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Electronic Supplementary Material

Catalysts for Heterolytic Split of H2 by Theoretical Design

by Łukasz Maj and Wojciech Grochala

Contents

S1. Comparison of essential molecular features for cubane–like M4C4H8 molecules (M=Ti, Zr, Hf) as

computed with the SDD and LANL pseudopotentials or with the 6-31** basis set on M atom.

S2. Comparison of vertical and relaxed ionization potential, electron affinity, Mulliken electronegativity, and

Pearson’s hardness for Ti4C4H8 (6-31** basis set on Ti) and Hf4C4H8 (SDD pseudopotential on Hf).

S3. Optimized geometries and selected molecular properties of M4Nm4H8 molecules (M=Ti, Zr, Hf; Nm=C,

Si) and of their dehydrogenation products.

S4. Optimized geometries and selected molecular properties of M4Nm4H8 molecules (M=Ti, V; Nm=B, C, N)

and of their most stable dehydrogenation products, except for Ti4C4H8.

S5. Optimized geometries and selected molecular properties of Ti4(N2B2)H8 and of its dehydrogenation

products.

S6. Optimized geometries and selected molecular properties of molecular analogues of ‘sub-surface alloys’

originating from perturbed Ti4C4H8, and of their dehydrogenation products.

S7. Optimized geometries and selected molecular properties of various isomers of the M4Si4H8 composition

(M=Ti, Zr), and of the Ti4Nm4H8 composition (Nm=B, N), except for those shown in S3 and S4.

S8. Optimized geometries and selected molecular properties of dihydrogen complexes and transition states for

reactions of H2 detachment from selected M4Nm4H8 systems.

S9. The experimentally observed dependence between an ‘efficient energy barrier’ for the homolytic H2

detachment and a thermodynamic reaction parameter (standard redox potential for the metal cation/metal pair

in the aqueous solution, E0), for a range of inorganic binary hydrides.

S10. Changes of the total electron density, electrostatic potential and selected molecular orbitals along a

schematic reaction path for the reaction: Ti4Si4H6 + H2 → Ti4Si4H6…H2 (H2C) → Ti4Si4H8* → Ti4Si4H8.

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S1. Comparison of essential molecular features for M4C4H8 molecules (M=Ti, Zr, Hf) as computed

with the SDD and LANL pseudopotentials or with the 6-31** basis set on M atom.

-------------- Ti4C4H8 cube -------------- LANL2DZ E=-389.5314 au Ti-C 2.031 A C-H 1.102 A Ti-H 1.734 A APT charges: q(Ti) = +1.19 q(C) = -0.77 q(H_Ti)= -0.49 q(H_C)= +0.07 E(HOMO)= -0.265 au E(LUMO)= -0.128 au Gap = 0.137 au EN = -0.197 au -------------- SDDAll E=-390.5262 au Ti-C 2.037-2.039 A C-H 1.102 A Ti-H 1.744 A APT charges: q(Ti) = +1.20 q(C) = -0.78 q(H_Ti)= -0.49 q(H_C)= +0.07 E(HOMO)= -0.261 au E(LUMO)= -0.127 au Gap = 0.134 au EN = -0.194 au -------------- 6-31G** E=-3554.8708 au Ti-C 2.036-2.038 A C-H 1.102 A Ti-H 1.745 A APT charges: q(Ti) = +1.24 q(C) = -0.82 q(H_Ti)= -0.50 q(H_C)= +0.08 E(HOMO)= -0.261 au E(LUMO)= -0.126 au Gap = 0.135 au EN = -0.194 au

-------------- Zr4C4H8 cube -------------- LANL2DZ E=-343.5507 au Zr-C 2.206 A C-H 1.104 A Zr-H 1.911 A APT charges: q(Zr) = +1.35 q(C) = -0.85 q(H_Zr)= -0.54 q(H_C)= +0.04 E(HOMO)= -0.250 au E(LUMO)= -0.116 au Gap = 0.134 au EN = -0.183 au -------------- SDDAll E=-345.4848 au Zr-C 2.211 A C-H 1.104 A Zr-H 1.917 A APT charges: q(Zr) = +1.37 q(C) = -0.88 q(H_Zr)= -0.54 q(H_C)= +0.05 E(HOMO)= -0.248 au E(LUMO)= -0.115 au Gap = 0.133 au EN = -0.182 au -------------- 6-31G** basis set not available for Zr --------------

-------------- Hf4C4H8 cube -------------- LANL2DZ E=-352.9015 au Hf-C 2.187-2.188 A C-H 1.102 A Hf-H 1.892 A APT charges: q(Hf) = +1.36 q(C) = -0.92 q(H_Hf)= -0.51 q(H_C)= +0.06 E(HOMO)= -0.247 au E(LUMO)= -0.121 au Gap = 0.126 au EN = -0.184 au -------------- SDDAll E=-349.3536 au Hf-C 2.214-2.215 A C-H 1.102 A Hf-H 1.916-1.917 A APT charges: q(Hf) = +1.37-1.38 q(C) = -0.92 q(H_Hf)= -0.51 q(H_C)= +0.06 E(HOMO)= -0.242 au E(LUMO)= -0.118 au Gap = 0.124 au EN = -0.180 au -------------- 6-31G** basis set not available for Hf --------------



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S2. Comparison of vertical and relaxed ionization potential, electron affinity, Mulliken

electronegativity, and Pearson’s hardness for Ti4C4H8 (6-31** basis set on Ti) and Hf4C4H8 (SDD

pseudopotential on Hf).

-------------- Ti4C4H8 cube -------------- IP

vert = 8.75 eV

IPrelax = 8.47 eV

EAvert = 1.94 eV

EArelax = 2.10 eV

ENMrelax = 5.29 eV

HPrelax = 3.19 eV

-------------- Hf4C4H8 cube -------------- IP

vert = 8.20 eV

IPrelax = 8.00 eV

EAvert = 1.76 eV

EArelax = 1.85 eV

ENMrelax = 4.93 eV

HPrelax = 3.08 eV

Hafnium is the most electropositive metal in the d block (Pauling EN is 1.30), Ti is more electronegative (1.54).

Hafnium atom is bigger than that of Ti (1.55 Å vs. 1.40 Å), and it is easier to remove valence electrons from Hf

than for Ti. In addition, relativistic effects play big role for Hf, while destabilizing part of the d valence set. Both

these effects make tetravalent state (d0 configuration) more stable for Hf than for Ti with respect to reduction

(electron affinity of HfIV is smaller than that of TiIV), as is well known from chemistry of these elements.

Our simplistic DFT calculations (see S1) fully confirm these trends:

- the computed Hf–C bond lengths are ~0.18 Å longer than the Ti–C ones, following the behaviour also

seen in experiment for solid metal carbides (2.318 Å vs. 2.164 Å);

- the APT charge on metal is more positive for Hf than for Ti by some 0.14 e;

- the APT charge on C is more negative for the compound of Hf than for that of Ti, by some –0.14 e;

- energy of HOMO and LUMO are more negative for Ti compound, by some –0.01–0.02 a.u.;

- the relaxed electron affinity of HfIV compound is 0.25 eV smaller than for the TiIV analogue;

- the relaxed ionization potential of HfIV compound is 0.47 eV smaller than for the TiIV analogue;

- in the consequence of the above, the Ti molecule is slightly harder and somewhat more electronegative

than the Hf one.



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S3. Optimized geometries and selected molecular properties of cubane–like M4Nm4H8 molecules

(M=Ti, Zr, Hf; Nm=C, Si) and of their dehydrogenation products.

Ia. Ti4C4H8 (cubane-like).

E = −3554.87081 au, EZPE = −3554.79284 au

R(TiC) = 2.038 Å, R(TiH) = 1.746 Å, R(CH) = 1.102 Å

μDIP = 0.0 D; APT charges: Ti +1.242 x4, C −0.822 x4, HTi =

−0.499 x4, HC = 0.080 x4

EHOMO = −0.262 au, ELUMO = −0.126 au, ΔHL = 0.136 au

Ib. Ti4C4H6 (partially dehydrogenated).

E = −3553.65427 au, EZPE = −3553.59006 au

R(TiC) = 1.858 – 2.056 Å, R(TiH) = 1.756 Å, R(CH) = 1.102 Å

μDIP = 6.2 D; APT charges: Ti +1.065 x1, +1.189 x2, +1.217 x1, C

−0.957 x1, −0.763 x2, −0.790 x1, HTi = −0.527 x2, −0.512 x1, HC

= 0.058 x2, 0.063 x1


IIa. Ti4Si4H8 (cubane-like).

E = −4560.33653 au, EZPE = −4560.27917 au

R(TiSi) = 2.543 Å, R(TiH) = 1.718 Å, R(SiH) = 1.496 Å

μDIP = 0.0 D; APT charges: Ti +0.804 x4, Si −0.304 x4, HTi =

−0.407 x4, HSi = −0.094 x4




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IIb. Ti4Si4H6 (partially dehydrogenated).

E = −4559.14262 au, EZPE = −4559.09670 au

R(TiSi) = 2.355−2.560 Å, R(TiH) = 1.724 Å, R(SiH) = 1.497 Å

μDIP = 5.2 D; APT charges: Ti +0.594 x1, +0.752 x2, +0.822 x1, Si

−0.253 x2, −0.297 x1, −0.509 x1, HTi = −0.421 x1, −0.423 x2, HSi

= −0.104 x1, −0.118 x2


IIIa. Zr4C4H8 (cubane-like).

E = −345.48476 au, EZPE = −345.41030 au

R(ZrC) = 2.211 Å, R(ZrH) = 1.917 Å, R(CH) = 1.104 Å

μDIP = 0.0 D; APT charges: Zr +1.369 x4, C −0.878 x4, HZr =

−0.538 x4, HC = +0.047 x4


IIIb. Zr4C4H6 (partially dehydrogenated).

E = −344.26275 au, EZPE = −344.20172 au

R(ZrC) = 2.018−2.232 Å, R(ZrH) = 1.932 Å, R(CH) = 1.104 Å

μDIP = 7.0 D; APT charges: Zr +1.081 x1, +1.308 x2, +1.347 x1, C

−0.779 x2, −0.829 x1, −1.034 x1, HZr = −0.548 x1, −0.562 x2, HC

= −0.029 x1, −0.009 x2




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IVa. Zr4Si4H8 (cubane-like).

E = −1351.00379 au, EZPE = −1350.94768 au

R(ZrSi) = 2.628 – 2.757 Å, R(ZrH) = 1.874 Å, R(SiH) = 1.499 Å

μDIP = 0.1 D; APT charges: Zr +0.928 x4, Si −0.389 x4, HZr =

−0.440 x4, HSi = −0.099 x4


IVb. Zr4Si4H6 (partially dehydrogenated).

E = −1349.80810 au, EZPE = −1349.76350 au

R(ZrSi) = 2.496 – 2.724 Å, R(ZrH) = 1.878 – 1.887 Å, R(SiH) =

1.450 – 1.502 Å

μDIP = 5.5 D; APT charges: Zr +0.662 x1, +0.882 x2, +0.975 x1, Si

−0.344 x2, −0.357 x1, −0.608 x1, HZr = −0.458 x3, HSi = −0.117

x1, −0.130 x2


Va. Hf4C4H8 (cubane-like).

E = −349.35358 au, EZPE = −349.27978 au

R(HfC) = 2.214 Å, R(HfH) = 1.916 Å, R(CH) = 1.102 Å

μDIP = 0.0 D; APT charges: Hf +1.375 x4, C −0.919 x4, HHf =

−0.512 x4, HC = +0.057 x4




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Vb. Hf4C4H 6 (partially dehydrogenated).

E = −348.12133 au, EZPE = −348.06068 au

R(HfC) = 2.025 – 2.240 Å, R(HfH) = 1.928 Å, R(CH) = 1.102 Å

μDIP = 6.9 D; APT charges: Hf +1.075 x1, +1.308 x2, +1.360 x1, C

−1.055 x1, −0.858 x1, −0.808 x2, HHf = −0.521 x1, −0.531 x2, HC

= 0.013 x2, 0.035 x1


VIa. Hf4Si4H8 (cubane-like).

E = −1354.86584 au, EZPE = −1354.80957 au

R(HfSi) = 2.621 – 2.766 Å, R(HfH) = 1.876 Å, R(SiH) = 1.498 Å

μDIP = 0.1 D; APT charges: Hf +0.907 x4, Si −0.371 x4, HHf =

−0.427 x4, HSi = −0.100 x4


VIb. Hf4Si4H6 (partially dehydrogenated).

E = −1353.65942 au, EZPE = −1353.61512 au

R(HfSi) = 2.508 – 2.740 Å, R(HfH) = 1.882 Å, R(SiH) = 1.497 Å

μDIP = 5.2 D; APT charges: Hf +0.688 x1, +0.904 x2, +0.970 x1, Si

−0.371 x1, −0.400 x2, −0.673 x1, HHf = −0.434 x1, −0.444 x2, HSi

= −0.112 x3




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S4. Optimized geometries and selected molecular properties of M4Nm4H8 molecules (M=Ti, V; Nm=B,

C, N) and of their most stable dehydrogenation products, except for Ti4C4H8.

VIIa. Ti4B4H8.

E = −3501.68954 au, EZPE = −3501.61969 au

R(TiB) = 2.208 – 2.221 Å, R(TiH) = 1.738 Å, R(BH) = 1.206 Å

μDIP = 0.0 D; APT charges: Ti +0.913 x4, B −0.351 x4, HTi =

−0.503 x4, HB = −0.059 x4


VIIb. Ti4B4H6[I]

E = −3500.49395 au, EZPE = −3500.43555 au

R(TiB) = 2.049 – 2.249 Å, R(TiH) = 1.735 – 1.751 Å, R(BH) =

1.202 Å

μDIP = 4.8 D; APT charges: Ti +0.475 x1, +0.756 x2, +0.760 x1, B

−0.118 x1, −0.194 x2, −0.438 x1, HTi = −0.475 x1, −0.517 x2, HB

= −0.098 x3


VIIIa. Ti4N4H8.

E = −3621.75915 au, EZPE = −3621.67481 au

R(TiN) = 1.896 – 2.100 Å, R(TiH) = 1.770 Å, R(NH) = 1.020 Å

μDIP = 1.7 D; APT charges: Ti +0.831 x2, +1.062 x2, N −0.553 x2,

−0.593 x2, HTi = −0.573 x2, −0.581 x2, HN = +0.203 x4




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VIIIb. Ti4N4H6[I]

E = −3620.55816 au, EZPE = −3620.48969 au

R(TiN) = 1.872 – 2.109 Å, R(TiH) = 1.760 – 1.785 Å, R(NH) =

1.020 Å

μDIP = 2.9 D; APT charges: Ti +0.456 x1, +0.633 x1, +1.201 x2, N

−0.538 x1, −0.612 x2, −0.616 x1, HTi = −0.511 x1, −0.546 x2, HN

= +0.157 x2, +0.176 x1


IXa. V4B4H8.

E = −3879.78477 au, EZPE = −3879.70662 au

R(VB) = 2.144 – 2.248 Å, R(VH) = 1.664 – 1.741 Å, R(BH) =

1.199 Å

μDIP = 4.7 D; APT charges: V +0.379 x1, +0.415 x1, +0.453 x1,

+0.500 x1, B −0.113 x2, −0.137 x1, −0.149 x1, HV = −0.115 x1,

−0.144 x1, −0.330 x2, HB = −0.076 x2, −0.113 x1, −0.149 x1


IXb. V4B4H6.

E = −3878.57964 au, EZPE = −3878.51719 au

R(VB) = 2.020 – 2.408 Å, R(VH) = 1.690 – 1.795 Å, R(BH) =

1.194 Å


+0.547 x1, B −0.024 x1, −0.053 x1, −0.094 x1, −0.179 x1, HV =

−0.326 x1, −0.432 x1, −0.478 x1, HB = −0.068 x1, −0.086 x2,




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Xa. V4C4H8.

E = −3932.86026 au, EZPE = −3932.77864 au

R(VC) = 1.857 – 2.100 Å, R(VH) = 1.686 Å, R(CH) = 1.098 Å

μDIP = 2.6 D; APT charges: V +0.503 x2, +1.009 x2, C −0.342 x2,

−0.445 x2, HV = −0.418 x2, −0.454 x2, HC = −0.069 x2, −0.078 x2


Xb. V4C4H6.

E = −3931.65685 au, EZPE = −3931.58945 au

R(VC) = 1.836 – 2.113 Å, R(VH) = 1.684 – 1.698 Å, R(CH) =

1.098 Å

μDIP = 3.3 D; APT charges: V +0.583 x1, +0.630 x1, +0.866 x2, C

−0.344 x1, −0.459 x2, −0.593 x1, HV = −0.419 x1, −0.438 x2, HC =

−0.061 x1, −0.071 x2


XIa. V4N4H8.

E = −3999.72914 au, EZPE = −3999.64134 au

R(VN) = 1.905 – 2.013 Å, R(VH) = 1.693 Å, R(NH) = 1.016 Å

μDIP = 2.7 D; APT charges: V +0.723 x2, +0.749 x2, N −0.446 x2,

−0.495 x2, HV = −0.442 x2, −0.453 x2, HN = +0.176 x2, +0.189 x2




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XIb. V4N4H6.

E = −3998.52582 au, EZPE = −3998.45511 au

R(VN) = 1.790 – 2.005 Å, R(VH) = 1.691 – 1.708 Å, R(NH) =

1.014 Å


+0.890 x1, N −0.521 x1, −0.536 x1, −0.595 x1, −0.642 x1, HV =

−0.464 x3, HN = +0.181 x1, +0.191 x1, +0.201 x1


XIIa. Zr4B4H8.

E = −292.29184 au, EZPE = −292.22399 au

R(ZrB) = 2.373 – 2.393 Å, R(ZrH) = 1.900 Å, R(BH) = 1.206 Å

μDIP = 0.0 D; APT charges: Zr +0.976 x4, B −0.398 x4, HZr =

−0.517 x4, HB = −0.062 x4


XIIb. Zr4B4H6[I]

E = −291.09613 au, EZPE = −291.04037 au

R(ZrB) = 2.213 – 2.513 Å, R(ZrH) = 1.898 – 1,918 Å, R(BH) =

1.198 – 1,208 Å

μDIP = 5.1 D; APT charges: Zr +0.444 x1, +0.764 x2, +0.789 x1, B

−0.112 x1, −0.158 x2, −0.416 x1, HZr = −0.498 x1, −0.539 x2, HB

= −0.122 x3




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S5. Optimized geometries and selected molecular properties of Ti4(N2B2)H8 and of its dehydrogenation

products.

XIIIa. Ti4(N2B2)H8.

E = −3561.74335 au, EZPE = −3561.66523 au

R(TiN) = 2.028 Å, R(TiB) = 2.001 – 2.146 Å, R(TiH) = 1.744 Å,

R(NH) = 1.024 Å, R(BH) = 1.234 Å,


B −0.706 x2, HTi = −0.477 x2, −0.485 x2, HN = +0.152 x2, HB =

+0.039 x2


XIIIb. Ti4(N2B2)H6 (dehydrogenated at TiB).

E = −3560.51402 au, EZPE = −3560.44927 au

R(TiN) = 2.002 – 2.035 Å, R(TiB) = 1.918 – 2.159 Å, R(TiH) =

1.756 Å, R(NH) = 1.024 Å, R(BH) = 1.236 Å,


−0.582 x2, B −0.671 x1, −0.746 x1, HTi = −0.497 x2, −0.517 x1,

HN = +0.133 x2, HB = +0.016 x1


XIIIc. Ti4(N2B2)H6 (dehydrogenated at TiN).

E = −3560.55588 au, EZPE = −3560.49306 au

R(TiN) = 1.886 – 2.049 Å, R(TiB) = 2.023 – 2.184 Å, R(TiH) =

1.750 Å, R(NH) = 1.024 Å, R(BH) = 1.234 Å,


−0.621 x1, −0.791 x1, B −0.671 x1, −0.746 x1, HTi = −0.493 x1,

−0.505 x2, HN = +0.154 x2, HB = −0.047 x1, +0.013 x1




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S6. Optimized geometries and selected molecular properties of molecular analogues of ‘sub-surface

alloys’ originating from perturbed Ti4C4H8, and of their dehydrogenation products.

XIVa. (TiCH2)(TiNH2)2(TiCH2).

E = −3588.30872 au, EZPE = −3588.22744 au

R(TiN) = 2.010 – 2.040 Å, R(TiC) = 2.001 – 2.042 Å, R(TiH) =

1.758 Å, R(NH) = 1.020 Å, R(CH) = 1.099 Å,


C −0.526 x2, HTi = −0.569 x2, −0.583 x2, HN = +0.214 x2, HC =

+0.075 x2


XIVb. (TiCH2)(TiNH2)2(TiC).

E = −3587.08863 au, EZPE = −3587.02161 au

R(TiN) = 2.019 – 2.034 Å, R(TiC) = 1.918 – 2.103 Å, R(TiH) =

1.761– 1.774 Å, R(NH) = 1.022 Å, R(CH) = 1.100 Å,


C −0.749 x1, +0.968 x1, HTi = −0.526 x2, −0.556 x1, HN = +0.141

x2, HC = +0.055 x1


XVa. (TiCH2)(TiBH2)2(TiCH2).

E = −3528.28218 au, EZPE = −3528.20703 au

R(TiB) = 2.104 – 2.248 Å, R(TiC) = 1.984 – 2.063 Å, R(TiH) =

1.741 – 1.756 Å, R(BH) = 1.236 Å, R(CH) = 1.102 Å,


−0.438 x2, C −0.676 x1, −0.745 x1, HTi = −0.488 x2, −0.516 x1,

−0.531 x1, HB = −0.082 x2, HC = +0.082 x2




14

XVb. (TiCH2)(TiBH2)2(TiC).

E = −3527.07184 au, EZPE = −3527.01216 au

R(TiB) = 2.203 – 2.281 Å, R(TiC) = 1.849 – 2.063 Å, R(TiH) =

1.755 Å, R(BH) = 1.214 Å, R(CH) = 1.102 Å,


−0.414 x2, C −0.709 x1, −0.817 x1, HTi = −0.505 x1, −0.540 x2,

HB = −0.112 x2, HC = +0.081 x1


XVIa. (TiCH2)(VCH2)2(TiCH2).

E = −3743.84912 au, EZPE = −3743.76940 au

R(TiC) = 1.984 – 2.054 Å, R(VC) = 1.934 – 1.980 Å, R(TiH) =

1.751 Å, R(VH) = 1.680 Å, R(CH) = 1.101 – 1.111 Å,

μDIP = 2.1 D; APT charges: Ti +1.101 x2, V −0.918 x2, C −0.575

x2, −0.662 x2, HTi = −0.503 x2, HV = −0.412 x2, HC = +0.064 x2,

+0.069 x2


XVIb. (TiCH2)(VCH2)2(TiC).

E = −3742.63564 au, EZPE = −3742.57078 au

R(TiC) = 1.828 – 2.054 Å, R(VC) = 1.900 – 2.012 Å, R(TiH) =

1.765 Å, R(VH) = 1.686 Å, R(CH) = 1.101 – 1.110 Å,

μDIP = 6.9 D; APT charges: Ti +0.912 x1, +0.997 x1, V −0.877 x2,

C −0.617 x2, −0.635 x1, −0.647 x1, HTi = −0.517 x1, HV = −0.436

x2, HC = +0.058 x2, +0.128 x1




15

S7. Optimized geometries and selected molecular properties of various isomers of the M4Si4H8

composition (M=Ti, Zr), and of the Ti4Nm4H8 composition (Nm=B, N), and of their dehydrogenation

products, except for those shown in S3 and S4.

IIc. Ti4Si4H8*

E = −4560.34337 au, EZPE = -4560.28448 au

R(TiSi) = 2.500 – 2.570 Å, R(TiH) = 1.500 – 1.554 Å, R(SiH) =

1.717 Å


−0.257 x2, −0.322 x2, HTi = −0.376 x1, −0.422 x2, −0.404 x1, HSi

= −0.016 x1, −0.094 x1, −0.104 x2

EHOMO (A'') = −0.226 au, ELUMO (A') = −0.148 au, ΔHL = 0.078 au

IVc. Zr4Si4H8*

E = −1351.01043 au, EZPE = −1350.95267 au

R(ZrSi) = 2.649 – 2.727 Å, R(ZrH) = 1.867 – 1.880 Å, R(SiH) =

1.498 – 1.560 Å


−0.358 x2, −0.376 x1, −0.408 x1, HZr = −0.411 x1, −0.435 x1,

−0.462 x2, HSi = −0.041 x1, −0.111 x3


VIIc. Ti4B4H6[II]

E = −3500.47896 au, EZPE = -3500.42996 au

R(TiB) = 2.050 – 2.269 Å, R(TiH) = 1.741 – 1.759 Å, R(BH) =

1.199 – 1.209 Å

μDIP = 6.0 D; APT charges: Ti +0.534 x1, +0.678 x1, +0.748 x1,

+0.787 x1, B −0.127 x1, −0.149 x1, −0.201 x1, −0.445 x1, HTi =

−0.490 x1, −0.518 x2, HB = −0.097 x3




16

VIIIc. Ti4N4H6[II]

E = −3620.54984 au, EZPE = −3620.48166 au

R(TiN) = 1.772 – 2.114 Å, R(TiH) = 1.757 – 1.785 Å, R(NH) =

1.020 Å


+1.275 x1, N −0.576 x1, −0.588 x1, −0.652 x1, −0.764 x1, HTi =

−0.532 x2, −0.596 x1, HN = +0.159 x2, +0.173 x1


XIIc. Zr4B4H6[II]

E = −291.09031 au, EZPE = −291.03495 au

R(ZrB) = 2.289 – 2.541 Å, R(ZrH) = 1.906 – 1,929 Å, R(BH) =

1.199 – 1,214 Å

μDIP = 6.3 D; APT charges: Zr +0.435 x1, +0.702 x1, +0.747 x1,

+0.822 x1, B −0.096 x1, −0.135 x2, −0.393 x1, HZr = −0.505 x1,

−0.542 x2, HB = −0.122 x3




17

S8. Optimized geometries and selected molecular properties of dihydrogen complexes and transition

states for reactions of H2 detachment from selected M4Nm4H8 systems.

Ic. Ti4C4H6 ... H2

E = −3554.84297 au, EZPE = −3554.76442 au

R(TiC) = 1.857 − 2.054 Å, R(TiH) = 1.760 Å, R(CH) = 1.102 Å,

R(HH) = 0.763 Å

μDIP = 6.3 D; APT charges: Ti +0.992 x1, +1.201 x2, +1.210 x1, C

−0.768 x2, −0.798 x1, −0.979 x1, HTi = −0.514 x1, −0.526 x2, HC

= +0.063 x3, H2 compl = −0.049, +0.136


Id. Ti4C4H6 + H2 (TS)

E= −3554.83063 au, EZPE= −3554.75349 au, υimg = −1225.5 cm–1 R(TiC) = 1.879 − 2.046 Å, R(TiH) = 1.750 Å, R(CH) = 1.102 Å,

R(HH) = 1.047 Å

μDIP = 3.6 D; APT charges: Ti +0.973 x1, +1.233 x3, C −0.780 x2,

−0.818 x1, −1.056 x1, HTi = −0.506 x1, −0.514 x2, HC = +0.069

x3, H2 TS = −0.364, +0.463


IId. Ti4Si4H6 ... H2

E = −4560.33336 au, EZPE = −4560.27267 au

R(TiSi) = 2.359 − 2.566 Å, R(TiH) = 1.722 Å, R(SiH) = 1.495 Å,

R(HH) = 0.797 Å


−0.292 x2, −0.306 x1, −0.524 x1, HTi = −0.421 x1, −0.428 x2, HSi

= −0.103 x3, H2 compl = −0.114, +0.260

EHOMO(A'') = −0.211 au, ELUMO(A') = −0.134 au, ΔHL = 0.077 au



18

IIe. Ti4Si4H6 + H2 (TS1)

E= −4560.33080 au, EZPE= −4560.27290 au, υimg = −800.3 cm–1 R(TiSi) = 2.388 − 2.561 Å, R(TiH) = 1.721 Å, R(SiH) = 1.496 Å,

R(HH) = 1.046 Å


−0.294 x2, −0.315 x1, −0.463 x1, HTi = −0.414 x1, −0.425 x2, HSi

= −0.101 x3, H2 TS = −0.279, +0.316

EHOMO(A'') = −0.217 au, ELUMO(A') = −0.141 au, ΔHL = 0.076 au

IVd. Zr4Si4H6 ... H2

E = −1350.99718 au, EZPE = −1350.93786 au

R(ZrSi) = 2.500 − 2.645 Å, R(ZrH) = 1.877 − 1.886 Å, R(SiH) =

1.500 Å, R(HH) = 0.785 Å


−0.358 x2, −0.372 x1, −0.626 x1, HZr = −0.455 x1, −0.462 x2, HSi

= −0.119 x3, H2 compl = −0.093, +0.237


IVe. Zr4Si4H6 + H2 (TS1)

E = −1350.99178 au, EZPE = −1350.93530 au, υimg = −986.5 cm–1

R(ZrSi) = 2.531 − 2.716 Å, R(ZrH) = 1.872 − 1.883 Å, R(SiH) =

1.499 Å, R(HH) = 1.088 Å


−0.372 x3, −0.574 x1, HZr = −0.447 x1, −0.463 x2, HSi = −0.115

x3, H2 TS = −0.303, +0.332




19

VIId. Ti4B4H6 ... H2[I]

E = −3501.68093 au, EZPE = −3501.60896 au

R(TiB) = 2.050 − 2.318 Å, R(TiH) = 1.736 − 1.752 Å, R(BH) =

1.204 Å, R(HH) = 0.760 Å


−0.156 x1, −0.191 x2, −0.449 x1, HTi = −0.479 x1, −0.515 x2, HB

= −0.093 x2, −0.102 x1, H2 compl = +0.025, +0.085


VIIe. Ti4B4H6 + H2[I] (TS)


R(TiB) = 2.008 − 2.310 Å, R(TiH) = 1.733 − 1.745 Å, R(BH) =

1.204 Å, R(HH) = 1.178 Å


−0.205 x1, −0.219 x2, −0.480 x1, HTi = −0.484 x1, −0.512 x2, HB

= −0.085 x2, −0.094 x1, H2 TS = −0.363, +0.366


VIIf. Ti4B4H6 ... H2[II]

E = −3501.67475 au, EZPE = −3501.60312 au

R(TiB) = 2.054 − 2.337 Å, R(TiH) = 1.744 − 1.759 Å, R(BH) =

1.200 − 1.210 Å, R(HH) = 0.760 Å


+0.824 x1, B −0.119 x1, −0.159 x1, −0.212 x1, −0.436 x1, HTi =

−0.477 x1, −0.508 x1, −0.521 x1, HB = −0.096 x2, −0.107 x1, H2 compl = +0.047, +0.104




20

VIIg. Ti4B4H6 + H2[II] (TS)


R(TiB) = 2.004 − 2.229 Å, R(TiH) = 1.733 − 1.749 Å, R(BH) =

1.203 Å, R(HH) = 1.081 Å


+0.858 x1, B −0.141 x1, −0.256 x2, −0.509 x1, HTi = −0.478 x1,

−0.508 x2, HB = −0.72 x1, −0.092 x2, H2 TS = −0.377, +0.345


VIIId. Ti4N4H6 ... H2[I]

E = −3621.75605 au, EZPE = −3621.67178 au

R(TiN) = 1.848 − 2.161 Å, R(TiH) = 1.752 − 1.778 Å, R(NH) =

1.020 Å, R(HH) = 0.829 Å


−0.630 x3, −0.824 x1, HTi = −0.459 x1, −0.529 x2, HN = +0.159

x2, +0.167 x1, H2 compl = −0.146, +0.312


VIIIe. Ti4N4H6 + H2[I]

(TS)


R(TiN) = 1.833 − 2.054 Å, R(TiH) = 1.765 − 1.778 Å, R(NH) =

1.019 Å, R(HH) = 1.064 Å


−0.525 x2, −0.571 x1, −0.745 x1, HTi = −0.563 x2, −0.575 x1, HN

= +0.179 x2, +0.207 x1, H2 TS = −0.409, +0.446

EHOMO (A')= −0.176 au, ELUMO (A')= −0.106 au, ΔHL = 0.070 au



21

VIIIf. Ti4N4H6 ... H2[II]

E = −3621.73722 au, EZPE = −3621.65374 au

R(TiN) = 1.770 − 2.121 Å, R(TiH) = 1.759 − 1.781 Å, R(NH) =

1.020 Å, R(HH) = 0.773 Å


+1.216 x1, N −0.538 x1, −0.558 x1, −0.621 x1, −0.659 x1, HTi =

−0.532 x2, −0.593 x1, HN = +0.145 x1, +0.159 x1, +0.174 x1, H2

compl = −0.034, +0.188


VIIIg. Ti4N4H6 + H2 (TS)[II]


R(TiN) = 1.813 − 2.092 Å, R(TiH) = 1.754 − 1.775 Å, R(NH) =

1.020 Å, R(HH) = 1.058 Å


+1.240 x1, N −0.566 x1, −0.590 x1, −0.607 x1, −0.876 x1, HTi =

−0.532 x1, −0.542 x1, −0.594 x1, HN = +0.169 x1, +0.176 x1, +0.188 x1, H2 TS = −0.345, +0.445


XIVc. (TiCH2)(TiNH2)2(TiC) ... H2

E = −3588.28189 au, EZPE = −3588.19938 au

R(TiN) = 1.982 – 2.094 Å, R(TiC) = 1.931 – 2.069 Å, R(TiH) =

1.761 Å, R(NH) = 1.021 Å, R(CH) = 1.100 Å, R(HH) = 0.795 Å


−0.521 x1, −0.662 x1, C −0.740 x1, +0.940 x1, HTi = −0.524 x2,

−0.537 x1, HN = +0.132 x1, +0.146 x1, HC = +0.058 x1, H2 compl =

−0.003, +0.220




22

XIVd. (TiCH2)(TiNH2)2(TiC) + H2 (TS)


R(TiN) = 1.994 – 2.091 Å, R(TiC) = 1.916 – 2.010 Å, R(TiH) =

1.733 – 1.751 Å, R(NH) = 1.022 Å, R(CH) = 1.101 Å, R(HH) =

2.206 Å


−0.695 x2, C −0.694 x1, +0.726 x1, HTi = −0.484 x1, −0.518 x2,

HN = +0.189 x2, HC = +0.073 x1, H2 TS = −0.498, +0.120


XVc. (TiCH2)(TiBH2)2(TiC) ... H2

E = −3528.26240 au, EZPE = −3528.18694 au

R(TiB) = 2.063 – 2.357 Å, R(TiC) = 1.921 – 2.070 Å, R(TiH) =

1.745 – 1.754 Å, R(BH) = 1.249 Å, R(CH) = 1.102 Å, R(HH) =

0.766 Å


−0.312 x2, C −0.747 x1, −0.834 x1, HTi = −0.504 x2, −0.518 x1, HB = −0.118 x2, HC = +0.078 x1, H2

compl = −0.101 x2


XVd. (TiCH2)(TiBH2)2(TiC) + H2 (TS)


R(TiB) = 2.115 – 2.290 Å, R(TiC) = 1.940 – 2.083 Å, R(TiH) =

1.745 – 1.756 Å, R(BH) = 1.238 – 1.250 Å, R(CH) = 1.102 Å,

R(HH) = 1.027 Å


+1.100 x1, B −0.320 x2, C −0.712 x1, −0.882 x1, HTi = −0.511 x1, −0.518 x1, −0.486 x1, HB = −0.097

x1, −0.147 x1, HC = +0.084 x1, H2 TS = −0.271, +0.359




23

XVIc. (TiCH2)(VCH2)2(TiC) ... H2

E = −3743.82526 au, EZPE = −3743.74549 au

R(TiC) = 1.836 – 2.055 Å, R(VC) = 1.904 – 1.993 Å, R(TiH) =

1.765 Å, R(VH) = 1.688 Å, R(CH) = 1.101 – 1.110 Å, R(HH) =

0.775 Å


C −0.613 x2, −0.630 x1, −0.647 x1, HTi = −0.522 x1, HV = −0.433 x2, HC = +0.066 x2, +0.115 x1, H2

compl = −0.085, +0.231


XVId. (TiCH2)(VCH2)2(TiC) + H2 (TS)


R(TiC) = 1.862 – 2.063 Å, R(VC) = 1.917 – 1.979 Å, R(TiH) =

1.758 Å, R(VH) = 1.682 Å, R(CH) = 1.101 – 1.109 Å, R(HH) =

1.036 Å


C −0.597 x1, −0.613 x2, −0.621 x1, HTi = −0.515 x1, HV = −0.417 x2, HC = +0.069 x2, +0.107 x1, H2

TS = −0.339, +0.444


XIId. Zr4B4H6 ... H2[I]

E = −292.28063 au, EZPE = −292.21174 au,

R(ZrB) = 2.213 – 2.446 Å, R(ZrH) = 1.899 – 1,919 Å, R(BH) =

1.199 – 1.207 Å, R(HH) = 0.756 Å


−0.135 x1, −0.148 x2, −0.434 x1, HZr = −0.504 x1, −0.537 x2, HB

= −0.119 x2, −0.129 x1, H2 compl = +0.034, +0.057




24

XIIe. Zr4B4H6 + H2[I] (TS)


R(ZrB) = 2.301 – 2.456 Å, R(ZrH) = 1.903 Å, R(BH) = 1.203 Å,

R(HH) = 1.551 Å


−0.120 x1, −0.146 x1, −0.251 x2, HZr = −0.519 x1, −0.529 x2, HB

= −0.041 x1, −0.078 x2, H2 TS = −0.270, +0.057


XIIf. Zr4B4H6 ... H2[II]

E = −292.27395 au, EZPE = −292.20574 au,

R(ZrB) = 2.242 – 2.535 Å, R(ZrH) = 1.907 – 1,930 Å, R(BH) =

1.199 – 1.214 Å, R(HH) = 0.756 Å

μDIP = 7.0 D; APT charges: Zr +0.323 x1, +0.706 x1, +0.756 x1,

+0.839 x1, B −0.088 x1, −0.121 x1, −0.157 x1, −0.401 x1, HZr =

−0.513 x1, −0.540 x2, HB = −0.116 x2, −0.129 x1, H2 compl = +0.046, +0.057


IIf. Ti4Si4H6 + H2 (TS2 between Ti4Si4H8 and Ti4Si4H8*)

E= −4560.33577 au, EZPE= −4560.27883 au, υimg = −243.7 cm–1 R(TiSi) = 2.495 − 2.601 Å, R(TiH) = 1.718 Å, R(SiH) = 1.496 Å,

R(HH) = 3.374 Å

μDIP = 0.4 D; APT charges: Ti +0.762 x1, +0.804 x3, Si −0.272 x2,

−0.314 x1, −0.329 x1, HTi = −0.412 x3, HSi = −0.087 x1, −0.099

x2, H2 TS = −0.064, −0.404




25

S9. The experimentally observed dependence between an ‘efficient energy barrier’ for the hemolytic H2

detachment and a thermodynamic reaction parameter (standard redox potential for the metal

cation/metal pair in the aqueous solution, E0), for a range of inorganic binary hydrides. Numerical data

from [1].

Comp. Tdec /oC

Tdec / K

3/2 kT Effective barrier

/eV

E0 /V Redox pair

LiH 720 993 2.06E-20 0.128 -3.04 LiI(aq)/Li0(s) BaH2 675 948 1.96E-20 0.122 -2.92 BaII

(aq)/Ba0(s)

SrH2 675 948 1.96E-20 0.122 -2.89 SrII (aq)/Sr0

(s) CaH2 600 873 1.81E-20 0.113 -2.84 CaII

(aq)/Ca0(s)

NaH 425 698 1.44E-20 0.090 -2.713 NaI(aq)/Na0

(s) YH3 350 623 1.29E-20 0.081 -2.37 YIII

(aq)/Y0(s)

MgH2 327 600 1.24E-20 0.078 -2.356 MgII (aq)/Mg0

(s) ErH3 373 646 1.34E-20 0.083 -2.32 ErIII

(aq)/Er0(s)

PuH3 250 523 1.08E-20 0.068 -2.00 PuIII (aq)/Pu0

(s) BeH2 250 523 1.08E-20 0.068 -1.97 BeII

(aq)/Be0(s)

AlH3 150 423 8.76E-21 0.055 -1.676 AlIII (aq)/Al0(s) UH3 250 523 1.08E-20 0.068 -1.66 UIII

(aq)/U0(s)

VH2 35 308 6.38E-21 0.040 -1.13 VII (aq)/V0

(s) [BH3]2 40 313 6.48E-21 0.040 -0.89 H3BO3/B0

(s) ZnH2 90 363 7.51E-21 0.047 -0.793 ZnII

(aq)/Zn0(s)

Ga2H6 -15 258 5.34E-21 0.033 -0.53 GaIII (aq)/Ga0

(s) PH3 25 298 6.17E-21 0.039 -0.502 H3PO3/P0

(s) CdH2 -20 253 5.24E-21 0.033 -0.402 CdII

(aq)/Cd0(s)

SnH4 25 298 6.17E-21 0.039 0.007 SnIV (aq)/Sn0

(s) SbH3 -65 208 4.31E-21 0.027 0.204 SbOI/Sb0

(s) BiH3 -40 233 4.82E-21 0.030 0.317 BiIII(aq)/Bi0(s) HgH2 -125 148 3.06E-21 0.019 0.854 BiIII(aq)/Bi0(s)

Here, ‘effective barrier’ has been calculated as the average thermal energy of a molecule, 3/2 kTdec, at

its thermal decomposition temperature, Tdec, and expressed in the eV units. It is related to, but of course

much smaller then the electronic barrier of the H2 detachment reaction which enters the kinetic

(Arrhenius) equation.



26

S10. Changes of the total electron density, electrostatic potential and selected molecular orbitals along a schematic reaction path for the reaction: Ti4Si4H6 + H2 → Ti4Si4H6…H2 (H2C) → TS1 → Ti4Si4H8* → TS2 → Ti4Si4H8.



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