Influence of the second layer on geometry and spectral properties of doped two-dimensional hexagonal boron nitride

Influence of the additional layer of hexagonal boron nitride (h-BN) on structure, energetics, and electronic spectra of a layer doped with magnesium, silicon, phosphorus, aluminum, or carbon atoms has been examined by theoretical methods. The h-BN layers are modeled as BN clusters of over thirty atoms with the defect in the center. The calculations show that atom positions undergo some modifications in the presence of the second layer, which in several cases lead to significant changes in electronic spectra, like (i) modifications of the character of some states from local excitation to a partial charge transfer; (ii) redshift of the majority of lowest excitations; (iii) absence or appearance of new states in comparison with the monolayers. For instance, a zero-intensity excitation below 4 eV for the carbon atom in place of boron transforms into a dipole-allowed one in the presence of the second layer. A comparison of the interaction energies of doped and undoped clusters shows a strong dependence of the stabilizing of destabilizing effect on the dopant atom, the replaced atom, and in some cases also on the stacking type (AA’ or AB). The stabilization energy per BN pair, calculated for two undoped clusters, is equal to − 31 and − 28 meV for the AA’ and AB stacking, respectively, thus confirming a larger stability of the AA’ stacking for the h-BN case. Electronic supplementary material The online version of this article (10.1007/s00894-020-04456-8) contains supplementary material, which is available to authorized users.

Theoretical considerations on the accuracy of the modified CAM-B3LYP functional for local and charge-transfer excitations The quality of the present functional for the bilayers of h-BN has been double-checked by performing calculations for the AA' stacked structure (the "sandwich" structure) of two borazine molecules. Additionally, two more advanced ab initio methods, algebraic adiabatic construction to the second order -ADC(2) 1 and equation-of-motion coupled cluster truncated to single and double excitations -EOM-CCSD, 2 have been used to obtain the spectrum for this complex with the same basis set. It turns out that the first excited state, as well as three lowest states with nonzero oscillator strengths are reproduced faithfully by the selected DFT functional. The excitation energy of the first excited state (which is dipole-forbidden) is equal to 6.79 eV, 6.37 eV, and 6.54 eV for TD-DFT, ADC (2), and EOM-CCSD methods, respectively, and the excitation character (performed by the analysis of orbitals taking part in the major electron promotions) confirms that all three methods describe the same state (i.e. that present TD-DFT produces no spurious CT states, which were reported whne some older functionals were utilized, see e.g. Ref. 3 ). The difference between the EOM-CCSD and the CAM-B3LYP-mod results can serve as the estimation of a systematic energy blueshift of this functional. As one can see, for the lowest state this shift is equal to 0.25 eV, while for three dipole-allowed states it becomes 0.4 eV (doubly degenerate states with the 7.53, 6.84, and 7.15 eV excitation energy and one state with the 7.63, 6.91, and 7.23 eV for these three methods, respectively). The actual shift could be about 0.1 eV higher since the EOM-CCSD method usually tends to slightly overestimate excitation energies, contrary to ADC (2), which has a tendency to underestimate them. One can therefore assume that the error resulting from the present calculations is about 0.35-0.5 eV. The character of the excited states, which are partially CT, assures that this type of states will be properly accounted for in the case of the h-BN dilayers with the CAM-B3LYP-mod functional.

The analysis of the energetic stability of complexes under study
The analysis of the stabilization energies of the complexes composed of the cluster with a defect and the cluster without a defect (presented in Table 1 of the main article), allows to make several interesting conclusions, the most important of which have been mentioned in the main article, like the greater stability of the AA'-stacked complexes with respect to the AB-stacked ones and a decrease of the difference between AA' and AB case for some cases, namely, for Al B and Mg B defects. For these cases both Al or Mg atoms are placed on top of the cone directed towards the second layer, while for the remaining cases the dopant atom resides outside the second layer or (for a single carbon defect) it (almost) does not distort the planarity of the h-BN surface. The change in stability of AB versus AA' for the dopant cone pointing towards the second layer can be explained by the fact that in this case also three neighbour nitrogen atoms are necessarily placed closer to the second layer and for the AA' stacking they seemingly are too close to the boron atoms of the second layer, while for the AB stacking these three atoms are placed "harmlessly" above the empty ring centers. For the remaining case of a diminished ∆E stab (C B -C N ) one can note that this observation agrees with a higher stability of the AB stacking for graphene. Therefore one can expect that a higher concentration of C B -C N defects could lead to an inversion of the AA' versus AB stability order.
Let us move to the discussion of the total SCS-MP2 stabilization energies. First one should emphasize that the complexes under study can be divided into three groups: (i) consisting of two closed-shell molecules, (ii) one closed-shell and one open-shell (spin doublet) molecule, (iii) two open-shell (both spin doublet) molecules. The first group is represented by undoped systems and by defects with Al and P, the third class: by the C B -C N case, while the remaining defects belong to the second case. As it can be expected, the lowest value of the stabilization energy (under -300 kJ/mol) occurs for the interaction of two open-shell molecules (the C B -C N defect). This case differs significantly in the interaction strength when compared to the next two cases with a low stabilization energy, for which the absolute value of this energy is over two times smaller.
Nevertheless, also for these two cases, i.e. the Al B (the energy around -140 kJ/mol) and the Mg B (the energy around -120 kJ/mol) -the distance between the Al or Mg and the closest nitrogen atom from the second molecule of the complex is so small that one expects beginnings of the creation of covalent bonding between Al and N or Mg and N.
The systems under study are quite rigid because of the network of conjugated bonds, so their deformation energies are in most cases below 10 kJ/mol. There are several exceptions, though. The largest deformation effects occur for the Al B and Mg B defects, followed by C B -C N and V N . Usually deformation energies for the AA' complexes are higher than for the AB counterparts, what can be explained by the fact that a smaller number of atoms are placed "face-to-face" for the latter type.
Next, one can compare the stabilization energies of the undoped and doped complex within the same stacking type, which shows the influence of a defect on a dilayer stability. The higher stabilization of the doped complex occurs for the C B -C N , Al B , and Mg B defects. This difference is especially pronounced for the C B -C N case, where two open-shell molecules interact with each other. The dopant atom has practically no influence on the stabilization energy differences for the C B , C N , and V B defects, while for all other cases it causes a small destabilization of the complex (between 5 and 27 kJ/mol). The highest destabilization occurs for the V N and Al N defects, followed by Si N and P N ones. Therefore, the replacement of the electron-rich nitrogen atom seems to enhance the destabilization effect in comparison to the boron case.
Finally, for closed-shell clusters one can evaluate the relative importance of various SAPT components, which are presented in Table TS1. For all presented cases the dispersion energy is the most important attractive component of the interaction energy. The induction energy is almost always smaller in absolute value (with the exception of Al B ) and additionally it is mostly damped the exchange-induction counterpart.
For the case of the Al B defect the dominance of the induction can be explained by a partial bond formation between the Al atom and the N atom of the second layer. The net first-order contribution is always repulsive.
It should be noted that the importance of dispersion contribution makes all DFT calculations of dilayers, which do not include a dispersion correction, highly unreliable. Additionally, one can notice a regular pattern in a behaviour of exchange energies, which are higher for the AA' than for the AB stacking. This behavior can be explained by a larger overlap of electron clouds for the former stacking.  Wave number x 10 -3 ((7)) C B -C N (AB) Wave number x 10 -3