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On the lower excited electronic states of biacetyl
CHEMICAL
Volume 57, number 1
ON THE LOWER EXCITED ELECTZONK
PHYSidS
LETTERS
1 July 1978
STATES OF BJACETYL
Tae-Kyu HA Laboratog
of Phpiial
Chemisny. Swiss Federal Insritute of Technology,
Ziwich. Swi:ze.riazd Recehed 12 Dtcembzr 1977 Revised manuscript recei;ed 22 March I978
An ab initio SCF .md CI study has been zxried out for the ground and electronklly excited states of biketyl (CH3CO-COCH3)The second absorption band in l &e 4.40 eV region has been assigned to a ‘Ag -+ ‘Bg nzr* transition_ The character of the loxrer-lying states has been analyzed in terms of the CI wavefunctions.
1_ Introduction Due to its importance
in photochemistry
and pho-
to$?hysics, biacety! (CIi,CO-COCiI,) has been studied extensively both by spectroscopic [I- I4] and theoretical methods [I%-171 _ The interest in biacetyl photochemistry is related iargely to its low-lying electronic states and the efficient -ktersystem crossing and radiation!ess transitions_ The assignment of the fowerlying eiectronic states which is essential for the interpretation of these various photochemical behaviours, however, has remained a controversy. WhiIe it is generally accepted that the iowest-lying singlet and triplet states of 22871 cm-l (2.84 eV) and 20422 cm-t (2.53 ev) above the groucd state are of A, symmetry [ 1’,14j _ the nature of the second singlet and triplet states 1s still disputable. Wit!& the frame of the one-elect&n LCAO MO picture it is possible to discuss the qualitative nature of rhese lowerlying excited states in terms of n+(a,), n_(b,), sr+*(an) and nq(b,) orbitals of the biacetyi moIecule which are associated with the n+ + 7~,*excitations_ Since only two lower-lying singlet states are observed in the absorption spectra it is generally assumed that these states are, within this one-electron picture, due to the two dipole-allowed n,fQ + &au) and n_(b,) += zr*_(bz) transitions *which result in two IA, states of different energies. These assignments have been proposed by several investigators [I ,15,18,19], in their interpretations of the absorption spectra of various
ar-dicarbonyls including the biacetyl molecule_ Based upon the emission, absorption and circular dichroism spectra of two ardicarbonyls and also based upon the szmiempirical CNDOiS studies, Amett et al. 1201, on the other hand, have pointed out that the above assignment for the second absorption band might be incorrect. They proposed that the second absorption band in the arilicarbonyl compounds is due to the dipole-forbidden n+ + rrz transition and thus the resulting excited state would be the lBs state for biacetyl. Kelder et al. [2 l] have also arrived at the same conclusion by studying the polarization of both nn* absorption bands of glyoxal. The conflict in the above assignments warrants a more thorough theoreticalexamination of the spectral features of this photochemically interestingmolecule_ In this work we report an ab initio SCF and CI study of the ground and variouselectronically excited states of biacetyl. Apart from the assignment of the second absorption band mentioned above, several other nn* and ITTH* singlet and triplet states have also been cakulated and compared with available expe_Gnentai values. The physical nature of the lowerlying states has been analyzed in terms of the CE wavefunctions.
CHEMICAL PiiYSICS LEl-lYERS
Volume 57, number 1
1
2. Calcdation
Table 1
Ab initio SCF calculations have been carried out for biacetyl employing two different choices of gausSian basis sets. The approximate Hartree-Fock SCF atomic orbitals used as a basis set in the molecular calculation were the gaussian lobe functions 1221. The fit basis set (basis set I) consists of three linear combinations of four, three and three priitive gaussians for s-orbitals and one contraction of five pairs of gaussians for each of the three p-orbit& of carbon and bxygen atoms. Each hydrogen s-orbital was represented by a linear combination of five primitive gaussians scaled by a factor of 2’i2. The second basis set (basis set II) is a slightly extended one, in which additional one-term long range pm functions of the same exponents and lobe separations as the most diff&e p-functions of C and 0 were added to basis set I. The total basis set thus contains 90 s-type gaussians and 96 p-type gaussians (basis set II), where a single p-function consists, in turn, of two symmetrically located spherical gaussians. The molecular geometry adopted for the SCF calculations was taken from the electron diffraction experiment of Hagen and Hedberg [23]. Table Z summarizes molecular energies obtained from the ground state SCF calculations for two different basis sets. MO’s with their symmetries are also listed. No previous ab initio calculations have been czried out for this molecule. As &own in table 1 the molecular SCF total energy for basis set I is lowered only 0.017 au as a result
calculation on biacetyl for two basis sets a)
h¶olecularorbitals and total energies from ground-state SCF
Table 2 Energies and symmetries of orbit& Orbital
Symmetry
Basis set I b)
Basis set Ii b)
-205935 -20.5935 -115082 -11.5082 -11.297s -11.2978 -1.4659 -1-439s -1.0625 -1.0349 -0.8958 -0.7200 -0.7090 -0.6679 -0.6676 -0.6135 -0.6132 -0.6061 -0.5736 -0.5347 --5.;;31 -0_4L-‘2
-205949 -20.5949 -11.4910 -11.4910 -11.2ss4 -11.2884 -1.4614 -1.4357 -1.0571
symmetry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 IS 16 17 18 19 20 21 22
%
5 3a; 3bu 4% 4%
5% Sb, 6% 6bu 7aS la, 7b, Sag lbg Sb, g% 2a, 9bu 2b,
total en& a) Atumic units. b) For defiition
-1.0301 -0.8898 -0.7160 -0.7050 -0.6726 -0.6633 -0.6133 (lb,) -0.6090 (8Q -0.6024 -0.5695 -0.5328 -0.5 140 -0.4 190
-304.2458
-304.2628
of the basis sets see rext.
of the addition of the long-range p,-functions to basis set I. However, the essential point of interest is that basis set II is considered to be much more flex-
ej (au)
Orbital
Symmetry
q (au)
25 26 27 28 29 30
3bg 4a, 4bg 5bg Sa, 6bS 6a,
-0.1772 -0.1469 -0.1458 -0.0674 -0.0591 -0.0544 -0.0494 -0.0235 -0.0224
lb, 8<
18 19 20 21
Sb”, (0) 9aS (a) 2au (x) 9b, (n_)
-0.6133 -0.6090 -0.6024 -0.5695 -0.5328 -05144
2bg (sr)
-0J140
32&*)
-0.2176
(z) fu)
lOa, (n3
a; For basis set II. The virtual orbitals, *d--p39 p16-e3
Orbital
of variable occupancies used to build confiiurations a)
16 17
:: 24
July 1978
-0.4190
3”: 33
(.rr*) (ir*) (n*) (& (z*) (x*) (or*?
7a, (z*) 7bg W)
were determined by the exchange maximization with occupied SCF orbitals,
65
1 July 1978
CHEMICAL PHYSICS LJIZlTERS
Vo!ume 57, number 1
TzbIe 3 her&s of biacetyfground and eIectronic&Iyexcited stateshsed on got;nd-state SCF orbit& and transformed virtual orb&Is
-
-
Reference coniiruration enemy
-3042628
-304.3118(35)_
23-24 17-24 21+25 23+31 23-32
-3039323 -303.7123 -303.6543 -3035286 -303.5066
-3&?.1960 (330) -303.9465 (330)
‘B s
21--24 23-25 18+24 21+31 21-32
-303.8357 -303.7583 -303.6232 -303A2fM -303.4049
-304.1228 (340) -303.9933 (340)
lBu
22-24 16+24 20425 22+ 31 224 32
-303.7534 -303.6129 -3035659 -303.4272 -303A107
-3039247 (362)
“%
20424 22425 20-331 20432
-303-9603 (356)
22+33
-303-7087 -3036129 -303.3883 -303.3727 -3032564
23-24 f7-'24 21+2s 19-24 23431
-303.9433 -303-7335 -303.6759 -303.6751 -303.5338
-304.2188(387) -303.9874(387)
n-n*
21424 23-+25 18+24 21-31 21-30
-303X472 -303.6086 -303.6279 -303.4338 -3035135
-304.X469(349) -303.8369(349)
n-c??
22-24 20-2s 16-24 22431 22-32
-303.8595 -3034086 -303.6338 -303.4433 -303.4185
-304.1174(178)
n+n*
20-'24 22425 36+25 20+31 2ft-32
-303.7620 -303.6875 -303.4830 -303.4003 -303.3840
-304.0457(212)
stdte
3s +l
ibfe as far as the zr-orbit& are concerned. ‘i&is basis set (basis set iI) provides among other things a larger set of variabIe orbitals, which can be trmformed to
CL energy (number of confii~tions considered)
Qualitative description of transition
Orbital promotion
Electronic
an optimal
set of s*-o&itak
to be used for the CI
treatment of the ground?nn* and zz* singlet and triplet excited states of interest.
1 July 1978
CHJ.%ICXL PHYSICS LETTERS
Volume 57, number 1
From the SCF ground-state calculation employing basis set II, 23 occupied qq 423 (e.g. table 1) and 25 virtual orbitak y@ereobtained_ Prior to the CL treatment a truncation of certain molecular orbitaI bases is unavoidab!e because of limitations k computational capabilities. First, those virtual orbitals with energies greater than z= 200 au (six such orbitak) are discarded, since such virtual orbitals, which are thought to be unimportant iu the description of bonding, arise as a consequence of the inclusion of the short-range (cusp) functions in the gaussian basis set. Among ground-state SCF occupied orbitals, eight higher-lying MO’s, q16-pz3
are selected as orbitals of variable occupancy. The remaining virtuai orbit& have been transformed in such a way that the sum of exchange integrafs between these and the variable set Of occupied orbitals, q16-I$23, was a maximUnL The
use of such transformed virtual orbitals obtained in this way proved to be usefill in obtaining better convergence using a Iimited number of configurations in the CL treatment [24] _ Among these 19 transformed
virtual orbita!s, 10 orbitals (all z* type orbitals) were selected to be used to build configurations_ Thus, we actually included 18 orbitals of variable occupancy for generating configurations_ Table 2 summarizes these orbitals along with their symmetries and orbital energies. A CI calculation [24,25] was carried out by generating configurations referenced to a particular state of interest, which include all second order interactions larger than the energy threshold of 3.0 X 104. Within this threshold convergence was obtained within 400 configurations for describing the ground and nsr*, m* electronically excited states of interest.
Table 4 Major coefficientsto the sound and excited stateCI wavefunctionsof biacetyl a) Configurations groundstate 222 * 242 22+24 22+ 25 20+31 204 32 222 -, 24,32 22+28 22-33 20429
‘A&
1-k
jAg
O-98
0.10
Confgurations
‘BgG)
21424 23+25 18-25 21-+31 21432 23433 22,23 + 242 23428 23+30 23-27 21+29 21,22424,25
0.78 0.40 0.15 0.25 0.22 0.14 0.14 0.14
0.38 0.78 0.18 0.28 0.30 0.15
__ ‘BgC1l) 0.25 0.75
0.12 0.27 0.35 0.30 0.22 0.14
0.76 0.47 0.25 0.23 0.17 c.15 0.17
Confgurations
‘A,U)
23-24 17-24 21425 23-‘31 23+32 23-29 19+24 17+3L 17+32 17-29 19431 19+32
0.85 0.14 0.20 0.28 0.25 0.18
‘A,tll) 0.85 0.15
3AuU) 0.85 0.15 0.22 0.28 0.25
0.12 0.32 0.30 0.15
%,*I) 0.70 0.25
0.35 0.30 0.25 0.15 0.20 0.17
3Bg(1)
‘Bg(II)
Confiiurations
‘B U
3BU
0.75 0.46 0.15 0.22 0.28 0.15
0.38 0.72
22424 16+24 22+31 22-32 22+29 20,22 + 242 20424 2042.5
0.76 0.21 0.30 0.30 0.16 0.23 0.23
0.83 0.22 0.25 0.23 0.14
0.13 0.17 0.23 0.24 0.25 0.14 0.11
0.20
0.15 0.14
a) Only those confii~tions with coeffkients largerthan 0.1 in magnitudein the Ci wavefunctionsare listed. ln the case of opensh%llconfkwtions, the coefficientlisted is for a pairof conf~nrations, 2-“*(@ * @ (see ref. [ZS]).
67
Volume 57, number 1
CHEMICAL
PHYSICS
Table 3 summarizes energies of biacetyl in the ground state and several electronically excited singlet and triplet states before and after the CI treatment. Reference configuration energies for the excited states included in tab!e 3 are undersrood as those energies which correspond to certain configurations due to orbital promotions, and which were not further optimized. A qualitative description of the transition from which excited states are built is also given. The CI wavefunctions for the ground and excited states which correspond to those energies shown in table 3 are summarized in table 4. We have listed onb those important configurations whose coefficients are lager than 0.1 in magnitude.
3. Discussion The absorption spectrum of biacety1 in the crystalhne state at low temperatures and its most detaiied interpretations have been reported in the 1955 study by Sidman and McClure [l] _ These have been partially conE=ed recently by Brand and Mau [14]_
1 July 1978
LETTERS
Table 5 A summaryof cakulated transitionenergiesof biacetyl and comparisonwith availableexperimentalvaluesa) Electronic state and orbital promotion
Transitionenergies (eV) cak
(I)
2.53
2.02-2.60
(2-53) b,c)
(nzr*) (I)
3-15
2.64-354
(2.83) b,c)
4.49
2.79 (?) d,=)
S-14
4.4-6.6
‘AA, (nx*) ‘A,
expt.
“B8 kr*)
(I)
‘Bg (nsr*)
(I)
3B, (m*) ‘Ag (m+)
5.29 7-24
‘B8 (nrr*) (Ii)
854
‘B8 (rm*) (II)
8.66
3Au (n#)
(II)
5.63-6.43
f-)
8.82
‘As (mr*)
9.56
‘A, (nn*) @Ii)
9.94
‘B, kc*)
(4.40) b)
6.20-6.60 (6.28) 8) I 7.09-752
(7.10) 8)
10.54
a) Values in the parentheses are the 0-O bands. b) Ref_ El]_ C) Ref. [ 14]_ d) Ref_ [13] _ e) Ref. Is]
_
Among other things, Sidman and McCIure have proposed that the lowest ‘Bg state should be located
f) Ref_ [2] _
about 403 cm-l
gies of biacetyl and compares with avaiiable experimental values. Based upon the calculation, the nature of the lower excited electronic states is discussed in some derail, below. (i) The transition from the ground-state to the first excited singlet state, IAa + lA,, which is dipoleallowed, is caIculated at 3.15 eV_ This is close to the experimental spectrum range of 2.64-3.54 eV with band origin at 2.83 eV reported in refs. [1,14] _ As shown in table 4, this excited state, IA,(I) state, contains the do _minant configuration which involves a promotion of an electron from the 23rd MO (% type n+ MO) to the 24th MO (au type n,” MO) with a coefficient of 0.85. This rAg + lAU(n+rrz) transition is polarized along the axis vertical to the molecular plane. (ii) Of special interest is the nature of the second excited singlet state, since there exists a serious controversy in the literature as mentioned previously_ As shown in table 5, the second excited singlet state is calculated at 5.14 eV above the ground state and the calculation predicts that this second absorption
below the lowest ‘A, state and also the difference in ener=v of 3Bg and 3A, states have been deduced from the energy gap between the direct absorption spectrum and phosphorescence spectrum in the crystalline phase- These assignments have been questioned by Drent and Kommandeur [ 153 and they proposed that the 3Bg state should be located above the ‘& state_ However, they pointed out that since the Bg states (n+ + rr’ and n_ + $) are opticaliy forbidden by symmetry, the location of these states (rB9 and 3Ba) is difficuh by direct optical means. Assuming that the second absorption band is the symmetry ailowed lA, state located at 1.70 eV above the first IA, state they speculated two possi5iiiSer; in locating the Da states, based upon the s---n_ orbital splitting measured by photoelectron spectroscopy. As menticned in the introduction of the present work, however, Amett et al. [20] and Kelder et al. 1211 have presented evidence against this assumption and proposed that the se dnd absorption band is due to the dipole-forbidden transition of I& + lBg. Ta%e 5 summarizes the calculated transition ener68
g) Ref. [6] _
Volume 57, number 1
CHEMICAL PHYSKS LETTERS
is due to the dipole-forbidden IA,, + IBg transition_ The calculated value is also close ?o the experimental spectrum range of 4.40-6.6 eV with band origin at 4.40 eV_ This excited state, the ‘BJI) state, contains the dominant configuration which involves a promotion of an electron from the 21st MO (bu type n_ MOj to the 24th MO (2, type rrz MO) with a coefficient of O-78 but with an appreciably large mixing of the 23rd MO (a, type n+ MO) to the 25th MO (bg type X” MO) km&ion. The next dipole ahowed transition of lAa + rA,(II), on the other hand, is calculated at 990 eV_ Based on this result the present calculation supports the view that the second absorption band is due to the dipole forbidden lAg + IBe transition, which corresponds qualitatively to the r+ + 7rz transition_ (iii) As far as the splittings of n+-n_ and rr+-ii-_ are concerned, the SCF result in table 1 shows that the n+-n_ splitting is relatively large while the n+-n_ splitting is much smaller, meaning that there is almost no a-conjugation over the central C-C bond. This is in agreement with a recent IR study of Durig et al_ 1261, who assigned a normal C-C single bond. This picture qualitatively correspond to possibility A
mentioned in ref- [ 1.5]_ (iv) The singlet-triplet splitting of the lowest excited states, IA,(I) and 3A,(I) states, is calculated as 0.62 eV compared to the difference in the experimental O-O bands of 0.30 eV. Previo_us semi-empirical CNDO/S calculation [ 161 war not capable of removing the degeneracy of these two nrr* states due to the inherent ZDO approximations involved in the calculation_ The 3A,(I) state calculated at 2.53 eV above the ground state agrees excellently with the experimental spectrum range of 2.02-2.60 eV with band maximum at 2.53 eV_ Major contributions of configurations in tabie 4 indicate that the 3Au(I) state is of same spatial nature as the ‘A,(I) state. (v) Drent et al. [13] reported a discrete change in the character of phosphorescence excitation spectrum of biacetyl at 445 nm and assigned it to the presence of the second triplet state at 445 nm (2.79 eV)_ Kaya et al_ [5] have confumed it independently using the technique of opto-acoustic spectroscopy_ According to these experimental results this triplet state may be assigned to the 3Bg state and it may lie very close to the lowest IA, state; only 2500 cm-l (0.31 eV) above the lowest 3A, state. The result of
1 Jnuly1978
the present calculation shows, however, that the second triplet state, the 3B,(I) state, lies between the lA,(I) and lB,(I) states with calculated ener_gg of 4.49 eV above the ground state. T,his is in disagreement with the experiental results. Experience with previous ab initio SCF CI studies [24,25] indicates that transition energies to the excited states with different electronic configurations, nn” , PST*,have in general different degrees of accuracy, using a limited number of orbital bases. The covalent excited states such as the (nsr*)l, (nrr*)3 and (rr~*)~ states of heterocyclic compounds, for example, are relatively well described even without using additional polarization functions in the basis set. For a better description of the “non-covalent” excited states such as the (rrn*)l state of ethylene, on the other hand, use of 2 large set of Sasis functions iu&ding polarization terms is shown to be essential_ _The relatively large discrepancy between the calculated results and the experimental values for the Bg states (lBg and 3B9) compared to the A, states (‘A, and 3A,) may be due to this difference in the covalent character of these states. Further refiiements and extensions in orbital bases would be necessary for a defmitive clarification_ (vi) Table 5 includes also scme higher lying excited states_ No detailed comparison between the experimental and calculated values has been carried out since recent experimenral studies are lacking to compare with. It is of some interest to note that the lowest mr* tripler state, 3B, state, lies very close to the lBg (nx’) state as the calculation indicates.
Acknowledgement We express our appreciation to the ETH Zurich Computer Centre for providing computer time and to Professor Hs_H. Ciinthard for his encouragement and advice. References [l] J-W_Sidmanand D.S. McCiure, J. Am_ Chem. Sot. 77 (l9.55) 6461. [2] G. Porter and M.W. Windsor, Proc. Roy. Sot. A245 (1958) 238.
69
%&me
57, number 1
CHEMICAL PfiYSICS LETTERS
[31 H.W. Sidebottom, CC. Badcock, J.G. CaIvert, B.R_ Rabe and E-K. Damon, J, Am_ Chem. Sot. 94 (1972) 13. f4f GM- &zClehand and J-T. Yardky, J. Chem. Fhys. 58 (1973) 4368 15) K, Kaya, W.R. Harshbarger and MB. Robin, J. Chem. Phyr 60 (1974) 4231. [6] R. Ells, J- Am_ Chem. Sot. 60 (1938) 1864. [71 NJ. Leonard, H-A. Laitinen and E.H. Mottus, J. Am. Chem_ Sot. ?5 (J954) 3300_ :8J H-L. ?.f&fur~, J. Chem. Phys. S (1941) 23X [9] R. van der Werf. D. Zevenhtijzen and J. Kommandeur, Chem, Phyx Letters 27 (1974) 325. ilO] C.S. Farmenter and H&f. Fohnd, J. Chem. Phys. 51 (1959) 1551_ [I 1 J B.J. Orr, Chem. Phys. Letters 43 (1976) 446. [12] 1-Y. Chan and S. Hsi, Mol. Phys. 34 (1977) 851. [l33 E. Drent, RF. van der Werfand J. Kommandeur, 3, Chem. Phys- 59 (1973) 206L [l-t] J.C.D_ Brand and A.W.H_ _Mau,J_ Am. Chem_ Sot. 96 (1973) 4380. [15] E. Drent and J_ Kommtmde-a, Chern Fhyr Letters 14 (1972) 321ff6] J-M- Lecfercq, C. %fijotie and P. Yvan, J. Chem. Phys. 64 (1976) 1+54_
70
1 July 1978
117 J R. Hoffmann, Accounts Chem. Res- 4 (197f) I[18] E Charney and L. Tsai, J. Am. Chem. Sot. 93 (1971) 7x23. (191 HJ. Mu-is &d SF_ 5lcG&nn, J_ Mot. Spectry. 42 (1972) J77,296. (20) 1-F. Anne& G. Newborne, W_L. Mattice and S.P. AfcGi~nn, J. Am. Chem. Sot- 96 (1974) 4385. i21] J. Kelder, H- Cerfontaht, J-K- Eweg and RF-H. Rettschnkk, Chem. Phys. Letters 26 (1974) 491_ [22] 3.X.. Whitten, f. Chem. Phys- 39 (1963) 349;44 (1966) 359. 1231 K. Hagen and KmHedberg, J- Am. Chem. Sot. 9.5 (1973) 8266. [24] T.-K. Ha, hiol_ Phys. 27 (1974) 753; T.-K. Ha and U.P. Wild. Chem. Phys. 4 (1974) 300; T.-K. Ha and L. KeBer, J. hfoi. Struct. 27 (1975) 225; T.-K. Ha, &foi_Phys. 29 C197.5) 1829; Theoret Chim. Acta 43 (1977) 337. 125 ] JJ-. Whitten and hi, Hac?oneyer, 3. Chem. Phyr 5 1 (1969) 5584; 54 (1971) 3739. [26] J-R. Durig, SE. Harmurn and SC. Brown, J_ Phys. Chem. 75 (1971) 1946.
Volume 57, number 1
ON THE LOWER EXCITED ELECTZONK
PHYSidS
LETTERS
1 July 1978
STATES OF BJACETYL
Tae-Kyu HA Laboratog
of Phpiial
Chemisny. Swiss Federal Insritute of Technology,
Ziwich. Swi:ze.riazd Recehed 12 Dtcembzr 1977 Revised manuscript recei;ed 22 March I978
An ab initio SCF .md CI study has been zxried out for the ground and electronklly excited states of biketyl (CH3CO-COCH3)The second absorption band in l &e 4.40 eV region has been assigned to a ‘Ag -+ ‘Bg nzr* transition_ The character of the loxrer-lying states has been analyzed in terms of the CI wavefunctions.
1_ Introduction Due to its importance
in photochemistry
and pho-
to$?hysics, biacety! (CIi,CO-COCiI,) has been studied extensively both by spectroscopic [I- I4] and theoretical methods [I%-171 _ The interest in biacetyl photochemistry is related iargely to its low-lying electronic states and the efficient -ktersystem crossing and radiation!ess transitions_ The assignment of the fowerlying eiectronic states which is essential for the interpretation of these various photochemical behaviours, however, has remained a controversy. WhiIe it is generally accepted that the iowest-lying singlet and triplet states of 22871 cm-l (2.84 eV) and 20422 cm-t (2.53 ev) above the groucd state are of A, symmetry [ 1’,14j _ the nature of the second singlet and triplet states 1s still disputable. Wit!& the frame of the one-elect&n LCAO MO picture it is possible to discuss the qualitative nature of rhese lowerlying excited states in terms of n+(a,), n_(b,), sr+*(an) and nq(b,) orbitals of the biacetyi moIecule which are associated with the n+ + 7~,*excitations_ Since only two lower-lying singlet states are observed in the absorption spectra it is generally assumed that these states are, within this one-electron picture, due to the two dipole-allowed n,fQ + &au) and n_(b,) += zr*_(bz) transitions *which result in two IA, states of different energies. These assignments have been proposed by several investigators [I ,15,18,19], in their interpretations of the absorption spectra of various
ar-dicarbonyls including the biacetyl molecule_ Based upon the emission, absorption and circular dichroism spectra of two ardicarbonyls and also based upon the szmiempirical CNDOiS studies, Amett et al. 1201, on the other hand, have pointed out that the above assignment for the second absorption band might be incorrect. They proposed that the second absorption band in the arilicarbonyl compounds is due to the dipole-forbidden n+ + rrz transition and thus the resulting excited state would be the lBs state for biacetyl. Kelder et al. [2 l] have also arrived at the same conclusion by studying the polarization of both nn* absorption bands of glyoxal. The conflict in the above assignments warrants a more thorough theoreticalexamination of the spectral features of this photochemically interestingmolecule_ In this work we report an ab initio SCF and CI study of the ground and variouselectronically excited states of biacetyl. Apart from the assignment of the second absorption band mentioned above, several other nn* and ITTH* singlet and triplet states have also been cakulated and compared with available expe_Gnentai values. The physical nature of the lowerlying states has been analyzed in terms of the CE wavefunctions.
CHEMICAL PiiYSICS LEl-lYERS
Volume 57, number 1
1
2. Calcdation
Table 1
Ab initio SCF calculations have been carried out for biacetyl employing two different choices of gausSian basis sets. The approximate Hartree-Fock SCF atomic orbitals used as a basis set in the molecular calculation were the gaussian lobe functions 1221. The fit basis set (basis set I) consists of three linear combinations of four, three and three priitive gaussians for s-orbitals and one contraction of five pairs of gaussians for each of the three p-orbit& of carbon and bxygen atoms. Each hydrogen s-orbital was represented by a linear combination of five primitive gaussians scaled by a factor of 2’i2. The second basis set (basis set II) is a slightly extended one, in which additional one-term long range pm functions of the same exponents and lobe separations as the most diff&e p-functions of C and 0 were added to basis set I. The total basis set thus contains 90 s-type gaussians and 96 p-type gaussians (basis set II), where a single p-function consists, in turn, of two symmetrically located spherical gaussians. The molecular geometry adopted for the SCF calculations was taken from the electron diffraction experiment of Hagen and Hedberg [23]. Table Z summarizes molecular energies obtained from the ground state SCF calculations for two different basis sets. MO’s with their symmetries are also listed. No previous ab initio calculations have been czried out for this molecule. As &own in table 1 the molecular SCF total energy for basis set I is lowered only 0.017 au as a result
calculation on biacetyl for two basis sets a)
h¶olecularorbitals and total energies from ground-state SCF
Table 2 Energies and symmetries of orbit& Orbital
Symmetry
Basis set I b)
Basis set Ii b)
-205935 -20.5935 -115082 -11.5082 -11.297s -11.2978 -1.4659 -1-439s -1.0625 -1.0349 -0.8958 -0.7200 -0.7090 -0.6679 -0.6676 -0.6135 -0.6132 -0.6061 -0.5736 -0.5347 --5.;;31 -0_4L-‘2
-205949 -20.5949 -11.4910 -11.4910 -11.2ss4 -11.2884 -1.4614 -1.4357 -1.0571
symmetry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 IS 16 17 18 19 20 21 22
%
5 3a; 3bu 4% 4%
5% Sb, 6% 6bu 7aS la, 7b, Sag lbg Sb, g% 2a, 9bu 2b,
total en& a) Atumic units. b) For defiition
-1.0301 -0.8898 -0.7160 -0.7050 -0.6726 -0.6633 -0.6133 (lb,) -0.6090 (8Q -0.6024 -0.5695 -0.5328 -0.5 140 -0.4 190
-304.2458
-304.2628
of the basis sets see rext.
of the addition of the long-range p,-functions to basis set I. However, the essential point of interest is that basis set II is considered to be much more flex-
ej (au)
Orbital
Symmetry
q (au)
25 26 27 28 29 30
3bg 4a, 4bg 5bg Sa, 6bS 6a,
-0.1772 -0.1469 -0.1458 -0.0674 -0.0591 -0.0544 -0.0494 -0.0235 -0.0224
lb, 8<
18 19 20 21
Sb”, (0) 9aS (a) 2au (x) 9b, (n_)
-0.6133 -0.6090 -0.6024 -0.5695 -0.5328 -05144
2bg (sr)
-0J140
32&*)
-0.2176
(z) fu)
lOa, (n3
a; For basis set II. The virtual orbitals, *d--p39 p16-e3
Orbital
of variable occupancies used to build confiiurations a)
16 17
:: 24
July 1978
-0.4190
3”: 33
(.rr*) (ir*) (n*) (& (z*) (x*) (or*?
7a, (z*) 7bg W)
were determined by the exchange maximization with occupied SCF orbitals,
65
1 July 1978
CHEMICAL PHYSICS LJIZlTERS
Vo!ume 57, number 1
TzbIe 3 her&s of biacetyfground and eIectronic&Iyexcited stateshsed on got;nd-state SCF orbit& and transformed virtual orb&Is
-
-
Reference coniiruration enemy
-3042628
-304.3118(35)_
23-24 17-24 21+25 23+31 23-32
-3039323 -303.7123 -303.6543 -3035286 -303.5066
-3&?.1960 (330) -303.9465 (330)
‘B s
21--24 23-25 18+24 21+31 21-32
-303.8357 -303.7583 -303.6232 -303A2fM -303.4049
-304.1228 (340) -303.9933 (340)
lBu
22-24 16+24 20425 22+ 31 224 32
-303.7534 -303.6129 -3035659 -303.4272 -303A107
-3039247 (362)
“%
20424 22425 20-331 20432
-303-9603 (356)
22+33
-303-7087 -3036129 -303.3883 -303.3727 -3032564
23-24 f7-'24 21+2s 19-24 23431
-303.9433 -303-7335 -303.6759 -303.6751 -303.5338
-304.2188(387) -303.9874(387)
n-n*
21424 23-+25 18+24 21-31 21-30
-303X472 -303.6086 -303.6279 -303.4338 -3035135
-304.X469(349) -303.8369(349)
n-c??
22-24 20-2s 16-24 22431 22-32
-303.8595 -3034086 -303.6338 -303.4433 -303.4185
-304.1174(178)
n+n*
20-'24 22425 36+25 20+31 2ft-32
-303.7620 -303.6875 -303.4830 -303.4003 -303.3840
-304.0457(212)
stdte
3s +l
ibfe as far as the zr-orbit& are concerned. ‘i&is basis set (basis set iI) provides among other things a larger set of variabIe orbitals, which can be trmformed to
CL energy (number of confii~tions considered)
Qualitative description of transition
Orbital promotion
Electronic
an optimal
set of s*-o&itak
to be used for the CI
treatment of the ground?nn* and zz* singlet and triplet excited states of interest.
1 July 1978
CHJ.%ICXL PHYSICS LETTERS
Volume 57, number 1
From the SCF ground-state calculation employing basis set II, 23 occupied qq 423 (e.g. table 1) and 25 virtual orbitak y@ereobtained_ Prior to the CL treatment a truncation of certain molecular orbitaI bases is unavoidab!e because of limitations k computational capabilities. First, those virtual orbitals with energies greater than z= 200 au (six such orbitak) are discarded, since such virtual orbitals, which are thought to be unimportant iu the description of bonding, arise as a consequence of the inclusion of the short-range (cusp) functions in the gaussian basis set. Among ground-state SCF occupied orbitals, eight higher-lying MO’s, q16-pz3
are selected as orbitals of variable occupancy. The remaining virtuai orbit& have been transformed in such a way that the sum of exchange integrafs between these and the variable set Of occupied orbitals, q16-I$23, was a maximUnL The
use of such transformed virtual orbitals obtained in this way proved to be usefill in obtaining better convergence using a Iimited number of configurations in the CL treatment [24] _ Among these 19 transformed
virtual orbita!s, 10 orbitals (all z* type orbitals) were selected to be used to build configurations_ Thus, we actually included 18 orbitals of variable occupancy for generating configurations_ Table 2 summarizes these orbitals along with their symmetries and orbital energies. A CI calculation [24,25] was carried out by generating configurations referenced to a particular state of interest, which include all second order interactions larger than the energy threshold of 3.0 X 104. Within this threshold convergence was obtained within 400 configurations for describing the ground and nsr*, m* electronically excited states of interest.
Table 4 Major coefficientsto the sound and excited stateCI wavefunctionsof biacetyl a) Configurations groundstate 222 * 242 22+24 22+ 25 20+31 204 32 222 -, 24,32 22+28 22-33 20429
‘A&
1-k
jAg
O-98
0.10
Confgurations
‘BgG)
21424 23+25 18-25 21-+31 21432 23433 22,23 + 242 23428 23+30 23-27 21+29 21,22424,25
0.78 0.40 0.15 0.25 0.22 0.14 0.14 0.14
0.38 0.78 0.18 0.28 0.30 0.15
__ ‘BgC1l) 0.25 0.75
0.12 0.27 0.35 0.30 0.22 0.14
0.76 0.47 0.25 0.23 0.17 c.15 0.17
Confgurations
‘A,U)
23-24 17-24 21425 23-‘31 23+32 23-29 19+24 17+3L 17+32 17-29 19431 19+32
0.85 0.14 0.20 0.28 0.25 0.18
‘A,tll) 0.85 0.15
3AuU) 0.85 0.15 0.22 0.28 0.25
0.12 0.32 0.30 0.15
%,*I) 0.70 0.25
0.35 0.30 0.25 0.15 0.20 0.17
3Bg(1)
‘Bg(II)
Confiiurations
‘B U
3BU
0.75 0.46 0.15 0.22 0.28 0.15
0.38 0.72
22424 16+24 22+31 22-32 22+29 20,22 + 242 20424 2042.5
0.76 0.21 0.30 0.30 0.16 0.23 0.23
0.83 0.22 0.25 0.23 0.14
0.13 0.17 0.23 0.24 0.25 0.14 0.11
0.20
0.15 0.14
a) Only those confii~tions with coeffkients largerthan 0.1 in magnitudein the Ci wavefunctionsare listed. ln the case of opensh%llconfkwtions, the coefficientlisted is for a pairof conf~nrations, 2-“*(@ * @ (see ref. [ZS]).
67
Volume 57, number 1
CHEMICAL
PHYSICS
Table 3 summarizes energies of biacetyl in the ground state and several electronically excited singlet and triplet states before and after the CI treatment. Reference configuration energies for the excited states included in tab!e 3 are undersrood as those energies which correspond to certain configurations due to orbital promotions, and which were not further optimized. A qualitative description of the transition from which excited states are built is also given. The CI wavefunctions for the ground and excited states which correspond to those energies shown in table 3 are summarized in table 4. We have listed onb those important configurations whose coefficients are lager than 0.1 in magnitude.
3. Discussion The absorption spectrum of biacety1 in the crystalhne state at low temperatures and its most detaiied interpretations have been reported in the 1955 study by Sidman and McClure [l] _ These have been partially conE=ed recently by Brand and Mau [14]_
1 July 1978
LETTERS
Table 5 A summaryof cakulated transitionenergiesof biacetyl and comparisonwith availableexperimentalvaluesa) Electronic state and orbital promotion
Transitionenergies (eV) cak
(I)
2.53
2.02-2.60
(2-53) b,c)
(nzr*) (I)
3-15
2.64-354
(2.83) b,c)
4.49
2.79 (?) d,=)
S-14
4.4-6.6
‘AA, (nx*) ‘A,
expt.
“B8 kr*)
(I)
‘Bg (nsr*)
(I)
3B, (m*) ‘Ag (m+)
5.29 7-24
‘B8 (nrr*) (Ii)
854
‘B8 (rm*) (II)
8.66
3Au (n#)
(II)
5.63-6.43
f-)
8.82
‘As (mr*)
9.56
‘A, (nn*) @Ii)
9.94
‘B, kc*)
(4.40) b)
6.20-6.60 (6.28) 8) I 7.09-752
(7.10) 8)
10.54
a) Values in the parentheses are the 0-O bands. b) Ref_ El]_ C) Ref. [ 14]_ d) Ref_ [13] _ e) Ref. Is]
_
Among other things, Sidman and McCIure have proposed that the lowest ‘Bg state should be located
f) Ref_ [2] _
about 403 cm-l
gies of biacetyl and compares with avaiiable experimental values. Based upon the calculation, the nature of the lower excited electronic states is discussed in some derail, below. (i) The transition from the ground-state to the first excited singlet state, IAa + lA,, which is dipoleallowed, is caIculated at 3.15 eV_ This is close to the experimental spectrum range of 2.64-3.54 eV with band origin at 2.83 eV reported in refs. [1,14] _ As shown in table 4, this excited state, IA,(I) state, contains the do _minant configuration which involves a promotion of an electron from the 23rd MO (% type n+ MO) to the 24th MO (au type n,” MO) with a coefficient of 0.85. This rAg + lAU(n+rrz) transition is polarized along the axis vertical to the molecular plane. (ii) Of special interest is the nature of the second excited singlet state, since there exists a serious controversy in the literature as mentioned previously_ As shown in table 5, the second excited singlet state is calculated at 5.14 eV above the ground state and the calculation predicts that this second absorption
below the lowest ‘A, state and also the difference in ener=v of 3Bg and 3A, states have been deduced from the energy gap between the direct absorption spectrum and phosphorescence spectrum in the crystalline phase- These assignments have been questioned by Drent and Kommandeur [ 153 and they proposed that the 3Bg state should be located above the ‘& state_ However, they pointed out that since the Bg states (n+ + rr’ and n_ + $) are opticaliy forbidden by symmetry, the location of these states (rB9 and 3Ba) is difficuh by direct optical means. Assuming that the second absorption band is the symmetry ailowed lA, state located at 1.70 eV above the first IA, state they speculated two possi5iiiSer; in locating the Da states, based upon the s---n_ orbital splitting measured by photoelectron spectroscopy. As menticned in the introduction of the present work, however, Amett et al. [20] and Kelder et al. 1211 have presented evidence against this assumption and proposed that the se dnd absorption band is due to the dipole-forbidden transition of I& + lBg. Ta%e 5 summarizes the calculated transition ener68
g) Ref. [6] _
Volume 57, number 1
CHEMICAL PHYSKS LETTERS
is due to the dipole-forbidden IA,, + IBg transition_ The calculated value is also close ?o the experimental spectrum range of 4.40-6.6 eV with band origin at 4.40 eV_ This excited state, the ‘BJI) state, contains the dominant configuration which involves a promotion of an electron from the 21st MO (bu type n_ MOj to the 24th MO (2, type rrz MO) with a coefficient of O-78 but with an appreciably large mixing of the 23rd MO (a, type n+ MO) to the 25th MO (bg type X” MO) km&ion. The next dipole ahowed transition of lAa + rA,(II), on the other hand, is calculated at 990 eV_ Based on this result the present calculation supports the view that the second absorption band is due to the dipole forbidden lAg + IBe transition, which corresponds qualitatively to the r+ + 7rz transition_ (iii) As far as the splittings of n+-n_ and rr+-ii-_ are concerned, the SCF result in table 1 shows that the n+-n_ splitting is relatively large while the n+-n_ splitting is much smaller, meaning that there is almost no a-conjugation over the central C-C bond. This is in agreement with a recent IR study of Durig et al_ 1261, who assigned a normal C-C single bond. This picture qualitatively correspond to possibility A
mentioned in ref- [ 1.5]_ (iv) The singlet-triplet splitting of the lowest excited states, IA,(I) and 3A,(I) states, is calculated as 0.62 eV compared to the difference in the experimental O-O bands of 0.30 eV. Previo_us semi-empirical CNDO/S calculation [ 161 war not capable of removing the degeneracy of these two nrr* states due to the inherent ZDO approximations involved in the calculation_ The 3A,(I) state calculated at 2.53 eV above the ground state agrees excellently with the experimental spectrum range of 2.02-2.60 eV with band maximum at 2.53 eV_ Major contributions of configurations in tabie 4 indicate that the 3Au(I) state is of same spatial nature as the ‘A,(I) state. (v) Drent et al. [13] reported a discrete change in the character of phosphorescence excitation spectrum of biacetyl at 445 nm and assigned it to the presence of the second triplet state at 445 nm (2.79 eV)_ Kaya et al_ [5] have confumed it independently using the technique of opto-acoustic spectroscopy_ According to these experimental results this triplet state may be assigned to the 3Bg state and it may lie very close to the lowest IA, state; only 2500 cm-l (0.31 eV) above the lowest 3A, state. The result of
1 Jnuly1978
the present calculation shows, however, that the second triplet state, the 3B,(I) state, lies between the lA,(I) and lB,(I) states with calculated ener_gg of 4.49 eV above the ground state. T,his is in disagreement with the experiental results. Experience with previous ab initio SCF CI studies [24,25] indicates that transition energies to the excited states with different electronic configurations, nn” , PST*,have in general different degrees of accuracy, using a limited number of orbital bases. The covalent excited states such as the (nsr*)l, (nrr*)3 and (rr~*)~ states of heterocyclic compounds, for example, are relatively well described even without using additional polarization functions in the basis set. For a better description of the “non-covalent” excited states such as the (rrn*)l state of ethylene, on the other hand, use of 2 large set of Sasis functions iu&ding polarization terms is shown to be essential_ _The relatively large discrepancy between the calculated results and the experimental values for the Bg states (lBg and 3B9) compared to the A, states (‘A, and 3A,) may be due to this difference in the covalent character of these states. Further refiiements and extensions in orbital bases would be necessary for a defmitive clarification_ (vi) Table 5 includes also scme higher lying excited states_ No detailed comparison between the experimental and calculated values has been carried out since recent experimenral studies are lacking to compare with. It is of some interest to note that the lowest mr* tripler state, 3B, state, lies very close to the lBg (nx’) state as the calculation indicates.
Acknowledgement We express our appreciation to the ETH Zurich Computer Centre for providing computer time and to Professor Hs_H. Ciinthard for his encouragement and advice. References [l] J-W_Sidmanand D.S. McCiure, J. Am_ Chem. Sot. 77 (l9.55) 6461. [2] G. Porter and M.W. Windsor, Proc. Roy. Sot. A245 (1958) 238.
69
%&me
57, number 1
CHEMICAL PfiYSICS LETTERS
[31 H.W. Sidebottom, CC. Badcock, J.G. CaIvert, B.R_ Rabe and E-K. Damon, J, Am_ Chem. Sot. 94 (1972) 13. f4f GM- &zClehand and J-T. Yardky, J. Chem. Fhys. 58 (1973) 4368 15) K, Kaya, W.R. Harshbarger and MB. Robin, J. Chem. Phyr 60 (1974) 4231. [6] R. Ells, J- Am_ Chem. Sot. 60 (1938) 1864. [71 NJ. Leonard, H-A. Laitinen and E.H. Mottus, J. Am. Chem_ Sot. ?5 (J954) 3300_ :8J H-L. ?.f&fur~, J. Chem. Phys. S (1941) 23X [9] R. van der Werf. D. Zevenhtijzen and J. Kommandeur, Chem, Phyx Letters 27 (1974) 325. ilO] C.S. Farmenter and H&f. Fohnd, J. Chem. Phys. 51 (1959) 1551_ [I 1 J B.J. Orr, Chem. Phys. Letters 43 (1976) 446. [12] 1-Y. Chan and S. Hsi, Mol. Phys. 34 (1977) 851. [l33 E. Drent, RF. van der Werfand J. Kommandeur, 3, Chem. Phys- 59 (1973) 206L [l-t] J.C.D_ Brand and A.W.H_ _Mau,J_ Am. Chem_ Sot. 96 (1973) 4380. [15] E. Drent and J_ Kommtmde-a, Chern Fhyr Letters 14 (1972) 321ff6] J-M- Lecfercq, C. %fijotie and P. Yvan, J. Chem. Phys. 64 (1976) 1+54_
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1 July 1978
117 J R. Hoffmann, Accounts Chem. Res- 4 (197f) I[18] E Charney and L. Tsai, J. Am. Chem. Sot. 93 (1971) 7x23. (191 HJ. Mu-is &d SF_ 5lcG&nn, J_ Mot. Spectry. 42 (1972) J77,296. (20) 1-F. Anne& G. Newborne, W_L. Mattice and S.P. AfcGi~nn, J. Am. Chem. Sot- 96 (1974) 4385. i21] J. Kelder, H- Cerfontaht, J-K- Eweg and RF-H. Rettschnkk, Chem. Phys. Letters 26 (1974) 491_ [22] 3.X.. Whitten, f. Chem. Phys- 39 (1963) 349;44 (1966) 359. 1231 K. Hagen and KmHedberg, J- Am. Chem. Sot. 9.5 (1973) 8266. [24] T.-K. Ha, hiol_ Phys. 27 (1974) 753; T.-K. Ha and U.P. Wild. Chem. Phys. 4 (1974) 300; T.-K. Ha and L. KeBer, J. hfoi. Struct. 27 (1975) 225; T.-K. Ha, &foi_Phys. 29 C197.5) 1829; Theoret Chim. Acta 43 (1977) 337. 125 ] JJ-. Whitten and hi, Hac?oneyer, 3. Chem. Phyr 5 1 (1969) 5584; 54 (1971) 3739. [26] J-R. Durig, SE. Harmurn and SC. Brown, J_ Phys. Chem. 75 (1971) 1946.