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On the nature of excited electronic states in cyanine dyes: implications for visual pigment spectra
CHEhlICiU
Volume 72, number 3
ON THE NATURE IMPLICATIONS
OF EXCITED FOR VISUAL
ELECTRONIC PIGMENT
15 June 1980
PHYSICS LE-LTERS
STATES
UU CYANINE
DYES:
SPECTRA
Urt DINUR * Department
of Ph] steal Chemrstry.
The Hebrew
Umverstty.
Ierusalem.
Israel
Barry HONK Department of P~~ysrolo~ and B~opl~ysxs. Urbana. Illmors 61801. US4
The Umvers~ty
of fiImots,
and Klaus SCHULTEN hlax-Plarrck-lnstttut
ftir B~opl~~s~kahsche
Chemte.
D-3400
GGttmgen.
West Germany
Rrcetved 22 January 1980; m tinal form 12 March 1980
CNDO/S Cl calculattons ate carned out on polyenes and on cyatune dyes In contrast to polyenes, doubly excited contigurattons have a strong eifect on the first opttcaby allowed ewtted state m cyanmes. Protonated Schlff bases of retmal ate closely related to cyanme dyes, wwh unportant consequences for models of visual pigment spectra and photochemistry.
1. Introduction
The excited rlectrotuc states of ltnear polyenes have been a sublect of Interest for many years. They were mtensrvely studted with Hiickel and free-electron techniques [l] pnor to the development of the PPP theory and have, to some extent, been “redncovered” due in part to their stmllanty to retmal, the chromophore of the vtsual pigments [2]. The earhest theorerrcal studres provrded a satisfactory quahtative descnptron of the spectroscopic propertres of hnear polyenes (see, e.g , ref. [3] ). Polyenilic tons related to cyanine dyes which contain an odd number of atoms have extremely long-wavelength absorption maxima (X,,) wiuch mcrease linearly wtth chatn length. The series of polyenes wtth an even number of atoms are considerably blue-slufted relative to cyanine dyes and exhrbrt an asymptotic versus chain length wluch levels off curve of A,, near 500 nm. * Present address: Department of Chemtstry, Harvard Unmerstty, Cambrrdge, Massachusetts 02138, USA.
In even polyenes, the matn absorption band results from a transition to a Si state and can be successfully described with a semiempttical rr-electron treatment including configuration interaction among singly excited configurattons (see, e g., ref. [4] )_ However, the inclusion of doubly excited configurations (D CL) is required for a proper description of the manifold of “covalent” states such as the IA- state which Lies close to the main absorption bai!d [S-7]. In cont~mst to the even polyenes there have been no D CL calculatrons carried out on odd polyenes such as cyanine
dyes. S Cl calculations can be parametenzed to yield excellent agreement with the experimental h,,chain length curve, but only when an unusually small resonance integral IS used [8]. Thus, it is difficult to obtain a quantitative description of the spectroscopic properties of both odd and even polyenes with a single set of semi-empirical parameters. Uncertainties as to the proper method of carrying out calculations on polyenes have led to serious di.fficulties in the mterpretation of visual pigment spectra_ The chromophore of the visual pigments is the 493
Volume
72, nunlbcr 3
CHEMICAL
protonated Schiff base of 1 I-cn retinal wluch absorbs 111solurlon at about 450 nm Protonated Schiff bases of r2tmal conram an even number of atoms but are nevertheless highly delocalized systems. As such they bear a resemblance tc both even and odd polyenes and 11 IS not clear. a pnon. which set of parameters should be used to descnbc therr spectroscopic properrics Calculations usmg parameters fit from cyanin dyrs yirld values of X,,, m the vlcmlry of 600 m-n [S] The expenmental v~~lue oi450 nrn IS r12wed AS resulting from a larg2 blue-shift due to a counter-ion or solvent dipoles [8.9] Calculations [ 10.1 I] usmg a standard s2t of parameters approprrate to 2v2n polyenes yield values of X,,, near 450 nm and have not m general accounted for possible eff2cts induced by a counter-Ion. Smce visual prgments absorb between -I30 .md 610 nm the uncertamtles m the calculatrons cober the cntlre range of visual plgrnent spectra This mrroduc2s obvious comphcatlons m any attempt to construLt mod& of chromophore-protein mteractlons that are based on semi-empirical calcularrons oi‘electronic spectra Our maJor concern m thus paper wdl be to e\plam the s\clrrd state propertIes of cyanme dyes In particuk. we wdl discuss the ~~11~2sof the failure of standard semrzmplncal methods to provide an adequatc descnptron of rhc spectroscoprc transltlon energy m thcsr molecules To tha end we report calculatrons. usmg the CNDO/S [ 121 method. on polyenes. cyanme dyes dnd the potonat2d Scluff base of retinal Our results demonstrak that electromc correlation has very dlffereni spectroscopic consequznces m polyenes and cyanme dyrs. Moreover. protonated Schrff bases of retinal are found to be closely relatsd IO cyanme dyes suggestmg that semi-emplncal methods cannot be applied m their standard form to the study of visual pigment spectra.
2. Method
of calculation
The Cr\!DO/S method [ 121 was employed m thus work since the cyamne dyes are lomc molecules and as a result have polanzrd u charge drstnbutrons. This and the partrclparron of hereroatoms in the x-electron system would have required an ad hoc parametenzatron had a n-electron method been used. The S CI calculations mcludsd the 50 lowest energy configura49-l
PH\ SICS LE-ITERS
15
June 1980
tions and mvolved both o and IT orbltak (although o-n* excltatrons made only negligible contnbutrons to the mam absorption band). Since all cakulatrons were carried out on planar systems doubly exerted configurations m the CI expansion were restncted to include only 7r orbrtak. The CI matrix reached a dimension of 703 for the largest molecules that were treated. The Ohno formula was used to approximate the two-center repulsion Integrals as 1s required when D Cl calculations are carried out [6] _ Methyl groups w2r2 not Included and were replaced by hydrogens m the calculatrons. Smgle bond lengths of 1 46 A and double bond lengths of 1.35 .% wer2 assumed for the polyenes. For the cyanmes all C-C bonds were set at 1.4 j, and the C-N bonds at 1.3 x Standard bond angles of 120” were assumed throughout
3. Polyenes The electromc sprctra of polyenes have been studred m detail m recent years and it has been found that correlatron effects play an important role m dcterrmmng transrtron energies [5--71 it IS usrful. m order to facdrtate comparrson to cl anmes. to re\121\ a number of th2 conclusions of prcvrous work [5--71 m terms of the CNDO/S results reported m table l. It IS evident that the contnbution to the correlatron energy from doubly excited configurarrons IS dlfferent for the various electronic states. The first elclted IA- stat2 IS reduced m energy (relatrve to the uncor2 eV whde relEted ground state) by approurmately the strongly allowed BG state 1s stabdlzed by onI> O-O.1 eV. the value Increasing wrrh mcreasmg cham Isngth. Thr result IS to place th2 optrcally forbidden A- state below the optrcally allowed Bi The effect o P doubly exerted configurarrons on the ground stat2 1s also grsater than on the Bi state. For 2xampl2, S CI cdculatrons on octatetraene yreld a transrtron energy of 4.29 eV, close to the expenrnental value. The inclusion of doubly excited configurations lowers the Bi state by 0 31 eV but lowers the ground stat2 by 1 eV; th2 net result is a transrtlon energy of 4 99 eV whrch IS clearly two high. In contrast, D CI calculations on butadiene mcludmg ground-state stabrhzatlon yreld a closer fit to the expenmental transrtron energy than do the S CI calculations The dlff2rence between butadrene and octatetraene
Volume 72, number 3 Table 1 Ewttatlon
CHEhIICAL
energies a) (m eV) for polyenes Ground state D CI b)
[CHz=CH-(CH=CH),-CH=CHz ‘A-
-0 52 -0.77 -1 00 -1 14 -1.46
0 1 2 3 4
PHYSICS
15 June 1980
LETTERS
] ‘B+u
B
Exp. c)
SC1
DC1
SC1
DC1
681 6.34 5.85
5 11 4.26 3.73
5 46
3.44
5 08
3 22
548 4.75 4.29 3 97 3.75
5-48 4.56 398 3 59 3.31
a) Taken relatwe to the uncorrelated ground state (for an explanation see refs. [6,7,21])_ b) Change m ground-state energy mduced by D CL cl AU results refer to the 0 -c 0 lute.
energes
‘Al
-0 19 -0 37 -0 4s -0 66 -0 89 a) See footnotes
to table 1.
b) Ret
e) Ref. [19J.
As IS evrdent from table 2, the srtuation is considerably different *&an that for even polyenes. In cyanmes doubly excited configuratrons lower the strongly allowed B2 state much more than they do the ground state. As a result S Cl calculations considerably overestunate the transitron energy. On the other hand, D CI calculations of the transition energy relahve to the SCF ground state yield wavelengths significantly lower than the experimental values, particularly for the longer chdmed molecules. One is left then with the problem of developing a semr-empincal scheme that will yield reasonable agreement with experunent for cyanine dyes_ An C CI parameterization has in fact been developed for this purpose [8] but, as might be expected, it yields less satisfactory results for the senes of even polyenes. Clearly, a semi-emprrical scheme appropriate to different classes of molecules must be sought_ ms wa requrre that the dependence of correlation energy on
(m eV) ior cpanmes a) [N(CHs)z-CH-(CHXH),zN(CH& Ground state DC1
[LB].
d) =) e) e) =)
4. Cyanine dyes
results from the mcreasmg unportance (and number) of trlply and higher excited configurations as the size of the molecule increases. Tnply excited configuratlons while conrnbutmg 10 the Bi state have httle effect cn the ground state smce at the Hartree-Fock level all matrix elements between tnply excited configurations and the ground state are zero. The actual value of the contrlbutlon from h&her configurations to the correlation energy of the Bz state can only be determmed from extensive and time consummg calculatlons on the longer polyenes. However, the relatlvely good agreement between the excitation energy obtamed from S Cl calculations and from D CI calculatlons (when the uncorrelated ground-state energy IS used) suggests that the unaccounted for correlation energy of the Bz state 1s comparable in magmtude zo the correlation energy of the ground state [6,7]. Tlus conclusion IS remforced by the fact that S CI and D CJ calculations succeed quite well in reproducmg the experimental relationship between absorptlon maxuna and polyene chain length (table 1). Table 2 Excltatlon
d) Ref
592 4.62 4.08 3.71 3.39
J* Eup. b)
‘B*
s Cl
DC1
SC1
DC1
9.06 6.22 557 5 10 4.64
8 2.5 5 03 3 87 3 04 2.48
606 4.50 3 65 3 08 2.69
591 3.77 2.70 2.03 155
5.53 3.96 2.98 2.39 198
[20]
495
CHCMIC4L PHkSlCS
Volume 72, number 3
chain length be e\phcltly taken mto aLcount_ It 1s mterestmg m this regard that for the shorter molecules in both thr polyenes and cy.mines, the D CI result with respect to the correlated ground state, pIeids excellent agreement with experiment (6 0 2V for butadlene and 4 15 eV for the first cyanme in the
out S Cl and D CI calculations of a series of protonated Schlff bases as shown m table 3. We find. m agreement with rr-elecrron studies already reported [ 161, that the Iowest singlet which IS responsible for the mam absorption band 1s strongly affected by elrctromc correlation Introduced by doubly exctted configurations The lowenng of tis state by -1 eV IS comparable to the magnitude of the eff2ct se2n m cyanine dyes It appears then that as for cyanmes, S CI cakulatlons wIuch use a standard parametenzatlon schem2 [ 10,l l] should not be used as a basis for discussing the protonated Schiff base of retinal It IS possible to use an S Cl param2tenzJtlon schemr appropriate to cyanines [8], or to estmrate transitton energies from more extensive configuration interaction We can obtain an estimate of ths eucltatlon energy m the protonated Schlff base of retmal by assuming that the error in the D CI calculations is comparable m magmtude to the discrepancy (0.43 eV) between the theoretical and expenmental value for the cyanme with twelve n elsctrons. Adding this value to the D CI transition energy of 1.82 eV we obtam Z 25 eV (550 nm), in good agreement with the value of 2.05 eV (=600 nm) obtamed from S CI calculations which were appropriately parametenzed [8] Since methyl groups were neglected m the D Cl calculations, the S CI result of 600 nm seems quite rrasonable
series) This IS the case since for these molecules, doubly ewlted coniiguratlons span most of Lonfigura-
bon space while higher evcitatlons have relatively small effects. By studying the effects of higher coniiguratlons on the longer chained molecules, it may be possible to arrive at an empn-rcal relatlonshlp which accounts for correlation efi2cts m both odd and even polyenes. This wdl be attempted m a subsequent pubhcatlon. The large correlation rnergp of the IB2 state m cyanm2s has an important effect on state ordermg. As can be sern from table 7, the optically allowed tB, state is predicted to be the first sxclted state. This may account for the short radiative llfetunes of cy.mmes [ 131 wh~h obey the Strtckler-Berg relatlonshlp. The much long2r radiative llf2tnnes of the even polyenes [ 14,151 has been attributed to the location of the ‘.A; state below the IBt [S--7].
5. Discussion
As was dtscussed above. the fact that the value of x mu, for protonated retinal Sckuff bases in soIutlon
As mentioned m section 1, In order to construct models for 1112 absorption maxima of visual plgments u IS important to determme a rehable theoretical es& mate for the ekcltatlon energ) of the protonated Schlfi base of retmal To tha end, we have carried Tabk 3 Ilvzltatlon
encrges
(in cV: for proromted Ground D Cl
0
1 2 3 4
-0 32 -0 50 -071 -0 93 -1 14
smtc
15June1980
LETTERS
IS blue-tit-ted relative to thus theoretical estunate IS due to the presence of a counter-ion or solvent dipoles in the vlcmity of the protonated rutrogen [8,9]. Smcea
Sch~lf bases a) [CH2=CH-(CH=CH),,-CH=NHz] -_ I*” ‘A’
E\p
s Cl
DC1
s Cl
DC1
7 6 5 5 4
6 29 4 83 3 98 3 14 3 08
5 16 4.24 3 61 3 21 2.96
4.67 3-47 2 68 2.16 1 82
21 24 61 11 69
a) See footnotes to rable 1 These Ions belong to the C, pomt group. The state ‘A’ corresponds the ‘At state In cyantnes whtlc ‘A” corresponds to ‘BL m polyencs and ‘B2 In cyarunes. b) Ref. [17].
496
b)
4.57 3 83 3 1s 2 90 2 80
to ths ‘Aestate in polyenes and
Volume 72, number 3
CHEMICAL PHYSICS LETTERS
counter-ion is almost certainly present in visual pigments as web, therr absorption maxrrna which range from 430-G IO nm, must be due to additronal chromophore protern mteractrons which induce redshrfts relntrve to the Am__ of protonated Schiff bases in sotution f8 f . Studies wrth artrkud retinals have recently located electrostatic interactrons focalized near the I I-12 double bond of the chromophore that shrft X,, of the protonated Schrff base of retinal to 500 nm in bovnre rhodopsm f17)
Acknowledgement This work has benefited from a grant by the Kultusmunstermm des Landes Nredersachsen for a Jerusdem-GBttmgen exchange program.
References 111 f-f Kuhn. 3 Chem Phls 17 (1949) it98 121 B. Honzg, Ann Rev Phys Chem. 29 (1978) 31. Elecuomc absorptzon spectra and geometry ot organtc molecules (Academtc Press, New York,
[ 31 H. Suzubr,
l967) [4] B Horug., U Dmur, R R. Birge and T-G. Ebrey, J. Am. Chem Sot. f 1980), to be pubhshed 15 J K Scbulten and hl. Karplus,Chcm Phys. Letters 14 (1971)
305
I.5 June E980
[61 b Schulten, I Ohmme and XI. Karplus. J. Chem. Phys.
64 (1976) 4422; 1. Ohmtne, M_ Katplus and K. Schulten. J. Chem_ Phys. 68 (1978) 2298. (71 P. Tavan and K. Schulten, J. Chcm. Fhys. 70 (1979) 6699. B. Homg, A. Greenberg, U. Du~ur and T-G. Ebrey. Bittchemistry 1.5 (1976) 4593. P Blatz and J. Mohler, Btochemistry 14 (197.9) 23B?. Lf. hfuthukamar and LJ. Wetmann,Chem. Phys. &etters 53 (1978) 436 S. Favrot, J.M. Leclercq, R. Robcrge, C. Sandorfy and D. VoceUe, Chem Phys. Letters 53 (1978) 433. 1 Del Bene and H.H. Jaff& J.Chem. Phys. 48 (L968) 1507. N.C.L. Roth and AC. Cratg, J. Phys. Chem. 7g (L974) 1155, C I. Troduell and CM. Meary, Chem. Phys. 42 (1979) 307. B.S. Hudson and BE. Kohfcr, Chem Phys. Letters 14 (1972) 299. J.R. Andrews and B S. fludson. Chem. Phys. Letters 57 (1978) 600. R.R. Buge and B hf Pterce. J. Chem. Phys. 70 (1979) 165. B. Hontg, U. Dinur, R. Nckandu, V. Ba.fo&Nair.Sf.A. Gawtnowtcz, M. Arnaboldt and MI.Motto. J_ Xm_Chem. sot. lOl(l979) 7084. R. McDnnmrd, Chem. Phys. Letters 34 (1975) 130. E.G.F. Sondhetmer, D.A Ben-Efnim and R. Wolovsky, 1. Am. Chem Sot 83 (1961) 1675. S. hfalhotra and Xi. Whrtfng, J. Chem, Sot. fL960) 38L2. P. Tavan and K Schuiten, Cham Phys. Letters 56 (1978) 700
Volume 72, number 3
ON THE NATURE IMPLICATIONS
OF EXCITED FOR VISUAL
ELECTRONIC PIGMENT
15 June 1980
PHYSICS LE-LTERS
STATES
UU CYANINE
DYES:
SPECTRA
Urt DINUR * Department
of Ph] steal Chemrstry.
The Hebrew
Umverstty.
Ierusalem.
Israel
Barry HONK Department of P~~ysrolo~ and B~opl~ysxs. Urbana. Illmors 61801. US4
The Umvers~ty
of fiImots,
and Klaus SCHULTEN hlax-Plarrck-lnstttut
ftir B~opl~~s~kahsche
Chemte.
D-3400
GGttmgen.
West Germany
Rrcetved 22 January 1980; m tinal form 12 March 1980
CNDO/S Cl calculattons ate carned out on polyenes and on cyatune dyes In contrast to polyenes, doubly excited contigurattons have a strong eifect on the first opttcaby allowed ewtted state m cyanmes. Protonated Schlff bases of retmal ate closely related to cyanme dyes, wwh unportant consequences for models of visual pigment spectra and photochemistry.
1. Introduction
The excited rlectrotuc states of ltnear polyenes have been a sublect of Interest for many years. They were mtensrvely studted with Hiickel and free-electron techniques [l] pnor to the development of the PPP theory and have, to some extent, been “redncovered” due in part to their stmllanty to retmal, the chromophore of the vtsual pigments [2]. The earhest theorerrcal studres provrded a satisfactory quahtative descnptron of the spectroscopic propertres of hnear polyenes (see, e.g , ref. [3] ). Polyenilic tons related to cyanine dyes which contain an odd number of atoms have extremely long-wavelength absorption maxima (X,,) wiuch mcrease linearly wtth chatn length. The series of polyenes wtth an even number of atoms are considerably blue-slufted relative to cyanine dyes and exhrbrt an asymptotic versus chain length wluch levels off curve of A,, near 500 nm. * Present address: Department of Chemtstry, Harvard Unmerstty, Cambrrdge, Massachusetts 02138, USA.
In even polyenes, the matn absorption band results from a transition to a Si state and can be successfully described with a semiempttical rr-electron treatment including configuration interaction among singly excited configurattons (see, e g., ref. [4] )_ However, the inclusion of doubly excited configurations (D CL) is required for a proper description of the manifold of “covalent” states such as the IA- state which Lies close to the main absorption bai!d [S-7]. In cont~mst to the even polyenes there have been no D CL calculatrons carried out on odd polyenes such as cyanine
dyes. S Cl calculations can be parametenzed to yield excellent agreement with the experimental h,,chain length curve, but only when an unusually small resonance integral IS used [8]. Thus, it is difficult to obtain a quantitative description of the spectroscopic properties of both odd and even polyenes with a single set of semi-empirical parameters. Uncertainties as to the proper method of carrying out calculations on polyenes have led to serious di.fficulties in the mterpretation of visual pigment spectra_ The chromophore of the visual pigments is the 493
Volume
72, nunlbcr 3
CHEMICAL
protonated Schiff base of 1 I-cn retinal wluch absorbs 111solurlon at about 450 nm Protonated Schiff bases of r2tmal conram an even number of atoms but are nevertheless highly delocalized systems. As such they bear a resemblance tc both even and odd polyenes and 11 IS not clear. a pnon. which set of parameters should be used to descnbc therr spectroscopic properrics Calculations usmg parameters fit from cyanin dyrs yirld values of X,,, m the vlcmlry of 600 m-n [S] The expenmental v~~lue oi450 nrn IS r12wed AS resulting from a larg2 blue-shift due to a counter-ion or solvent dipoles [8.9] Calculations [ 10.1 I] usmg a standard s2t of parameters approprrate to 2v2n polyenes yield values of X,,, near 450 nm and have not m general accounted for possible eff2cts induced by a counter-Ion. Smce visual prgments absorb between -I30 .md 610 nm the uncertamtles m the calculatrons cober the cntlre range of visual plgrnent spectra This mrroduc2s obvious comphcatlons m any attempt to construLt mod& of chromophore-protein mteractlons that are based on semi-empirical calcularrons oi‘electronic spectra Our maJor concern m thus paper wdl be to e\plam the s\clrrd state propertIes of cyanme dyes In particuk. we wdl discuss the ~~11~2sof the failure of standard semrzmplncal methods to provide an adequatc descnptron of rhc spectroscoprc transltlon energy m thcsr molecules To tha end we report calculatrons. usmg the CNDO/S [ 121 method. on polyenes. cyanme dyes dnd the potonat2d Scluff base of retinal Our results demonstrak that electromc correlation has very dlffereni spectroscopic consequznces m polyenes and cyanme dyrs. Moreover. protonated Schrff bases of retinal are found to be closely relatsd IO cyanme dyes suggestmg that semi-emplncal methods cannot be applied m their standard form to the study of visual pigment spectra.
2. Method
of calculation
The Cr\!DO/S method [ 121 was employed m thus work since the cyamne dyes are lomc molecules and as a result have polanzrd u charge drstnbutrons. This and the partrclparron of hereroatoms in the x-electron system would have required an ad hoc parametenzatron had a n-electron method been used. The S CI calculations mcludsd the 50 lowest energy configura49-l
PH\ SICS LE-ITERS
15
June 1980
tions and mvolved both o and IT orbltak (although o-n* excltatrons made only negligible contnbutrons to the mam absorption band). Since all cakulatrons were carried out on planar systems doubly exerted configurations m the CI expansion were restncted to include only 7r orbrtak. The CI matrix reached a dimension of 703 for the largest molecules that were treated. The Ohno formula was used to approximate the two-center repulsion Integrals as 1s required when D Cl calculations are carried out [6] _ Methyl groups w2r2 not Included and were replaced by hydrogens m the calculatrons. Smgle bond lengths of 1 46 A and double bond lengths of 1.35 .% wer2 assumed for the polyenes. For the cyanmes all C-C bonds were set at 1.4 j, and the C-N bonds at 1.3 x Standard bond angles of 120” were assumed throughout
3. Polyenes The electromc sprctra of polyenes have been studred m detail m recent years and it has been found that correlatron effects play an important role m dcterrmmng transrtron energies [5--71 it IS usrful. m order to facdrtate comparrson to cl anmes. to re\121\ a number of th2 conclusions of prcvrous work [5--71 m terms of the CNDO/S results reported m table l. It IS evident that the contnbution to the correlatron energy from doubly excited configurarrons IS dlfferent for the various electronic states. The first elclted IA- stat2 IS reduced m energy (relatrve to the uncor2 eV whde relEted ground state) by approurmately the strongly allowed BG state 1s stabdlzed by onI> O-O.1 eV. the value Increasing wrrh mcreasmg cham Isngth. Thr result IS to place th2 optrcally forbidden A- state below the optrcally allowed Bi The effect o P doubly exerted configurarrons on the ground stat2 1s also grsater than on the Bi state. For 2xampl2, S CI cdculatrons on octatetraene yreld a transrtron energy of 4.29 eV, close to the expenrnental value. The inclusion of doubly excited configurations lowers the Bi state by 0 31 eV but lowers the ground stat2 by 1 eV; th2 net result is a transrtlon energy of 4 99 eV whrch IS clearly two high. In contrast, D CI calculations on butadiene mcludmg ground-state stabrhzatlon yreld a closer fit to the expenmental transrtron energy than do the S CI calculations The dlff2rence between butadrene and octatetraene
Volume 72, number 3 Table 1 Ewttatlon
CHEhIICAL
energies a) (m eV) for polyenes Ground state D CI b)
[CHz=CH-(CH=CH),-CH=CHz ‘A-
-0 52 -0.77 -1 00 -1 14 -1.46
0 1 2 3 4
PHYSICS
15 June 1980
LETTERS
] ‘B+u
B
Exp. c)
SC1
DC1
SC1
DC1
681 6.34 5.85
5 11 4.26 3.73
5 46
3.44
5 08
3 22
548 4.75 4.29 3 97 3.75
5-48 4.56 398 3 59 3.31
a) Taken relatwe to the uncorrelated ground state (for an explanation see refs. [6,7,21])_ b) Change m ground-state energy mduced by D CL cl AU results refer to the 0 -c 0 lute.
energes
‘Al
-0 19 -0 37 -0 4s -0 66 -0 89 a) See footnotes
to table 1.
b) Ret
e) Ref. [19J.
As IS evrdent from table 2, the srtuation is considerably different *&an that for even polyenes. In cyanmes doubly excited configuratrons lower the strongly allowed B2 state much more than they do the ground state. As a result S Cl calculations considerably overestunate the transitron energy. On the other hand, D CI calculations of the transition energy relahve to the SCF ground state yield wavelengths significantly lower than the experimental values, particularly for the longer chdmed molecules. One is left then with the problem of developing a semr-empincal scheme that will yield reasonable agreement with experunent for cyanine dyes_ An C CI parameterization has in fact been developed for this purpose [8] but, as might be expected, it yields less satisfactory results for the senes of even polyenes. Clearly, a semi-emprrical scheme appropriate to different classes of molecules must be sought_ ms wa requrre that the dependence of correlation energy on
(m eV) ior cpanmes a) [N(CHs)z-CH-(CHXH),zN(CH& Ground state DC1
[LB].
d) =) e) e) =)
4. Cyanine dyes
results from the mcreasmg unportance (and number) of trlply and higher excited configurations as the size of the molecule increases. Tnply excited configuratlons while conrnbutmg 10 the Bi state have httle effect cn the ground state smce at the Hartree-Fock level all matrix elements between tnply excited configurations and the ground state are zero. The actual value of the contrlbutlon from h&her configurations to the correlation energy of the Bz state can only be determmed from extensive and time consummg calculatlons on the longer polyenes. However, the relatlvely good agreement between the excitation energy obtamed from S Cl calculations and from D CI calculatlons (when the uncorrelated ground-state energy IS used) suggests that the unaccounted for correlation energy of the Bz state 1s comparable in magmtude zo the correlation energy of the ground state [6,7]. Tlus conclusion IS remforced by the fact that S CI and D CJ calculations succeed quite well in reproducmg the experimental relationship between absorptlon maxuna and polyene chain length (table 1). Table 2 Excltatlon
d) Ref
592 4.62 4.08 3.71 3.39
J* Eup. b)
‘B*
s Cl
DC1
SC1
DC1
9.06 6.22 557 5 10 4.64
8 2.5 5 03 3 87 3 04 2.48
606 4.50 3 65 3 08 2.69
591 3.77 2.70 2.03 155
5.53 3.96 2.98 2.39 198
[20]
495
CHCMIC4L PHkSlCS
Volume 72, number 3
chain length be e\phcltly taken mto aLcount_ It 1s mterestmg m this regard that for the shorter molecules in both thr polyenes and cy.mines, the D CI result with respect to the correlated ground state, pIeids excellent agreement with experiment (6 0 2V for butadlene and 4 15 eV for the first cyanme in the
out S Cl and D CI calculations of a series of protonated Schlff bases as shown m table 3. We find. m agreement with rr-elecrron studies already reported [ 161, that the Iowest singlet which IS responsible for the mam absorption band 1s strongly affected by elrctromc correlation Introduced by doubly exctted configurations The lowenng of tis state by -1 eV IS comparable to the magnitude of the eff2ct se2n m cyanine dyes It appears then that as for cyanmes, S CI cakulatlons wIuch use a standard parametenzatlon schem2 [ 10,l l] should not be used as a basis for discussing the protonated Schiff base of retinal It IS possible to use an S Cl param2tenzJtlon schemr appropriate to cyanines [8], or to estmrate transitton energies from more extensive configuration interaction We can obtain an estimate of ths eucltatlon energy m the protonated Schlff base of retmal by assuming that the error in the D CI calculations is comparable m magmtude to the discrepancy (0.43 eV) between the theoretical and expenmental value for the cyanme with twelve n elsctrons. Adding this value to the D CI transition energy of 1.82 eV we obtam Z 25 eV (550 nm), in good agreement with the value of 2.05 eV (=600 nm) obtamed from S CI calculations which were appropriately parametenzed [8] Since methyl groups were neglected m the D Cl calculations, the S CI result of 600 nm seems quite rrasonable
series) This IS the case since for these molecules, doubly ewlted coniiguratlons span most of Lonfigura-
bon space while higher evcitatlons have relatively small effects. By studying the effects of higher coniiguratlons on the longer chained molecules, it may be possible to arrive at an empn-rcal relatlonshlp which accounts for correlation efi2cts m both odd and even polyenes. This wdl be attempted m a subsequent pubhcatlon. The large correlation rnergp of the IB2 state m cyanm2s has an important effect on state ordermg. As can be sern from table 7, the optically allowed tB, state is predicted to be the first sxclted state. This may account for the short radiative llfetunes of cy.mmes [ 131 wh~h obey the Strtckler-Berg relatlonshlp. The much long2r radiative llf2tnnes of the even polyenes [ 14,151 has been attributed to the location of the ‘.A; state below the IBt [S--7].
5. Discussion
As was dtscussed above. the fact that the value of x mu, for protonated retinal Sckuff bases in soIutlon
As mentioned m section 1, In order to construct models for 1112 absorption maxima of visual plgments u IS important to determme a rehable theoretical es& mate for the ekcltatlon energ) of the protonated Schlfi base of retmal To tha end, we have carried Tabk 3 Ilvzltatlon
encrges
(in cV: for proromted Ground D Cl
0
1 2 3 4
-0 32 -0 50 -071 -0 93 -1 14
smtc
15June1980
LETTERS
IS blue-tit-ted relative to thus theoretical estunate IS due to the presence of a counter-ion or solvent dipoles in the vlcmity of the protonated rutrogen [8,9]. Smcea
Sch~lf bases a) [CH2=CH-(CH=CH),,-CH=NHz] -_ I*” ‘A’
E\p
s Cl
DC1
s Cl
DC1
7 6 5 5 4
6 29 4 83 3 98 3 14 3 08
5 16 4.24 3 61 3 21 2.96
4.67 3-47 2 68 2.16 1 82
21 24 61 11 69
a) See footnotes to rable 1 These Ions belong to the C, pomt group. The state ‘A’ corresponds the ‘At state In cyantnes whtlc ‘A” corresponds to ‘BL m polyencs and ‘B2 In cyarunes. b) Ref. [17].
496
b)
4.57 3 83 3 1s 2 90 2 80
to ths ‘Aestate in polyenes and
Volume 72, number 3
CHEMICAL PHYSICS LETTERS
counter-ion is almost certainly present in visual pigments as web, therr absorption maxrrna which range from 430-G IO nm, must be due to additronal chromophore protern mteractrons which induce redshrfts relntrve to the Am__ of protonated Schiff bases in sotution f8 f . Studies wrth artrkud retinals have recently located electrostatic interactrons focalized near the I I-12 double bond of the chromophore that shrft X,, of the protonated Schrff base of retinal to 500 nm in bovnre rhodopsm f17)
Acknowledgement This work has benefited from a grant by the Kultusmunstermm des Landes Nredersachsen for a Jerusdem-GBttmgen exchange program.
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