The CNDO geometry of ethylene in the first singlet excited state

Volume 3. number 8

CHE&!ICAL PHYSICS LETTERS

THE IN

THE

CNDO

GEOMETRY

FIRST

SINGLET

OF

Au--t

1969

ETHYLENE

EXCITED

STATE

G. H. KIRBY and K. MILLER * Departmenl of Chmzistry , University of Reading. Wkitcknigkts, Reading, UK

Received 28 May 1969

Approximate open shell SCF MO theory in the CNDO/2 scheme confirms the 90° twisted geometry singlet excited ethylene and gives values of 114’ for angle HCH and 1.38h for Y&.

1. INTRODUCTION Differing interpretations of the vibrational structure in the r* - i; (V - N) electron@ transition of ethylene in the region 1600- 22OOA have led to conflicting views about the geometry of the molecule in its first singlet excited state. Wilkinson and Mulliken [l] photographed the spectra of C2H4 and C2D4 and assigned the long series of bands of C2H4 to the C-C stretching vibration vi in the excited state by analogy with the ShumFn-Runge system of 0,. A value of = 1.69-4 was estimated for the C-C bond length in the excited state. McDiarmid and Charney [2] made temperature variation studies of the C2H4 and C2D4 spectra and re-assigned the long vibrational series to progressions in the twisting vibration vi of the excited state. They concluded that the two CH2 groups of ethylene are twisted relative to each other by 90° in the excited state but found no evidence for the C-C stretching vibration. Very recently McDiarmid [3] has used the relative intensities of the bands in the long progressions to obtain an upper state rotational constant A’ of 5.677 cm-I for C $4. assuming a harmonic potential barrier. However, Ogilvie [4] has suggested that the out-of-plane bending vibration vi2 could equally well account for the magnitude of the vibrational intervals and the effects of isotopic substitution. Such an interpretation points to an almost eclipsed, non-planar structure for the excited state of ethylene. Finally, Merer and Mulliken [5] claim reasonable agreement with the observed spectra by YO

* Present address: Slough College of Technolo,y, Slough. UK.

of

computing the vibrational structure produced if both C-C stretching and twisting vibrations contribute to the spectra and assuming a sinusoid& potential barrier. The equilibrium geometry of the excited state is assumed to have the two CH;? groups twisted by 90° relative to each other and a C-C bond length of 1.44& It is also postulated that with increasing quanta of twist vi the C-C bond stretches, reaching 1.80A near the top of the barrier where the molecule is effectively planar. The 90’ twisted configuration for the geometry of the first singlet excited state has been predicted by Mulliken [S] for a long time. The same conclusion was reached by Walsh [7] who additionally expects an out-of-plane bending producing a pyramidal bond arrangement around each carbon atom. Further discussions have been based on

the many ground state SCF MO calculations which have been carried out for ethylene (see for example ref. [8] and references given therein). Two recent papers [9, lo] ?ave described approximate open shell SCF MO‘methods within the CNDO scheme for calculation of molecular structures in singlet excited electronic states. These are based upon Roothaan’s open shell SCF theory [ll] as extended by Huzinaga [12]. We report here an investigation of the geometry of ethylene in its first singlet excited state, the V state, by the open shell SCF MO method of Kroto and Santry [lo]. 2. METHOD The Kroto-Santry method [lo] differs &om the Huzinaga treatment [12Jof Roothy’s open-shelI 643

Volume 3. number 8

CHEMICAL PHYSICS LETTER5

self-consistent field theory in that it applies to the special case of a singlet excited state, and that certain off-diagonal muitipliers are neglected in formulating a set of matrices diagonalization of which yields new LCAO coefficients. This last point results in a loss of orthogonality between open shell orbitals and closed shell orbitals of the same symmetry. The application of this method within the CNDO/2 framework to a variety of small molecules [lo] gave quite satisfactory results for excited state bond angles, in spite of a small loss of orthogonality between some orbitals. In applying the Kroto-Santry method to geometrical deformations of excited states it seems sensible to choose, where possible, deformations which preserve the maximilm symmetry, thereby reducing the number of off-diagonal multipliers which are approximated to zero. Dixon [9] has used the Huzinaga scheme for formtidehyde and obtained results which are in general agreement with bond angles calculated using the Kroto-Santry theory. A detailed comparison is difficult since Dixon used the CNDO/l parameterzation, but it seems likely that the more rigorous approach may not, within the CNDO approximations, necessarily lead to significantly better results. In applying the method of Kroto and Santry the potential energy for different geometrical configurations was calculated using eq. 2.31 of ref. [lo] but with IVg defined, in the symbolism of that paper, as

August 1969

symmetry group. In twisted ethylene the symmetry is reduced to D2 except for the 90° twisted case where it is D2d. A ground state CNDO calculation was used to give the initial input orbitals for the open shell SCF MO computer program. The electron configuration of the first excited state was taken to be, in species symbols appropriate to D2h, (ag)2(bIu)2(b2u)2(ag)2(b3g)2(b3u)

(b2g)

‘BI,,

where the bSu orbital is the i; orbital and the b2g orbital is the pi* orbital. In all the calculations made for the excited state we have used 7CH = l-09& estimated by comparison with C2H6 and CH20 [13]. Table 1 summarises the results. Firstly variation of 7& was made at the angles of twist shown in the table, with angle HCH fixed at 120°. For all bond lengths investigated, from 1.25i to l-70& the 90’ twisted geometry is the most stable. There is only a small change in the magnitude of YCC which minimises the energy of the excited state molecule at 90’ of twist (1.38A) compared with that for no twist (1.43A). Calculations of the energy of the excited state were made for various HCH angles in the 90° twisted configuration and resulted in a value of 114’ for the HCH angles at the lowest energy. The value of 1.38A for ?-Cc at the most stable configuration was unchanged by this improvement in HCH angle. No significant change in HCH angle was found for another angle of twist.

+CA

,$

+?AZBiRAB

where

This definition of Wg makes eq. 2.31 equivaIent to the expression given by Roothaan [ll] for the energy of excited singlet statss. The incorrect inclusion of Opv by Kroto and Santry where we have LcLy in the equation for Wg appears to be an error introduced in production of the manuscript since their results are in agreement with our definition of Wg.

The bgu(T) and b2g(r*) orbitals of the untwisted molecule correlate with a non-bonding e orbital in the 90’ twisted configuration. For intermediate angles of twist the Kroto-Santry method gives some loss of orthogonality between the two open shell orbitals, though this is serious only for small angles of twist where it causes convergence problems. The values of ?-CC and angle HCH which minimise the energy of these intermediate configurations are, however, consistent with the values at the 90° twisted and the untwisted limits, where the open shell orbit& are orthogonal by symmetry. Table

&c 1.43A

HCH

&H (ass)

3o”

1.42A

115”

60°

1.39A

l.osA ~.osA

SO0

1.38A

1140

1.092%

T

3. RESULTS In the ground

bond lengths Y:

Least state

gle HCH = 117.6% [l3], 644

ethylene

= 1.339A,

stable

is p\anrz,with

gH = 1.086Aand

an-

and it belongs to the D2h

1

Geometries of the first singlet excited state of ethylene optimised at various angles of twist (T). Energy increases from the bottom of the table

Most stable

O”

l.ogA

Volume

3. number

8

CHEMICAL

PHYSICS

The effect of moving the hydrogen atoms out of the C-CH2 planes to give a pyramidal arrangement of atoms around each carbon was investigated with values of 1.38& and 1.5& for Y& and HCH angles of 120° and llO”. Such a bending of the molecule (the Ogilvie geometry) from the untwisted planar configuration did lead to 2 reduction in energy for the excited state but a further progressive reduction could then be produced by an increasing twist of up to 90° about the C-C bond. However, in the 90’ twisted configuration the energy was lower with the C-CH2 groups planar than with the hydrogen atoms out of plane (the Walsh geometry). This no matter what deformations were made, the only minimum found was for the 90’ twisted configuration with planar C-CH2 groups. The transition energy from the CNDO ground state to the most stable geometry for the excited state was calculated to be 5.17 eV. The magnitudes of the coefficients in the excited state molecular orbitals are available upon request.

LETTERS

August 1969

such a large variation in Y& t3-f~ woukf have been apparent from our calculations. The CNDO geometry of C2H4 in this excited state suggests a value of 5.0 cm-l for the rotational constant A '.The larger value obtained try McDiarmid (31 implies, for ~6~ = 1.09 * 0.OIA, an HCH angle of 108O * 2O. representing a much larger decrease than might be expected in view of the planar arrangement of bonds around each carbon atom. We have not attempted to investigate the shape or the height of the potential barrier since calculations based on CNDO are not expected to give reliable results in this respect. ACKNOWLEDGEMENTS GHK acknowledges a Shell Research Fellowship and KM an SRC Research Fellowship.

REFERENCES 4. DISCUSSlON P. G. Wilkinson and R. S. Mulliken. J. Chem. Phys. 23 (1955) 1895. [2] R. McDiarmid and E. Charney. J. Chem. Phys. 47 (1967) I.51 7. [3] R. McDiarmid. J. Chem. Phys. 50 (1969) 1794. [-&I J. F. Ogilvie, J. Chem. Phys. 49 (1968) 474. [S] A. J. Merer and R. S. Mulliken. J. Chem. Phys. 50 (1969) 1026. [S] R. S. Mulliken. Phys. Rev. 41 (1932) 751. [i] A. D. Walsh. d. Chem. Sot. (1953) 3325. [S] U. Kaldor and I. Shavitt, J. Chem. Phys. 48 (1968) 191. [9] R.N.Nixon. Mol. Phys. 12 (1967) 53. [lo] H.W.Kroto and D. P.Santry. J. Chem. Phys. 47 11967) 2736. Ill] b. C.h. Roothaan. Rev. Mod. Phvs. 32 (1960) 179. 1121 S. Huzinaga. Phvs. Rev. 120 (19‘60) 866. [13] G. Herzberg, Molecular spectra and molecular structure III (V-n Nostrand. Princeton. 1966). [14] G. A. Segal. J: Chem. Phys. 47 (1967) 1876. [l]

The results presented here give no support either to the geometry suggested by Ogilvie [4] nor to that part of Walsh’s prediction [7] concerning a pyramidal arrangement of bonds about each carbon atom. There is good agreement with the model assumed by Merer and Mulliken [5] for the lowest vibrational level. However, the open shell calculations give no F Jidence for the enormous postulated increase of 0.36A in Y&C with decreasing angle of twist CNDO/B has given reasonable agreement witl. experimental trends in ground state bond lengths, and in particular C-C bond lengths for small Folecules are calculated correct to about 0.05 A[14], though apparently always on the low side. We think that if there were

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