Structure and harmonic vibrational frequencies of cyclopentadiene in the lowest singlet states

Journal of Molecular 0166-1280/94/$07.00

Structure (Theochem), 303 (1994) 11-82 0 1994 - Elsevier Science Publishers B.V. All rights reserved

Structure and harmonic vibrational frequencies cyclopentadiene in the lowest singlet states Tom%

of

KovBf, Hans Lischka*

Institut ftir Theoretische Austria (Received

71

Chemie und Strahlenchemie,

4 May 1993; accepted

Universitdt

Wien, Wtihringerstrafie

17, A.1090

Vienna,

17 May 1993)

Abstract MCSCF calculations are reported for the electronic ground state and the two lowest excited singlet states of cyclopentadiene. Molecular geometries have been optimized for each state individually and the complete harmonic force field calculated. Similar to the situation found for cis- and trans-butadiene the CC double bond length significantly increases on electron excitation and the CC single bond length within the cis-butadiene substructure decreases. The changes in the vibrational frequencies and in the character of the vibrational modes on excitation is documented in detail. Whereas the electronic ground state and the 1 ’ B2 state have CZvsymmetry (with the carbon ring system and the CH bonds in one plane) the 2 ‘A, state is predicted to have a lower symmetry with a very shallow minimum for the respective torsional modes.

Introduction Recently, the absorption spectrum of the NV, transition of cyclopentadiene has been analysed in detail [ 1,2]. The main reason for these investigations was to gain a better understanding of the lowest electronic singlet excitations in dienes in general. Most of the studies on dienes have concentrated so far on trans-butadiene. In that case, the most interesting observation is the inherent diffuseness of the absorption bands corresponding to the lowest B, state [3] and the absence of any emission from this state [4]. This diffuseness is believed to be due to nonradiative relaxation of the B, state into the 2 ‘A, state. The experimental verification of the existence of the latter state has turned out to be very difficult [5]. Theoretical calculations show that the 1 ‘B, and 2 ‘A, states are located close to each other [6-111. From minimal basis set calcu* Corresponding

author.

SSDI 0166-1280(93)03406-W

lations it can be seen that the global minimum for both states is nonplanar [9910] and model calculations show [ 121 that out-of-plane deformations especially are responsible for the fast internal conversion of the S, to the So state. Therefore, in order to avoid the complications due to the flexibility of butadiene towards the just mentioned out-of-plane modes, it was desirable to study these electronic excitations in a similar but more rigid molecule. Cyclopentadiene was a natural candidate for that purpose. In the first attempt by Sabljic and McDiarmid [l] to analyze the NV, systems of cyclopentadiene and cyclopentadiene-de, the vibrational fine structure in the cyclopentadiene-dh case was treated as a single vibrational progression of z 750 cm-’ and assigned to the totally symmetric C=C stretching mode. This model reproduced the experimental data very well. However, it was noted that an additional unresolved progression also appeared to be active. An extraordinarily large elongation of the

T. Kovdiand

12

C=C bond of about 0.2 A was deduced from this analysis. The spectrum of cyclopentadiene is more complex

and was not analyzed

In a subsequent

investigation

in that much detail. [2] the absorption

spectra of cyclopentadiene and cyclopentadieneL& were measured at higher pressures than before in order to observe “hot” bands and to uncover the as yet “hidden” vibration in cyclopentadiene-de. As a consequence

of these measurements,

an addi-

tional ring deformation vibration was found to be active and the one-mode model could not be considered adequate any more. Few theoretical investigations on the excited states of cyclopentadiene exist (see Refs. 13 and 14, and references cited therein). Therefore, for the purpose of comparison it is useful to discuss the analogous butadiene system first for which much more detailed calculations are available. However, even here most of the calculations concentrate on excitation energies at fixed geometries (see, for example, Refs. 668). Only in recent years have systematic ab inito optimizations of excited state butadiene geometries been performed. Complete multi-configuration self-consistent field (MCSCF) and partial multi-reference configuration interaction (MRCI) geometry optimizations with flexible basis sets have been presented for the lowest two (S, and S,) excited singlet states of cis- and trans-butadiene [ 11,151 in planar geometries. The global minima for these two states and harmonic vibrational frequencies were obtained from minimal basis MCSCF STO-3G calculations [9,10,16]. These investigations give a good classification of the stationary points on the energy hypersurface but suffer from the fact that the STO-3G basis does not contain diffuse functions, which are necessary for an adequate description of the 1 ‘B, state. The harmonic force fields for the 1 ‘A, and 2 ‘A, states are reported in Ref. 17 with particular emphasis on the discussion of the aB C=C stretching mode in the series butadiene, hexatriene and octatetraene. For more details see the extensive review on the spectra of short polyenes [18]. To our knowledge, no ab initio calculations are available for the analogous excited states of cyclopentadiene.

Hans Lischka,‘J. Mol. Srrucr. iTheochem)

303 (1994) 71-82

Extensive semiempirical investigations on conjugated 7r-systems using the QCFF/PI method have been carried out by Karplus and Zerbetto

and co-workers

[ 199201

and Zgierski [21]. Their work includes

geometry optimizations and calculations of excited state vibrational frequencies and Franck-Condon factors. Most relevant is the FranckkCondon absorption

spectrum

to our investigations here analysis performed for the of

cyclopentadiene

by

Zgierski and Zerbetto [ 131. The other semiempirical calculations on cyclopentadiene (e.g. Ref. 14) treat vertical excitations only and are thus not helpful for the discussion of the vibrational fine structure. Even though the QCFF/PI method is very well parametrized for the calculation of geometries and vibrational frequencies of polyenes in excited states, it is certainly very important to have independent ab initio results available. Thus, in extension of our previous MCSCF and MRCI investigations on truns- and cis-butadiene excited states [11,15], our aim here has been to perform a consistent set of MCSCF calculations for the electronic ground state and the two lowest excited singlet states of cyclopentadiene. Excitation energies, optimized geometries, harmonic force fields and vibrational frequencies are reported. In the spectroscopic investigations mentioned before [1,2] a Cl\, structure had been assumed for the excited state geometries of cyclopentadiene. Since in the butadiene case the equilibrium structures are nonplanar [9,10,16] we also want to investigate whether the rigidity of the ring structure of cyclopentadiene can enforce the planarity of the carbon system. Computational

methods

MCSCF calculations employing an analytic gradient procedure were performed in order to obtain optimized geometries for the different electronic states. Force constants were obtained by numerical differentiation of the analytic gradient. The COLUMBUS program system [22-241 including analytic gradients [25526] was used. In analogy to our previous investigations on butadiene [ 1l] we chose

T. Kc&f

and Hans LischkalJ.

a complete

Mol. Struct.

(Theochem)

active space (CAS) wave function

303 (1994)

within

71-82

13

small. The QCFFjPI

calculations

[ 131 show a much

the rr space consisting of four b, and two a2 MOs. In this selection one orbital centered mainly at the CH2 group and one diffuse (Rydberg-type) orbital is

larger elongation (0.085 A) of the C=C bond in the 1 ‘B2 state compared to our results described above. For the other geometry parameters agree-

included.

Within

ment with our results is better.

functions

were obtained

this space 95 configuration

state

for the ‘A, states and 80

for the ‘Bz state. The gaussian A0 basis was constructed from a MIDI 3 set [27] augmented by two sets of diffuse p functions (exponents 0.07 and 0.02) on each carbon atom. In symmetries lower than Czv the MOs kept their main characteristics owing to the small geometrical distortions necessary for performing the numerical differentiation of the analytical gradients. The internal coordinates were constructed according to the suggestions of Pulay et al. [28]. Harmonic vibrational frequencies were calculated according to the standard Wilson GF method [29]. Results and discussion Optimized geometries for the 1 ‘Ai, 2 ‘A, and 1 ‘B, states of cyclopentadiene in C2” symmetry are given in Table 1 and compared with experimental data [30], with QCFFjPI results [13] and with our previous calculations on cis-butadiene [ 151. Experimental geometry data are available only for the ground state. In that case agreement with our results is quite good even though the CC bond lengths (in which we are mainly interested) are slightly too large. However, our goal was not to perform optimal calculations for the ground state alone but to obtain a balanced description of three electronic states at the same time. Large changes of the bond lengths belonging to the cis-butadiene fragment are observed on electron excitation. The C2C4 bond (C=C in the ground state) is significantly stretched (1 ‘B2, 0.047A; 2 ‘A,, 0.165.A) and the C4C5 bond (C-C in the ground state) is shortened (1 ‘B2, -0.084 A; 2 ‘A,, -0.060 A). As a result, these bond lengths are now practically equal in the 1 ‘B2 state. The respective geometry effects follow very closely those in cis-butadiene. The ClC2 distance, in which the carbon atom of the CH2 group is involved, remains almost unaffected. The variation of bond angles is remarkably

Vertical energies

and

minimum-to-minimum

are shown

in Table

excitation

2. In the case of ver-

tical excitations the transition energies for the 1 1B2 and 2 ‘Ai states are practically identical. The energetical stabilization due to geometry relaxation in the excited state is much more pronounced for the 2 ‘A, state, leading to a substantially reduced minimum-to-minimum excitation energy. The situation is similar to our findings for tram- and cis-butadiene [l 1,151. From our experience with these calculations we expect the vertical excitation energy to the 1 ‘B, state to be too high by at least 0.7 eV. The excitation energy to this state is notoriously very difficult to calculate and much more sophisticated wave functions than those employed here must be used for that purpose. We refer to the literature [6,8,11 ,151 for further discussions concerning this problem. In Table 3 the calculated harmonic vibrational frequencies for the electronic ground state are with experimental results [31]. given, together

Hl

b

H4

Fig. 1. Atomic numbering scheme for cyclopentadiene.

1.507 1.352 1.464 1.075 1.075 1.106 100.1 111.7 108.2 109.6 127.1 127.4

1.521 (1.506) 1.352 (1.345) 1.483 (1.468) 1.076 (1.078) 1.076 (I ,080) 1.095 (I .099) 102.3 (102.9) 109.7 (109.2) 109.1 (109.3) 105.9 (106.3) 126.5 (127.1) 126.3 (126.0)

-0.459707

ClC2 C2C4 c4c5 C2Hl C4H3 ClH5 C2ClC3 ClC2C4 C2C4C5 H5ClH6 HlC2C4 H3C4C2

&lCSCFe

120.9 118.2

126.8

1.346 I .472 1.078 1.081 .~

cis-Butadiened

a Bond lengths in angstroms, angles in degrees. b For the definition of the atomic numbering scheme see Fig. 1 ’ Experimental values [30] are given in parentheses. d Ref. 15. ’ Total energy + 192 in hartree.

Ref. 13

I ‘A,

This workC

Parametera,b

1.494 1.437 1.397 1.071 1.073 1.107 99.4 112.5 107.9 109.4 125.3 125.2

1.500 1.399 1.399 1.075 1.074 1.092 101.9 109.6 109.4 107.1 125.7 125.2 -0.223970

Ref. 13

in comparison

This work

1 ‘B2

Table 1 Geometries and total energies for ground and excited states of cyclopentadiene

120.3 118.2

123.9

1.396 1.389 1.076 1.078

cis-Butadiened I .491 1.492 1.399 1.067 I .070 1.108 101.4 111.4 107.9 109.1 125.1 124.5

1.525 1.517

-0.257684

1.075 1.014 1.098 103.2 109.8 108.6 104.9 125.1 124.8

1.423

Ref. 13

This work

2 ‘A,

with results for cis-butadiene

119.6 117.2

124.6

1.504 1.411 1.076 1.077

cis-Butadiened

T. Kowiiand

Table 2 Excitation

Hans LischkalJ.

Mol. Struct.

(Theochem)

303 (1994)

techniques energies for cyclopentadiene”

Excitation energy

1 ‘Bz

2 ‘A,

Vertical minimum-to-minimum

6.65 6.41

6.74 5.50

15

71-82

(see for example,

Ref. 28) are used fre-

quently and quite successfully in order to remove systematic errors. Scaling works well mostly for closed shell molecules in the electronic ground state. In the case of excited states, however, there are not enough reference data available and, therefore, scaling cannot be performed in a reliable way.

a All values in electronvolts.

Thus, we left our calculated Comparison of these data show that, as usual, the calculated frequencies are too large. This fact comes on the one hand from limitations in the quantum chemical method used to compute the harmonic force constants and on the other hand from the neglect of anharmonicities in our calculations. For molecules of the size of cyclopentadiene a complete calculation of anharmonicity effects is pactically impossible. In order to account for the deficiencies of harmonic frequencies, scaling

harmonic

frequencies

unchanged and concentrated mainly on the relative ordering and the differences in the vibrational frequencies between the ground state and excited states. Because of the relatively strong coupling of the individual internal displacement coordinates in ring systems a unique assignment of the individual modes is difficult. In Table 3 we have used a kinetic and potential energy distribution (TED) [32] for the characterization of the vibrational modes. In order to obtain a better view of these modes, in

r

L

084

1020

929

i

@

, 1218

Fig. 2. Displacement

coordinates

1493

of the totally symmetric vibrational modes for the electronic ground state. Frequencies given in cm-‘.

are

a Ref. 31

bl

a

Symmetry

Table 3 Calculated

1100 941 700 516

twist

CH, CH out-of-plane CH out-of-plane Ring torsion

1232

978

750 538

720 367

CH2 CH CH Ring

rock out-of-plane out-of-plane torsion

CH2 stretch

1002 976

805

Ring deformation

891

3156

959

stretch

CCH bend, C=C C-CH2 stretch

1205 101 I

350

664

2900 925 891

1239 1090

1580 1292

CCH bend CH, wag

3105 3043

3322 1691 1438 1386

3346

929 884

ring deformation

456

915 802

bend

CCH C-C stretch C-CHz stretch Ring deformation

1218 1020

CH stretch CH stretch C=C stretch,

787 582

994

bend

CCH

1378 1365 1106

stretch scissor

C-C CH,

1614

1557 1493

2886 1500

CH2 stretch

3127

753 529 297

2335 874

809

925 820

1130

2452 1612 1228

2488

919

893 797 770

972

1163

1561 1293

2456 2278

3075

2502

3091

Calc. (cm

‘)

Cyclopentadiene-d,

and cyclopentadiene-rl,

CH stretch

Exp.” (cm-‘)

for cyclopentadienee

CH stretch

(cm- ‘)

frequencies

3354 3329

MC.

vibrational

Assignment

and experimental

Cyclopentadiene

harmonic

C-CD2

stretch

torsion

stretch

state

stretch

CD out-of-plane Ring torsion

CD, rock CD out-of-plane

CD,

CD2 wag

Ring deformation

C-CD, stretch, CD2 wag CD, wag, CCD bend Ring deformation

CD stretch C=C stretch

CD stretch

Ring

CD2 twist CD out-of-plane CD out-of-plane

C-CD2

C-C

stretch

bend

ground

CCD

Ring deformation, Ring deformation

C-C,

C-C stretch, CD2 scissor

CD2 stretch C=C stretch

CD stretch CD stretch

Assignment

in the electronic

107 494 276

2177 807

714

835 765

1000

2294 1522 1231

2324

545 434

847 751

710

823 734

934

1235 1047

2130 1466

2289

2333

Exp.” (cm-‘)

T. Kovciiand

Hans Lischka/J.

Mol. Struct.

(Theochem)

303 (1994)

mode. We obtain

Fig. 2 the displacement coordinates for the totally symmetric vibrations (excluding the CH vibrations) are depicted.

These drawings

77

71-82

the CC single bond vibrations at respectively. However, inspec-

1020 and 929 cm-‘,

very clearly show the

tion of Fig. 2 shows that the CCH bending

motions

complexity of the normal modes. The assignments given in Table 3 agree reasonably well with those reported in the experimental investigation [3 11.

also contribute significantly to these two modes and that in this case a straightforward classification based on a single type of internal coordinate is pro-

From

blematic.

The lowest a, mode

802cm-t)

is a ring deformation,

Fig. 2 and Table 3 one can clearly recognize

the C=C vibration soring

motion

at 1614cm-’

at 1.558 cm-t.

and the CH2 scis-

The next two vibra-

at 884cm-’ in agreement

(exp., with

Refs. 13 and 31.

tions (1493 and 1218 cm-‘) are classified as CCH bending vibrations. A similar picture arises from the experimental assignments given by Castellucci et al. [31], even though the higher of these two bands (at 1365 cm-‘) is of a rather complex nature in their analysis. Zgierski and Zerbetto [13] on the basis of their QCFFjPI calculations arrive at a somewhat different result. They assign the just mentioned frequency at 1365 cm-’ to a C-C stretching

From the nontotally symmetric modes we want to mention the antisymmetric C=C vibration, from which is shifted in our calculations 1614 cm-’ (symmetric mode) to 1691 cm-‘. This shift of 77cm-’ agrees well with the experimental shift (80cm-‘). Comparing our results with those based on the QCFFjPI calculations [13] we observe the fact that no CH2 wagging and rocking motions are reported in the latter work. We obtain these

1

*

767

Fig. 3. Displacement

coordinates

1008

936

of the totally

symmetric

vibrational

modes

for the 2 ‘A, state.

Frequencies

are given in cm-‘.

T. Kowiiand

Hans LischkalJ.

1

Mol. Struci.

i Theochem)

303 (1994) 71-82

1

@

* 1225

* 1506

1547

* L

1

1596 Fig. 4. Displacement

coordinates

of the totally

symmetric

vibrational

modes at 1386 and 1002 cm-‘, respectively. The lowest frequencies correspond to ring torsion modes. However, substantial coupling with the motion of the hydrogen atoms is also found there. Deuteration most affects the positions of the CH stretching frequencies and all other modes in which the hydrogen atoms are directly involved (see Table 3). Owing to coupling effects the other frequencies are also modified, but to a much smaller extent. For example, the C=C stretch vibrations (in which we are mostly interested) are shifted to lower frequencies by 53 (a,) and 79 (b,) cm-‘. Moreover, the C-C single bond stretch frequency (a, symmetry) is increased significantly from 1020 because of coupling with the CCD to 1293cm-’ bending vibration. It is now situated even above the CD2 scissor mode. In Tables 4 and 5 harmonic vibrational frequen-

modes

for the 1 ‘B2 state.

Frequencies

are given in cm-‘.

cies for the 2 ‘Ai and the 1 ‘Bz states are collected. In analogy to Fig. 2, Figs. 3 and 4 show the displacement coordinates for the respective totally symmetric normal modes of these excited states. As a general trend one finds that the internal displacement coordinates are much more strongly coupled in the excited states than in the ground state. Thus, a straightforward and simple characterization of the normal coordinates is now even more difficult. It has already been stated that the minimum energy structure of the carbon ring system changes significantly upon electron excitation: the CC double bond (C2C4) is elongated considerably and the CC single bond within the diene system (C4C5) is shortened. These changes in geometries are also reflected in the vibrational frequencies. In agreement with the increase in the CC double bond length the corresponding vibrational

T. Kovciiand Hans LischkajJ. Mol. Struct. (Theochemj

Table 4 Calculated harmonic vibrational Symmetry

303 (1994)

frequencies for cyclopentadiene

Cyclopentadiene Frequency

and cyclopentadiene-dh

in the 2 ‘Al state

Cyclopentadiene-dh Assignment”

Frequency

3381 3362 3078 1648 1608 1445 1189 1008 936 761

CH stretch CH stretch CH2 stretch C4C5 stretch CH2 scissor CCH bend CCH bend C4C5, C2C4 stretch ClC2 stretch Ring deformation

2509 2481 2240 1609 1268 1180 929 857 784 718

1214 499 310 25li

CH2 twist CH out-of-plane Ring torsion CH out-of-plane

b2

3368 3350 1484 1410 1331 1089 933 729

CH stretch CH stretch CH2 wag CH2 wag, CCH bend CCH bend, CH2 wag C2C4, ClC2 stretch, CCH bend C2C4, ClC2 stretch Ring deformation

2486 2464 1288 1205 1104 842 787 688

CD stretch CD stretch Ring deformation, C2C4 stretch CD2 wag, ClC2 stretch CD2 wag, CCD bend CCD bend, C2C4 stretch, CD2 wag C2C4, ClC2 stretch, CD2 wag Ring deformation

bt

3085 976 388 88i 369i

CH2 stretch CH2 rock CH out-of-plane Ring torsion CH out-of-plane

2283 193 298 72i 286i

CD2 stretch CD2 rock CD out-of-plane Ring torsion CD out-of-plane

at

a2

a For the numbering

(cm-‘)

19

71-82

874 402 277 192i

(cm-‘)

AssignmenP CD stretch CD stretch CD2 stretch C4C5 stretch CCD bend, ClC2 stretch CD2 scissor All CC stretches CCD bend ClC2 stretch, CCD bend Ring deformation CD2 twist CD out-of-plane Ring torsion CD out-of-plane

scheme of the carbon atoms see Fig. 1

frequencies are considerably reduced. Moreover, from the TED analysis given in Tables 4 and 5 we observe the fact that the C2C4 stretching coordinate does not dominate one particular normal mode but is distributed to a varying amount over several modes. For example, the totally symmetric CC double bond vibration (at 1614 cm-’ in the ground state) is now found at 1008cm-’ in the 2 ‘Ai state and at 1547 cm-’ in the 1 ‘B2 state. But there are additional significant contributions from the C2C4 bond to vibrations at even lower frequencies. Similar changes can be seen in the case of the antisymmetric CC double bond mode. The CC single bond frequency (C4C5) located at

1020cmP’ in the ground state is shifted to higher frequencies, in accordance with the reduction of the corresponding bond length. It is now the highest frequency besides those frequencies belonging to the CH vibrations. The C-CH2 bond length does not change very much upon electron excitation and the same behavior is found for the corresponding vibrational frequency. The CH stretch frequencies are only affected to a relatively small extent by the electron excitation when compared to the changes discussed above for the CC bonds. However, it is interesting to note that the CH out-of-plane modes change significantly. This is especially true for the 2 ‘A, state

T. Km&and

80

Table 5 Calculated harmonic vibrational Symmetry

frequencies for cyclopentadiene

Hans LischkaiJ. Mol. Smut.

and cyclopentadiene-dh

Cyclopentadiene-dh

Frequency

Frequency

(cm-‘)

303 119941 71-82

in the I ‘B, state

Cyclopentadiene (cm -‘) Assignment”

iTheochem)

Assignment”

3380 3366 3131 1596 1547 1506 1225 II60 944 897

CH stretch CH stretch CH2 stretch C4C5 stretch, CCH bend CH7 scissor, CCH bend, C2C4 stretch CH2 scissor CCH bend, C4C5 stretch C4C5, C2C4 stretch ClC2 stretch Ring deformation

2519 2492 2280 1536 1384 II31 1021 919 820 788

CD stretch CD stretch CD2 stretch C4C5, C2C4 stretch C4C5, C2C4 stretch, CCD bend CD2 scissor C4C5, C I C2 stretch Ring deformation, CCD bend Ring deformation ClC2 stretch, CCD bend

1294 I141 875 497

CH2 twist CH out-of-plane CH out-of-plane Ring torsion

1000

CD2 twist, CD out-of-plane CD out-of-plane CD out-of-plane Ring torsion

bz

3372 3357 1554 1451 1419 II65 976 883

CH stretch CH stretch Ring deformation, CCH bend CCH bend, CH, wag CH1 wag C2C4 stretch, CCH bend ClC2, C2C4 stretch Ring deformation

2498 2482 1432 1256 1145 898 824 793

CD stretch CD stretch Ring deformation, C2C4 stretch CD? wag, ClC2 stretch CD2 wag, CCD bend Ring deformation. C2C4 stretch Ring deformation, CCD bend CD2 wag, C1C2 stretch

b,

3195 1100 1019 746 325

CH2 stretch CH out-of-plane, CH out-of-plane, CH out-of-plane, Ring torsion

2365 956 794 547 261

CD2 stretch CD out-of-plane. CD out-of-plane CD out-of-plane Ring torsion

a1

a For the numbering

919 663 417

CH2 rock CH, rock CH2 rock

CD2 rock

scheme of the carbon atoms see Fig. I

as is discussed below. The vibrational modes for the deuterated species are even more strongly coupled in terms of internal displacement coordinates than the H compounds. See Tables 335 for further details. In the case of the 1 ‘B2 state, only real frequencies are computed (see Table 5) which means that the C,, structure corresponds to a local minimum on the energy hypersurface. However, as can be seen from Table 4, we obtain three imaginary frequencies for the 2 ‘A, state. The corresponding modes are out-of-plane motions with respect to the carbon ring. The deformation of a2 symmetry leads to a twisted structure of C2 symmetry and the

bt deformations to a structure of C, symmetry. Preliminary calculations for these out-of-plane distortions show that the energy surface is very flat. Our choice for the CAS contains only 5~ orbitals and keeps the c orbitals doubly occupied. Since 0-x separation is not valid any more owing to these distortions a more extended wave function including correlation effects for the other orbitals should be used. However, such an investigation goes beyond the scope of our present work. Nevertheless, because of the flatness of the potential in these out-of-plane coordinates we do not expect that the C=C stretching vibrations - in which we are particularly interested - will change significantly.

T. Kovriiand

Hum LischkalJ.

Mol. Struct.

CTheochem)

81

303 (19941 71-82

Conclusions

settle the question

of the minimum

structure

of the

2 ‘A, state conclusively. A detailed

comparison

of the structure

and the

harmonic vibrational spectrum of cyclopentadiene in the electronic ground state and in the lowest excited singlet states (1 ’ B, and 2 ‘A,) has been car-

Acknowledgments

ried out. As far as excitation

This “Fonds

are concerned

energies and geometries

we find a close parallelism

to our

previous calculations on cis-butadiene [ 151. In particular, we do not confirm the large increase of about 0.2A for the C=C double bond distance on excitation to the 1 ‘Bz state reported in the original paper by Sabljic and McDiarmid [l]. We find an increase of only X 0.05& a value which is even smaller than that obtained by the QCFFjPI method [13]. The changes in the vibrational modes on electronic excitation follow the trends in the geometries, i.e. the increase in the C=C bond length is accompanied by a decrease in the vibrational frequency which, however, is not as large as originally assumed in Ref. 1. Our analysis of the vibrational modes also clearly shows the strong coupling of the internal displacement coordinates, especially in the excited states. This fact makes a unique classification of most of the modes in terms of internal coordinates difficult if not impossible. This just mentioned strong mixing of modes is in very good agreement with the findings by McDiarmid and Gedanken [2] that a single-mode model for the FranckkCondon analysis is not appropriate. The 1 ‘B2 state is a local minimum on the potential energy surface, in agreement with the interpretation of the experimental data [1,2] and with the QCFFjPl results [13]. For the 2 ‘A, state we find that the CZv structure corresponds to a saddle point of third order. Our preliminary investigations for cyclopentadiene structures of Cz and C, symmetry along the modes belonging to the imaginary frequencies (CH out-of-plane motion and ring torsion) show that the energy surface is extremely flat with respect to these coordinates and large amplitude motions are to be expected. Because of these very small energy effects much more extended calculations including electron correlation contributions for the 0 orbitals are necessary in order to

work was sponsored zur Forderung der

Forschung”,

Project

by the Austrian Wissenschaftlichen

No. P7979. The calculations

were performed on the IBM ES/9021-720 of the computer center of the University of Vienna within the European Academic Supercomputer Initiative (EASI) sponsored by IBM. We are grateful for the ample supply of computer time.

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10 11 12 13 14 15 16 17

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