Ab initio studies on the electronic structure of the FSO radical

Chemical Physics 52 (1980) 33-38 @ North-Holland Publishing Company

AB INlTiO STUDIES ON THE ELECTRONIC STRUCTURE OF THE FSO RADICAL Shogo SAKAI and Reiji MOROKUMA Lsriruiefor Molecular Schce, Myodoil,. Okvzakl444,

fapan

Received 21 April, 1980

The geometries of the FSO radica! in the ground (‘A”, and first excited (*A’. n + x’) state have been calculated with the ab initio UHF SCF gradient method. The geometry in the first excited state is predicted to be rm= 1.693 A. rs~= 1.609A, and f.FSO = 95.5”. The force constants, vibrational frequencies and dipole moments have also been calculated. The predicted ‘A’+‘A” transition energy, calculated at the optimized geometries with an UHF-NO-C1 method, is 3.9 eY for the vertical excitation, 0.9eV for the vertical emission and 2.6 cV for the electronic term value. The oscillator srrength is also calculated. A brief discussion is given on the role of bond funnions on the calculated geometry.

1. Introduction The structure of the HO* radical has been extensively studied by microwave and laser magnetic resonance spectroscopy. The HSO radical, an analogue of the peroxy radical, has recently been studied spectroscopically by Schurath et al. [l] and Kakimoto et al. [2] and the structure of not only the ground but also of the first excited state has been determined. A theoretical study of HSO has been pubfished by Sannigrahi et al. [3]. Endo et al. [4] have very recently carried out a microwave study of a new radical FSO and determined its geometry and vibrational frequencies in the ground state. However, other physicochemical properties of interest such as the geometry, dipole moment and vibrational frequencies in the first excited state, and the transition energy and oscillator strengths are still unknown. In this communication we calculate the electronic states of the FSO radical in its ground and first excited state using ab initio SCF and SCF-CI methods. The calculated results are compared with the corresponding experimental and theoretical data for HSO and with known experimental results for FSO. We also present a

short discussion on the role of polarization or bond functions on the geometry of FSO and HSO.

2. Computationoll method The basis set chosen for the present study is the split-valence 4-31G set [5], augmented on both SO and SF bonds with a set of s-type (exponent 5 = 1.39965) and p-type (4 = 0.904293) gaussian bond functions [6]. The geometries of the FSO radical in the ground (‘A”, it radical) and first excited (‘A’, u radical) states were optimized by the use of the analytically calculated energy gradient [7] within the ab initio UHF (unrestricted Hartree-Fock) method. The locations of the bond functions were also automatically optimized. The configuration interaction calculations were carried out according to a standard procedure by use of natural orbitals (NO) derived from UHF MO’s [8]. Seven inner-shell MO’s were held doubly occupied in all configurations, while all other MO’s were available for variable occupation by the remaining 19 electrons of the system. All singly- and doubly-excited

34

S. Sakai, K. Morokuma / Electronic stmcture of the FSO radical

where &f is the energy of the reference configuration, A&(T) is the CI energy lowering obtained by diagonalizing the CI matrix selected with the threshold T, EL:!,,(T) is the sum of the second order perturbation energy of unselected configurations at this threshold, and A is a parameter to be determined. We evaluated A by the following equation:

where Egic,(T) is the sum of the second crder perturbation energy of all selected configurations_ Here we are assuming that the ratio of the CI energy lowering and the second order energy sum for. selected configurations is equal to that for unselected configurations. We examine the validity of our procedure for HSO in table 1, where similar recent extrapolation procedures by JackeIs [ll] and Buenker et al. [lo] are also examined for comparison. In the Jackels procedure A&(T) plotted against E&(T) for a few values of T is extrapolated linearly with a least-squares fit to the limit E&(T) = 0.A major difference between ours and Jackels’ method is that ours requires the CI only at one value of T, whereas the other requires the calculation at least at two or three values of T. In the more sophisticated Buenker procedure E&T) is plotted against T for several small values of A and extrapolated nonlinearly to E&O); it requires &r(T) for several small values of T. Table 1 indicates that these methods are reasonably reliable for T s 100 phartree, though the present scheme has not been tested for many cases. The force constants with a basis set containing floating bond functions were calculated as follows. Let x(x~, i= 1,. . . , n) and y(yi, i= 1,..*, m) be the small displacement vectors of atoms and floating orbitals, respectively, from their fully optimized positions. The total energy up to second order is

A = bEc,(T)E%(T).

W=;x’fxi-x’gy++y’hy.

configurations with respect to the single reference configuration for each state in the CI expansion were generated, but only those capable of lowering the reference configurations by more than 60 phartree (threshold T) in second order perturbation were included in the secular equation actually solved. The contribution of the remaining unselected configurations was then taken into account by an extrapolation procedure described below. All calculations were carried out by means of the program IMSPACK consisting of GAUSSIAN70, HONDO and own gradient, geometry optimization, force constant, and CI programs E91. The extrapolation procedure: When configuration selection techniques are used, it is often important to extrapolate for the contribution of unselected configurations [lo]. We estimate the extrapolated CI energy, Ecr, using the following equation: EC1= E,.! + A&(T)

+ AE’*’ drop (T) >

(1)

(2)

(3)

Table I Comparison of extrapolated Selection threshold T

CI energies for the HSO moleculea’ NCP’

This method

Jack&’ method

Buenker’s method

A

ECI

Eci

&I

0.881 0.877 0.876 0.877

-467.8116 -467.8097 -467.8091 -467.8989 -467.8091

-467.8116 -467.8100 (30.50.80,100)” -467.8092 (50,80.10) -467.8G78 (80,100) -

-467.8116

(tiartre!) 0 (exact)

30 50 80 100

1840 1080 851 712 637

” Energy in hartree. For the ‘A” state with the STO-3G* basis set. ” The number of configurations selected out of the total number of configurations ” Threshold values used for a least-squares fit of the linear extrapolation.

generated.

-467.8107 (A = 1.217)

1840.

S. Sakai, K. Morokunla / Electronic structureof the FSO radical

Then

Table 2 Summary of SCF results for FSO

a wjax’ = fx + g y,

(4)

aW/ay’=g’x+hy.

(5)

Since the position of the floating orbitals should be reoptimized for any displacement of x, the following relation can be derived from eq. (5): y = -h-‘g’x.

(6)

Inserting eq. (6) to eq. (4), one obtains a w/ax’= (f - gh-‘g’)x.

(7)

Differentiation of eq. (7) by x leads to the force constant matrix F: F=f-gh-‘9’.

35

(8)

The matrices f, g and h, calculated by a numerical differentiation of the energy gradier.t, were used to obtain F.

Cal.

rso(& k& LFSO(deg) w,(SO)(cm-‘) wz(SF)(cm-‘) w,(LFSO)(cm-‘) Force constant (md/A)” &, &z F33 FE F23 S3

3.1. UFH caicdatiort The equilibrium geometrical parameters for both the ‘A” (r radical) and ‘A’ (U radical) states are listed in table 2. The calculated geometry for ‘A” is in excellent agreement with experiment. The values for “A’ for which experimental data are not available constitute a prediction. To correct systematic errors in calculation we assume that the ratio between the observed and calculated values for the experimentally known “A” state is also valid for the ‘A’ and obtain the scaled values for “A’. The SF bond length is nearly equal for both states; the same trend is found for the SH bond length in HSO [2,3]. A large change in the SO bond length is predicted in going from the ‘A” to the “A’ state, as the excitation takes place from 12a’, a non-bonding n-type orbital on the oxygen atom into 4a”, the SO antibonding nT* orbital. A comparison with the SO bond length for HSO (1.494 A experimental [2], and 1.58 A SCF [3] for ‘A” and 1.661 A experimental and 1.70 A SCF for ‘A’) shows that in the ‘A’ state the SO bond length is nearly equal for both

1170 680 450

8.690 5.545 0.675 0.289 0.088 0.379

1.452 1.602 108.32 1215 763 396.2

Cd.

1X& 1.56, 95,

scaledb’ 1.6g3 1.60, 95,

780 910 330

[9.2] 4.08 0.5382 0.140 0.050 [O.O]

3.804 5.849 0.414 0.275 0.137 -0.020

1.662 34.9”

1.9 46

Dipole moment*’ PD’

3. Results and discussion

1.44, 1.56, 107.9

ohs.“’

2.3 36”

1.4

” From ref. [J]. Vibrational frequencies are obtained from the force constants below. Force constants in brackets are assumed. ‘) Scaled based on the ratio (experimental/calculated) in the ” Internal coordinates chosen are: ,$ = Srso, Q2 = SrsF, and Q3 = rUFS0. where r = ksOrsp) d’ The dipole moment points to the direction bisecting the FSO angle. 8 is the angle betaeen the dipole moment and the S-O axis.

molecules. In the ground ‘A” state the bond length is substantially shorter for FSO than for HSO, which can be rationalized by saying that the large electronegativity of the F atom reduces the repulsion between the above described n-type electrons on the 0 atom and the electrons on the S atom, to result in a shorter b&d length. The bond angle in the excited state is smaller than that in the ground state; again the same trend as in the HSO radical. A comparison with HSO (106.6” experimental and 101’ SCF for ‘A” and 95.7” experimental and 95” SCF for ‘A’) indicates that in the ground state the FSO angle is larger than the corresponding HSO angle. In the ‘A” state the repulsion between the 0 and F lcne pairs

:

S. Sakai, K. Morokuma / Eiectronic struclureof he FSO radical

Y

should be strong, resulting in a large bond the calculated atomic and . The ground state has its nearly equally by v* orbie S atom, The excited state in localized on the a orbital

0f the 0 olrom. 7k

c&ulrted vibrational frequencies and b in both states are shown in table el NJ-15% error in vibrational qlscnucs and force constants in the SCF callirtinn at this lcvcl of basis set [12]. The trend Ircequcncychanges going from the *A” to the ir the lame as that of the HSO moleted, a substantial (2530%) ~~~~t~~~ t&m plocc in the SO stretching as rlD 511in Ihc bonding frcqucncy. An experiIIJEWJJIcslimatc of force constants for the *A“ Itrrr been abtnincd by fitting centrifugal d&trxtlnn ~trnslenta and inertia defects of the ~~~~~~v~ rpeclra: P, I= 9.2 (assumed), F;* =

d,Wt. PBarw 0.53112, PIJ = 0.14, F;, = 0.050 and F# 14~tJ tulkvuncd) md/& leading to the esti~rg~t~dwlbratlonal frcqucncics: W, = 1215, w2 = 7GJ snd 6#** 391r.2 cm ’ [4]. The correspon~~~~:~~N#KWI fhc crrtculrtcd and estimnted f~~~tlJ~~~t~~ rend force con~trnte is reasonable,

FMIl9

(0.029)

'A* 5lAR

I

except for F~J which was assumed to be zero in the experimental estimate. The calculated dipole moments for both states are also shown in table 2. At this level of calculation an overestimate of 1~1by 40% is not surprising. The direction, however, agrees very well with experiment and a qualitative argument: the S+‘O-’ bond moment is larger than the SA6F-’ bond moment, and as the result the direction of p should be closer to the direction of the SO axis, i.e. B<45’. The excitation of an electron from the oxygen lone pair to the W* orbital should reduce the SO bond moment, and therefore, reduce 1~1and increase 8, A scaling of the calculated value by the ratio pFaJpobs for 2A” gives a prediction of 1.4 D for the dipole moment for the ‘A’ state. 3.2. CI calculation fn table 3, we show the results of CI calculations for the 2Afr and *A’ states at two UHF optimized geometries: the II geometry corresponding to the equilibrium geometry for the 2A” state, and, the I geometry, corresponding to that for the 2A’ state, both taken from table 2. UHF MO’s for each state and geometry were used to calculate UHF-NO’s for CL The vertical transition energies and the electronic term vatue calculated are schematically shown in fig. 2. A large change in the SO distance between the two states is expected to cause a wide spreading of absorption and emission bands. The predicted transition energies for FSO are larger than those for HSO. This is because the lone pair (no) MO is more stabilized in FSO than in HSO, whereas the x* MO remains unchanged; for instance, in the UHF calculation for the ‘A” state at the lI geometry, P?~ = E(no) = -0.603 and E?, = ~(rr*) = -0.404 for FSO, and E& = atno) = -0.472 and E& = E(x*) = -0.401 hartree for HSO. An examination of MO coefficients suggests the following interpretation: in FSO the electronegativity of F and a mixing with the antibonding SF v orbital lowers the energy of no relative to that in HSO. where a mixing with the bonding SH Q orbital raises its energy.

In order to compare

the ‘A’-

‘A” transition

intensity at the II and Z geometries. culated the transition

moment

we cal-

R andthe

oscil-

later strength / in the length representation:

A comment

on the effect of bond functions

on the molecular

geometry

may be in order.

is well known for some sulfur compounds

R = N’?A”J(

r: r,l’P’r*A’J),

1

MO’s

in *(‘A”)

j/R/' JE.

is rather cumbersome

are non-orthogonal

we used here the ‘A”

the inclusion of pofarijration

to MO’s

in

with T =

In calculating f the transition

functions or bond

is essential for the prediction

rect geometries,

if

RHF MO’s for

both states and selected configurations 10IJ phartree.

(9,

functions

Since the calculation q?A’J.

f =

of cor-

In table 5 we show the opti-

mized geometries

of FSO and HSO in their ‘A”

state with or without functions described the SO bond only

bond functions. Ihe

bnnd

in section 2 are plactd

on

or both on the SO and the SF

energy UT was taken from fig. 2. The results

bond. with their positions optimized.

are shown in table 4. The calculated

4-3lG

oscillator

With

normal situation

T* transition

and a bond angle within 5” of experimental

or maybe

a bond distance within

values [ 131. Table

geometry.

function is essential for the prediction

the case of HSO, geometry

where the intensity at a II

is predicted

tude larger than

lo be an order of magni-

at a Z geometry [3].

5 indicates that

0.02

of the SO

bond distance and the XSO angle for both FSO and HSO.

Wbrle

the SH bond distance does no!

require a bond function. tancc is obtained

a correct SF bond dis-

nnly with the SF bond

fUrK~lOri~. UIc consider

,qumctr;

that the good aprrzmrnt

~,lth cxpcr~ment is part13 dot

optimization

Fig. 2. Crrlculared transition enerlyn for FSO Tbc ordinate qualitatively rcprewnts the S-O bond dzstanrr (‘I calcuhtion~.

A

the SO bond

slightly stronger af the II than at the Z This appears to be in contrast with

the

SCF callculation one can expect in the

strength suggests that the intensity of this n-c should be comparable

11

that

of the location of the

bond

in

tu the

of

S. S~~koi,K. Morokuma / E/ecrronic smtcrure rheES0 radical’

38

Table5 Effectsof bondfunction on geometryparameters of HSO andFSO Bondfunctions EXp? none

HSOd8.1 r&Q

1.738 1.358

LHSO(degj 96.5

SO

I.541 1.365 102.0

SOand sx 1.543 1.332 102.3

:-;: 1.441 FSO r&j r&A) 1.664 1688 . . 1694 . .GSO(deg) 100.6 106.9 107.9

1.494 1.389

advices.We would also like to acknowledge ProfessorsE.,Hirota and S. Saito and Dr.-Y. Endo for providing their experimental’data prior to publication.The work tias in part supported by the IMS Joint Studies Program. The numericalcomputationswere carried out at the Computer Center of IMS.

References

106.6 :‘$ . _ 108.3

” Fromref.[2].

functions. The change of exponents of the bond functions is not criticalto the cptimized geometry [14]. The largest errors in the geometricalparameters of HSO with no optimization of the location of the bond functions (fixedat the center of the bond) are 0.0868, and 5.6”;with the optimizationwe actually reduced the errors to 0.047 fi and 4.6”,respectively,withthecenterof thebondfunctions located near the S atom, as is found for FSO in fig. 1. The population analysis(not listed) shows that the r type bond functions have a larger population than the r type functions,suggesting the larger contribution of the former.

Acknowledgement We are extremely grateful to Dr. Shigeki Kato for many stimulatingdiscussionsand

[I J U. Schurath,M. Weber and K.H. Becker,J. Chem. Phys.67 (1977)110. [2] M. Kakimoto. S. Saito and E. Hirota, J. Mol. Spectry. 80 (1980)334; N. Ohashi,M. Kakimoto,S. Saito and E. Hirota, J.

Mol.Spectry,to be published. [3] A.B. Sannigrahi,K.H. Thunemann, SD. Peyerimhoff and RJ. Buenkcr, Chem.Phys.20 (1977)25. [4] Y. Endo, S. Saito and E Hirota, J. Chem.Phys.,to be published. [5] R. Ditchfield,W.J. Hehre and J.A. Pople,J. Chem. Phys.54 (1971)724. [6] R.J. Buenker and S.D. Peyerimhoff,Chem.Phys.8 (1975)324; Chem. Phys.Letters 16 (1972)235. ‘[7] A. Komornicki,K. Ishida, K. Morokuma,R. Ditchtield and M. Conrad, Chem. Phys.Letters45 (1977)595.

[S]A.T.AmosandG.G.Hall,Proc.Roy.Sot. AZ63 (1961)483. [9] K. Morokuma, S. Kato,K. Kitaura,I. Ohmine and S. Sakai,IMS ComputerCenter LibraryProgramNo. 0372 (1980). [IO] RJ. BuenkerandSD. Peyerimhoff, Theoret.Chim.

Acta35 (1974)33; 39 (1975)217. [ill C.F.Jackels, J. Chem.Phys.70 (1979)4664. [12] P. Pulay,Moderntheoreticalchemistry, Vol.4, ed. H.F.Schaefer(PlenumPress,NewYork,1977). [13] W.A.Lathan, W.J.Hehre,L.A.CurtissandJ.A. Pople,J. Am.Chem.Sot. 93 (1971)6737. [I41 P.G.BurtonandN.R.Carlsen,ChemPhys.Letters46 (1977)48; N.R. Carlsen,Chem. Phys.Letters47 (1977)203.