The bonding of hydrogen in HNb6I11. A model for interstitial hydrides

Volume 88, number 5

CIIChlICAL

PIIYSICS

LCTTCRS

A MODEL FOR INTERSTITIAL HYDRIDES

THE BONDING OF HYDROGEN IN HNb&.

F. DijBLER, H. MiiLLER and Ch. OPITZ Sektiotl Clwmie

der Friedrcllr-Scltrller-Universit~f,Steiger 3, H. 3, DDR-6900 Jerrn, DDR

Rccelvcd 15 hkuch 1982

and for Ihe s, s1em “hydrogcd m WIThe cluster-bulk analog) is consldcred for (he compounds Nb6111 and IINbJ,, aIs”. Calculations ol tic clccuon~c suuc~rc of these compounds and rhc modclhng of a possibleprnctrarlon mechamsm for hydrogen by SW Xa and IIHT mcrhods show the snmlari~y of the mrcrsnu~l II -metal

of the cluster-bulk

I. Introduction

metals” The analogy of the chemical condlhons

nuclear transitron-metal and Ihe chemisorptlon

complexs

m poly-

of correspondmg

materials).

llgands on

Cluster

compounds

group atoms H,

polyhedron

W&I

C, N, P, As, Sb, S accommodated

responding

mtcrstitial

analogr hydrides,

conccrnmg

metal-meral (table I [Gl).

the cor-

PI. these analoges

have scarcely

siderations

to Ihc inlcrsririal

LIW, licld of research

attractive.

A

msthods

m sohd-

IS] reported

on thus

Among other results, mcrcascd drstsnccs during H inscrtron arc found

hgands

first-mcnlloncd [7]

clusrcrs bccausc

hydride

cluslcrs thatdo not involve

I IhB61, I (more exactly &Nb6&)&)

HCsNb6 I,, have been known

and

been

We restnct our con-

hydndc

tl-stormg

as

aspect IS the fact thdt this area of

Only lnterstltlal carbonyl

Thcoret~cally

make

unporlant

rcsrarch IS a ~CSI field of rhcorcrical

carbides, and so on

considered (set e.g. rcfs. [3.4]).

m m

corrcspondcncc.

III

holes of rhe metal cage) sugesc spcc~al

aspects of a cluster-bulk

(for Instance hydrides

stale studies. Chnu and Longom

aloms (main-

InterstiUaI

further

the system “hydrogen

due to the apphcation

Also unsolved problems, as hydrogen

brltllemcnt,

cxtendcd metal surfaces on the other led IO the concept of the cluster-surface analogy (set c.b ref. [ 11).

analogy,

is very unportant

energy production

on the one hand

bond.

qwipound

and srrucrurally

up to now (fig

was synthcsucd

chnrucrcrucd

by Simon

I). The

by Swoon 171 and

Table 1

Cluster compounds \\nh m~crstlrul hbdrogrn Clurtcr compound

Lengrhcnmg of Me-Me

Kelatcd la~ncc

dlslrnces (Ar)

I)

cnlargemcnt

(bee, fee)

of Iltc unit cell volume by 0.19%/0.X%

I7A ar=‘lpm

(HCo6(CO)ls)-

pes

191

(HRU6(co)16)(H4-,hz(C0)2~P-

n=2,3

Ar = 2-7 pm Tar MC 3dJBccnl lo H 19 1

W+nRhdC0)24)“n = 2.3.4 bee

(H’%,Whd3-

0 009-2614/82/0000-0000/S

02.75 0 1982 North-Holland

467

CHCMICAL

Volume 88, number 5

PHYSICS

n

21 May 1982

LETTERS

for the bridge-over between these compounds and the system “H in metals”, analogy.

Particularly,

(i) different

in view of the cluster-bulk we expect

results

concerning

models

for the hydrogen-metal bond, (il) diffuson of hydrogen, and (ih) lattice structure: modifications during H penetration.

2. Quantumchemical

approximation

methods

The SW Xa method was chosen for the calculation of the electronic structure of the starting compound h%611, and the product HNb61,, of the reaction (I) of the polymeric

rig. I. Clus~cr UIIII (H)l\lbblalbp

poundsNbbllt Batcman

[I 1,12). With this method onegets, with comparably small computatlonal effort, in most casesbetter results m comparison to HF methods. hloreover, this

com-

and IINb6111.

ct al. [IO) _ There

IS widespread

interest

UI

Nb61 I 1 and HNb611 1 because they are exceptIonal among the lower halogenides of the fifth-group transition metals wtth their characteristic Nbs18 umt instead of a M6X,, cluster. As a result they are electron dcftctent and show a spectal reactivtry to hydrogen according to Nb61,, t;H$+lNb

6 I II .

(1)

is situated in the center of The hydrogen in HNb,l,, the Nb, octahedron. The objecttve of this paper IS to show the possibdities of quantum-chemtcal cdculatlons of these species

procedure

~nth the muffin-tin

approvlmation

ts very

suitable for handling Iti@-symmetry cluster compounds. This mcrhod has been successfully appltcd thts class of compound

We used touching atomic spheres according to the structural data of Bateman et al. [IO] and averaged atomic diskmces(ideaked 0, symmetry). All input dztta are listed in table 2. We restrict our cakulatlon to the Nb, octahedron rvlth the fist coordmation sphere of 8 iodine atoms only (fig. I). Selfert [ 13) showed for analogous cluster compounds that the Influence of the outer sphere of halogen atoms on the energy-level

scheme

of the whole

complex

is very

small. For niobmm we used the parameter a = I bc-

Table 2

Input data for S\V Xa and EHT calcuhtlons CHT

valenceorbual

S-l-0

VSIP 1161 (kJ/mol)

59.3

IS

1311.9

sphere ndlus (pm)

0.97804

IS

Nb

1.0

3s, 3p, 3d, 4s, 4p, 4d, 5s

142.4

5s 4d 4P

653.0 693.6 3709.8 [18]

5.921 11.238 14.085

1

0.70006

4s, 4p, 4d, 5s. 5p

144.5

5s

2002.2

13.404

5P

1008.7

Il.612

outer sphere 111

468

z I171

H

mtcratomlc rcflon II

to

[ 13,141.

0.82861

-

495.9

0.81861

-

-

1

CHEAIICAL

Volume 88. number 5 cause then the orbttal

energy

PHYSICS

of the 4d state hes,

other 4d metals, below the energy for the Ss atomic orbital. Therefore the s/d character of the density of states for the Nb, octahedron is very stmilar to the bulk value [ 191. A more detaded consideration of reaction (1) necessitates the calculation of a number of very low-symmctry configuratrons during the penetratron of hydrogen in the Nb, octahedron. According to the present avidability of parameters for semi-empirical methods, the EHT method is surtable [20]. Such an LCAO hl0 interpolation of the SW Xo results for Nb,I, 1 and analogous

HNb,l,

a fittmg

of the EHT

Nb, I,$!’

HNb,- I;’

H

to tile

1 presumes

21 Slay 1982

LCTTCRS

t

parameters

into the SW Xa results; tn this field we have gamed some experience 1211. Because the EHT results arc m good quahtattve agreement with all cssentral features (energy-level scheme, magnctlsm, bond model) ofscc-

tton 3.1, we disregarded adJusttng the EHT parameters and employed

the LCAO

procedure

Hrllh tie

usual

parameters (SW also table 2).

3.

Results and discussion

3.1. Electronic stnrcture llc

cncrgy-level

of A%&*

atId HAfb,&+

schcmcs according to the SW XCY

crrlculatron of the two compounds arc shown tn fig. 2. They are very srmllar to each other and possess an analogous orbrtal sequcncc, but they differ trcmcndously

m the energy

of the lowest

ale

level (131~’

la’,,), whtch is substanttzily lowered tn HNb,li+. The partial-wave contrtbutions of latg/la&, 2a,,J 2a;P, 2tZu/2t& clearly deviate from each other as well (see below). The highest occupied molecuhrr orbital 2tzu (HOhlO) is filed with 5 (6) electrons m Nb,li+ (HNb,@). This is in accordance wrth measurements of the magnetic susceptrbtlity which revealed paramagnetism

for the first compound

and

dumlagnetism for the second [7,22]. The magnetrc moment at low temperatures (2090 K) for Nb,lt I (p = 2.24 BM) lies between the values for 1 and 2 unpaired electrons in the Fermi level. The occupied energy levels can be classified m the following manner; lea, la?,, IaLa (only for Nb&‘), 1tzg, lttu, 2alg, I$,,, le, and 2tIg are responsible for the Nb(4d)-I(5p) bond. The molecular orbit& 2tl,, 3tag and 2tau are d-like levels of the Nb-Nb bond (with slight I(5p) participation).

In fig. 2 the most important mtcracting molecular are connected by dashed lures because of tlw discussion of the hydrogen-metal bond III Ntlb,l, , . A clearly cnergetrcally lowered bondmg orbital (fig. 2) IS formed by mtcraction of the hydrogen Is and the orbit&

Table 3

Rruakrvc

contubutrons (ur clcclron)

of csscntul molecular

orbwds MO

1=0

I=1

I=2

H 1s

1.00

-

-

kg

0.10

13ig ag xg 212” 21; ”

0.78 0.54 0.39

0.58 0.17 0.41 0.93 0.14

0.94 0.65 0-4s 0.22 4.16

-

0.0

4_91

469

VOIUIIIC 88. nunlbcr 5

21 hlsy 1982

C~IChIICALPHYSICS LIX-I-ERS

Nb&+

Ia,, wavcfunctions, which mvolves 0.6 hydrogen elcciron. From our EHT calculation we obtam the consldcrable bond energ for hydrogen of 260 kJ/mol. Such results correspond with the fact that, heating the cluster compound up to 773 K (beginning dccomposltion of the substance), cannot hberate the

brings about a bonding metal-hydrogen interaction, which secondly causes a redistnbution of metal (d) charge m favour of the Fermi level 2t;,. Because of the pure metal(d) contributions of this MO and its responsibtlity for the bond framework withm the Nb6 octahedron, a change of the occupation in this orbital

accommodated

considerably

hydrogen

[7]. The 2alr: function

effects the whole bond scheme of the

losesNb(4d)contrlbutlonsdurmgH inkrtion but, however,gainsl(5p) charge. Theselost d contributions, togcthcrwvh the remainmg0.4 hydrogen electron,

compound. Comparingthe molecular-orbital picturesfor the laig and lalg m fig. 3 illustrates the metal-hydrogen

mainly appear in the HOMO (2&) as additlonal d charge (see also table 3). Firstly the la& wavefunctIon

bond and the antibonding influence of the hydrogen atom on the Me-Me bond (weakening of the bond between nelghbouring Nb atoms). The geometrical situation, that means the “largeness of the octahedral site” (maximum possible radius rH of the hydrogen sphere) - in comparison to the different radh of the hydrogen atom (rH(covdent) = 30 pm, rH(van der WaidS)= 120 pm, ‘H - = 208 pm) - shows the possibility of a negative partial charge on the interstitial

H atom, A comparison of the charge

transferm variousregionsof spaceof the cluster during H insertion [AQ = Q(HNb&+) - Q(Nbsli+)] leads to the following result (table 4). As a reference system we use the free hydrogen atom in the XCV approximation. So we find 0.38 electron in a sphere of a free hydrogen atom with a radius equal to that of

r-l&3. Plots of *(SW Xa) m the x-y plane (see ri. 1) for the a values 0.0, +O.OOS,*0.025, *O-075, kO.2; (a) lalg, (b) la’*g, (C)Ztiu.

Volume

88, number 5

CHEMICAL

PIIYSICS

Table 4 Charge drffcrences (In electron) III sevcrsl cluster spaces after H cncapsuhtion (set AQ in section 3.1)

~QII

AQIII

6AQNb

84Qt

AQtt

0.14

-0.01

050

-0.30

0.64

the hydrogen sphere tn the cluster compound (this result

is approximately

1s” wavefunctlon).

the same if WC use the exact In comparison

with

the charge

of

the

H atom in HNb6fi+ in the same space (0.64 electron) there is a clear charge increase. Thrs is a strong

argument

for the existence

hydrogen

atom

m the cluster

of a negatively compound.

A very similar charge balance for transition-metal monohydrides on the basis of APW calculations by Swrtendrck [24] shows an incrcasc of 0.35 electron in the H sphere (determined by the muffin-tin radius of the calculation) of the hydrides. Quahtatively, the same result was derived by Adachl et al. [7_5] for the system Nb/H. Our EHT calculation provrdes an H charge of =:I .48 electrons. The excess of charge mainly orrginates from the Nb atoms accordmg to a common population analysis (QNb = -0.42 c). In the SW Xa picture thts addrtional H charge is mainly caused by charge transfer from outer regions of the cluster (outer sphere, iodme atoms) to the center. is therefore

low concentration hydrogen prcfcrs tetrahedral srtcs in bulk mobium. Thus IS often c~plamcd on the bans of electrostatic concepts. Thus the occupation of octahedral and tetrahedral holes should not dcpcnd on their stzes but on thctr electronic propcrtics. The main feature of the hydrogen-metal bond m the cluster compound as well as in the system l‘H m mctats” js very srmdar. Calculations by Switcndrck 1281 for TIH~ show that 1.15 hydrogen electrons arc tncorpontcd in low-lying s-llkc states and 0.85 clcctron in d states near the Fermi Icvcl. Thcsc results arc m agreement with our calculation for HNb,l, , .

charged

the CNDO results.

rnsertion

21 Xlsy 1982

The

charge transfer IS in accordance wrth our investigation into the hydrogen insertion in naked metal clusters [23] concerning the SW Xa descnption but contrary to

Hydrogen

LCll-CRS

accompmied

For a prelrminary mvcstrgatron of the inscrtron mechanism of hydrogm WCconstdercd two posstblc “reaction paths”. The unsymmetrical contiguratrons of the system Nb,li+ + H(X, R) were calculated with the abovementroncd LCAO method (fig. 4). The most strrkmg results arc tllc small actrvation cncrgics E,, In both paths during hydrogen

insertion

[SO kJ/mol

(X),

10 kJ/mol (R)]. This corresponds wrth the “mrld”

by a

contraction of the whole c11xgc towards the cluster center. Recently Finley et al. [26] and NOMand Anderscn [27] carried out calculations of the electronic structures for the compounds Nb61tt and HNb6frt considering the real geometry. They could explain the phase transitions at 274 and 324 K. These phase transition are the first examples of a “spin-crossover” phenomenon in a cluster compound. The two effects of hydrogen insertion into the metal cage are also discussed by Chini and Longont [5] for interstitial hydride clusters involving carbonyl ligands. The weakening of Me-Me bonds in metals with a high hydrogen content can be explained by the increasing occupation of antibonding Me(d) states. At

rig. 4. Totcll cncrglcs or the system (II + Nb&*)

along the

two dlscossed “rcactron paths” (X, R) for hydrogen, 01 C, Nb6 octahedron-face ccntcr. OEC, Nb6 octahedron-edge ccntcr. CCC, Ig cubesdgc ccntct.

471

Volume 88. number 5

conditions

of the reaction

Iledrol site” (Nb,l) IS

CIIlXICAL

wth

(I).

Some

a certain

kind of

minimum

“tetra-

ts small (Ml, lctr = 135 kJ/mol)

trary to the octahedral hole (Af$t Furthermore, If IS worth noting hon process rcsu1l.s it1 a charge

References

m energy

passed III path R. The bond energy for hydrogen

this arrangement

in

con-

= 260 kJ/mol). that the penetraof Aq = 0.5

transfer

electron to the hydrogen atom. The neutral stale of the hydrogen atom m path X IS nearly maintained at the potnts CEC and OEC (dq = 25 %) in contrast

path

R, where

(qHICb = 0.89

barrier

the H atom is poslttvely e) at

the tetrahedral

to the octahedral

to

charged

site. On crossing

the

results will certamly

rection of phenomenological tion mechanism of hydrogen Finally, hydrogen

one should

contribute pictures

to a cor-

of the absorp-

[7].

expect

that the motton

of the

atom between octahedral and tetrahedral

sites does not tahc place from the ground state of vibration but from an excited state, which greatly facilitates

the transitton

wetl. Various octahedral

to a neighbouring

calculations

basts of the dtffcrently

were carried shaped

and tetrahedral

potential

wells for the

sites. By means of harmonic

kl/mol) contrary to the tetrahedral well wiih only one bonding state. Up to now all considerations have been done with a fmed geometry, although all structural analyses of interstltial atom clusters show changes tn geometry ;~frer encnpsulntion (see dso table 1). Hence tl,e penetration mechamsm should be studted under sitnultaneous optimtzatton of geometry (cf. our study of the system Nl/H [23]).

4. Conclusions

clusters

preliminary

analogy

results show that the

of the studted

interstitial

leads to useful

hydride

conclusions for the system “H in metals”, regardmg magnettsm, tiffuslon, bonding models, and structural changes. The subject discussed (cluster-bulk analogy) may contnbute to further

cooperation between chemists and physicists_ 472

[6l 171 [S] [9]

1101 (111

[ 121 [ 13 I

~~.TeBcr~ndR.Bou,Suuct.Bond~n~44(1981) 1. A. Simon, Z. Anorg. AU& Chcm. 355 (1967) 31 I. H. lmotoand J.D.Corbctt, Inorg_Chem. 19 (1980) 1241. D.W. Hart, C.R.Tellcr, Ch.Y. WCI, R. BXI, G. Longoni, SL Campanelkt, P. Chuu and ThI. Koctdc, Anpcw. Chem. 18 ( 1979) 80. L.R. Bawman, J.T. Blount nnd LX. Dahl, J. Am. Chcm. Sot. 88 (1966) 1082. J.C. Slatcr, J. Chcm. Phys. 43 (1965) 228. K.H. Johnson, Advan. Quantum Chem. 7 (1973) 143. G. Seikrt. C. Cmssmnnn and H. hliitler, J_ Mol. Su-ucr. 64 (1980) 93.

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lmcl

J.

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[ 161

out on the

we obtained for the octahedral site two w brational states (I$‘:’ = 145 kJ/mol and Efy = 240

The reported

Lab. 28 (1980) 654. [3] H. hliillcr, Habrhtationsschrdt Fncdrich-SchlcrUnivcrsitit Jcna (1968). 141 J-W. Luher, Tmnnr Am_ Crysl. Assoc. 16 (1980) 1. [S] P. Chini and C. Longoni, Advti. Chetn. Ser. 167 (1978)

potential

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cluster-bulk

[I ] E.L. htucucrucs, Chem. Rev. 79 (1979) 91. [ 2 I VG. Albano and S. hlartincngo, Nachr. Chcm. Tcchn.

hole the H atom is neutral-

place tt ized (QI bm = 1.01 e),and at the octahedral wdl be negatively charged again (q?t = 1.48 c). Such and simdar

21 May 1982

PHYSICS LCTTCRS

[ I7

]

IX.

hloorc,

Atomic

energy

Icvek,

NBS

Cncular

467

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