Insight into anomalous hydrogen adsorption on rare earth metal decorated on 2-dimensional hexagonal boron nitride: a density functional theory study

Hydrogen interaction with metal atoms is of prime focus for many energy related applications like hydrogen storage, hydrogen evolution using catalysis, etc. Although hydrogen binding with many main group alkaline and transition metals is quite well understood, its binding properties with lanthanides are not well reported. In this article, by density functional theory studies, we show how a rare earth metal, cerium, binds with hydrogen when decorated over a heteropolar 2D material, hexagonal boron nitride. Each cerium adatom is found to bind eight hydrogen molecules which is a much higher number than has been reported for transition metal atoms. However, the highest binding energy occurs at four hydrogen molecules. This anomaly, therefore, is investigated in the present article using first-principles calculations. The number density of hydrogen molecules adsorbed over the cerium adatom is explained by investigating the electronic charge volume interactions owing to a unique geometrical arrangement of the guest hydrogen molecules. The importance of geometrical encapsulation in enhancing electronic interactions is explained.


S2. Validation against existing work.
For additional validation, the binding of rare earth element Eu on graphene was computed and compared with previous results [3]. Valence configuration for Eu was taken as 5p 6 6s 2 .
The binding energies of Eu and Yb on graphene was found to be -0.85 eV and -0.27 eV which is close to reported value of -0.90 eV and -0.32 eV. The slight discrepancy may be due to the difference in the exact nature of pseudopotentials used.

S3. Selection of Hubbard parameter, U.
The effect of U level on the nature of interaction between the adatom and the planar substrate can be found from the partial density of states of the constituent atoms as shown in Fig. S3.1. Plain GGA (with U=0 eV) calculations are known to underestimate the band gap. This is more pronounced for species consisting of highly localized f-electrons like transition metals including lanthanides. Thus, for heavy elements like cerium with highly correlated f electrons, the strong self-interaction terms due to localized d and f electrons are not sufficiently cancelled while applying plain LDA or GGA [4]. To assess the localized nature of these f-electrons, values of the Hubbard parameter, U on the Ce f-electrons are increased through 2, 3 and 5 eV. Without any Hubbard correction, the strongly correlated Ce felectrons are severely delocalized and indicate spuriously narrower band gaps. Table S3.2 shows the varying band gaps as U levels are increased. As U is increased, new states corresponding to cerium f-orbitals start appearing. Consequently, a band gap of 0.8 eV is observed for Ce adsorbed on h-BN with U correction of 5 eV as compared to 0.22 eV without Hubbard. Indeed, the appropriate value of U is arrived at by empirical comparison with any particular observable like lattice parameter or formation energy or band gap or bulk modulus etc. [2], [5]. Thus, the choice of U is widely debated and is dictated mainly by the measured property. Without delving into an in-depth study, in accordance with other extensive studies on appropriate U values of Cerium based compounds [6], [7] we henceforth adopt a U = 5 eV and J = 0 eV throughout for all calculations.

S5. Effect of Ce adsorption on charge distribution and interatomic distances.
Adsorption   Overall, the Ce adatom has excess positive charge and so do the nearest B atoms in first shell (B1-3 in Fig. S5.1). Contrarily, the nearest N atoms in the first shell (N1-3 in Fig. S5.1) have excess negative charge. Since Ce settles at the HC site, one expects the strain due to its addition to be uniformly distributed radially. However, the first shell N atoms do not shift as much as the first shell B atoms (N1-3 and B1-3 in Fig. S5.2). Therefore, one can rationally conclude, that the strain has two different origins: mechanical and electrostatic. Both mechanical strain and electronic repulsion between positively charged Ce and the adjacent B atoms add up and cause the first shell B atoms to be pushed out notably in xy-plane and slightly downwards (B1-3 in Fig S5.2 and S5.3). However, electronic attraction between oppositely charged Ce and N overcomes some of the structural strain and as a result, the nearest N atoms are only pushed downwards slightly (N1-3 in Fig. S5.3) with much less noticeable displacement in the xy-plane (N1-3 in Fig. S5.2). As a result of first shell B atoms' large displacement in xy-plane, the second shell N atoms witness a large push outwards (N4-6 in Fig. S5.2) as well as downwards (N4-6 in Fig. S5.3). The second shell B atoms (B4-6 in Fig. S5.3) attached to the first shell N atoms are pushed upwards. Thus, there is some warping of the h-BN substrate due to adsorption of a heavy element like Ce. Expectedly, B-N bonds closest to the HC site are elongated by ~0.8% (Fig. S4.2).

S6. Charge density difference on hydrogen adsorption.
Charge density difference isosurfaces are drawn for n hydrogen adsorbed Ce decorated h-BN.