On Chem i cal Bond i ng Be tw ee n He l ium and Ox y g enbeta.chem.uw.edu.pl/people/WGrochala/HeO.pdf · On Chem i cal Bond i ng Be tw ee n He l ium and Ox y g en by W. Grochala1,2

On Chem i cal Bond ing Be tween He lium and Ox y gen

by W. Grochala1,2

1The Fac ulty of Chem is try, The Uni ver sity of War saw, Pas teur 1, 02-093 War saw, Po land2The In ter dis ci plin ary Cen ter for Math e mat i cal and Com pu ta tional Mod el ing,

The Uni ver sity of War saw, Pawiñskiego 5a, 02-106 Warsaw, Polande-mail: [email protected]

(Re ceived March 31st, 2008)

A brief anal y sis of the He–O chem i cal bond, pres ent in cationic (HeO+·) and a few hy po -thet i cal an ionic spe cies (XHeO–, X = F, Cl), is per formed at var i ous lev els of the ory.We are also able to pro pose two can di dates for the first metastable neu tral mol e culewhich con tains he lium chem i cally bound to ox y gen: (HeO)(CsF) and (HeO)(NMe4F).

Key words: helium, Density Functional Theory, noble gases, post Hartree-Fock methods

This work is ded i cated to Pro fes sor Grzegorz Cha³asiñski at his forth com ing 60th

birth day, em i nent Pol ish quan tum chem ist and friend, in rec og ni tion of his re -mark able con tri bu tions on in ter ac tions of dioxygen, ox y gen and ox y gen an ions withno ble gases [1,2] and on weak in ter ac tions and many-body ef fects [3].

MOTTO“(…) re cent ev i dence (…) makes it seem al most cer tain that he lium has a to tal not

of eight but of ei ther two or four elec trons. As sum ing that he lium is the only el e mentbe tween hy dro gen and lith ium and that it has two elec trons, then it is ev i dent from thein ert char ac ter of he lium, and from the re sem blance of this el e ment to the other in ertgases, that here the pair of elec trons plays the same role as the group of eight in theheavier at oms, and that in the row of the pe ri odic ta ble com pris ing hy dro gen and he -lium we have in place of the rule of eight the rule of two.”Gilbert New ton Lewis (‘The atom and the mol e cule’) 1916 [4].

IN TRO DUC TION

He lium – the light est of so called ‘no ble’ gases [5] – en joys a par tic u larly sta ble1s2 elec tronic con fig u ra tion, which was rec og nized by Lewis as an in ter est ing ex cep -tion among sta ble “cu bical at oms” [4]. Now a days Lewis’s ideas are for mu lated as in -ert ‘dou blet’ and ‘oc tet’ and they truly be long to the most im por tant found ingcon cepts of mod ern chem is try. But it is not just elec tronic con fig u ra tion it self, butalso the val ues of as so ci ated elec tronic pa ram e ters which are re spon si ble for chem i -cal re ac tiv ity or in ert ness. Hence, H– (hy dride an ion), which is cer tainly isoelectronic to He, is by far and away more re ac tive than an iso lated he lium atom. In deed, with itsfirst ion iza tion po ten tial, IP, of 24.6 eV [6], and its null elec tron af fin ity, EA = 0 eV

Pol ish J. Chem., 83, 87–122 (2009) PHYSICAL CHEM IS TRY

(which may be trans lated to huge Mulliken electronegativity and Pearson’s hard ness,mM = hP = 12.3 eV), he lium is also the most re luc tant to bond ing amongst all chem i calel e ments. And yet de spite its deep-ly ing (in the en ergy scale) and sig nif i cantly con -tracted 1s or bital, and de spite its im mense 1s–2s gap, he lium does form chem i calbonds; this hap pens when a hole is gen er ated in he lium’s 1s2 set, i.e. when the sta bleLewis pair is bro ken in two. Thus, the He1+· rad i cal binds eas ily to many dif fer entneu tral at oms, E, in clud ing H [7] (Fig ure 1), O [8], F [9], and even an other He [10].Of course, the elec tronic hole in ques tion is largely trans ferred to the other atom, E,in the pro cess of He–E bond cre ation and thus it is prob a bly fair to talk of a neu tralHe atom which solvates pos i tively charged very strong Lewis ac ids, such as H+,O+, F+, V3+ [11] etc. In this ap proach, HHe+ is writ ten as: He ® H+, with He0 serv ingas a Lewis base to wards na ked pro ton. The ‘da tive bond’ for mu la tion is cer tainly ofvalue, as it al lows one to make the con cep tual link be tween var i ous He-con tain ingcat ions and the fas ci nat ing com plexes of neu tral Xe0 with heavy tran si tion metalcat ions, such as, for ex am ple, Hg2+Xe [12] or Au2+·Xe4 [13] and oth ers (see Ap -pen dix) [14].

Re gard less of which for mal de scrip tion of the cationic He spe cies is ap plied, itmust be re al ized that chem i cal bonds formed by He have so far been seen only for thepos i tively charged spe cies in strict iso la tion, usu ally in the high-vac uum cham bers ofmass spec trom e ters. Ne ces sity of their pro tec tion is not co in ci den tal: there is a pen -alty of in tro duc ing even a par tial hole into the He(1s) states and all these cat ions are

88 W. Grochala

Fig ure 1. HHe+, isoelectronic to H2, is one of many He-con tain ing cat ions known. The CCSD(T) bond

length is shown above that of MP2 (in ital ics) and B3LYP (in brack ets). The Kohn-Sham

orbitals (shown at 0.1 e Å–3) ex hibit a char ac ter is tic fea ture of the electronegativity-per turbed

com pounds: the oc cu pied s or bital is cen tered on a more electronegative el e ment while the un -

oc cu pied s* or bital on a more electropositive one. The com puted HOMO/LUMO gap is huge

(25 eV), thus ex plain ing sub stan tial sta bil ity of this spe cies to wards dis so ci a tion.

enor mous ox i diz ers. They would readily dis ap pear in con tact with any neg a tivelycharged Lewis base, even the one which is the most re sis tant to wards ox i da tion (F–):

HHe+ + F– ® HF + He (1a)

FHe+ + F– ® F2 + He (1b)

OHe+· + F– ® ·OF + He etc. (1c)

De cay of, say, OHe+· upon its re ac tion with F– may be viewed as an ul ti mate trans ferof hole rem nants from He to a less electronegative el e ment (here: O em bed ded in the·OF prod uct), i.e. as a re dox re ac tion. Hole trans fer is driven mostly by the large dif -fer ence be tween va lence or bital en er gies of He (24.6 eV) and of all other bond-form -ing el e ments (F: 17.4 eV, O 13.6 eV, etc.); to put it in other words, the hole in theva lence 1s2 set of He is an ex tremely strong ox i dizer. As one goes down Group 18, theva lence elec trons be come less bound (Ne: 21.6 eV, Ar: 15.8 eV, Kr: 14.0 eV), whichfa cil i tates chem i cal bond for ma tion (es pe cially for F and O con nec tions). This isspec tac u larly dem on strated by the suc cess ful iso la tion of the first gen u ine com pound of ar gon, HArF, in cold ma tri ces (2000) [15], and by the ex is tence of more than fivehun dreds neu tral chem i cal com pounds of Kr and Xe [5] with KrF2 (1963) and‘XePtF6’ (1962) as their first his tor i cal rep re sen ta tives [16,17].

Re ac tions de scribed in Eqs.1a–1c serve to re mind that it is much more dif fi cultto achieve chem i cal bond ing to he lium for a neu tral spe cies than for the cationic one.In deed, re cent the o ret i cal stud ies have shown that al though HHeF is a lo cal min i mum at the po ten tial en ergy sur face [18,19], it ex hib its tiny bar ri ers to wards de com po si -tion [20]; in con se quence, HHeF, iso lated in the gas phase, is not a sta ble mol e culebut a very short lived spe cies, with a life time in the pi co sec ond range [20]. In ad di -tion, the pres ence of light hy dro gen fa cil i tates tun nel ing: HHeF is pre dicted to de cayby tun nel ing even in its low est vi bra tional state [20]; the ben e fi cial ef fects of H ® Dsub sti tu tion have not been es ti mated, but cer tainly they can not change the fate of thekinetically un sta ble HHeF.

Ap pli ca tion of an ex ter nal pres sure may lead to sig nif i cant al ter ation of sta bil ityand struc ture [21]. For ex am ple, novel com pounds of no ble gases which are not sta ble as sol ids at am bi ent con di tions, such as e.g. HgXe or XeI2, might be sta bi lized at ex -per i men tally fea si ble pres sures not ex ceed ing 1 mln atm [5]. Ex ter nal pres sure isthought to pre vent re dox re ac tions and thus re verse the fate of many chem i cal re ac -tions. It is also sup posed to play an im por tant role for sta bi liz ing frag ile HHeF. Spe -cif i cally, it has been pre dicted that ‘HHeF pres sur ized in solid he lium at pres sures of15 GPa or higher’, has a life time ex ceed ing miliseconds or even lon ger [22]. Thesecal cu la tions have been per formed for an iso lated HHeF mol e cule em bed ded in sidea small clus ter of He at oms. Yet sin gle mol e cules are not en coun tered in the usualhigh pres sure ex per i ments, where a sev eral mi cron-sized chunk of a solid re sides be -tween two di a mond sur faces and a gas ket. It is ex tremely likely that if the iso la tioncon di tion van ishes and HHeF mol e cules ap proach one an other, new im por tant

On chem i cal bond ing be tween he lium and ox y gen 89

intermolecular dis so ci a tion chan nels (via dipolar Hd+…Fd– cou pling) will open, thuslead ing to a com plete dis in te gra tion of HHeF mol e cules ac cord ing to Eq. 2:

n HHeF ® (HF)n + n He (2)

The HHeF story, as ex cit ing as it is, in fact does not bring us much closer to thefirst neu tral com pound of he lium, which would be sta ble as an iso lated mol e culeat am bi ent pres sure con di tions. HeF2 is a more dis ap point ing case, since it is not evena lo cal min i mum at the po ten tial en ergy sur face [23]. But what about (meta)sta blean ionic spe cies which con tain he lium?

In prin ci ple, it is much eas ier to sta bi lize high ox i da tion states of chem i cal el e -ments while em bed ding them into an an ionic spe cies rather than keep ing them neu -tral. This trend has been tes ti fied by nu mer ous ex am ples rang ing from the chem is tryof strongly ox i diz ing flu o rides, via ni trides, to sub stan tially re duc ing hy drides, andmany more. For ex am ple, AgF3 has been ob tained with dif fi culty as late as 1991 [24],and it is a ther mally un sta ble solid, while quite ther mally sta ble AgF 4

- salts have beenknown since the 1950’s [25]. Sim i larly, ReH7 has never been de tected, even in no blegas ma trixes, while ther mally sta ble ReH 9

2- salts are clas sic ex am ples of Re7+ in atricapped trigonal prism en vi ron ment [26]. More over, CrN2 has never been syn the -sized, de spite many at tempts, while an ionic nitrido com plexes of Cr6+ in the solidstate CrN 4

6- have been ac cessed rather eas ily [27]. The o ret i cal pre dic tions go as faras sug gest ing that de riv a tive of Ar(VIII) might be sta bi lized in ArNO 3

- [28]. The listof ex am ples may be ex panded.

The lack of sta bil ity of chem i cal con nec tions of el e ments in their high est ox i da -tion states is ob vi ously due to re dox re ac tions be tween the cen tral atom, En+, and theneigh bour ing lig ands, Lm–. There fore, the above-men tioned trend of the sta bi li za tion of high ox i da tion states in an ionic spe cies can be as cribed to the re duc tion of ox i diz -ing prop er ties of the cen tral cat ion due to in creased elec tron den sity, com pared to theneu tral sys tem. But will this ef fect be strong enough to in duce (meta)sta bil ity of thechem i cal con nec tions of he lium? It seems that the an swer is pos i tive.

In 2005 Li et al. cal cu lated the prop er ties of [F–…HeO] (Fig ure 2) and foundthat this spe cies is sta ble with re spect to (i) F– + Ng + 1O (these prod ucts are at about+0.88 eV with re spect to [F–…HeO]), and (ii) 2F + Ng + 2O– (at +0.71 eV),and metastable with re spect to (iii) F– + Ng + 3O (at –1.28 eV), and (iv) FO–

+ Ng(at –2.37 eV) [29]. The en ergy bar rier for the most ther mo dy nam i cally fa vouredFO– + Ng dis so ci a tion chan nel was cal cu lated to be about 0.84 eV. Clearly, the[F–…HeO] an ion has a rea son able chance to sur vive as an iso lated spe cies at lowtem per a tures.

In 2007 Antoniotti et al. fol lowed a prom is ing path and they have found that[F–…HeBN] should be a metastable spe cies as well [30]. Very re cently, their the o ret i -cal stud ies have been ex tended to [F–…HeS] [31]. All of the three above-men tioned – and as yet hy po thet i cal – an ionic spe cies re side in deep wells on the sin glet po ten tialen ergy sur faces, pro tected by siz able bar ri ers with re spect to the prod ucts.

90 W. Grochala

We have the o ret i cally ac cessed the [F–…HeO] an ion in de pend ently of the au -thors of [29] whilst be ing un con scious of their work. Lundell and I [32] ini tially stud -ied the o ret i cally the prod ucts of no ble gas in ser tion into the RO bond of the ROFspe cies (R = H, F, OF). Use of the ROF spe cies re lied mostly on the ex tremely ox i -diz ing prop er ties of all ther mo dy nam i cally un sta ble mem bers of the fam ily:hypofluorous acid (HOF), ox y gen flu o ride OF2, and dioxygen difluoride O2F2. Un -for tu nately, our ‘chem is try by force’ ap proach was a fail ure and we have not suc -ceeded in de tect ing lo cal min ima for the prod ucts of in ser tion of He into the RO bondof any of these spe cies (Ar and heavier mem bers yielded true min ima, though). Thenone of us (WG), guided by the rule that it is eas ier to sta bi lize high ox i da tion states ofchem i cal el e ments in an ionic rather than neu tral spe cies turned to novel He-con tain -ing an ions [33]. [F–…HeO] was stud ied first, and to my sur prise it has con verged to alo cal min i mum; re lated [Cl–…HeO] and [HO–…HeO] were stud ied next (see Ap pen -dix). This ex am ple is hope fully of some di dac tic value since it shows how ametastable [F–…HeO] an ion may be pre dicted not by plain co in ci dence but ratherby ap ply ing chem i cal in tu ition.

The In tro duc tion has been long yet not with out a pur pose; it has served to ac -quaint the reader with sev eral com pre hen sive path ways of re search in the emerg ingchem is try of he lium, and to dem on strate the im por tant fact that the ease of sta bi liz ingchem i cal con nec tions of he lium as iso lated mol e cules greatly de pends on the to talcharge car ried by these spe cies, and var ies in the or der:

Cat ion >> An ion >> Neu tral Spe cies (3)

The or der ing sug gested here is dif fer ent to the one an tic i pated pre vi ously by the au -thors [29], who state: “Since the no ble gas atom has “sat u rated” shells of elec trons,it is gen er ally held that the pos i tive charged ions are eas ier to form than the neu tralno ble gas mol e cules, and the neg a tive charged ions would be even less sta ble.”We feel that suf fi cient ev i dence has been shown for ap pli ca bil ity of the gen eral in -equal ity ex pressed in Eq. 3 above.

Sum ma riz ing this sec tion, many dif fer ent He-con tain ing cat ions have beende tected in mass spec trom e ters up to now; in ad di tion, a few an ionic spe cies have re -cently been pre dicted by the ory. How ever, in di cat ing a can di date for a neu tral mol e -cule con tain ing chem i cally bound he lium still re mains an un dis pu ta ble chal lenge


Fig ure 2. [F–…HeO], iselectronic to very sta ble HF2- , and to un sta ble HeF2, is one of very few hy po thet i -

cal He-con tain ing an ions, pre sumed to be metastable at low tem per a tures. The CCSD(T) bond

lengths (in Å, com pare with those from Ref. [29]) are shown above those of MP2 (in ital ics)

and B3LYP (in brack ets).

[34]. The con cep tual de sign of such a spe cies and sub se quent quan tum me chan i calcal cu la tions of its prop er ties is the ma jor con cern of the cur rent con tri bu tion [35].

COM PU TA TIONAL METH ODS

Mol e cules stud ied in this work range from model (HeH+, HeO+· ) and more com plex (AgHe42+ × ,

BeHe42+ , AlHe

63+ , ScHe

63+ , MOHe+, where M = Li, Cu, Cs, NH4) cat ions, via neu tral sys tems

([HeO]n, n = 2–4, (HeO)(HF), (HeO)(LiF), (HeO)(BeO), [FHeOH], Cs+[F–…HeO], NH4+ [F–…HeO],

NMe4+ [F–…HeO]), to model ([F–…HeO], [F–…BeO]) and novel an ions ([Cl–…HeO], [HO–…HeO]).

We have also stud ied pos si ble de com po si tion prod ucts for the most im por tant sys tems; e.g. for(HeO)(CsF) these are: He, 1O, 3O, CsF and CsOF.

We have ap plied sev eral dif fer ent lev els of the ory, rang ing from Den sity Func tional The ory (DFT)with the B3LYP func tional, via Hartree-Fock (HF) cal cu la tions fol lowed by a Møller-Plesset cor re la tionen ergy cor rec tion trun cated at sec ond and fourth or der (MP2, MP4), to the cou pled clus ter cal cu la tionsus ing dou ble sub sti tu tions from the Hartree-Fock de ter mi nant, CCD, or both sin gle and dou ble sub sti tu -tions, CCSD, and also in clud ing tri ple ex ci ta tions non-iteratively, CCSD(T). All optimizations were fol -lowed by har monic fre quen cies cal cu la tions. Fre quen cies listed have al ways been com puted based onthe most abun dant iso topes, no ta bly for 4He.

Ini tially we con tem plated us ing Dun ning’s cor re la tion con sis tent ba sis sets; how ever, the el e mentsHe, Li, and Be do not have dif fuse func tions de fined within these ba sis sets [36], which is clearly a de fi -ciency, in par tic u lar for an ionic spe cies. We have there fore ap plied Pople’s 6-311++G** tri ple-zeta ba sisset, which seems to be a rea son able com pro mise given the di verse char ac ter of the approximtely 30 dis -tinct spe cies stud ied in this work. Com par i son of re sults ob tained with the 6-311++G** set (this work)and two Dun ning’s sets (dou ble- and quin tu ple-zeta) [29] is given in Ta ble 1.

Ta ble 1. The cal cu lated He–O and He–F bond lengths [Å], and the har monic fre quen cies, n [cm–1] forthe [F–…HeO] an ion as cal cu lated at the CCSD(T) level with three dif fer ent ba sis sets.

6-311++G** aug-cc-pVDZ# aug-cc-pVQZ#

R(He–O) /Å 1.152 1.132 1.100

R(He–F) /Å 1.653 1.656 1.621

nsym (s) / cm–1 299 N.D. 331

nbend (p) / cm–1 408 N.D. 449

nasym (s) / cm–1 1146 N.D. 1273

# re sults from Ref. [29]. N.D. = not de ter mined.

The com par i son re veals that the 6-311++G** ba sis set yields slightly lon ger he lium-el e ment bonds(by ca. 0.03–0.05 Å) than the aug-cc-pVQZ set. Weak en ing of the bonds af fects har monic fre quen cies,which de crease (scal ing up uni formly) by ~10% as com pared to the aug-cc-pVQZ re sults. A sim i lar ef fectmay be no ticed [29] for the smaller Dun ning’s set aug-cc-pVDZ, which yields bond dis tances com pa ra bleto those cal cu lated by us (Ta ble 1). The sen si tiv ity of the cal cu lated He-el e ment (in par tic u lar H–O) bondlength on the choice of the ba sis set and of the com pu ta tional method is not sur pris ing; as we show be lowthe He–O bond owes its very ex is tence to a small charge sep a ra tion (Hed+–Od–), and it is sen si tive toany elec tric field, such as that gen er ated by the small F– an ion. Im por tantly, these re sults sug gest thatthe mol e cules pre dicted to be sta ble in the cur rent work may turn out to be even more sta ble at theCCSD(T)/aug-cc-pVQZ level of the ory.

For Cs and Ag (pres ent in two mol e cules stud ied) we have used rel a tiv is tic pseudopotentials fromLos Alamos (LANL) with a stan dard dou ble zeta ba sis for the va lence elec trons. The LANL set is meantto cor rectly re pro duce ge om e tries, and less so re ac tion en ergy as pects, of the heavy metal spe cies.

92 W. Grochala

In this work we fre quently an a lyze Kohn-Sham mo lec u lar orbitals for se lected spe cies; the orbitalsare al ways ex tracted from the DFT cal cu la tions for mol e cules preoptimized at the DFT level. Their com -par i sons with HF orbitals cal cu lated at CCSD(T) – op ti mized ge om e tries re vealed very small qual i ta tivechanges. We also list val ues of Pearson’s hard ness (hP) and Mulliken electronegativity (mM) for mostspe cies stud ied, as com puted at the DFT level.

En ergy dif fer ences are listed with out Ba sis Set Su per po si tion Er ror (BSSE) and Zero Point En ergy(ZPE) cor rec tions, un less stated oth er wise.

RE SULTS AND DIS CUS SION

1. Com par i son of HeO0 and HeO+ · sys tems.De spite a mis lead ing 1963 pre dic tion [37] it has been known since 1966 [38] that

HeO is not bound (Fig ure 3). Its lack of sta bil ity em pha sizes the fact that the empty 2p orbitals of a neu tral O atom do not have suf fi cient acid ity to force the con tractedLewis pair of the He atom into do nor–ac cep tor bond ing. The in ter ac tion po ten tialsbe tween a sin glet He atom and an ox y gen atom (ei ther the ground state trip let, or theex cited sin glet) show a strongly re pul sive na ture [1]. At He–O sep a ra tion of 1.5 Å theground 3P state has en ergy larger by ca. 1 eV than that for the dis so ci ated sub strates(3O and He). The re pul sion of 1O and He is smaller, es pe cially for the 1S state, but 1Sis an ex cited state set ~1 eV above the ground state (at 1.5 Å). Doubts may nat u rallyarise as to what ever there is re ally the pos si bil ity of a short, sub stan tially co va lentHe–O chem i cal bond at even shorter in ter atomic sep a ra tions.


Fig ure 3. The in ter ac tion po ten tials be tween a sin glet He atom and an ox y gen atom (the ground state

trip let, and the ex cited sin glet) have a strongly re pul sive na ture. Might there be a chance for a

short, largely co va lent He–O chem i cal bond at in ter atomic sep a ra tions be low 1.5 Å? (by cour -

tesy of G. Cha³asiñski [1]).

One ob vi ous trick to sta bi lize a He–O bond is to re move one elec tron from HeO,thus gen er at ing the rad i cal cat ion HeO+·. In con trast to HeO, the cationic spe cies ismod er ately bound with re spect to He and 2O+· while in the low est–dou blet 2P state(Fig ure 4). The CCSD(T)-com puted equi lib rium bond dis tance is 1.230 Å (1.215 Å at the DFT level), the stretch ing vi bra tion is pre dicted to fall at 1002 cm–1 (DFT:1099 cm–1), and the ZPE-cor rected dis so ci a tion en ergy equals 0.37 eV (DFT over es -ti mates it by a lot, yield ing 1.58 eV). The He–O stretch must be quite an har mon ic,since a tri pled har monic vi bra tion is suf fi cient to com pletely break the bond in2HeO+·. Only a very small spin (–0.02 e) re sides on He, which points to a de scrip tionof 2HeO+· as a closed-shell He atom in ter act ing with O+·. This view is fur ther cor -rob o rated by mo lec u lar or bital (MO) anal y sis for this spe cies (Fig ure 4). It is a lone2p pair of O which ac cepts a hole.

An iso lated O+· – one com po nent of the HeO+· rad i cal cat ion – has an elec troniccon fig u ra tion of 1s22s22p3 with three half-filled 2p orbitals. The quar tet ground stateis there fore to be ex pected. In deed, our CCSD(T) cal cu la tions show that the low estquar tet 4S state is about 0.44 eV be low the 2P state (ver ti cally, at the equi lib rium ge -om e try of the lat ter); DFT yields a qual i ta tively dif fer ent re sult by plac ing 4S about+0.24 eV above 2P (this is cer tainly in part due to a shorter equi lib rium sep a ra tionpre dicted by DFT for 2HeO+·). How ever, in both types of cal cu la tions the elec tronicstates in ques tion ap pear in the same en ergy win dow, and they cross at an in ter atomicsep a ra tion which is close to the equi lib rium bond length of 2HeO+·; this ren dersa cor rect the o ret i cal de scrip tion of the HeO+· rad i cal cat ion quite chal leng ing.More ad vanced treat ments are needed, par tic u larly those which ex plic itly in volvespin-or bit cou pling and nonadiabatic ef fects.

94 W. Grochala

Fig ure 4. Op ti mized mo lec u lar ge om e try of the HeO+· rad i cal cat ion in its bound ex cited 2P state. The

CCSD(T) bond length (in Å) is shown above that of MP2 (in ital ics) and B3LYP (in brack ets).

The Kohn-Sham orbitals are shown at 0.05 e Å–3. The Fermi level of the mol e cule is marked

with the dot ted line.

The 4S state is ei ther un bound (i.e. spon ta ne ously dis so ci at ing into He and 4O+·)or at best ex hib its a small van der Waals min i mum at very large in ter atomic sep a ra -tion (> 2 Å). Also this elec tronic state will be dif fi cult to eval u ate with out invokinga better level of the ory.

Con clud ing this sec tion we no tice that the in tro duc tion of a hole in the 2p set of Ohas im proved the sit u a tion with re spect to the re pul sive He0–O0 sys tem. Un for tu -nately, the im prove ment is not sat is fac tory, since 2HeO+· re sides in a shal low min i -mum and ex hib its an intersystem cross ing with the dis so ci at ing 4HeO+·. More over,2HeO+· can not sur vive at tach ment of F–. Our CCSD(T) cal cu la tions show thatthe en ergy of re ac tion (1c) (lib er a tion of the ·OF rad i cal and He) is as neg a tive as–15.1 eV (in ter est ingly, DFT also yields –15.1 eV). The anal o gous tetramolecularpro cess lead ing to 2 He and O2F2 must be even more pre ferred. One im por tant mes -sage from these num bers is that even a tiny share of ox i diz ing holes des per ately seeksto be ex pelled from the partly de pop u lated 1s2–d va lence or bital of He. And that weneed much better con cepts to achieve sta bi li za tion of the He–O bond.

2. [F–…HeO] and re lated an ions.As men tioned in the In tro duc tion, [F–…HeO] is a vi a ble can di date for the first

metastable an ion con tain ing chem i cally bound He [29]. Let us thus take a closer lookat this in trigu ing spe cies.

2.1. Mo lec u lar ge om e try, har monic fre quen cies and metastability.In Ta ble 2 we pres ent the cal cu lated He–O and He–F bond lengths, har monic

fre quen cies, Mulliken charges on at oms, and the rel a tive en er gies of the first ver -ti cally ex cited trip let state vs. the op ti mized sin glet state for the lin ear [F–1…HeO]an ion (C¥v), as ob tained with var i ous meth ods. We also list en ergy of [F–1…HeO]with re spect to three dif fer ent sets of prod ucts:

F–HeO ® OF–1 + He (4a)

F–HeO ® 3O + F–1 + He (4b)

F–HeO ® 1O + F–1 + He (4c)

The [F–1…HeO] an ion is not bound at the HF level show ing up just as a shal -low (slightly deeper than just a typ i cal van der Waals, vdW) min i mum at largeinternuclear sep a ra tion. In clu sion of the elec tronic cor re la tion dra mat i cally im -proves sta bil ity. Optimizations at MP2, MP4, CCD, CCSD(T) and DFT lev els lead toshort He–O dis tance of 1.070–1.196 Å and a sub stan tially lon ger He–F sep a ra tionof 1.618–1.722 Å. There is no doubt that the He–O dis tance of 1.07–1.20 Å cor re -sponds to an in cip i ent chem i cal bond, since these val ues are com pa ra ble with the sum of (em pir i cal) co va lent ra dii of O and He at oms (1.05 Å) and they are much shorterthan the sum of the cor re spond ing vdW ra dii (2.92 Å). It is in ter est ing to note thatDFT yields the lon gest He–O bond de spite the fact that DFT is known to ex ag ger atethe strength of chem i cal bond ing.


Ta ble 2. The He–O and He–F bond lengths (R/ Å), har monic fre quen cies (n/ cm–1), Mulliken charges onat oms (q/ e), the rel a tive en er gies of the first ver ti cally ex cited trip let state vs. the op ti mized sin gletstate (DE/ eV) and en ergy with re spect to three dif fer ent sets of prod ucts, for lin ear [F–1…HeO] an ion (C¥v) as ob tained with var i ous meth ods. The 6-311++G(d,p) ba sis set was al ways used. En ergydif fer ences are given with out ZPE and BSSE cor rec tions.

HF MP2 MP4 CCD CCSD(T) DFT/B3LYP

R(He–O) 1.725 1.070 1.127 1.101 1.152 1.196

R(He–F) 2.485 1.640 1.618 1.722 1.653 1.631

nsym (s) / cm–1 39 310 330 259 299 297

nbend (p) / cm–1 83 467 450 400 408 423

nasym (s) / cm–1 337 1594 1294 1444 1146 1199

q(He) / e +0.030 +0.189 +0.163 +0.194 +0.163 +0.149

q(O) / e –0.042 –0.312 –0.290 –0.290 –0.273 –0.439

q(F) / e –0.988 –0.877 –0.873 –0.904 –0.890 –0.710

(3E–1E) [eV] –2.85 +4.33 +3.43 +2.53 +2.91 +2.42#

(a) DE vs. He, 1OF–1 +2.12 +2.48 +2.44 +2.39 +2.43 +2.02

(b) DE vs. He, 3O, 1F–1 +3.37 +1.90 +1.76 +2.05 +1.74 +0.91

(c) DE vs. He, 1O, 1F–1 –0.08 –1.05 –0.99 –0.42 –0.55 –1.84

# Time-de pend ent (TD) cal cu la tion yields the first ver ti cally ex cited (trip let) state at +2.02 eV.

The cal cu lated har monic fre quen cies point to a gen u ine min i mum na ture of[F–1…HeO], in agree ment with [29]. Cal cu la tions lo cate the asym met ric stretch ingmode at 1146 cm–1 (CCSD(T)) to 1594 cm–1 (MP2) and the sym met ric one at259 cm–1 (CCD) to 330 cm–1 (MP4), with the dou bly de gen er ate bend ing modein between the two, at 400 cm–1 (CCD) to 467 cm–1 (MP2). One no tices large sen si -tiv ity of the fre quency of the asym met ric stretch ing mode (dis crep an cies reach 28%)and of the He–O dis tance (dis crep an cies reach 10%) on the choice of a com pu ta tionalmethod, these two pa ram e ters be ing mu tu ally cor re lated in a stan dard way (theshorter the bond, the stiffer the vi bra tional mode).

Based on the CCSD(T) cal cu la tions we pre dict that [F–1…HeO] is sta ble with re -spect to F– + He + 1O (Eq. 4c) by +0.55 eV (com pare +0.88 eV [29]), and metastablewith re spect to F– + He + 3O (Eq. 4b) by –1.74 eV (com pare –1.28 eV [29]), and toFO–

+ He (Eq. 4a) by –2.43 eV (com pare –2.37 eV [29]). These num bers mean thatboth the bend ing dis so ci a tion chan nel (Eq. 4a) and the stretch ing one (Eq. 4b) may inprin ci ple in flu ence the ki netic sta bil ity of [F–…HeO]. The au thors of [29] con cludethat the bar rier for dis so ci a tion via bend ing is large enough and si mul ta neously thelo ca tion of the sin glet–trip let intersystem cross ing for dis so ci a tion via stretch ing isdis tant enough from the lo cal min i mum in ques tion to en sure mac ro scopic life timesat cryo genic con di tions. Lack of hy dro gen pre vents an ef fi cient tun nel ing, in con trast to HHeF.

The rea sons for metastability of [F–…HeO] must be of a com plex na ture. Theywill be ex plored in the forth com ing sec tions.

96 W. Grochala

2.2. Lo cal charge-in duced di pole and the strongly cor re lated na ture of [F–…HeO].The sen si tiv ity of com puted mi cro scopic pa ram e ters on the choice of com pu ta -

tional method (sec tion 2.1.) tells us some thing im por tant about the na ture of a frag ileHe–O bond in [F–…HeO].

We an tic i pate that the He–O bond owes its sta bil ity in [F–…HeO] due to (i) sig -nif i cant polarizability of the [HeO] unit and (ii) mod est trans fer of neg a tive charge toit. In deed, Mulliken pop u la tion anal y sis yields the fol low ing charges: F from –0.71 e(DFT) to –0.90 e (CCD), He from +0.15 e (DFT) to +0.19 e (CCD), and O from–0.27 e (CCSD(T)) to –0.44 e (DFT) ([29] uses other pop u la tion schemes which yield even more pro nounced charge sep a ra tion and a more ionic de scrip tion of the [HeO]unit). A lo cal [Hed+–Od–] di pole may be dis tin guished, which car ries an ex traelec tron den sity of –0.3 e (DFT) to –0.1 e (CCD). The metastability of the [F–…HeO]an ion thus arises largely from the strong an ion-in duced sta bi li za tion of the elu sive1HeO com pound (i). This ef fect is not gen u inely flu o ride an ion-spe cific since[Cl–…HeO] also en joys a mod er ate metastability (see sec tion 2.6. and Ap pen dix).A lo cal ized neg a tive charge is needed to gen er ate the [Hed+–Od–] di pole and there -fore a small and hard F– an ion serves best for this pur pose. Polarizability andhyperpolarizability of [F–…HeO] and re lated spe cies and its nonadiabatic dy nam icsaround the intersystem cross ing cer tainly merit fur ther stud ies but their ac cu ratere pro duc tion may not be easy.

An other im por tant ef fect re spon si ble for metastability of the [F–…HeO] an ion iscon nected with a par tial trans fer of elec tron den sity from F– to the [HeO] sub unit (ii).This ef fect my be ra tio nal ized in terms of a da tive bond be tween hard Lewis base (F–)and hard Lewis acid (HeO) and it was in fact the in spi ra tion for our search for themetastable mol e cules con tain ing chem i cally bound he lium (In tro duc tion). An ex traneg a tive charge di min ishes the ox i diz ing prop er ties of holes pres ent at the pos i tivelycharged He cen ter and thus al lows for the He–O bond for ma tion with out ir re vers ibleox i da tion of the ad ja cent O cen ter. Rec ol lect, dis so ci a tion to 1O, F–1 and He (Eq. 4c)on the sin glet sur face re quires over half an eV, which trans lates to over 13 quanta ofthe sym met ric stretch ing mode (as sum ing its harmonicity) or sub stan tially more (as -sum ing anharmonicity).

Dis so ci a tion of [F–…HeO] along the sym met ric stretch ing co or di nate is un usual, since the two bonds (F–…He and He–O) are bro ken at the same time (1HeO is notbound on its own). This is dif fer ent from the dis so ci a tion of many other Lewisbase-sta bi lized an ions (such as isostructural F–…BeO, see Ap pen dix), which elim i -nates the weaker Lewis base with out con com i tant rup ture of the re main ing neu tralunit. This fea ture of [F–…HeO] her alds un usu ally strong three-body ef fects [3].It also ex plains why de par ture from the sin gle-de ter mi nant de scrip tion is in dis pens -able to cor rectly re pro duce its sta bil ity and why the ex tent of elec tronic cor re la tionat var i ous lev els of the ory has such an enor mous im pact on the cal cu lated prop er tiesof this spe cies.

It is not ob vi ous which Lewis struc ture might best de scribe [F–…HeO]. By anal -ogy with [FArH], which is also a ‘push–pull’ com pound (| | |F Ar H

-® +), [F–…HeO]


might be viewed as | | |F He O- ® . Note that it is an elec tron-rich no ble gas atom whichserves for mally as a Lewis base to wards elec tron-poor H/O in these un usual spe cies.How ever, one should re mem ber that the Lewis struc ture sug gested above for [F–…HeO] does not re pro duce the im por tant fact that one 2p or bital at O is un oc cu pied, and thatone elec tron pair oc cu pies a He–O antibonding or bital (see sec tion 2.4.).

An or ganic chem ist who de signs a new mol e cule first (usu ally just in his mind)draws a rea son able Lewis struc ture for it, thus iden ti fy ing all elec tron pairs, thosewhich are called bonds and those which serve as non-bond ing lone pairs. An in or -ganic chem ist of ten at tempts the same. The strongly cor re lated na ture of [F–…HeO]and lack of a rea son able Lewis struc ture which might de scribe it well, seems to be ma -jor rea son why it took so long to de sign this un usual spe cies.

It would be very in ter est ing to study [F–…HeO] us ing a va lence bond method,and to es ti mate con tri bu tions from var i ous res o nance struc tures. We an tic i pate thatthe (F–…He ® O) struc ture of a mixed co va lent/ionic char ac ter will dom i nate, withthe less im por tant fully ionic de scrip tion (F–…He2+…O2–). Nev er the less, the lat teris needed to ac count for charge de ple tion at He.

2.3. The [HeO] ~ [HF] isoelectronic anal ogy.The HeO unit pres ent in the [F–…HeO] an ion is isoelectronic to HF [39]. It is

thus tempt ing to com pare prop er ties of the [F–…HeO] an ion to those of the [F–…HF]moi ety. The lat ter is pres ent in a mul ti tude of acidic difluoride salts (such as CsHF2 etc.)which con tain an es sen tially sym met ric HF 2

- an ion, as well as in solid HF. The lat tercase is in ter est ing, since this acid is known to form in fi nite (HF)¥ 1D chains (bent onF at oms) with short HF sep a ra tion of 0.964 Å and the short est amongst hy dro genbonds (F–…H) of 1.581 Å (num bers for deuterated HF [40]). We note that the ra tio ofthe F–H and F–…H dis tances for solid DF (0.610) is close to the ra tio of the O–He andF–…He dis tances com puted for the [F–…HeO] an ion at the CCSD(T) level (0.697).The HeO ~ HF anal ogy sug gests that po si tion of He in the Pe ri odic Ta ble shouldbe right aside H. This will be fur ther ex plored in sec tion 7.

Greater ‘af fin ity’ of He to O than of He to F is counterintuitive, since the match ofthe va lence or bital en er gies is worse for the first pair of el e ments (He(2s): –23.4 eV,O(2p): –14.8 eV) than for the lat ter one (F(2p): –18.1 eV) (see Ap pen dix). We an tic i -pate that it is a better match of the 2s sets of these el e ments which ac counts for re ver -sal of affinity (O(2s): –32.3 eV, F(2s): –40.0 eV). Our sur mise has been cor rob o ratedby MO anal y sis (see next sec tion). One may also ex plain the sub stan tial asym me tryof the [F–…HeO] an ion by the ten dency of He to avoid get ting hypervalent (com pareelec tronic de scrip tion from the pre vi ous sec tion). This makes [F–…HeO] sim i lar tomany asym met ric spe cies of heavier no ble gases, such as for ex am ple [SbF 6

- …KrF+][5]. This fea ture will also be ap par ent from the MO anal y sis, which will be dis cussednext.

Gen u ine hypervalence, like the one seen for XeF2, could oc cur for He only uponin volve ment of its 2p set, which po lar izes the 1s set a lit tle. How ever, the 2p set is es -sen tially in ac ces si ble for He and such hy brid iza tion is not al lowed; this is why

98 W. Grochala

[F–…HeO] ex hib its sig nif i cant asym me try. A suc cess ful the o ret i cal de sign of novelHe-con tain ing mol e cules should thus al low He to pre serve its non-hypervalent na -ture, and also uti lize large ba sis sets for He.

2.4. Mo lec u lar or bital struc ture of [F–…HeO].In Fig ure 5 we show the Kohn-Sham orbitals of the [OHe…F–] an ion. Three S

orbitals ly ing deeply in the en ergy scale are com posed pre dom i nantly of the 2s atomic orbitals of He, O, and F, with the mid dle one es sen tially cen tered on F–. There is verylit tle elec tron den sity in the internuclear re gion be tween He and F, but there is lots ofelec tron den sity shared by H and O in the low est-ly ing S or bital. These ob ser va tionscon firm: (i) the ionic na ture of the F–…He bond, (ii) greater af fin ity of He to wards Othan to wards F, which re sults from a better match be tween 2s man i folds of the for mertwo el e ments, and (iii) the ten dency of He to avoid be com ing hypervalent. In ter est -ingly, bind ing of O to an electropositive acidic Hed+ cen ter and the an ionic na ture ofF– both re sult in the switch ing of the rel a tive en er gies of the 2p lone pairs of O and F(P orbitals), the for mer hav ing sub stan tially lower en ergy. The sim i lar ity of or bitalen er gies for pre dom i nantly F(2p) S and P com bi na tions fur ther sup ports the viewthat F– is bound to He by mostly ionic forces.

The He–O bond ing and He–O antibonding S com bi na tions are both oc cu piedwhich ex plains why the He–O bond is so frag ile. Its very ex is tence is due to a for tu -nate, small 2p(O)–2s(He) bond ing con tri bu tion and to the ef fect of vir tual atomicorbitals from the ba sis set which tend to de crease the antibonding char ac ter of the up -per 2s(O)–2s(He) S or bital. Ob vi ously, the p over lap be tween 2p(He) orbitals andthose of the neigh bour ing el e ments is neg li gi bly small due to the in ac ces si bil ity ofthe dif fuse vir tual 2p set of He.

There are 16 va lence elec trons in the sys tem, 8 of which might be ar bi trarilyas signed to ionic F–. The re main ing 8 is par ti tioned be tween He and O, 4 of whichen ter the bond ing and antibonding s com bi na tions and the other 4 form two lone pairs on O. This leaves one 2p or bital of O nearly un oc cu pied and con sti tutes an ac cep torfunc tion of the mol e cule (LUMO). The or bital in ques tion is some what He–Oantibonding and there fore elec tronic ex ci ta tions re sult ing in par tial oc cu pa tion ofLUMO should re sult in dis so ci a tion of the mol e cule. This is fur ther con firmed bythe na ture of the first ver ti cally ex cited trip let state (see the next sec tion).

The do nor func tion of the mol e cule is dou bly de gen er ate in the DFT cal cu la tionsas it is com posed of two P lone pairs of F. The en ergy dif fer ence be tween HOMOand HOMO-1 is ac tu ally small, some 0.10 eV, and the or der of these orbitals is re -versed in the HF cal cu la tions fol low ing the MP2 and CCSD(T) optimizations: HFsets P orbitals 0.16 eV be low S (HOMO).

De spite lim ited ap pli ca bil ity of the MO de scrip tion for anal y sis of the elec tronicstruc ture of strongly cor re lated spe cies, we find the MO pic ture utile in at tempts tosta bi lize the [OHe…F–] moi ety by ap pro pri ate cat ions (see sec tion 3).


2.5. Rel a tive en ergy and the na ture of the first ver ti cally ex cited trip let state, andthe HOMO/LUMO gap.

The HOMO/LUMO gap, DEHL, and the re lated ver ti cal ex ci ta tion en ergy,(DEexc), are amongst the most fun da men tal fac tors which de ter mine sta bil ity and re -ac tiv ity of any closed shell spe cies. DEHL is for mally re lated to the Pearson’s hard -ness, hP, via DEHL = 2 hP (upon as sump tion of the ap pli ca bil ity of Koopman’sthe o rem). Since ac ti va tion of the chem i cal re ac tion in volves by ne ces sity the low estun oc cu pied or bital of a mol e cule, hard spe cies are more kinetically in ert than softones.

Our DFT cal cu la tions yield the hP of 2.76 eV; this num ber is much smaller thanthe cor re spond ing value of 7.13 eV ob tained in the HF cal cu la tions which fol low ge -om e try op ti mi za tion at the CCSD(T) level. Un der es ti ma tion of the HOMO/LUMOgap is one of key de fi cien cies of DFT meth ods, which are con cerned with re pro duc -tion of the ground state and not the ex cited state prop er ties. On the other hand the HFap proach is known to yield too large val ues of DEHL. The true value of Pearson’shard ness of the [OHe…F–] an ion is likely to fall some where in be tween the DFT andHF pre dicted val ues.

Let us now turn to the cal cu lated ver ti cal ex ci ta tion en ergy. Our sin gle point en -ergy un re stricted cal cu la tions lo cate the first ex cited trip let state at 2.42 eV (DFT) to4.33 eV (MP2) above the sin glet state min i mum, with an in ter me di ate CCSD(T)value of 2.91 eV (Ta ble 2). The Time-De pend ent (TD) DFT cal cu la tion yieldsa com pa ra ble value of 2.02 eV. These num bers are in gen eral agree ment with

100 W. Grochala

Fig ure 5. The Kohn-Sham orbitals of the [OHe…F–] an ion; isosurfaces shown at 0.05 e Å–3.

the re sults ob tained in [29] and they con firm that the first ex cited trip let state isrea son ably sep a rated from the lo cal min i mum on the sin glet po ten tial en ergy sur face.But what is the na ture of the first ex cited trip let state?

The cal cu lated Mulliken charges on at oms in the trip let state (CCSD(T) re sults)(He –0.016 e, O –0.067 e, F –0.918 e) may be com pared to those for the ground statesin glet (Ta ble 2); a neu tral iza tion of the pos i tive charge on He and O and a slight in -crease in the neg a tive charge on F are im me di ately ap par ent; this points to anO–to–He charge-trans fer char ac ter of the spin for bid den sin glet–trip let ex ci ta tion,which also her alds ease of the mol e cule’s dis so ci a tion to He, 3O and F– (ac cord ingto Eq. 4b). In deed, the Con fig u ra tion In ter ac tion (CI) cal cu la tions us ing sin gle ex ci -ta tions and the TD DFT cal cu la tions pre dict that the first ex cited trip let state arisesmostly from elec tron trans fer from the de gen er ate purely O-cen tered P orbitals tothe LUMO (S); rec ol lect LUMO is also O-cen tered but it has some elec tron den sityon He, as well (Fig ure 5).

The na ture of the first ex cited trip let state is fi nally cor rob o rated by anal y sis ofthe spin den sity in the first ver ti cally ex cited trip let state (CCSD(T) re sults, Fig ure 6). The ma jor ity of the un paired elec tron den sity in deed re sides on O (1.73 e) (which in -di cates its near 3O char ac ter) and on He (0.25 e). It is the s He–O bond, the weak estbond of the [OHe…F–] an ion, which is bro ken upon the sin glet–trip let ex ci ta tion.

Hav ing stud ied the [OHe…F–] in de tail, we will now briefly an a lyze two re latedhy po thet i cal an ionic spe cies.

2.6. An ions re lated to [F–…HeO]: [Cl–…HeO] and [HO–…HeO].Metastability of the [F–…OHe] an ion en cour aged us to ex tend the quest for

metastable He-con tain ing an ions to the re lated [Cl–…HeO] and [HO–…HeO] (seesec tion A2 of Ap pen dix).


Fig ure 6. Spin den sity and its Mulliken dis tri bu tion for the low est ver ti cally ex cited trip let state of the

[OHe…F–] an ion; den sity isosurfaces shown at 0.01 e Å–3 (top) and 0.0004 e Å–3 (bot tom).

[Cl–…HeO] turns out to be a lo cal min i mum at the B3LYP, MP2 and CCSD(T)lev els, yield ing no imag i nary vi bra tional modes. Ac cord ing to Mulliken pop u la tionanal y sis, the He atom ac cepts par tial pos i tive charge of 0.22 e (CCSD(T)), sim i larlyas for [F–…OHe]. How ever, the equi lib rium HeO sep a ra tion is 1.226 Å (CCSD(T)),thus over 0.07 Å lon ger than the cor re spond ing value for [F–…HeO]. In con se -quence, the He–O stretch ing fre quency is also smaller, by ca. 30%. Ap par ently, theHe–O bond is much weaker for [Cl–…HeO] than for its lighter homologue. This re -sults in the low est ver ti cally ex cited trip let state be ing lo cated a mere 1.29 eV abovethe bound sin glet. The intersystem cross ing must be much closer to the equi lib riumge om e try of the sin glet state than for [F–…OHe]. This trend is also il lus trated by thelarger pro pen sity of [Cl–…HeO] to wards dis so ci a tion to Cl–, He and 1O; the en ergyof this re ac tion is cal cu lated to be +0.10 eV (CCSD(T)), and thus it is less positivethan for [F–…OHe] (+0.55 eV). With out any doubt, [Cl–…HeO] will be kineticallyless sta ble than [F–…OHe].

The re lated [HO–…HeO] is bound at the DFT and MP2 lev els of the ory, but itdis so ci ates in the CCSD(T) cal cu la tion. We as so ci ate the de creased sta bil ity of[Cl–…HeO] and [HO–…HeO] with re spect to [F–…HeO] with a smaller ca pa bil ity topo lar ize the HeO unit by the larger and softer Cl– and HO– an ions as com pared tosmall and hard ‘point charge-like’ F–.

2.7. Po lar iza tion of the [HeO] unit by hard (Li+, Cu+) and soft (Cs+, NH 4+ ) cat ions.

Sta bi li za tion of the HeO unit via its po lar iza tion by a lo cal charge in[Fd–…Hed+Od–]– sug gests that one might also at tempt to sta bi lize this moi ety bya pos i tive charge placed at the other end of the HeO di pole, [Hed+Od–…Md+]+.How ever, this sur mise proves in cor rect, as our cal cu la tions for M = Li, Cu show.The lin ear HeOLi+ cat ion in its sin glet state tends to dis so ci ate He thus be com inga com plex of Li+ at tached to 1O. Sim i lar be hav iour is seen for the HeOCu+ cat ion.Fail ure to sta bi lize the HeO unit via its po lar iza tion by a cat ion placed in the vi cin ityof O can be at trib uted to: (i) in abil ity of the O cen ter bound to He to fur ther bind a cat -ion (rec ol lect, one S lone pair of O is not oc cu pied and it con sti tutes the LUMO of[F–…OHe]), and (ii) com pe ti tion be tween He0 and Li+ for a weak Lewis base (1O),which must ob vi ously ter mi nate in a with drawal of O from He.

Fail ure to sta bi lize [HeO…M+] com plexes us ing small and hard M+ cat ions,which com pete for 1O with He, has urged us to in ves ti gate anal o gous com plexes formuch larger and softer M+ cat ions, such as Cs+ and NH 4

+ . How ever, it turns out thatthe sit u a tion is not im proved sat is fac to rily. Some of these com plexes are weaklybound in the B3LYP and MP2 cal cu la tions, but they dis so ci ate at better lev els ofthe ory (MP4, CC and CCSD(T)).

2.8. Po lar iza tion of the [HeO] unit by small mol e cules with a large di pole mo ment(HF, LiF, BeO).

And what about the pos si bil ity of sta bi liz ing the HeO unit due to its po lar iza tionby an ad ja cent lo cal di pole mo ment? We have tested this pos si bil ity by op ti miz ingge om e tries of three ad ducts of HeO with small dipolar mol e cules: [HeO…HF],

102 W. Grochala

[HeO…LiF], [HeO…BeO]. It turns out (see Ap pen dix) that [HeO…HF] and[HeO…LiF] are bound at the DFT and MP2 lev els. The cal cu lated HeO dis tance isquite large, 1.382 Å for [HeO…HF], and the ver ti cally ex cited trip let state is lo catedat over 1 eV be low sin glet (MP2 re sults). These fea tures her ald a pos si ble lack ofsta bil ity at better lev els of the ory. In deed, the spe cies stud ied are ei ther mar gin allybound ([HeO…LiF]) or sim ply dis so ci ate at the CCSD(T) level ([HeO…HF]).Re gret ta bly, [HeO…LiF] ex hib its a neg li gi ble bar rier to wards dis so ci a tion, in agree -ment with [29]. Fail ure to sta bi lize the [HeO] unit by an isoelectronic dipolar [HF]unit of com pa ra ble size is es pe cially dis ap point ing.

The case of [HeO…BeO] is still dif fer ent since a com plete trans fer of the O atomto Be is seen lead ing to the for ma tion of the [BeO2] struc tural unit with He weaklybound to Be (see Ap pen dix).

In con clu sion, the He–O bond is ei ther un sta ble or too weak in these spe cies tosur vive for a rea son ably long time, even at very low tem per a tures, and these neu tralsys tems are not metastable.

2.9. Les sons from [F–…HeO] and re lated spe cies: Sum mary.The the o ret i cal stud ies of [F–…HeO] and sev eral re lated spe cies, pre sented in the

pre vi ous sec tions, per mit us to con struct sev eral im por tant gen er al iza tions.(i) [F–…HeO] owes its lo cal mi nim um cha ract er to sub stant ial po lar iza tion of the

[HeO] unit by a ne gat ively char ged F– pla ced oppo site to O. At tempts to po lar izethe [HeO] unit by po sit ively char ged spe cies pla ced in the vi cin ity of O were unsuc -cessf ul, largely due to the ab sence of a lone pair at O which po ints in the direc tionoppo site to He.

(ii) Che mic al bon ding be tween He and O is sub stant ially cova lent and re sults from the2s(He)/2s(O) over lap; the ma tch be tween 2s(He)/2s(F) func tions is poor and theHe–F bond is io nic in cha ract er and much lon ger than the He–O bond.

(iii) The sub stant ial asymm etry of [F–…HeO] ma kes it si mil ar to the isoe lectr onic[F–…HF] unit fo und in so lid ifi ed HF, and also to va rious spe cies of he avier no blega ses, such as e.g. [SbF 6

- …KrF+] and [Sb2F11- …XeF+]. Hy per vale nce of He which

would re sult in two com par able bond lengths, should be avo ided in a suc cessf ulde sign of a can did ate for the first neu tral He-con tai ning mo lec ule.

(iv) The for mal oxi dat ion sta te of he lium may be as sig ned as He2+, which is of co ursefar from any re alis tic char ge po pul ati on; real char ge is pro bab ly 10% of this va lue.In any case, elect rone gat ive He in deed se rves as a Le wis base to wards the elect -ron-poor oxy gen in [F–…HeO].

(v) The He–O bond length and its stre tching frequ ency are va lua ble mar kers of thestrength of He–O bon ding and they are cor rel ated with each other in a mo not onicway, si mil ar to other che mic al bonds. Al though a lar ger set of data is ne eded to va -lid ate the re lat ionsh ip be tween the He–O bond length and the dis soc iati on energy,one in tui tively fe els that the short er He–O bond cor res ponds to a more stron gly bo -und, and also a more ki net ica lly sta ble spe cies. The cry stall ogr aphic, spec tros copic,


ther mod yna mic and ki net ic cri ter ia (bond length, har mon ic frequ ency, dis soc iati onenergy and bar rier for dis soc iati on) are in prin cip le in terc hange able.

(vi) [F–…HeO] owes its me tas table cha ract er to elect ronic cor rel ati on and its cal cul ated mo lec ular pa ram ete rs are extre mely sen sit ive to the extent of cor rel ati on used at va -rious levels of the ory. [F–…OHe] dis soc iates (sin glet sur face, sym met ric stre tchingco ord ina te) by si mult ane ous bre aking of a He–O and He–F bonds. This ma kes[F–…OHe] si mil ar to other stron gly cor rel ated spe cies such as e.g. the Be3 clu ster,which dis soc iates by bre aking all three Be–Be bonds at once [41].

(vii) The DFT and MP2 met hods con tain an in suff ici ent level of elect ronic cor rel ati on tocor rect ly re prod uce the sta bil ity of [F–…HeO] and the re lat ed spe cies, and theyusua lly ove resti ma te sta bil ity. Never thel ess, they are useful in a pre lim ina ry se archfor novel sys tems and may be used to de tect a lo cal mi nim um on the sin glet sur face.

Equipped with this knowl edge we may now search for novel metastable spe cieswhich con tain a He–O bond, and in par tic u lar for neu tral sys tems.

3. Hy po thet i cal salts of [F–…HeO] with cat ions of small Lewis acid ity: Cs+, NH 4+ ,

NMe 4+ .

The fail ure to de tect gen u ine metastability for [HeO…LiF] has pushed us to in -ves ti gate three re lated spe cies, [HeO…CsF], [HeO…NH4F] and [HeO…NMe4F].In do ing so we have been again in spired by the rule of thumb that high ox i da tionstates of chem i cal el e ments (here: he lium) are sta bi lized in a ba sic en vi ron ment.All three flu o ride mol e cules at tached to the [HeO] unit are much stron ger Lewisbases than LiF. One might phrase it dif fer ently: large and soft Cs+, NH 4

+ , and in par -tic u lar a sterically pro tected NMe 4

+ , are much weaker Lewis ac ids than Li+, andthere fore they should do nate F– an ion to the [HeO] unit with more ease. In deed,NMe 4

+ is known as one of the most weakly co or di nat ing cat ions and NMe4F is a ‘flu o -ride superbase’, i.e. a source of ‘na ked’ flu o ride an ion [42].

To our de light, this sim ple strat egy has re sulted in a sig nif i cant sta bi li za tion of[HeO…CsF] and [HeO…NMe4F] ad ducts (see Fig ure 7 and Ta ble 3) as com pared to[HeO…LiF]. [HeO…CsF] is bound at the MP4, CC and CCSD(T) lev els while[HeO…NMe4F] con tains as many as 20 at oms and there fore we have per formed onlythe DFT and MP2 stud ies for this spe cies.

[HeO…CsF] and [HeO…NMe4F] both ex hibit a bent [OHe…F–] unit with theflu o ride an ion shared be tween two acidic spe cies: [HeO] and the counterion (Cs+,NMe 4

+ ). The cal cu lated He–O bond length is lon ger by a mere 0.01–0.02 Å from itsvalue for the na ked [HeO…F–] an ion at the MP2 level. The same re sult is found for[HeO…CsF] at the CCSD(T) level. Since a short He–O bond length is cru cial toachieve a mol e cule’s sta bil ity (see the pre ced ing sec tion), one may an tic i pate that[HeO…CsF] and [HeO…NMe4F] should be less weakly bound than the [F–…OHe]an ion. In deed, the first ex cited trip let state is lo cated at +2.04 eV above the op ti mizedsin glet for [HeO…CsF] (CCSD(T) re sults), and at 3.12 eV for [HeO…NMe4F] (MP2re sults). These num bers are about 1/3 smaller than the cor re spond ing val ues for the[F–…OHe] an ion (2.91 eV CCSD(T), 4.33 eV MP2), again sug gest ing a de creased

104 W. Grochala

sta bil ity of [HeO…CsF] and [HeO…NMe4F] to wards dis so ci a tion via the He–Ostretch ing chan nel, as com pared to the par ent [F–…OHe] an ion. But such is theprice paid by an ionic spe cies of el e ment at its un usu ally high ox i da tion state, if theyare forced to be come neu tral (non-charged).

Sim i larly as for [F–…OHe] (com pare Eq. 4 and Ta ble 2) we have es ti mated theen ergy of dis so ci a tion (Ta ble 3) for three im por tant paths:

[HeO…CsF] ® 1CsOF + He (5a)

[HeO…CsF] ® 3O + CsF + He (5b)

[HeO…CsF] ® 1O + CsF + He (5c)

We have dis carded the path lead ing to ionic prod ucts (Cs+ + OF–) since salts ofhypofluorous acid are sta ble to dis so ci a tion at the CCSD(T) level, de spite an anom a -lous ox i da tion state of O found in HOF and its de riv a tives [43]. For [HeO…NH4F]and [HeO…NMe4F] re ac tions anal o gous to those de scribed by Eq. 5 in volve interalia NH4F or NH4OF and NMe4F or NMe4OF prod ucts; these are best viewed as[NH3…HF], [NH3…HOF], [NMe4…F], and [NMe4…OF], re spec tively.


Fig ure 7. Op ti mized mo lec u lar ge om e try of [HeO…NH4F], [HeO…CsF] and [HeO…NMe4F] mol e -

cules in their bound sin glet state. The CCSD(T) bond length (in Å) is shown above that

of MP2 (in ital ics) and B3LYP (in brack ets). ND = not de ter mined, DIS = dis so ci a tion.

Ta ble 3. The He–O and He–F bond lengths (R/ Å), har monic fre quen cies (n/ cm–1), Mulliken charges onat oms (q/ e), the rel a tive en er gies of the first ver ti cally ex cited trip let state vs. the op ti mized sin gletstate (3E–1E/ eV), and en ergy of [HeO…CsF] (CS), [HeO…NMe4F] and [HeO…NH4F] (CS) withre spect to three dif fer ent sets of prod ucts, as ob tained with MP2, MP4, CC, CCSD(T) and DFTmeth ods. En ergy dif fer ences are given with out ZPE and BSSE cor rec tions. ND = not de ter mined.DIS = dis so ci a tion.

[HeO…CsF] MP2 MP4 CC CCSD(T) B3LYP

R(He–O) 1.319 1.131 1.145 1.162 1.208

R(He…F) 1.738 1.717 1.864 1.752 1.683

nstr(He–O) 375 1296 1164 1117 1104

q(He) +0.258 +0.229 +0.275 +0.217 +0.215

q(O) –0.298 –0.273 –0.308 –0.251 –0.410

q(Cs) +0.936 +0.936 +0.934 +0.934 +0.921

q(F) –0.896 –0.893 –0.901 –0.901 –0.726

(3E–1E) [eV] +3.65 +2.94 +2.29 +2.04 +2.01#

(a) E vs. 1He, 1CsOF +2.62 +2.60 +2.46 +2.55 +2.20#

(b) E vs. 1He, 3O, CsF +2.26 +2.10 +2.36 +2.10 +1.37

(c) E vs. 1He, 1O, CsF –0.68 –0.61 –0.11 –0.19 –1.38

[HeO…NH4F] MP2 MP4 CC CCSD(T) B3LYP

R(He–O) 1.223 DIS DIS DIS 1.222

R(He…F) 2.128 DIS DIS DIS 2.128

nstr(He–O) 656 DIS DIS DIS 895

q(He) +0.144 DIS DIS DIS +0.217

q(O) –0.134 DIS DIS DIS –0.220

q(NH4) +0.421 DIS DIS DIS +0.421

q(F) –0.431 DIS DIS DIS –0.418

(3E–1E) [eV] +0.50 DIS DIS DIS +0.89&

(a) E vs. 1He, 1[NH3… HOF] +3.03 DIS DIS DIS +2.73

(b) E vs. 1He, 3O, NH4F +2.81 DIS DIS DIS +2.18

(c) E vs. 1He, 1O, NH4F –0.14 DIS DIS DIS –0.57

[HeO…NMe4F] MP2 MP4 CC CCSD(T) B3LYP

R(He–O) 1.096 ND ND ND 1.177

R(He…F) 1.823 ND ND ND 1.749

nstr(He–O) ND ND ND ND 1137

q(He) +0.228 ND ND ND +0.213

q(O) –0.229 ND ND ND –0.304

q(NMe4) +0.824 ND ND ND +0.775

q(F) –0.825 ND ND ND –0.684

(3E–1E) [eV] +3.12 ND ND ND +1.26@

(a) E vs. 1He, 1NMe4OF +2.64 ND ND ND +3.16

(b) E vs. 1He, 3O, NMe4F +2.48 ND ND ND +2.61

(c) E vs. 1He, 1O, NMe4F –0.46 ND ND ND –0.14# TD cal cu la tion yields the first ver ti cally ex cited (trip let) state at +1.56 eV.& TD cal cu la tion yields the first ver ti cally ex cited (trip let) state at –0.81 eV.@ TD cal cu la tion yields the first ver ti cally ex cited (trip let) state at +1.68 eV.

106 W. Grochala

The cal cu lated en ergy of dis so ci a tion at the sin glet sur face along the He–Ostretch ing co or di nate equals to 0.19 eV for [HeO…CsF] as com pared to 0.55 eV for[F–…OHe] (CCSD(T) re sults). The first ver ti cally ex cited trip let state is at +2.04 eVfor [HeO…CsF] as com pared to 2.91 eV for [F–…OHe] (CCSD(T) re sults). Both fea -tures in di cate that the intersystem cross ing for [HeO..CsF] is at R(He–O) value which is closer to the equi lib rium sep a ra tion than for [F–…OHe]. The en ergy of dis so ci a tion cal cu lated for [HeO…CsF] at the sin glet sur face is small as the po ten tial en ergy wellmay ac com mo date about five har monic sym met ric stretch ing modes (the cor re spond -ing value for [F–…OHe] is four teen). In ad di tion, the bend ing chan nel also of fersa fac ile path for de com po si tion, es pe cially that the F–He–O unit is bent. In ser tion ofO into the long and ionic CsF bond with the for ma tion of CsOF should be rel a tivelyeasy, since the as so ci ated ge om e try re ar range ment is not large; note, the CsOF mol e -cule is roughly T-shaped, with two large Cs…O and Cs…F sep a ra tions, sim i larly asseen for [HeO…CsF]. These fea tures ren der [HeO…CsF] more prone to dis so ci a tionthan its par ent an ion, [F–…OHe], but the mol e cule might be suf fi ciently long-lived to be de tect able at very low tem per a tures. Im por tantly, [HeO…CsF] does not con tainlight H and there fore it should be much less sus cep ti ble to tun nel ing than e.g. HHeF.In sec tion A5 of the Ap pen dix we have listed the cal cu lated vi bra tional fre quen ciesof the [HeO…CsF] adduct, which might help to iden tify this spe cies if its syn the sissuc ceeds.

The cal cu lated en ergy of dis so ci a tion at the sin glet sur face along the He–Ostretch ing co or di nate is 0.46 eV for [HeO…NMe4F] as com pared to 1.05 eV for[F–…OHe] (MP2 re sults). Also this mol e cule seems to be a vi a ble can di date for ametastable spe cies. Re gret ta bly, we could not per form stud ies of this large sys tem atbetter lev els of the ory. One nat u rally ex pects that [HeO…NMe4F] should be moresta ble than [HeO…CsF] be cause the NMe 4

+ cat ion co or di nates an ions much moreweakly than Cs+.

[HeO…NH4F] is dis tinctly dif fer ent from [HeO…NMe4F], and it breaks thetrend of sta bil i ties ex pected from the rank ing of flu o ride ab strac tion ca pa bil ity ofCs+, NH 4

+ and NMe 4+ cat ions (con sis tent with their Lewis acid ity: Cs+ > NH 4

+ >NMe 4

+ , as known from the solid state). [HeO…NH4F] is a lo cal min i mum at theB3LYP and MP2 level but it is not bound at MP4, CC and CCSD(T) lev els. The rea son for this is in the na ture of the [NH4F] moi ety, which is not ionic, but in stead ex hib its ahy dro gen bond, [NH3…HF]. This fea ture largely re duces the di pole mo ment of the[NH4F] unit, which in turn proves in suf fi cient to po lar ize and sta bi lize the fragile[HeO] moi ety [44].

In con clu sion of this sec tion, [HeO…NMe4F] and [HeO…CsF] ad ducts are thefirst can di dates for weakly bound neu tral spe cies, which con tain chem i cally boundHe and might be metastable at very low tem per a tures. We are now in prog ress of cal -cu lat ing en ergy bar ri ers for dis so ci a tion via the bend ing chan nel, as well as the lo ca -tion of the sin glet/trip let intersystem cross ing, to better quan tify the metastability of[HeO…CsF] and [HeO…NMe4F] and to es ti mate their life time at low tem per a tures.


4. Hy po thet i cal [HeO][BaO] adduct.The [F–…HeO] an ion is isoelectronic to a hy po thet i cal [O2–…HeO] dianion.

While iso lated [O2–…HeO] is un sta ble due to a spon ta ne ous elec tron loss, it is of in -ter est if its neu tral salts with dou bly pos i tively charged cat ions could con sti tute realmin ima at the PES. Large and soft Ba2+ is the most weakly co or di nat ing amongst allatomic dications and has been cho sen for this study. Un for tu nately, the CCSD(T) cal -cu la tions show that a hy po thet i cal [HeO][BaO] adduct in its sin glet state spon ta ne -ously dis so ci ates to He, 1O and BaO mol e cule and no gen u ine min i mum could bede tected which ex hib its chem i cal bond ing of O to He. Thus [HeO][BaO] shares thefate of [HeO][BeO] (see sec tion 2.8). In view of this find ing, pos i tively charged ad -ducts [HeO][CsO+] and [HeO][NMe4O+] were not scru ti nized.

5. Mu tual po lar iza tion of (HeO) sub units within the (HeO)n clus ters.The suc cess ful sta bi li za tion of the [HeO] unit via its po lar iza tion by F–, CsF and

NMe4F poses an in ter est ing ques tion: could a sim i lar sta bi li za tion be achieved viamu tual po lar iza tion of a larger set of [HeO] units? We have ad dressed this ques tionby per form ing cal cu la tions for dimers, tri mers, tetramers and hexamers of [HeO] atthe DFT and MP2 lev els (Fig ure 8 and Ap pen dix).

108 W. Grochala

Fig ure 8. Op ti mized mo lec u lar ge om e try of the (HeO)n clus ters in their low est sin glet state – com par i -

son of the B3LYP and MP2 re sults. The He–O bond lengths and sec ond ary con tact are shown

in Å . Note the ‘po lar iza tion ca tas tro phe’ which leads to the chem i cal bond for ma tion for n = 2

at the B3LYP level and for n = 4 at the MP2 one. Com pare sec tion A4 of Ap pen dix.

It turns out that (HeO)2 and larger clus ters are bound at the DFT level, in con trastto the HeO mono mer. MP2 cal cu la tions, how ever, in di cate for ma tion of weak He–Obonds (1.319 Å) for (HeO)4, and even shorter ones (1.249 Å) for (HeO)6, while thesmaller clus ters do not cor re spond to chem i cally mean ing ful min ima. In other words,the ‘po lar iza tion ca tas tro phe’ oc curs for 3 < n < 4 with MP2. Clearly, both meth odspre dict that dra matic co op er a tive (many-body) ef fects are op er a tive for (HeO)n. Thestrength of these ef fects is not suf fi cient, though, since the low est ver ti cally ex citedtrip let state is about 0.5 eV be low the sin glet, while higher multiplets cor re spond ingto si mul ta neous ex ci ta tion at sev eral HeO units are at even lower en er gies. The cal cu -lated en ergy of dis so ci a tion of (HeO)4 into four He at oms and four 3O at oms ap -proaches 12 eV (MP2) while en ergy of de com po si tion into four He at oms and two 3O2

mol e cules is close to 20 eV (sic!). If metastable, (HeO)4, would be an ex cel lent ex plo -sive. How ever, this proves not to be the case. Both DFT and MP2 sig nif i cantly over -es ti mate the strength of He–O bond ing, and there fore, it is not sur pris ing that (HeO)4

and (HeO)6 oli go mers are not bound at the MP4, CC and CCSD(T) lev els.It would be very in ter est ing to the o ret i cally study much larger clus ters com posed

of [HeO] units as well as an in fi nitely large pe ri odic (HeO)¥ sys tem in the solid state.How ever, we doubt if mu tual po lar iza tion of the [HeO] units will prove suf fi cientlylarge to achieve rea son ably short He–O bond lengths (< 1.2 Å) and in duce meta -stability of higher oli go mers, or of the cor re spond ing solid. Po lar iza tion ef fectstend to ex po nen tially sat u rate at a rel a tively small sys tem size, so that the ben e fi cialef fects of at tach ing one more (HeO) unit can not be very large for a mod er ate-size(HeO)n clus ter. In other words, the ‘po lar iza tion ca tas tro phe’ may be shifted to ei thervery large val ues of n, or not take place at all, at better lev els of the ory. Nev er the less,there is an in tel lec tual open ing here, since an ex ter nal elec tric field should be able togreatly im prove the sta bil ity of (HeO)n oli go mers. Model stud ies of one He and onesin glet ox y gen atom, 1O, and of larger as sem blies of such atomic pairs, em bed ded ingi ant ex ter nal elec tric fields, are greatly en cour aged; dra matic be hav iour at ‘crit i cal’ex ter nal field, and even ferro elec tric or der ing of (HeO) units, may be an tic i pated.

Sub ject ing a sys tem of HeO com po si tion to ul tra high ex ter nal pres sures is an -other prom is ing path of re search [5,21]. In ter atomic sep a ra tions de crease at highpres sures and atomic va lence orbitals of ad ja cent at oms are firmly squeezed into onean other. This in duces a ten dency for pair ing up of for merly un bound elec trons andthus sta bi lizes chem i cal bond (i.e. a shared elec tron pair) by push ing higher multi -plets up in enthalpy. This trend is most pro nounced for main group el e ments, but itmay hap pen even for tran si tion met als with ‘non-mag netic iron’ at p > 15 GPa as oneim pres sive ex am ple [45]. Since mo lar vol ume de creases as a solid is sub jected tohigher pres sures, dissociative chan nels re lated to bond stretch ing and (less so) bondbend ing are usu ally blocked. Thus, high pres sures should, in prin ci ple, sta bi lizea solid com posed of sin glet HeO mol e cules, es pe cially if they are ar ranged in a ferro -elec tric fash ion. There is just the mat ter of how large the pres sures needed are toachieve ther mo dy namic, or at least ki netic sta bil ity, of he lium ox ide with re spect tophase sep a ra tion into com pressed he lium and poly meric ox y gen.


6. Chem i cal bond ing to he lium: brief sum mary.In the pre vi ous sec tions we have de scribed the re sults of a sys tem atic the o ret i cal

study of var i ous spe cies con tain ing chem i cally bound He, with an em pha sis on thosewhich ex hibit a He–O bond. We have been able to pro pose two neu tral sys tems,[HeO…CsF] and [HeO…NMe4F], which con tain soft, weakly co or di nat ing cat ions(Cs+, NMe 4

+ ) at tached to the [F–…HeO] an ion (the lat ter is it self metastable). Bothneu tral spe cies in their bound sin glet state ex hibit a short He–O bond of 1.10–1.16 Åand they re side within a po ten tial en ergy well, sep a rated by en ergy bar ri ers from themore fa voured min ima. The most sta ble min i mum cor re sponds to an iso lated He atom and hypofluorate (OF–) of Cs+ or NMe 4

+ , re spec tively, which may be reached viabend ing of the [F– …HeO] an ion; the sec ond most sta ble min i mum cor re sponds toan iso lated He atom, 3O and flu o ride (F–) of Cs+ or of NMe 4

+ , and it may be reachedvia sym met ric stretch ing of the F–He–O moi ety to the point where intersystem cross -ing oc curs of the sin glet and trip let sur faces. Anal o gous dis so ci a tion of [HeO…CsF]and [HeO…NMe4F] at a sin glet sur face lead ing to He, 1O and flu o ride (F–) of Cs+ orof NMe 4

+ , re quires en ergy of the or der of 0.2–0.5 eV. The re lated [HeO…NH4F]spe cies is not sta ble and it spon ta ne ously dis so ci ates at the sin glet sur face.

En ergy of dis so ci a tion of the [HeO…X]q spe cies (where q is the charge) atthe sin glet sur face, lead ing to He, 1O and the re main ing prod uct:

[HeO…X]q ® 1O + 1He + 1Xq (6)

is an im por tant in di ca tor of the strength of the He–O bond ing. If the dis so ci a tionen ergy, Edis, is pos i tive, then the sys tem can be con sid ered metastable and onemay at tempt to quan tify how large the bar ri ers for dis so ci a tion are via F–He–Obend ing and via F–He–O sym met ric stretch ing (intersystem cross ing). But ifEdis is neg a tive, the sys tem is not bound at all.

In Ta ble 4 we have ar ranged twenty sys tems which con tain a He–O bond (cat ions, an ions, and neu tral spe cies) with re spect to the value of Edis (cal cu lated at theCCSD(T) level, and with out the ZPE cor rec tion). We have la beled them as ‘strongly’, ‘mod er ately’, ‘weakly’, ‘mar gin ally’ and ‘non-bound’ us ing the value of Edis as thesole cri te rion for la bel ing. The list of [HeO] spe cies is sup ple mented by [F–…HeS](with Edis de fined in an anal o gous way as for [F–…HeO]) and by ten other He-con -tain ing sys tems, for which Edis is de fined sim ply as the en ergy of dis so ci a tion lead ingto one He atom and the re main ing prod uct:n[HeX]q ® 1He + nXq (7)

Spe cies con sid ered here are al ways in their sin glet state (n = 1) ex cept for HeO+·

(dou blet).Sev eral im por tant trends emerge from anal y sis of Ta ble 4 and of Edis val ues.

The first one:[F–…HeO] (0.55 eV) > [Cl–…HeO] (0.10 eV) > [HO–…HeO] (spon ta ne ous dis -so ci a tion),il lus trates the ex tent of sta bi li za tion of the [HeO] moi ety due to its po lar iza tion bysmall an ions (F–, Cl–, HO–). An other im por tant re la tion ship:

110 W. Grochala

[F–…HeO] (0.55 eV) > [NMe4F…HeO] (0.46 eV) > [CsF…HeO] (0.19 eV) >[LiF…HeO] ~ [NH4F…HeO] (spon ta ne ous dis so ci a tion),re flects the ef fect of the in creas ing acid ity of the MF spe cies on the sta bil ity of[HeO…MF] ad ducts (‘salts’ of the [F–…HeO] an ion).

These trends, con sis tent with chem i cal in tu ition, were in fact used in our at temptto de sign the neu tral spe cies con tain ing he lium chem i cally bound to ox y gen.

Ta ble 4. La bel ing of a va ri ety of spe cies which con tain chem i cally bound He (cat ions, an ions and neu tralspe cies) as strongly, mod er ately, weakly, mar gin ally bound and non-bound sys tems. Pa ram e ter Edis

has been used as the sole cri te rion for la bel ing (see text for def i ni tion).

cat ions an ions neu tral spe cies

strongly boundEdis > 1 eV

HeH+, HeF+ —

mod er ately bound1 eV > Edis > 0.5 eV

HeBe2+, He2Be2+

He3Be2+, He4Be2+[F–…HeO]

[F–…HeBN] $ —

weakly bound0.5 eV > Edis > 0.0 eV

HeO+ · # [Cl–…HeO][F–…HeS] @

[HeO…NMe4F] &

[HeO…CsF]

mar gin ally boundEdis < 0.0 eV, bar rier

? ? [HeO…LiF]*

non-bound(spon ta ne ous dis so ci a tion)

HeO…NH4+

HeO…Cs+

HeO…Li+

HeO…Cu+

[HO–…HeO][F–…HeNH][F–…HeNF][F–…HeClF]

[HeO…BeO] [HeO…BaO][HeO…HF] [HeO…(HF)2]

[(HeO)2…HF] [HeO…NH4F]FHeOH, FHeOF, FOHeOF

$ Dis so ci a tion to F–, He and 1BN; 1.05 eV ob tained with Dun ning’s ba sis set [30].@ Dis so ci a tion to F–, He and 1S; com pare [31].# Ex cep tion ally, Edis for this rad i cal is de fined for the dou blet sur face (lead ing to He and 2O+·).& Edis should fall be tween +0.55 eV (for [F–…HeO]) and +0.19 eV (for [CsF…HeO]) ac cord ing to CCSD(T) cal cu la tions; here we used the +0.46 eV value de rived at the MP2 level.* Re sults from [29]; our cal cu la tions yield dis so ci a tion, due to dif fer ent ba sis set used.

7. Re marks on the po si tion of he lium in the Grand Pe ri odic Ta ble of the Chem i calEl e ments.

The pe ri odic law of chem is try rec og nizes that many prop er ties of the chem i cal el -e ments are pe ri odic func tions of their atomic num ber. The Pe ri odic Ta ble is an ar -range ment of the chem i cal el e ments or dered by atomic num ber in col umns (groups)and rows (pe ri ods) pre sented so as to em pha size their pe ri odic prop er ties. Im por -tantly, monotonic vari a tion is seen for the ma jor ity of physicochemical prop er ties asone goes down the group, and this trend is bent in sev eral cases for higher pe ri ods dueto strong rel a tiv is tic ef fects.

As sign ment of the light est el e ment, H, as a Group 1 mem ber, has been quite trou -ble some (Fig ure 9). It is partly be cause dif fer ences of prop er ties be tween el e ments ofthe first and sec ond pe riod are much larger than those of the sec ond and third pe riod.But the story is much more com pli cated since the H atom (i) ex hib its huge ion iza tionpo ten tial and a sub stan tial elec tron af fin ity, (ii) it is a di atomic gas at am bi ent con di -tions, which can not be pushed into the me tal lic state as a solid; both fea tures are un -usual for a typ i cal al kali metal. Con se quently, H has some times been placed above F,


as a mem ber of Group 17; in deed, the ra dii of H– and F– an ions are sim i lar and manyionic and co va lent hy drides and flu o rides are isostructural. But hy dro gen is still dif -fer ent from halo gens be cause its cat ion (H+) is very fre quently found (in con trast to,say, F+) due to its sub stan tial sta bi li za tion by sur round ing Lewis bases. The unique -ness of H has prompted the In ter na tional Un ion of Pure and Ap plied Chem is try(IUPAC) to as sign it to a sep a rate ‘Group 0’.

And this leaves hy dro gen’s Pe riod 1 sib ling, he lium, alone and still re sid ing in the‘no ble gas’ fam ily.

Yet the par a digm of the ‘no bil ity’ of the Group 18 el e ments no lon ger holds.These monatomic gases – es pe cially the lighter ones – are ad mit tedly re sis tant to -wards chem i cal bond for ma tion, but they are not com pletely in ert. For ma tion ofneu tral mol e cules which con tain the rare gas el e ments has al ways been viewed asa break through. So, Xe and Kr lost their no bil ity in the 60’s of the last cen tury [16,17], and Ar in 2000 [15], while in this work we have sug gested the can di dates fora metastable neu tral spe cies con tain ing He chem i cally bound to O. Yet there is stilla puz zle re lated to the re main ing rare gas, Ne. Our cal cu la tions show that in all casesde scribed in this work, wher ever for ma tion of a chem i cal bond to he lium has beensuc cess ful, we could not achieve sta bil ity of an anal o gous mol e cule con tain ing Ne.Thus, [F–…NeO], [Cl–…NeO], [NeO…CsF], [NeO…NMe4F], all spon ta ne ouslydis so ci ate, and the lo cal min i mum at the sin glet sur face can not be de tected. Is neonac tu ally more ‘in ert’ than he lium…? We note that other au thors have failed to de tectlo cal min ima for HNeF [18,19], [F–…NeO] [29], [F–…NeS] [31], but they have cho -sen not to an a lyze the rea sons for this un usual find ing. [F–…NeBN], with its Edis of

112 W. Grochala

Fig ure 9. Four pos si ble po si tions of He in the Pe ri odic Ta ble of Chem i cal El e ments: (a) clas si cal ver sion

plac ing H in Group 1 and He in Group 18; (b) al ter na tive ver sion, which em pha sizes sim i lar ity

of H to halo gens; (c) ver sion plac ing He out of the no ble gas group, close to H and si mul ta -

neously above Be (and not above Ne); (d) IUPAC-supported ver sion plac ing H in a dis tinct

group No. 0, while He stays in Group 18. Our re sults sup port ver sion (c). Com pare also sec -

tions A6 and A7 of Ap pen dix.

0.49 eV [30] – again much smaller than the cor re spond ing value for the anal o gous Hespe cies (1.05 eV) – is the only metastable an ion of Ne pre dicted so far. But no neu tralmol e cules con tain ing Ne have been pre dicted to date. Thus, why is neon so stub -bornly in ert, while he lium could form short- or even mod er ately-long lived neu tralmol e cules?

Tak ing a look at the en ergy of the va lence atomic orbitals – based on ex per i men tal val ues of the first ion iza tion po ten tial and as sum ing the ap pli ca bil ity of Koopman’sthe o rem – for H, Li, Na, He, Be, Mg, F, Cl, Ar and Ne (Fig ure 10), one may im me di -ately no tice that the en ergy of 2s(He) is more neg a tive than that of 2p(Ne). The factthat the 2p(Ne) set ap proaches 2p(F) sug gests an en hanced ca pa bil ity of Ne withre spect to He for chem i cal bond for ma tion to F. Sur pris ingly, our the o ret i cal eval -u a tions led to a smaller dis so ci a tion en ergy (with out ZPE cor rec tion) for NeF+

(1.61 eV) than for HeF+ (2.02 eV), in agree ment with the lit er a ture [46,47]. The in -trigu ing be hav iour of Ne breaks the monotonic trend which is ex pected for all NgF+

con nec tions and sug gests a cer tain de gree of dis sim i lar ity of He to the heavier mem -bers of Group 18. The dis tinct char ac ter of He is fur ther sup ported by its mod er ate af -fin ity to ox y gen (as de scribed in pre ced ing sections), which is not the case for Ne.

If one ac cepts the fact that He should be found at the right side of H in the Pe ri odicTa ble – by anal ogy to all other pairs of el e ments of the same Pe riod, which dif fer byone elec tron – then one could ei ther as sign H to Group 1 and He to Group 2, or al ter na -tively H to Group 17 and He to Group 18. How ever, the lat ter as sign ment bends an -other monotonic trend, namely that of ion iza tion po ten tials of Group 17 el e ments(Fig ure 10). H(1s) falls in be tween Cl(2p) and Br(3p) rather than fall ing be low F(2p),which would be ex pected if H gen u inely be longed to Group 17. It thus seems that thepo si tion ing of H to Group 1 and si mul ta neously of He to Group 2, of fers the only so lu -tion to keep log i cal monotonic trends pre served of chem i cal prop er ties as one goesdown any main Group of the Pe ri odic Ta ble. Ours is by no means the first sug ges tionof this type; cer tain ver sions of the Pe ri odic Ta ble in deed place He right aboveBe [48]. Re mark ably, Bent [49] and Scerri [50] have been ad vo cat ing for yearsthat He should be placed in Group 2. In ter est ingly, the [F–…BeO] an ion bears somere sem blance to asym met ric [F–…HeO] since the cal cu lated Be–O sep a ra tion isshorter than the Be–F one (see sec tion A6 of Ap pen dix), de spite the fact that ionicra dius of ox ide an ion is nom i nally larger than that of the flu o ride an ion.

It is not the pur pose of this work to list the ex haus tive list of pros and cons forand against plac ing He in Group 2 in stead in Group 18. How ever, hav ing in mind im -por tant fea tures of He and Ne, we feel that as sign ment of He to Group 18 is equallyun just as putt ing H into Group 17. If the unique ness of H (and of He!) is to be fur therem pha sized, then it is ad vis able to in tro duce He into a sep a rate block of the Pe ri odicTa ble, now called Group 0. Group 0 would then con sist of two el e ments, H and Heside by side (0A and 0B ?).

Im por tantly for the search for novel spe cies which con tain chem i cally boundlight ‘no ble’ gases, the shift of He to Group 0 (or Group 2) ren ders Ne the most in ertel e ment of the trun cated Group 18, and also in the ab so lute sense. Our prop o si tion of


the neu tral spe cies which con tains chem i cally bound He, re quired some con cep tualwork, but it seems that the o ret i cal pre dic tion and suc cess ful syn the sis of the firstchem i cally bound Ne spe cies may be an even harder nut to crack.

CON CLU SIONS AND PROS PECT

We have con ducted a the o ret i cal study of a va ri ety of hy po thet i cal spe cies con -tain ing chem i cally bound He. Qual i ta tive anal y sis of bond ing in the [F–…HeO] an -ion and of the rea sons for its sta bil ity has led us to two neu tral spe cies, (HeO)(CsF)and (HeO)(NMe4F). These are the first can di dates for a gen u inely metastable neu tralmol e cule con tain ing the He–O bond. The big chal lenge is to syn the size these ex oticmol e cules us ing low tem per a ture ma trix iso la tion tech niques. Re ac tion path waysto wards (HeO)(CsF) and (HeO)(NMe4F) are not straight for ward. Per haps, one couldde posit CsF or NMe4F mol e cules in the he lium ma trix, and at tack them by in-situgen er ated ex cited 1O at oms. If clus ter ing is pre vented of flu o ride mol e cules intolarger ag gre gates, such as (CsF)n, and if iso la tion of re ac tive 1O at oms from otherspe cies of the same type is achieved, chances ex ist for a con certed re ac tion lead ingto the de sired prod uct. How ever, if a CsF (or NMe4F) mol e cule first re acts with 1Oyield ing the most sta ble CsOF (or NMe4OF) prod uct, then the de sired re ac tion willnot take place.

Anal y sis of var i ous hy po thet i cal mol e cules con tain ing He and of the or der ing ofatomic va lence orbitals of chem i cal el e ments leads us to con clude that he lium should

114 W. Grochala

Fig ure 10. En ergy of the va lence atomic orbitals (based on ex per i men tal val ues of the first ion iza tion

po ten tial) for ten Group 1 and Group 17 el e ments: H, Li, Na, He, Be, Mg, F, Cl, Ar and Ne.

be placed in Group 2 of the Pe ri odic Ta ble of El e ments, i.e. above Be and on the rightof H. Neon is the most in ert amongst rare gases, and it still pre serves its no bil ity;there are no pre dic tions of neu tral spe cies which con tain chem i cally bound Ne [51].

In forth com ing works we will an a lyze the pros pects for sta bi liz ing the [HeO] unit as a dis tinct mol e cule in the sin glet state, ei ther chemisorbed at se lected ferro elec tricsur faces of ionic crys tals, at tached to se lected dipolar mol e cules, em bed ded in ferro -elec tric mo lec u lar cav i ties or con tained in other an ions than those stud ied in thiswork. We will also ex plore the pos si bil i ties of syn the siz ing novel bi nary solid[HeO]¥ at ul tra-high pres sures.

Ac knowl edg ments

The con tin u ing sup port of ICM and of the Fac ulty of Chem is try (The Uni ver sity of War saw) is grate -fully ap pre ci ated. Cal cu la tions were per formed on the ma chines of the ICM super com puter cen ter us ingGaussi an ’03. The au thor would like to thank to Prof. Roald Hoffmann (Cor nell Univ., USA) for sug gest ingref er ences to early the o ret i cal works on He-con tain ing cat ions and to Prof. Pekka Pyykkö for var i ous valu ablesug ges tions. I am very grate ful to Mr. An drew James Churchard M.Res. for care ful proof read ing. My spe cialthanks go to Jan Lundell (Hel sinki, Fin land) who has un der taken the ef fort to visit our lab o ra tory in War sawto dis cuss the hy po thet i cal XHeOF spe cies (X = H, F, OF) [32].

Ap pen dixA1. Com plexes of He and mul ti ply charged metal cat ions: DFT and CCSD(T )re sults.

Fol low ing the anal ogy be tween He ® H+ and Xe ® Hg2+ (see In tro duc tion), onemight at tempt to ex tend the chem is try of he lium to highly charged cationic com -plexes, such as those of Ag2+·, Be2+, Al3+, Sc3+ (Fig ure A1 and Ta ble A1) etc. Allthese spe cies turn out to be lo cal min ima in the B3LYP cal cu la tions, yield ing noimag i nary vi bra tional modes. Ac cord ing to Mulliken pop u la tion anal y sis, He at omsac cept par tial pos i tive charge of 0.15 e (Ag2+·He4) to 0.22 e (Be2+He4). The APTanal y sis [52] yields smaller charge val ues of the or der of +0.03 to +0.07 e. In the caseof the only rad i cal cat ion stud ied, Ag2+·He4, the un shared elec tron (spin) den sity re -sides largely on sil ver (0.87 e), leav ing a neg li gi ble share on he lium (0.03 e) (Mul -liken). Clearly, He at oms are suf fi ciently re sis tant to wards ox i da tion to with stand thepres ence of a mul ti ply charged cat ion (even the enor mously ox i diz ing na ked Ag2+·

[53]) in its vi cin ity; not many other neu tral lig ands are ca pa ble of do ing the same [54]. We note that sim i lar com plexes as those pro posed here, which con tain neu tral Arat oms as lig ands (no ta bly AgAr 4

2+ ), have been ob served by ex per i ment [55].


Fig ure A1. Il lus tra tion of He act ing as a ligand to wards very strong Lewis ac ids, mul ti ply charged metal

cat ions: Be2+, Ag2+·, Al3+ and Sc3+. Re sults of the B3LYP cal cu la tions.

Ta ble A1. The cal cu lated metal–he lium bond lengths, R(M–He), and the larg est and the small est har monicfre quency, nmax and nmin, re spec tively, for four com plexes of He with mul ti ply charged metalcat ions.

Be2+He4 (Td) Ag2+ ·He4 (D4h) Al3+He6 (Oh) Sc3+He6 (Ci) *

R(M–He) /Å 1.475 2.044 1.739 2.055

nmax / cm–1 800 (T2) 438 (Eu) 735 (Eu) 518 (Au)

nmin / cm–1 179 (E) 155 (B2u) 176 (B2u) 35 (Au)

* de vi a tion from Oh sym me try is very small (0.001 Å) and the cor rect sym me try as sess ment ne ces si tates use of more ad vanced the o ret i cal tools.

Cal cu la tions were also per formed at the CCSD(T) level for Be2+He (C¥v),Be2+He2 (D¥h), Be2+He3 (C3v) and Be2+He4 (Td). The op ti mized He–Be bondlengths are 1.455 Å, 1.458 Å, 1.468 Å, and 1.484 Å, re spec tively, the larg est Be–Hestretch ing fre quency is 848 cm–1, 958 cm–1, 856 cm–1, and 784 cm–1, re spec tively,and the dis so ci a tion en ergy of one He atom is 0.85 eV, 0.84 eV, 0.70 eV, and 0.63 eV,re spec tively. No imag i nary fre quen cies have been de tected for these spe cies.It is in ter est ing that the strength of the Be–He bond ing de creases rather slowly within creas ing n. It can not be ex cluded that some of He-con tain ing cat ions stud ied heremight be metastable in pres ence of weakly co or di nat ing an ions, such as for ex am pleSb2F11

1- , or Sb3F161- .

A2. Hy po thet i cal [Cl–…HeO] and [HO–…HeO] an ions (Fig ure A2 and Ta ble A2).

Ta ble A2. The cal cu lated ox y gen–he lium and el e ment–he lium bond lengths, R(O–He) and R(X–He), re -spec tively, the har monic fre quen cies, n, the Mulliken atomic charges on at oms, q, the ver ti cal en -ergy dif fer ence be tween the first ex cited trip let and the low est sin glet state, 3E–1E, and en ergy withre spect to three dif fer ent sets of prod ucts, for two an ionic spe cies [X–…HeO], where X = Cl, HO.Re sults of the B3LYP, MP2 and CCSD(T) cal cu la tions are com pared.

[Cl–…HeO] MP2 CCSDT B3LYP [HO–…HeO] # MP2 B3LYP

R(O–He) /Å 1.108 1.226 1.299 R(O–He) /Å 1.092 1.301

R(X–He) /Å 2.236 2.224 2.167 R(X–He) /Å 1.642 1.726

nO–He / cm–1 1281 751 814 nO–He / cm–1 1402 1043

nX–He / cm–1 165 158 168 nX–He / cm–1 288, 370 223

nOHeX / cm–1 320 284 282 nOHeX / cm–1 507, 644 305, 383

q(He) /e 0.251 0.199 0.193 q(He) /e +0.303 +0.176

q(O) /e –0.276 –0.215 –0.427 q(O) /e –0.394 –0.551

q(X) /e –0.975 –0.984 –0.766 q(X) /e –0.909 –0.625

(3E–1E) [eV] +2.87 +1.29 +0.83 (3E–1E) [eV] +4.17 +1.36

(a) DE vs. He, 1OCl–1 +3.27 +2.96 +2.50 (a) DE vs. He, 1OOH–1 +3.60 +2.80

(b) DE vs. He, 3O, 1Cl–1 +2.38 +2.10 +1.43 (b) DE vs. He, 3O, 1OH–1 +1.82 +0.68

(c) DE vs. He, 1O, 1Cl–1 –0.56 –0.19 –1.32 (c) DE vs. He, 1O, 1OH–1 –1.12 –2.07

# dis so ci a tion at the CCSD(T) level.

116 W. Grochala

A3. Mo lec u lar ge om e try of 1(HeO)(AB) (AB = HF, LiF, BeO) as op ti mized atthe B3LYP and MP2 level (Fig ure A3 and Ta ble A3).

Ta ble A3. The cal cu lated O–He and H/Li–F bond lengths, R(O–He) and R(H/Li–F), re spec tively, thehar monic fre quen cies, nstr(He–O), nstr(H/Li–F) and nmin, the Mulliken atomic charges on at oms, q,the ver ti cal en ergy dif fer ence be tween the first ex cited trip let and the low est sin glet state, 3E–1E,the en ergy of the first ex cited trip let state ac cord ing to CIS and TD cal cu la tions, E(1st exc trip),and en ergy of three dif fer ent de com po si tion re ac tions, for two neu tral spe cies [HeO…MF], whereM = H, Li. Re sults of the B3LYP and MP2 cal cu la tions are com pared.

[HeO…MF] (CS) M=H # M=Li #

MP2 B3LYP MP2 B3LYP

R(He–O) 1.382 1.273 1.150 1.225

R(H/Li–F) 0.922 0.932 1.636 1.666

nstr(He–O) 228 719 990 895

nstr(H/Li–F) 4080 3867 809 739

nmin 84 85 177 270

q(He) /e +0.080 +0.192 +0.199 +0.210

q(O) /e –0.044 –0.145 –0.087 –0.165

q(H/Li) /e +0.246 +0.247 +0.606 +0.538

q(F) /e –0.282 –0.294 –0.718 –0.583

(3E–1E) [eV] –1.07 +0.12 +1.77 +1.27

E(1st exc trip) * –1.55 –1.16 +1.26 +0.53

(a) DE vs. He, 1MOF +3.10 +2.85 +2.52 +2.27

(b) DE vs. He, 3O, 3MF +2.82 +2.22 +2.41 +1.68

(c) DE vs. He, 1O, 1MF –0.12 –0.53 –0.53 –1.07# dis so ci a tion at the MP4, CC and CCSD(T) lev els.* from CIS for MP2-op ti mized spe cies, and from TD cal cu la tion for DFT-op ti mized ones.


Fig ure A2. Op ti mized mo lec u lar ge om e try of two XHeO– an ions (X = Cl, HO) in their low est bound sin -glet state. The CCSD(T) bond lengths (in Å) are shown above those of MP2 (in ital ics) andB3LYP (in brack ets). DIS = dis so ci a tion.

Fig ure A3. Mo lec u lar ge om e try of (HeO)(HF), (HeO)(LiF) and (HeO)(BeO) as op ti mized at theB3LYP and MP2 lev els. The MP2 bond lengths (in Å, in ital ics) are shown above those ofB3LYP (in brack ets).

A4. Mo lec u lar ge om e try of 1(HeO)4 and 1(HeO)6 as op ti mized at the B3LYP andMP2 level (Fig ure A4 and Ta ble A4).

118 W. Grochala

Fig ure A4a. Mo lec u lar ge om e try of (HeO)4 as op ti mized at the B3LYP and MP2 lev els bond lengths in Å.

Views em pha size a nearly pla nar B3LYP ge om e try (with a nearly square pla nar He4 frame)

and a dis torted cube MP2 ge om e try (with a close to tet ra he dral He4 frame).

Fig ure A4b. Mo lec u lar ge om e try of (HeO)6 as op ti mized at the B3LYP and MP2 lev els bond lengths in Å.

Views em pha size a sand wich [(HeO)3]2 B3LYP ge om e try (with a nearly pla nar (HeO)3 unit

and oc ta he dral He6 and O6 frames) and a ‘dou ble cube’ MP2 ge om e try (with a close to dis -

torted cube (HeO)4 unit, sim i lar to that seen for the (HeO)4 oligomer).

Ta ble A4. The cal cu lated O–He bond lengths, R(He–O), the short est sec ond ary con tacts, R(He…O), thelarg est and small est har monic fre quen cies, n(He–O)max, and nmin, re spec tively, Mulliken atomiccharges on at oms, q, en ergy dif fer ence be tween the first ver ti cally ex cited trip let, or highermultiplets and the low est sin glet state, xE–1E, x = 3, 5, 7, 9, 11, 13, and en ergy of re ac tion lead ing tofour dif fer ent sets of prod ucts (a)–(d), for three neu tral clus ters [HeO]n, where n = 2, 3, 4, 6. Re sults of the B3LYP and MP2 cal cu la tions are com pared. NC = not con verged. ND = not de ter mined.Com pare Figs. A4a and A4b.

[HeO]n n=2 n=3 n=4 n=6 n=2 n=3 n=4 n=6

MP2 MP2 MP2 MP2 B3LYP B3LYP B3LYP B3LYP

R(He–O)/Å 2.034 1.967 1.319 1.2491.298

1.269 1.237 1.227 1.2311.2321.232

R(He…O)/Å 3.271 3.261 2.757 2.669 2.605 2.252 2.157 2.335

n(He–O)max 98 125 375 ND 729 851 900 855

nmin 12 12 115 ND 57 115 26 50

q(He) /e +0.007 +0.008 +0.098 +0.106+0.127

+0.188 +0.205 +0.206 +0.217+0.219+0.220

q(O) /e –0.007 –0.008 –0.098 –0.104–0.130

–0.188 –0.205 –0.206 –0.217–0.219–0.220

E(1st exc trip) # –3.22 –3.18 NC –0.81 –1.15 NC NC –1.25

(3E–1E) /eV –3.50 –2.75 –1.04 +1.01 +1.65 +0.81 +2.84 –2.93

(5E–1E) /eV –4.90 –7.07 NC –7.57 +1.59 +1.35 +1.70 –1.44

(7E–1E) /eV — –8.25 NC +2.27 — +1.97 +4.26 –3.87

(9E–1E) /eV — — –1.14 –1.28 — — +3.33 –2.84

(11E–1E) /eV — — — NC — — — –5.29

(13E–1E) /eV — — — NC — — — –4.19

(a) E vs. (1He, 1O) –0.03 –0.05 –0.07 –0.16 –0.73 –1.28 –1.78 –2.67

(b) E vs. (1He, 3O) +5.87 +8.79 +11.72 +17.54 +4.77 +6.97 +9.22 +13.83

(c) E vs. (1He, 12

1O2) +9.61 +14.41 +19.21 +28.76 +8.29 +12.24 +16.25 +24.38

(d) E vs. (1He, 12

3O2) +10.95 +16.40 +21.86 +32.78 +9.96 +14.75 +19.59 +29.39

# from CIS for MP2-op ti mized spe cies, and from TD cal cu la tion for DFT-op ti mized ones.

A5. The cal cu lated IR spec trum of [HeO…CsF] adduct (Fig ure A5).


Fig ure A5. The cal cu lated IR spec trum of [HeO…CsF] adduct (MP4, CC and CCSD(T) re sults).

A6. Re sults of the DFT, MP2 and CCSD(T) cal cu la tions for [F–…BeO] an ion(Fig ure A6).

A7. Pe ri odic Ta ble rep re sen ta tion by Górski [48] (Fig ure A7).

REF ER ENCES AND NOTES

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2. (a) Cybulski S.M., Burcl R., Szczêœniak M.M. and Cha³asiñski G., J. Chem. Phys., 104, 7997 (1996);(b) Cybulski S.M., Kend all R.A., Cha³asiñski G., Severson M.W. and Szczêœniak M.M., J. Chem.Phys., 106, 7731 (1997); (c) Buchachenko A.A., Jakowski J., Cha³asiñski G., Szczêœniak M.M.and Cybulski S.M., J. Chem. Phys., 112, 5852 (2000); (d) Buchachenko A.A., Szczêœniak M.M.and Cha³asiñski G., Chem. Phys. Lett., 347, 415 (2001); (e) Krems R.V., Buchachenko A.A.,

120 W. Grochala

Fig ure A6. Op ti mized mo lec u lar ge om e try of the FBeO– an ion in its low est sin glet state. The CCSD(T)

bond lengths (in Å) are shown above those of MP2 (in ital ics) and B3LYP (in brack ets). Note

the asym me try of the an ion, rem i nis cent of [F–…HeO], which may be due to larger ‘af fin ity’

of Be to wards O than to wards F.

Fig ure A7. One ver sion of the Pe ri odic Ta ble of El e ments [48] where He is placed close to H and si mul ta -

neously above Be (and not above Ne).

Szczêœniak M.M., K³os J. and Cha³asiñski G., J. Chem. Phys., 116, 1457 (2002); (f) Buchachenko A.A.,Szczêœniak M.M., K³os J. and Cha³asiñski G., J. Chem. Phys., 117, 2629 (2002); (g) Jakowski J.,Cha³asiñski G., Gallegos J., Severson M.W. and Szczêœniak M.M., J. Chem. Phys., 118, 2748 (2003);(h) Jakowski J., Cha³asiñski G., Cybulski S.M. and Szczêœniak M.M., J. Chem. Phys., 118, 2731 (2003).

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4. Lewis G.N., J. Am. Chem. Soc., 38, 762 (1916).5. Un usual bond ing to ‘no ble gases’ has re cently been re viewed: (a) Grochala W., Chem. Soc. Rev., 36,

1632 (2007). For older re views see: (b) Frenking G. and Cremer D., No ble Gas and High Tem per a tureChem is try (‘Struc ture and Bond ing’ se ries), Springer Berlin (1990) p. 17; (c) Selig H. and Hol lo way J.H.,in: In or ganic Chem is try (‘Top ics in Cur rent Chem is try’ se ries), Springer Berlin (1984) p. 33.

6. www.webelements.com , ac cessed Mar 27 (2008).7. (a) Beach J.Y., J. Chem. Phys., 4, 353 (1936). In the early days of quan tum me chan ics, Beach cor rectly

pre dicted that the dis so ci a tion en ergy of HHe+ is close to 2 eV.8. Petrov A.N. and Panin A.I., Opt. Spectrosc., 90, 367 (2001).9. Harland P.W., Mac lagan R.G.A.R. and Simpson R.W., Far a day Trans. II, 84, 1847 (1988).

10. (a) Pauling L., J. Chem. Phys., 1, 56 (1933); (b) Weinbaum S., J. Chem. Phys., 3, 547 (1935). He2+ ×

is even more strongly bound than HHe+.11. Con nec tions of He with sin gly or mul ti ply charged cat ions are of ten called ‘helides’. See for ex am ple:

(a) Hotokka M., Kindstedt T., Pyykkö P. and Roos B.O., Mol. Phys., 52, 23 (1984); (b) Jemmis E.D.,Wong M.W., Burgi H.B. and Radom L., J. Molec. Struct. (Theochem), 93, 385 (1992); (c) Hughes J.M.and von Nagy-Felsobuki E.I., Eur. Phys. J. D, 6, 185 (1999). Reader is also re ferred to nice re viewon chem is try of he lium: (d) Grandinetti F., Int. J. Mass Spectr., 237, 243 (2004).

12. (a) Seppelt K., Z. Anorg. Allg. Chem., 629, 2427 (2003); (b) Hwang I.C., Seidel S. and Seppelt K.,Angew. Chem. Int. Ed. Engl., 42, 4392 (2003).

13. Seidel S. and Seppelt K., Sci ence, 290, 117 (2000).14. He

2+ × is ob vi ously a light con ge ner of Xe

2+ ×; the lat ter is known from the solid state: (a) Drews T.

and Seppelt K., Angew. Chem. Int. Ed. Engl., 36, 273 (1997). Higher cationic oli go mers have alsobeen iso lated: (b) Seidel S., Seppelt K., van Wullen C. and Sun X.Y., Angew. Chem. Int. Ed. Engl.,46, 6717 (2007).

15. Khriachtchev L., Pettersson M., Runeberg N., Lundell J. and Räsänen M., Na ture, 406, 874 (2000).16. Grosse A.V., Kirshenbaum A.D., Streng A.G. and Streng L.V., Sci ence, 139, 1047 (1963).17. Bart lett N., Proc. Chem. Soc. Lon don, 218 (1962).18. Wong N.W., J. Am. Chem. Soc., 122, 6289 (2000).19. Lundell J., Chaban G.M. and Gerber R.B., Chem. Phys. Lett., 331, 308 (2000).20. Chaban G.M., Lundell J. and Gerber R.B., J. Chem. Phys., 115, 7341 (2001).21. Grochala W., Feng J., Hoffmann R. and Ashcroft N.W., Angew. Chem. Int. Ed. Engl., 46, 3620 (2007).22. Bihary Z., Chaban G.M. and Gerber R.B., J. Chem. Phys., 116, 5521 (2002).23. (a) Allen L.C., Erdahl R.M. and Whitten J.L., J. Am. Chem. Soc., 87, 3769 (1965). Com pare: (b)

Lourderaj U. and Sathyamurthy N., Chem. Phys., 308, 277 (2005).24. Žemva B., Lutar K., Jesih A., Casteel W.J., Wilkinson A.P., Cox D.E., Von Dreele B.R., Borrmann H.

and Bart lett N., J. Am. Chem. Soc., 113, 4192 (1991).25. Hoppe R., Z. Anorg. Allg. Chem., 292, 28 (1957).26. (a) Knox K. and Ginsberg A.P., Inorg. Chem., 3, 555 (1964); (b) Abrahams C., Ginsberg A.P. and

Knox K., Inorg. Chem., 3, 558 (1964).27. See for ex am ple: Niewa R., Zherebtsov D.A. and Hohn P., Z. Krist. New Cryst. Str., 218, 163 (2003),

and ref er ences therein.28. Pyykkö P., Chem. Eur. J., 6, 2145 (2000).


29. (a) Li T.-H., Mou C.-H., Chen H.-R. and Hu W.-P., J. Am. Chem. Soc., 127, 9241 (2005); (b) Liu Y.-L.,Chang Y.-H., Li T.-H., Chen H.-R. and Hu W.-P., Chem. Phys. Lett., 439, 14 (2007).

30. Antoniotti P., Borocci S., Bronzolino N., Cecchi P. and Grandinetti F., Chem. Phys. Lett., 111,10144 (2007).

31. Borocci S., Bronzolino N. and Grandinetti F., Chem. Phys. Lett., 458, 48 (2008).32. Lundell J. and Grochala W., manu script in prep a ra tion (2008). The re sults were ob tained in Apr 2007.33. The re sults were ob tained in Feb 2008.34. We no tice that at least three neu tral sys tems con tain ing He have been ob served and/or pro posed up to

now: OBeHe, SBeHe and H3BOBeHe. How ever, in all these sys tems He serves as a hard Lewis base to -wards a rather na ked metal cat ion, Be2+, and the na ture of this do nor/ac cep tor bond in these spe cies isvery dif fer ent from those which are dis cussed in this work (trip let state is not lim it ing their sta bil ity).Cf. (a) Koch W., Col lins J.R. and Frenking G., Chem. Phys. Lett., 132, 330 (1986); (b) Borocci S.,Bronzolino N. and Grandinetti F., Chem. Phys. Lett., 384, 25 (2004); (c) Borocci S., Bronzolino N. andGrandinetti F., Chem. Phys. Lett., 406, 179 (2005). The larg est pre dicted Edis is 0.26 eV.

35. These re sults were first pre sented dur ing ICM User Ses sion, Mar 27 2008, War saw Po land.36. See the Gaussi an 03 tu to rial.37. Jørgensen C.K., “In or ganic Com plexes,” Ac a demic Press Inc., New York, N. Y., 1963, p. 33.38. Allen L.C., Lesk A.M. and Erdahl R.M., J. Am. Chem. Soc., 88, 615 (1966).39. Rec ol lect that HF is a clas si cal case, where the in clu sion of elec tronic cor re la tion is in dis pens able

for cor rect pre dic tion of its dis so ci a tion en ergy. All mol e cules which con tain the HeO moi ety showa sim i lar fea ture.

40 John son M.W., Sándor E. and Arzi E., Acta Cryst. B, 31, 1998 (1975).41. Bulski M. and Cha³asiñski G., Chem. Phys. Lett., 128, 25 (1986).42. See for ex am ple: (a) Christe K.O., Wil son W.W., Wil son R.D., Bau R. and Feng J.A., J. Am. Chem. Soc.,

112, 7619 (1990); (b) Sun H.R. and DiMagno S.G., J. Am. Chem. Soc., 127, 2050 (2005), and re -lated lit er a ture on new sources of ‘na ked’ flu o ride an ions.

43. See: Berski S., Lundell J., Latajka Z. and Leszczyñski J., J. Phys. Chem. A, 102, 10768 (1998), andref er ences therein.

44. Hy po thet i cal spe cies re lated to [HeO…NH4F] are of im por tance since they of fer a the o ret i cal pos si bil ityof block ing the mol e cule’s most im por tant dis so ci a tion chan nel (via the F…He…O bend ing mode).This is be cause the F– an ion is no lon ger ‘na ked’ in these mol e cules but has one pro ton firmly at tachedto it. In con se quence, in ser tion of O into the H–F bond should not be easy (with re spect to for ma tionof the ‘na ked’ OF– an ion as in the case of [F–…HeO]) and the ki net ics of de com po si tion of[HeO…NH4F]-like spe cies is thought to be slowed down. Deuteration is an other com mon trick whichis worth con sid er ing.

45. Shimizu K., Kimura T., Furomoto S., Takeda K., Kontani K., Onuki Y. and Amaya K., Na ture, 412,316 (2001).

46. Liebman J.F. and Allen L.C., J. Am. Chem. Soc., 92, 3539 (1970).47. For a no ble gas-solvated pro ton the trend is re versed (NeH+ 2.22 eV, HeH+ 2.04 eV) and it fol lows Lewis

ba sic ity of no ble gases which is re flected in their va lence or bital en er gies.48. Górski A., Pol. J. Chem., 79, 1435 (2005).49. Bent H., New Ideas in Chem is try from Fresh En ergy for the Pe ri odic Law, AuthorHouse, Bloomington,

USA, 2006.50. Scerri E.R., The Pe ri odic Ta ble: Its Story and Its Sig nif i cance, Ox ford Uni ver sity Press, Ox ford, UK,

2007.51. It has been claimed that all Ng2 mol e cules (Ng = He…Xe) ex cept He2 and Ne2 ex hibit chem i cal bond ing

if em bed ded in side the C60 fullerene: Krapp A. and Frenking G., Chem. Eur. J., 13, 8256 (2007).52. Cioslowski J., Phys. Rev. Lett., 62, 1469 (1989).53. Grochala W. and Hoffmann R., Angew. Chem. Int. Ed. Engl., 40, 2742 (2001).54. Guan J., Puškar L., Esplugas R.O., Cox H. and Stace A.J., J. Chem. Phys., 127, 064311 (2007).55. Walker N.R., Wright R.R., Barran P.E., Cox H. and Stace A.J., J. Chem. Phys., 114, 5562 (2001).

122 W. Grochala

On Chem i cal Bond i ng Be tw ee n He l ium and Ox y g enbeta.chem.uw.edu.pl/people/WGrochala/HeO.pdf · On Chem i cal Bond i ng Be tw ee n He l ium and Ox y g en by W. Grochala1,2

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