3-6*, Alexander F. Goncharov,7,8, Elissaios Stavrou,7,9 Sergey Lobanov,7,10

Gabriele Saleh,5 Guang-Rui Qian,3 Qiang Zhu,3, Carlo Gatti,11 Volker L. Deringer12, Richard Dronskowski12,

Xiang-Feng Zhou,1, 3* Vitali Prakapenka,13 Zuzana Konôpková,14 Ivan Popov,15 Alexander I. Boldyrev15 and

Hui-Tian Wang1,16*

1School of Physics and MOE Key Laboratory of Weak-Light Nonlinear Photonics, Nankai University, Tianjin 300071, China

2Center for High Pressure Science and Technology Advanced Research, Beijing 100193, China

3Department of Geosciences, Stony Brook University, Stony Brook, New York 11794-2100, USA

4Skolkovo Institute of Science and Technology, 3 Nobel St., Moscow 143026, Russia

5Moscow Institute of Physics and Technology, 9 Institutskiy Lane, Dolgoprudny city, Moscow Region, 141700, Russia

6International Centre for Materials Discovery, Northwestern Polytechnical University, Xi’an, 710072, China

7Geophysical Laboratory, CIW, 5251 Broad Branch Road, Washington, D.C. 20015, USA

8 Key Laboratory of Materials Physics and Center for Energy Matter in Extreme Environments, Institute of Solid

State Physics, Chinese Academy of Sciences, 350 Shushanghu Road, Hefei, Anhui 230031, China

9Lawrence Livermore National Laboratory, Physical and Life Sciences Directorate, P.O. Box 808 L-350, Livermore, California 94550, United States

10Sobolev Institute of Geology and Mineralogy Siberian Branch Russian Academy of Sciences, 3 Pr. Ac. Koptyga, Novosibirsk 630090, Russia.

11Istituto di Scienze e Tecnologie Molecolari del CNR (CNR-ISTM) e Dipartimento di Chimica, Universita’ di Milano, via Golgi 19, 20133 Milan, Italy

12Chair of Solid-State and Quantum Chemistry, RWTH Aachen, D-52056 Aachen, Germany

13Center for Advanced Radiation Sources, University of Chicago, Chicago, IL 60637, USA

14Photon Science DESY, D-22607 Hamburg, Germany

15Department of Chemistry and Biochemistry, Utah State University, Logan, Utah 84322, USA.

16 Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, 210093, China

Stable compound of helium and sodium at high pressure

© 2017 Macmillan Publishers Limited, part of Springer Nature. All rights reserved.

SUPPLEMENTARY INFORMATIONDOI: 10.1038/NCHEM.2716

NATURE CHEMISTRY | www.nature.com/naturechemistry 1

0

10

20

30

Fre

que

ncy(

TH

z)

WKWXLW

Supplementary fig. 1. Phonon dispersion curves of Na2He at 300 GPa, computed using PHONOPY and VASP.

0 200 400 600 800

-0.137

-0.136

-0.135

-0.134

-0.133

-0.132

-0.131

-0.130

G(e

V/a

tom

)

temperature(K)

Supplementary fig. 2. Predicted Gibbs free energy of formation of Na2He as a function of temperature at the

pressure of 300 GPa.

Supplem

GPa after

reflecting

is in cont

Supplem

were reco

mentary fig. 3.

r laser heatin

g Re gasket),

tact with He m

mentary fig. 4.

orded at 300 K

. Microphoto

ng to >1500 K

which consis

medium that i

-200

Ram

an In

tens

ity (a

rb. u

nits

)

Raman spec

K using differ

graph of the

K. The sampl

sts of mixture

is seen as a tr

0

Na

ctra of Na2He

rent excitatio

DAC high-p

le (dark area

of tI19 Na an

ransparent are

Na2He+

Raman Shi

200

a

e at 140 GPa.

n wavelength

ressure cavity

close to the c

nd Na2He det

ea near the edg

+Na 140 GPa

ift (cm-1)

400

532 nm 488nm

660 nm

Na

The sample

hs.

y in reflected

center of the

termined by X

ge of the gask

600

a2He

was laser he

d and transmi

diamond cule

XRD and Ram

ket.

ated to >1500

itted light at

et surrounded

man spectrosc

0 K. The spe

140

d by

copy,

ectra

Supplem

conventio

mentary fig. 5.

onal cell. The

He

Na

2e

Computed ch

e color bar giv

harge density

ves the scale.

(eÅ -3) of Na

a2He at 300 GGPa, plotted inn the [110] pla

0.37

0.20

0.54

ane of the

0.0 0.2 0.4 0.6 0.8 1.0-0.1

0.0

0.1

0.2

0.3

0.4

H

form

atio

n(e

V/a

tom

)

composition, He/(Na+He)

Supplementary fig. 6. Predicted enthalpies of formation in the Na-He system at 200 GPa - i.e., the elements sodium

(left-hand side) and helium (right-hand side) are set as the energy zero.Na2He is predicted to be thermodynamically

stable.

Supplementary fig. 7. Predicted enthalpies of formation in the (a) K-Ne and (b) Na-Ne system at 1000 GPa. In both

cases, there is no structure with negative formation enthalpy relative to the elements (that is, below zero) over the

entire compositional range. There are no K–Ne or Na–Ne compounds.

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.5

1.0

1.5

Hfo

rmat

ion(

eV/a

tom

)

composition, Ne/(Na+Ne)

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.5

1.0

1.5

Hfo

rmat

ion(

eV

/ato

m)

composition, Ne/(K+Ne)

a b

Supplem

The upp

electrons

interstitia

mentary fig. 8.

er bands sho

s. Such band s

ally localized

-53

-43

-33

-23

-13

-3

7

Ener

gy (

eV

)

L

W

. Electronic b

own include

structures are

electrons). T

L

band structure

both valence

e typical of sa

The inset show

X

e of Na2He a

e and conduc

alts, in this ca

ws charge den

KW

at 300 GPa, in

ction bands,

ase we have a

nsity of the hig

ndicating pre

are mostly d

an electride (a

ghest-occupie

Na 2s

Na 2p

He 1s

W

edominant cha

due to inters

a salt made o

ed bands.

aracter of ban

stitially locali

f ionic cores

nds.

ized

and

Supplem

zero. Tot

Bader vo

volumes1

Supplem

Na-He an

approxim

mentary fig. 9.

tal DOS unit

olumes (inclu1, 2. For inters

mentary fig. 1

nd He-ES int

mation (TB-LM

0

2

4

0.0

0.1

0.2

0.0

0.2

0.4

0.0

0.4

0.8

D

ensi

ty o

f st

ates

Total and pro

ts are states/e

uding intersti

titial electron

0. Calculated

teractions, ob

MTO-ASA p

-2 0

ojected densit

eV. In this ca

itial electron

ns, we use hyd

d integrated

tained using

program). ES

0 2

Total

Na_s Na_p Na_d

He_s He_p

Energy

InterstitiaInterstitia

ties of states (

alculation, w

s) and calcu

drogen orbital

crystal orbita

tight-binding

represents “e

4 6

y (eV)

al_sal_p

(DOS) of Na2

e project the

ulate the corr

ls to project.

al Hamilton

g linear muffi

empty sphere

8

2He at 300 GP

Kohn-Sham

responding de

populations (

in-tin orbital m

es”, which are

10

Pa. The Ferm

m wave functi

ensity of sta

(ICOHP) for

method in the

e inserted in

mi energy is se

ions onto ato

ates within th

r Na-ES, Na-

e atomic sphe

the center of

et as

omic

hese

-Na,

eres

f the

empty Na

He and E

Supplem

at high an

pressures

simple-cu

the LMT

dominate

both case

above are

sketched

Supplem

pressure.

subseque

a8 cubes to de

ES 1s (2p, 3d

mentary fig. 11

nd ultrahigh p

s of around 10

ubic Na fram

TO computatio

ed by electros

es, the He 1s o

e practically z

here and elab

mentary fig. 12

We take a

ently relaxing

escribe the lo

downfolded).

1. Simplified d

pressures. Na

00 GPa (left-hework to the

ons above). W

static interacti

orbitals are no

zero); nonethe

borated in the

ener

gy(e

V)

2. Energies of

3*3*3 face-

the structure

calized electr

. For further i

drawing, illus

atoms are dr

hand side), th

1s orbitals us

When pressure

ions, in line w

ot involved in

eless, the pres

e main text.

0 1013

14

15

16

17

18

19

ener

gy(e

V)

f the Na-3s an

-centered cub

at the specifi

rons (2e). The

interpretation

strating the bo

awn in gray,

here are coval

sed to describ

e is increased

with the increa

n the covalent

sence of He i

20 30 40

pressure

nd He-1s orbi

bic (fcc) supe

fic pressure.

e valence con

n of the ICOH

onding pictur

He atoms in g

ent contributi

e localized in

further (righased charge tr

t interactions

s the key dete

0 50 60

e(GPa)

Na 3sHe LUM

itals relative t

er-cell of He

nfigurations ar

HP results, see

re obtained fro

green, and int

ions from the

nterstitial elec

t-hand side),

ransfer as dis

(and thus the

erminant for t

70 80

MO

to He matrix

e and replace

re Na 3s (3p,

e the cartoon b

om COHP an

terstitial elect

3s orbitals of

ctrons (“2e”; d

the compoun

cussed in the

e correspondin

the stabilizati

HOMO level

e the central

3d downfold

below.

nalysis for Na2

trons in blue.

f the

denoted “ES”

nd becomes

main text. In

ng ICOHPs

on mechanism

l as a function

l atom with

ded),

2He

At

” in

n

m

n of

Na,

Supplementary table 1. Description of the experimental runs.

Run # Pressure

(GPa)

Na Phase Na

Lattice

parameter

Na Vp.a.

Heating

Conditi

ons

Na2He

Lattice

parameter

Na2He

Volume

Comments

APS

5 141 tI19 7.0820, 3.488 9.064 After LH 4.296 79.285 Na2He observed after LH.

W used as pressure marker.

4 155 tI19

7.028, 3.420

8.753

After LH 4.260 77.309 Na2He observed before

and after LH at each

pressure

4 150 tI19

tI19 at Na2He

7.010, 3.438

7.000, 3.430

8.753

8.708

After LH 4.245 76.495 Na2He observed before

and after LH at each

pressure

4 140 tI19

tI19 at Na2He

7.100, 3.482

7.090, 3.475

9.089

9.051

After LH 4.315 80.342 Na2He observed before

and after LH at each

pressure

4 130 tI19 at Na2He

oP8 at Na2He

7.180, 3.480

4.750, 3.010,

5,240

9.277

9.364

Before

LH

4.345 82.029 The first heating for the

run#4.

Na2He observed before

and after LH.

4 110 cI16 5.462 10.184 RT - - Na2He not observed

4 100 FCC Na 3.484 10.57 RT - - Na2He not observed

3 135 tI19

oP8?

7.19, 3.5 9.37 After LH 4.29 78.953 Na phases are away from

Na2He and at lower

pressure. Estimated lattice

parameters suggest lower

pressure for Na.

3 113 FCC Na

oP8 or tI19

3.498 10.70

After

LH

4.41 85.76 Large pressure gradient.

Different phases at

different points. Na2He

is seen near the position

where traces of oP8 and/or

tI19 phases are observed.

PETRA

2 110 cI16 5.446 10.098 RT - - Na2He not observed

2 117 cI16 5.401 9.850 RT and 323 K

- - Na2He not observed

Supplementary table 2. Miller indices (hkl), interplanar distances (dcal) and peak intensities (Ical) calculated for the

Fm-3m Na2He phase at 141 GPa, with unit cell parameter a= 4.2960 Å3 together with observed interplanar distances

(dobs) and peak intensities (Iobs).

hkl dcal (Å) Ical dobs (Å) Iobs dcal-dobs 111 2.4803 1.8 2.4790 <5 0.0013 200 2.1480 100 2.1480 100 0 220 1.5188 93 1.5178 98 0.001 311 1.3143 0.5 Not observed 222 1.2401 22 1.2392 21 0.001 400 1.0740 12 1.0757 20 -0.0017 331 0.9856 0.1 Not observed 420 0.9606 23 0.9669 27 -0.0063

Supplementary table 3. Atomic radii in K-Ne and Na-Ne systems at 1000 GPa. Radii were obtained for

the most stable structures of compounds with the same stoichiometry A2Ne (A=K, Na), using the

same method as in Table I.

Compounds A Radius (Å) Ne Radius (Å) Radius ratio

(RNe/RA)

Formation enthalpy

(eV/atom)

Na2Ne 0.59 0.62 1.05 +0.23

K2Ne 0.86 0.68 0.79 +0.90

K2Ne has a better radius ratio than Na2Ne, yet has a higher enthalpy of formation. Stability of Na2He

is not just a result of favorable packing of the atoms (in that case, Na2Ne should be even more stable).

Supplementary table 4. Charge density, kinetic energy density per electron and total energy density per

electron at the bond critical points in Na2He at 300 GPa. In the first and second line, values obtained

from PBE-DFT and Hartree-Fock calculations, respectively, are reported. In the first column, the

attractor of the associated bond paths are given. All values are in atomic units. Kinetic energy density

was calculated according to the following equation: G(r)= 1/2 (’)(1)(r,r’)r=r’ . The total

energy density was obtained as H=G+V, where V was calculated according to the local form of the

virial theorem reported in ref G1.

Attractors ρBCP∙102 GBCP/ρBCP HBCP/ρBCP

He-Na 4.76

4.27

1.72

1.97

0.19

0.31

Na-Na 3.59

3.11a

1.77

2.09a

0.30

0.45a

He- Interstitial 3.57

3.32

0.71

0.84

-0.23

-0.19

Na- Interstitial 5.30

5.68

0.62

0.79

-0.30

-0.31 a Using Hartree-Fock Hamiltonians, no Na-Na bond critical points were found. We report the value of properties at Na-Na midpoint

(which corresponds to a ring critical point in this case)

Supplementary table 5. Calculated Bader charges and radii (relative to Na), at pressures of 200, 300 and

500 GPa. For comparison, we list Bader charges in hP4-Na.

pressure hp4-Na Na2He

(GPa) Item charge item charge radius radio

200

Na1 0.571 Na 0.599 1.000

Na2 0.505 He -0.174 0.852

2e -1.076 2e -1.022 0.772

300

Na1 0.603 Na 0.601 1.000

Na2 0.508 He -0.159 0.834

2e -1.108 2e -1.043 0.755

500

Na1 0.644 Na 0.612 1.000

Na2 0.511 He -0.146 0.820

2e -1.155 2e -1.079 0.740

Mulliken charges have surprisingly similar values to Bader charges, at 300 GPa they are:

He(Na2He) -0.162, Na(Na2He) +0.621, Interstitial (Na2He) -1.081

Na1(hP4-Na) +0.503, Na2(hP4-Na) +0.552, Interstitial (hP4-Na)- 1.055

Supplementary table 6. SSAdNDP and NBO results for the Na2He system at different pressures. In this study ccemd-2 basis set was used to represent the projected plane-wave density using a 7x7x7 k-point grid. This basis set was selected so that on average less than 1% of the density of each occupied plane wave band was lost in projecting into the AO basis to guarantee that the density matrix used in the SSAdNDP procedure accurately represents the original plane wave results.

0 GPa 100 GPa 300 GPa 500GPa

NBO: q(He)=0.00 q(Na)=0.00 ON(LP on He)=1.99 |e| Na: 0.95 |e| on 3S orbital 0.02 on each three 3P orbitals 2.00 |e| on 2S orbital 2.00 |e| on each three 2P orbitals He: 2.00 |e| on 1S orbital 0.01 on 2S orbital 0.00 on each three 2P orbitals SSAdNDP: I) ON(LP on He) = 1.99|e| a) ON(8c-2e over Na8 empty cube)=1.40 |e| b) ON(14c-2e over Na8He6)=1.41 |e| II) ON(8c-2e over Na8 empty cube)=1.39 |e| ON(9c-2e over Na8He cube) = 2.00 |e|

NBO: q(He)=+0.13 q(Na)=-0.07 ON(LP on He)=1.84 |e| Na: 0.43 |e| on 3S orbital 0.23 |e| on each three 3P orbitals 1.96 |e| on 2S orbital 1.98 |e| on each three 2P orbitals He: 1.84 |e| on 1S orbital 0.03 on 2S orbital 0.00 on each three 2P orbitals SSAdNDP: I) ON(LP on He) = 1.84|e| a) ON(8c-2e over Na8 empty cube)=1.80 |e| b) ON(14c-2e over Na8He6)=1.82 |e| II) ON(8c-2e over Na8 empty cube)=1.75 |e| ON(9c-2e over Na8He cube)=1.97 |e|

NBO: q(He)=+0.22 q(Na)=-0.11 ON(LP on He)=1.74 |e| Na: 0.23 |e| on 3S orbital 0.34 |e| on each three 3P orbitals 1.93|e| on 2S orbital 1.97 |e| on each three 2P orbitals He: 1.74|e| on 1S orbital 0.04 on 2S orbital 0.00 on each three 2P orbitals SSAdNDP: I) ON(LP on He) = 1.74|e| a)ON(8c-2e over Na8 empty cube)=1.88 |e| b) ON(14c-2e over Na8He6)=1.90 |e| II) ON(8c-2e over Na8 empty cube)=1.81 |e| ON(9c-2e over Na8He cube)=1.95 |e|

NBO: q(He)=+0.25 q(Na)=-0.13 ON(LP on He)=1.70 |e| Na: 0.18 |e| on 3S orbital 0.37 |e| on each three 3P orbitals 1.91 |e| on 2S orbital 1.97 |e| on each three 2P orbitals He: 1.70 |e| on 1S orbital 0.05 on 2S orbital 0.00 on each three 2P orbitals SSAdNDP: I) ON(LP on He) =1 .70|e| a)ON(8c-2e over Na8 empty cube)=1.89 |e| b) ON(14c-2e over Na8He6)=1.91 |e| II) ON(8c-2e over Na8 empty cube)=1.82 |e| ON(9c-2e over Na8He cube)=1.94 |e|

Supplementary method

PERIODIC CALCULATIONS WITH CRYSTAL14

BASIS SET

Triple zeta basis sets were used for all atoms. Such basis functions were taken from Refs. 3,4 (for Na and He,

respectively) and slightly modified to be apt for high-pressure calculations. Indeed, due to the fact that such basis

sets were optimized for solid state structures at zero pressure (Na) and for isolated atoms (He), it was not possible to

obtain convergence without modifying the exponents.

Additional basis functions centered on non-nuclear charge density maxima were employed. Such functions were

identical to the ones used for He with the only difference that the most internal, very contracted s shell was not

considered (due to the fact that interstitial electrons have no nuclei and therefore there is not a strong contraction of

electrons towards the maximum as it happens for atoms). Numerical values for exponents and contraction

coefficients for 300 GPa calculations are given in the following table (for Hartree-Fock calculations, used to obtain

bond critical points properties, an additional shrinking of the basis functions of Na was necessary to obtain

convergence. For those basis functions where a different exponent was used for Hartree-Fock calculations, its value

is reported in brackets).

Type of function exponent Contraction coefficient

Na atom

s

2.60E+04 6.18E-04

3.91E+03 4.78E-03

8.89E+02 2.45E-02

2.52E+02 9.48E-02

8.17E+01 2.69E-01

2.89E+01 4.79E-01

1.06E+01 3.33E-01

s 5.38E+01 1.95E-02

1.63E+01 9.27E-02

2.37E+00 -3.99E-01

s 9.57E-01 1.64E+00

4.08E-01 5.57E-01

s 6.75E-01

(1.62E+00)1.00E+00

s 1.97E-01

(4.02E-01)1.00E+00

p

1.38E+02 5.80E-03

3.22E+01 4.16E-02

9.98E+00 1.63E-01

3.48E+00 3.60E-01

1.23E+00 4.49E-01

p 4.01E-01 1.00E+00

(9.63E-01)

p 1.97E-01

(4.03E-01)1.00E+00

d 1.05E+00

(2.51E+00)1.00E+00

d 5.31E-01

(1.08E+01)1.00E+00

He atom

s

2.34E+02 2.59E-03

3.52E+01 1.95E-02

7.99E+00 9.10E-02

2.21E+00 2.72E-01

s 6.67E-01 1.00E+00

s 2.09E-01 1.00E+00

p 3.04E+00 1.00E+00

p 7.80E-01 1.00E+00

d 1.97E+00 1.00E+00

Interstitial electron s 6.67E-01 1.00E+00

s 2.09E-01 1.00E+00

p 3.04E+00 1.00E+00

p 7.80E-01 1.00E+00

d 1.97E+00 1.00E+00

GRID OF K-POINTS

In the following table, details regarding the k-nets for the crystal systems considered in the paper are reported. The

‘Gilat net’ is used for the calculation of the density matrix

Pressure system shrink factor in

the input

total k-points in

reciprocal space

(IBZ)

total k-points for

‘Gilat net’

300 GPa

Na2He 24 48 413 2769

Na 12 24 133 793

He 12 24 133 793

GRID FOR DFT

For the evaluation of charge density to be used in DFT calculations, we used the following input, corresponding to

unpruned grids (see http://www.crystal.unito.it/Manuals/crystal14.pdf for full description of the various parameters)

RADIAL

1

x

99

ANGULAR

1

9999.0

13

TOLLDENS

9

where x was 3.0, 3.0 and 2.0 for Na2He, Na and He, respectively.

Finally, regarding the evaluation of bielectronic integrals (TOLINTEG option), we used

TOLINTEG=12,12,12,12,22 for Na2He and hp4-Na, while for He we used TOLINTEG=11,11,11,11,22 (see

http://www.crystal.unito.it/Manuals/crystal14.pdf for full description of the various parameters)

INTERACTION OF ZERO-FLUX SURFACES, CRITICAL POINT ANALYSIS AND GENERATION OF

GRID FILES

The program TOPOND7 (incorporated in CRYSTAL 14) was used for the evaluation of properties. To obtain the

deformation density isosurfaces, the grid files were produced with TOPOND, and transformed into ‘cube’ standard

format with the program NCImilano (Ref. 5). Isosurfaces were produced with MOLISO (Ref. 6) giving the files in

‘cube’ format in input.

For the integration over zero-flux surfaces, we used 64 and 48 ϕ and θ angular points outside the β-sphere. Inside

the β-sphere, 120 radial points were used. For the number of radial points outside the β-sphere and the angular

points inside the β-sphere, we used the option IMUL=2, which corresponds to doubling the number of points with

respect to the default value.

Atomic energy was calculated according to the following equation:

E()=K()(1+V/T)

where

K()= -1/4(2 +‘2)(1)(r,r’)r=r’d . is the space enclosed by zero-flux surfaces, and V/T is the virial ratio obtained from the SCF calculation.

Supplementary References

1 Bader, R. F. Atoms in molecules. (Wiley Online Library, 1990). 2 Henkelman, G., Arnaldsson, A. & Jonsson, H. A fast and robust algorithm for Bader decomposition of charge density.

Comput. Mat. Sci. 36, 354-360 (2006). 3 Peintinger, M. F., Oliveira, D. V. & Bredow, T. Consistent Gaussian basis sets of triple‐zeta valence with polarization

quality for solid‐state calculations. J. Comput. Chem. 34, 451 (2013). 4 Woon, D. E. & Dunning, T. H. Gaussian basis sets for use in correlated molecular calculations. IV. Calculation of static

electrical response properties. J. Chem. Phys. 100, 2975 (1994). 5 Saleh, G., Lo Presti, L., Gatti, C. & Ceresoli, D. NCImilano: an electron-density-based code for the study of

noncovalent interactions. J. Appl. Crystallogr. 46, 1513 (2013). 6 Hubschle, C. & Luger, P. MolIso-a Program for Colour-mapped Iso-surfaces. J. Appl. Crystallogr. 39, 901 (2006). 7 Gatti C., Saunders V. R., Roetti C. Crystal field effects on the topological properties of the electron density in

molecular crystals, J. Chem. Phys. 101, 10686-10696 (1994)