Phor,,~hemiurryundPhurubiology. 197 I . Vol. 13, pp. 423-429. Pergarnon Press. Printed in Great Britain

THEORETICAL CALCULATIONS OF T H E TRANSITIONS OF PHOTOCOLORED FORMS OF CHROMENES

LAWRENCE EDWARDS, JAROSLAV KOLC, and RALPH S. BECKER Department of Chemistry. University of Houston, Houston, Texas 77004, U.S.A.

(Received 20 July 1970; in revised form I5 September 1970)

Abstract - Theoretical prediction (MO-SCF-CI) of numbers. energies and intensities of transi- tions are compared with experimental data for the photocolored products of three types of chromenes. Generally good results are obtained. Several conclusions resulted from variation of parameters: ( 1 ) When all carbon-carbon bonds are considered equal in length, there is good agreement between experiment and theory regarding band locations and intensities, however, very poor correlation exists between theory and experiment when calculations are done on a model where the carbon-carbon bonds are alternately single and double, (2) theoretical calcula- tions employing the Mataga approximation for the two-center repulsion integrals gives superior correlation with the experimental spectra in comparison with the Pariser-Parr approximation, and ( 3 ) variation of certain parameters (as I.P., E.A., p ) did produce changes in the results, especially in the oscillator strengths, but there was no clear best choice. and therefore, conven- tional parameters were used.

I N T R O D U C T I O N

CHROMENES were found to give colored forms on irradiation with U.V. light. An o- quinonemethide structure, suggested for the photocolored product [ I]. is in agreement with chemical evidence [2] (a participation of mesomeric forms cannot be excluded, of course). In this paper an attempt is made to correlate experimental and calculated spectra of the photocolored forms for three chrornenes: 2,2-dimethylchromene(Ia), 2,2-dimethyl-5,6-benzochromene( 1 la), and naturally occurring lapachenole [3] (1 1 la), a representative 7.8-benzochromene.

la Ib

I la I Ib

l l l a 423

l l l b

424 L. EDWARDS, J. KOLC and R. S. BECKER

The structure ofthe photocolored forms can be written as Ib, Ilb and 1 I Ib. The question of importance is: What is the nature of the bonding in the colored forms such that a substantial energy lowering occurs in the wavelength of the first several transitions compared to the uncolored forms? Consequently, we have performed theoretical cal- culations to determine the number, energy and intensity of the electronic transitions expected for several models of the colored forms Ib, IIb, and IIIb. These results have been compared with the experimentally observed electronic transitions.

MATERIALS AND METHODS

All compounds were studied in rigid 3-methylpentane at 77°K. Irradiations were done with a 1 kW mercury-xenon arc lamp (with a filter cut off below 240 nm). The spectra were recorded while the sample was still at 77°K. A comparison of the initial (before irradiation) and final spectra resulted in the spectra of the photocolored forms presented in the figures.

Theoretical calculations were done using a LCAO-MO-SCF-CI 'procedure (n- electrons only)[4]. Variations were made in the approximation for the repulsion integrals (Pariser-Parr vs. Mataga), in other parameters (such as p), and in the geometry in an attempt to get the best fit to the experimental spectra.

RESULTS A N D DlSCUSSlOfl

The first transition, in all three cases, is relatively strong indicating that it is not of the T* + n type. Thus, all transitions are assigned as T* + T. The unusual spectral prop- erty of note is the relatively low energy of the longest wavelength band of photoproduct compared to either the parent uncolored molecule or systems with a comparable extent of conjugation (e.g., polyene or polyene aldehydes). For example, the longest wavelength band maximum in dimethyl chromene (la) shifts upon irradiation from 308 to 460 nm. This is at significantly lower energy than a corresponding polyene aldehyde (- 327 nm), a structure originally thought to be parallel to that of the photocolored product (Ib). This qualitative observation was verified by theoretical calculations. That is, if it is assumed that bond alternation occurs (as in a polyene or polyene aldehyde), the results are in very poor agreement with the experimental spectra of photocolored products (see Tables 1 and 2). Thus, it was assumed in the remainder of the calculations that all bond lengths involved were more benzene-like, an assumption which markedly improved the results of the calculations. In fact, using bond lengths of 1-40 A for all carbon- carbon bonds, 1.21 A for the carbon-oxygen double bond, all angles of 1 20", and - 2.40 eV for all resonance integrals (calculations were done on species where hydrogen atoms replaced the two methyl groups), satisfactory results were obtained which proved help- ful in interpreting the spectra; see discussion below and Tables 1-3 and Figs. 1-3. Variation in ionization potential (IP), electron affinity (EA), resonance and repulsion integrals as suggested by Zahradnik, Tichy, and Reid[5] were made with no significant improvement in the spectral correlation. Therefore, conventional parameters (for instance, see Streitweiser[6]) were used except that pc=o = - 2.40 eV. In the case of lapachenole, -OCH, was considered to be -OH and a = - 2.40 eV 151 proved to give results nearly identical with those obtained using the more conventional value of

= - 1-92 eV. Consequently, in the results presented, the former value of was used.

Two different approximations were used for the two-center repulsion integrals. A

Transitions of the photocolored forms of chromenes 425

Table 1. Comparison of theory and experiment for the colored form of 2.2-dimethylchromene (Ib). All wavelengths ( A ) in nm and numbers in parentheses are energies in eV. The f values are the rela-

tive oscillator strengths, and those in brackets are absolute values from calculation.

Transition Structure Model 1 2 3 4

Experiment A460(2.70) A350(3*55) A27514.51) fl.00 f I .33 f I *42

' '0

Pariser-Pam 393(3.16) 276(4.49) Bond alternation 1~00[0~401 0~10[0~041

Pariser-Parr 379(3*27) 283(4.39) Bond alternation 140[0~50] 0.74[0.37]

Pariser-Parr 426(2.91) 298(4.16) Benzenoid bonds I40[0.50] 0.91 [0.45]

Mataga 449(2.76) 332(3.74) Benzenoid bonds 140[044] 0.89[0.391

Mataga 491(2.53) 345(3.60) Benzenoid bonds I *00[0.191 0.75[0.15]

25 l(4.95) 2.89[ 1. IS]

242(5* 12) 220(5.65) 0.1 8[O.O9] 0.28 [O . 141

254t4.88) 2220.59) O.lO[0.05] I66[0.83]

268(4.64) 251(4.95) 0.41 [ O . 181 0.43[0.19]

282(4-40) 2435.06) 0.55[0*I I ] 0.55[0.l I ]

A I n 4 Fig. I . Experimental (-) and theoretical spectra (vertical bars) of the colored form of 2.2- dimethylchromene(lb), see text. The dotted portion represents an estimation considering

absorption of the uncolored form.

426 L. EDWARDS, J. KOLC and R. S. BECKER

Table 2. Comparison of theory and experiment for the colored form of 2,2-dimethyl-5,6-benzo- chromene(l1b). All wavelengths (A) in nm and numbers in parentheses are energies in eV. The f values are the relative oscillator strengths, and those in brackets are absolute values from calculation

Structure Model Transitions

ep-

?$

‘0

Experiment A 3W3.20) A 347(3-58) A 3034.07) A 291(4.26) f 1.00 f 0.39 f2.11

Pariser-Parr 3533.49) 307(4-05) 278(4.47) Bond alternation 1.00[0.42] 0.84[0.35] 1.05[0.44]

Pariser-Parr 403(3.08) 303(4-09) 288(4*30) Benzenoid bonds 140[0.83] 0*08[046] 0.27[0.22]

Mataga 403306) 364(3-41) 296(4*17) 273(4*55) Benzenoid bonds 1.00[0*42] 0.75[0.32] I .35[0.57] 0.53[0.22]

Mataga 448(2.77) 364(3.41) 297(4.17) 273(4.54) Benzenoid bonds 1.00[0.19] 0.91[0.18] 2.10[0.41] 0+37[0.17]

L 10 500

A Inml Fig. 2. Experimental (-) and theoretical spectra (vertical bars) of the colored form of 2,2-

dimethyl-5,6-benzochromene(l Ib), see text.

Tab

le 3

. Com

pari

son

of t

heor

y an

d ex

peri

men

t fo

r th

e co

lore

d fo

rm o

f la

pach

enol

e (I

IIb)

. All

wav

elen

gths

(A) i

n nr

n an

d nu

mbe

rs in

par

enth

eses

are

ene

rgie

s in

eV

. The

f va

lues

are

the

rela

tive

osci

llato

r st

reng

ths,

and

thos

e in

bra

cket

s ar

e abs

olut

e va

lues

from

calc

ulat

ion

Tra

nsiti

ons

Stru

ctur

e M

odel

1

2 3

4 5

H,C

O

Exp

erim

ent

A 46

q2.7

0)

A 35

1(3.

54)

A 31

q3.8

9)

A 29

8(4.

16)

A 28

7(4.

32)

p:: f 1

.00

f 0.04

f0.5

3 f 2

.3 1

H°F

/

Mat

aga

475(

2.61

) 32

8(3.

78)

3 lO

(4.0

1)

286(

4.35

) 27

6(4.

50)

Ben

zeno

id b

onds

14

0[0.

69]

044[

0.03

] 0.

53[0

.36]

0.

05[0

.03]

1.

05[0

.72]

Mat

aga

506(

2.45

) 33

9(3.

67)

314(

3.95

) 29

7(4.

18)

278(

4.59

) B

enze

noid

bon

ds

1.00

[0.3

6]

0.06

[0.0

2]

0.23

[04U

3]

0.46

[0.1

7]

0.80

[0.2

9]

428 L. EDWARDS, J . KOLC and R. S. BECKER

Fig. 3. Experimental (-) and theoretical spectra (vertical bars) of the colored form of lapachenole (Illb), see text.

fairly extensive comparison of the Pariser-Parr and the Mataga approximations showed that the Mataga approximation gave comparative universal lowering of all transition energies by 0.1 to 0.5 eV. Further, while no method gave excellent intensity predictions, the Mataga approximation correlated with observed intensity trends better than the Pariser-Parr approximation. Hence, based upon both the energy and intensity con- siderations, the Mataga approximation was used for final spectral correlations, see Tables 1-3, and Figs. 1-3.

Further verification of the correctness of this theoretical approach (uide supra) is obtained when comparison is made of the spectral location of the lowest energy transi- tion among the colored forms Ib, Ilb and Illb. Experiment shows that despite the ostensibly less extended conjugation in the simple chromene (Ib) vs. the 5,6-benzo- chromene (IIb), the lowest energy transition of Ib (460nm) is - 0.5eV lower in energy than that of Ilb (388nm). The results of calculations of the type described (uide supra) were in agreement with experiment predicting the band of Ib to be - 0.3 eV lower in energy. Moreover, the calculations were capable of predicting the marked difference in the spectral location of the lowest energy transition of Ilb and Illb (388 and 460nm, respectively). The results of calculations on the colored form of 2,2- dimethyl-7,8-benzochromene and its hydroxy substituted derivative (1 I Ib), showed that 25 per cent of the shift is due to the structural change from a 5,6 benzo-(Ilb) to a 7,8-benzochromene (1Ilb) with the remainder resulting from the introduction of the hydroxy (or methoxy) group. Hence, it is quite reassuring that the theory is able to correctly predict subtle and apparently unusual changes in the spectra resulting from changes in the molecular structure.

The geometrical conformation of the photocolored product is not uniquely defined. In the experiments, the chromenes were irradiated in a rigid 3-methylpentane matrix. Surely the methyl groups will sterically interact with the carbonyl oxygen forcing some twisting about either the carbon-carbon double bond or pseudo single bond of the “polyene” chain. Calculations of the pure cis- and trans-forms were carried out (recall

Transitions of the photocolored forms of chromenes 429

that the methyl groups were replaced by hydrogens in the calculations) in an attempt to answer this question, but the results were not definitive. I n general, the results based on the cis-form seem to give slightly better predictions for the locations of higher energy transitions, while those based on the trans-form better predict the maximum of the first transitions, Tables 1-3. However, the first band is more sensitive to small perturbations, of both intra- and intermolecular origin, and correlations of this band were considered a poorer criterion for geometry selection than the overall fit of the first several transitions. Prediction of intensity patterns, while somewhat different for cis- and trans-forms indi- cated that no definite conclusion could be drawn. Data pertinent to both the cis- and trans-forms appear in the Tables 1-3 while data for the cis-forms (Mataga approxima- tion) appear in the spectra, Figs. 1-3.

Thus, a comparison of the theoretical and experimental results suggests that the bond- ing in the colored photoproducts of the chromenes is more benzenoid-like that polyene- like. Confidence in the theoretical results is justified as exemplified by the ability to satisfactorily predict the correct number of transitions as well as their spectral loca- tions and intensities, especially the relatively unusual locations of the first bands of each of the photoproducts discussed.

Acknowledgements -This research was supported by the National Aeronautics and Space Administration, grant NGR 44-005-091. We also wish to acknowledge the assistance of Dr. Josef Michl. University of Utah, in performing some initial calculations of the chromenes.

R E F E R E N C E S I . R . S. Becker and J. Mich1.J. Am. Chem. Soc. 88.593 I (1966). 2. J . Kolc and R . S. Becker.J. Phys. Chem. 71.4045 ( 1967). 3 . J . Kolc and R . S. Becker, Photochem. Phofobiol. 12,383 ( 1970). 4. R . S. Becker. K. lnuzuka and J . King.J. Chem. Phys. 52.5 I64 (1970). 5. R. Zahradnik, M. Tichy, D. H. Reid, Tetrahedron 24,3001 (1968). 6. Andrew Streitweisser, Jr . . Molecular Orbital Theoryfor Organic Chemists, Wiley, New York ( I 96 I ) .

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