Non-empirical SCF and CI study of the SOH radical

ChemicalPhysics 20 (1977) 381-389 .O North-HollandPublishingCompany

NON-EhlPIRICAL SCF AND CI STUDY OF THE SOH RADICAL A.B. SANNIGRAHl*

, SD. PEYERIMHOFF

Lehrstuhl plr Theoretische Chemie der Universitiit Bonn. Wegelerstmsse 12, D-5300 Bonn, Germany

and RJ. BUENKER Instihtt fur Physikalische Chemie der UniversitUt Bonn. Wegelerstrasse 12. D-5300 Bonn, Germany

Received16 September 1976

:.

Ab initio SCF and CI calculations using a double-zeta plus polarization (DZP) AO basisare reported for the determination of the geometry and dipole moment of the SOH radical in its ground @‘A”> and first excited ‘A’ state; the *A’ + ‘A” electronic transition including its vibrational characteristics is also studied. The radiative life time of the ‘A’ state is calculated to be in the order of 3 x 16’ sand the To value is predicted to be 0.6-O-7 eV; the absorption maximum is calculated to occur when all three vibrational modes of the upper state possess their lowest quantum number (i.e., there is almost no difference in geometry between the two states). The dipole moment at the ground state equilibrium geometry (O-H = 1.802 bohr, S-O = 3.08 bohr and 4 SOH = 109’) is found to be 1.82 debye for the Z’A” and 1.76 debye for the 2A’ states respectively. Extensive comparison with the HSO isomer is also undertaken, whereby SOH is calculated to be more stable than HSO by 12 kcal/mole.

1_ Introduction The HSO radical has been studied experimentally in its ground and lowest electronically excited state [I ,2] , and quite recently ab initio SCF and CI calculations have been reported for this system [3] _To date neither experimental nor theoretical information is available for its isomeric partner SOH, however. It is thus the aim of the present study to apply the same theoretical SCF and CI procedure to SOH as has been employed previously for HSO in order to obtain a good estimate of its various properties, including structure in ground and first excited state, dipole moment, vertical electronic transition energy and corresponding oscillator strength, as well as to allow for a detailed comparison of these results with the

corresponding data already available for HSO (and in some cases also for HO-& 2. Equilibrium geometry For the present study the SOH molecule is placed in the xy plane with the oxygen atom at the origin of the coordinate system and the SO bond collinear with the x axis (the hydrogen atom has negative x and positive y coordinates). The same basis set as has been used in the previous study [3] of HSO is employed, i.e., a contracted [614], [412] and 12111 set for the sulfur, oxygen and hydrogen atoms respectively, augmented with optimized pi and s functions in the SO bond. Potential curves are calculated (SCF technique) for the SOH radical in its *A” ground and lowest A’ excited state as a function of the three intemaI coordinates (spec:ifically

l

Alexander van Humboldt Fellow, on leave from the Department of Chemistry, Indian Institute of Technology, Kharagpur - 721302, India.

for H-O

values of 1.60,

l-70,

1.8243, 1.92 and 2.00 bohr, for angles SOH of 97, 105,110,115 and 130 degrees and S-O bond lengths of 2.88,298,3.08,3.16 and 3.3?.bohr respectively);

A.B. Sannigrahi et al fNon-empinkal SCFand CI study of the SOH radical

382

Table 1 Equilibrium molecular constants for the SOH radical ob taioed from SCF calculations (distances in bohr,.angles in d&e, force consfants in mdyn/A, frequencies in cm-’ and energies in hartree)

state)

TA' (excited state)

s-o 4 SOH

1.802 3.09 Go8$~ 112

1.807 3.15 114 (11 l)a)

~ww v1

9.51 4060

9.16 3984

k_cso> v3

5.49 (7.o)a) (1035)a) 916

4.43 a51

Constants

(ground

z*A”

O-H

0.92 c1.0,a)

kc& SOH) F2

1247

E (SCF)

-4729171’

(1308)a)

0.58 (0.54)=) 989 (9561a) -4;2.9021

a) The values in parentheses are obtained via a polynomial fit to three points of the corresponding CI curve.

polynomial molecular

fits to these curves yield the equilibrium constants

collected

in table l_

First it is seen that the OH bond length is practically the same in both states, this value in turn lying very close to that of typical OH bonds such as in Hz0 141. The calculated ground state SO bond length is considerably larger than the corresponding value in SO (2.82 bohr) or SO, (2.704 bohr) 141, however; but again only a relatively small change in this quantity (0.06 bobr) occurs in going from the ground to the excited state, in contrast to the situation in both HO, [S] and HSO [3]. The calculated ground state bond angIe is somewhat larger than in isovalent HO, (106O [S J ), with a small increase in the value being predicted to occur upon transition to the 2A’ excited state of SOH. This general trend (although normally somewhat stronger) would have been expected on the basis of qualitative MO theory C6lThe calculated OH stretching frequency compares well with that observed for Hz0 (3756 cm-l [7]), especially since such calculations appear to generally overestimate AH stretching frequencies by 510% IS] *- The small decrease in n3 upon excitation l

Note that little change is expected between the SCF and

CI OH stretching potential curves.

seems to be consistent with the corresponding small increase in SO bond Ieagth in going from ground to excited state. It is interesting that the calculations predict a relatively large change in the curvature of the bending potential as a result of the 2A’ + 2A” transition, even though there is very little difference in the calculated equilibrium angles of the upper and lower states.

3. The i2A)

C- z2A”

transition

Although structural parameters can quite often be obtained to satisfactory accuracy using the SCF procedure, this is not the case for transition energies. Thus CI calculations, which take into account correlation effects, are carried out in order to determine

the transition energy to the first excited state Z’A’, as well as its radiative lifetime. Furthermore since the equilibrium parameters determined by the SCF method might also significantly change as a result of inclusion of electron correlation (see also table l), configuration mixing was also undertaken for several points around the SCF ground state minimum (i.e-, at angles 105”, 112”, 120° and SO bond distances of 3.00,3.094 and 3.20 bohr respectively). 3. I. CI procedure The general features of the CI procedure employed are given elsewhere [9] ; the details are essentially equivalent to those used for the calculation of HSO [3] . The six innershell MOs (la’ to Sa’ and la”) are held doubly occupied in all configurations while all other MOs with the exception of the five highestlying species (inner-shell complements) are available for variable occupation by the remaining 13 electrons of the system. All singly- and doubly-excited species with respect to each of the dominant configurations in the CI expansion are generated in each case, but only those capable of lowering the total CI energy by more than 20 microhartree are included in the largest secular equation actually solved. The contriiution of the remaining unselected species is taken into account by an extrapolation procedure [9] based on perturbation theory.

AA?. Sannigrahiet aL/Nonsmpiricai SCFand CI study of the SOH radical 3.2. Energies The Cl energies obtained for a few key points around the ground state equilibrium geometry for the two states z2A” and z2A’ are given in table 2 along with various technical details. It is seen that the expansion of the ground state wavefunction contains, in addition to the leading term, one other dominant species with a coefficient of approximately 0.07 wheR ground state SCF MOs are used in the calculation; no such configurations of secondary importance occur in the a2A’ excited state if its own SCF MO basis is employed. The secular equations actually solved for both states are of comparable size (table 2), although the generated configuration space for the ground state is almost twice as large as for the excited species. The correlation energy of ground and excited state is very similar, the difference being only in the order of 0.18 eV, this result is in some contrast to the situation in HO, [lo], in which this difference is approximately 0.30 eV, or in HSO (0.50 eV f33 ). A golynomial fit to the data of table 2 gives a total CI energy for the SOH ground state of 473.1124 hartree and a vertical electronic energy difference between g2&’ and %‘A’ of 0.591 eV, compared to the SCF value of 0.408 eV (table I).

In order to make th& prediction of the %‘A’ + z2A” transition in SOH more meaningful the theoretical treatment has been extended to ineXude a vibrational analysis of the intensity distribution associated with this band system. The oscillator strengthffor the transition between the two states in question (or alternatively the radiative lifetime of the excited state) is obtained in either the dipole length or velocity form from the following equation:

&) =~l(Jl’leZr,~~~~l~“,12~ or f(~)‘~I(Jl’leZvP,~,I~‘12/~_ The half-life time of the upper state is then related to

f by the formula 173 *:

co~esponding formula as wricen in ref. [7] gives a value of 24 for the proportionality factor, but recalculationu&g the variouspltysical constants shows the correct value for this quanti~ to be 1.50.

* The

383

A.B. Sannigahi

et al/Non-empinkal

Sinc’e the calculation of the electrpnic transition moment is rather cumbersome ifnon-orfhogonal MO basis sets ate used, as has been done in the above CI treatment (2A’ SCF MOs of the z2A’ staie are not orthogonal to the x2A” SCF MOs used for the ground state). additional CI calculations are undertaken for the ground state in the 2A’ SCF MO representation. The corresponding values for the oscillator strengths and their variation with SO bond length and SOH bond angIe are shown in figs. 1 and 2. It is seen that the fvalues obtained by the length and velocity operators are widely different, even more so than in

.2.a 1.5 -1.0 3.10

SCF and Cf study. of the SOHradical

HO, [I 01, &hot& similar (and larger) values are obtained for f(r) and f(V) in HSO 13) _According to general experience the f(r) value is the more reliable one since it is less sensitive to details of the wavefimction representation (111. The latter point is illusfrated by the resultti of table 3, which show the influence

aU single-excitation

configura-

* AIthou

the correct method would be to calculate &;a. = S! j-K~,~R,~,.~ tiv**)i2ti (and similarly with Ye-,**>, approximation it was decided to use the Fran&-Condon (i.e., f * *I = $RR,,a*q~ *I$ v)~) since Re*ge is not found to c?&g very signifi&& over the tirst few vibrational levels ffgs, 1 and 2); krhermore the absolute accuracy of R,*g is not high enough to warrant the extra effort of evaluating the somewhat mom complkated matrix element including Re.e%

3.20

SO distance

of including

tions automaticahy (which is generally necessary for the calculation of properties) is greater for thef(V) than for the f(r) value. In any event it should be pointed out that differences between f(r) and f(v) values of orders of magnitude have so far been obtained only in exceptional cases in which quite small absoIute values off are observed, in which case cancellation effects of small numbers become increasingly important. The best inference for the radiative life time of the Z2A’ state in SOH in the resent treatment is thus in the order of 3 X 1 O- f s, somewhat larger than in I-IO, (see table 3). In order to predict how the intensity.of this electronic transition is distributed over the various constituent vibrational species it is necessary to compute the Franck-Condon factors for the three internal coordinates.* For this purpose the SC% potential sur-

Ibohr)

Fig. 1. Calculated asciktor strengthsf&) and f(v) for the ?A’ + PA” transition in SOH as a function of the SO bond Iengtn (0-H = 1.802 bohr, 4 SOH = 112”).

Ta bIe 3 Oscillator strengths and life-times calculated by CI techtiques for SUH and comparison with corresponding values in HOa and HSO f(r) SOW) SO&

-c

r

100

z 110 Angle

120 SOH

Fig. 2. C&Mated oscillator strengthsf(r) andflv) for the ??A’ *PA’* transition in SOH as a function of the SOH angle (O-H = 1.802 bohr, S-O = 3.087 bohr).

205 232 2 1.4

Probabl@) fr ,s

f(V) x X x x

10-6 1O-6 10-s lo*

2.00 3.94 1.8 1.9

x x x x

10-n 10-a 10-3 10-4

3x 2x 4x

1o*s M3s 10-5s

a) O-H = 1.802 bobr, S-O = 3.09 bohr and d SOH = 1129 ‘) Same bond 1engtb.sas in a) but 4 SOH = 109’; ali singly excited configurations with respect to the main configuration are included explicitly in the wavefunction. c, See also the fust footnote in section 3.3.

Table 4 Franck-Condon factors (~$~v**\Jt;>~)for the %*A” -*PA’ transition En SOH calculated undes the assumption of mcoupled normal mocics (u” = 0)

v’ =o

V’= 1 u’=2

YlKw

v&% SOW)

USGO)

0.9996

0.980

0.873

0.0003 0.0

0.012 0.007

0.1 IS 0.010

perience with HO, and HSO seems to indicate that calculations of this genre slightly underestimate such quantities it can be expected that in SOH the true 0-O band occurs at around 0.6-0.7 eV_

4. Dipole moments Fimdly the dipole moment of the SOR radical is calculated for both the “x2A” ground and g2i2A’ excited states for several: nuclear arrangements in the neighborhood of the ground state equilibrium geametry; the variation with a~ngle and SO bond length is shown in figs. 3a, b, while additional details are given in table 6. The change in absolute magnitude of p between ground and excited state is quite small, whereby the greater distinction is noted in the x component (table 6), causing the dipole moment vector to be rotated by some 6 degrees. A similar situation has been encountered in HO,, for which the calcuIated value changes from 2.29 debye to 2.14 debyz upon excitation while 0 varies from 58.3” to 64.?’ (33 * This change is in effect a small S + 0 charge trsnsfer, as is also apparent from examination of the innershell orbital energies listed in table 7. The la’ (S Is) energy becomes lower upon excitation, indicating a more positive environment around the sulfur atom in 2A’ than in ‘A”; similarly the increase in the Za’(0 Is) energy reflects the change towards increased negative environment around the oxygen nucleus (121- The calculated change in &pole moment cannot be explained on the basis of a simple distinction in orbital

faces are employed in the equations for the vibrational nation (Le., as prescnied by the BomOppe~e~er approximation). The computed Franck-Condon factors are given in table 4 whereas the corresponding energies for the vibrational levels are collected in table 5. fn calculating the vibrational wavefunctions it is assumed that the various modes are separable: I,&,is thereby expanded in a series of Hermite polynomials whiSe the corresponding potential is approxim&ed in the form of a power series in the displacement variable; the expansion coefficients for the wavefunction are obtained via an energy minimization (Cl) procedure. Thus the treatment goes beyond the harmonic approximation but neglects cou$ing between the various normal modes. St is seen that the excitation from the ground state zerothtibrational level occurs with greatest probabiiity to the vf = 0 states of each of the modes of deformation in the upper electronic state. Taking into account aU.vibrational con’tributions the *A!@OOj c 2A”(C100) transition energy is calculated to be 0.57 eV, which value should also coincide with the location of the absorption maximum in this case. This. To result is defmitely smaller than the corresponding finding in HO,, for which a Al& value of 0.85 eV has been computed [I 01 compared with a measured To value of 0.87 eV (1.43~) 151. Siica exTable S

Occupation (lOa’ + 3a”). however, since the contribution of the individual diagonal elements to the

total dipole moment is quite different in the tWo states (table 8), thereby indicating a substantial

nn .

Calculated vibrational energy fevels of the ground X’A” and fust excited PA* state of the SOB radical in diiferent independent vibrational modes (energies in cm-‘) i

or i

E;;p 0

1 2

q(rc SOHl

@I (OH) E”’ _- .-.__ .-_-

2019

$904 9657

1997 5904 9854

c

-

v&i01 __-__..._1

Eg

&“r

&*I _ -.-_^

-%I* _ -_ --_-_--1-

593 175s 2919

483 1427 2305

461 1361 2261

1273 2129

433

386

A.B. Sarinigahi

et allNon-empirical

SCFand

Ustudy

of the SOH radical

Table 6 Dipole moment (debye) of the SOH radical in two electronic states at the ground state equilibrium structure”) (OH = 1.802 bohr, SO = 3.087 and 4 SOH = 1o9”)b)

h

PY

Ang&e

IPl

0.350 0.344

-1.792 -1.785

79” 79”

1.826 1.818

0.050 0.149

-1.820 -1.755

88.50 85”

1 X42 1.76

I 3.10 SO

u Idebyel

3.20

distance

(bohrI

Angle

‘.

4

Q

4

>n’ x.2

-90

. . . .

180

.&

Table 7 Comparison of the inner-shell orbital energies (ii hartree) of SOH in ground and excited states for various geometries (notation as in table 2); la’ is localized at the sulfur atom while 2a’ is essentially &e 1s oxygen orbital

-

i

a) Dipole vector is drawn toward the negative center of charge (Le., the S atom is somewhat negative in both electronic states). b, The Values in the second row always refer to the calculition in which all single-excitation species are included automatically. c) Angle measured clockwise between the positive x axis and the dipole moment vector.

, 1aJ

110 Angle

la’

120 SOH

Fig. 3. Calculated dipole moments for the %?A,’ ground and the f=st excited 2A’ state in SOH as a function of the SO bond length (a), and the internuclear SOH angle (b). (O-H = 1.802 bohr, S-O = 3.087 bohr and 4 SOH= 112’ tinless varied) The angle f3 of the dipole moment vector measured clockwise from the positivex axis is also givenfor both states.

26

Geometry

z2A”

YI aA

g2A”

PA’

1 2 3 4 5

-92.0211 -92.0283 -92.0346 -92.0271 -92.0292

-92.0245 -92.0309 -92.0373 -92.0302 -92.0312

-20.6241 -20.6203 -20.6162 -20.6256 -20.6139

-20.6068 -20.6049 -20.6033 -20.6096 -20.5994

change in the orbital composition of the n-type (a”)

orbitaln from one state to the other.

5. Comparison of SOH and HSO Prqbably the most interesting feature in comparing the calculations for HSO and SOH is the fact that SOH is predicted to be more stable than HSO by 12 kcal in the CI treatment (the SCF value is 14 kcal). This observation might appear somewhat surprising since it is well known that in other HAI3 systems such as HCO+, HCO, HNO+ 1131, HCN and HNO the preferred structure is always that with the

Table 8 Contribution of the diagonal elements to the dipole moment of SON in the z2A” and A' states. (Values in atomic units, OH = 1.802 bohr, SO = 3.087 bohr, 4 SOH = 109”)

;a

ffAU

>A’

MO tx1 9a* 10a’ 2a” 3a”

I.379 2.867 1.971 1.009

tv> -0.149 0.016 0.271 2.922

tx> 1.233 3.013 0.506 2.67?

tv> -0.111 -0.002 0.018 0.004

A.B.

Sannigrahi

et

387

aLfNon-empiricnl SCFand CI study of tlze SOH radical

more electranegative constituent at the terminal position, although, for example, HNC has &so been identified experimentally 1141. The indication from all these examples is that the AH bond being formed is a less important factor in determining the preferred nuclear arrangement for such systems [6] than is the strength of the AB bond. Thus isoelectronic systems with larger differences in electronegativity between partners A and B such as the HCOjCOH pair are expected to have a larger isomerization energy than the HNOc/NO& couple; indeed the stability difference for the former is calculated by SCF methods to be 23 kcal/mole while the analogous difference in HNO*/NO@ is ouly -5 kcal/mole [ 131 (CI changes this value to +I 1 kcat). On the other hand it seems plausible that the strength of the Al3 bond probably becomes less important as the AB anti-bonding rrg-type orbitals become more heavily populated. In systems such as HCO or HNO+ only one electron is in such antibonding MOs (actually the 7a’ component of the 1~a is almost Al3 non-bonding due to the heavy hydrogen mixing) while in HSO or SOH they contain three electrons. It seems quite conceivabIe then that as the distinctions between the two possible types of Al3 bond formation become less significant as a result of greater population of the rg species, that the strength of the AH or BH bond in such systems becomes the dominant factor in determining the relative stability of HAB isomers. According to this line of reasoning, which is wholly similar to that of the relative stability of the various nuclear arrangements in triatomic ABC molecules [6] as a function of the number of electrons, one would expect the difference in HABIHBA stability to decrease with the increase in number of valence electrons beyond 10 (taking into accaunt electronegativity differences in A and B), a supposition which awaits testing in subsequent work. in the present context, however, the greater stability of SOH can easily be rationalized in this scheme. In order to facilitate further comparison with HSO, some pertinent data obtained for the latter molecule [3] are smnrnarized in table 9. As expected the SO bond length is found to be larger in SOH (by 0.17 bohr) than in HSO, i.e., by analogy to the situation in HCO/COH, HNO+/NOHf or HCO+/COv for which A3 differences of 0.20,0.12 and 0.11 bohr are

Table 9 Molecular constants of HSO pertinent for a comparison with SOH, obtained from previous theoretics] studies :31.

S-O (bohr) 4 HSO (degree) P (debye)

Dipolemoment angle8 Orbital la’ energy 2a’ Gastree)

?‘A’* state

~A’state

2.98 (2.91 CI) 100 101 (CI)

9.5

3.22

2.274

1.785

24.6O -92.0535 -20.6441

45.5) -92.@325 -20.6499

calculated between the two isomeric forms (with the shorter Ai bond always occurring when H is attached

to the less electronegative heavy atom). The intemuclear angle on the other hand is calculated to be smaller for HSO than for SOH, in contrast to the situation for systems with two Iess valence electrons such as in COH or NOti, which possess smalier internuclear angles* than their HCO or HNOf counterparts; alternatively one could say that the more stable isomer in either case possesses the larger bond angle. The slight increase in internuclear angle upon excitation in SOW would be considered quite typical for HAB systems with this number of valence electrons i6], but the definite decrease in this quantity in HSO is not predicted in the usual qualitative MO picture; in HO2 or HSz, which qualify as intermediate cases in this respect, essentially no change in bond angle between ground and first excited state is observed [5,15]. Although there is very little increase in the SO bond Iength between ?A” and Z2A’ states in SOH (table I), a marked increase in this quantity is found in HSO (table 9 and refs. [2,3])_ This fact leads to the observation that in HSO the absorption maximum occurs in the neighborhood ofv; = 1 or 2, while in SOH u; = 0 defmitely corresponds to the most probabIe transition. For the two other vibrational modes the preferred upper Ieveis are u; = 0 and u; = Clin both isomers. The value of Z&O is markedIy smaUer in SOH than in HSO, for which a value of I .56 eV is calculated compared with the experimental result of 1.778 eV. Again this finding is in agreement with other data for (n, n*) smaller bending force constants in the case of COH+vs NCO’(both beinglinearin their sound states).

* Or

388

A.B. Sa&?nahi et al./iVon-empiricai SCFand

Table 10 Comparison of orbital energies (ii bartree) of SOH and HSO iu their ?A” state at the respective SCF equilibrium geometrv Orbital

SGH

HSO

CJstudy

of theSOH

stronger for this MO in HSO, thereby making it much more stable in the latter isomer. The make-up of the Za” and 3a” MOs is almost completely r-eversed in the two systems: in SOH the 2a” is localized predominantly

at the oxygen,

more nearly resembles ld 2a’ 36 4a’ 59 6a’ 7a’ 8a’ 9a’ 1Oa’ g,, ,,

3i’ (openshell) E (SCF)

-92.0283 -20.6203 -9.0066 -6.6946 -6.6926 -1.4027 -0.9104 -0.6880 -0.5704 -0.3726

-92.0535 -20.6441 -9.0343 -6.7239 -6.7221 -1.3701 -0.9403 -0.6517 -0.5907 -0.4682

-0.5732 -6.6949

-0.4912 -6.7216

-0-4163

-0.5429

-472.91707

-472.89408

transitions in HAB systems: AE invariably decreases as the electr&egativi@ of the centralatom increase-s,

and from comparison with HOi (with an experimental Too0 value of 0.87 eV) and HS, [ 15 1, one can conclude that AE also decreases with deererisingelectronegativi@ of the terminalatom (The different life times of the (n, n*) excited states have already been discussed in connection with table 3). Distinctions in charge distribution between the two isomers can be seen from the various orbital energies (table 10) and from the calculated dipole moments. All inner-shell orbital energies are somewhat higher in SOH than in HSO, thereby indicating a somewhat more negative environment for sulfur and oxygen atoms in SOH than in HSO. Such behavior seems reasonable since the more electronegative oxygen atom is better able to withdraw charge from the hydrogen atom in SOH, for which it is situated adjacent to the latter species. The largest differences in orbital stability between the two isomers are observed for the three highest species lOa’, 2a” and 3a”. Inspection of the A0 expansion coefficients shows that the 10a’ MO is somewhat polarized toward the sulfur atom in SOH, while oxygen and hydrogen participation is relatively

radical

while the 3a” species

a sulfur prr AO, with the

oppo-

site situation holding in the case of the HSO system. As a result the 2a” is more stable in the SOH isomer, i.e., again reflecting the greater electronegativity of oxygen, while 3a” species possesses a lower orbital energy in HSO. Finally it is seen that the dipole moment of HSO in its ground state is much larger than that of SOH, and furthermore that in HSO the change in p upon excitation to the Z2A’ state is quite substantial whereas it is nearly negligible in SOH (tables 6,7). The latter effect is also seen from the marked change in inner-shell orbital energies during the (n, n*) transition in HSO (compare table 9 with table 7). The direction of the change in dipoIe moment vector, i.e., a clockwise rotation caused by the charge transfer from the terminal to the middle position, is the same in all three molecules HO,, HSO and SOH. Since the central position is more negative once the more electronegative atom is located there (as in SOH), the effect of the charge transfer in this direction is much more pronounced in HSO than in either of the other isovalent species mentioned above.

Acknowledgement The authors wish to thank the Alexander von Humboldt Foundation for financial support given to this work. The services and computer time made available by the University of BOM Computer Center are also gratefully acknowledged.

References [l] K-H. Becker, M.A. hmoceneio and U. Schuratb. ht. J. Chem. Kinetics Sl (1975) 205. [2] K.H. Becker, U. Schuratb and M. Weber, to be published. [3] A.B. Sannigrebi, K.H. ‘Tinmemarm, S.D. Peyerimboff and R.J. Buenker, Cbem. Phys. 20 (1977) 25. 14 ] L.E. Sutton, Tables of Intermolecu~ Distances and Configurations iu Molecules and Ions (London, The Chemical Society, 1965).

A-B. Sannigrohi et al/Non-empirical SCF and CI study of the SOH radical [S] H.E. Hunziker and H.R. Wendt, J. Chem. Phys. 60 (1974) 4622; K.H. Becker, E.H. Fink, P. Lange and U. Schurath, J. Chem. Phys. 60 (1974) 4623; H.E. Hunziker and H.R. Wendt, 12th International Symposium on Free Radicals (1976) p. 12; K.H. Becker, E.H. Fink, A. Leiss and U. Schurath, ibid., p. 13. [61 R.J. Buenker and S.D. Peyerimhoff, Chem. Rev. 74 (1974) 127. [7] G.M. Barrow, Introduction to Molecular Spectroscopy (McGraw-Hill. New York, 1962). [S] P. Pulay and W. Meyer. Mol. Phys. 27 (1974) 473. [9] RJ: Buenker and S.D. Peyerimhoff, Theoret. Chim. Acta (BerL) 35 (1974) 33; 39 (1975) 217.

389

Chem. Phys. I101 kJ_ Buenker and S.D. Peyerimhoff, Letters 37 (1976) 208. t111 A.F. Starace, Phys. Rev. A3 (1971) 1242; A8 (1973) 1142. [I21 RJ. Buenket and S.D. Peyerimhoff, Chem. Phys. Letters 3 (1969) 37. and R.J. Buenker, J. Mol. r133 P-J. Bruna. SD. Peyerimhoff Structure 10 (19751323: 32 (1976) 217; C Marian. P.J. Bruna, Rj. Bienke; and &D_ Peyerimhoff, J. Mol. Spectry. (19771, to be published. t141 D.E. Milligan and M-E_-Jaco>, J. Chem. Phys. 39 (1963) 712; 47 (1967) 278: LE Snyder and D. Buhl, Bull. Am. Astmn. Sot. 3 (1971) 388. WI Results for HSz obtained by the authors. to be published.