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The concept of aromaticity has been advanced beyond the framework of organic chemistry, and multiple aromaticity (σ, π, and δ) has been observed to account for the highly symmetric structures or unusual stability of the clusters. In the present study, the electronic structures and chemical bonding of small monolanthanum boride clusters are investig...
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Context 1
... LaB clusters. The global minimum of LaB À shows a higher quartet state, while that of the neutral LaB cluster has a quintet spin multiplicity. According to the present theoretical calculations, the quartet state of LaB À is more stable than its doublet state by 0.52 eV, while the low- lying triplet and singlet states of the neutral LaB are 0.45 and 0.57 eV, respectively, higher in energy than the quintet state. Additionally, it is notable that the La–B bond is much weaker than the B–B bond in all the clusters shown in Fig. 3. The La–B bond length ranges from 2.325 to 2.574 Å, while the B–B bond length is much shorter by around 1 Å. Careful inspection of the structures in the figure reveals that the B atom prefers to bond to the B vertex rather than the La atom when a successive B atom is added to the LaB x À 1 À /0 clusters to form larger LaB x À /0 clusters, likely due to the stronger B–B bonding. Furthermore, as shown in the figure, the doped La atom in each cluster resides on the outer-side of the B x unit, and hardly changes the frame structures of the B x unit. To validate our calculated lowest-energy structures, we computed the theoretical ADEs and VDEs of the LaB 2 À and LaB 3 À clusters, which could be compared with our experimentally measured values. Such a comparison is a particularly useful test to diagnose the accuracy of theoretically proposed structures and bonding mechanisms. 48–52 The calculated ADEs and VDEs are listed in Table 1. A comparison of the theoretical and experimental values for ADE results in good agreement with the values deviating by 2% and 7% for LaB 2 À and LaB 3 À , respectively. Meanwhile, the differences between the experimental and calculated VDE values for the clusters are within 0.1 eV. This is on par with many previous studies, in which deviations of VDEs are in a similar range. 51,52 In addition, as shown in Fig. 1 and 2, the PES of LaB 2 À and LaB 3 À are both vibrationally-resolved, yielding vibrational frequencies of 483.9 and 423.9 cm À 1 , respectively, for the ground states of neutral LaB 2 and LaB 3 . Our calculations show that the frequency of symmetric La–B stretching mode of the ground state of LaB 2 is estimated to be 495.0 cm À 1 while that of antisymmetric La–B stretching mode of the ground state of LaB 3 is about 455.8 cm À 1 , which are consistent with our measured values. Therefore, these results give us confidence that the predicted lowest-energy structures depicted in Fig. 3 are correct. Having found the optimized geometries of the anionic and neutral LaB x ( x = 1–4) clusters, we now turn our attention to the relative stability of these clusters. To get insights into the relative stability, we consult two pieces of evidence. The first ‘‘pointer’’ that we used is the energy gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), namely H–L gap, which could provide chemical stability of the clusters. Generally speaking, the clusters with larger H–L gaps are more stable and chemically inert. 53 The calculated H–L gaps for the anionic and neutral LaB x ( x = 1–4) clusters are plotted against the number of B atoms, which are shown in Fig. 4. In the case of the anionic cluster series, the LaB 2 À cluster has the largest H–L gap of 1.91 eV. The LaB 3 cluster displays a larger H–L gap than its neighboring clusters in the neutral series. Therefore, it seems that the LaB 2 À and LaB 3 clusters are more stable in their respective cluster series. As an additional criterion for stability, we calculated the energy loss by removing one of the B atoms in the clusters, defined by D E B = E (LaB x À 1 ) + E (B) À E (LaB x ). Here, E (LaB x À 1 À /0 ), E (B), and E (LaB x À /0 ) are the total ground state energies of the corresponding species. A larger value of D E B corresponds to the larger energy which is required to form a smaller cluster by removing a B atom. Fig. 5 shows the plots of removal energies for the anionic and neutral LaB x ( x = 1–4) clusters, and the peaks indicate energetic stability. As evidenced in the figure, there is a maximum for both the LaB 2 À and LaB 3 clusters in the corresponding anionic and neutral cluster series, attesting for their enhanced stability. This result is in accordance with the H–L gap trend mentioned above. Therefore, it is reason- able to suggest that the LaB 2 À and LaB 3 clusters are more stable in their respective cluster series. Additionally, it is important to note that in general a low ADE signifies stability of the neutral clusters as it is relative easy to remove an electron form the anion, while a high ADE is indicative of the stability of anions. As shown in Table 1, the experimentally measured ADE of LaB 2 À (1.32 eV) is higher than that of the LaB À cluster (1.13 eV), qualitatively indicating that LaB 2 is more stable than LaB 3 , while the neutral LaB 3 is more stable. This experimental finding is consistent with our calculated H–L gaps and D E results (Fig. 4 and 5). Having found the LaB 2 and LaB 3 clusters to be more stable in their respective cluster series studied here, we endeavor to shed light on the origin of their enhanced stability. The B 3 À and B 4 clusters, which are isovalent to the present LaB 2 À and LaB 3 clusters, respectively, are well-known aromatic species. 13 The B 3 À anion was found to have both p and s aromaticity, i.e. , doubly aromatic. Neutral B 4 features triple aromaticity, i.e. , p aromatic and doubly s aromatic, which is similar to Al 42 À . 13,54 These results led us to explore whether the La-doped boron clusters could preserve such aromaticity, which is also the motivation of this study for understanding the influence of the d-electron on the doped boron clusters as mentioned in the Introduction part. The chemical bonding and aromaticity of the LaB 2 À and LaB 3 clusters were probed by using an analysis of their occupied valence molecular orbitals (MOs), which are displayed in Fig. 6. The MOs of the isovalent B 3 À and B 4 clusters calculated at the B3LYP/aug-cc-pVTZ level of theory, which are in good agreement with previously reported results, 13 are also listed in Fig. 6 for comparison. The natural bond orbital (NBO) analysis was also performed to elucidate the chemical bonding in these clusters. 55 Before investigating the chemical bonding in LaB 2 À , we discuss the molecular orbitals of its isovalent B 3 À first. As shown in Fig. 6, the HOMO À 1 in B 3 À is a completely delocalized p orbital with two electrons, giving rise to the p aromaticity, while the HOMO is a delocalized s orbital formed by the p s -radial orbitals of the three boron atoms that renders the s aromaticity for B 3 À . Other MOs in B 3 À , namely HOMO À 2, HOMO À 3, and HOMO À 4, which are s orbitals formed primarily by the 2s orbitals of the boron atoms with some hybridization of the p orbital, responsible for the localized bonds of B 3 À . 13 Analogous to the HOMO À 1 in B 3 À , the HOMO À 2 orbital of LaB 2 À is a delocalized p -type MO. However, unlike the conventional delocalized p orbital (HOMO À 1 in B À ) formed by the overlap of the p p atomic orbitals (AOs) of atoms, the present delocalized MO consists of the contribution from the 5d AO of the La atom. It is formed by the overlap between the 5d AO from the La atom and the p p orbitals from the remaining boron atoms, which could be considered to be a delocalized d–p hybridized MO. Two electrons filled in this new-type delocalized p MO satisfy the H ̈ckel (4 n + 2) electron rule for n = 0, and render the p aromaticity for LaB 2 À , which can be named as d–p hybridized p aromaticity. Furthermore, the HOMO À 1 of LaB 2 À is a delocalized s orbital, resulting from the overlap between the 5d AO from La and two radially oriented in-plane p orbitals from another two boron atoms. This MO gives the characteristic of d–p hybridized s aromaticity for LaB 2 À . As for neutral LaB 3 (Fig. 6), according to our NBO analysis, the HOMO À 1 and HOMO À 2 are both delocalized. The HOMO À 1 is a delocalized s orbital formed by the tangentially oriented orbitals with some contribution from the 5d AO of the La atom, which enables the LaB 3 cluster preserve s aromaticity. Moreover, analogous to the HOMO À 2 in LaB 2 À , the effective overlap between the 5d AO of La and the p p orbitals of the three boron atoms in HOMO À 2 of neutral LaB 3 enables the two electrons delocalized over the entire system, rendering the p aromaticity. Interestingly, our NBO analysis shows that there is almost no contribution from the 5d AO of La to anticipate into the bonding in the HOMO of LaB 3 (Fig. 6). This s MO is formed primarily by the radially oriented p orbitals of the three boron atoms. This MO is partially delocalized over the triangular B 3 unit, which is similar to the HOMO of B 3 Si À . 56 The lack of effective overlap between d and p orbitals in this MO could be explained by the geometrical change upon doping. As mentioned earlier, the La–B bond is much longer than the B–B bond (Fig. 3). Replacing one B atom in neutral B 4 by a La atom significantly deforms the geometry of the cluster, elongating the distance between the La atom and the overlap region (approximately the center of the remaining three born atoms). Such a deformation in geometry prevents the overlap between the d and p orbitals. This implies that the d–p hybridized aromaticity described here is sensitive to the geometry of the cluster. Thus, on the basis of the discussion above, LaB 3 is expected to be a doubly aromatic system, i.e. d–p hybridized s and p aromatic, which may partly explain its enhanced stability. To further confirm the aromatic characters of the LaB 2 À and LaB 3 clusters, we have calculated the nucleus-independent chemical shift (NICS) values, which is one of the most popular tools for diagnosing aromaticity proposed by Schleyer et al. 57 This model, based on the ‘‘absolute magnetic shielding’’ taken at the center of a ring species, is ...
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... parallel to the laser polarization, and the measured anisotropy parameter ( b ) is about 1.55. Such a high b value indicates that the detachment process likely arises from the molecular orbital of mainly s -type character. 46,47 The b parameters for transitions A and B were also obtained, which are 0.48 and 0.13, respectively, as listed in Table 1. Fig. 2 shows the photoelectron images and corresponding PES from the detachment of LaB 3 À at 532 nm. One primary peak (X) can be seen from the spectrum with a VDE value of 1.13 eV. There are also vibrationally-resolved transitions observed in this band (X), and the EA of the neutral LaB 3 is determined to be 1.13 eV. Analogous to the band X in the 532 nm spectrum of LaB À , the PAD of transition X in LaB À presents preferential parallel distribution with respect to the laser polarization as well. Another feature, which is temporarily assigned as A (around 2.30 eV), is close to the photon energy limit (2.33 eV) used here. This energy value could be just assigned as the lower limit of its VDE since this peak is partially cut off near the zero-kinetic energy region. The experimentally measured ADEs, VDEs, and b parameters for both the LaB 2 À and LaB 3 À clusters are summarized in Table 1, and will be compared with the theoretical results below. An extensive search for the global minima of the anionic and neutral LaB x ( x = 1–4) clusters with different spin multiplicities was performed. Fig. 3 shows the lowest-energy structures of these LaB x À /0 clusters, and the corresponding low-lying energy isomers are depicted in Fig. S1–S3 in the ESI. † It is evident that all clusters shown in Fig. 3 have planar structures. Most of the ground states of the clusters exhibit the lowest multiplicity except for the anionic and neutral LaB clusters. The global minimum of LaB À shows a higher quartet state, while that of the neutral LaB cluster has a quintet spin multiplicity. According to the present theoretical calculations, the quartet state of LaB À is more stable than its doublet state by 0.52 eV, while the low- lying triplet and singlet states of the neutral LaB are 0.45 and 0.57 eV, respectively, higher in energy than the quintet state. Additionally, it is notable that the La–B bond is much weaker than the B–B bond in all the clusters shown in Fig. 3. The La–B bond length ranges from 2.325 to 2.574 Å, while the B–B bond length is much shorter by around 1 Å. Careful inspection of the structures in the figure reveals that the B atom prefers to bond to the B vertex rather than the La atom when a successive B atom is added to the LaB x À 1 À /0 clusters to form larger LaB x À /0 clusters, likely due to the stronger B–B bonding. Furthermore, as shown in the figure, the doped La atom in each cluster resides on the outer-side of the B x unit, and hardly changes the frame structures of the B x unit. To validate our calculated lowest-energy structures, we computed the theoretical ADEs and VDEs of the LaB 2 À and LaB 3 À clusters, which could be compared with our experimentally measured values. Such a comparison is a particularly useful test to diagnose the accuracy of theoretically proposed structures and bonding mechanisms. 48–52 The calculated ADEs and VDEs are listed in Table 1. A comparison of the theoretical and experimental values for ADE results in good agreement with the values deviating by 2% and 7% for LaB 2 À and LaB 3 À , respectively. Meanwhile, the differences between the experimental and calculated VDE values for the clusters are within 0.1 eV. This is on par with many previous studies, in which deviations of VDEs are in a similar range. 51,52 In addition, as shown in Fig. 1 and 2, the PES of LaB 2 À and LaB 3 À are both vibrationally-resolved, yielding vibrational frequencies of 483.9 and 423.9 cm À 1 , respectively, for the ground states of neutral LaB 2 and LaB 3 . Our calculations show that the frequency of symmetric La–B stretching mode of the ground state of LaB 2 is estimated to be 495.0 cm À 1 while that of antisymmetric La–B stretching mode of the ground state of LaB 3 is about 455.8 cm À 1 , which are consistent with our measured values. Therefore, these results give us confidence that the predicted lowest-energy structures depicted in Fig. 3 are correct. Having found the optimized geometries of the anionic and neutral LaB x ( x = 1–4) clusters, we now turn our attention to the relative stability of these clusters. To get insights into the relative stability, we consult two pieces of evidence. The first ‘‘pointer’’ that we used is the energy gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), namely H–L gap, which could provide chemical stability of the clusters. Generally speaking, the clusters with larger H–L gaps are more stable and chemically inert. 53 The calculated H–L gaps for the anionic and neutral LaB x ( x = 1–4) clusters are plotted against the number of B atoms, which are shown in Fig. 4. In the case of the anionic cluster series, the LaB 2 À cluster has the largest H–L gap of 1.91 eV. The LaB 3 cluster displays a larger H–L gap than its neighboring clusters in the neutral series. Therefore, it seems that the LaB 2 À and LaB 3 clusters are more stable in their respective cluster series. As an additional criterion for stability, we calculated the energy loss by removing one of the B atoms in the clusters, defined by D E B = E (LaB x À 1 ) + E (B) À E (LaB x ). Here, E (LaB x À 1 À /0 ), E (B), and E (LaB x À /0 ) are the total ground state energies of the corresponding species. A larger value of D E B corresponds to the larger energy which is required to form a smaller cluster by removing a B atom. Fig. 5 shows the plots of removal energies for the anionic and neutral LaB x ( x = 1–4) clusters, and the peaks indicate energetic stability. As evidenced in the figure, there is a maximum for both the LaB 2 À and LaB 3 clusters in the corresponding anionic and neutral cluster series, attesting for their enhanced stability. This result is in accordance with the H–L gap trend mentioned above. Therefore, it is reason- able to suggest that the LaB 2 À and LaB 3 clusters are more stable in their respective cluster series. Additionally, it is important to note that in general a low ADE signifies stability of the neutral clusters as it is relative easy to remove an electron form the anion, while a high ADE is indicative of the stability of anions. As shown in Table 1, the experimentally measured ADE of LaB 2 À (1.32 eV) is higher than that of the LaB À cluster (1.13 eV), qualitatively indicating that LaB 2 is more stable than LaB 3 , while the neutral LaB 3 is more stable. This experimental finding is consistent with our calculated H–L gaps and D E results (Fig. 4 and 5). Having found the LaB 2 and LaB 3 clusters to be more stable in their respective cluster series studied here, we endeavor to shed light on the origin of their enhanced stability. The B 3 À and B 4 clusters, which are isovalent to the present LaB 2 À and LaB 3 clusters, respectively, are well-known aromatic species. 13 The B 3 À anion was found to have both p and s aromaticity, i.e. , doubly aromatic. Neutral B 4 features triple aromaticity, i.e. , p aromatic and doubly s aromatic, which is similar to Al 42 À . 13,54 These results led us to explore whether the La-doped boron clusters could preserve such aromaticity, which is also the motivation of this study for understanding the influence of the d-electron on the doped boron clusters as mentioned in the Introduction part. The chemical bonding and aromaticity of the LaB 2 À and LaB 3 clusters were probed by using an analysis of their occupied valence molecular orbitals (MOs), which are displayed in Fig. 6. The MOs of the isovalent B 3 À and B 4 clusters calculated at the B3LYP/aug-cc-pVTZ level of theory, which are in good agreement with previously reported results, 13 are also listed in Fig. 6 for comparison. The natural bond orbital (NBO) analysis was also performed to elucidate the chemical bonding in these clusters. 55 Before investigating the chemical bonding in LaB 2 À , we discuss the molecular orbitals of its isovalent B 3 À first. As shown in Fig. 6, the HOMO À 1 in B 3 À is a completely delocalized p orbital with two electrons, giving rise to the p aromaticity, while the HOMO is a delocalized s orbital formed by the p s -radial orbitals of the three boron atoms that renders the s aromaticity for B 3 À . Other MOs in B 3 À , namely HOMO À 2, HOMO À 3, and HOMO À 4, which are s orbitals formed primarily by the 2s orbitals of the boron atoms with some hybridization of the p orbital, responsible for the localized bonds of B 3 À . 13 Analogous to the HOMO À 1 in B 3 À , the HOMO À 2 orbital of LaB 2 À is a delocalized p -type MO. However, unlike the conventional delocalized p orbital (HOMO À 1 in B À ) formed by the overlap of the p p atomic orbitals (AOs) of atoms, the present delocalized MO consists of the contribution from the 5d AO of the La atom. It is formed by the overlap between the 5d AO from the La atom and the p p orbitals from the remaining boron atoms, which could be considered to be a delocalized d–p hybridized MO. Two electrons filled in this new-type delocalized p MO satisfy the H ̈ckel (4 n + 2) electron rule for n = 0, and render the p aromaticity for LaB 2 À , which can be named as d–p hybridized p aromaticity. Furthermore, the HOMO À 1 of LaB 2 À is a delocalized s orbital, resulting from the overlap between the 5d AO from La and two radially oriented in-plane p orbitals from another two boron atoms. This MO gives the characteristic of d–p hybridized s aromaticity for LaB 2 À . As for neutral LaB 3 (Fig. 6), according to our NBO analysis, the HOMO À 1 and HOMO À 2 are both delocalized. The HOMO À 1 is a delocalized s orbital formed by the tangentially oriented orbitals with some contribution from the 5d AO of the La atom, which enables the LaB 3 ...
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Citations
... The delocalized p bonding is similar to that in [Sc]C 2 RR 0 , a metalla-cyclopropene reported by Zhang et al. 95 and that in LaB 2 À and LaB 3 molecules. 40 Aromaticity is a useful concept despite its many facets. NICS values are oen used to assess aromaticity because the negative value of the diamagnetic anisotropy suggests delocalization, also consistent with its aromaticity. ...
The concept of metalla-aromaticity proposed by Thorn-Hoffmann (Nouv. J. Chim. 1979, 3, 39) has been expanded to organometallic molecules of transition metals that have more than one independent electron-delocalized system. Lanthanides, with highly contracted 4f atomic orbitals, are rarely found in multiply aromatic systems. Here we report the discovery of a doubly aromatic triatomic lanthanide-boron molecule PrB2 - based on a joint photoelectron spectroscopy and quantum chemical investigation. Global minimum structural searches reveal that PrB2 - has a C 2v triangular structure with a paramagnetic triplet 3B2 electronic ground state, which can be viewed as featuring a trivalent Pr(III,f2) and B2 4-. Chemical bonding analyses show that this cyclo-PrB2 - species is the smallest 4f-metalla-aromatic system exhibiting σ and π double aromaticity and multiple Pr-B bonding characters. It also sheds light on the formation of the rare B2 4- tetraanion by the high-lying 5d orbitals of the 4f-elements, completing the isoelectronic B2 4-, C2 2-, N2, and O2 2+ series.
... Therefore, significant discrepancy exists in previous experiment and theory regarding what type of electron (4π or 9σ ) is attached to the neutral VO giving rise to VO − . To eliminate this contradiction, advanced photoelectron-imaging spectroscopy is considered as the most appropriate and straightforward approach, which can reveal the information of the atomic orbital from which the photodetachment takes place by detecting the angular distributions of the detached electrons [38][39][40][41][42]. Additionally, many theoretical studies attempted to reproduce the experimental EA of VO. ...
The electronic structure of the diatomic VO anion was explored by combining the photoelectron-imaging spectroscopy and high-level theoretical calculations. The electron affinity (EA) of VO is determined to be 1.244 ± 0.025 eV from the vibrationally resolved photoelectron spectrum acquired at 532 nm. The anisotropy parameter (β) for the EA defined peak is measured to be 1.59 ± 0.02, indicating that it is the 9σ electron attachment leading to the formation of the ground state of VO−. The present imaging experiment provides direct evidence that the ground state of VO− is X3Σ− with a (3π)4(8σ)2(9σ)2(1δ)2 electron configuration, which resolves the significant discrepancy in previous experiment and theory. In addition, the molecular orbitals and bonding involved in the anionic VO cluster are also examined based on the present high-level theoretical calculations.
... 1-4 A large number of investigations on boron clusters, and their derivatives doped by other elements, have been also reported. [5][6][7][8][9][10][11] Recent studies showed that the stability of tubular forms of B14, B16 and the fullerene forms of B18, B20 ...
... [23][24][25][26][27][28][29][30][31] Zaitsev et al. 32 used Knudsen effusion mass spectrometry to investigate thermodynamic properties of Si-B alloys in which boron content is from 1.5 up to 100 at.%. By using band calculations with pseudopotential method, electronic densities of states of -B, BnSi, B6Si and B3Si or B4Si were calculated by Imai et al. 33 Recently, some of us investigated systematically the singly boron-doped silicon clusters SinB (n = 1- 10) in various charge states (-1; 0; +1) using the G4 and CCSD(T) methods. 34 The growth mechanism of the SinB clusters has been established in which the attachment of one Si atom into the smaller-sized Sin-1B is preferred over that by the addition of a B atom into the pure Sin clusters. ...
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... In one of our recent studies about the electronic structures of the boron-doped lanthanum clusters (29), the number of unpaired electrons in neutral LaB was calculated to be four, which is identical to that of a rare earth atom Nd ([Xe] 4f 4 6s 2 ). Additionally, the electron configurations of La and B are [Xe] 5d 6s 2 and [He] 2s 2 2p, respectively, and it was found that the B atom generally contributes its three valence electrons to the valence molecular orbitals of boron-doped rare earth clusters (29). ...
... In one of our recent studies about the electronic structures of the boron-doped lanthanum clusters (29), the number of unpaired electrons in neutral LaB was calculated to be four, which is identical to that of a rare earth atom Nd ([Xe] 4f 4 6s 2 ). Additionally, the electron configurations of La and B are [Xe] 5d 6s 2 and [He] 2s 2 2p, respectively, and it was found that the B atom generally contributes its three valence electrons to the valence molecular orbitals of boron-doped rare earth clusters (29). Thus, the number of valence electrons of LaB is six, which is isovalent with Nd. ...
... The augmented correlation consistent polarized triple-zeta valence (aug-cc-PVTZ) basis set was used to describe the atomic orbital of boron (39,40), whereas the SDD (Stuttgart-Dresden effective core potential) with the Stuttgart-type small core (28 core electrons) and relativistic effective core potential was used for the Nd atom (41,42). The method and basis sets used here have been proven to successfully predict the electronic structures of similar boron-doped lanthanide clusters (29). To reinforce the ground-state structures and take into account the zero-point energy correction, vibrational frequencies of different clusters were also calculated. ...
Significance
Superatom concept has been found to be promising in designing atomic clusters to mimic the chemistry of scarce or expensive elements. Also, longstanding interest and challenge exist in searching for suitable candidates to mimic the valuable properties of rare earth elements owing to their highly important application in modern technologies and extremely low yield. Herein, by using photoelectron imaging spectroscopy, we provide direct experimental evidence that well-designed boron-doped clusters, namely LaB and NdB, could be promising candidates to mimic the magnetic properties of corresponding rare earth atoms Nd and Eu, respectively, because the same numbers of valence electrons, unpaired electrons, and magnetic moments are found in both of the counterparts. This finding opens up an exciting possibility for rare earth mimicry using the superatom concept.
... Additionally, as presented in the photoelectron image, transition X displays a preferably parallel photoelectron angular distribution (PAD) with respect to the laser polarization, and an anisotropy parameter (β) of 1.25 ± 0.02 is obtained for the most intense peak in transition X, which may imply that the detachment process more likely occurs from a molecular orbital composed mainly of the s-type character. 35,36,50 Another feature appears in the higher binding energy region, beginning from about 2.00 to 2.33 eV, of the figure, and we temporarily assign it as A. It seems that there are several resolved peaks in this band, which are also consistent with the inner rings located in the photoelectron image ( Figure 1). These peaks probably stem from the removal of deeper lying electrons giving rise to the neutral cluster in vibrationally or electronically excited states. ...
... Other MOs in ZrC 2 , namely, HOMO−4, HOMO−5, and HOMO−6, are localized MOs, which are similar to the lowest three valence MOs in LaB 3 . 36 As for forming the anionic ZrC 2 cluster, the extra electron can occupy one of the SOMOs of neutral ZrC 2 , which are HOMO or HOMO−1 in ZrC 2 , to produce the doublet ground-state ZrC 2 − . According to our theoretical calculations, as shown in Figure 3, the excess electron occupies the singly occupied 5a′ state of ZrC 2 that mainly comprises the sd z 2 hybrid orbital on Zr. ...
We present a joint photoelectron imaging spectroscopic and theoretical investigation on the triatomic ZrC2(-) anion. Vibrationally resolved spectrum was acquired at 532 nm photon energy. Electron affinity for the neutral ZrC2 cluster was determined to be 1.60 ± 0.07 eV. The CCSD(T) level of theory was used to explore the ground-state geometries and vibrational frequencies of the anionic and neutral ZrC2 clusters. Our vibrationally resolved PES reveals two vibrational frequencies (564.6 and 1774.0 cm(-1)) of the neutral ZrC2 cluster, which correspond to the symmetric Zr-C2 and C-C stretching modes, and these experimental findings are in good agreement with the calculated values. Additionally, the molecular orbitals and chemical bonding in the anionic and neutral ZrC2 clusters are also discussed to disclose the interaction between the transition metal atom (Zr) and C2 unit.
The CeH 13 and CeH 14 ⁺ exhibit remarkable stability in the doublet state with C s and C 2v symmetry, respectively. Both CeH 13 and CeH 14 ⁺ demonstrate significant hydrogen storage capacities, with values reaching 8.5 wt% and 9.1 wt%, respectively.
The bond dissociation energies of early transition metal diborides (M-B2, M = Sc, Ti, V, Y, Mo) have been measured by observation of the sharp onset of predissociation in a highly congested spectrum. Density functional and CCSD(T) ab initio calculations, extrapolated to the complete basis set limit, have been used to examine the electronic structure of these species. The computations demonstrate the formation of bonding orbitals between the metal d orbitals and the 1πu bonding orbitals of B2, leading to the transfer of metallic electron density into the bonding 1πu orbitals, strengthening both the M-B and B-B bonds in the molecule. This runs counter to most metal-ligand π interactions, where electron density is generally transferred into π antibonding orbitals of the ligand.
This study investigates the structural, electronic, elastic and dynamic properties of the lanthanum tetraboride through Density Functional Theory (DFT) and Density Functional Perturbation Theory (DFPT), using the Generalized Gradient Approximation (GGA), Local Density Approximation (LDA) and Local Density Approximation plus Hubbard (LDA + U) exchange-correlation potentials. The obtained lattice constants and atomic positions are in good agreement with the available data presented in literature. The band structure illustrated that LaB4 is a conductor and the partial density of states and electronic localization function (ELF) analysis indicated the existence of covalent character in B–B and B–La bonds, which indicate that this material is an intermetallic in nature. We discussed the physical significance of the obtained elastic constants, stress-strain relations and the other relevant quantities, such as shear, bulk and Young's moduli, Poisson's ratio, hardness, and Debye temperature. The results revealed that the lanthanum tetraboride is mechanically stable, brittle, hard and anisotropic. Finally, we estimated the thermodynamic properties such as the Helmholtz free energy, internal energy, entropy and specific heat capacity in the 0–2000 K temperature range, within the phonon-dispersion and the phonon density of states curves.
