Calculated photoelectron spectra of singlet and triplet methylene

CHEhlICAL

Volume 54, number 3

CALCULATED

PHOTOELECTRON

H.L. HASE. G. LAUER,

Receired

19 November

LJZITERS

SPECTRA OF SINGLET AND TRIPLET METHYLENE

K--W. SCHULTE,

Fackbereich Plzysikalische Chernie der

PHYSICS

Unwenitcii,

A. SCHWEIG

15 March 1978

*

and W. THIEL

D 3550 Marburgh.uhrr. Germany

1977

Vertical lonizatron potentials for smglet and triplet methylene are calculated by a CI perturbation method based on ab initio SCF molecular orbitsls (6-31 G** bansj. The shape and vlbrattonal fine structure of the first photoelectron band are investigated using the MIND0/3 method. The computed singIet-triplet splittmg for methylene is 16 4 kcal/mol. in reasonable agreement with the experimental value of 19 5 kcal/mol.

1. Introduction The UV absorption spectra of singlet and triplet methylene have been observed by the flash photolysis technique [l-3] _ Likewise, it seems conceivable that the corresponding UV photoelectron spectra can be recorded if methylene is generated in the spectrometer as a transient species from suitable precursors. As an aid to their identification, we report the calculated photoelectron spectra of singlet and triplet methylene.

2. Vertical

ionization

potentials

Vertical ionization potentials are obtained as the difference between the total energies of the ionic state of interest and the molecular ground state, at the ground state geometry. The state energies are calculated by a CI perturbation method [4] which is based on ab initio SCF MO wavefunctions for the neutral closed-shell system. Each state is specified by one or more main configurations; the CI perturbation calculation includes all spin and symmetry adapted configurations either with single or with single and double excitations from the main configurations (SEC1 singly excited CI, DECI doubly excited CI). The state energy is computed by performing a CI calculation for a set of selected con* Part 74 of Theory and Apphcations of Photoelectron Spectroscopy. Part 73, see- H. Schmidt, A. Schwetg, W. Thiel and M. Jones, Chem. Ber., to be published.

494

figurations [4] and then adding the contributions from the remaining configurations as estimated by secondorder Brdlouin-Wigner perturbation theory. Table 1 lists the calculated vertical ionization potentials for singlet (lA1) and triplet (3Br) methylene. Geometries were taken from a recent study [S] believed to be close to the Hartree-Fock limit: lA1 R = 1.097 A, 0 = 102.9”, and 3B1 R = 1.070 A, 8 = 129.5”. The SCF calculations were carried out by the POLYATOM program system [6] using a standard 6-31 G** basis [7] (double-zeta plus polarization functions). As main configurations, we chose for the singlet both lat2atlb23aT and la~2a~lb~lb~, and for the triplet laz2aflb23al 3 lb,. For each of the ionic states, the Koopmans’ configuration was the only main configuration. The total number of singly and doubly excited configurations was 17.59 for the singlet and 3344 for the triplet (see table 1 for the ionic states). The selection parameters [4] were set to T = 0.01 eV and G = 13.605 eV leading to typically 60-120 selected configurations for each state. In table 1, the vertical ionization potentials of the singlet were obtained by DECI, and those of the triplet by SEC1 calculations. This discrepancy is dare to the limitations of our program which, at present, can treat the excited ionic states derived from the triplet only by SECI. There are, however, reasons to believe that the two sets of results are compatible: For the first ionization potential of the triplet, the DECI value of 10.11 eV differs from the SEC1 value by only 0.17 eV. Also, the calcuiated DECI band splittings in the singlet spec-

CHEhlICAL

Volume 54, number 3 Table 1 Calculated

vertical ionization

potentials

Initral state

Ionization from hf0

Ionic state

IV”)

‘At

3at

*Al

1890

10.02 14 97

3B1

lbz

*Et2

1894

2a1

*A1

1890

Ia1

*At

1890

lbi

*AI

331

2B*

lb2 lb2

129

lPvert (eV)

b)

22 87 29.599 IO 28 ‘1

2038

10.66

4A2

1284

14 15

*A2

2018

15.90

lb2

2Az

2018

16 55

2al

4B*

1272

19 31

2%

*RI

2038

23 09

2a1

*B1

2038

25.64

4Bt

1272

292.95

la1

PHYSICS

la,

*B*

2038

295.59

Ia1

*B*

2038

295.90

u) Total number of confi_rurations mcluded for the ionic state (DECI values for ions dcnved from ‘Al, SEC1 vaiues for

ions derived from 3 Bi). initral states. ‘At A’DECI = 1759, 3B1 A&i = 566. b, Results from third-order Raylrqh-Schrodinger perturbation correctrons to SCf eigenwlues I151 - IP (‘A,) 9 80, 15.06,23.18, 293.75 eV. ‘) INOCI [16]. IP t3B1) 1001 eV.

LETTERS

15 hlarcb 1978

berg series; a similar error might be expected for the first ionization of singlet methylene. According to our results, the maxima of the first two bands in the triplet spectrum are separated by only 0.38 eV: both bands should have comparable intensities stnce the photoionization to the lBl state of the eon is dn allowed oneelectron process, contrary to the srtuatron wrth the singlet. Finally we note that removal of an electron from a doubly occupied orbital in trrplet methylene leads to a cation wrth three unpaired electrons whrch gives case to one quartet and two doublet states: the resulting doublet-quartet and doublet-doublet splittings are quite appreciable (see table I)_

3. Band shape and vibrational fie

structure

The first photoelectron band seems pdrttcularly important for the spectral identrficdtion of methylene. We have therefore investigated rts structure in Inore detar1 usmg the MIND0/3 method [8] which has alreddy been shown to provide a realistic descrrptton of neutral singlet and triplet methylene [9] _ Table 2 contains the MINDO/S results for CHZ(3Bl. and CH;(‘B,). the values for ‘A1 ), CH;(“Ai), H20(tAI) and H,0*(2B;) are included for comparison. Open-shell species were treated by the half-electron method [lo] ; optimrzed geometries were obtained by the Davidon-Fletcher-Powell algornhm [ 1 I], and vtbratronal frequencies by normal coordmdte analysis

trum (cf. table 1) are well reproduced by SECI, e.g. for the first two bands 4.95 eV (DECI) versus 5.10 eV (SECI), or for the first and third band 12.85 eV (DECl)

[12].

versus 12.75 eV (SECI). Hence we expect the DECI ionization potentials of the triplet to differ from the SEC1 ones by only about O-l-0.2 eV. The He1 photoelectron spectrum of singlet tnethylene is predicted to consist of two bands only, at 10.02 eV and 14.97 eV. In addition, there can be ionizationexcitation bands associated with a very low intensity_ The first such band corresponding to the two-electron process CH2(IAl) + CHz(“BI) is calculated to occur at 1144eV. The predicted He1 photoelectron spectrum of triplet methylene shows six bands. The calculated value for the first ionization potential (SECI: 10.28 eV, DECI: 10.11 eV) is somewhat lower than the experimental value of 10.396 eV [2] obtained as the limit of a Ryd-

different from CH,(lA,) , whereas Cl&(ZBl) 1s simtldr to CH7(‘AI) and very different from CHZ(~BI). Thus the ionizations (a) CH2(3Bl) + CHt(‘A,), (b) CHj(“B,) -+ CH,(tA,) should lead to sharp bands with an intense O-O peak, and the ionizations (c) CHz(tAI) + CH5(2A,), (d) CHT(?Bt) + CHZ(3Bt) to very broad

It is obvious from table 2 that, with r-espect to their structures, CHt(‘A,) is simrlar to CH,t3BI) and very

bands. Accordingly, MlNDO/S predicts the differences between the vertical and adrabatrc ionrzation potentrals to be (a) 0.01 eV; (b) 0.01 eV (experimental 0.0 eV

[ 131): (c) 0.59 eV; (d) 0.62 eV (experunentalO.6

eV

5 (a, c)- Cdculated

as the dlffereme bctwccn t!w total cncrgies of the cation at the optmlized geometries of tl~c neutral molecule .md the cation (neglectIn_e zero-point vlbrJt1ond effects of tile order of 0.01 eV); malogous definitron for (b, d).

495

*

Volume 54, number 3 Table 2 MlNDD/3

CHEMICAL

PHYSICS

results a) for bond lengths R, bond angles e, bending frequencies Molecule

0 (deg)

R (A)

CH2 ‘Bt

1 078(X

1.122(1.11)

IO0 2(102 138.2 b,

Cli;

‘AI

1091

CH;

2B1

1.144

b)

LJand Isotope shifts Au (XHa -+ XDa) Au (cd

Y (cm’)

CHa IA:

078)

15 hkirch 1978

LETTERS

133 8(136) 4)

99.9(99)

)

Ref.

1139(==1200)

288(=300)

13,131

1328

352

121

1053

265

HZ0 ‘AI

O-949(0.957)

103 9(104

5)

1330 1537(1595)

353 381(417)

I21

H20+ ‘B,

0974(0999)

108.4(110

3)

1331+1380)

355 (=400)

1171

[131

a) Experime ntal values in parentheses.

b)INOCI[16]-R=1.107i\.0=14030. [ 131). In view of the good agreement between theory and experiment for thephotodetachment processes (b. d), the MIND0/3 values for the photoionization processes (a, c) seem reliable The frequency of the bending vibration is calculated to be 1053 cm-l for CHs(“A,) and 788 cm-l for CD$(?A*) which corresponds to an isotope shift of 265 cm-l. Comparison with the data for CH2 (3B, ), H20(lA1), and H70+(“B,) shows (see table 2) that MIND013 tends to underestimate the frequency of the H-X-H bending vibration by about 60 cm-l, and the isotope shift by about IO-40 cm-l _Hence we estimate a corrected value of 1110 cm-* for the frequency and 290 cm-* for the isotope shift. in any case, these values obtarned within the harmonic oscillator approximation should be compared only to the difference between the O-O and O-l vibrational peaks since CH$(‘A,) must properly be described by a double-well potential; the MIND013 barrier for the inversion of CH;(‘Al) is

5.65 kcal/mol (1980 cm-*). According to our calculations, the first two vertical ionizations of triplet methylene are separated by only 0.38 eV (see table 1). MIND013 predicts the difference between the vertical and adiabatic ionization potential of the second band to be O-13 eV. Thus the first two bands in the triplet spectrum will overlap, but only to an extent that the O-O and O-l vibrational peaks of the first band can still be observed distinctly_ We can now combine the data available: For triplet methylene, the O-O peak at IO.40 eV (experimental value) should be the most intense one in the first band. For singlet methylene, the first band is predicted to start at about 9.43 eV and to reach its maximtim at 10.02 eV; judging from the triplet results, these values might be too low by about 0.2 eV. In both cases, the vibrational interval between the O-O and O-I peaks should be 1110 cm-’ for CH$(’ A,)and 820 cm-1 for CD;(2A,).

Table 3

Singlet-tnplet

splitting AE, total energies E,and method for treating correlation Ref.

AE (kul/mol)

present

16 4

-39.0404

-39

[18.191

13 8

-39.0121

-38.9898

9.2

PO1 1211 K=l 1221 496

effects Co::elation

E (au)

0143

CI perturbation IN0 CI

-39.0754

-39 0607

IEPA

15.4

-39

-39

CI

17.8

-39.0628

-39 0345

UMP2 perturbation

15.3

-39.0805

-39

UMP3 perturbation

0564

0319 0562

CHEMICAL PHYSICS LETTERS

VolLme 54, number 3

4. Singlet-triplet

splitting

[41 H-L Hdse,G. Lauer, K.-W. Schulte and A. Schneig. subTheoret. Claim. Acta, fo be published.

Over the past years, there has been considerable interest in calculating the energy difference between singlet and triplet methylene [ 141. Table 3 lists the results of some recent ab initio studies all of which use

basis sets of at least double-zeta

15 March 1978

quality

with polariza-

tion functions and take account of correlation effects. Our present DECI value of 16.4 kcal/mol for the singlet-triplet splitting is closer to the experimental value of 19.5 f 0.7 kcal/mol [13] than most other theoretical values. This is somewhat su&ising since

our basis set is inferior to some of those used previously (cf. table 3). It might indicate that o:r CI perturbation method treats the correlation in singlet and triplet methylene in a fairly balanced way.

Acknowledgement

This work was supported by the Deutsche Forschungsgemeinschaft and Ihe Fonds der Chemischen Industrie. The calculations were carried out using the TR 440 computer of the Rechenzentrum der Universitat Marburg--One of us (W-T.) thanks the Fonds der Chemischen Industrie for a Liebigstipendium.

References 1 G. Herzberg, Proc. Roy. Sot. A 262 (1961) 291 1 G. Herzberg. Molecular spectra and molecular structure, Vol. 3. Electronic spectra and electronic structure of polyatomic molecules (Van Nostrand, Princeton, 1966). 1 G. Herzbeg and J.W C. Johns, J Chem. Phys. 54 (1971) 2276.

[51 J II. bleadov s and H-1‘ Schaefer ISI, J Am. Cncm. Sot 98 (1976) 4383. [61 I G. Csizmadia, M-C. Harrison. J-W_ Xlosco\\Itzand B-T Sutchffe, Theorct. Chun. Acta 6 (1966) 19 1,

Program No 199. Quantum Chemistry Program l%zhan~c. 1ndLindUnlvernty, Bloommgton, lndldna [71 P C. Harlhalan and J A Poplc, Thcoret. Chuu. Acta 28 (1973) 213. I81 R C Bingham, b1.J S Del\dr and D H. Lo, J. Am Chem Sot. 97 (1975) 1285 191 hi J.S Deax. R C lladdon,W K. LI, W. Thlcl and P.K Weiner. J Am Chem. Sot 97 (1975) 4540. ilO1 hf 1 S Dcwdr, J-A Hashmall and C G. Vemer. J Am Chem sot. 90 (1968) 1953. [ 111 R Fletcher and M J D. Po\xell, Comput J 6 (1963) 163. IV C. Davldon, Comput. J. 10 (1968) 406 1121 hl J S Deaar and G-P. r‘ord. J Am.Chem. Sot 99 (1977) 1685 1131 P I-. Zlttel, G.B Elhson. S V. O’hell, E Herbst. W_C Lmeberser 2nd W-P Reinhardt. J. Am. Chem. Sot 98 (1976) 373’ [141 J-l-. Harrison. AccountsChem. Res 7 (1974) 378 [ 151 D-P. Cbong, r G. Hcrrmg and D. McWdhams, J Chem Phys. 61 (1974) 958. 1161 C I‘. Bender and H 1 _Schaefer Ill, J. blot Spcctr? _37 (1971) 423 [171 D-W. Turner, C Baker. A D Baker Jnd C R Brundlc. MolecuLr pnotoefectron spectroscopy (\Vile) -1ntcrxxnce. New York, i970) 1181 C.1‘. Bende. H I-. Schaefer III, D R I rancheschctti .md L C Allen. J Am. Chem. Sot. 94 (1972) 6888 [I91 D R McLaughlm,C F Bender and H I Schaefer III, Theoret Chim. Acta 2.5 (1972) 352. [20] V Staemmler, Tbeoret.Chim. Actd 31 (1973) 49 (211 A H Pakian and NC. Handy, Theoret.Chim Actd 40 (1975) 17 [221 J A. Popie. J.S. Bmklty and R. Seeger, intern J. Quantum Chem. 10s (1976) 1.

497