Comprehending the Quadruple Bonding Conundrum in C2 from Excited State Potential Cite This: Chem

Chemical Science

View Article Online EDGE ARTICLE View Journal | View Issue

Comprehending the quadruple bonding conundrum in C2 from excited state potential Cite this: Chem. Sci., 2020, 11, 7009 † All publication charges for this article energy curves have been paid for by the Royal Society of Chemistry Ishita Bhattacharjee, Debashree Ghosh * and Ankan Paul *

The question of quadruple bonding in C2 has emerged as a hot button issue, with opinions sharply divided between the practitioners of Valence Bond (VB) and Molecular Orbital (MO) theory. Here, we have

systematically studied the Potential Energy Curves (PECs) of low lying high spin sigma states of C2,N2,

Be2 and HC^CH using several MO based techniques such as CASSCF, RASSCF and MRCI. The analyses 2S+1 of the PECs for the Sg/u (with 2S +1¼ 1, 3, 5, 7, 9) states of C2 and comparisons with those of relevant dimers and the respective wavefunctions were conducted. We contend that unlike in the case 7 + + of N2 and HC^CH, the presence of a deep minimum in the S state of C2 and CN suggests a latent quadruple bonding nature in these two dimers. Our investigations reveal that the number of bonds in the nd Creative Commons Attribution-NonCommercial 3.0 Unported Licence. ground state can be determined for 2 row dimers by ﬁguring out at what value of spin symmetry

a purely dissociative PEC is obtained. For N2 and HC^CH the purely dissociative PEC appears for the

septet spin symmetry as compared to that for the nonet in C2. This is indicative of a higher number of Received 24th April 2020 bonds between the two 2nd row atoms in C as compared to those of N and HC^CH. Hence, we have Accepted 10th June 2020 2 2 struck a reconciliatory note between the MO and VB approaches. The evidence provided by us can be DOI: 10.1039/d0sc02336a experimentally veriﬁed, thus providing the window so that the narrative can move beyond theoretical rsc.li/chemical-science conjectures.

This article is licensed under a Introduction have been several attempts by diﬀerent groups which either concur or refute the presence of a fourth bond in C2. The Bonding in homodiatomic 2nd period elements constitutes the incongruity in views from diﬀerent corners arise from the multi- 1 s 14

Open Access Article. Published on 11 kesäkuuta 2020. Downloaded 1.10.2021 3.15.28. bedrock of our understanding of chemical bonding. Though reference nature of the orbitals in C2. Incidentally, MO based bonding in many of these homodiatomic species is well approaches have by and large refuted the case of quadruple 7,10 understood, the bonding situation in C2 presents an excep- bonding, with some exceptions. Zhong and co-workers have tionally enigmatic scenario. A routine inspection of molecular tried to point out some similarities between the MO based and

orbitals (Hartree Fock orbitals) of C2 would suggest that the the VB approaches for C2 regarding a key orbital which was 2 15 bond order of C2 is 2.0 arising from the two p bonds. However, achieved through unitary transformation of CASSCF orbitals. decades back a typical Wiberg bond index computation con- However, their nal Eﬀective Bond Order study with the same 3 ducted on C2 indicated the presence of four bonds. The last few orbitals suggested that the dimer in question has a bond order years have witnessed a steep spike in interest to comprehend of 2.15. Alternatively, magnetic shielding studies based on MO 4–12 “ ” the state of bonding in C2. This has led to intense debate on based approaches by Karadakov et al. suggested a bulkier 13 11 the aspect of quadruple bonding in C2. Shaik and co-workers bond compared to that of acetylene. Nevertheless, it can be  have investigated the electronic structure of C2 within the VB argued that there is no direct or de nitive proof of the presence

manifold and have concluded that the bonding in C2 is best of four bonds in C2 from a MO standpoint. The lack of existence described as a case of quadruple bond and have went on to of reconciliation on this issue between the VB and the MO predict that the strength of the fourth bond is approximately approaches still has kept the debate wide open and given the 12 kcal mol 1.4,5 These ndings were contested by Frenking and conicting views it may not be unfair to comment that the co-workers who mainly disagreed on the approach adopted by overall understanding is still nebulous. Here we report our view 7,10 Shaik of estimating the strength of the fourth bond. There point on the bonding in C2 by conducting extensive studies on potential energy curves of excited states of C2, largely covering

the cases of high spin states of C2 along with similar investi- School of Chemical Sciences, Indian Association for the Cultivation of Science, gations on N and HC^CH. Our ndings provide clinching Jadavpur, India. E-mail: [email protected]; [email protected] 2 † Electronic supplementary information (ESI) available. See DOI: evidence in support of the presence of quadruple bonding in C2 10.1039/d0sc02336a or rather the ability to form two bonds by electrons in orbitals in

This journal is © The Royal Society of Chemistry 2020 Chem. Sci.,2020,11,7009–7014 | 7009 View Article Online Chemical Science Edge Article

s symmetry thus establishing reconciliation between MO and Results and discussion VB manifold of methods.

The quintessential signature of bonding between two atoms As the bonding in C2 is suspect, we decided to investigate the  lies in the presence of a well-de ned discrete minimum in the nature of the PECs of high spin states of C2 and see at which potential energy curve (PEC) plotted against the interatomic spin state a purely dissociative state is obtained. A cursory

distance of the two atoms. For instance, in the case of H2 estimate obtained from the primary Hartree Fock (HF) MO 2 ground electronic state the PEC shows the presence of a distinct picture of the C2 would suggest that C2 has only two p bonds. minimum and has a signicant dissociation energy. This is due The four electrons in the s orbitals would appear not to 2 to the presence of a s bond arising from 1sg in the H2 mole- contribute to bonding as there are two electrons in a bonding cule.16 If this electron pair in the bonding orbital is broken and orbital and two electrons in an antibonding orbital. It must be s one of the electrons is promoted to the corresponding 1 u one noted that the Be2 dimer with the same s electron population would nd that the bonding stabilization is negated and as and no p electron shows a total absence of bonding at HF and 19 a result a dissociative PEC with no minimum is obtained for the CASSCF levels of theory. Hence, one is tempted to infer that C2 3 + Su state. Hence one can create a high spin state corresponding will have just two p bonds arising from the two p electrons. A to the rupture of a bond that generates a PEC without full valence CASSCF calculation on the ground electronic state

a minimum. This seemingly simple argument may be extended of C2 reveals the multireference character of C2. The dominant to multiply bonded species as well, albeit with some intrinsic conguration state functions (CSFs) are with 70.9% and 13.6% limitations which are discussed later. Multiple bonding contributions. The 2nd CSF may suggest that it can contribute

between two atoms in the ground state would certainly leave two s bonds in the ground electronic state of C2 (see Table 1). footprints on the excited state PECs. Unlike H2,N2 which is The no. of bonds arising from s orbitals is the bone of multiply bonded exhibits high spin triplet and quintet states contention, whereas there is no debate as to the presence of two with respective minima.17 This becomes more evident when one p bonds in the ground electronic state. VB theory predictions s

Creative Commons Attribution-NonCommercial 3.0 Unported Licence. compares and contrasts spectra of diatomics with and without from Shaik and others suggest that indeed two bonds are 18 multiple bonding. present. Due to the multi-reference character of C2, simple MO Hence, in the multiply bonded diatomic species one may based electronic structure theories are inadequate to predict the generate high spin states by breaking bonding electron pairs no. of s bonds. However, as discussed earlier the high spin state within the valence orbitals and promoting electrons from PECs can be investigated to gauge the bonding situation in the

a particular bonding orbital to the corresponding antibonding ground electronic state. Using a full valence CASSCF for C2,N2, orbital such that for a particular high spin state a set of bonding CN+ and HC^CH we have investigated the dissociation PECs + orbital/s and respective antibonding have single occupation for high spin S states (see Fig. 1(a), (b) and (c) for C2,N2 and CN with parallel spins. This would lead to high spin states of 2S+1S+ and Fig S1 in ESI† for acetylene respectively). The high spin S This article is licensed under a states. A step by step procedure can be adopted such that states are created in such a way that it would have lesser number particular types of bonding may be negated by the proper choice of electron pairs in bonding orbitals. Such an exercise imme-  ^ † of orbital symmetry. If speci c orbitals are chosen to generate diately reveals that for N2 (Fig. 1(b)) and HC CH (Fig S1 ) the 7 + Open Access Article. Published on 11 kesäkuuta 2020. Downloaded 1.10.2021 3.15.28. high spin electronic states, one can gradually generate elec- lowest lying Su state is purely dissociative. This would suggest tronic states which eliminate bonds one by one and reach that only three electron pairs contribute to bonding in the a high spin state which would correspond to the total absence of ground electronic state and when all of them are disrupted to any bonds between the two atoms resulting to a purely disso- create a high spin state of septet symmetry it leads to a purely

ciative state. The no. of bonds in the ground state of the dissociative PEC. Intriguingly, the same exercise with C2 reveals diatomic species would determine at which high spin state the a purely dissociative PEC is obtained for the S state of nonet 7S + purely dissociative PEC would be reached. For instance, in H2 spin symmetry, with u displaying a distinct minimum. The which has only one bond the triplet state is purely dissociative, trends immediately suggest that probably the no. of electron

whereas for N2 which is known to have three bonds the septet pairs contributing to the bonding in the ground state of C2 is state is purely dissociative.16,17

Table 1 Percentage of the major contributing CSFs for the ﬁve spin states of C2 at equilibrium

Spin multiplicity Major contributing CSF Percentage

1 + 2 2 2 2 Sg |2sg 2su 1pux 1puy i 70.9 2 2 2 2 |2sg 3sg 1pux 1puy i 13.6 3S + s 2 s 1 p 2 p 2 s 1i u |2 g 2 u 1 ux 1 uy 3 g 86.3 2 2 1 2 1 2 1 2 2 1 |2sg 1pux 1puy 2su 1pgy i +|2sg 1pux 1puy 2su 1pgx i 3.6 5 + 2 1 1 2 1 1 2 1 2 1 1 1 Sg |2sg 2su 1pux 1puy 3sg 1pgx i +|2sg 2su 1pux 1puy 3sg 1pgy i 81.7 2 2 1 1 1 1 |2sg 2su 1pux 1puy 1pgx 1pgy i 6.7 7S + s 2 s 1 p 1 p 1 s 1 p 1 p 1i u |2 g 2 u 1 ux 1 uy 3 g 1 gx 1 gy 97.8 1 1 1 1 2 1 1 |2sg 2su 1pux 1puy 3sg 1pgx 1pgy i 0.5 9 + 1 1 1 1 1 1 1 1 Sg |2sg 2su 1pux 1puy 3sg 1pgx 1pgy 3su i 100.0

7010 | Chem. Sci.,2020,11,7009–7014 This journal is © The Royal Society of Chemistry 2020 View Article Online Edge Article Chemical Science Creative Commons Attribution-NonCommercial 3.0 Unported Licence.

17a + Fig. 1 PECs corresponding to the (a) five spin states of C2, (b) four spin states of N2, (c) five spin states of CN and (d) five spin states of BN. This article is licensed under a

more compared to those for N2 and HC^CH. Our hypothesis is were used to draw up the PECs (see ESI, Section S1†). The nature p Open Access Article. Published on 11 kesäkuuta 2020. Downloaded 1.10.2021 3.15.28. based on the fact that on promoting electrons to the high spin of the dominant CSF suggests the elimination of only one states eliminate bonds. With that one needs to go the nonet bond and one s bond w.r.t that of the ground state, using the 9S + spin state ( g ) for the purely dissociative state. It suggests that same line of argument which was employed in the previous four bonding pairs have to be disrupted to decimate any form of case. The dominant CSF at the minimum of the PEC for the 7 + bonding between the two atoms. lowest lying septet S state, Su shows a total absence of p

Further inspection of the excited state PECs of C2 along with bonding but the presence of a deep minimum indicates stability

the dominant CSF at the minimum at the PEC is instructive. conferred from the electron pair in 2sg orbital. The dominant 3 + 7 + The lowest lying Su is dominated by a CSF which has the septet state CSF at the Su PEC minimum shows a marked presence of two p bonds (see Table 1). The electron distribution absence of p bonding, yet this is the third state which has one s s 3S +  in orbitals in u space avoids any signi cant participation bond w.r.t that of the ground electronic state as it has parallel  s s from con gurations which will have simultaneous double spins in 3 g and 2 u akin to the dominant CSF in the PEC s s 3S + 5S + occupation in 2 g and 3 g orbital. Also, the dissociation energy minima of u and g states. As mentioned earlier, all of the 3 + 1 + 9 + of the Su state is lower compared to that of the ̃Sg state by bonding interactions are annihilated at the Sg state leading to about 27 kcal mol (see ESI Table ST1†). The dominant CSF of a purely dissociative PEC. This fact is in conjunction with the 3 + 2 1 4 1 7 + Su at the PEC minimum, |2sg 2su 1pu 3sg i may be viewed fact that Su state PEC has a distinct minimum which strongly 2 0 4 2 nd as an excitation from the CSF |2sg 2su1pu 3sg i (the 2 most indicates that the ground electronic state of C2 has four bonds, important CSF present in the ground state minimum) (see two s and two p. s Fig. 2), which is essentially breaking a bonding pair of 3 g and Though we have noted earlier that for N2 and acetylene s s 3S + putting parallel spins in 3 g and 2 u. It may be argued that u purely dissociative state appears only when one reaches the p s 7S + 5S + essentially maintains 2 bonds and eliminates plausibly one septet spin state ( u ), unfortunately the corresponding g bond, which shows up in the decrease of the dissociation state PECs do not show presence of distinct minima. Further 5 + 5 + energy. The Sg is riddled with strong signatures of avoided investigations reveal that the situation for the Sg state is 5 + crossings. State averaging by including four low lying Sg states extremely complex as it involves signicant contribution from

This journal is © The Royal Society of Chemistry 2020 Chem. Sci.,2020,11,7009–7014 | 7011 View Article Online Chemical Science Edge Article

Fig. 2 Formation of the triplet state from the desired singlet state upon one electron excitation.

7 + CSFs which have partially lled p and s orbitals. Moreover, character. Our MRCI results on BN also suggest that the Su

some majorly contributing CSFs also show participation from state is dissociative, indicating unlike C2 it does not have 7 + 3su orbital. State averaging does not alleviate the problem and a quadruple bond. Incidentally, the S states of C2 and BN have such issues are well documented.17b However, it must be noted not been studied experimentally. Our computations suggest

Creative Commons Attribution-NonCommercial 3.0 Unported Licence. 5 + 7 + that though the Sg state for N2 does not show a distinct that the Su state of C2 lies 9.4 eV above the ground state. 7S + minimum, the PEC is certainly not purely dissociative in nature. Hence, the proof of existence of a minimum in the u for C2 Moreover, previous studies with MRCI and Multi-Reference and the absence of such a minimum in the equivalent case for 5S +  Coupled Cluster suggested that the g state of N2 does BN is likely to corroborate our ndings on quadruple bonding possess a shallow minimum.17a,c Furthermore, the nature of in these two cases. Furthermore, CN+ being an ionic species can + 20 bonding in diatomic systems BN and CN isoelectronic to C2 be investigated in an ion trap. The case of presence of a bound were also investigated using the same stratagem. Interestingly, 7S+ state can be veried experimentally. + we do nd that for CN the lowest four spin states display The most perplexing aspect of bonding in C2 is the question s s This article is licensed under a a distinct minimum on their respective PECs, while its nonet of the presence of two bonds, while bonds are distinctly

state is purely dissociative. Hence, by the extension of the same absent in Be2 despite both having largely four electron pop- line of argument it can be suggested that CN+ has signature of ulation in s orbitals (see ESI Section S2 and Fig S2†).19 We quadruple bonding in agreement to the ndings of Shaik and ventured to understand what would happen if we articially Open Access Article. Published on 11 kesäkuuta 2020. Downloaded 1.10.2021 3.15.28. 5 co-workers (see Fig. 1(c)). Contrary to the ndings of Shaik et al. prevent formation of p bonds in C2, a situation akin to Be2 where

we nd BN, which is also isoelectronic to C2, does not have the electron population is zero in the p orbitals. We resorted to a quadruple bond as suggested by the purely dissociative PEC the use of the RASSCF technique which allowed us to restrict the 7 + for S state (see Fig. 1(d)). Our strategy of counting bonds population of p orbitals with one electron in each of them for C2,

suggests it has three bonds which conforms to the usual Lewis thus negating the possibility of any p bonding. Whereas, for Be2 structure prediction.2 This difference may be ascribed to the we restricted the population of p orbitals to zero. This ensured ff  electronegativity di erence in the case of BN, which is that the dominant con gurations both in Be2 and C2 would be +  s completely absent in C2 and quite reduced in CN .A er exci- restricted to four electrons in four orbitals. Such an approach 7 + tation in BN to S (with major contributing CSF: |[core] helped us to examine the PECs of Be2 and C2 without any 2 *1 1 1 1 *1 *1 2s 2s 1px 1py 3s 1px 1py i), the fourth electron pair gets contribution to bonding from the p orbitals. Gratifyingly, we 5 + mostly localized as a lone pair on the nitrogen atom in contrast found that the RASSCF based PECs for Sg state of C2 with 1 + to C2 where the excited electrons remain on each C atom. This dominant CSFs show a distinct deep minimum, whereas for Sg 7 + may be the reason why S state of BN is unbound, even though Be2 was totally dissociative (see Fig S2 in ESI† and Fig. 3(a)). VB theory shows a quadruple bond.5 RASSCF studies show that on imposition of similar restrictions 7S + One is disposed to question what happens if dynamic on the two low lying u states the PECs have deep minimum in correlation is roped in. Does it change the scenario and the each state. Further analysis reveals that this is due to the pres- inferences derived from it? To address this question MRCI ence of a single s bond in each of these states (see Fig. 3(b)). The + 2 1 2 2 1 computations were conducted for C2, BN and CN (see ESI Fig dominant CSFs of these two states are |2sg 3sg 1pu 1pg 2su i 1 2 2 2 1 S3–S5†). The general trends of the PECs for the different S states and |2sg 3sg 1pu 1pg 2su i respectively, indicating that indeed 7 + for C2 remain unaltered. The Su state PEC still exhibited two sets of s electron pairs do give rise to two s bonds. a distinct minimum and the dissociation energy was estimated Frenking and others have questioned the basis of quadruple 1 9S + to be 69 kcal mol and the g shows pristine dissociative bonding by comparing the force constants of the bond in C2

7012 | Chem. Sci.,2020,11,7009–7014 This journal is © The Royal Society of Chemistry 2020 View Article Online Edge Article Chemical Science

Fig. 3 (a) PEC corresponding to the RASSCF computation for the quintet spin state of C2 and (b) PECs corresponding to the RASSCF computation for the two septet spin states of C2 along with their dominant conﬁgurations.

with that of HC^CH, with the bond in C2 being weaker than congurations moving the bonding electron to the antibonding that of HC^CH.7 In the light of our ndings this may stand as electron would not create a sigma state with higher spin a contradiction. Here we must reiterate that the dominant symmetry.21 If this may seem confusing one may modify our p ﬀ determinant of the ground state of C2 contributes only two strategy from a di erent viewpoint. Associated with these two Creative Commons Attribution-NonCommercial 3.0 Unported Licence. 1 bonds. Hence, analysis of force constants is likely to reect the congurations is a low-lying singlet Dg conguration. From the

attribute of primarily the dominant determinant of C2 and may lowest lying singlet state bonding pairs have to be broken to not serve as a good metric for this purpose. The latent create high spin sigma states and the corresponding wave- + quadruple nature of the bond in C2 and CN can only be functions and their respective PECs have to be inspected to recognized through the PECs of the excited states. arrive at a proper conclusion regarding the number of bonds Though our approach possibly brings in an avenue to present in them (see Fig. S8 in ESI†). This tailored strategy

understand the bonding situation in C2, a probable question would yield two bonds for O2 and a single bond in B2. While our may arise that whether this hypothesis can be applied to approach appears to be simple it would be prudent to add

This article is licensed under a comprehend the number of bonds in all diatomic systems and a cautionary note, particularly for the quintet states of p-block what are its intrinsic limitations. Naturally, one is inclined to elements. As has been discussed earlier, we nd that for the ask whether this technique can be extended to molecules with p-block elements the quintet S state PECs are fraught with triplet ground states like O and B . Here we rst discuss the multiple avoided crossings as the dominating congurations

Open Access Article. Published on 11 kesäkuuta 2020. Downloaded 1.10.2021 3.15.28. 2 2

case of O2 to illustrate how this approach can be tailored to can arise from electron bond pair breaking of the s orbital or 3S p address cases where the ground state is g within the from orbital. One has to ensure that adequate state-averaging 3S framework of traditional MO theory. In the case of the g is conducted to reveal the true nature of the state PECs of these s ground state of O2, a formal bond order of 2.0, one from and dimers. Admittedly, the approach has to be tested further on the other from p is assigned from the electronic distribution metal dimer systems to see whether proper inferences can be 2 2 2 4 2 [core]2sg 2su 3sg 1pu 1pg . One can generate a higher spin drawn from analogous high spin state PECs regarding the 2 state by breaking the bonding pair in the 3sg bonding orbital number of bonds in their respective ground states.

and promoting an electron to 3su, thus eliminating the s bond. In order to disrupt the bonding arising from p orbitals one needs to excite a single electron from p to p* creating Conclusions  p 3p 3 p 4p 2 a con guration of the type u g from u g of the ground In summary we provide overwhelming evidence which brings state. This would eliminate the single p bond without out the quadruple bonding nature in C and CN+ with two s and ascending on the spin ladder. This is obviously diﬀerent from 2 1 + two p bonds. However, our approach indicates that BN, which is the molecules with singlet ground state Sg that has p bonds ^ isoelectronic to C2 at the most has three bonds. Additionally, we (consider the case of N2 or HC CH). Armed with this simple + 7 + 3 + suggest that for both CN and C2,a S state exists which has information one would expect to obtain Su with a minimum 5 + a clear distinct and deep minimum, which opens up a window (conventional bond order ¼ 1) and a Sg with a purely disso- for experimental verication. ciative curve (conventional bond order ¼ 0) (see Fig. S6(b) and S7(b) in ESI†). Indeed the ndings from the previously reported S CASSCF/MRCI PECs of high spin states show that the Conﬂicts of interest approach holds good, it must be emphasized that for triplet p 3p 3 p 4p 2 ground state diatomic systems arising from u g and u g There are no conicts to declare.

This journal is © The Royal Society of Chemistry 2020 Chem. Sci.,2020,11,7009–7014 | 7013 View Article Online Chemical Science Edge Article

Acknowledgements 11 P. B. Karadakov and J. Kirsopp, Chem. –Eur. J., 2017, 23, 12949–12954. AP would like to thank Professor Debashis Mukherjee and 12 J. M. Matxain, F. Ruipérez, I. Infante, X. Lopez, J. M. Ugalde, Professor Eluvathingal D. Jemmis for enlightening discussions G. Merino and M. Piris, J. Chem. Phys., 2013, 138, 151102. and thoughtful inputs. AP would like to acknowledge nancial 13 (a) S. Shaik, H. S. Rzepa and R. Hoffmann, Angew. Chem., Int. support from DST SERB CRG/2019/006685. DG would like to Ed., 2013, 52, 3020–3033; (b) L. T. Xu and T. H. Dunning Jr, J. acknowledge DST-SERB grant EMR/2017/001054 for the nan- Chem. Theory Comput., 2014, 10, 195–201; (c) S. Shaik, cial support. IB would like to acknowledge nancial support in D. Danovich, B. Braida and P. C. Hiberty, Chem. –Eur. J., the form of a research fellowship from CSIR, Govt. of India 2016, 22(52), 18977–18980; (d) M. Piris, X. Lopez and (Award Number: 09/080(1065)/2017-EMR-I). J. M. Ugalde, Chem. –Eur. J., 2016, 22(12), 4109–4115. 14 P. F. Fougere and R. K. Nesbet, J. Chem. Phys., 1966, 1, 285– References 298. 15 R. Zhong, M. Zhang, H. Xu and Z. Su, Chem. Sci., 2016, 7, 1(a) R. C. Fischer and P. P. Power, Chem. Rev., 2010, 110, 3877– 1028–1032. 3923; (b) P. R. Schreiner and H. P. Reisenauer, Angew. Chem., 16 K. K. Lange, E. I. Tellgren, M. R. Hoffmann and T. Helgaker, Int. Ed., 2009, 48, 8133–8136. Science, 2012, 337, 327–331. 2 I. N. Levine, Quantum Chemistry, Allyn and Bacon, 2nd edn, 17 (a) A. Engels-Putzka and M. Hanrath, Mol. Phys., 2009, 107, 1974, p. 321, table 13.2. 143–155; (b) R. S. Mulliken, J. Chem. Phys., 1962, 37, 809– 3 P. V. R. Schleyer and P. Maslak, Tetrahedron Lett., 1993, 34, 813; (c) H. Werner and P. J. Knowles, J. Chem. Phys., 1991, 6387–6390. 94(2), 1264–1270. 4 P. Su, J. Wu, J. Gu, W. Wei, S. Shaik and P. C. Hiberty, J. 18 (a) G. S. Scuseria, T. P. Hamilton and H. F. Schaefer III, J. Chem. Theory Comput., 2011, 7, 121–130. Chem. Phys., 1990, 92, 568–573; (b) W. D. Laidig, P. Saxe 5 S. Shaik, D. Danovich, W. Wu, P. Su, H. S. Rzepa and 86 – Creative Commons Attribution-NonCommercial 3.0 Unported Licence. and R. J. Bartlett, J. Chem. Phys., 1987, , 887 907. P. C. Hiberty, Nat. Chem., 2012, 4, 195–200. 19 J. M. Matxain, F. Ruipérez and M. Piris, J. Mol. Model, 2013, 6(a) S. Shaik, H. S. Rzepa and R. Hoffmann, Angew. Chem., Int. 19, 1967–1972. Ed., 2013, 52, 3020–3033; (b) D. Danovich, S. Shaik, 20 A. L. Padellec, J. B. A. Mitchell, A. Al-Khalili, H. Danared, H. S. Rzepa and R. Hoffmann, Angew. Chem., Int. Ed., 2013, A. Källberg, A.˚ Larsen, S. Rosén, M. Ugglas, L. Vikor and 52, 5926–5928. M. Larsson, J. Chem. Phys., 1999, 110(2), 890–901. 7 G. Frenking and M. Hermann, Angew. Chem., Int. Ed., 2013, 21 (a) H. Liu, D. Shi, J. Sun, Z. Zhu and Z. Shulin, Spectrochim. 52, 5922–5925. Acta, Part A, 2014, 124, 216–229; (b) H. Partridge, 8 D. Danovich, P. C. Hiberty, W. Wu, H. S. Rzepa and S. Shaik, C. W. Bauschlicher Jr, S. R. Langhoff and P. R. Taylor, J.

This article is licensed under a Chem. –Eur. J., 2014, 20, 6220–6232. Chem. Phys., 1991, 95(11), 8292–8300; (c) H. Lefebvre-Brion, 9 D. W. O. Sousa and M. A. C. Nascimento, J. Chem. Theory H. P. Liebermann, J. M. Amero and G. J. V´azquez, J. Chem. Comput., 2016, 12, 2234–2241. Phys., 2016, 144(14), 144302. – 22 – Open Access Article. Published on 11 kesäkuuta 2020. Downloaded 1.10.2021 3.15.28. 10 M. Hermann and G. Frenking, Chem. Eur. J., 2016, , 4100 4108.