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Fig. 1 NICS(0) values of Cu3* at different levels of theory. Numbers | to 17 on the horizontal axis denote different basis sets which are employed for geometry optimization and computation of NICS values: (1) Aug-cc-pVDZ-PP, (2) Aug-cc-pVTZ-PP, (3) Lanl2DZ, (4) Lanl2TZ, (5) Lanl2TZ(f), (6) DZVP (DFT orbital), (7) cc-pWDZ-PP, (8) cc-pWTZ-PP, (9) Def2-TZVP, (10) Def2-TZVPP, (11) Def2-QZVP, (12) Def2-QZVPP, (13) 6-311G(d), (14) 6-311+G(d), (15) aug-cc-pVDZ, (16) aug-cc-pVTZ and (17) aug-cc-pVQZ. The absolute values of the isotropic NICS(0) are larger than those of the out-of-plane NICS; this shows that in contrast to the considered hydrocarbons, in-plane (ring) electronic current in Li;* is not the most effective electronic current in the cluster. It is worth mentioning that the situation is reversed in NICS(1); the absolute values of the out-of-plane NICS(1) are larger than those of the isotropic NICS. It is also suggested that the negative NICS in the centre of this cluster is somehow related to the presence of a non-nuclear attractor in the centre of this species.2!?* In order to estimate the influence of geometry variation, arising from the method/basis set dependence of geometry, on the magnitude of NICS in this cluster, NICS values at various levels of theory were computed at the geometry of Def2-QZVPP, the largest studied basis set, with three functionals. Tables S-13 and S-25+ show the differences between NICS values at the optimized geometries and those computed at the fixed geometries (ANICS values), and the variations in bond lengths due to the influence of various methods/basis sets (ABL). ABL just like ANICS is defined by comparing the bond length of the cluster Table S-2+ and Fig. 1 show that the type of employed basis set affects considerably the magnitude of NICS(0) values,

Figure 1 NICS(0) values of Cu3* at different levels of theory. Numbers | to 17 on the horizontal axis denote different basis sets which are employed for geometry optimization and computation of NICS values: (1) Aug-cc-pVDZ-PP, (2) Aug-cc-pVTZ-PP, (3) Lanl2DZ, (4) Lanl2TZ, (5) Lanl2TZ(f), (6) DZVP (DFT orbital), (7) cc-pWDZ-PP, (8) cc-pWTZ-PP, (9) Def2-TZVP, (10) Def2-TZVPP, (11) Def2-QZVP, (12) Def2-QZVPP, (13) 6-311G(d), (14) 6-311+G(d), (15) aug-cc-pVDZ, (16) aug-cc-pVTZ and (17) aug-cc-pVQZ. The absolute values of the isotropic NICS(0) are larger than those of the out-of-plane NICS; this shows that in contrast to the considered hydrocarbons, in-plane (ring) electronic current in Li;* is not the most effective electronic current in the cluster. It is worth mentioning that the situation is reversed in NICS(1); the absolute values of the out-of-plane NICS(1) are larger than those of the isotropic NICS. It is also suggested that the negative NICS in the centre of this cluster is somehow related to the presence of a non-nuclear attractor in the centre of this species.2!?* In order to estimate the influence of geometry variation, arising from the method/basis set dependence of geometry, on the magnitude of NICS in this cluster, NICS values at various levels of theory were computed at the geometry of Def2-QZVPP, the largest studied basis set, with three functionals. Tables S-13 and S-25+ show the differences between NICS values at the optimized geometries and those computed at the fixed geometries (ANICS values), and the variations in bond lengths due to the influence of various methods/basis sets (ABL). ABL just like ANICS is defined by comparing the bond length of the cluster Table S-2+ and Fig. 1 show that the type of employed basis set affects considerably the magnitude of NICS(0) values,

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Table 1 Number of imaginary frequencies at various levels of theory for Den CsH37~
Table 1 Number of imaginary frequencies at various levels of theory for Den CsH37~
Table 2 Number of imaginary frequencies at various levels of theory for Den CsHs?*
Table 2 Number of imaginary frequencies at various levels of theory for Den CsHs?*
Fig. 2 NICS(0);,. (circles) and NICS(0),, (triangles) in ppm versus bond length in A in Cu,” cluster. This plot includes all data, computed by B3LYP, BP86 and M06 methods and different basis sets. The hollow circles and triangles represent NICS values computed by the 6-31 1G(d) basis set Fig. 2 (see Fig. S-36+ for NICS(1)) depicts the NICS(0) values versus bond length in this cluster. Fig. 2 shows that there is a fair relationship between bond length and NICS; as the bond length decreases, the NICS values become slightly In Ag3" , NICS(0) values do not show a considerable basis set dependency at three DFT levels. On the other hand, NICS(1) values show more basis set dependency; see Fig. S-14A and S-14B.7 It is worth noting that at the three DFT levels t computed NICS values by DZVP (DFT orbitals) basis set are more positive than other NICS values computed by other basis sets. Also, at BP86, the computed NICS values are genera more negative compared to those of B3LYP and M06. Final it should be noted that in the Ag3* cluster there is a fair relationship between bond length and magnitude of NICS li ne ly y; Ke
Fig. 2 NICS(0);,. (circles) and NICS(0),, (triangles) in ppm versus bond length in A in Cu,” cluster. This plot includes all data, computed by B3LYP, BP86 and M06 methods and different basis sets. The hollow circles and triangles represent NICS values computed by the 6-31 1G(d) basis set Fig. 2 (see Fig. S-36+ for NICS(1)) depicts the NICS(0) values versus bond length in this cluster. Fig. 2 shows that there is a fair relationship between bond length and NICS; as the bond length decreases, the NICS values become slightly In Ag3" , NICS(0) values do not show a considerable basis set dependency at three DFT levels. On the other hand, NICS(1) values show more basis set dependency; see Fig. S-14A and S-14B.7 It is worth noting that at the three DFT levels t computed NICS values by DZVP (DFT orbitals) basis set are more positive than other NICS values computed by other basis sets. Also, at BP86, the computed NICS values are genera more negative compared to those of B3LYP and M06. Final it should be noted that in the Ag3* cluster there is a fair relationship between bond length and magnitude of NICS li ne ly y; Ke
Fig. 3 NICS(0) values of Sc3~ at different levels of theory. Numbers | to 12 on the horizontal axis denote different basis sets [(1) Lanl2DZ, (2) Lanl2TZ, (3) Lanl2TZ(f), (4) Def2-TZVP, (5) Def2-TZVPP, (6) Def2-QZVP, (7) Def2-QZVPP, (8) 6-311G(d), (9) 6-311+G(d), (10) aug-cc-pVDZ, (11) aug-cc-pVTZ and (12) aug-cc-pVQZ] employed for geometry optimization and computation of NICS values.
Fig. 3 NICS(0) values of Sc3~ at different levels of theory. Numbers | to 12 on the horizontal axis denote different basis sets [(1) Lanl2DZ, (2) Lanl2TZ, (3) Lanl2TZ(f), (4) Def2-TZVP, (5) Def2-TZVPP, (6) Def2-QZVP, (7) Def2-QZVPP, (8) 6-311G(d), (9) 6-311+G(d), (10) aug-cc-pVDZ, (11) aug-cc-pVTZ and (12) aug-cc-pVQZ] employed for geometry optimization and computation of NICS values.
Fig. 4 NICS(0) values of Y3~ at different levels of theory. Numbers | to 9 on the horizontal axis denote different basis sets [(1) Lanl2DZ, (2) Lanl2TZ, (3) Lanl2TZ(f), (4) DZVP (DFT orbital), (5) Def2-TZVP, (6) Def2-TZVPP, (7) Def2-QZVP and (8) Def2-QZVPP] employed for geometry optimization and computation of NICS values. The results of all basis sets by each method are similar but NICS values computed by the DZVP (DFT orbitals) basis set are more positive compared to the other basis sets. In this cluster, again, all Def2-XZVP and Def2-XZVPP (X = T and Q) basis sets show very close NICS values at the three levels of theory. The relationship between the bond length and NICS(0) values in this cluster is not clear but it seems that the NICS values decrease to some extent as the bond lengths decrease. The nature of electronic currents in this cluster must be studied by the state-of-art ab initio methods since there is no general agreement between the computed NICS,, values at different DFT levels. Here, this should be emphasized that the The relationship between the bond lengths and NICS values in this cluster, like Y3_, is very complicated (see Fig. S-41). Although the ABL values in this cluster are not considerable, the ANICS values are relatively large. This suggests that the
Fig. 4 NICS(0) values of Y3~ at different levels of theory. Numbers | to 9 on the horizontal axis denote different basis sets [(1) Lanl2DZ, (2) Lanl2TZ, (3) Lanl2TZ(f), (4) DZVP (DFT orbital), (5) Def2-TZVP, (6) Def2-TZVPP, (7) Def2-QZVP and (8) Def2-QZVPP] employed for geometry optimization and computation of NICS values. The results of all basis sets by each method are similar but NICS values computed by the DZVP (DFT orbitals) basis set are more positive compared to the other basis sets. In this cluster, again, all Def2-XZVP and Def2-XZVPP (X = T and Q) basis sets show very close NICS values at the three levels of theory. The relationship between the bond length and NICS(0) values in this cluster is not clear but it seems that the NICS values decrease to some extent as the bond lengths decrease. The nature of electronic currents in this cluster must be studied by the state-of-art ab initio methods since there is no general agreement between the computed NICS,, values at different DFT levels. Here, this should be emphasized that the The relationship between the bond lengths and NICS values in this cluster, like Y3_, is very complicated (see Fig. S-41). Although the ABL values in this cluster are not considerable, the ANICS values are relatively large. This suggests that the
Fig. 5 NICS(0) values of La3~ at different levels of theory. Numbers | to 7 on the horizontal axis denote different basis sets [(1) Lanl2DZ, (2) Lanl2TZ, (3) Lanl2TZ(f), (4) Def2-TZVP, (5) Def2-TZVPP, (6) Def2-QZVP, (7) Def2-QZVPP] employed for geometry optimization and computation of NICS values.
Fig. 5 NICS(0) values of La3~ at different levels of theory. Numbers | to 7 on the horizontal axis denote different basis sets [(1) Lanl2DZ, (2) Lanl2TZ, (3) Lanl2TZ(f), (4) Def2-TZVP, (5) Def2-TZVPP, (6) Def2-QZVP, (7) Def2-QZVPP] employed for geometry optimization and computation of NICS values.
Table 3 Number of imaginary frequencies at various levels of theory for Dan Cu
Table 3 Number of imaginary frequencies at various levels of theory for Dan Cu
Fig. 6 NICS(0) values of Cu,’~ at different levels of theory. Numbers | to 14 on the horizontal axis denote different basis sets which are employed for optimization and computation of NICS values [(1) Aug-cc-pVDZ-PP, (2) Aug-cc-pVTZ-PP, (3) Lanl2DZ, (4) Lanl2TZ, (5) Lanl2TZ(f), (6) DZVP (DFT orbital), (7) cc-pVDZ-PP, (8) cc-pVTZ-PP, (9) Def2-TZVP, (10) Def2-TZVPP, (11) Def2-QZVP, (12) Def2-QZVPP, (13) 6-311G(d), (14) 6-311+G(d), (15) aug-cc-pVDZ and (16) aug-cc-pVTZ]. At M06/Aug-cc-pVTZ-PP, BP86/ cc-pVDZ-PP and B3LYP/cc-pVDZ-PP, self consistent field (SCF) did not converge. Agy”. In contrast to Cu,” , isotropic NICS values of Aga are more negative than its NICS,, values in the ring centre. However, | A above the ring plane, the situation changes and out-of-plane NICS values are more negative than the isotr the opic values. This is basically different from what is expected for a usual o-aromatic species based on NICS methodology. The N values computed at the BP86 level are more negative than t ICS hose obtained by B3LYP and M06 for Ag,” . The method dependency of NICS values is more apparent for NICS(0) values compared to the NICS(1) values. Similarly, changing the basis sets afl fects NICS(0) values more than NICS(1) or NICS(2) values; effective core potential-Peterson’s basis sets and DZVP (DFT orbi basis set show the most deviation, compared to the rest of stu tals) died basis sets. Again like other clusters, NICS values computed by the DZVP (DFT orbitals) basis set show a positive deviation compared to other basis sets, while NICS values computed by the Peterson’s basis sets show negative shifts at the B3LYP and BP86 methods. At the M06 computational level, NICS values
Fig. 6 NICS(0) values of Cu,’~ at different levels of theory. Numbers | to 14 on the horizontal axis denote different basis sets which are employed for optimization and computation of NICS values [(1) Aug-cc-pVDZ-PP, (2) Aug-cc-pVTZ-PP, (3) Lanl2DZ, (4) Lanl2TZ, (5) Lanl2TZ(f), (6) DZVP (DFT orbital), (7) cc-pVDZ-PP, (8) cc-pVTZ-PP, (9) Def2-TZVP, (10) Def2-TZVPP, (11) Def2-QZVP, (12) Def2-QZVPP, (13) 6-311G(d), (14) 6-311+G(d), (15) aug-cc-pVDZ and (16) aug-cc-pVTZ]. At M06/Aug-cc-pVTZ-PP, BP86/ cc-pVDZ-PP and B3LYP/cc-pVDZ-PP, self consistent field (SCF) did not converge. Agy”. In contrast to Cu,” , isotropic NICS values of Aga are more negative than its NICS,, values in the ring centre. However, | A above the ring plane, the situation changes and out-of-plane NICS values are more negative than the isotr the opic values. This is basically different from what is expected for a usual o-aromatic species based on NICS methodology. The N values computed at the BP86 level are more negative than t ICS hose obtained by B3LYP and M06 for Ag,” . The method dependency of NICS values is more apparent for NICS(0) values compared to the NICS(1) values. Similarly, changing the basis sets afl fects NICS(0) values more than NICS(1) or NICS(2) values; effective core potential-Peterson’s basis sets and DZVP (DFT orbi basis set show the most deviation, compared to the rest of stu tals) died basis sets. Again like other clusters, NICS values computed by the DZVP (DFT orbitals) basis set show a positive deviation compared to other basis sets, while NICS values computed by the Peterson’s basis sets show negative shifts at the B3LYP and BP86 methods. At the M06 computational level, NICS values
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