Structure and potential energy functions for acetaldehyde: Ab initio calculations of X̃1A′ , Ã1A″ , and B̃1A′ states

JOURNAL OF MOLECULAR

SPECTROSCOPY

112, 285-303 (1985)

Structure and Potential Energy Functions for Acetaldehyde: Ab lnitio Calculations of )?‘A’, #A”, and E’A’ States JAMES S. CRIGHTON’ AND STEPHEN BELL Department of Chemistry, Universityof Dundee, Dundee DDI 4HN, U. K. The geometrical structure of the ground state of acetaldehyde obtained by optimization of ab initio SCF energies is compared with a number of experimental structures derived from microwave spectra. The optimum geometries of acetaldehyde in its two lowest singlet excited states, AlA” and S’A’, are also determined A force constant matrix found for each of the ?A and B’A states is used to calculate the vibrational wavenumbers of the four isotopic species, CHsCHO, CHsCDO, CDsCHO, and CD$ZDO, and thus to check assignments of observed wavenumbers from infrared spectra. The potential energy function for internal rotation of the methyl group is also studied in each of the three states and for inversion in the 2 state. Reasonable agreement is obtained between ab initio barrier heights and values derived from 8 1985 Academic press, Inc. IIIhOWaVe, far infrared, and UhViOkt spectra. I. INTRODUCTION

Since acetaldehyde is one of the simplest carbonyl compounds, a large number of ab initio SCF calculations have been made of this molecule. Although many of these deal with the barrier to internal rotation, most of them do no geometry optimization or only partial. Only a few studies deal with excited states and none seem to have calculated force constants or vibrational wavenumbers. As an aid to interpreting the electronic absorption spectrum of acetaldehyde, it was the purpose of this study to make ab initio electronic structure calculations of the optimum geometrical parameters, vibrational wavenumbers, and barriers to internal rotation of the molecule in the AlA” and 8 ‘A’ states. Since good values of these properties are lacking for the ground state, it must first be studied in detail. For the ground state of acetaldehyde, the first complete geometry optimization was that of Del Bene el al. (I). They used a minimal basis set (STO-3G) and they constrained the methyl group to have Cs symmetry. Bernardi et al. (2) later repeated this optimization allowing the in-plane C-H bond length and HCC angle of the methyl group to have different values from the other two C-H bond lengths and HCC angles. The most stable conformation of the ground state of acetaldehyde is that in which one of the hydrogen atoms of the methyl group is eclipsed with respect to the oxygen atom. By also optimizing the geometry at the higher, staggered conformation, the latter (2) calculated the barrier to internal rotation in the ground electronic state and they obtained a value which is in fairly good agreement with the experimental value. Their CI calculations of the barrier to internal rotation ’ Rresent address: Standard Oil Company (SOHIO), Research Center, 4440 Warrensville Center Road, Cleveland, Ohio 44128. 285

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286

CRIGHTON

AND BELL

using the optimum geometries obtained from the SCF calculations show that electron correlation lowers the barrier only a little. Hehre et al. (3) had earlier obtained a value for the barrier to internal rotation in the ground electronic state from SCF calculations using a 4-31G basis set but they did not fully optimize the geometry. Since our calculations were made Williams et al. (4) have optimized the geometry using the 4-21G basis and not assuming C, symmetry for the methyl group. Vertical transition energies for the k*A”-2’A’ (?r* - n) transition have been calculated at the SCF and CI levels by Ha and Keller (5) and Del Bene et al. (1). Ha and Keller used a DZ basis but carried out the calculation at the experimental r. geometry of the ground state (6). Del Bene et al. used the optimum geometry of the ground state but used a minimal basis set (STO-3G) for the calculations. Geometry optimization has been carried out for the g3A” state (7, 8) using the STO3G basis and, in these studies, the minimum conformation, barrier to inversion, and barrier to internal rotation have been determined in this state. It is surprising that the i*A’ state of acetaldehyde has never been studied using ab initio calculations since there has been some controversy over the assignment of the 182-nm system @‘A’-f’A’) in the absorption spectrum [see references in Moule and Walsh (9)]. This region of the spectrum was studied by Walsh (IO), who suggested that the complicated vibrational structure of this system was due to the superposition of two electronic transitions. Lucazeau and Sandorfy (II) copied this idea and assigned some of these vibrational bands to a (3s - n) Rydberg transition, while others they assigned to the (a* - n) transition. Ab initio calculations on formaldehyde (12) predict that the u* state is some 3 eV higher in energy than the 3s Rydberg state and so, by analogy, we would expect that this would also be true of acetaldehyde. This absorption system is due to a single electronic transition and a detailed interpretation of the system will be presented separately. Since the work reported here was done, the lowest Rydberg state of acetaldehyde has been observed by multiphoton ionization spectroscopy by Heath et al. (13), but their calculation of the barrier to internal rotation is inadequate as indicated by Gordon (14), whose barrier is also not qualitatively correct. The aims of this study were therefore (i) to calculate the optimum geometries of acetaldehyde in the $A’ (ground state), k’A” (n, ?r*), and B ‘A’(3s) states and thus to obtain adiabatic transition energies for the (?r* - n) and (3s - n) transitions; (ii) to calculate harmonic vibrational wavenumbers using the force constant matrix obtained by update during the optimization of the geometry; and (iii) to calculate barriers to internal rotation in the three states and a barrier to inversion in the 2’A” state where the molecule is not planar at the carbonyl carbon. II. THEORETICAL

METHODS

All the SCF and GVB calculations of the present study were carried out using the POLYATOM program. The basis sets used were very similar to those used in the formaldehyde study (12), i.e., the standard Huzinaga-Dunning (15, 16) doublezeta Gaussian basis with a single diffuse s function of exponent 0.023 centered on the carbonyl carbon atom and a single diffise s function of exponent 0.032 centered on the oxygen atom. This basis is labeled DZs and it was found that, for

ACETALDEHYDE

STRUCTURE:

AB INITIO

287

formaldehyde, this basis would adequately describe the 3s Rydberg state and it is expected that this would also be the case for acetaldehyde. A more extensive basis labeled DZds was used for some of the calculations, which included a set of six d polarization functions of exponent 0.8 centered on the carbonyl carbon atom. It was found in the case of formaldehyde that one set of polarization functions on the carbonyl carbon atom was sufficient and so more extensive sets were not used in the present study. As for formaldehyde, some information on the effects of electron correlation on the calculated transition energies of acetaldehyde was obtained by GVB/2PP calculations (17). For the 2lA and B’A’ states the 8~’ (CO u bond) and the 2a” (CO ?r bond) were represented by GVB pairs, while for the k’A” state the two highest molecular orbitals were represented by GVB pairs since the orbitals all have the same symmetry. All geometry optimizations were carried out using our MINIT optimization program (18) which uses the quasi-Newton BFGS method (19). Quite realistic force constants were obtained during the iterative determination of the molecular geometry as previously checked out for formaldehyde (12). The internal coordinates which were used for the geometry optimizations are defined in Fig. 1. In all the calculations, the methyl group was assumed to have C, symmetry. This assumption was made for economy in computing time and also to be consistent with the rigid rotor model which was adopted for the experimental study of internal rotation in the $A and B ‘A’ states. III. GROUND

STATE

Geometry Several experimentally determined molecular structures for the ground state of acetaldehyde have been reported in the literature (6, 20, 21). An r. structure was obtained by Kilb et al. (6) from a study of the microwave spectra of acetaldehyde and its deuterated isotopomers. Since vertical electronic transition energies should be calculated from the ground vibrational level rather than from the equilibrium point on the potential surface, this r. geometry was used when calculating the vertical transition energies. The optimum geometries, however, are attempts at calculating the equilibrium molecular geometry and so should be compared with

FIG. 1. Internal coordinates for acetaldehyde.

288

CRIGHTON

AND BELL

the r, structure rather than the r. structure. Iijima and Tsuchiya (20) have obtained an r, structure and have tried to estimate a partial r, structure for the methyl group; it is this mixed rz/re structure that we will use for comparison of our optimized geometries of the ground state. An r, structure has also been given by Nosberger et al. (21) in which the methyl group is not constrained to have C3 symmetry but since all the structures in the present work were obtained using the assumption that the methyl group was a symmetric top, the r, structure was not used for comparisons. The optimum molecular geometries and SCF energies for the ground state of acetaldehyde obtained using various methods and basis sets are shown in Table I. The entries in the column headed “Geometry” refer to the type of geometry optimization carried out. The conformer in which the methyl C-H is eclipsed with respect to the C-O is designated by E and the staggered conformer by S. If the methyl top axis angle, y, was optimized the geometry is designated as T, but if the tilt angle is not optimized but fixed at zero it is given as Z. These symbols are combined together; for example S@ET means that the calculation reported was for the staggered conformer but the bond lengths and angles were those obtained by optimizing the geometrical parameters for the eclipsed conformer with the methyl top axis allowed to tilt. TABLE I Molecular Geometries and SCF Energies for the Ground State of Acetaldehyde’ Method

Expt

. b

Geometry

r

a

s

t

”

8

c

Y

T

Energy

1.087

108.7

1.512

1.114

1.207

115.3

124.2

0.5

0.0

STO-3G ’

E@ET

l.OMd

108Ad

1.536

1.104

.217

14.3

124.3

0.4

0.0

-150.9460

S&T

1.086d

loud

1.541

1.104

.217

14.9

123.9

-0.1

60.0

-150.9442

4-21Ge

E@ET

1.08Zd

109.1d

1.511

1.087

1 .210

14.9

124.4

-0.1

0.0

-152.55881

1.086

108.3

1.501

1.114

.216

17.5

123.9

o.og

0.0

-152.870134

1.083

108.8

1.504

1.088

.220

16.3

124.1

o.og

0.0

-152.870710

60.0

-152.868881

1.083

108.8

1.504

1.088

1 .220

116.2

124.2

0.6

DZS

sJre

f =0 E@E2 SW2 GET S@ET

DZds

S@ST

1.083

108.6

1.509

1.087

.220

117.3

123.3

=0

1.086

108.3

1.501

1.114

1.216

117.5

123.9

o.og

E@E.?

1.086h

108.7

1.479

1.091

1.194

115.0

124.9

o.og

-1.2

S@Ez E@ET

l.086i

108.7i

1.504

l.091i

1.194’

115.8

124.4

l.086i

108.7’

1.510

1.0911

1.194l

116.9

123.3

0.5

S@ET S@ST

a) b) d) fj h) 1)

Lengths in f, angles in degrees, and energies in a.~. From ref. (20). c) From ref. (2). Averane over all three methvl hvdroneo atoms. e) From Experkntal r statue c&j. . S) Assumed. Fixed at r0 “a Pue since fairly independent of rest of structure. Fixed at [email protected] value since they are fairly independent of y and x.

-1.5

ref.

0.0

-152.870722

60.0

-152.868810

60.0

-152.868992

0.0

-152.913879

0.0

-152.914890

60.0

-152.912983

0.0

-152.914962

60.0

-152.913098

60.0

-152.913308

(4).

ACETALDEHYDE

STRUCTURE:

AB INITZO

289

Test calculations showed that the addition of the diffuse Rydberg functions to the basis set made virtually no difference to the optimum geometries of this state and lowered the SCF energy by only about 0.001 a.u. These diffuse functions were included in the bases for the ground state calculations so that transition energies for the B’A”-$A’ (3s - n) transition could be calculated using the same basis set in both states. The optimum geometries in Table I obtained using the DZs and DZds bases are similar, and in fairly good agreement with the experimental rr/re structure. The main difference is with w, the C-O bond length, which, as for formaldehyde (22, 12) is too long without and too short with polarization functions in the basis. More polarization functions are unlikely to make significant changes but better agreement with experimental is expected with CI. The STO-3G optimum geometries of Bernardi et al. (2) and the 4-21G optimum geometry of Willaims et al. (4) are shown in Table I. The values of r and (11quoted are weighted average values since in their calculations the methyl group was not constrained to have C, symmetry. Also, for the same reason the value of the methyl axis tilt angle, y, is an effective tilt angle. The STO-3G optimum geometry is similar to that obtained with the DZs basis except that the optimum C-C bond length is too long. AS expected for a split-valence basis, the 4-2 1G optimum geometry (4) is very similar to the DZs geometry E@EZ or E@ET. Vibrational Wavenumbers It was shown in the case of formaldehyde (12) that reasonable force constants could be obtained, at no extra cost in computing time, from the quasi-Newton geometry optimization procedure. Thus, a similar procedure was followed to obtain the force field of acetaldehyde, and this is shown in Table II in comparison with the experimental valence force fields of Hollenstein and Gunthard [H + G (23)] and Cossee and Schachtschneider [C + S (24)]. The force constants given in Table II are expressed in terms of the a’ symmetry coordinates used by Hollenstein and Gunthard. The calculated force constants are in fairly good agreement with the experimental values but since the calculated force field contains many more coupling constants than have been determined experimentally, it is probably better to compare the calculated wavenumbers with the observed values rather than comparing force fields. Harmonic wavenumbers were obtained from the calculated force constants using the ASREF program and these wavenumbers are shown in Table III in comparison with the observed values. In column 1 of Table III descriptions of the modes [based on the potential energy distributions (24)] are given but these are only approximate since the actual normal coordinates are linear combinations of the symmetry coordinates. In particular, yg and u9 each contain significant contributions from the two coordinates. In the CD3CH0 and CD3CD0 isotopomers, a similar situation exists with v7 and 9. Some confirmation of the assignments of Hollenstein and Gunthard is obtained from the agreement of their potential energy distributions and the ab initio ones, except for 1047 cm-’ in CD$DO (25). The calculated wavenumbers in Table III are similar to the experimental values (23, 26) but, due to systematic overestimation of the calculated force constants and

290

CRIGHTON

AND BELL

TABLE II Experimental and Calculated Force Constants’ in the 2l.4’ and B’A’ States of Acetaldehyde Hffi b

Expt.

Parameter

r0

r(C-H,) s(C-c) tee-El,) w(C-0) a(mx)

B(CCH,) C(CCO) Y (Tilt) F matrixd

1.086 1.5005 1.114 1.2155 108.3 111.5 123.9 0

Ground State C+S b Expt. rO 1.086 1.5005 1.114 1.2155 108.3 117.5 123.9 0

DZS Ni?WtOll E@ET 1.0833 1.5038 1.0880 1.2199 108.84 116.22 124.21 0.57

2.2 2.3 2,4 2.6 2.7 2.8 299 2,lO

4.938

5.028

5.963 0.324 0.100 -0.037 0.045 -0.072 0.027 -0.080

3,3 3.4 3,6 3.7 3,s 399 3.10

4.138 +0.335

4.247

4.4 4.6 4,7 4,8 4.9 4,lO

11.01 -0.356

4.391 0.125 0.012 -0.027 0.046 0.027 0.060 11.054 -0.105 0.031 -0.062 0.121 0.155 0.665 -0.057 0.297 -0.063 0.034 0.636 -0.302 -0.013 -0.055 5.387 0.020 -0.091 0.790 0.193 0.89

6,6 6.7 638 6.9 6.10 7.7 7.8 7.9 1.10 838 8.9 8,lO 9.9 9.10 IO.10 a) b) c) d)

10.528 -0.206

-0.531 0.091 0.641 -0.031 0.192 0.062

-0.119

0.070 0.525 -0.278 -0.067 4.633

0.106 0.515 -0.381 -0.121 0.025 4.820

0.111 0.575 -0.186 1.00

0.694 -0.051 0.88

0.647 -0.044

0.088

g *A’ DZs Newton

’

E@ET 1.084 1.419 1.080 1.264 109.6 121.4 123.3 4.4 4.878 0.297 0.100 0.017 -0.017 0.117 0.054 -0.002 6.695 1.199 0.204 0.051 0.856 0.175 -0.097 11.288 -0.169 -0.009 0.483 0.242 0.367 0.643 -0.030 0.059 -0.065 0.059 0.140 -0.405 -0.026 0.003 5.465 -0.060 0.054 0.863 0.180 0.682

Lengths in 8, angles in degrees, and F’s in ndynelk Hffi (23) and C+S (24) in symmetry coordinates of WC, but according to the numbering of modes in Table III. From update during the quasi-Nevtoo optimization. PI1 and F55 not found because of C3 methyl.

due to anharmonicity, some of the calculated wavenumbers are larger than the observed values. The scale factors necessary to convert the calculated wavenumbers to the observed values can be used to scale the calculated wavenumbers for the excited electronic states. All the calculated methyl stretching and bending wavenumhers should be reduced by 10%. The exception to this rule is the symmetric methyl deformation for CD3CD0 which is not overestimated. The reason for this is probably that the calculated potential energy distribution is not correct for this

ACETALDEHYDE

STRUCTURE:

291

AB INITIO

TABLE III Acetaldehyde Ground State a’ Vibrational Wavenumbers Mode a

Asym.

Me str.

CD3CW

Obs.

ca1c.

Obs.

Calc.

2262

2495

Calc.

Ohs.

C.%lC.

3014

3347

3014

3347

2262

2495

Obs.

1

b

CD3CHO

CH3CDO

CH3CHO

2

Sym. Me .3tr.

2923

3242

2922

3226

2120

2312

2125

2345

3

Aldehydic

2750’

2822

2059

2119

2750’

2856

2054

2103

4

c-i)

1743

1766

1743

1737

1 743c

1760

1735

1728

5

Asym.

1433

1594

1432

1590

1038

1140

1151

1148

6

C-H in-plane

1395

1357

105gd

990

1387

1374

1026

1022

7

Sym. He def.

1352

1504

1356

1493

1131

1239

1047e

1238

8

C-C

1118

9

In-plane

C-H str.

str. Me def. wag

str. Me rock

1121

1109

1122

960’

973

938

936

877’

1025

840’

1021

750=

793

747

793

509

534

500

526

444

507

436

500

10

CC0 bend

a)

Approximate descriptions from the potential energy distribution (24). Hollenstein and Gunthard (23) and Hollenstein (26). Adjusted for Fermi resonance. Calculated value since this mode was not observed in the infrared spectrum of CH3CD0. Hollenstein and Gunthard assigned this wavenumber to a non-totally symmetric mode but it must be totally symmetric. it appears as a hot band in the 182 nm system (25).

b) C)

d) e)

since

isotopomer. This is hardly surprising since the assignment of the wavenumbers used by Hollenstein and Gunthard in their force constant refinement was not correct for this isotopomer. v9 is overestimated by 16% for isotopomers containing the CH3 group and by 5% for isotopomers containing the CD3 group. Similarly, the CC0 bending mode vlo is overestimated by 5% for isotopomers containing the CH3 group and by 12% for isotopomers containing the CD3 group. All other calculated wavenumbers are in fairly good agreement with the observed values. Barrier to Internal Rotation Internal rotation of the methyl group of acetaldehyde in its ground electronic state has been studied many times using various experimental techniques (6, 20, 27-31) and several values for the barrier height have been obtained from these studies. However, as will be pointed out later (25), none of these values adequately represent all of the experimental information. The experimental data were therefore reanalyzed and new values for the potential constants V3 and V, were obtained. These new “experimental” values are listed in Table IV with the values calculated by different methods. Also shown for comparison are the results obtained by Bemardi et al. (2) using the STO-3G basis. They found that the inclusion of electron correlation has the effect of decreasing the barrier, but that this effect is small. Thus in the present study the effect of electron correlation on the calculated barriers to internal rotation is ignored.

292

CRIGHTON

AND BELL

TABLE IV Barriers in the 2, A, and 8 States of Acetaldehyde (in cm-‘)

x’

'A' State

ca1c.

opt.

Method

Geometrya

Expt. STO-3GC DZS

DZds

x ‘A”

State

State

b) d)

415

22

E@ET/S@ST

395

E@EZ/S@EZ

401

E@ET/S@ET

420

E@ET/S@ST

380

E@EZ/S@EZ

419

E@ET/S@ET

409

E@ET/S@ST

363

d

653

DZS

S@SP/E@SP

351

0

NonP

573

6

S@SP/E@SP

435

0

NonP

697

0

HRKFE e

755

C+B b

880

E@EZ/S@EZ

469

E@ET/S@ET

821

E@ET/S@ST

643

E@EZ/S@EZ

482

E@ET/S@ET

800

E@ET/S@ST

637

Expt.

DZda

E@ET/S@ST: as eclipsed apart from

C+B b

NAL

DZs

*)

“6

Expt .

DZds

% ‘A’

B. 1””

“3

785

1371

full optimization of staggered aa well E@ET/S@ET and E@EZ/S@EZ: conformer. r, the staggered conformer has same

internal coordinates From ref. (25). From Noble et al.

as (35).

eclipsed. C) e)

From From

ref. Heath

(2). et

al.

(13).

All the values of V3 in Table IV obtained without reoptimization of the geometry in the staggered conformation are in good agreement with the experimental value, which was obtained using a semirigid model not allowing for relaxation of the methyl group. The calculated barriers with geometry optimizations in both conformers are lower than the experimental value. [Using a model in which the methyl group was not constrained to be rigid, Bauder and Gunthard (28) obtained the values V3

ACETALDEHYDE

STRUCTURE:

AB

293

INITIO

= 400.5 and V, = 10.8 cm-‘.] As for molecular geometries, there Seems to be no advantage in including polarization functions in the basis set. One calculated value of V6 is given in Table IV which is not in good agreement with the experimental. As pointed out by Bauder and Gunthard (28) and others, the effect of the nonrigidity of the methyl group on the barrier height is of the same magnitude as the Va term. Thus, the experimental value of V6 quoted in Table IV, is essentially a fitting parameter and probably has very little physical significance. V6 was assumed to be equal to zero in the other calculated barriers. IV. THE ,$A” STATE

Geometry

The optimum geometries obtained using the various methods and basis sets are shown in Table V. In order to be consistent with the ground state calculations, the two diffuse s Rydberg functions were included in the basis set even though these are not required to give an adequate description of this state. It is not expected that these would influence the optimum geometries of this state however, and their addition to the basis causes a lowering of the SCF energy by only 0.0008 a.u. The notation for the geometry type is similar to that used for the ground state: S@SP or E&P refers to a structure planar at the carbonyl C and to staggered or eclipsed conformers as before, and NonP means that a full nonplanar optimization was

TABLE V Molecular Geometries and SCF Energies for the A’A” State of Acetaldehydti Method

Geometry

DZS

=0

b

S@SP

a

s

t

w

e

z

Y

x

T

1.086

108.3

1.501

1.114

1.216

117.5

123.9

0’

oc

oc

-152.756745

1.084

108.0

1.498

1.069

1.408

128.0

116.9

1.1

OC

60.0’

-152.794836

o.o=

-152.793235

13@SPd NonP

DZda

1.084

108.3

1.505

1.078

1.412

65.9

-152.798414

NOllPd

35.9

-152.797135

NOIIPd

5.9

-152.795805

=0 S@SP

121.8

114.5

0.8

39.4

1.086

108.3

1.501

1.114

1.216

117.5

123.9

0’

OC

OC

-152.789097

1.084e

108.3e

1.495

1.071

1.377

128.2

116.7

1.2

OC

60.0’

-152.819724

o.o=

-152.817742

E@SPd NonP

1.084e

108.3e

1.503

1.080

1.377

119.5

113.5

0.8

NonPd

‘3) b) d) e)

Energy

r

Lengths in 8, anglea in degrees, and energies in a.“. Assumed. Ground state geometry (6). C) Apart from 1, internal coordinates are as above. For economy fixed at DZs values elnce almost independent

of

polarization

45.7

64.1

-152.825972

4.1

-152.822794

functions.

294

CRIGHTON AND BELL

carried out. The torsional angle, 7, was also optimized in the full optimization but in order to maintain C, symmetry in the planar configuration was set equal to 60”. The addition of polarization functions to the basis does not greatly affect the predicted C-C and aldehydic C-H bond lengths s and t but, as expected, there is a 2.5% decrease in the predicted C-O bond length when these functions are added. No experimental structure has been determined for this state of acetaldehyde but, from the results of similar calculations on formaldehyde (12), it is expected that the true value of w should be closer to the DZds value of 1.377 A. An overestimation by 2.5% is observed in formaldehyde and hence a corrected value of 1.343 A may be better. Both the optimum angles 0 and e are smaller when polarization functions are included in the basis. By comparison with formaldehyde, the DZds results are probably to be preferred. With both basis sets, it was found that the methyl group is tilted 0.8” from the C-C bond such that the eclipsed methyl hydrogen is moved away from the oxygen atom. This is similar to the ground state structure in which the methyl group is tilted 0.6” away from the oxygen atom. The torsional angle, 7, has an optimum value of 65.9” using the DZs basis and 64.1“ using DZds, and these are in good agreement with one another. Thus, it is fairly certain that there is a change of phase of the torsional potential function from that of the ground state. The largest discrepancy between the two optimum geometries is in the predicted out-of-plane angle, x (6” difference). Similar results were obtained for the corresponding (n, 7r*) state of formaldehyde with the predicted values in this case being 38.0“ and 34.2” with and without polarization functions, respectively. The experimental value for formaldehyde is 33.6” (32) and so it would seem that the values of x obtained using the bases without polarization functions are closer to the experimental values than those obtained using bases with polarization functions. The best SCF optimum geometry of this state is probably that obtained using the DZds basis set except that the predicted value of C-O length should be reduced to a value of 1.343 %, to allow for systematic overestimation using this basis set. Also, the out-of-plane angle is probably closer to the DZs value of 39.4”. This predicted structure is similar to the STO-3G optimum structure of the c3A” state (7, 8) except that, as with the STO-3G optimum geometry of the ground state, the STO-3G predicted C-C bond length ( 1.523 A) is almost certainly too long. Also, the torsional angle, T, obtained by them of 75” or 45.6“ is not very close to the value of 64.1’ obtained for the singlet state. Vibration (Inversion) Apart from carbonyl stretching little experimental information is available on the vibrational wavenumbers in the ‘A” state (33-35) and so we restrict the discussion here to the potential function for inversion. Some time ago (33), it was proposed that the spectral data were consistent with an out-of-plane bending wavenumber of 480 cm-‘. More recently (34), a barrier height of 138 cm-’ and an out-of-plane angle of 26” have been derived from the electronic spectrum, but these figures must be doubtful in view of the incorrect assignment of the origin and vibrational quantum numbers (35). Also, for ring compounds there is good reason to expect a

ACETALDEHYDE

STRUCTURE:

AB INITIO

295

quartic potential function for out-of-plane vibration (36) but for noming compounds the harmonic-Gaussian potential function fits better (32, 37). It seems unlikely that a molecule like acetaldehyde should have an almost quartic potential energy function for inversion. For formaldehyde, the inversion coordinate depends on all the geometric parameters and not just the out-of-plane angle and, when calculating the barrier to planarity, it was essential to optimize the geometry at the top of the barrier as well as the equilibrium configuration. For acetaldehyde, by similar calculations the barrier to planarity is 785 cm-’ using the DZs basis set and 1371 cm-’ using the DZds basis set (Table IV). From formaldehyde the barrier height obtained using the DZs basis may be in better agreement with the experimental value. The STO-3G barrier of 804 cm-’ for the i3A” state (8) is in surprisingly good agreement with the DZs prediction. The inversion coordinate for formaldehyde was predicted well by the ab initio calculations. From Table V it can be deduced that the inversion coordinate for acetaldehyde involves principally 0, c, and T as well as x. The inversion coordinate is such that for a 15” increase in x there is a 3” decrease in 8, a lo decrease in c, and a 1” increase in 7. We would therefore expect that in the A’A” state, the vibrational mode involving out-of-plane bending, would be strongly coupled to the modes involving CC0 bending, CCH bending, and internal rotation.

Internal Rotation The barriers to internal rotation in the ,$A” state, which were predicted by SCF calculations, are shown in Table IV. In these calculations the semirigid rotor approximation to internal rotation was used, i.e., no geometry optimizations were carried out at the top of the barriers. From Table V, the torsional potential function in this state is approximately 60” out of phase with that of the ground electronic state. A similar result was found for the corresponding k’A” state of nitrosomethane by Emsting et al. (38), where the barrier was determined experimentally to be 500 + 100 cm-’ and it was found that there was a change of phase of the barrier to internal rotation with respect to that of the ground electronic state. The fact that this change of phase occurs in nitrosomethane, and also that the potential function calculated at the planar configuration of the k’A” state of acetaldehyde is also 60” out of phase with that of the ground state, suggests that the change of phase occurs as a result of a change in the electronic structure of the carbonyl group and not just as a result of the aldehyde hydrogen being bent 39.4” out of plane. A value of V, was also calculated using the DZs basis but since the results of the ground state calculations indicated that the calculated values of V, did not agree well with experiment, this value is probably not physically meaningful and so in the other calculations it was assumed to be zero. The calculated values of V3 for the ground state agreed well with the experimental and so the values predicted for the .#A” state are expected to be reliable, with the DZds result being best. The barrier to internal rotation in the k’A” state is predicted to be 697 cm-‘, with the most stable conformation having a dihedral angle T = 64.1 O. The STO-3G barrier to internal rotation in the c3A” state is 326 cm-’ (7) or 357 cm-’ (8).

296

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The recently determined experimental barriers to internal rotation (34, 35) of 660 and 653 cm-’ are in excellent agreement with the ab initio barrier. However, the experimental studies did not indicate that the potential in the excited state is almost exactly out of phase with the ground state. This is evident from the intensities of the torsional progressions (35) which increase along the progression with a low Franck-Condon factor for the (0, 0) band.

The k’A”-f’A’(r* - n) Transition The calculated changes in molecular geometry and transition energies for the kf transition are shown in Table VI. Two experimental transition energies are given, an adiabatic (TO) (35) and a vertical (TV) (34); the NonP calculations should be compared with the adiabatic and the other calculations with the vertical. CI calculations of the vertical transition energy have been made by Del Bene et al. (I) using an STO-3G basis and by Ha and Keller (5) with a DZ basis, and these are also shown in Table VI for comparison. No attempt has previously been made to calculate adiabatic transition energies. The adiabatic transition energies calculated at the SCF level are about 1 eV too low as for formaldehyde. This is mainly because the SCF method gives a poor description of the a system of the carbonyl group in the ground state. This can be improved by performing a GVB/2PP calculation in which the CO c and ?r bonds in the both states are represented by GVB pairs, and this gives an increase of 0.46 TABLE VI Transition Energies and Geometry Changes for the A-x and B-2 Transitions Method

x

lA”-x

‘A’

Geoma

Tvb

DZS

DZds

Aa

As

At

AV

A6

AE

AY

AT

24690 15730

3.09 1.95

0 0.001

0 -0.5

0 0 0.001 -0.010

0 0.192

0

5.6

-9.7

0.2

39.4

65.9

=0 NonP

27390 19530

3.40 2.41

0 0.002

0 0 0 -0.4 -0.001 -0.011

0 0.183

0 4.7

0 -10.9

0 0.3

0 45.7

0 64.1

35000 35330 34440

4.34 4.38 4.27

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

6.82 0

0

0

0

0

0

0

0

0

0

Transition

Experiment

TO

55024

DZ

=0

77380

9.60

0

6.03 5.91 6.34

0 0.001

0 0 0 0.8 -0.025 -0.008

0 0.044

0 5.2

0 -0.9

0

i&T E@ET

48654 47666 51150 49241 48659

6.11 6.03

0 0

0 0 0 1.0 -0.024 -0.010

0 0.045

0 7.1

0 -1.8

0

a&T

DZstGVB

AX

=0 NoaP

DZS

DZda

b) c)

Ar

4.28 3.69

STO-3G(CI)= r STO-3G(CI) i&Z mxd =0

a)

EteV

34500 29771

TO

‘A,

-1

Transition

Experiment

-1 B A’-tt

e/cm

3.8

3.7

r implies that the ground state e. geometry was used in both states. B8 ET implies that both optimized thus, but the excited state was nor optimized for E@BZ. VerticaL transition energy from Ref. (34). Adiabatic transition energy To from Ref. (35). Prom ref. (1). Prolo ref. (5).

state8were

0

ACETALDEHYDE

STRUCTURE:

AB INITIO

297

eV in the calculated adiabatic transition energy. Due to expense in computer time, a GVB/2PP calculation was not carried out using the DZds basis set but, if we assume that the increase in transition energy would be at least 0.46 eV, then we would be approaching the experimental value but still lower due to neglect of important configurations. The geometry changes for the adiabatic transitions predicted using the two basis sets are very similar even though the actual values of the parameters for each state sometimes differed quite drastically depending on which basis set was used. The reason for this is that the parameters tend to change by about the same amount in both states with the addition of polarization functions to the basis, as in formaldehyde (12). As can be seen from Table VI, the major changes in geometry between the ground and excited states are the large increases in T, x, and w but there are also significant changes in 19and t. As mentioned previously, the change in the C-O bond length, w, is probably overestimated and so Aw should probably be closer to 0.126 A. This is still a large increase and is consistent with the long progressions of ca. 1120 cm-’ observed in the electronic spectrum (33, 34). From the geometry changes, as well as out-of-plane C-H inversion, we expect the in-plane aldehydic C-H wagging mode and the in-plane CC0 bending mode to be Franck-Condon active. These have not yet been identified in the spectrum, but in the jet-cooled spectrum (35) there is clearly much to be assigned. Since the torsional potential function of the k state is out of phase with that of the ground state, we would expect the torsional fine structure to be like the corresponding transition of nitrosomethane (38) with the most intense torsional band being that from the lowest torsional level of the ground state to a torsional level near the top of the barrier in the excited state and the (0,O) torsional transition rather weak. This seems exactly to be what is observed. Perhaps the other predictions from the ab initio calculations will aid the interpretation of the spectrum further. V. THE

&‘A (3s RYDBERG)

STATE

Geometry The optimum molecular geometries and SCF energies for the B state of acetaldehyde obtained using various methods and basis sets are shown in Table VII. As well as the results obtained using the DZs basis, a calculation is included which used the DZ basis without diffuse Rydberg functions. We can see from the results that the inclusion of the diffuse functions causes an energy lowering of over 0.132 a.u., showing that the inclusion of these functions in the basis set is essential for this state. As for the ground and k states, the optimum geometries for the B”state are fairly similar for the two basis sets. The major exception as before is that the optimum C-O bond length decreases by 2% when the polarization functions are added to the basis. Also the optimum CCH angle, 0, obtained using the DZds basis is lo smaller than that obtained using the DZs basis. Since the in-plane parameters are normally predicted more accurately with a basis set with polarization functions, the structure obtained using the DZds basis is probably to be preferred.

298

CRIGHTON

AND BELL

TABLE VII Molecular Geometries and SCF Energies for the B’A’ State of Acetaldehyde’ Method

DZ

DZS

Geometry b =0

r

1.086

a:

108.3

s

1.501

t

w

1.114

1.216

e

117.5

c

Y

123.9

0.0

1.084

109.6

1.483

1.080

1.264

122.4

122.3

0.0

1.084

109.6

1.479

1.080

1.264

121.4

123.3

4.4

S@ET S@ET S@ST

=0 E@EZ

0.0

-152.652708

60.0

-152.650570

0.0

-152.653539

30.0

-152.651663

60.0

-152.649800

109.5

1.488

1.080

1.265

122.6

122.7

0.5

60.0

-152.650611

1.086

108.3

1.501

1.114

1.216

117.5

123.9

0.0

0.0

-152.689520

1.086d

109.7

1.478

1.082

1.239

123.8

121.7

0.0

1.086e

109.7e

1.476

1.082e

1.23ge

122.9

122.6

1.086e

109.7e

1.485

1.082e

1.23ge

124.1

121.9

4.2

@ET S@ST

-152.516288

1.083

S@EZ E@ET

gnergy

-152.640449

S@Ez E@ET

a) b) d) e)

0.0

'0 E@KZ

DZds

lC

Lengths in 8, angles in degrees, and energies Ground state experimental str”ctwe (6). Fixed at I value since fairly independent of Fired at Ee EZ value as in Table I.

a.“. c) rest of

0.4

0.0

-152.692510

60.0

-152.690313

0.0

-152.693257

60.0

-152.689611

60.0

-152.690356

in

Assumed str”ct”re.

or

fixed.

Vibrational Wavenumbers The force constant matrix for the & state of acetaldehyde obtained from the geometry optimization calculations using the DZs basis set is shown in Table II and the calculated harmonic wavenumbers obtained using ASREF are given in Table VIII. No force constants were available for the asymmetric methyl stretching or deformation modes v1 or us and so the diagonal force constants were taken to be the same as those for the corresponding symmetric modes and no coupling constants were included between these two modes and the other totally symmetric modes. As for the ground state, the calculated wavenumbers are systematically too high and so must be reduced by a scale factor to give good agreement with the experimental values. Thus, all calculated methyl wavenumbers were reduced by lo%, u9 was reduced by 16 and 5% for isotopomers containing the CH3 and CD3 groups, respectively, and the CC0 bending mode, vlo, was reduced by 5 and 12%, respectively. These scaled wavenumbers, also shown in Table VIII, are to be compared with the values obtained from an experimental study of the 182-nm system of acetaldehyde (25).

ACETALDEHYDE

STRUCTURE:

AB ZNITIO

299

TABLE VIII Vibrational Wavenumbers of the !?‘A’ State of Acetaldehyde

1

Asym.

Me str.

2

sym.

3

Aldehydic

ne

4

C-O

str. C-H

str.

str.

5

Asym.

6

C-H

Me def.

7

Sym.

8

C-c

9

In-plane

in-plane

wag

Me def. str. He rock

10

CC0 bend

a)

Scale

factors

from

CD3CDO

CD3CHO

CH3CW

G-l 3CHO

Mode

ca1c.

Scaleda

C.%lC.

Scaled

ca1c.

Scaled

Calc.

Scaled

3032

2129

3032

2729

2267

2040

2267

2040

2900

2610

2918

2626

2098

1888

2095

1886

3477

3477

2523

2523

3469

3469

2536

2536

1771

1771

1758

1758

1754

1754

1731

1731

1712

1541

1701

1531

1252

1127

1233

1110

1404

1404

937

937

1408

1408

1093

1093

1563

1406

1559

1403

1203

1083

1259

1133

1055

1055

1186

1186

990

990

904

904

1114

936

1093

918

845

803

845

803

477

453

471

447

453

339

448

394

ground

state

observed/calculated

wavenumber

ratios.

Barrier to Internal Rotation The barriers to internal rotation of acetaldehyde in the 8 state, calculated by the SCF method using various geometries and basis sets, are shown in Table IV with our experimental results (25) and those of Heath et al. (13). As with the ground state results, the best agreement with our experimental values of I’, is obtained if no geometry optimization is carried out at the top of the barrier, i.e., if the semirigid rotor model is used as for the experimental determination of the barriers. Also, as expected the value of I’, which was obtained from the ab initio calculations does not agree well with the experimental value. To obtain a reasonable value of V, from the SCF calculations, it is essential to allow the axis of the methyl group to tilt away from the C-C bond and take up its optimum value. The equilibrium structure shows that the methyl group is tilted 4.2” away from the oxygen atom, and this tilt is mainly responsible for the large barrier to internal rotation in this state. The importance of performing geometry optimizations and in particular of allowing for tilt of the methyl group can further be seen by comparing the results of some calculations by Heath et al. (13). They attempted to obtain a value for the barrier to internal rotation in the B’ state by performing SCF calculations on the lowest ionic state using a DZ basis set. The assumption that the lowest ionic state should mimic the B’ state is probably justified but they used the r. structure of the ground state and performed no geometry dptimizations. This latter reason is probably why their calculated value of 223 cm-’ is not even qualitatively correct. A similar poor barrier height was obtained by Gordon (14) from CND0/2 calculations since he also carried out no geometry optimizations.

300

CRIGHTON

AND BELL

The barrier heights obtained in this study, using the two different basis sets are in fairly good agreement with one another and both basis sets correctly predict a barrier to internal rotation in the B’ state which is approximately twice that of the ground state. The $A’-Z’A’

(3s - n) Transition

As mentioned in the Introduction, there has been controversy over the assignment of the 182~nm system of acetaldehyde, with some previous workers assuming that the system arose from two overlapping electronic transitions (a* - n and 3s - n transitions). By analogy with formaldehyde, the transition probably arises from a single-(3s - n) electronic transition. The experimental evidence for the assignment of the system to a single Rydberg transition is good and an interpretation follows (25). Further evidence for the assignment of the 8 state to a Rydberg state is gained from the SCF calculations since the addition of diffuse s functions to the DZ basis set causes an energy lowering of only about 0.001 a.u. for the valence states, but an energy lowering of 0.132 a.u. for the B’ state. Also, examination of the coefficients of the 10a’ orbital confirms that this orbital is almost totally Rydberg in character. The transition energies and changes in molecular geometry calculated using the two basis sets are shown in Table VI. With the exception of the calculations of the vertical transition energies using the ground state r. structure, all the calculations involved geometry optimizations in both electronic states and the transition energies obtained are therefore adiabatic transition energies. The experimental adiabatic transition energy was obtained from the vacuum ultraviolet spectrum (25). The adiabatic transition energies obtained from the SCF calculations are about 0.8 eV too low. This is consistent with the results obtained for the k state and for the formaldehyde transition energies (12). The reason, as discussed previously, is the inability of the SCF method to adequately describe the A system of the carbonyl group in the ground state. The transition energy obtained from a GVB/2PP calculation in which the 8a’ (CO u-bond) and the 2a” (CO r-bond) orbitals were expressed as GVB pairs is also shown in Table VI. While better than the SCF value, this is still too low and a larger MCSCF or CI calculation is required to obtain accurate transition energies as for the k state. The changes in geometry between the two electronic states predicted using both basis sets are virtually identical with the exception of AB and AC. However, even these changes are in qualitative agreement, the values obtained using the DZds basis probably being closer to the true values. Thus, for calculation of the changes in molecular geometry between the two electronic states it is not essential that polarization functions be included in the basis set although this may give a slight improvement in the values for the CCH and CC0 angles. In the corresponding transition of formaldehyde (12) the predicted changes in geometry, apart form the C-O length, are not significantly changed by allowing for electron correlation. The reason is that changes in optimum geometry produced by performing CI (or GVB) or adding polarization functions to the basis set tend to change the optimum geometries of both electronic states so that the differences in geometry between the

ACETALDEHYDE

STRUCTURE: AB INITIO

301

two states remain almost constant. The change in the C-O bond length for formaldehyde was greatly overestimated at the SCF level and it was significantly_ reduced when a GVB/2PP calculation was used. The C-O bond length in the B state of acetaldehyde may not be significantly different from its ground state value. From the predicted geometry changes (with the assumption that there is no change in C-O length), we would expect that the aldehydic in-plane wagging, the CC0 bending, and the in-plane methyl rocking modes would certainly be FranckCondon active in the 182~nm system. It is also likely that we would observe the C-C stretching mode, the aldehydic C-H stretching mode and the symmetric methyl deformation mode although these would probably be weaker since there is a smaller change in geometry involved. VI. CONCLUSIONS

For the ground state of acetaldehyde the optimum geometries obtained using the DZs and DZds basis sets are very similar, and these are in fairly good agreement with the experimental geometry. The major difference between the geometries obtained using the two bases was that the addition of polarization functions caused a systematic decrease in the optimum C-O bond length. This was also true of the bond lengths in the excited electronic states although for these states some of the optimum angles obtained using the two basis sets were significantly different, particularly the out-of-plane angle in the A state. Experience with formaldehyde suggests that geometries obtained with polarization functions are to be preferred (except for the out-of-plane angle in the k state). In general, the differences in geometrical parameters between two electronic states are nearly independent of basis set. Thus, the predicted geometry for the excited electronic states is best obtained by adding the predicted changes in geometry to the experimental ground state geometry. Predicted structures for the excited states of acetaldehyde, obtained in this way are shown in Table IX. As discussed above the predicted changes in the C-O bond length between the two electronic states are generally overestimated at the SCF level. Thus, the values of w for the excited states were reduced to allow for this by the fraction that the C-O distance is overestimated in the corresponding states of formaldehyde (12). It has been shown that good agreement can be obtained between SCF calculated barrier heights V3and the experimental barriers to internal rotation using a semirigid model. It is essential, however, that the molecular geometry be fully optimized (within the semirigid rotor model) in the state concerned. The SCF adiabatic transition energies are about 1 eV too low and, while these are improved slightly by performing GVB/2PP calculations, such calculations still do not include a sufficient number of configurations in the wavefunction to give good agreement with the experimental transition energy. The predicted structures for the electronic excited states, together with the predicted potential energy barriers and harmonic wavenumhers for these states, provide a useful aid to the interpretation of the electronic spectrum of acetaldehyde. In a following paper the 182-nm system will be interpreted in the light of these SCF predictions.

302

CRIGHTON

AND BELL

TABLE IX Preferred Values of Geometrical and Barrier Parameters for the Electronic States of AcetaldehydeO Parameter

x stateC

5 St.ateC

r (C-H,)

1.087

1.089

1.087

9 (C-c)

1.512

1.511

1.488

t

(C-H,)

1.114

1.103

1.104

v

(C-0)

1.207

1. 343d

1.225d

108.7

a (HCH,)

108.3

109.7

9 (Cal,)

115.3

120.0

122.4

c (CC01

124.2

113.3

122.4

Y (Tilt)

0.5

0.8

4.2

x (Out)

0.0

39.4e

0.0

I (Torsion)

0.0

64.1

0.0

415

“3

a)

a stareb

Lengths

in

2,

Constants In

in

degrees,

and

potential

b)

r Jr

C)

&P &vxetry based on predicted changes by DZds basis. Corrected from formaldehyde results, since Au is systematically overestimated. Prom DZs calculation.

d) e)

geometry

an les cm- 8 .

800

697

(20).

ACKNOWLEDGMENTS We thank Dr. J. L. Duncan for the use of his force field program, ASREF, and the Dundee University Computing Centre for their help and services. RECEIVED:

December 27, 1984 REFERENCES

1. J. E. DEL BENE, G. T. WORTH, F. T. MARCHESE,AND M. E. CONRAD, Theoret. Chim. Acta. 36, 195-206 (1975). 2. F. BERNARDI,M. A. ROBB,AND G. TONACHINI,Chem. Phys. Left. 66, 195-198 (1979). 3. W. J. HEHRE,J. A. POPLE,AND A. J. P. DEVAQUET,J. Amer. Chem. Sot. 98,664-668 (1976). 4. J. 0. WILLIAMS,C. VAN ALSENOY,J. N. SCARSDALE,AND L. SCHAFER,J. Mol. Struct. Theochem. 86, 103-109 (1981). 5. T. K. HA AND L. KELLER,J. Mol. Struct. 27,225-232 (1975). 6. R. W. KILB, C. C. LIN, AND E. B. WILSON,.I. Chem. Phys. 26, 1695-1703 (1957). 7. J. A. ALTMANN, T. A. M. BUST, AND A. D. OSBORNE, Chem. Phys. Left. 69, 595-599 (1980). 8. M. R. PETERSON, G. R. DEMARE, I. G. CSIZMADIA,AND 0. P. STRAIJSZ,J. Mol. Struct. Theochem 86, 131-147 (1981). 9. D. C. MOULEAND A. D. WALSH, Chem. Rev. 75,67-84 (1975). 10. A. D. WALSH, Proc. R. Sot. A 185, 176-182 (1946).

ACETALDEHYDE

STRUCTURE: AB INITIO

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