Chemical Bonding Forces and Metallization of Hydrogen Ivan I. Naumov Geophysical Laboratory, Carnegie Institution of Washington Naumov & Hemley, Accts. Chem. Res., 47(12), 3551 (2014)
Importance of Fundamental Studies of Hydrogen and Hydrogen-rich Materials H in a metallic state is expected to exhibit high Tc (Neil Ashcroft, 1968) Evidence for Tc near 200K in hydrogen-rich sulfur compound (Eremets et al.) Hydrogen-dominant materials could be important for (i) hydrogen storage (ii) general energy storage (as high density materials) (iii) for solving structural problems in nuclear industry (hydrogen embrittlement) Understanding pure hydrogen over the broadest range of P-T is an important starting point
Goals To discuss the properties of dense hydrogen from the chemical point of view To argue that they are controlled by closed shell effects over a wide range of pressures To touch the question why hydrogen behaves so differently from simple alkali metals
New Hydrogen Phase Diagram Zha, Liu, Ahart, Boehler, & Hemley, Phys. Rev. Lett. (2013) [Zha, Liu, Ahart, Boehler, & Hemley, Phys. Rev. Lett. In press]
New Hydrogen Phase Diagram Disordered Ordered Pbcn, Cc, Pc Cmca-4 C2/c [Zha, Liu, Ahart, Boehler, & Hemley, Phys. Rev. Lett. (2013)] [Zha, Liu, Ahart, Boehler, & Hemley, Phys. Rev. Lett. In press]
C2/c and Pbcn structures C2/c (III) Pbcn (IV ) A B C D D C D C. J. Pickard and R. J. Needs, Nat. Phys., 3, 473 (2007) ; Phys. Rev B, 214114(2012).
Cmca-4: graphite-like structure A side view primitive unit cell A B top view A Naumov, Cohen & Hemley, Phys. Rev. B, 88, 045125 (2013)
Closed Shell Effect Noble atoms have a closed valence shell Molecules occupied Metallic clusters W. D. Knight et al., Phys. Rev. Lett. 52, 2141 (1984). 1D nanowires A. I. Yanson et al., Nature, 400, 144 (1999). Ag: N=1,2,5 2D thin films D.- A. Luh et al., Science, 292, 1131 (2001). 3D solids Insulators, Quasicrystals, Hume-Rothery phases
Analogy between 1s electrons in hydrogen and π electrons in carbon (C 6 H 6 ) H 6 Naumov & Hemley, Accts. Chem. Res., 47(12), 3551 (2014)
H 6 ring vs nonplanar isomers O h - octahedron D 3d staggered trigonal prism D 3h - trigonal prism D 3d D 3h D. A. Dixon et al. Faraday Discuss. Chem. Soc., 62, 110 (1977).
Total energies per atom for H n rings (n = 3 10) DFT-GGA Hückel s rule: Aromatic compounds must have 4N+2 π electrons, N=0, 1, 2, 3..., to fill a π shell n=6,10 Correlation corrections: Lower the total energy but have only little effect on energy differences Naumov & Hemley, Accts. Chem. Res., 47(12), 3551 (2014) ]
Total energies per atom for H n rings (n = 3 10) DFT-GGA Hückel s rule: Aromatic compounds must have 4N+2 π electrons, N=0, 1, 2, 3..., to fill a π shell n=6,10 Correlation corrections: Lower the total energy but have only little effect on energy differences Naumov & Hemley, Accts. Chem. Res., 47(12), 3551 (2014)
Total energies and interatomic distances in H n rings B3LYP/6-311G(d,p) Calculations Naumov & Hemley, Accts. Chem. Res., 47(12), 3551 (2014
H 6 molecular energy levels and vibrational frequencies Bonding a 1g, e 1u, and a 2u orbitals go down in energy with pressure a 2u stems from the 2p z atomic orbitals B3LYP/6-331G(3df,3pd) Kekulean B 2u vibrational mode becomes stable Naumov & Hemley, Accts. Chem. Res., 47(12), 3551 (2014)
H 6 molecular energy levels and vibrational frequencies Bonding a 1g, e 1u, and a 2u orbitals go down in energy with pressure a 2u stems from the 2p z atomic orbitals B3LYP/6-331G(3df,3pd) Kekulean B 2u vibrational mode becomes stable fo r < 0.86Ǻ 0.86 Ǻ ~ 500 GPa Naumov & Hemley, Accts. Chem. Res., 47(12), 3551 (2014)
H 6 ring energetics with respect to the B 2u mode D 6h D 3h (2r/ 3) Naumov & Hemley, Accts. Chem. Res., 47(12), 3551 (2014)
Correlation between the molecular orbitals for D 6h and D 3h structures: L U M O H U M O The 3rd lowest unoccupied MOs a 2u and aˈˈ2 are bonding states stem from the atomic 2p z electrons
From isolated rings to 2D lattices Optimized distance Energy Relative to ring r (Å) E (Ha) ΔE (Ha) triangle 4.23-0.451 0.075 square 4.35-0.451 0.052 graphenelike 1.18-0.555 0.009 The graphene structure is far more stable than the other two
From H 6 to H-graphene Semimetal Exhibits two inequivalent Dirac levels K and Kˈ; 1s derived But the second level at Г is of 2p z nature
Gap opening: Peierls distortions Nestings between the valence and conduction bands: Naumov, Cohen & Hemley, Phys. Rev. B, 88, 045125 (2013) TO, LA
TO-mode a TO-mode at k=k (Kekulean distortion) E (ev/atom) 0.0-0.2-0.4-0.6 a=1.40 Ǻ -0.8-0.4 0.0 0.4 0.8 E (ev/atom) 0.00-0.05-0.10-0.15 a=1.18 Ǻ 3 3 superstructure ( can be recognized in C2/c) E (ev/atom) -0.20-0.6-0.4-0.2 0.0 0.2 0.4 0.6 0.020 0.015 0.010 0.005 0.000 a=1.00 Ǻ -0.005 δ= 0 δ>0 δ<0-0.2-0.1 0.0 0.1 0.2 δ
3D Candidate Structures Pbcn 3x2 Cmca-4 Insulator due to a 3 2 superlattice stabilized by Peierls-like distortions Naumov, Cohen & Hemley, Phys. Rev. B, 88, 045125 (2013) Naumov & Hemley, Accts. Chem. Res., 47(12), 3551 (2014)
Energy Level Diagram Z=1 Z=3 Z=11 H Li Na 3s 2s 3p 2p 3d 3s 2s 3p 2p 3d 3s 3p 3d 1s 2s 2p 1s 1s ε p - ε s =10.2 ev ε p - ε s =4.4 ev ε p - ε s =4.2 ev
Comparison between H and Li H graphene, rs =1.43 Li graphene, rs =2.68 1s -s character of WF s px+py 8 0.001500 0.002888 6 WF at K 0.004275 0.005663 4 0.007050 0.008438 Y Axis Title 2 0.009825 0.01121 0 0.01260-2 -4 s-p hybridization -6-8 -8-6 -4-2 0 2 4 6 8 X Axis Title Li: direct band gap and interstitial valence charge!
Li: interstitial localization in 1D A Hydrogen-like behavior B C A,B,C a= 9.0, 8.7 and 6.0 Bohr Li treated as having valence=2
Topology and interstitial localization in 1D Z 2 = additive group of the integers mod 2 or two-valued invariant A Z 2 =0 or Berry phase =0 B only via a (semi) metallic state C Z 2 =1 or Berry phase =π P.Jadaun,et al. Phys. Rev. B 88, 085110 (2013)
Summary H 6 rings and hydrogenic graphene-like layers are especially stable due to aromatic and closed shell effects. This stability is inherited by 3D structures of dense H. Metallization of compressed H should occur by destroying the closed shell electronic structure, f.e. by lowering the bonding states associated with 2s and 2p orbitals.