n → π∗ Transitions in the azines

JOVRXAL

OF MOLECULAR

SPECTROSCOPY

n --f r*

Tl’hitmorr

C’hemical

Laboraforg,

6, 109-137 (1961)

Transitions

in the Azines

The Pennsgltunia Pennsglz~arriu

State University,

L’niversitg

Park,

Theory and experiment are reviewed and extended for n --f K* transitions in monocyclic azines. Intensities: A good description is obtained for t,he allowed transitions in terms of approximate sp2 lone-pair-orbitals and simple LCAO MO ?r*-orbitals without invoking charge redistribution effects. Previous estimates of t,he pyridine oscillator strength are suggested to be too low, arising from t.he assumption of inadequate band width. Singlet-Triplet Intervals: S-T intervals range from 2,500-6,000 cm-l and are poorly predicted by sp2 lonepair-orbitals. It is suggested from the S-T interval evidence that rehybridization takes place upon n-electron promotion, decreasing the s-character to -0.1 in all the azines. Hand Shapes: The recent conclusions from vibrational analyses that some of the excited stat,es are nonplanar is discussed with respect, to ahsorption and emission features. It is speculated that lack of ?r* -+ n fluorescence may result from this non-planarity, and that fluorescence should be observable in the two-planar cases, pyridazine and s-tetrazine. A notable feature in the solution ahsorption spectra is the very large variation in the strength of the 04) hand over the six azines discussed in this paper. The most promitlcnt vibrational sequence involves a ring angular distortion mode. Transition EnercqiaSs: So satisfactory treatment has been given. Recent calculations are criticized as having physically imprecise empirical parameters. 1. IXTROI)I:CTIO?;

In the dwade 1950-60 our mlderstanding of the electronic t)ransitions due to the promotion of nonbonding electrons in the nzines has reached the stage where certain regulariCes and conclusions are apparent. This development has been to a great part, due to t,hc combined theoretical and experiment,al approach, where experimental study is complemented with detailed theoret,iral considerations, theory and experiment thus guiding rarh ot,her. The purpose of this paper is to discuss t,hesr derclopment,s in three areas-intensities, singlet-kiplet intervals, and band shapes; t,o dram general c,onclusions and predictions; and to suggest further experiment and t,heory. This paper should not be construed as a complete review. For a complete bibliography of n + K* t,rnnsitions through September, 19.57 refer to Sidman ( 1). We restrkt detailed attention to pyridine 109

GOODMAX

110

the three diazines

pyridasine

and to two higher monocyclic

pyrimidine

pyrazine

azines, s-triazine and s-tetrazine

The initial examination of the near-ultraviolet and visible vapor absorption bands of the single ring azines by Henri (2)) Sponer (3)) Uber (4)) Koenigsberger (5) and others led to the interpretation that the long-wavelength band systems were the counterparts of t’he s * I? transitions found in the parent molecule, benzene. Subsequently Kasha (6) assigned these long wavelengbh absorptions to transitions arising from promotion of a nonbonding (n) lone pair nitrogen electron (of u-symmetry) to a a* (antibonding) orbital. Kasha’s assignment was based on the blue shift of these transitions in hydroxylic solvents, on their low intensity, and on the “sharp” appearance of the vapor spectra, relative to ?r + a* bands. To this evidence should be added the blue shift on conjugative substitution (7, 8). This effect is strikingly opposed t,o the red shifts established for r 3 ‘IT* transitions (9). The assignment of the long-wavelength azine bands as n -+ K* transiGons is now generally accepted. This assignment is rigorously substantiated by the very recent rotat,ional analysis carried out by Innes and coworkers (10) on the O--O bands of the previously assigned n - r * t,ransition in pyridazine, pyrimidine, and pyrazine, and by Mason (11) for s-t,etrazine, which show that the elect,ronic transition moment in each case is perpendicular to the plane of the molecule. Innes’ and Mason’s experiment’s show quit’e clearly that these t,ransitions are caused by n -+ a* promotion. II. INTENSITIES

Orgel (12)) Platt (IS), Sidman (1) , and Mason (I/,) have discussed some of the factors entering into the intensity of azine n + ?r* transitions. None of these treatments is complete, however, and an attempt is made in this sect,ion to discuss the intensities in a comprehensive fashion for the allowed transitions. Discussion of intensit’ies of n -+ ?r* transitions is complicated by three factors:

n -+ T* TRASSITIOKS

IN

TABLE OSCILLATOR

STRENGTHS

OF

THE

111

AZIKES

I

AZINE n --t X* TRANSITIONS

-

-

r

C&-

,

Compound

astern’

f Pyridine Pyridazine

’ 0.003b ~ 0.0058

37,000 29,410

Pyrimidine

i 0.0069

1 33,500

Pyrazine s-Triszine s-Tetrazine

I

0.0104 0.0210 0.0042” O.OOlb.”

,

30,515 36,000” 18,560 31,250

117.5”

116”

~ 115.1” / 113.2” / 116’ ~

0.133 0.164j 0.094” 0.164; 0.094k 0.188 0.163 0.231 0.133

g 0.177 0.164j 0.072k 0.13Oj 0.09Sk 0.166 0.135 0.220 0.120

/ i

Theoretical oscillator strength1

h 0.162j 0.073k 0.137j 0.061k 0.191 0.215 0.129

0.37 -

0.0060 0.0083’ 0.0025” 0.00721 0.0015” 0.011 0.014 0.011 0.0066

0.39 0.40 0.44 0.39

-I

-

9 I_ktermincd in cyclohesane solution by Mason (14) II The value of the oscillator st.rength is tentative inasmuch as this band is partially ob scured by an overlapping T -+ ** band. c First II 4 +* band. ct Second II ---t ?r* band. e l~~stimatrd vrnxl for the (allowed ;lr’ * .-~;TL- r* t,ransition. The ent,ire band contains 4n + T* transition (3 forbidden and one allowed). ’ Single-crnt,er, single configuration, benzene orbit,al, constant s-character approsima tion. E JIulti-center, single configuration, perturbed orbital, constant s-character approximation 1~&lulti-center, double configuration, perturbed orbital, constant s-character approsimation. 1Computed from Qh using esperimental Y,,,~~ and the s-character calculated from ohserved Ch’C angles. j rli --) ngexcitation corresponding to the first n + K* allowed t,ransition. 1. ,!1 -) ?r? excitation corresponding to the (unobserved) second II 4 n* allowed t,ransition. 1For references see Mason (14). 111 Computed by nonequivalent orbital approximation. C. A. Coulson, “Valence,” pp. 193-5. Oxford l’niv. Press, Oxford. 1952.

( 1‘I The r-electron approximation breaks down when t’he number of n-electrons in a syst,em is changed; in that the sigma descript,ion is not the same (15) (apart from occupancy) for both ground and excited st,ates. (3 ) The s-orbitals are not the same (apart’ from occupancy) for both ground and excited states (12). (3) There is strong evidence that the excited st,ates of the single ring azines are nonplanar. and to different degrees (IO, 11). Thus Franck-Condon factors may play an important role. Mason ( 14 ) has carefully det,ermined the oscillator strengths ot n ----j a*

112

GOODMAN

“I=2 I-. ,: ‘..

:

..;:‘.$j$.. ‘...,

(nn.$

--_:.;,*

-.. “2

..

:

‘,

‘j:,:...

..y

b

‘?& --:>,;y.

..===.

3yrr2f~.,~~

.-----_I’.( ‘... n-rr .. I 2 ,....‘nimz ‘cz~:a....,‘. ‘..._. ,: nillz “F2 .___...

w 3qooo

(npg)

*. .,

.C

E;~>J *: ---

Yi$~....~W

z T

g 20,000 i FIG. 1. Correlation of low-energy (n,?r*) singlet states in the azines. Heavy lines designate experimental energies. The remaining state energies have been estimated by the method of Ref. 8. A dashed line designates a state forbidden by a dipole transition from the ground state. Brackets designate U states (absence of a local electric dipole in the transition moment).

transitions in a number of azines. These are tabulated in Table I. Features in this tabulation are the general weakness of the bands and the striking dependence of the oscillator strength on the orientation of the nitrogen atoms, encompassing a factor of 20. The oscillator strengths may be discussed most conveniently through the usual dipole length formulation, f = CV&~,where C = 1.085 X 10” if v is expressed in cm-’ and Q is the transition moment integral

In the ground state both the sigma and pi wave functions are closed shells and we = (a,)2(n,)2(a,)“, where gQ refers to the bonding, and write $, = (~,)‘(?r,)~ ng to the nonbonding part of the Z, wave function. The superscript “2” schematically denotes closed shells, and it is understood that’ the wave functions are antisymmetrized. For the excited st.ate both Z and II parts are open-shell and we write Ge = (a,‘)2(n,)(7r,‘)27r*. Both ug’ and ?rg’ have the same occupancy as

n + K* TRAh-SITIONS

0076

IS THE AZIXES

113

1.32

0.96<->N

0.96

-

-* UY6

-

-

a66 -’

1.02

0.144

. . ..<-.$I6

<-Z&o00

0.875

.

1.12

.

0.895

/

_--

NwN

o*93s

N+O

<

<

N-

No.900

N-

N

>

N-N

o-88s

-.

1.043

<;

;yz,,

Fro. 2. ?r*-orbital coefficients. The unperturbed benzene orbit& are given in the first entry. The nitrogen positions shown preserve the symmetry properties of T~,TZ Multiplicative factors, hv, derived from the nit,rogen perturbations, are listed next to each azine. The net coefficient is the product of the unperturbed r* and XV. Where r* has a zero, XV represents the net coefficient. rTu and 7r* , respectively, but are different, wave functions in the sense that ?rOis t,he eigenfuuction of a 2N a-electron Hamiltonian plus a S core whereas z~’ is the

eigenfunction of a 2N + 1 a-electron nonbonding part n, = ,ng’2/ni’.

Hamiltonian

plus a different

Z core. The

114

GOODMAN TABLE

II

EXCITED STATE WAVE FUNCTIONS: SYMMETRIES~AND FORMS Allowed state& Gee

Azine

Pyridine Pyridazine

A2

Pyrimidine

A2

0.95n1%ia2 - 0.3+?$~7?* 0.95ni2nllr2 + 0.3n1%iq

Pyrazine

Ah

ni2n17r2

s-Triazine

E"

s-Tetrazine

BIU

n7r2 ffll?lZTlrZ + 0.05niklxz ni*nl7rz - 0.05n~2ni7r$

A2

n12n+n~%~7r2 + 0.04ni2n?n2%~?r2 ni2n22n&z~a2 - 0.04n~zn~2nz*nza~

-

-

8 Irreducible representation for idealized planar excited states with z axis perpendicular to molecular plane. b Defined through Eq. (4) for Dth . For the diazines n1.i = (2)-l/2(,,, f (T,,,), for s-tetrazine n1.i = $4 ((~2+ (r3 f ~7~f uf,), n2.2 = (~2 + (r3 + (~5f ~6). c States allowed by dipole transition from ground state are in bold face type. d Estimated from the configurational interaction integrals given in Table III. e First entry represents the wave function for the lowest energy allowed state; the second entry, the wave function for the second allowed state. f Zeroth-order configurational interational interaction determined through symmetry.

In the monocyclic azines the low-lying (n, r*) states (Fig. 1) result from the promotion of nonbonding electrons to the normally vacant benzene-like-rorbitals 1r2,2(Fig. 2). If all atoms had equal electronegativity az,$ would be 2-fold degenerate. The nitrogen perturbations split, this degeneracy for CzU and D2h orientations in the first order, but not sufficiently to yield rigorous single configuration descriptions of the excited states, except in two cases (pyridine and pyrazine). In these cases symmetry diagonalizes the configurational interaction matrix (see Table II). Therefore we write for the general case Se = F A&,‘)*(n,J

(?r,‘)27rj*

(.i = 29%.

(2)

If the first two complications listed above are neglected. then 4, = (g)2(n)2(a,)” (that is, the u, n, and qe = c Aij(a)2(ni) (?r,)‘?rj*, abbreviated c Aijnisj* and T orbitals are identical [apart from occupancy] in the ground and excited state). In this approximation the transition moment integral becomes Q = F Aij 1 nirer;*

dr

(j = 2, Q),

(3)

n +

,r* TRANSITIONS

IN THE

115

AZINES

where Ihe third complicating factor has been ignored by assuming the value of unit,y for the rovibrational factor multiplying the electronic transition moment integral. It is clear from Eq. (3) that the electronic transition moment is predict,ed for allowed 1~-+ r* t,ransitions (eit,her ‘W +- ‘A or ‘C +- ‘A) to be perpendicular to the molecular plane. It, is convenient to expend the n-orhitals in terms of lone-pair functions, u,, , through symmetry-generated coefficients: ni = c,, b;,a, itabulat)ed in Table II ). For example, in the case of s-triazine (Ds), flj, j = L&

g

e+~*~J~i~~‘ap)

(4)

where N,, is the number of lone pair centers. The integer j takes on values j = 0, fl, which generate funct,ionx belonging to t#he irreducible representations shown in Table II. The expansion of t,he ?rz,2-orbitals over the 2p, carbon and 2pZ nitSroger A4O yields T2,z = A&

i5i

=$ 1, @iv’3 f e-““;““)pZ,)

where the coefficients A, take into account functions gc in the n-orbital set are hybrid have the form up = &,s,

the nitrogen perturbations. The basis functions, which for sp’ hybridizat,ion

i6)

)

+ &$ZP

formed from the nitrogen 2s and 2p A0 with orientation shown in Fig. 3. We first discuss pyridine in some det,ail in terms oi Eq. (3). Reference to Table 11 shows t,hat inasmuch as A02 = 1 and A02 = 0, the single configuration IJ~ = (~j”(n)(T,)27r2* is a good description of tjhc excit,ed statme. Then if we resolve pz, as is shown in Fig. 3, int,o p,, and pn componcnt,s along and perpendicular, respectively, t,o the

b/ /

e/2

F c

z Y

X

814

pa-

\ v

s

p* F~ti. 3. Resolution

of p, into d and q components.

For

spz hybridization

0 = 120”

116

GOODMAN

N-C

bond, Eq. (3) becomes, assuming the u orbital is sp2, slxekp,,

dr

- X2

slxkep

22

dr

+9 spq

xkpz, dr

2

)I

.

(7)

In obtaining Eq. (7)) the identity apparent from Fig. 3, p, = tip, + fi/2p, , has been used. It is apparent that the integral J p,,,zekp,, dT does not contribute to Q, inasmuch as p, is antisymmetric but both xk and p,, are symmetric to reflection through the plane determined by the N-C bond and the Z axis. The A0 coefficients in 1r2, Xl/d on the nitrogen atom (atom 1) and X,/a on the adjacent carbon atoms (atoms 2 and 6) have also been used. Finally, transition moment integrals between AO’s centered on nonadjacent atoms are neglected because of their smallness. Evaluation of the atomic transition moment integrals yields, in terms of A and B integrals (16))

s s s

160 (PN, PCLN~)~” s1 zepZl dr = y 43 (UN*+ WVJ6 s1

zepz2 dr =

p,, xep12dr

(&Np

C)5’2 1/3 R6 [A&$, 6264

+ IMA2

=

hvd2 2048 + MA2

-

Ad

+ BdAo

R6 [As(& -

Ad

- B2) + As(&

- &)

-

Ad

+ A&

+ B2L40 -

Ad

- Bo) + A1(B2 - Bd

+ &Lb

- &) + &Lb

-

A211

+ AI& -

-

&)

A211,

For R = 1.35 A and Slater values of PN and pc (1.91 and 1.56, respectively), and assuming identical screening constants for the nitrogen 2s, 2p,, and 2p, orbitals (XN = 3.82), s

s1 zepZl dr = 0.756 atomic units

s s s1

zep,, dr = 0.045

p,, xepZzdr = 0.047.

The coefficients X1 and XZ take into account the nitrogen perturbation on the a*-orbital. If the pyridine nitrogen atom had the same electronegativity as the benzene carbon atoms (and bond distances were all the same) X1 and X2 would equal unity. Since nitrogen is more electronegat,ive than carbon, X1 < 1 and XZ> 1. It is difficult to estimate the precise magnitudes of X1 and X2 , but they are not very different from unity. A realistic estimate by the method outlined in (8)

gives X1 = O.%, X2 = 1.:32. Finally, it should be noted that, the expression for Q given in Eq. (7 :) should, strictly speaking, be multiplied by a factor (1 - ,\I)-““, taking into uwount the overlap integrals bet,ween p, orbibals. For X = 0.25, this fac.t,or’s magnit!ude is only 1.1.5; hence we omit, it’ from furt,her discussion. Slrbstit,uting in Eq. (7) yields a calculated (s = 0.22 a.~., which gives (utilizing the wperimental frcquenc’y) a calculated .f = 5.1 X 10P”. C’omparison of the cxlculntcd value with the espcrimeutal value given in Table I shows that, the calcl&~ted vallw is too high by something less than a fwtor of two. Inasmuch a.~ the Iradiug t,crm, f sr zep-_, dr, calculated t.hrough Slat.rr orbitals is expected to he high (for csamplc Hartree-E‘ock frmctions lead t.o a smaller leading term ( 19 I)~ this discrepancy is not too disturbing. In passing we note that if n-e neglwt t,he I wo-wntrr transition moment integrals in Cl. (7 ) wc romputc ,f =: 6.0 X 1OF’. 1~~~ can t,hereforc conclude that the low intjcusity of the obserrcd pyridine ‘~1---) g* transition is primarily dlu! to the smalhwss of t,he atomic transition moment 2~ --j 2z, in nitjrogen. This resuhs basically from the low spatial overlap of the nitroget] 2s- and 2p,-orhit’als. A11 additional factor of -,lO -’ in the intensity results from the worbit)al having only about J d s character and from the dclocnlization of the ?r*-orbit>al over 6 nt,oms. Thcw simple conclusions regarding pyridine are capable of rst.ension to t.hc higher aziltcs. If we regard the c-orbit.& as being identical in all the axiltrs, then the owillntor strength for any n * a* transition is controlled entirely t)y the d(%ailcd nature of the drlowlization of the &orbital over the carbon and nitrogen at,oms of t#he azine, the transition frequency, and t,he effect of “loading” the molrcwlc with a number of nonbonding centers. In pyridinc the nitrogen perturbation has lit#tle effect’ on the coefficienb (X1 = O.%) of the 2s + 2p at omit transition moment, in 7r*. If we generalize this pointj the effect, of the nitrogen pertlnbations on r* may bc ignored (A,. = 1) and g.?,, are equal to the benzrue furwtions given in Eg. (5). The roeCent of p, is thus determined by the rot,ationsl transformation properties of r2.5 and shorn the pronolmccd orientation depcndcnre given in Fig. 2. We not,c that. the leading source of error in arriving nt the ~ocf&ir~nt of p, through this approximation is that, the single ronfiguration dwwiption of the (tl, K*) stat?, valid in pyridinr, is not valid in thr gcwral caw ( CUlr ,infra’) . 13~ making the following 6 assumptions: (i) u,, is the same for all nit,rogen atoms in all the azines; (ii) neglect all transition moment integrals other than J s1 zopZ1 dr ; (iii, neglect all overlap integrals; (iv) transition energy factor in owillator strength is assumed constant; (v) assume the carbon and nitrogen atoms have identical r-orbital elcctronegativity; (vi) describe escitrd states by single configurations, the ‘n + r* trsnsitjion moments, Q, for any azint wnsidcred here become

118

GOODMAN

(1)

(I,21 (I,31 (I,41 (1,3,5) AZINE ORIENTATION

(1,2,4,5)

FIG. 4. Relative oscillator strengths of the azines. The oscillator strength of pyrazine has arbitrarily been taken equal to 2. Solid lines: calculated oscillator strengths on basis of simple loading and delocalization model (assumptions i-vi). Dashed lines: oscillator strengths by full calculation. Upper line is for lowest energy allowed transition. Lower line is for second allowed transition.

Qnj +

1~2= (3N,)-1’2

Qnj +

~2 = (3Nn)-“2

i (8)

s

0 is the smallest central angle between any 2 nitrogen atoms [0 = 0 for pyridine, r/3 for s-tetrazine]. If we set the oscillator strengt,h of pyridine arbitrarily equal to 1, then we obtain for the lowest energy allowed n -+ r* transition the oscillator strength orientation rule where

(l):(o):(m):(p):(1,3,5):(1~2,4,5)

= (1):(3/2):(3/2):(a):(3):(3).

(9)

This intensity rule is analogous to the Sklar-Forster relationship (18) for the lowest energy ?r -+ 7r* transition in the same series of compounds. For comparison, the Sklar-Forster rule is (1) : (1) : (I ) : (4) : (0) : (4). The comparison between prediction and experiment is shown in Fig. 4. Here the oscillator strength ratios are based on pyrazine rather than pyridine because of the considerably higher accuracy in the pyrazine experimental value. It is clear that the main qualitative trends in t’he experimental intensities are accounted for by the de-

n + T* TRANSITIONS

IN THE A7,Ir\jES

119

localizat,ion and loading factors. However, significant anomalies are present: The total observed orientation effect encompasses a fact’or of 20 versus a predicked factor of 6, and the n -+ ?r transitions in s-tctrazine are far weaker than predicted by Eq. (8). We now discuss -the six simplifying assumptions leading to Eqs. (8) and thus t.o t.he simple orient,ation rule c.9). The most significant! of these is (vi j, approximat,ion of the two-configuration wave functions of Eq. (2) by a single configuration. Removal of approximat,ions (i)-(v) only yield minor refinements. Thus the> CKC and CNN angles (Table I) range from 113” in s-triazine to 117.5” in pyridine, yielding for the s characters of the lone-pair orbit,als (Table I) 0.370.14 instead of the const,ant, value assumed. Inclusion of thr two-center transit ion moment, int.egrals lower all t.he calculat,pd oscillator skengths by 20-30 5, hut change the rat,ios by lesser amount,s. The overlap int,egral het~mrrn adjacent, lone-pair orhitalx is est,imated as 0.074.10 (8, 1,/t) and therefore overlap effects modify the intensities in only a minor way. The assumption of constant transitioll energy is important, in only one case--the long wavelengt,h (18,000 rrn- ‘) b:and in s-tctrazine. Utilization of the act.ual transition enrrgy in this WW, rcduccs the predicted intensity by .I,<, and places this case in better agreement. with experiment. Estimates of the effect of t,he nitrogen perturbat,ions on t,hc P* orbit,als are given in the orbit,al diagrams in Fig. 2. In sornc’ cases the nitrogen c*oefficients are wfliciently changed t,o produce a sizeable correction to the int#ensit,y ratio. In all wscs except pyridazine and the lowest, energy transition in s-t,et,razine t,hc nitrogen coefficient is reduced, lowering the contribut,ion of J slxep,, c/r to (1 and hence decreasing .f. For pyridazine the nitrogen coefficient is increased and hence so is f. For the long wavelengt,h s-t,etrazine transition the nit’rogen perturbat,ion produces no change in the p, orbital coefficients and f remains unaffected. Reference to Table II shows t.hat. in only two cases, pyridine and pyrazine. is the single configuration approximation rigorously justified by symmet’ry. In a third case, s-triazine, t,hc degree of mixing of configurations 7111r2with ‘niat is (dontrolled cbntirely by the CT3generated degeneracy. This “zerot,h-order” configurat)ion inttmction has been included in the orientation rule (9). The three remaining azines: pyridazine, pyrimidine, and s-tetrazine, have two configurations of t,he same symmetry allowed by a dipole kansibion from the ground stak. Thcst are the B? configurations nlaz and nir9 in pyridazine and pyrimidine and the Bl,, configurations in s-tetrazine, nl?rZ and nir2 . In these cases then we need to solve t.he rigenvector equat,ion (P - ~1) (A ‘, = 0 of rank 2 with 1’1’2=

s

(0)2(11j)(Tg)2T*

C P.V

;:1(a)*(ni)(7r,)‘7r2d7 (IO)

120

GOODMAX

The sign of PI2 is important inasmuch as inspection of Fig. 2 and Table II shows that the two terms of Eq. (3), s nj zek TZ d7 and J n, zek a2 dT, are directed in the opposite sense. Hence if ~12 > 0 the transition moments will be in phase for the lowest energy transition and the intensity will be reinforced. If on the other hand PIZ < 0 the t’ransition moments will oppose each other and the intensity will be reduced. fiubstitution of the expressions given by Eqs. (4) and (5) for n and r* in Eq. (lo), and imposing the differential overlap assumption (46), yields (njaz 1nim)

= -K/4

&

(nznj I mm)

= -J/4

ti

Pa = (J - X)/4

ill>

&L

where

The sign of PI2 is clearly given by the sign of J - 2K. The atomic integrals entering the calculation, J - 2K, and PI? are all tabulated in Table III. As is the case of the transition moment integral, the low spatial overlap of n and n orbitals keeps the configurational interaction integral small even though J - 2K is sizeable. The terms J and K themselves contain large integrals (Table III), but the nodal pattern of 1r2and 7~ causes extensive cancellation.’ For s-tetrazine PI2 < 0, for pyrimidine PIZ > 0, and for pyridazine PI2 N 0. In the case of pyrimidine, the lowest energy (n, n*) state is predicted to partially lose its nodal character between the nitrogen atoms [as shown in the diagram

ml,

(I) qE =

ni7Q

$e = 0.95 ni 7r$+ 0.3 721~2

Approximate distribution of promoted energy n + ?r* transition in pyrimidine.

n-electron

among

pz orbitals

arising from lowest

with the consequence that there is considerable enhancement in the predicted intensity. The wave function coefficients Aij given in Table II were calculated using the observed state energies for the diagonal elements of the perturbation matrix in the case of s-tetrazine, and semiempirically calculated ones (8, 14) in

1 Such cancellation also takes place in the case of still higher order C.I. interaction of the low-lying configurations with nj?ra).

(e.g., in the

IL --) K* TRAXSITIONS

IK

TABLE

THE

1’1

AZIXES

III

COXFICCRATION INTERACTION INTEGRALS" COlTlpOUnd

(aa I 22)

X0 integrals (uu 133)

(VU j 44)

K”

ev

J”

J-2K

PI?‘ ev

ev

Pyridazine Pyrimidinc

7.780 6.844

5.03e 5.036” 5.573c

3.648 3.65

1 .3-l 1.46

2.55 3.61

0.13 -0.69

0.02 -0.10

s-Triazinr s-Tetrazine

6.S44 7.780

5.573 5.573’ 5 ,036”

3.65 3.90

1.1s 1.32

4.16 2.25

-1.SO 0.39

-0.30 0.06

a Xotation: (olo, 1psvpzv).The integrals (OU 111) = 12.075 ev and (~1 1a 1) = 1.472 ev are common to all cases. iidditional small integrals are (u, 1 / 022) = 0.048 cv and (0~1 1ca3) = G.017 ev. k’ Nit,rogen-carbon interact,ion. c ?jit,rogen-nitrogen interaction. dK =

- cr:]

ia,p,,

) o,p,,jxs,xT~

p J = - C” c* Xs&b,a, I P.~PZbIIN. f PI: = “(r/,x2 j ,ni~) - (nin, 1 ?rzas) = (J -

2k’)/4&.

the other two cases. The large separat,ion of t’he two states in s-tetrazine keeps the mixing of configurations in this case small. The complete predictions obtained by removal of assunlptions (ij through (vi ) are shown in Fig. 4 and Table I. The principal discrepancies between theory and esperimellt are in the t’n-o ortha azincs, where the predicted oscillator strengths arc considerably higher t,han those observed.” It is difficult t,o give a precise discussion of the effect of reorganization of the \- and T frnmcworks on the int,ensities. Turning t’o pyridine as an example of Urge cdhxge reorganization, Eq. (3) becomes, in terms of the wave function (2 ),

The effect of the additional a-electron is to slightly expand and polarize the co orbit& and, as a result of t,he decreased screening engendered by the loss of a lone-pair electron, to contract and rehydridize t’he worbit’al. Since the change in screening constants, p’ -P, is small (only 0.12 for the nitrogen orbit’als) (19) and since t,he magnitudes of the one-center overlap int’egrals between initial and final smte AO, 8, = J (2s)(2s’) dr and S, = J” (2p)(2p’) dr, depend only upon 1 = (fi’ -p)/(p + p’) (for t = 0.1 S,, X, > 0.95), the overlap integral 2 The large discrepancy for the second n + ?r* transition in s-tetrazine (f predicted = 0.007, .f observed = 0.001) may be partially due to the uncertainty in the measurement arising from the overlapping strong r --) K* band.

122

GOODMAX

between the initial

Z-electron distribution and the final distribution, j” (c,)’ (~9” dr f (n>(n’> d r, is very close to unity (consistent with tN = 0.03-U.04, tc = 0.01&0.02). Regarding the n-orbital hydridization, in the excited state the positive charge at the nitrogen atom will lower the 2s term value relative t,o 2~; consequently the bonding u’ orbitals will tend to higher s character, and the nonbonding orbital to higher p character. For small increases in p character J nn’ dr - 1, since if a2, (Y” and p”, PI2 represent the s and p chracters in the ground and the excited states, J nn’ d T = CYQI’ + p/Y where or’ < (Yand 0’ > p. Similarly, changing the C 2p, basis functions t,hrough t,he extra screening from the 1r2electron has negligible effect on S, . The calculated value of J (T~)‘(T~‘)~ d7 = 0.97 from this effect. But re-evaluation of the 2s --+ 2p atomic transition moment integral using the less screened 2~~ yields 0.68 a.u., versus 0.76 a.u. utilizing 2pnr . The change in a-MO through construction of a new Hartree-Fock Hamiltonian for the excited state is more important,, yielding an overlap integral of -0.8 between the initial and final ?r charge distribution, derived mainly from the increased electron flow to the most attractive site--the N atom (201. The discussion given above differs from that, previously given (la). It concludes that while charge reorganization effect,s do significant,ly influence t.he intensities of azine n --f 7r* transitions, the reduction in intensity through t’hese effects is estimated to be no more than a factor of 2 in the case of pyridine, and considerably less in the remaining azines. This may account for the somewhat low intensity of pyridine (Fig. 4), but see Section IV. We conclude that wit.h the possible exception of pyridine, the intensities of n 3 ?r* transitions can be understood with considerable validity in terms of the ground state orbitals. At the present time no careful study of the Franck-Condon factor has been published for azine n --+ ?r* transitions. Because of the different geomet,ry of the excited states in the various azines (10, 11, 21) such a study is needed for a full discussion of the intensities. A few remarks will be appended here concerning t’he ortho azines. It will be recalled that these are the cases where thr observed intensities are anomalously low. In the ground state, as shown in the diagram (II), “T

-t+

B--B

nl

1‘ 1.08Y h c---F f 0.93r

i5

t&5 r

---"r

;;

+I-& Pyridazine

=Tior

(II)

: 0.8611 0.931

+I=~ s-Tetrazine

J

n + r* TRAYHITIO?iS

IN THE AZINES

123

both antibonding and bonding n orbitals are occupied, leading to a lone pair repulsion (8) of 27 [ - 1.08 + 0.931 = -0.3~ for pyridazine. The value of y, the a-orbital exchange integral, has been estimated (8, 14) as -0.75 ev, so that in the ground state the total lone pair repulsion is of the order 0.25 ev, and t,he N--n’ bond should be slightly long. Promotion of an antibonding electron (from ni) removes the lone pair repulsion and leaves an N--n’ bond formed from t’he n orbitals with bond energy = 0.78~ - 0.6 ev. Thus the X--N bond should undergo a sizeable contraction in the excited stat’e. As a consequence of the change from the lone pair repulsion situat,ion in the ground state to the X--N bonding situation (formed mainly from the r_,, orbitals) in the excited statme, the p character should increase in the excited state over and above that expected from t.he positive charge engendered by n ---) A* promot,ion. In the ot,hcr ~,non ortho) azines no such radical changes in bond distances due t’o bond order c+fects (Sect,ion IV) are expected. In t’he long-wavelengt,h s-tetrazine excitation, nz --$ ~2, the situation is exactly similar: t,he ground-state lone pair repulsion is 0.61~ - 0..5 ev or 0.25 ev per K-N bond, the excited stat’e n orbital stabilization is 0.477 - 0.3 - 0.4 ev or O.l.i0.2 ev per N-N bond. The low intensities in these ortho compounds may be due to t,he combination of a large> changcb in n-orbital hybridization (causing j n n’ d r < 1 j and a sizeable shortrning of the Y-N bond length. Further studies are clearly needed. I’inallv, mention should be made of the contribution of the forbidden (‘\I’ c i ad) transitions to the intensity of the (allowed) transitions. With the exception of pyridazine, all the higher azines have forbidden ‘I+’ +- ‘A transitions at approximately the same energy as the lowest energy allowed ‘W +- ‘A transition. .\lhrecht’s t)heory of the intensificat,ion of forbidden transitions ( 22’) wrms part~iculnrly applicable to -the forbidden azine ‘II’ - ‘ii hands, and work along these lines is needed. III. SINGLET-TRIPLET

INTERVALS

The obwrvat’ion and assignment, of azine n * ?r* mult,iplicit,y forbidden (singlet’-triplet ) transitions is quit,e recent, the best st’udied molecule being pyrazmr’ B-26). Verv recently, lowest, energy n + a* multiplicity forbidden t,ransitions have been observed in pyrimidine (27)) pyridazine (68)) and s-triszinc ( 2.9) (Section IV). The ensuing singlet-triplet, intervals (Table IVj range from ~500-6000 cm-’ confirming an early prediction of Goodman and Shull (30) that (n, r*) S-i intervals in heterocyclic molecules are sizeable (lo”-10’ cm-‘) for t)he 15’ states. With the usual assumpt,ion of identiral spatial wave funct,ions (lack of spin polarizaGon) and identical molecular geometries for the singlet. and triplet stat,es tht> ,+‘-7’ interiral, ‘E - ‘E;, becomes ‘E -

‘I? = X,,*,J

+ A,, ,

(13j

123

GOODMAN TABLE

IV

SINGLET-TRIPLET INTERVALS I

Observed frequencies

(cm-l)

I

‘E-SE observed

(cm-1 1

Pyridine Pyridazine Pyrimidine Pyrazine s-Triazine s-Tetrazine

34,430 26,790 30,930 26,560 30,610 31,574" (26,000) (32,350)"

/ 17,880

,_i_i_

(23,500) 28,300 26,530 (26,400)

Trih

t

T

ass:gnment

<4800 (3300) 2630 4065 (6000)

4200 3900 2950 4100 6400

<5.9 2.8 2.54 2.40 3.0

/-‘-

8 Observed in isopentane solvent. References: Pyridine (44), pyridazine (I$), pyrimidine (27), pyrazine (f4), s-triazene (21)) s-tetrazine (14). b Assigned by Brinen (21): as the 1.4: t ‘A (allowed) transition. c Assigned by Brinen (21) as the ‘E” + ‘A, (forbidden) transition. d Observed in isopentane solvent. References: pyridine (33), pyrazine (231, s-triazene (29). e Assigned by Evans (33) as the 3_41+ 1.4,~ * r* transition. Hence the ‘n ---’ **(S --j T’) transition lies at a higher energy. f Observed in isopentane-methylcyclohesane glass corrected for rigid media effect escept for s-triazene which was observed in EPA glass wit,hout rigid media correction. References: Pyridazine (28), pyrimidine (27), pyrazine (24), s-triazine (29). g I,ifet,ime (0.5 set) is consistent with a forbidden transit,ion. See Footnote c. h Computed by Eq. (15) assuming 0.10 s character for the ereit.ed state tr-orhitals and an exchange integral appropriate to s4’~$“3N (Fig. 5).

where Al3 takes into account the multi-configurational form of the wave functions. Because of the highly polar nature of the (n, ?r) states the spin-polarization assumption may be less valid than in the ( a, r*) case. Parks and Parr (31) have discussed the spin polarization problem in det,ail for t.he formaldehyde n ---f K* transitions. Unfortunately the simplifying assumption leading to Eq. (13) would be only moderately valid in that, case. Further theoretical studies are needed in this area. We discuss first the application of Eq. (13) to the TV (B,) states of pyridine. In this case the excited states are described by a single configuration (Table II), and the singlet-t,riplet interval becomes ‘E -

3E = ~x~[a’2(s’z’ / s’x’) + p’2(.dz’/ x’x’)],

(14)

where (s’z’ 1s’z’) and (~‘2’ 1x’x’) are exchange integrals between t,he excited state 2p, and 2s, and 2p, and 2p, nitrogen orbitals, respect,ively. In arriving at Eq. (14) through the expansion of K,,, tZover atomic intgrals the differential overlap approximation (17) has been utilized. The magnitude of the exchange int,egral (sx 1sx) is related t,o the unpairing

n ---f ?i* TRhh-SITIOTS

IS THE AZINEc;

125

energy ($s?) of a 2s orbital and is in the vicinity of 3-J ev. The magnitude of the integral (.rz j J-Z) is related to the unpairing energy of 2p orbital and is 2 1c\;. Hence, if we assume that the amounts of s and p charact.er, a” and in thr excited state n-orbital correspond to sp2 hybridization, w B‘*, respectively, calculate ‘13 - “f3 2 1 - 2 eV (recalling X1’- 0.9 [E’ig. 21). Evans (33) has ol+ served a well-defined singlet, 7’ triplet absorption in pyridinc (Table IV ) convspending to a S-T internal of 4800 crtP. Howe~cr, he has assigned this trattsit,ion i through solvent’ perturbations) to a 7r - r* orbital promotion. Hctwr the singlet ----)triplet transition corrcspondittg to the lowest energy ?t 3 g* promotion must lie at a higher energy. l~urther, it is not likely in light of the well-resol\-ccl twrds obserwd by Evans that the II - I* ttxxit.ion underlies or signifkutttl~ overlaps the k -+ R* transition. Therefore it is very probable that the n 3 K* transition is at considerably higher energies and tha(. the 1%+ T* S-l itttw\.;tl is IIO more than ,I$ e\-. It is not likely t,hat, the estimated one-center exchange terms are far off. ‘I’hcrrfnre, the large discrepancy between prediction and experiment for pyridiw is st,rong cClcnce for a change in n-orhital hybridization upon excitation. .I significaant dwreaae in s chatxcter is required: (We should keep in mind, howe\-or, that, t.his cwnc*lusiott is predicated upon the :wsttmpt.iott of identical spatial f~m(ations for both t,hc singlet, aud t’riplrt, stat,es. j The degree of s-p hybridizatiott may be determined from an ac*curate knowledge of the IJVOexchange terms. L1tttto ( 3,; ) has evaluated the one-center nitrogen cwhange integrals from the Skinner-Pritchard yalence state energy scheme (:?6). In terms of the Slater(‘ondon G c*o&cients, (SZ ! sx) = G1 , ( .I’Z1xx) = :-jG? . Skitmcr and I’rit(*h:trd have given two sets of G valucsPottc for LV’+)which approximates the exited state of pyridinc. Here G1’ = 27,500 cm-’ and G,’ == 2.3% cm-‘. The ot,hcr fat _VCS”‘“~‘~“), eqrtivalrnt to a ground state sp’ nitrogen atom. Here G, = 2:i,>O.i (‘111PI aid G, = 2045cm-‘. rl?hc calculated magnitude of (~‘2’ 1u’z’) as a function of (Y’hybridization is shown for both :V and I\i’, in Fig. 5. Only for very lonvalues of the s character (a” - 0.1 ) is the calculated S-T itttewal rcdttcrd to reasonable magnitudes. A sitnple extension of t,he singlet, triplet inter\-al calculation to the etttirc set. of aziues wn be made by assunling t,hat to a first approximation the nitrogcatt hybridizat.ion in t.he excited stat.e is identical for all the azines (s rharactcr = 0.10). With this assumption the wnt~rolling factor in the $2’ intervals over :t series of azines is the delocalization factor (8), so that, ‘E-

3E = &xsP( C’X’1dd j + i118,

(131

where aj, is the benzene a*-orbit’al i10 coefficient (Fig. 2). The experimental and predicted S-T intervals are showtt in Fig. 6 and Table IV.3 The intervals 3The predicted S-T interval for pyriciazine in Ref. 8 is in error.

126

GOODMAN

,

I

I 0.1

I

I

I

0.2 e& CHARACTER

I

I

0.3

I, 0.4

I

I

0.5

-

FIG. 5. Dependence of one-center exchange integral (uz 10%)on s character of m-orbital. Solid curve: (a’do 10’2’) based on Nf valence state. Dashed curve: (CZ 1OZ)based on neutral N (s+P’3) valence state.

predicted from Eq. (15) are in qualitative agreement with the observed orientation effect. The energetic effect of configurational mixing is important in only one case-s-triazine, where the effect of CI is to increase the predicted S-T interval significantly (A13 = 2k,,,, and 2k,,,, for the AZ” and lowest energy EN states, respectively [36]). In passing we note that the configurational interaction integrals (Table III) are reduced in magnitude upon reduction of s character, so that the single configuration descriptions of the excited state are probably somewhat better (with the trivial exception of s-triazine) than estimated in Section II. The assumption of constant hybridization in the excited state is probably not as unreasonable as it might appear at first thought. We can speculate that an important cause for rehybridization is probably the reduction in the screenings of the nitrogen and 2p, and 2s orbitals by the loss of a CT electron with - f$s and -35 p, character. This reduction in screening is common to all t,he azines. In

‘n +

x* TRAIWITIONS

IN THE

137

A%ISES

the different azines the variable factor is the partial compensations in screening of the 2s and 2p, orbitals by the increased p, density. It is not unlikely that p,-s and p-p, screening is small compared to 2~2s and 2p,-2p, screening. A more fundamental test of our assumpt,ion of constant hybridization in the excited states is provided by recalling that the intensities also vary with the delocalization factor. Hence, if the hybridization is indeed constant vmnx (‘E-

3E) N,/j -

constant

(16)

This relationship, using observedvalues forall quantities, is borneout in TableIF’. In summary: in contrast to the intensity discussion, where a satisfactory account of the oscillat,or strengt,hs could be given in terms of the ground state orbitals, the S-T intervals are rationalized only by assuming, upon excitation, a radical readjustment of the lone pair orbitals. Their excited form is est’imated as -0.1 s character, but this value should be regarded as tentative. IV. BAND

“SHARP"

ABSORPTIOS

SHAPES

SPECTR.~:

The first, measurements on t,he n -+ r* absorpt,ion bands of the gaseous azinrs were made by Henri and Argenot (W) and Sponer and co-workers (37) (pyridine‘) . Halverson and Hirt (38, 2626) (pyridazine pyrazine), Uber (4) (pyrimidine) Hirt, et al. (t39) (s-triazine), Iioenigsberger and Vogt, (5 j and Curtius et ab. (40) (s-t'etrazine) .

I ,ooc I

(1)

I

I

(42)

AZINE

FIG. 6. Singlet-triplet intervals Eq. (16). Quarter circle-observed (n,rr*) S-T intervals.

I

(L3)

I

1

(1,4) UP,51 (G&4,5)

ORIENTATION

in the azines. Solid line: calculated S-2’ intervals, by (r,x*) S-T interval (see text). Full circles-observed

128

GOODMAN

5510 FIG. 7. Rotational [after Mason (1111.

structure

5515

WAVELENGTH (ii) of s-tetrazine O-O band,

5520 showing

prominence

of Q branch

More recently Innes (IO), Mason (11 , ,$l ) and Brinen (21) have obtained evidence, from vibrational and rotational analysis of the vapor spectra, for the geometries of the excited states. A characteristic feature of n --+ ?r vapor phase absorption spectra (involving an allowed transition) is the atomic sharpness of the individual vibrational bands. The rotational analyses carried out by Imies (10, 50) and Mason (11) indicate that the sharp lines are due to narrow and strong rotational Q branches, as illustrated in Fig. 7 for the G-0 band of s-tetraxine. This in turn is a consequence of the small change in the average moment of inertia in going from the ground to the excited states. The vibrational analyses of the vapor spectra indicate a complex vibrational envelope with several or many normal vibrations excited. A feature of unusual interest is that the most prominent vibration is always one of the totally symmetric ring angular distortions v6a , vg, or v12(see Table V and Diagram III). This can be clearly seen in t’he hydrocarbon solution spectra (Fig. 8) where these are the only resolved vibrations. In ?r --f ?r* transitions in these and similar molecules, prominent totally symmetric vibrations are ring stretching modes such as v1 (,@?). Since the ring stretch vibrations do not appear as prominently in n 3 ?r* transitions and since there seems t,o be no correlation with the T* bond order (Fig. 2), one is led to the conclusion that the principal electronic factor det,ermining the shape of the excited state is the g rehybridiaation (Section III). Perhaps this conclusion is not surprising in view of the fact that none of the six bonding a-electrons have been promoted. Other prominent vibrations in pyrazine, pyrimidine (10) and s-triazine (21) are the “chair-form” modes v4 and ~16(IV). The reason for the prominence of these nontot’ally symmetric out-of-plane vibrations must arise from the electronic wave function having some chair-form character, and therefore pyrazine, pyrim-

n +

7i* TILA3XITIONS TABLE

Benzene”

Pyridazinee Totally

YE:, (el, 1 % V;‘,ib, ,‘,I VIZ V(:”(ez,

V

VIBRATIONAL FREQUENCIES IN AZIN~: IL 3

PROMINENT

606 1010 1178

)

665 373

-

Pyrimidinec symmetric

PyrazineC

583

1015 -

_ 1220

703 405 -

s-triazine~l

675 1132 1140 -

1106 Konplnnnr

Y:’ ih, J Y,’ Y&,fcq,) &z

r* ‘I’RANSITIONS~

-

s-tetrazine”

vibrations

679 530 1071

-

Y!S,

It’!)

IN THIS MINES

725 605 _. > 1520

vibratious (ha,)257 477

(a?)344

(8)3-u 488

-’ -.

b T&en from Ref. 47. c T:tken from Ref. 10. d Taken from Ref. 21. e Taken from Ref. 41.

t

1)6~

le2,)

Wa,,)

idine, and s-triazine are evidently nonplanar in the excited state. It is noteworthy that t,he polarization of these vibrational bands is expected to have an in-plane component. On t,he other hand, Tincher and Imles careful study of pyridazine (10, 52) vapor spectra reveals no prominent, out,-of-plane vibrations, and yields the conclusion that this molecule is planar in the excited electronic stat)e. The discussion in Section I indicates that this o&o azines may have a compelling reason to remain planar in an excited state arising from t,he excitation of an antibonding n-elect8ron. Konplanarity would reduce the strength of the p,-p,, bond by lowr-

A I

I

I 400

I

I

I

I (I,31

-

I I

I

I

k w 0

-

? 0

(I,41

ceook 8

g400 I=

-

x ii w Q e -I

0. 750-

I (1.3.5)

ii

w 0

-

2 E z 2 E s

CM-’

x 10-3

FIG. 8. n --, r* absorption bands in the azines. from references given in footnote (a), Table IV. 130

-

Solvent:

isopentane

or isoctane.

Taken

n -+ P* TRANSITIONS

IN

THE

AZINES

18 1

ing t,he p,-character of the a’-orbital. From a less detailed analysis Mason (,$l ) has concluded that s-tetrazine is also planar. A notable feature of the rotational constant#s found by Innes (10) and Mason ( 11) for these molecules is that on excitation the rot,ational constant for s-tet,razine increases whereas for the other azines st,udied (pyridazine, pyrimidintt, pyrazine) there is a decrease. The increase in t,he moment, of inertia of thr s-tet’razine molecule upon excitation is consistent with t$he predicted shortening of the N--N bond4 (Section I). Mason also observed a red shift in t#he O-O band on deut,eration, indicating that’ the molecule is more strongly bound in the c>xcited state. ,\ remarkable and surprising feature of t,he vibrat.ional envelopes (E’ig. 8) is the very marked variation in the int,ensity distribution and band width in the sol&w azine ‘n --f A* bands. The Dfh azinex, pyrazine and s-t,et’razinr, exhibit a strong 0-O band and short, vibrational progressions (band width -3000 cm-.‘). Tht C?,. azines, pyridazine and pyrimidine, exhibit remarkably weak 0-O bands envelopes (-8000 cm-‘). The D3,( azinc I Q-O - l-i0 clllax) and wide vibrational ( s-t,riazinc ) exhibits a very weak O--O band ( ~~~~~ - ,I,.50tK,;,,) and a verywidr band width (-12,000 cni-‘). The vapor spectra, however, shon- strong & --0 bands in all cases except for s-triazine. Thus the C-H frequcnciw may be contributing t#o t,he shift of t,he maximum in the solution spectra and the suppositiolI that, the pyridazine and pyrimidine transitions are Franck-Condon forbidden has little support. The s-triazine band widt#h and shape is probably accounted for by the presence of multiple transitions. Brincn (21 ) has assigned, from the tcmptrature dependence of the vapor spectrum and the presence of a s;t,rong Q branch, the band system with origin at VU_-0= 31,574 cm-’ as the allowtl ‘,,lJ c 1A’ t#ransit,ion. Approximately 1000 cm-’ further to the blue the onsrt, of a srrond and diffuse clect,ronic t,ransition is observ(>d. The vibrational envelope of the pyridine transit,ion is not subject to direct obscrl-ation because of the overlapping strong ?r -+ ?r* transition; however Kasha and St8ephenson (&) observed that. the bands in t,he long wavelength (48 4 A similar tional

constant

shortening (0.0004)

is predicted for pvridazine. The observed small decrease in rotamay arise from t,he lengt,hening of the parallel C-C bond.

region of the n -+ T* t.ranaitjion are weak. This implication that the pyridine n -+ a* transition is of I;ranck-Condon forbidden type suggests a wide band and hence a st’ronger oscillator strength than that, given in Table 1. The cxpcrimentjal est’imates of the pyridine oscillator strength, first by Stephenson (4/t) and more recently by Mason ( 24 ) assume that the pyridine band is only 3000 cm-l in widt,h, whereas examinat,ion of I+?g. 8 shows that it might be double this, if the band shape approaches that) of pyrimidine rather than pyrazine. “DIFFUSE”

ABSORPTIOS

%‘ECTItA:

In at least two azines, s-triazine, and pyrazine, there are diffuse or broad bands superimposed upon t,he sharp system. Brinen and Goodman (36) have discussed the int.ernctions leading to the splitting of the (n, n*) states in s-triazine. The situation is analogous to that for the (a, r*) stat,es in benzene, i.e., the highest, filled n-orbitals (nl , ni) and the lowest interact,ion vacant ?r*-orbit,als (~2 , q) are degenernt,e, so t,hat configurat,ional on the zerot,h-order level controls the splitting. Four low-energy states of At, E”, -4: , and h”’ symmetry are predict,ed to be grouped within 1 ev, and hence are assumed t,o be contained wit[hin t,he observed band envelope (-3000 A). If sp2 u-orbitals are assumed in t#he excited states, the predicted ordering of st’ates is E’ < A: < E” < AT . But Brinen’s low-resolution analysis (20) shows t’hat, the observed long wavelengt,h (sharp) bands clearly belong to an allowed system. If a-orbitals with 0.1 s charact#er are assumed in the excited states, in conformitjy with the conclusions of t&heprec,eding scct,ion, the predicted ordering of st.ates is A; < RF:” < E” N A:. The conclusion that the lowest energy transition is allowed is st,rong evidence for reduction of s-charact,er in the “excited” cr-orbitals inasmuch as all four stat,es have identical charge dist,rihutions. The onset, of the diffuse region begins -1000 cm-” to the blue of t’he sharp system O-O band. It, is unreasonable to invoke photodissociation as the cause of the diffuseness inasmuch as all evidence points t.o only slight reduction in binding in the azine excited states. It is likely that the diffuse region marks the ‘E” +- ‘A transition, t.he diffuseness result,ing from t,he Jahn-Teller splitting (.42) of the E” state. The degenerate state will split within the t’ime of a (asymmetric) molecular vibration, not allowing time for vibrational cluant,ization to take place. The complete blurring of the vibrat’ional structure of the short lvavelength region of the 3200-A band vapor spectrum is consistent with this pict.ure. The diffuseness observed by Ito et al. (45) in pyrazine is of another type. Here the vibrational structure is preserved, only the atomic sharpness is lost. Ito explained these broad bands by assigning them to the forbidden BQ + A, transition. More recently, Innes (IO), in his recent analysis, has shown that they can be fit,ted into t,he sharp series (B,,, +- A, t’ransit’ion) as the out-of-plane bs, vibration. It is not surprising that these bands should be broader than the perpendicularly polarized bands, inasmuch as a b 3g vibration allows borrowing

7~ --)

?r*

TRANSITIONS

from r + # bands with result’ing here is probably due to prominence

IN THE

AZINES

133

in-plane polarization. The loss of sharpness of the I’ and It ljranchts.

I:MIGSIONSPECTRA: Ko fluorescence emission has been observed, up to t,his time, corresponding to au azine (n, T) state. Several phosphorescrwe emissions have been obsrrwd, however (Fig. 0, Table IV) with widely varying quant’um yields. The two principal problems that need discussion are the lack of fluorcwence and the direction of polarization of the phosphorescence emission. The first) tha jide observation and assignment of an nzine lnrnincsccnc~c :w I

(

I

I

1

’

Frc:. 9. Phosphorescence Footnote (f) of Table IV.

emission

bands

in t,he azinea.

’

’

(1,3)

Taken

-

from references

givrn

in

184

GOOIlMAN

a 3 r~ in orbital type was carried out in rigid media at 77°K for pyrazine by Goodman and Kasha (23). The quantum yield for the pyrazine phosphorescence is very high, so that with usual excitation conditions t,he emission is intense. Recently ?r -+ n phosphorescence emissions have been observed for several azines. The pyramidine emission spectra was recently studied by Krishna and Goodman (27) ; the s-triaeine phosphorescence by Hirt, et al. (29) ; and very recently, the pyridazine emission, by Brinen and Goodman (28). In every case, except for s-triazine, the band envelope of the phosphorescence is such as t,o show an approximate mirror image relationship wit.h the corresponding absorption spectra (Fig. 9). The s-triazine emission has a lifetime of 0.5 sec., consistent wit’h an orbitally forbidden transition, and hence may not correspond to t,he orbital characterization of the lowest singlet state (lAt). It, most probably represents the %” --$ ‘A’ transit,ion, corresponding to t.he second singlet state. In t.he other cases, there can be no doubt that t’here is a one-to-one correspondence between the lowest allowed singlet, and triplet states. The same ring dist,ort’ion vibrat,ions as in t,he absorpt,ion spectra, involving opening of the CNC angle, are prominent. A very noteworthy feature of the azine phosphorescence emissions is the very large variation in quantum yields. Observations of the emission intensity under similar excitation and concent,ration conditions are : pyrazine (vs) , pyrimidine (s), pyridazine (VW), s-triazine (vvw). An unsuccessful attempt was made in this laboratory to obtain the s-tetrazine emission using a det,ector sensitivity lo3 times that used for the pyra,zine emission. The wide variation in emission intensity cannot be explained by a corresponding variation in the absorption spectra. Pyrazine and pyridazine have similar v max in bot,h the ?r + A* and n --z r* regions yet, the pyrazine emission intensity is greater by a factor of lo3 than the pyridazine emission int,ensit,y. The large variation in phosphorescence quantum yield implies that the int,ersystem crossing probability is undergoing a considerable variation. In the two cases of strong emission, pyrazine and pyrimidine, the excited singlet stat,es are somewhat, nonplanar. In contrast, the t’wo cases of very weak or absent, phosphorescence emission, pyridazine and s-tetrazine, are planar in the excited singlet stat,e. [We disregard s-triazine because of the forbidden chara.cter of t,he emission.] It is well known that for (n, T*) states t,he inter-system crossing probability becomes large if the molecule is nonplanar (4S), with consequent weak fluorescence. Hence, one may speculate that the lack of azine K* - 7~ fluorescence proceeds from t,he special geometries of the excited st,ates. If this is true, and since there is little evidence for an intrinsically high intersystem crossing probability, pyridazine and s-t#et,razine should fluoresce. A t,horough search for t#he fluorescence emissions is needed. Clementi and Kashn (47~) and Sidman (48) have carried out calculations on spin-orbit coupling between the emitting t,riplet and the perturbing singlet

n + 8 TRANSITIO?;S

IN THE AZINER

I 3.5

states. They conclude that all n + T* intercombination transitions should br polarized in plane, inasmuch as the perturbing singlet states are (?r ,?r*) in orbital characterization. A particular success of these calculations, which assumc a cylindrical spin-orbital potential field in a cent’ral field approximation, is that they predict strong spin-orbital int’eraction in (a,~*) excited states, accounting for the short lifetimes (-lo-’ see) of the phosphorescence emissions. It should bc noted however, that, nonplanarity may allow mixing of the (n, x*) triplet and singlet stat’es. 1Jurther experimental work in this area is strongly needed, both in the fluorcscence problem and in the det’erminat’ion of the polarizations of the S-T transitions. V. SUVIMARY AND CONCLU’HIOIGi The discussions in the preceding s&ions concerning intensities, singlet triplet intjervala, and band shapes outline the salient factors characterizing II -+ g* t,ransitJions. For the allowed transit,ions a simple pict,ure in terms of ground state approximate s$ lone pair-orbit’als and simple LCAO-MO n*-orbi tals appears t,o give a good desrript8ion of the inten&ies. On the other hand the S-7’ intervals are very poorly predicted by ground stat)e u-orbit,a.ls and providch Ftrong cvidcncae for a significant’ decrease in s-charact,cr in the excited state. If the s-character in the excited st,atrs is assumed 0.1, a useful description of thtx S-7’ intervals is obtained. The conclusion obtained from vibrational analyses that, some of the (n,.rr*) excited stat’es are nonplanar and some planar is cluitc> surprising and undoubtedly has an important rffect, on certain of the spwtroscopic observables. For example, in the band shape problem further clarification of the excited statme pot,ential energy surfaces would he welcomed. The obsrrvation of a -+ n phosphorescence emissions with low quanl.um yields suggests the possibility of ?r --, n fluorescewe in thew molecules. However, no azinc, g - II fluorescence has as yet, been observed. Our understanding of energy conversion in thrse molecules seems t,o be on 110 firmer ground than it, was ten yclars ago. Continued studies in this area, part8iculnrly through the clarification of the dctnils of the molecular geomrtry in the excited state, may resolve this dilemma. Finally, mention must be made of t,hc t!ransition energy prohlcm. Orgel (12 1 has qualitat,ivcly discussed t,he effect, of charge redistribution on the a-functions. Anno (34, 52 ) and Anno and Sado (95 , @‘I, in several papers, have calculated the 7~ ---) ?r* t,ransition energies in pyridinc and pyrazine utilizing ASMO tbcor? with empirical electron repulsion integrals and considerable configuration interaction. Mason (7, l/t) and Goodman and Harrell (8) have given useful oneelectron semi-empirical procedures. None of these approaches are concept,ually satisfactory. Only by reducing the n-orbital s-character to low values (0.1 for pyrazine and 0.2 for pyridine) in both ground and excited st,ates does Anno ohtain reasonable agreement with experiment. It does not appear t,o the author

that low ground state s-characters are likely (e.g., the bond angles and the intensities would be rationalized only with difficulty; also the 0.2 s-charact,er in the pyridine excited state yields difficulties with the S-T int,erval). From the discussion in Se&on III, however, it is apparent that a low s-character is appropriate for the excited state. It, would appear that in the Anno calculations the s-character is an empirical parameter without, precise physical meaning as to state. Similarly t,he frankly empirical Mason-Goodman-Harrell calculations predict substitution and orientation eff&s in qualitative agreement with experiment, but fail quantitatively. The basic problems appear to lie both in n-electron rehybridization upon excitation and in the calculation of the ?r-electron affinity of the heterocyclic. The usual MO [including t,he Pariser and Parr] approaches do not handle electron affinities well, probably due to both the Z: and II frameworks changing with the number of rr-electrons. It is this basic failure of a-elect’ron t,heory that makes the transition energy probably t,he t,heoretically least firm aspect of n -> ?r* transitions. A reorganization study such as that carried out on formaldehyde n -+ T* transitlions by Parks and Parr (31) would clarify things greatly. ACKNOWLEDGMENT The author’s interest in these transitions received its main stimulus from Professor M. Kasha, during his tenure as a Fellow in his laboratory. The author acknowledges useful and clarifying discussions and correspondence with Professors J. R. Platt and K. K. Innes. He is especially grateful to Mr. J. S. Brinen and Mr. V. G. Krishna for numerous critical discussions

and refinement,s.

RECEIVED

NOVEMBER

25,196O REFERENCES

1. J. W. SIDMAN, Chenl. Revs. 68,689 (1958). 2. V. HENRI AND P. ANGENOT, J. Chi?,~. Phys. 33,641 (1936). 3. H. SPONER AND H. STUECKLEN, J. Chem. Phys. 14.19 (1946). 4. F. M. UBER, J. Chena. Phys. 9,777 (1941). 5. J. KOENIGSBERGER AND K. VOGT, Physik. 2. 14, 1269 (1913). 6. M. KASHA, Disc. Faraday Sot. 9, 14 (1950). [See G. J. Brealey and M. Kasha, J. Am. Chew Sot., 77, 4462 (1955) .] 7. 8. F. MASON, J. Chem. Sot-. p. 1247 (1959). 8. L. GOODMAN AND R. W. HARRELL, J. Chew. Phys. 30, 1131 (1959). 9. J. R. PLATT, J. Chem. Phys. 16, 1168 (19501. 10. K. K. INNES, J. A. MERRITT, W. C. TINCHER, AND S. G. TILFORD, Nature 187, 500 (1960). 11. S. F. MASON, J. Chem. Sot. p. 1269 (1959). 12. I,. E. ORGEL, J. Chew. Sot. p. 121 (1955). 13. J. It. PI,ATT, J. Opt. Sci. A7n. 43, 252 (1953). 14. S. F. MASON, J. Chem. Sot. p. 1240 (1959). f5. J. R. HOYLAND AND L. GOODMAN, J. Chem. Phys. 33, 746 (1960). 16. R. S. MULLIKEN, C. A. RIEKE, 11. ORLOFF, AND F. ORLOFF, J. Chew Phys. 17, 1248 (1949).

n 4

r* TRANHITIOKS

IN THE

A%INES

13’i

17. R. PARISER AND R. G. PARR,J. Chew. Phys. 21,466,767 (1953). 18. A. I,. PKLAR, J. C'hem. Phys. 10, 135 (1942) AND T. FOI~STER, Z. Natt~rjorsrh. 2a, 149 (1947). 19. R. I>. BRADS AND bl. L. HEFFERNAN, Tr~n.5.Fur~tlnj/&K. 64,757 (1958). ?O. L. GOODMAN (unpublished work). .!t. ,J. S. BRIsEN, doctoral dissertation, The Pennsylvania State University, January, 19Gl. 32. .4. C. ALBRECHT, J. Chenl. Phys. 33, 156 (1960). .!3. L. (;OODi%IANAND M. KASH.4, .J. .b'o/. f+!ctrOSco~~/ 2, 58 (1958). 24. 17. (i. KRISHXA AND L. (+ooux~s, J. (‘hem. Phys. 33,381 (1960~. 95. T. Aszo ASL) A. 8ADo, J. Chem. Phys. 32, 619 (1960). ,?fi. R. C. HIRT, Spectrorhim. dicta 12, 114 (1958). 67. V. (;. KRISHNA AND I,. GOODMAX, J. .-ln,. (‘hem. Sot. (to he published). _‘8. .J. 8. BRINEN AND L. C:OODMAN (to be published). 9.9. P. PARIS, 1~. C. HIRT, AND It.C;.~:('HMITT(preprint received March, 1960). 30. J,. (:oounxa~ AP;D H. Sm-m, J. (‘het~. Phys. 22, 1184 (1954). $1. 3. -22. PARKS AND It.G. PARR, J. (‘hem. Phys. 32, 281 (19600). 3,“. H. A. SKINNER AND H. 0. PRITC'HARD, (%?!I!.. Rws. 66, 745 (19%). 33. I).F. I';VANS,J. Chem. sot,. p. 3385 (1957). 34. T. Asso, J. (‘hem. Phys. 29, 1161 (1958). 55. H. A. SKISXER AND H. 0. PRITCHARD. Truns. Faraday Sot. 49, 1254 (1953). S8. .J. S. BRINEK AXU L. GOODMAN, J. (‘hens. Phys. 31, 482 (1959). J7. II. SPONER ANI) J. H. I~USH, J. <'her,!,. Phys. 17, 556 (1949); J. H. 1117~~AND H. SPONER, J. (‘hem. Phys. 20, 1847 (1952). $8. F. HALVERSON AND R. C. HIRT, .I. (‘hem. Phys. 17, 1165 (19-19). 39. 11. C. HIRT. F. HALVERSON, AND R. (+.SCHMITT,J. Cherrr.Phys. 22, 1148 (1954). 40. CURTIC+, I~AROPSKY, AND M~:LLER, Her. 40, 8-l(1907). 41. 8. F. M_4SON, J. Chem. sot-. p. 1260 (1959). 42. II. ~PONER AND E. TELLER, Revs. &Jodern Phys. 13, 75 (1941). $3. SI. K.~SHA (private communication). See M. Kasha, “The Nature and Significance of II - T* Transitions,” in Syn~posittn~ o?r Light tend Li.f~~. Johns Hopkins Univ. Press, Balt,imore, 1960. 44. H. P. STEPHENSON, J. Chew. Phys. 22, 1077 (1954). 45. 32. ITO, It. SHIYADA, T. KURAISHI. AND W. MIZCSHIMA, J. Chem. Phys. 26, 1508 (1957). 46, Xl. KAsIIA, Radiation Research Suppl. 2, 243 (1960). 47. R. C’. LORD, 8. L. MARSTON, ANI) F. A. ?~IILLER,Spectrochirn. Ada 9, 113 (1957). 47,. B. ~LEi~~IE~TI ANE M. KASH.4. 1. drol. Spectrostopy 2, 297 (1958:. 48. J. W. SIDMAN, J. Mol. Spectroscopy 2, 333 (1958). 49. T. ~NP~O AKU iz. SAM), J. Chem. Phys. 29, 1170 (1958). 50. J. A. iuERRITT .~ND Ii.K. INNES, Spectrochim. .-Lc~u 16, 945 (1960). 51. T. .~SNII,.I. Chem. Phys. 32, 867 (1960). 51’. W. C. TINVFIER, Ph.D. Thesis, Vanderbilt Universit,p (1960).