All-valence-electron Cl calculations on the electronic spectrum of diborane

Chemical Physics 11 (1975) 25-40 Q North-Holland Publishing Company

ALL-VALENCE-ELECIRON OF DIBORANE S.T. ELBERT,

Cl CALCULATIONS

S.D. PEYERIMHOFF

ON THE ELECTRONIC

SPEClRUM

and R.J. BUENKER*

LehrsruhJ fir 7Xeoretische Qlemie der UniversifCt Bonn, 53 Bonn, Wegelersfmsse 12, West Germany Received 4 June 1975

AU-vatcnce-elcctron CI ~culafions have been carried out for dibonne BzHe and its positive ion employing I rSher targe double-zeta A0 basis induding polarization functions in order to study the electronic spectrum of this system. Tranritions from four different wdencc MOs are found to lead to low-lying electronic unnsitions of both Rydberg and valence type in each use. Admixture of valence character in the otherwise Rydberg-likc (nx. 3s), (ny, 3s) and Co. 3pz) tmnsitions calculated to lit between 11.0 and 11.6 eV is indicated s being primarily responsible for the hi&ly intense shoulder found in this reg&m of the BzHs specrrum. The other strong feature with essentially continuous absorption peaking at 9.3 :V is suggested to result from superposition of several Rydberg-type transitions in the generally broad absorption pattern cxp~od for the ‘(n, rr*) species at significanlly higher vertical excitation energy. @ite good agccment is obtailined between calcuktion and experiment for all of the six lowest IPs of diborane and also for the locations of the ‘(n. n*) snd ‘(a.#) transitions previously assigned to the two weak features observed at 6.8 and 8.3 CV in this spectrum.

1. introduction

ment of the excited states of diborane yet reported in the literature. Experimentally the optical spectrum Of Bzti6 is found to be continuous at all frequencies [Sl and hence seems to offer very little insight into the molecule’s electronic structure 161. The best results avaiIable show a weak continuous band centered at 6.8 eV (f= 0.002), a shoulder around 8.3 eV (e = 800) and two stronger features at 9.3 cV (ema =Z8000) and 1.5 000) respectively, with the latter ab10.7eV(e= sorption being followed by a broad shoulder of roughly equal intensity leading to the continuum beyond the first ionization potential. The 6.8 and 8.3 eV systems are believed (61 to correspond to the symmetryforbidden transitions n(lbzg) --c n*(lb,,) and ~(3%) + n*(lb3g) respectively. while it has been suggested that the much more intense regions of the spectrum at higher energy result from the corresponding dipole-allowed n(lbzu) + n+(lb3,) and ~(3%) + oL(nblU) excitations; no definite assignment of the various diborane absorption systems has yet been possible, however. Since the electronic spectra of a number cf related systems such as water, ethylene, ethane and diimide

The electronic structure of diborane has been a subject of broad interest for many years, particularly as it relates to the general study of polycentric bonding in chemical systems. Theoretical investigations have centered mainly on the structure and properties of this system in its electronic ground state. A survey of all these aspects given recently by Long [ 11 includes a discussion of ab initio calculations of the diborane equilibrium geometry, while treatments at or beyond the Hartree-Fock level dealing with the decomposition energy of BIH6 into two BH3 molecules have recently been summarized by Marynick et al. [Z]. The ionization potentials of this sytem have also been studied theore$xlly via Koopmans’ theorem [3] and the Green’s function technique [4]. Aside from the work of Brundle et al. [3], which employs ground state SCF results (including virtual MO quantities) to evaluate excitation energies, there appears to be no ab initio treat* Senior US Sckntist Awardec of the Alexander van Humboldt Foundatioo, on krve from the Department of Chemistry, _University OFNebraska. USA. _.

--

._.

..

.

26

-:.

ST. EIbert

et aL/Eiicfronic spctmm

have been represented quite satisfactorily by means of recent 5 initio Cl calculations [7,8], it seems of interest to apply the analogous theoretical techniques to the study of diborane in order to attempt to relofve some of the uncertainly regarding the stability and properties of its excited states. To this end allvalence double-excitation CI calculations have been carried out for all low-lying singlet-singlet intervalence excitations in this system, as well as for a lars number of neighboring Rydberg transitions. In addition to determining the transition energies for the associated ground state excitations, oscillator strength cakufations have also been undertaken in order to better facilitate a comparison with available experimental data for the electronic spectrum of this sytem.

2.AObssisset Some preliminary calculations have been carried out in order to determine a satisfactory A0 basis set for the desired electronic spectra treatment. The first results were obtained with Whitten’s double-zeta gaussian lobe function set [lo] [a (10,s) basis on boron contracted into (4.2) groups and a scaled fivecomponent function on each hydrogen] augmented by one s and two pn bond functions and an (s, p) complement of Rydberg (diffuse) functions located at the inversion center of the molecule; thus this set conrists of 33 groups. The scaling parameters for the bridge and terminal hydrogen AOs were varied independently, but contrary to previous experience [ 1 l] with a more contracted version of the Wbitten boron basis, it was found that both types of H AOs preferred essentiall the same value for the scaling factors, namely I$ = T$ - 1.5. A lowering of 0.23 eV in the ground state SCF energy and 0.13 eV for that of the lowest singlet (n.n*) excited state (IBIB) is observed

compared to the corresponding results obtained using f= l.gandr$= 1.7 *. The initial set of diffuse hmctions does not include a n*(dyr) species but in sirbsequent work this apparent deficiency was corrected by replaciig the sinde Rydberg-We 3py bondcenteidd * llre fact that the excited state function is ku sznsiciveto tho lyf&& scalingappears to reflect thi: fact that the amount of BH bonding characteris signiriuntfydeueased asexdktion f:om the II to I* MO occur. The optimal values fer nk end et 8rc found to be the sarce for t+ st?tcs, however.

_-

_

. .. -

__

--_

:: ,. -

._ : ;_

..

-.:

.

_I,

of

dilxuane

species with two equivalent functions located at the boron nuclei; this procedure had essentially no effect on the ground state SCF result and, more irnportantly, led to an improvement in the energy of the n * nU(lBtg) state of only 0.01 eV. Scaling of the boron py double-zeta species was also considered but again no significant effect is observed on the n + n* SCF transition energy. The best result for the ground state SCF energy obtained from the basis under discussion is thus -52.78723 hartree (using Bartell and Carroll’s data [ 121 for the equilibrium structure of hH4); the r (n, a*) SCF excitation energy is thereby found to be 8.19 eV. Finally, Huzinaga’s somewhat larger (IO,@ basis set [ 13,141 has been employed in a highly contracted manner found useful in previous work [ 151. This treatment leads to a significantly lower total energy (-52.80074 hartree) but to the same value for the ‘(n, I?;‘) excitation energy (8.19 ev). Because the two optimized basis sets considered agree quite well on the

value of the l(n,n*)

transition energy it was decided

that further experimentation with still more flexible basis sets would not be fruitful in this study; instead the larger Huzinaga basis (given in table 1) has been used for all subsequent investigations dealing with the diborane electronic spectrum. The equilibrium geometry assumed for diborane in the majority of published calculations and in those discussed up to this point in the present paper is that taken from Bartell and Carroll [ 121; nonetheless an apparently more accurate structure has been reported by Kucbitsu [16.1]*. Use of the coordinates for the latter diborane conformation (table 2) in SCF calculations employing the basis set of table 1 leads to a total energy for the diborane ground state of -52.80144

hartree. which in turn is O-43 k&/mole lower than the analogous result obtained using the Bartell and Carroll geometry $. Because of the present study’s emphasis on the uertiaI &&ronic spectrum of dibove. it was therefore decided to use tire structural parameters given by Kuchitsu in the ensuing calculations. In this connection it is interesting that the foregoing change

:

S. T. E&et 1 Gaussian lobe function

Table

et aL/Ekctmnic

basis set used in BlH6 alcdations (coordinate

Boroa

of diborane

spectrum

27

system is given in table 2) a)

Hydrogen

symmetry

exponents

9 s s I 5 s s 5 9

6249.59 916.065 202.205 55 834 17.8587 6.25286 2.3177 0 68236 17.3587 6.25286 2.3111 0.68236 0.26035

S

s S S

s

0.0894

P

15.4594

coemcients

b)

0.000474 0.003808 0.020382 0 080414 0.231031 0.428034 0.353750 0 044842 -o.o52080 -0.114136 -0.169988 0.073918 0.604352

symmetry

exponents

e. dl

s s s 5 s

48.59019 7.439655 1.72170 0.488775 0 164108 A

0.03154 0.22826 LOQPQQ 2.41509 1.89710

s

bond function exponents 1.20

coefficients 1.0

coefficients

S

0.03

P0c.Y)

0.40

I_0

m

pti.:)

0.02

1.0

1 000000

izG%i

; Q

3.48347 1.06577 0 39278

P P PCYonly)

o= 0.057221 0.02

2.989890 oJ395075

5 961350 7w 3.29908 1.000000

-52.80144

Es=

=

E&

= -52.80355

a) Lobt displacement (r) is n function of chc exponent (a): I= 0.03 CX-‘/‘. b) Horizontal lines represent separate contracted functions. c) Scaled by $ = 1.5 from the atomic values. d) Using hvo hydrogen functions with contraction

indicated by dashed line.

Table 2 Nuclear coordinates

employed

for diiorane

(in bolus) a)

Nucleus

x

Y

B B H H

0.0 0.0

0.0 0.0 0.0

2.76796

-1.96826

0.0

2.76796

::

-1.96826 1.96826

0.0

1.96826

H H

0.0 0.0

1.87364 -1.87364

I 1.67244 -1.67244

-2.76796

0.0 0.0

a) V&es taken from ref. [ 161.

ent from that of the ground state, a point which is not at all surprising in light of qualitative considerations stemming from application of the Mulliken-Walsh modeltothissytem[11.17]. 3. SCF treatment of the B2H6 spectrum Selfxonsistent field calculations have been carried out for all low-lying singlet and triplet states of Bz& obtainable in the present A0 basis (and accessible in the normal Hartree-Fock Roothaan scheme employed in this study) as well as for the Eve most stable dollblet states of the corresponding positive ion. The cAcuIated

in

geometrical data does have a definite effect on the vertical excitationener& to the 1 Bt, state, causing

orbital energies for the ground state treatment are listed in table 3, both in the canonical and the ICSCF

it to increase to 8.30 eV when the coordinates of table 2 are employed. This result indicates thai the excited state potentiill surf& is significanUy differ-

(internally consistent [I%]) MO representation. It is

:

-_. .-..

‘_._

clear from these results that the /our highest occupied

orbitals in diboranc lie relatively close to one another

28

S T. El&M et alfEIectronic spectrumof dibomnc

TaHe 3 SCF orbital em&es

for the

Bali6

contracted (but scaled) function for each of the hydrogen atoms, the analogous results were also obtained in a larger basis in which the original five-term function was decomposed into three and two terms respectively (table 1); results for this 40 function basis are also given in table 4. Although the total energy of the various states is lowered by as much as 0.06 eV by this procedure, only the (n,3px) transition energy is found to be altered by more than 0.02 eV (thereby moving more in line with the result for the *(n, 3pz) excitation). The effects of employing the more Rexible basis should become somewhat more apparent in the CI treatment, but the lack of any larger change in the SCF results nevertheless indicates that the additional computational effort required over the use of the basis set of table 1 is not justified in the present study. Ihe corresponding singlet-triplet SCF splittings are given in table 5 and show the usual variations from Rydberg to valence and perpendicular to parallel

ground slate ICSCF

C8IlOIlical

-7.62092 -7.62034 -0.88460 -0.64003 -oss952 -0.53970 -0.51416 -0.47080 0.12967 0.01053 0.05ool 0.05776 0.05876 0.05116 0.33590 0.41706 0.63803

-8.38429

-8.38363 -1.85424 -1.66036 -1.54585 -1.55727 -1Sla45 -1.49662 -1.16070 -1.05113 -1.03108 -1.02462 -1.02429 -0.98610 -0.92829 -0.84945 -0.65631

transitions respectively [ 19,201. The splittings are re-

ir_ energy, thereby indicating that the corresponding excited states resulting from electron promotion out of these species should also be found in roughly the same region of the electronic spectrum. The next lowest occupied MO is the 2biu (~so,), but it appears to be separated from the highest four by a significantly larger energy gap (e 0.10 hartree or 2.7 ev). The actually calculated SCF transition energies from the ground to the various excited singlet states of B2H6 (table 4) as well as the corresponding ionization energies bear out these qualitative conclusions quite faithfully. In order to check whether important effects were being overlooked as a result of using only one

latively small for Rydberg-type states, with values invariably somewhat larger for 3s than for 3p members of series corresponding to the same initiating orbital. The intervalence singlet-triplet energy differences (involving then* MO) are always larger than their

Rydberg counterparts, with values increasing markedly as the orientation of the transition changes from perpendicular (out-of-plane) to parallel (in-plane). Nevertheless it is interesting that in this case the (Ir, n*) splitting is still relativeli small (= 2.5 eV) compared to

the values in isoelectronic systems such as ethylene [19,20], in which case the

(planar) and formaldehyde

Table 4 SCF ringletexcitation energies a) (ev) for &He

ry+ 3i 3pr

3st.v 3px

n*

-

8.301 8.31 9.92f 9.92 10.45/1a45 10.25/10.24 10.34/10.41

1242f 1241

9.121 9.14

11.4Of11.41

11.23/11.25

11.40f11.42 23.301 13.401

10.04/10.04 11.76/11.75

12.30/1229

11.33111.33 11.61/11.6Ct 12.27112.26

1206/12.05

25.28/ 14.26f

13.131 14.631 -14.81/

12.15112.14 23.871 !4.21/

14.99/ 27.121

16.99f

8)V~colcft~rlPsb~f~~bvir~tgivenintaMe 1(34funF0ionr),*ortoLtrc~tydf~arthc~in~thccob &ted hydren A0 b decome into a ihrce and twy tam gmup as -ted ia tabk 1; y~diug40’fupctba~att08&& Gcomddpttemrgy is -5280144fS2.80355 hartra.’ -. .. : _ : _, : _. _,.

_,

S. 7: Elbcrt et al./Electronie

29

spectrum of dibomne

Table 5 SCF values for the singlet-triplet

WY*

3s 3pl 3PY 3px n*

0.459 a) 0.114 0.085 0.011 0.033 (-52.00070)

al CI splitting is 0.249 eV.

splittings(eV) of excited BzHe states

0.540 (-52.40320) b) 0.096 0.050 0.037

a.440 0.157 0.014 0.016 (-52.35541) 1.980

2.462 0.256 0.047 (-52.36935) 0.014 0.135

i-657 0.254 (-52.15311) 0.015 0.834

b) Triplet total energy.

corresponding results are calculated in the 4-5 eV range. The explanation for this result can be found in the early work of Pitzer [21] and Mulliken [22], in which it is pointed out that the n MO in diborane (but not then’) contains a significant amount of hydrogen A0 character (see also fig. 6 of ref. [I l]), in distinct contrast to the situation for CzH4 and H2CO; as a result the overlap of the II and II* orbital charge distributions is considerably smaller in diborane, hence leading to a smaller value for the exchange integral K(lr, n*) and therefore a reduced singlet-triplet splitting for the (n. n’) species in this instance. On a more quunfifutive basis, however, the SCF transition energy results are not expected to be very satisfactory because of the probable distinctions in correlation energy among the various B2H6 (and Bzk6) electronic states. Before discussing the results

of Cl calculations for these quantities, however, it is interesting to consider another approach for obtaining transition energies within the one-electron approximation. namely the ICSCF method [IS]. In this formalism the occupi&l orbital energies sun exactly to the total energy, while energy differences beLween the orbitals yield the spin-averaged transition energies between the corresponding MOs. Experience with such results indicates that while they are generally satisfactory in obtaining the correct ordering among transitions with the YUne initiating orbital, they are less effective in predicting relative energies for species with different initiating MOs. As a result there appears fo be merit tn employing a semiempirical adjustment procedure in which each occupied MO in the ground state is assigned a different scaling factor with which to multiply all its associated transition energies. In the

Table 6 Scaled ICSCF transition energies to the low-lying excited states of Bz H6 Excitation t%

n

a

IlX

nY

9.40 9.97 9.83 9.96 10.78 12.00 13.67 17.74

8.19 10.69 11.30 11.15 11.30 12.18 13.50 15.31 19.72

8.89 11.35 11.95 11.80 11.94 12.80 14.11 15.87 20.19

11.95 12.60 12.44 12.59 13.52 14.91 16.83 21.48

0.776 11.79

12.87

0.024 13.51

0.888 14.01

7.09

a1 Koopmanr’ theorem valuessukd

0341

by 0.92 1231.

:

9.30

2%

2soa

11.09 14.13 13.97 14.12 14.97 16.26 18.01 22.29

16.19 18.74 19.37 19.21 19.36 20.26 21.61 23.46 27.96

0.816 16.02

0.858 22.14

13.53

ST. Eibcrt et aL/Elccmwzicrpcmtm ofdihnmw

30

present s?tdy these scaling parameters are obtained by fitting the ICSCF Rydberg transition energies to the corresponding SCF ionization potentials (table 4) in each case; term values of 3.10,2.43 arid 1.33 eV respectively for 3s,3p and 3d Rydberg series have been assumed thereby, as recommended by Robin [231. The resulting average scaling parameters and KSCF transition energies are given in table 6. These results will be discussedin more detail subsequently along with tie corresponding CI transition energies.

4. Cl treatment The general features

of the CI treatment

used in

the present work are given elsewhere [9]. Of the 34 MOs in the basis only the two inner-shell species are

Tabk 7 Deaaiption of the NCh wed in the CI NO label =)

: 3 4 5 6 7 8 9 10 11 12 13 14 15

Stare

:p tB:g ‘BB I Bag ‘AU ‘A”

calculations

-Input SCFMO

Selection b,

x X

4M4R

903 693

(n, w*) (0, KY’) (n. 3s) (ax, WY’) (nx.nY*) c)

SMZR 4M4R 2M2R 2M2R 3MIR 3M3R

(n. 3vM

3M3R

(n. 3-G) (n. 3pa) (n. 3~x1 (or 3pt) (nY,V’) (%3PY) (nv. 3s)

3hl3R 4M4R 4M4R 4M4R 3M2R

(nn.-1 (a. -1 (0. -1 (nx. -) (ny.-) (2so”. -)

lMlR

Ser eq.

size

882 414 451 266 145 594 533 789 896 828 450 138

3M3R 5M2R

516

held fvced as a doubly occupied core throughout, while the two inner-shell complement MCk (10 ag and 8 bt,) have been neglected entirely, leaving a total of 30 valence species to form the desired configuration space. This set is then used to generate all single- and doublcexcitation species with respect to a series of reference configurations found to be important for each state of interest; the Cl energy for the total configuration set is then obtained by means of a combineJ selection and extrapolation method. In the latter all those species which satisfy the spin and symmetry requirements of the state under investigation and are capable of lowering one of the fist n roots of the test matrix by a value greater than a specific threshold T(i.e. pass the selection criterion) are

a) To be used lo characterize the NOs in tables 8-10. h) Selection mMnR means that the selection process in

included in the final Cl treatment, whereby the test matrix is built up from elements of the configuration

species which exhibit a final Cl expansion coefficient in excess of 0.1 need to be included in the reference set.

to be tested and the set of reference species. When this procedure is carried out for a series of Tvalues and the effect of all neglected species at a given threshold is estimated on the basis of their energy lowering effect in the test matrix it is possible to extrapolate the results back to the value for the full (T= 0) single- and double-excitation space [7,8]. In this way the CI eigenvalue for the entire list of generated configurations in the range of 1500 to over 18000 can be obtained to quite satisfactory accuracy while only requiring the direct solution of secular equations with corresponding orders of 736 to 3 I60 in the present study. The choice of the reference con-’

In most cases thii criterion requires the use of only one or two reference species, but for some states this

figurations is a critical factor in obtaining con&en; .

-.

_-.

. \..’ I

16 17 18 :‘, 21

258 414 350

2M2R SM2R c)

1MlR IMlR 1MlR

$49

258

carried out with m reference (main) configurations based on n roots. c) A configuration with expansion coefficient greater than

0.1 was not included as a reference configuration.

results for the various electronic states of a given system; as in previous work it has been assumed that all

number increases to as high as five. Approximate NO basis sets are generally used to form the desired configuration space. Such species were obtained in the present work by carrying out a

high-threshold (T- 200 J hark generally) CI calculation of the type‘discussed above employing an ap propriate set of SCF_MOb. followed by diagonal&g the resulw first-order density matrices for each state of interest [9] ; more smc getails cqnc&rting the FO @er+m &II be found in.table .7;,in many ~$9 NOs for more than one rtateir&e b&n tibta&ed from ,the sarnk.sec~Iti cquki&(hi$i& r$s). ekeby add-.

>I!,/,

I-

__

ST. Elberr et alhlectronic

31

spectrum of d&wane

Table 8 Ground state energy of Bat!6 obtained from various treatments a) CalC “cl.

&CT = 0) W

E(T = 20) C)

Basis d)

Sec. eq. size T= 20

tiding term in Cf expafision

1

-52.9604

-52.9569

X

2 3 4 5 6

-52.9509 -52.9565 -52.9561 -52.9555 -52.9541

-52.9568 -52.9534 -52.9528 -52.9520

l(1) 11W 9(l) 11(2)

926 736 922 916 832

0.963 0.963 0.959 0.959 0.954

7

-52.9540

-52.9515 -52.9506

14(l) 130)

964 762

0.957 (X) 0.951 (X)

00 (X) CG (X) (X)

a) Always lMlR-selection; secular equation size at T = 0 is 1536. b) VAte for the extrapolated energy to zero threshold, in hartree. c) Energy obtained at a threshold of T = 20 minohartree. d) X refers to ground stale SW MOs; the other numbers in parentheses indicales whcthcr the NOs result from di%onalletig fist or the second root of the calculation indiatcd in table 7.

figurations

ing to the efficiency of the overall procedure. The results of the calculations

carried out in this

ground

being required

state a number

the

in some cases. AS in the

of CI treatments have been of these excited species in or-

manner are summarized in table 8 for the B2Hg ground state. in table 9 for the corresponding excited

carried out for certain

states,

taken. From the treatments labelled 10 to I2 in table 9 for the (n.v*) t Blp state of B2H6. for example, it appears that the NO basis is preferable in the sense that it leads to a lower CI energy at a given threshold (T = 20 /.I hartree) than either of the other treatments using l(n,srv_+) SCF MOs (and to a,smaller configuration set); on the other hand this advantage is diminished once the extrapolated energy values For zero threshold are compared, an observation which is entirely in line with previous findings 191. The relia-

and finally

in table

10 for the various

positive

ion species; accompanying details of the treatments undertaken are also included. A value of -52.9604 hartree is obtained for the ground state energy of diborane after extrapolation to zero threshold (with a single reference species, I Ml R) *. This result is only slightly dependent on the choice of the NO transformation, despite the variety of methods employed to obtain them (table 8); the largest discrepancy is only 0.0064 hartree or 0.17 eV. Altogether the ground state wavefunction is marked by a single dominant term, and no secondary configuration with expansion coefficient greater than 0.05 is found to occur. The situation for a number of excited states is quite different, however, with several reference con-

der to check the reliability of the calculations under-

bility of the extrapolation calculations

‘%!+uad = (1-C;) &!$,o”b is Used t0 estimate the correlation energy of all quadruply excited spe-

cb in this case. an additional lowering of 0.0115 hartree is indicated, yielding a total energy of -52.9719 hartree.

Under the assumption of a total correlation energy (i.e. total molecular energy of -53.268 hartree [ 241 corrected for relativistic e&c& 1251 to -53.258 hartree. minus the Hartree-Fock limit (2.241 of -52.8331 hartree) for this system of 0.452 bartree. it is seen that the present basis accounts for some 409A of this quantity, or 50% of the correspending valence-shell correlation energy (if the inner-shell contriition is estimated to be twice the value for the He gTound state).

minimum

Tvalues

of 2 and 20 p hartree.respectively have been employed for an otherwise equivaicnt treatment: the discrepancy in the corresponding to be only 0.0004

* If the ,&tiOnship

procedure itself is tested in

9 and 10, for which

extrapolated

eigenvalues

is seen

hartree, in good ageemcnt with analogous results for other systems [9.76!, indicating that the error in the extrapolation procedure as a whole should be roughly 0.01 eV for each root obtained in this work. The effect of increasing the number of reference configurations (from which al1 single and double excitations are generated) is quite often seen more clearly in the T= 0 result than in the truncated Cl data, particularly when SCF MOs are used, as may be judged from calculations 11 and 12. In terms of excitation energies the differences in the various ’ Bl, values obtained from calculations 9 through

bqicr

CA. no.

8 9 10 11

12 13 14 is I6 17 18 :‘o 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 Ef 40 41 42. 43 44 4S 46 47 48 3: 51

for the low-lying excited states of BlH6 obtzined Qom various treatmcntsa~

state

EW-

0)

EW = 20)

B&S

-0.6997 -0.6888 -0.6892 -0.6926 -0.6886 -0.6577 -0.6315 -0.6289 -0.6223 -0.6060

-0.6849 -0.6883 Cl -0.6822 -0.6804 -0.6804 -0.6504 -0.6190 -0.6185 -0.6111 -0.5952

(n, WY *t 3(l) 3(l)

2MlR

ZT’ 4$ 7U) 6(t) 5(l) a(2)

JMlR IMlR 2MIR 3MlR 2MlR 2MlR 4M2R

-0.6070 -0.6013 -0.5928 -0.5922 -0.5991 -0.5989 -0.5934 -0.5710 -0.5657 -0.5640 -0.5653 -0.5659 -0.5582 -0.5544 -0.5555 -0.5484 -0SS2S --OS485 -0.5384 -0.5487 -0.547 1 -0.5374 -0.5331 -0.5328 -0.5326 -0.5260 -0.5319 -0.5331 -0.5176 -0.5161 -0.5156 -0.5089 -0.4863 . -0.4469

-0.5952 -0.5875 -0.5848 -0.504 1 -0.5886 -0.5882 -0.5858 -O.S589 -0.5529 -OS530 -0.5557 -0.5553 -0.5501 -0.5467 -0.5423 -0.5409 -OS445 -0.5404 -0.5327 -0.s41s -0.5 164 t) -0.s195 -0.5243 -0.2233 -0.5231 -0.5179 -0.5200 -0.5 107 -0.5096 -0.5089 -0.5074 -0.4997 -0.4775 -0.4399

7(2) 9w l(1) X 11CU 12(I) X l(2) 3(2) 3(2) ‘13<21 lf(2) 14(I) X 9(2) X 11(31 X l(l) X +Cu 313) bY * 3s) lS(2) 14(21 X S(2) 2(3) 4~2) 40) l(3) ky, 3px) (=y 3s) X0(4) l

.se~rctionb) IMlR 7,MlR

4M2R 3NlR 3MlR 1hllR 3MlR 3MlR lMlR 4M2R 3hl2R 2MlR 3N2R 4M2R 2MlR 1MlR 3M2R IMlR 2MlR IHiR 4M2R 1MlR 4M3R 3M2R SMZR 2MlR 5MlR 1MlR sM2R 1MlR 2M2R 3M2R IMlR 5M2R 1MlR

Secular eq. ske T=ZOIT=O 1?80/5193 2481i9128 1298/9 128 1390/18057 1402/317O 1270!6O+4 1436/8942 1361f6126 143816227 3056114781 2683/15114 - 15701887 l 112tif8871 1392/3231 143liSWl 1418~8871 l404/3173 187917612 2833/8698 165816175 2329J8873; 2so9/tis1s 128616100 133W3086 2599~887I 133313088 127616094 1333/3138 2077/11066e) 1467;3230 227l/lsaso 2039il3M)S 2886!12567 1276;6099 1231/12567 140113228 2487113241 2153i12685 1235f3219 230915594 194915373 134013169 28Wl2S67 1472f323l

tiding term in CI expansion 0.952 (n, ay*) 0.947 (n,ny*I 0.948 (II, my.1 0.948 (n.ry*) 0.948 (n. IT*) 0.950 (a,lCP) 0.944 (nr,ny*) 0.945 (n. my*) 0.948 (n, 3s) 0.898 In, 3pyl -0.309 (nx,ny-) 0.946

in,ii$sy)

0.944 (n, 3pz) 0.943 (n. 3~2) 0.943 (n, 3pz) 0.949 (n. 3p*) 0.949 (n, 3~x1

0sg4’ %ii3w) 0.953 (n, 3dyz) 0.919 tn. 3dyzl 0.918 Gy.xv*) 0.919 by. ny*) 0.959 (cz3PY) 0.945 Co, 3& 0.938 (a. 3px) 0.944 ((i. 3pr1 0.953 (cr.3FzI 0.943 (cr.32) 0208 (0.3pzn) 0.936 (nx. .3r) B) h) 0.957 (WY 38 0.960 iv&; 36 0.957 (wJ@, 38 0.945 k.y.3s1 o-936 $.% 3Pe l

0.954 by. 3p) 0.9S233dy”’

.

0.96 L by; 3~x1 0.913
91 Rncrgy valuer m gkvcn in hcrucc, zero of’encrgy is -56.00 hlftrec. The notction h rta&& k &t in t&la 8. d) 0.607
ST. Elbert et ai./i!Jectmntc spccmtm ofdibmne

33

Table 10 Total energies for the positive ions of BnHe a)

talc

Seadar

lt0.

.

52

:$2&t

-0.5177 -0.4754

-0.5101 -0.4681

16(tL? 17(1>

-0.4588

-0.4475

-0.4308 G.3690 -0.1684

-0.4217 -0.3566 -0.1467

53

1 ‘bsn 8 1 %J

54 55

‘2B~o 22Ag

56 57

3)

=

Selection

BDSiS

Err=

0)

E(T

20)

slate

eq.

size Leading term in CI expansion

T= 20/T= 0

1MlR

I275/2930

0.948 In. -1

190)

1MtR 2MlR

112Oj2839 126919550

0.955 io* -> 0.948 Qrx,-)

20(l) 2l(l) 18(Z)

IMlR 3MlR 4MIR

114412936 1214/14957 1233/17519

0.962 Cry. -1 0.9-to (2SOu,04) 0.910
Encrpy values UC given in haruec, ZCIOof energy is -56.00 hartrea. The notation isanalogous to that in table 9.

12 is only in the order of O.iO eV *; tire majority of calculations for the other BgHe states are similar to that of treatment 10 for the t Bt, species, with appro. priate NO basis sets (as described in table 7) being used in each case. Additional comparison between results obtained with SW MOs and approximate NOs can be found in the case of the higher excited states as well, as for example in caiculations 40 and 41 for the 2l Bg, (v, 3s) species. In order to obtain essentially equivalent results at T = 0 if SCF MOs are employed, a 5M2R c~cu~tion is required, compared to the 2M I R selection procedure using appropriate NOs, as a result secular equations of more than double the size need to be solved in the SCF MO Cl treatment (table 9). In many cases the ground state SCF MOs were also used to form excited state wavefunctions (num~rs21,24,31,33,35,37~d43).~ex~cted~e~ MCk produce somewhat higher energies (especially since a co~espondin~y smaller number of reference configurations was often used in these treatments)

than the optimized NO sets, with the T= 0 discrepancies being generally larger than the corresponding quantities at T = 20 ~1hartree. Nevertheless the extcapolated energies in the ground state MO bases are never more than 0.2 eY above the best results obtained for the corresponding excited state. By the same token one notes from tabie 8 that discrepancies of quite C&IIilar magnitude are found when the ground state CI wavefunction is represented by an excited state NG basis (calculations 3 to 7). The poorest results are produced when the approx~ate NOS of the ground state are employed to represent various of the diborane excited states (nos. 20 and 36), but this finding is cfearly related to the fact that the correlation orbit& in this case do not allow an at all satisfactory description of the strongly occupied terminal orbiial in the transition of interest. Taken as a whole the experience with different NO tr~sfo~ations indicates rather strongly that the results for such relatively large configuration space as employed in the present work are quite stable with respect to the manner in which such orbital sets are chosen. Fitrat& it should be noted that in only one instance were more than two roots required in the selection procedure in order to represent a @en exP”-:! state to satisfactory accuracy, namely in the treatr :nt of the 3tR3, (trr, 3s) species, since this state rn!-- .s strongiy with each of the two Iawer~Iying roats of the same symmetry. The larger number of selected configurations in this case necessitated the use of a higher Tvalue (T = 40 ~1hartree) than usual, thereby resuRing in a posribly poorer extrapolation than in the-other C&XIWions listed in tables 8-10.

* If the contribution of h&her excitations is estimated according to perturbation theory as discussed in the preceding footnote. a t Btgenerm of -52.7080 hartree is iadiczttedfrom eafculation no. 12. Taken witfi the corresponding gotmd state value this resultI&s to a t(n,n*) excitation energy of 7.18 eV in this approximation, compared to the best Tr:Orcsultof7.29eV(iTonlyalMiRtrccrtnentisusuf for both state% the vahle iaueases to 7.39 CV). it is intewstingia~conncctMnUuttbe’BsgstattTsfouglIchrvt the rmnd taqtst correlation energy (I.0 eV more than the . groundsta&,for exampfe) of any of the %fie (01 b&t statestreated. ~

.

_:

. ..

:

.

. _. *. ‘.

. . .

34

ST. Elberr

5. Calculation characteristics

of oscillator

strengths

et al. /Elecmmic

and upper state

To facilitate the interpretation of the diborane spctrum oscillator strengths have also been calculated for the various dipole-allowed transitions obtained in the Cl treatment. Both the dipole-length(r) and dipole-velocity (V) operators are used for this purpose. The ground and excited state wavefunctions were always expanded in the same orthogonal basis and generally correspond to a T = 20~~ hartree selection process. Specific details of these calculations as well as the resultingfvalues are contained in table 11. It is found that in general the agreement between correspondingf(r) and f(V) values is quite satisfactory; discrepancies are of the same order as have been found in related calculations [7.8]. The distinctions in correspondingfvalues obtained with different orthogonal basis sets are also found to be relatively minor. The ground state (X) MOs appear to be fairly adequate for the representation of the various Rydberg excited species (with the possible exception of the Z1 B2,, table 9) and thus only this basis has been used to Calculate the oscillator strengths for the highersnergy

Table 11 Oscillator strengths for the lowest-enerpy allowed txansitions in B& Upper state

cak.

Upper state

no. a)

1 * Bau Cn. 3pz)

.

1 ‘BI,, 0% 3~) ~‘BI,

fall into three categories: that of the very strong intervalence (QJ,v*) transition, the much smaller values for the lowest (Rydberg) states of Bsu, B,, and Blu symmetry respectively, and fiially the three results of intermediate magnitude for higherenergy species of somewhat mote complicated composition (table 1 I). The ‘(v, 7ry*) result is normal for such a parallel polarized valence-shell transition, and similarly the relatively small intensities of the l (n, 3pz). l (n, 3px), l(a,3px) and l(u, 3py) excitations are quite consistent with the expected diffuse character of the upper states in these cases. The fairly high absorption

intensity

* A cakulation for the

2’ BI, (ny. ny*) has also been urried out employing the X MOs. The resulting wavefunction has 3 considerable admixture of other states lo.881 (rry.ny*) + 0.305 (ny. 3dyz) - 0.103 (o.o’)] and is rather poorly represented because of the failure to include the two secondary configurations in the associated reference set for this tieatmwt; as a result the conespondingfvalue is somewhat overestimated in this case If@) = 0.454 andf(V) = 0.3091. The inadequacy of this ueatrnent also clearly shows up in the large deviation of 0.034 hartxee in the total energy for this state compared to the best results of table 9.

obtained from various treatments

9w

0.055

0.051

x

lC0 X 110)

0.036 0.036 0.020

I

24

X

O.MZ 0.M2 0.030 0.026

130)

0.324

E 30

li<2) 14(l)

0.335 0.020

.

:: 37 43

~0.019 0.291 0.294 0.014

X

0.024

0.012

x x X X.

0.048 0.165 0.157 0.140

0.038 0.105 0.131 0.144

L

i Y -x 2

* y

a) The number given in this c&mm refefs to the &in6 calculation in hbti 9, bl The n&tion for the basis is that described in table 7: the byis was alkyr used far ground bil c&al

: -

__

L_ . -.. ;.

_., ._

calculated

for the other three transitions appears to reflect a signilkant admixture of valence-shell character in the corresponding upper states, despite their predominantly diffuse or Rydberg-Iike composition. In the case of the (7rx.3~) and (7ry,3s) species, for example, it is

19

31

2’b,b~,39

transitions *. In general the cakulatedfvalues

20 21 22

2’B u(o,3px) 3 ‘B:,, CJ. 3pz) 3 * Bs,, (nx. 3s)

of diborane

Polarization

<=Y.uY*)

1 ’ &” k3PY)

spectrum

-;

_‘.’ .m .,

-..

state va~uncti?nr .-. -‘. _, -1. -_ .-:., -_:I._. _.; ._ _ :. : ._ - . __; : ,__ .’ -.:- ‘.-___.;,”: .. . _. : -. :_-. ..__ ._ _.. . . I -, -,. . ;:.._.___.~_ -_ _ .. . I ; , . ,:. ...-_..> ., :. -1~ -’-., ,_. ._ __ L\ I ..; _- ._- ;:

35

ST. Elbert et al fElectronicspectrum of diborane Table 12 Orbital expection values in different electronk states of BsH+ (Values are given in atomic units..)

Table 13

Orbital

AOs a)

@JO/MO)

St.ote

Or%

(y%

3lQ

3 r B3u Cn. 3~0 3 ‘Br, (a. 3~) X 1 r Bu, (n. 3~x1 2 t Bs, G-G3~x1 X t ’ Bsu io, 3py) X 3 ’ BJ, (w, 3s) 2 t Bzo kv. 3s) X 2 ’ BI, (=y.ny*) X

14.31 14.25 15.29 41.26 4 1.22 42.89 13.17 13.90 14.93 10.66 1580 2.20 4.18

14.34 42.80 14.28 42.86 15.32 45.00 13.77 13.37 13.75 13.36 13.78 14.30 39.47 14.62 41.68 15.27 15.25 10.95 11.56 8.43 16.09 11.40 6.59 8.45 12.54 14.14

3pt

3PY 3s

r?v*

tz2)

Expansion coefficients of tie

3s orbital (hlO~N~} in

differ-

ent states

(l/r) 0.1383 0.1401 0.1299 0.1443 0.1444 0.1375 0.1454 0.1380 0.1869 0.2678 0.1769 0.3390 0.3192

quite clear from the orbital expectation values of table 12 that the 3s orbital in these transitions is much more compact than the majority of 3p orbit& calculated. Fkamination of the pertinent expansion coefficients in table 13 far the 3s orbital in three different basis sets does in fact show sizeable contributions from the boron 2s.type AOs in each instance and, in the case of the (zy, 3s) upper state, even a significant cons t~bution from the bridged hydrogen species; the fatter point aiso shows up in the considerably smaller 6r2), (y2> and (z2) matrix elements calculated far this orbital compared to the result obtained for the other two 3s counterparts (table 12). By contrast the 3p Rydberg species appear to be much less dependent on the nature of the state for which they are calculated. The large distinction in the oscillator strengths of the 1(n,3pt) and %,~Pz) transitions calculated in table 11 hence appears to result from the fact that, while both pertinent 3pz upper orbitals have roughly equal admixtures of valence (o*) character in their composition, the orientation of the initiating orbital is along the azrm axis as lhe upper MCI in the Ianer case but afang a perpendicuIar axis in the weaker (n. 3pa) excitation. Similar results have already been noted in the case of ethane IS), in which a three-fold larger intensity is ca]cul&ed for the parallel polarized o(3a$ -k 3po Rydberg-like transition than for the

corresponding’perpendicular lek -) 3pu spedies. even .though both upper states exhibit roughly equivalent .

s3

Y terminal h 3s bridge h 3) sj on

-0.03 1 -0.776 -0.034 1.859 0.049

-

-0.126 -0.634 -0.032 1.752 0.052

-0.468 -0.168 -0Jl47 1.292 0.167

represents +ssen&Ily the wntracted

pert of rite 2s A0 the boron atoms. white Q is the long-rarx5ePart thereof.

A0 composition, in particular with each containing significant contributions from the valence-sheU2pcP orbital.

6, Comparison of the calculations with the experimental spectrum of B,H,

IIre best resuln obtained in the present CI study for the transition energies to the iowest excited singlet states of diborane are contained in table 14 along with a comparison of the calculated and experimental [3) vertical ionization potentials for this System. Several features stand out quite clearly, namely the good agreemerit found between theory and experiment on the location of the vertical Ii% and also the regularity observed for the members of the various Rydbecg series treated. Although the SCF results (table 4) allow for relaxation of the core electrons upon ionization, they clearly ignore important correfation effects which in this instance lead in almost all cases to an overestimation of the rrsults compared to experiment. Nevertheless the correlation energy differences bctween ground state and positive ions in B$i6 are seen to be much smaller than in related systems such as ethylene and water [7] and thii fact is seemingIy consistent with the good agreement (largest error is less than 0.3 eV) found between the CI and expe~men~ values for the IR in this case *_ The importance of the CI is especially clear in comparison of the results for the

* That it, !&ICC it om only

be

reasonably hoped that such Ct

dimin&&t&cdistinctionsin cotreialion energies between ground and ionic stams but not remove ulenl entirely.

treatments sobstaotMUy

ST. Elbert et al..IElecrronic spctram ofdibwamc

36 Table 14 Sin&t excitation enewies (in

CW

and most probable oscillator skengths ob&ncd

from (he Cl treat&nt

7.18 b) 3s

9.20 9.77 (KG)

3pr SPY

9.64

3pr

9.83 (0.03) 10.74

3dyz 0*

b

- (expW

Il.81

a)

12s c) 10.60 lo.99 b) (0.16) lo.91 (0.02) 11.02 (0.0s) 12.09

11.20 (0.16) 11.66

11.63 (0.14) Il.95 b)

11.51

12.10

11.63

12.28

13.9

14.7

14 oc) Il.88 b)

13.3

16.06

21.55 21.4

ref. 131

a) The dipole-allowed

transitions are always underlined. the conespondingfvalues are indicated in parentheses. from 1 MlR cll&tion and perturbation theory to estimate quadruple and higher excitations. The corresponding wlues from the best CI treatment are 7.28 cV (n, ny*). Il.09 cV ((I, 3pz). 12.04 eV (v. 3pz). 12.04 eV (n,-hl3.19 CV b. 4. C) Not ti configurations with expansion coefficients with mgnitudc > 0.1 were included in the referena tet; thus the value b) Values obtained

might be too high by as much as 0.5-1.0 eV.

zrx and qv ionization potentials, in which case the SCF calculations show the two values to be inverted relative to experiment; after Cl the ny IP is (correctly) predicted to be higher than the m counterpart by 0.76 eV, in excellent agreement with the experimental fmdinp (A/Z= 0.8 eV) [3]. AU in all these results speak well for the reliability of the present Cl calculatioos in ordering the various diborane states. In particular the indication is that because of the smaller car-’ relation energy differences between ground and excited species of diborane itself such theoretical treatments should be even more effective in predicting transition energies for this system than in previous examples in which the differential correlation effects are sometimes &kedly.larger [7,27]. Finally it is worth noting that because of a cancellation of relaxation and correlation effects Koopmans’ theorem predicts the diborane 1Ps better than the straightforward use of&e SCF method. but the former results are still consider_- ably inferior to those of the Cl treatment. Since the Rydberg s&s are in many ways simii to the c~orresprqding ionic species it is reasonable to _expect that thediscrepancies betieen Cl and actual v&al transition energies to such diffuse states wiR ’ : @r& df Ute same,order of magnitude as has_&& foti$

_:

_. __.

in the lP comparisons. i.e. smaller than 0.3 eV; in fact experience with other systems [7,28] indicates that the Cl calculations generally predict the Rydberg (and valence-fhell) levels to higher accuracy than the corresponding ionic results. In each of the four diborane Rydberg series studied the 3s Rydberg level is calculated to lie wetl below the corresponding 3p species, which in turn are invariably found clustered in a

relatively small energy interval, with 3py the most and 3px the least stable of the three *. The average term values for the four series are found to be 2.60, 2.15 and 1.08 eV for the 3s, 3p and 3d members respectively, consistently lower than the values (3.10. 2.43 and 1.33 ev) suggested by Robin [23]. A comparison between the calculated Cl energy levels’and the known experimental spectrum of diborane

is given in fig. .I, $onj with corresponding SCF tid s&led ICSCF results ^_ (sect: predictions of an ._ 3)‘and _’ .. .

_

ST.

Elbcn et aL/Electmnicspectrum ofdibomne

37

Energy (eV1

A

___A----

m,Ky-J

8.0

Ref.[3]

Fii

1. Low-lyingexciled

statesof

&He

SCF

ICSCF (scaled

obtakqed from several treatments

earlier theoretical treatment (3). AU SCF results are seen to lie above the corresponding CI fiddings, indicating that the correlation energy of the &Qj closedshell gr&nd state is mu&r than fc@any, of the openshell ejtcited skies treated.:The relative spacing betwee? the SCF levels is apprdxi+ely what is expected ._,

CI 1

-

Experimental Ref. [6] (Solid lines indicaterymmetry-dowcd

transitions.)

for Rydberg series members a& these data a!e seen to be in relativety good accord with the corresponding CI energy differences. The values for the scaled ICSCF excitation energies (table 6) are in generally better agreement with the CL results, showing a clear trend toward overestimation of the results for the

38

S f. E&err er al/Elecrmnic

Rydberg transitions while underestimating the corresponding findings for valence-shell species. This distinction between Rydberg and valence-shell excitations in the ICSCF formalism is easily understood, however, since the calculated results correspond to spin-averaged transition energies (with $ weighting to the trip lets in the usual case, for example). Consequently this averaged excitation energy represents the singlet levels relatively adequately if singlet-triplet splittings are small (as in Rydberg states) but underestimates them considerably for states with large multiplet splittings; if the results of table 5 were used to take account of this effect the ICSCF singlet excitation energies would all be larger than the corresponding CI values (although not uniformly so). Finally it is found that the results of the earlier virtual MO calculations of Brundle et al. [3] for the various low-lying transitions into the n* MO are significantly higher than the present Cl findings in each case, with discrepancies of 1.37, 1.42, 1.38 and 1 .l I eV being obsebed for the four cases for which comparison is possible. The Cl results in table 14 show only four intervalence singlet-triplet transitions lying below the first (n) ionization potential in diborane, all of these occurring to the n* orbital, whereby the lowest three *(n,Iry*), t(o,rry*)and *(rrx,n~~*j are all forbidden by the dipole selection rules. The lowest-energy process involving the (I* appears to occur in the neighborhood of 14 eV, over :! eV above the minimum IP. Considering the broad continuous nattlre of the BzH, SpeCtNm (as sketched in fig. 1). with its two regions of relatively intense cf> 0.3) absorption below 12 eV, it is quite clear that the present calculations cannot explain the experimental findings solely on the ba&

of dipole4owed vertical excitahbns am&g the valence MOs of this system In particu!ar the interpretation given recently by Robin 161, in which the peaks at 9.3 and IO.7 eV are assigned as rr + A* and (I -+ a* vertical transitions, respectively, is inconsistent with the present Cl excitation energies. Furthermore, given the very good agreement between calculated and measured (vertical) IR in the present study (table 14). it seems unlikely that the failure to support the two. valence-transition interpretation of the diborane spectrum can be traced to the inadequacy of the theoretical treatment. The assignment of the Rrst weak feature around’ 6.82 eV to the forbidden *(n, n*) transition is well

specncrm of diborane substanhated by the present CI study; the calculated vertical energy difference is 0.36 eV above the pertinent absorption maximum, which in turn is likely to correspond to an excited vibrational level of the upper

state. An earlier analysis of the geometrical characteristics of the ground and excited states of diborane and ethane [ 111 suggests that excitations into the antibonding n* MO should be accompanied by significant geometrical changes relative to the B2H6 ground state. including eradication of the inversion symmetry of the molecule. Distortions of the latter type render the l(n,a*) transition allowed (C, point group), thereby leading to a situation in which (lower-energy) non-vertical transitions would be expected to predominate *. The assignment [3,6] of the shoulder at 8.3 eV as the l(o.n*) absorption is also nicely supported by the CI results. Because of the influence of the strong neighboring transition 8000 cm-t to the blue of this feature, however, it is difficult to infer the location of this species with any high degree of accuracy from present experimental data. The peak at 9.3 eV in the spectrum is quite welldefined, but there does not appear to be any candidate among the available strong transitions in B,H, which has a vertical energy difference falling near this value. The *(n,n*) species is calculated to lie 1.45 eV above the location of the peak absorption, indeed in close proximity

to the more intense

maximum

occurring

beyond the first band system in question. There are two allowed Rydberg species at 9.77 and 9.83 eV (n * 3pr and n + 3px) respectively, but the associated f-values are too small to account for the entire experimentally reported oscillator strength of 0.3 [6]. There are also a number of forbidden transitions in the 93 eV region (table 14 and fig. 1, also triplet species), but even taking account of possible geometrical distortions it seems questionable whether such species could pro-

duce such relatively high intensity. In considering this point further it is also noted that the trough between the 9.3 eV (E = 8000) and 10.7 eV (e = 15 000) absorption peaks 16) itself c&respends to rather slzeable intensity (e = 5000); which again emphasis the continuous nature of the diborane “Alu,recallfiomr$athnt~cboagerintheBzHs gwmeby are accomplnkd by~dcfite atteratiom in the ‘(a, r*) ekitatian e?rgy, again i@iting that the potential surfrecs for gr&nd and exdted-kxte in thio case am far from : paraltd.

.. .

-:. /.

_:

_-__

.

: .. -

-. I

‘. ;

.._ ‘: ..

. _

f

ST.

E&err et aLIElectmnic

of

39

dibome

tion of more diffuse AOs to the present basis set would produce the corresponding higher-lying memhers of the associated Rydberg species, for which the intensity is smaller than for the titt members but

spectrum.

‘Ihis observation coupled with the results of the present study suggests that what is involved in this absorbing

sgwctnm

region might be one (or more) dissociative

upper states. The most promising candidate appears to be the l (n. n*) species, since excitation out of the bonding A in::, the antibonding n* MO most likely

nevertheless could still be significant; in the related ethane molecule the f-value for the (3sLg,4pa) transition. for example, is calculated to be about 50% of

leads (among other distortions) to dissociation along the weak BB bond. Under this assumption a broad absorption pattern would be expected for this strong. ly allowed transition, with the intensity falling off rather slowly from the point of vertical excitation Calculated to occur around 10.7 eV. In other words there is reason to believe that a good portion of the absorp tion pattern in the 8-11 eV region, notably in the neighborhood of the peak at 9.3 eV, might still be due to the underlying t(rr, n*) absorption. The peuk

that for the n = 3 member. In any event the pure valence u + Zpo* transition does not seem to be directiy involved in this region of absorption (table 14). The total oscillator strength for the three n = 3 Rydberg transitions found in the 1 I .O- 1 I .6 eV spectral region is calculated to be 0.46 in this work, and when this amount is added to the underlying L(tr.n*) contribution plus those from the related Rydberg members of slightly higher energy one obtains a total

itself seems !4ely to result from the ‘(n, 3~2) and

intensity which is consistent with the observed

‘(n, 3px) Rydberg-like transition (table 14). whereby the 0.4-0.5 eV distinction between absorption maxi-

trum in this region.

mum and calculated ver?ical energy is very close to what has been obtained in ethane [8] for a similar ab. sorptiorr system in the neighborhood of 9.4 eV [28,29] In summary then the best explanation for the fist

strong peak in the diborane spectrum which can be drawn from the present CI treatment involves superposition of two Rydberg transitions on the underlying absorption caused by the dissociative t(l~, n*) state nt higher vertical excitation energy. The strongest feature in the diborane spectrum is the broad shoulder starting at 10.7 eV. Despite the

location of the l(rr,rr*) vertical excitation at almost precisely this energy value, only a portion of the overall absorption intensity should be attributed to this electronic transition. The remainder appears to be caused by the three relatively strong Rydberg-type transitions (each withfivalues of roughly 0.15) calculated at 10.99 (u, 3pz), 11.20 (nx, 3s) and 11.63 eV (try, 3s) respectively. The fist of these species contains a significant amount of (a, a*) character (similar to the 3al, + 3pu and (J+ a* states of ethane IS]), hence accounting for its relatively large calculatedf-value, while the compactness of the 3%type MO involved in the two other transitions appears to be responsiile for the strength of these two species. Furthermore, addi-

spec-

Acknowledgement *. The authors wish to thank the Deutsche Fonchungsgemeinschaft for the financial support given to this work. The services and computer time made availabbe by the University of Bonn computer center are gratefully acknowledged.

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