Supporting InformationKorzhavyi et al. 10.1073/pnas.1115834109SI TextElectronic Structure. The calculated electron densities of states ofCuH, CuOH, and Cu2O are shown in Fig. S1. Our calculationspredict all three compounds to be semiconductors; the calculatedbandgaps, 0.64 eV for CuH and 0.80 eV for CuOH, are similar tothe value 0.53 eVobtained for Cu2O. The experimental bandgapof Cu2O (2.17 eV) is known to be underestimated by density func-tional theory calculations that employ local or semilocal func-tional; the same may be expected for CuH and CuOH.

Crystal Structure, Lattice Parameters, and Atomic Positions. Cu2O:Thermal-expansion anomaly. The experimental lattice parametervalue of Cu2O given in Table 1 (main text) has been obtainedin previous experimental observations (1–3), whereas the presentand previous (4) generalized gradient approximation (GGA) cal-culations tend to overestimate the lattice parameter of Cu2O byabout 1%.

Cuprite Cu2O is known to have a low value of thermal-expan-sion coefficient around room temperature and to exhibit negativethermal-expansion coefficients at low temperatures (1–3, 5).Qualitatively, this anomalous behavior is captured by our quasi-harmonic calculations (Fig. S6). The anomaly has been attributedto negative Grüneisen parameters for certain zone-boundaryacoustic phonon modes that correspond to twisting of neighboringcorner-sharing Cu4O tetrahedra in the cuprite structure with re-spect to each other (6, 7). The frequencies of these transversemodes of vibration are low, and they decrease further upon volumecompression. Therefore, at low temperatures, the crystal latticecan gain some additional vibrational entropy by shrinking the vo-lume. When the temperature is increased above a certain thresh-old, so that the higher-lying modes are excited whose frequenciesdecrease upon expansion, the thermal-expansion behavior returnsto normal (5, 6). Cu2O is not unique in showing thermal-expansionanomaly; an even stronger anomaly is exhibited by Ag2O (also thecuprite crystal structure, with linearly coordinated cations) (7).

CuH: Atomic positions and vibrations. Our calculations show thatCuH tends to form a ZnS-type crystal structure typical of semi-conductors with predominantly covalent type of chemical bond-ing. In agreement with the present and past (8) experimentalobservations, the hexagonal form (wurtzite) of CuH is calculatedto be more stable than the cubic form (sphalerite) (Fig. S5). Bothpolymorphs of CuH have the same tetrahedral coordination ofcations and anions. In contrast to Cu2O, CuH shows no ther-mal-expansion anomaly.

Fig. S8 shows the root-mean-square atomic displacements cal-culated for Cuþ and H− ions in CuH as a function of temperature.One can see that already at 0 K the amplitude of zero-point mo-tion of hydrogen ions is about 0.5 Å (approximately 1 bohr) andrapidly increases with temperature, whereas the amplitude ofcopper ion displacements remains small for the temperaturesof interest.

CuOH: Structure and stability. The starting solid-state configura-tions of Cuþ, Hþ, and O2− ions in our search for stable ionic con-

figurations were created in accordance with Pauling’s coordi-nation rules, namely

∑i

zi∕qi ¼ zCu þ zH − zO∕2 ¼ 0.

Here zi and qi are the coordination number and the formalcharges of ion i. Initial configurations for cuprous hydroxide wereconstructed to be completely devisable onto individual Cu–O–Hstructural units (molecules). The alternative, hydrated oxide con-figurations, consisting of two separate Cu–O–Cu and H–O–Hnetworks, were excluded from the present search. The symmetryof each supercell was then set to zero, and all its lattice and inter-nal parameters were fully optimized.

The final configurations exhibiting a twofold coordination ofthe copper ions (like in cuprous oxide) are found to be energe-tically preferred relative to higher-coordination number struc-tures. Typical bond distances and angles are summarized inTable S1. The table also shows that the bond lengths and anglescalculated for solid CuOH are similar to those of free CuOHmolecules. The calculated vibration frequencies for molecularCuOH are 630 (Cu–O stretching), 3,705 (O–H stretching), and820 cm−1 (Cu–O–H bending); they are in reasonable agreementwith experimental (9) frequencies (respectively, 628; 3,738; and744 cm−1), as well as with the corresponding peaks in the calcu-lated phonon spectrum of CuOH (Fig. S4).

In order to calculate the enthalpies and free energies of for-mation for the considered Cu–O–H compounds, their calculatedenergies must be expressed relative to the energies of pure ele-ments in standard states (including two gases, O2 and H2). Exist-ing approximations in density functional theory are known to givethe energies of molecular species quite inaccurately, see ref. 10.Thus, the stability of an O2 dimer is overestimated by 1.01 eVandthat of an H2 dimer underestimated by 0.21 eV within the GGA.Accordingly, the stability of Cu2O (for example) is underesti-mated if calculated relative to the overstabilized O2 dimer (11).In our analysis of thermodynamic stability of Cu–O–H com-pounds, this problem is eliminated by correcting the calculatedenergies of O2 and H2 dimers by the known values of GGA ato-mization energy error for these elements. Our treatment of ther-modynamic properties (6) is thus completely ab initio for the solidsubstances Cu, Cu2O, CuH, and CuOH (the electronic and pho-non contributions are included), semiempirical for the gaseousO2 and H2 species (empirical data, refs. 10 and 12, are usedfor correcting the dimer energy and for the temperature-depen-dent contributions), and completely empirical for liquid H2Owater (data from thermodynamic tables, ref. 12, are used,although, accidentally, the atomization energy of a water mole-cule is accurately described by the GGA). Eliminating the largesterrors due to density functional approximations allows us toachieve the required accuracy of about 10 kJ · mol−1 for makingtheoretical estimates of thermodynamic stability of Cu–O–Hcompounds (6).

1. White GK (1978) Thermal expansion of cuprous oxide at low temperatures. J Phys C

Solid State Phys 11:2171–2174.

2. Schäfer W, Kirfel A (2002) Neutron powder diffraction study of the thermal expansion

of cuprite. Appl Phys A Mater Sci Process 74:s1010–s1012.

3. Fornasini P, et al. (2006) Local behaviour of negative thermal expansionmaterials.Nucl

Instrum Methods Phys Res B 246:180–183.

4. Laskowski R, Blaha P, Schwarz K (2003) Charge distribution and chemical bonding inCu2O. Phys Rev B Condens Matter Mater Phys 67:075102.

5. Bohnen K-P, Heid R, Pintschovius L, Soon A, Stampfl C (2009) Ab initio lattice dynamicsand thermal expansion of Cu2O. Phys Rev B Condens Matter Mater Phys 80:134304.

6. Korzhavyi PA, Johansson B (2010) Thermodynamic properties of copper compoundswith oxygen and hydrogen from first principles. Technical Report TR-10-30 (SwedishNuclear Fuel Waste Manag Co, Stockholm).

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7. Mittal R, Chaplot SL, Mishra SK, Bose PP (2007) Inelastic neutron scattering and latticedynamical calculation of negative thermal expansion compounds Cu2O and Ag2O.Phys Rev B Condens Matter Mater Phys 75:174303.

8. Goedkoop JA, Andersen AF (1955) The crystal structure of copper hydride. Acta Crys-tallogr 8:18.

9. Whitham CJ, Ozeki H, Saito S (2000) Microwave spectra of CuOD and AgOD:Molecularstructure and harmonic force field of CuOH and AgOH. J Chem Phys 112:641–646.

10. Kurth S, Perdew JW, Blaha P (1999) Molecular and solid-state tests of density func-tional approximations: LSD, GGAs, and meta-GGAs. Int J Quantum Chem 75:899–909.

11. Soon A, Todorova M, Delley B, Stampfl C (2006) Oxygen adsorption and stability ofsurface oxides on Cu(111): A first-principles investigation. Phys Rev B Condens MatterMater Phys 73:165424.

12. Chase MW (1998) NIST-JANAF Thermochemical Tables. Fourth Edition. Part II, Cr-Zr(Am Inst of Physics, New York).

Fig. S1. Density of electron states (DOS) in copper(I) hydride CuH, hydroxide CuOH, and oxide Cu2O. The DOS is normalized per formula unit (f.u.) specified ineach panel. Labels near peaks of the DOS indicate the predominant character of the corresponding states. The insets magnify the DOS at energies near thebandgap.

Fig. S2. Phonon spectrum and density of states (DOS) in cuprous oxide Cu2O calculated at the experimental lattice parameter a ¼ 4.27 Å. Experimental dataderived from Raman scattering (1) and inelastic neutron scattering (2) are shown as open squares and open circles, respectively.

1. Yu PY, Shen YR (1975) Resonance Raman studies in Cu2O. I. The phonon-assisted 1 s yellow excitonic absorption edge. Phys Rev B Condens Matter Mater Phys 12:1377–1394.2. Bohnen K-P, Heid R, Pintschovius L, Soon A, Stampfl C (2009) Ab initio lattice dynamics and thermal expansion of Cu2O. Phys Rev B Condens Matter Mater Phys 80:134304.

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Fig. S3. Phonon spectrum and density of states (DOS) in cuprous hydride CuH (wurtzite) calculated at a lattice parameter a ¼ 2.87 Å.

Fig. S4. Phonon spectrum and density of states (DOS) in cuprous hydroxide CuOH (configuration 2 of Fig. 3B, base-centered orthorhombic Cm2a structure)calculated at molecular volume of 30.7 Å3. The notations for q vectors are as follows: Γ ¼ πð0;0;0Þ; X ¼ πð1∕a;1̄∕b;0Þ; Z ¼ πð0;0;1∕cÞ; M ¼ πð1∕a;1∕b;1∕cÞ;R ¼ πð2∕a;0;1∕cÞ; N ¼ πð2∕a;0;0Þ.

Fig. S5. (Left) Calculated heat capacities of CuH in the hexagonal (wurtzite) and cubic (sphalerite) ZnS-type structures. (Right) Relative stabilities of the hex-agonal and cubic crystal structures of CuH, in terms of enthalpy H and Gibbs free energy G, calculated within the quasi-harmonic approximation. Wurtzite isfound to be the lowest-energy crystal structure of CuH in the considered temperature domain.

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Fig. S6. Calculated thermodynamic properties of Cu2O: thermal (volume) expansion coefficient β, and constant-pressure heat capacity CP. Note that our quasi-harmonic calculations (1) qualitatively reproduce the low-temperature thermal-expansion anomaly of Cu2O reported experimentally (2, 3) and describedtheoretically (3, 4). Experimental heat-capacity data are from refs. 5–7.

1. Baroni S, Giannozzi P, Isaev EI (2010) Density-functional perturbation theory for quasi-harmonic calculations. Rev Mineral Geochem 71:39–57.2. Bohnen K-P, Heid R, Pintschovius L, Soon A, Stampfl C (2009) Ab initio lattice dynamics and thermal expansion of Cu2O. Phys Rev B Condens Matter Mater Phys 80:134304.3. Schäfer W, Kirfel A (2002) Neutron powder diffraction study of the thermal expansion of cuprite. Appl Phys A Mater Sci Process 74:s1010–s1012.4. Fornasini P, et al. (2006) Local behaviour of negative thermal expansion materials. Nucl Instrum Methods Phys Res B 246:180–183.5. Hu J-H, Johnston HL (1951) Low temperature heat capacities of inorganic solids. IX. Heat capacity and thermodynamic properties of cuprous oxide from 14 to 300 °K. J Am Chem Soc

73:4550–4551.6. Gregor LV (1962) The heat capacity of cuprous oxide from 2.8 to 21 °K. J Phys Chem 66:1645–1647.7. Chase MW (1998) NIST-JANAF Thermochemical Tables. Fourth Edition. Part II, Cr-Zr (Am Inst of Physics, New York).

Fig. S7. X-ray diffraction pattern of CuH and Cu powder recorded at ambient atmospheric pressure and temperature after different periods of time since thespecimen preparation. Labels on the graph indicate the atomic planes producing Bragg reflections. The as-prepared sample consists of mostly CuH. As the timeof exposure of CuH to air increases, the intensity of CuH reflections decreases. At the same time, the intensity of diffraction peaks from metallic copperincreases, indicating that CuH loses hydrogen and transforms to Cu. Very small peaks from Cu2O and CuO are also present in X-ray diffraction pattern from2-d-old sample.

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Fig. S8. Root-mean-square displacements for Cu and H atoms in wurtzite CuH, calculated in the quasi-harmonic approximation (1).

1. Baroni S, Giannozzi P, Isaev EI (2010) Density-functional perturbation theory for quasi-harmonic calculations. Rev Mineral Geochem 71:39–57.

Table S1. Bond lengths and bond angles in solid and molecular CuOH

Substance, source Bond lengths, Å Bond angle, deg.Cu–O O–H H⋯O Cu–O–H

CuOH solid, calculation 1.88 0.99 2.19 110CuOH molecule, calculation 1.77 0.98 107CuOH molecule, experiment (9) 1.77 0.96 110

H⋯O stands for a hydrogen bond.

Table S2. Thermodynamic stability of copper(I) compounds in comparison with that ofwater H2O

Substance Structure ΔHð0Þ, kJ∕mol ΔHð298.15Þ, kJ∕mol ΔGð298.15Þ, kJ∕mol Ref.

Cu2O cuprite −160.6 −161.9 −140.9(−168.9) (−170.7) (−147.9) (1)

CuH wurtzite +39.5 +36.7 +50.9(+27.5) (+54.0) (2)(+27.6) (+40.3) (3)

CuOH conf. 1 −195.4 −199.8 −158.2CuOH conf. 2 −196.5 −200.8 −160.8H2O liquid — (−285.8) (−237.1) (1)

Calculated data include an empirical correction to the ground state energy of oxygen and hydrogenmolecules. Experimental data are given in parentheses. ΔHð0Þ and ΔHð298.15Þ are the enthalpies offormation at 0 and 298.15 K, respectively. ΔG is the Gibbs free energy of formation.

1. Chase MW (1998) NIST-JANAF Thermochemical Tables. Fourth Edition. Part II, Cr-Zr (Am Inst of Physics, New York).2. Burtovyy R, Utzig E, Tkacz M (2000) Studies of the thermal decomposition of copper hydride. Thermochim Acta 363:157–163.3. Burtovyy R, Włosewicz D, Czopnik A, Tkacz M (2003) Heat capacity of copper hydride. Thermochim Acta 400:121–129.

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