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A variational plus perturbational calculation of triplet states of polyatomic molecules. II. Aliphatic carbonyls and azabenzenes
ChemicalPhysics 22 (1977) 233-243 B North-HollandPublishi% Company
AVARIATIONAtPLUSPER~RBATIONALCALCULATIONOFTRlPLETSTATES OFPOLYATOMICMOLECULE$H.ALtPHATICCARBONYLSAND AZABENZENES J.LECLERCQ,P.YVAN Laboratoire d’optique Appfiquge.kale Polytechnique. 75230 ParisCeder 05, Frame
and J.M. LECLERCQ Centrede Mkanique
OndulatoireAppliquie,
75019 Paris,Fmnce
Received31 August 1976 Revisedmanuscript received 24 January 1977
The two lowest triplet states of some aliphatic carbonyls(fonnaldehyde, formic acid, acetaldehyde, acetic acid,acnldehyde, acrylicacid and acetone) and the lower triplet states of the six knownazabenzenesare described by: (i) a SCFcalctliationin the open-shellone-operator for&ii of Roothaan using semi-empiricaIZDOparametrizations;(ii) a treatment of the electronic correlation of the SCF states by a second-order perturbation expansion. The orctiator strengths of the lowest energy tripletsinglet transitions are investigatedfor eachcompound. Spinandspatial symmetry-adapted functions are used in these cakulations.
1. Introduction In a previous paper [I] (hereafter Teferred to as I), we briefly specified the self-consistent field equations for any non-multiconfigurational triplet state with two open shells in the one-operator formalism of Roothaan [2,3] with the onIy hypothesis of a set of zero clifferential overlap (ZDO) basis functions. Then the outline of a treatment of the eIectronic correlation energy of these SCF triplet states by a second-order perturbation expansion was presented [4]. Besides,as trial applications of this work, we reported conformational analyses ofthe me&stable triplet state of some compounds using the CNDO/Zparametrization [S] . Other applications were developed successfuIly elsewhere [6--91. In this paper, we present and discuss: (i) in section 2, an investigation of the two lowest. triplet-singIet transitions of some aliphatic carbonyls, in the outline of the CNDO/Sparametrization [lo] ; further, distinct descriptions of the vertical and O-O T, + So transitions, using the CNDO/2parametrization are reported;
(ii) in section 3,aninvestigation in the CNDOjS parametrization of the lower triplet-singlet transitions of the six known azabenzenes. Although the aliphatic carbonyls which we have investigated and the azabenzenes are not large compounds (ab initio calculations have been carried out for some of them), we have considered them because they are among the most studied systems both experimentally and theoretically. ExceUent reviews of the general re-; levant literature have been reported [I I-131. Besides, most of these compounds were investigated by Jaffe; et al. [14,15, and references therein] in the outline bf the CNDO/Sparametrization, both by VO-Cl calculations (S&F S, molecular orbitals; configuration interaction restricted to the lowest singly-excited contigurations with respect to the SCF S, contiguration) and by direct self-consistent field calculations of triplet stat& (without eIectronic correIation energy calculations). In addition, we have computed the oscillator strengths fof the Tj + S, transitions for the lowest nn* and m* triplet states. These calculations have been carried out
234
J. Leclixq et a!./Ttipietstates. II
with the usual one-electron one-center approximation of the spin-orbit hamiltonian (for instance, see ref[7]). After various trial calculations, we may point out that refinements of the wavefunctions beyond a threshold of accuracy do not introduce significant alterations of the/(Tj f So) values. Taking into account this fact, to overcome the difficulty which follows from the non-orthogonality of the SCF molecular orbit& of distinct states, the matrix elements of the spinorbit hamiltonian have been derived from wavefunctions issued from extended VO-CI CNDO/S calculations (SCF So MO, CI extended to doubly-excited configurations). Spin and spatial symmetry-adapted functions are used in all these investigations.
2. The lowest nn* and nf
triplet states of some
aliphaticcarbonyls The carbonyl compounds present very interesting tests of our methodology. Firstly, they contain both x and lone-pair electrons. Secondly, experimental studiesof formaldehyde [16], acraldehyde [ 171, benzaldehyde [I81 and acetophenone [I91 reported an elongation of about 0.1 A of the C=O bond length from S, to St or T, states. The previous study I lets us hope to account for this one significant difference which other Investigations show to be essential for a correct evaluationof the spin dipole-dipole contnbution to the zero-field-splitting parameters of the me&table triplet state of aromatic carbonyl compounds such as benzaldehyde [8] and benzophenone [9]. ; In this section, the T, + So and Tz f So transitions )f formaldehyde, formic acid, acetaldehyde, acetic sid, tram-acraldehyde (trans.acrolein, trans-propenal), crylic acid and acetone are obtained In the outline of he CNDO/S parametrization, which is the adequate ;DO parametrization for theoretical spectroscopic tudies of such compounds. For these investigations of +e vertical Ti + So transitions, we have proceeded with be ground state experimental geometries reported by tton 1201 and the axes conventions are shown in . 1. However,this parametrization is inadequate to tribe the alteration of geometry and we hav: atpted to characterize the vertical and the 0-O T, + transitions in the outline of the CND0/2 paramePization (it is well established that this parametrization
I
2
0
-I-.. II
/YY
R
R’
Fig. 1. Ives conventions for the aliphatic carbonyls: fomaldehyde and formic acid (RsH, R’=H,OH), acetaldehyde and acctic acid (R&Ha, R’=H,OH), acraldehyde and acrylic acid (R=CHt=CH-, R’=H,OH), acetone (R=R’=CHs).
is inadequate for the investigation of the higher states). For these latter investigations, we have assumed for the Ti state the theoretical values of the C=O bondlength reported in I. Moreover, we have computed the oscillator strengths of the T, f So and T2 + So transitions. Such computations have been carried out before for the nrr* triplet states and the qualitative (if not quantitative) interpretation is unambiguous, but this is not true for the m* triplet states (for instance, see the following discussion for formaldehyde). In the computation of the electric dipole moments of the singlet-singlet and triplettriplet transitions, the two-center integrals Qs(A), n 2~,03)),
where u Ex,y,z and A and B (#A) stand for carbon or oxygen atom of the carbonyl group, were taken into account in addition to the one-center integrals. On the other hand, trial computations of the matrix elements of the spin-orbit hamiltonian, using the values of the two-center integrals (2s(A), ‘Bxl’3B2p,,(B)L - - .>Qp,(A), &Jr;
2~#3)),
.--9
reported by Tokuhiro et ai. [21], have shown that the introduction of these integrals leads to modifications of the values of oscillator strengths of the triplet-singlet transitions less than 5%. Consequently, these latter Integrals have been neglected. 2.1. Fommldehyde The T1 + So transition in formaldehyde with origin (O-O band) at = 3.12 eV is known for a long time [22 -241. From trapped-electronspectra, the vertical tm-
J. Leclercq et al./Tdplet states. II
235
and the oxygen atoms of the carbonyl group, is necessitions T, + So and T, (3A,) +- So are found at 3.75 sary because the ratio of the one-center to the twoand 6.20 eV, respectively [25]. center integrals is less than two while the coefficients Many theoretical investigations of the electronic which arise from LCAO expansions are of similar order. structure of this compound have been carried out. The Hence, the x component of the electric dipole moassignments of the vertical lower singlet-singlet and ment for the S3 4 S, transition is -0.1464 eB (leading triplet-singlet transitions have been defmite for many years but, as far as we know, the change of geometry be- tof(T, + So) z 1.5 X 10W7)from atomic-polarization tween the ground and excited states has been onIy inves- caIcul&ons and -0.0366 eA from atomic-plus valencepolarization calculations. Our valuef& + So) = 13.0 tigated by Buenker and Peyerimhoff [26]. Our values X IO-‘, twenty times weaker than f(T1 + So), is conissued from caIculations with CNDO/S parametrization sistent with the estimation reported by Becker (ref. are consistent with the ab initio investigations. The SCF [13] ,p. 161). values for the vertical Ti + So transitions are even better, the semi-empirical parametrization taking a certain 2.2. Acetaldehyde, acraidehyde mid acetone amount of correIation into account. The CNW2 investigation is more significant. The values, resulting Our energy for the vertical T, -+ So transition, alfrom SCF calcrdations plus perturbation treatment, of though always improved by correlation treatment, the vertical and the O-O T1 +S, transitions (3.85 and corresponds rather to the O-O band than to the vertical 3.03 eV) are in good agreement with experimental data transition itself (this is true also for the values reported (3.75 and 3.12 eV). Unfortunately, this parametrizaby Jaffe et al. [14] for acraIdehyde and acetone, see tion is inadequate for the description of the higher exconclusion).The energy of the vertical Tz 4 So transicited states because of the undue mixing of (Tand R tion is in agreement with the experimental data for aceorbit&. taldehyde and acetone (see table 1). For these two Many theoretical studies of the spin-orbit coupling compounds, the correlation treatment improves the SCF in the 3& + So (IA,) transition have been reported value in a significant manner. On the other hand, the [27-29,151. Our valuefiT + So) = 2.5 x 10-7, tbou$l energies of the O-O and vertical T, + So transitions smaller than the estimation of DiGiorgio and Robinson issued from CNDO/Z calculations are in good agreement [16], is consistent with the values obtained by Yonezawa et al. [27] (6.7 X IO-‘/) and Jaffe et al. [28] with the experimental data. In particular, it may be pointed out that the differential correlation effect for (2.4 X 10e7). Tire study of the oscillator strength of the T, + So transition is more significant. Kearns and acetone is very important. Our vahref(T1 + So) = 3.3 X lo-’ for acetone is Case [30] have previously reported an estimation f(TZ + So) = 1.3 X 10-9, taking only into considerain agreement with the estimation issued from the extion the coupling between the S, and T2 states. Inperimental data: r? = 0.4 ms and 4, = 0.03 in rigid deed, our study shows that the $A1 (T,) state is chiefly ether-IPA at 77 K, while @lC= 1.0 +O.l [35]. For perturbed by the lowest ‘B, (S3) state and not by the this molecule, as for acetaldehyde and acraldehyde, S1 state. Besides, it must be pointed out that the calthe met&able triplet state is chiefly perturbed (via the culated value off(T2 + So) for such compounds is spin-orbit interaction) by the fust excited Inn* state proportional to the oscillator strengths of the singletand the T1 + So transition is polarized in the molecular singlet or triplet-triplet rr* + n and rr* + D transitions. plane, along or nearly along the C=O bond. On the These oscillator strengths are zero jn any ZDO approxiother hand, the f(T2 + So) values are of the same order mation for planar molecules. The introduction of atomof magnitude and consistent with the estimation of ic polarization, i.e. the integrals (2s (A), u 2p,(A)), Becker [ 131. where u zx,y, z and A stands for the carbon or oxygen atom of the carbonyl group, leads to overestimated 2.3. Fomic, acetic and amylic acids values for these oscillator strengths for such compounds which are in fact nearly-diatomic systems. The.introThe O-O band of the S, (mr*) + S, transition is duction of valence polaiization, i.e. the integrals (2s(A), located at x 5.0 eV for formic and acetic acids [ 1 l] u 2p,(B)1, where A and B (#A) stand for the carbon instead of 3.49 and 3.56 eV for formaldehyde and ace-
J. Lectercq et at./Trt@tetstates. II
‘236 Table 1
Thetwo triplet-singlet transitions of some carbonyl compounds (t: vertical transition TjtSo;O-0:
0-O band of the Tj-
So
transitions) Compound
State
Trans.
E(Ti>- E(So) (eV)
SCFa) formaldehyde
3A* 3AI
formic acid
3**.
aA’ accetaldehyde
acetic acid
3A”
3A’ 3A” 3 t
A
acraldehyde
3hrP
3Al acrylic acid
3
A
.*
accfone 3A,
t
3.02
o-o t t
6.26
O-O t t
5.38
o-o t t o-o t t o-o t t o-o t t o-o t
3.70
3.00
SCF f 3.65 2.88 4.06 3.39 3.54 2.52
6.09 3.65
3.24 6.69 4.03 5.71 3.22
3.96
2.98 2.03
3.20
3.64 2.52
3.21
2.91 5.69
3.85 3.03
3.15 2.43
exp.
3.75 [25] 3.12 [22-241 6.20 1251
4.34 3.67 4.02 3.06
3.15 c) -3.10 1311 6.40 c)
4.58
10’
talc. b)
WLp.
2.5 (z)
al2.0 [ 161
0.13 (x) 15.0 (2 >y) 0.24 (x1 2.3 (z %y) 0.07 (xl 13.0 (z > Jg
3.80
3.16
3.28
‘)
6.48 3.94
5.43 2.10
A&*)
f(Tj+$)X
5.75 2.78
3.10 3.79 3.29 3.17 3.17
0.49 (x) 10.0 (z > ,I)
4.05 3.01 [3394]
0.06 (x) 15.0 (z %y)
4.63 3.55 4.13 3.42
6.09
4.15 d) ==3.50[35,363 6.25 d)
0.30 (x) 3.3 (2)
2.8-4.2 e,
0.02 (x)
a) WithCNDO/Sparametrization (on the left) and with CNDO/2 parametrization (on the right). b)x,y andz stand for the theoretical polarization of the T- +-+ So transitions (fig. 1 shows the axes conventions). ‘) TI *Se: 3.8eV [321,3.75eV [251;T2 *So:635 eV’[32],6.40 eV [25]. d)T1 +-S1,:4.15eV [3732,25],4.16 eV 1381-T , 2 +S,-,: 6.25eV [37,25],5.88 eV [38],6.3 eV [32]. e, From vaIues of rp and+ for the TI -L Se transition (see text).
taldehyde, respectively:Unfortunately, few experimental and theoretical data about the triplet states of these compounds are available from the literature. McGlynn et al. [39] report for formic and acetic acids a phosphorescence from a state they assumed to have TV* character when the theoretical investigations of Basch et al., Peyerimhoff and Buenker [40] and Jaff6 et al. [10,14] locate the 3nn’ state of formic acidlower than the 37rir*one. Our results are consistent with these latter studies. However, we have not carried out conformational analyses for the 3mr* state and we do not rule out the possibility of an important change in the equilibrium
geometry of this state. It may be pointed out that the oscillator strengths of the triplet-singlet transitions, specially the 3~n* t- So ones, are increased in a significant manner with respect $0 the aldehydes ones. Moreover, for these carboxylic acidsas well as for the
aldehydes,the introduction of the two-center integrals in the electric-dipole-momentcalculationsis shownto be essential.
3. The lower triplet states of azabenzenes Fig. 2 shows the geometries that we have assumed
J. Leclercq et al.lTriplet states. Ii
Pyridine’
Pyr imidine
Pyrazine
237
Table 2 The labelling of n, P and P* SE molecular orbit& of ezaknspecies, in ground state
zenes, according to group-theoretical
CNDO/S calculations
D 2h
Compound
Labels of n orbitals
pyridine
n: 7al
pyrazine
n_
s-Triazine
Lables of n* o:bitals
C2”
: 3b,u
n+ : 4ag Pyridarine
Lables of 51orbitals
b
s-Tetrazintb
pyrimidine
n+ n_
: 7al : 5b2
.nl : lb3, r2 : lb2g 7r3 : lblg ‘il : lb1 ail : laz 7r3 : 2b1
pyridazine
n+
: 7al
n_ : Sb2
CP”
%h
D2h
sym-triazine
nl
: 3ai
n2 : 4e” Fig. 2. Geometries and axes conventions for the azabenzenes. Unless different values are specified, all C-C bond lengths are
equal to 1.38 A, all C-H bond lengths are equal to 1.08 A and all angles are equal to 120’. (a) Idealized geometry with all C-C bond lengths equal to 1.40 A; (b) see ref. [ 201.
sym-tetrizine
nt
: la’;
~1~: .le”
na
: 46
?Tj :
nl
: 3bzu : 3bm
rrl : lb3u f2 : lblg n3 : lbzg
n2
n3 :4a
g
le”
nz,: 2bag for these compounds. The axes were labelled according to Mull&en’s conventions [41] and the review of Innes et al. [42]. Table 2 specifies the labelling of the SCF
n, n and n* molecular orbitals, according to grouptheoretical species, in ground state CNDO/S calculations. It allows an easy correspondence between our labelling in table 3 and the more usual ones [21]. In table 3, we report the energies of the lower triplet states (CNDO/S parametrization), with respect to the corresponding ground state energies (vertical transitions). As examples, table 4 shows the detailed contributions to AE(2) of the symmetry-adapted functions for the metastable triplet state of pyridazlne and table 5 summarizes the second-order perturbation treatment of the electronic correlation for some states. The inclusion of all the symmetry-adapted functions into the perturbation expansion is justified once again (the results of
columns four and five of table 5 show that the.totaI contributions of functions such as lSE~211> 0.01 eV is always < 30% of A@‘)_
3.1. Fyridine Evans [43] has observed triplet-singlet absorption bands and located a triplet level at 3.67 eV. He suggested that this state is rrrr* and the lowest one. Contrary to this assignment, Hoover and Kasha [44] predicted that the lowest triplet state must have nrr* character and lies about 3.50 eV above the ground state. In a more recent paper, Japar and Ramsay [45] assign two weak bands at * 3.68 eV to a triplet-singlet mr* transition, similar to the 3400 A band system of benzene (a distinct band system is observed between 3.87 and 4.13 eV but no de&rite assignment can yet be made). On the other hand, some electron-impact investigations [46; 47, and references therein] and several semi-empirical calculations 48-511 have been reported. Our “SCF + AE Q)” results for the three lowest
3h 3B2g
pyrazinc
Al
I
I A2
3El ‘A’;
?A’;
3
% jA2 % 3A* 3B2 3AI 3gr
pyridczinc
sym-trinzinc
3BI 3Az 3h 3Az 3A* 3B*
pyrimidinc
-3
301 3A1 % 3AI jSZ
pyridinc
3Au 3h” 3BzU 3%~ 3B*U
stntcc)
Compound
2.97 3.38
3.89 3.89 5.92
4.05 3.52 4.93
2n*
+ 2e”
5.58
5.17
5.11
3 2e”
4c’
lc”
4.72
+ 2c” A 2e”
le”
4.31
4.65
4.61
4e’
-t 2e”
-+ 2e”
-+
lc”
4c’
la2
4.59
4.47
4.44
4.61
4.74
4.06
4.94
4.84
3.59 [62,70]
0.01 (2j
1.5oF>y)
4.82
-t 2a2, Ia2 -c3b,
2bl
4.37
5.97 5.02
+ 3bl
2bl
1.9(x =y>z) 0.06 (x)
0.53 tj. 2)
4.81
3.01--3.206)
I
4.55
4.14
2bI -+2a2
+3bl,
la2
3.20
4.6R
4.45
4.42
1.1 f_!Jax) [Gl]
2.6 (x)
-3.70
1.2 (v > 2)
1.2 (VI 2.2 (x)
0.0
1.4 (2)
0.95 (x)
1.2 (z)
talc.
4.01
3.43-3.58C)
3.22-=3.50d)
3.68 143,453
n3.50 144)
cxp.
3.94
3.31
4.04
a&) -
fO;.'SO)X IO'
3.70
3.59 4.75
3.57 4.70
32a2 + 3bl, 7~11 --r2az
5bz
5bz
4.18
4.35
+ 232
2bl
7a1
2bI
4.78
-r2i2,2b,-+3b,
la2
4.73
4.65
-r3b,,7q-c2a2
4.22
4.53
4.13
-e 2az
5bz
5%
3.85
4.22 4.74
4.88
lblg * 2bm
lbng -, 2bm
5.39
4.67
3.90
+2az,5bl-r3b,
4.78
3.65 3.76
6.04
lbzg -, Ia,
+3bi,lazh2az
4.22 4.25
3.89
3.49
4.76
3.56
4.40
4.14
3.75
4.25
4.84
+3b,
3.84 4,lO
3.92 3.65
3.31 5.02
4ag + 2b3u 3bm + 2b3, -+ la, 43g lb,g -, la,
la2
2bi
la2
-+2n2,2bl-+3bl *2a2 * 3bl, Ia23 2a2 2bl
3.63
3.61
SW *
SCP
3.99
vo-Cl
f:‘(Tj) - fi(So) (cV) c,
7aI -+3b,
Leading confiyrntions b,
. -p--
Table 3 ?11elower triplet stntcs of aznbcnzcncs (CNDO/Sparamctrlzation)
-
0.01 - 0.12h)
cxp.
:
.,
12
:
..’
.
‘.
.'
J. Leclercq et
@/Trip&t states. II
239
triplet states are: 3B, at 3.63 eV, 3AI at 3.84 eV and 3 B2 at 4.10 eV (it may be pointed out that our lowest SCF state is 3 B, as in the studies of Gaffe et al. [ 14,5 11). These values are totally consistentwith those of Chen
and Hedges[SO] and are not in disagreementwith the photoabsorption data [43-45]. However,the precision of our calculationsbeing 2 0.15 eV at least for each state, we must conclude that no definite assignment may be suggested for the lowest triplet state of pyridine. In fact, the smali spacing between the two lowest nrr* and rrrr* triplet states we obtained (consistent with previous work [49,50]) would indicate large vibromc coupling between these states as suggested for instance by Hochstrasser and Marzzacco 1521 for pyridazine. Because of ‘the lack of any experimental data, our values~(3Bl(nn*)+So)= 1.2X 10e7 andf(3A,(nlr*)
+ So) = 0.95 X 10m7can only be comparedwith other theoretical values [49,51,53,54]. For the first transition, the agreement is good. For the second transition, our value is consistent with that of Vanquickenborne and McClynn [54] but somewhat different from those reported by Yonezawa et al. [49] and by Jaffe et al. [51]. This may be explained by the gag we obtained between the energies of the perturbed AI state and of the most perturbing state, the lowest ‘B, state. 3.2. i’?zedinzines: pyrazine, pyrimidine a& pyrihzine Most of the authors agree with the nrr* character of the lowest triplet state of the diazines [55-651. Our results for this state are in fairly quantitative agreement with experimental data for pyrirnidie and pyridazine. For pyrazine, our “SCF + A@J” value (2.97 eV) is somewhat smaller than the experimental value (see table 3) but better than the values reported by YoneZaWa et ti. [49] (2.65 eV) and by Chen and Hedge
[50] (2.82 eV) in similar calculations and this failure is probably due to an insufficiency of semi-empirical parametrizationsrather than specificcharactersof our investigations.Our value (4.04 eV) for the lowest 3B1u (nn*) =+So vertical transition is consistent with the ab initio values reported by Hackmeyer and Whitten [66] (4.11 eV) and by Wadt and Goddard [67] (4.07 eV). However, the outstanding point of our investigation consists in the obtained values for the other mr* transitions:Indeed, we Iocate a 3B, (n-a:) + S,-,transition at 3 38 eV and a 3Au (n+nz) ES,-, transition at 3.49 eV. Evenin takmginto account an error of0.3-0.5 eV for
J.Leclercq et affTriplet states. II
240
Table4 Mailed contributions to A!+‘) of the spin and spatial symmetry-adapted functions for the metastable triplet state of pyridasine class a)
Contributions > 0.0 1 eV b,
AUthe contributions
number
number
$“*)6E$%)
m
-t”C!
0
0.0
k
-rmC)
0
0.0
k
+u
p.IJ+l k, m k,.nt k, k k. k
+ %t -tn,v
3 0 3 1
k,
1
.k,m kk k, 1 k, l k 1
--‘“,” *WV
*u,u
+P*P+l +u,t +u.t -rm,u
‘V,”
-+u,r
total
0 3 4 1 0 10 0 3
0.0 -0.1098 -0.1997 -0.04 29 0.0 -0.2324 0.0 -0.0417
7 5 165 10 90 60 98 168 18 1410 882 1641 1008 15012
28
-0.8394
20574
-0.0894 0.0 -0.1088
-0.0147
ZJ&$)(eV) 0.0 0.0
-0.122 -0.006 -0.136 -0.029 -0.025 -0.211 -0.232 -0.269 -0.040 -0.814 -0.097 -1.376 -3.357
3, Weuse the indices k, I for the closed-shell orbitals, m, n for the two open-shell orbitals (ttt = p orp + 1, n = p + 1 orp, respectively) and u, I for the virtual orbitak b, Contributions of the functionsJ such as j6E 5“1 z 0.01 eV, where 6.Ep'= - ~~IHlO~/[~~lHIJ~-~OIH(O~j;z$@standsfor the summation on these functions while ZJ stands for the summationon all the functions. c, BriUouin’stheoremis fubilled for these classes. these vertical-excitationenergies
[in accord&e
with
the lowest 3 Bg, (n+n,*) + So investigation] our cakulations indicate that it seems plausible that the adiabatic energies of the lowest 3 B and 3Au states are in the % range 3.540 eV, just below or just above the adia-
batic energy of the ‘%u state. The spin-orbit interaction is spatial-symmetry forbidden between the ‘B3,, and 3B2, states but allowed between the ‘B3u and 3A,, states and the matrix element of the spin-orbit hamiltonian (H&I is (1B,uIH,,13Au)= 0.6 cm” while
Table 5 Second-order perturbation energy AS(‘) for some triplet states of azabenzenes. (All values are in ev) Compound
pyridine pyrazine pyrimidine pyridazine sym-triaziie sym-tetrazine
‘1 See footnote b) of table 4.
State
3Bt (7ar 3bt) 3&u (lbtg la”) ‘Ba (2bt 2aa) ‘BI (Sbz 2~4 3E” (4e’ 2e”) 3Bz~ (lbzglau)
Contributions Z 0.01 eV a) number
Zy.‘)6$)
A.!+)
(OlH)O)
25 28 19 28 25 23
-0.77 -0.90 -0.36 -0.84 -0.71 -0.45
-3.57 -3.01 -2.66 -3.36 -3.33 -2.40
-343237 -3565.81 -3553.99 -3616.47 -3646.08 -3738.75
J, Leclercq et al./Triplet states. II
~1B3,1H,,13B,U~=6.6 cm-l. Consequently, the 3Au state seems a second plausible origin of the perturbations observed in the lB3,, bands, which might be important if the adiabatic energies of the two states are very close. For pyrazine, our valuef(T1 + So) = 1.4 X 1K7 is consistent with the limits reported by Jamattona and Goodman 1591: f= l-10 X I@. Forpyrimidine, taking into account the experimental value for pyrazine [59] AT, + So) may be estimated equal to 0.04 0.50 X lo-’ from the work of Hochstrasser and Lin [62] . On the other hand, Shimada 1641 measured a radiative lifetime TV% 10 ms for the metastable triplet state, leading tof(T1 + So) = 4 X 10e7 from the values rePorted by Cohen and Goodman [68]. of$ and& For the three diazines, our values agree with the other theoretical calculations [l&49,53,69]. 3.3. Sym-ttizine and sym-tetrazine For sym-triazine, our SCF cakulations (in a oneconfiguration scheme) with the 4e’ (n) and 2e” (n”) So SCF MO as trial open-shell MO, lead to four degenerate solutions. Because of the one-contiguration approach, these solutions are not A’;, A’; and E” symmetry-adapted functions. They are physically equivalent (the C, and C, operations of the D3n group lead from one to the others.) In the same way, the SCF calculations with the le” (rr) and 2e” (jr*) So SCF MO as trial open-shell MO lead to four degenerate solutions which are not A;, Aa and E’ symmetry-adapted functions. Ibe two distinct manifolds (a 3nrr* one and a 3rrrr* one) issued from these calculations are reported in table 3 as 3E” (mr*) and 3A; (ma*) but in fact each degenerate solution is a linear combination of symmetry-adapted functions (A’;, A’; and E” for the first manifold, A;, A; and E’ for the second). Though our investigation of the triplet states of symtriazine is only a first approach, the “SCF + AIZ(2)yy energy for the vertical transition 3E” (3A’;, 3Ai) f-S, (4.06 eV) is consistent with the experimental data (O-O band located at 3.59 eV 162,701). Indeed, it is obvious that the breakdown of the degeneracy by an improved approach, will lead to, an energy somewhat smaller for the vertical T, 4 So transition’(from VOCI calculations, T, has a E” character Our value f(T, + So) = I .5 X lo- $*is larger than the experimental value equal to 0.01 - 0.12 X 1O‘7 from
241
ref. [62], taking into account +he results of ref. (591. However, this value is an estimation only and, on the other hand, it is essential to keep in mind that the oscillator strength is an observable more sensitive to the breakdown of a degeneracy than the energy. For the 3A; (nn*) + S,, transition, we obtainf= 1 X IO-‘. Via the spin-orbit interaction, the 3A’r state is chiefly perturbed by the lowest ’ E” (nrr*) states. The results for sym-tetrazine show our treatment of the electronic correlation to be remarkablysuccessful. Our “SCF t A.$*)” energy for the lowest vertical 3 B,, (mr*) + So transition is equal to I .87 eV, in fairly quantitative agreement with the experimental data (O-O band located at 1.65-1.75 eV [72,74], absorption system extending to = 2.20 eV 174)) while the VO-CI value (291 ev) and tbe SCF value (3.22 eV) are in poor agreement. Our value f(T1 -+ So) =‘4.3 X lo-’ is practically consistent with the estimation of McDonald and Brus [73] . For the lowest 3 B,, (II?T*) + S, transition, the order of magnitude seems correct. On thetther hand, it is interesting to point out that the lowest 5 (nn”) state is chiefly perturbed by the first ‘B3e (nrr ) state [(3AelHsoI lB,J = -5.8 cm-’ via the interaction between the 2b3, (n,) and 4an (n3) MO] ; this perturbation leads to a polarization of the lowest 3Aa -+ S, transition perpendicular to the molecular plane.
4. Conclusion To recapitulate the discussion developed above, we may point out: (i) for non_multiconfigurationaI triplet states, the SCF values are equivalent to the results obtained by VO-CI calculations; (ii) in any case, except for the T, + S,, transition of formaldehyde, the treatment of the correlation energy improves the CNDOlS results (for instance, see the me&table triplet state of the three diazines and sym-tetrazine), in spite of the fact that such semi-empirical parametrization takes this correlation energy into account; (iii) for the CND0/2 investigations, the improvement due to the treabnent of the correlation energy is sometimes spectacular: = 0.5 eV for the O-O T, + So transition of acetaldehyde, * 1.0 eV for the O-O and vertical T, + So transitions of acraldehyde and acetone.
242.
‘J. Leckrcq et a/./Triplet states. II
However, we must point out that our treatment &nnot’remedy the intrinsic weak points of the semiempirical parametrizations. Thus, the VO-CI CNDO/S result for the vertical S1 +.SO transition of formaldehyde is 3.4 eV [lo] while the exqimental values for the O-O and vertical transitions are = 3.5 and 4.1 eV, respectiveIy. This failure leads to too small values inall the CNDO/S investigations of the vertical T, + So transitions of the carbonyl compounds. The necessity of an elaborate treatment of the correlation energies for correct predictions of the transition energies has already been pointed out for an initio calculations. The results of this work support this remark for semi-empirical ZDO calculations. However, an adaptation of the usual parametrizations (CNDO/2 and CNDOIS) to these treatments of the correlation energies seems necessary. We think that it would be more adviiable to substitute the use of rigorous ZDO basis functions sets in calculations. This point of view will be d&Cussedin the other papers of this series. On the other hand, the outstanding points of the calculations of the oscillator strengths reported in sections 2 and 3 are: the necessity of the introduction of some two-center integrals to obtain credible values for the lowest 3m* -+ S, transitions of the carbonyl compounds; the same magnitudes of the oscillator strengths of the 3nn* C- So and the ‘ns” + So transitions of the azabenzenes.
References [I J I. Leclercq and J.M. Leclercq, Chem. Phys. 22 (1977) 221. 121 C.C.J. Roothaan, Rev. Mod. Phys. 32 (1960) 179. [3J C.C.J. Roothaan and P.S. Bagus, Methods Comp. Phys. 2 (1963) 47. [4] For a general review of the treabnent of the electronic correlation energy by perturbation expansions, see B. Huron, J-P. Malrieu and P. Rancurel, J. Chem. Phys. 58 (1973) 5745, and references therein. [51 J.A. Pople,D.P. San@ and GA. SegaI,J. Chem. Phys. 43 (1965) S129; J.A. Pople and GA. &gal, J. Chem. Phys. 43 (1965) S136;44 (1966) 3289; D-P. Sarmy and GA. Segd, J. Chem. Phys. 47 (1967) 158. [6] C. Mijoule, Compt. Rend. Acad. Sci. (Paris) 278 (1974) 857; R. Alvarado, J.-Ph. Grivet and C. Mijoule, Chem. Phys. Letters 35 (1975) 403. [ 7] J.M. Leilercq, C. Mijoule and P. Yvan, J. Qlem. Phys. 64 (1976) 1464.
(81 C. Mij&Ie and P. Yvan, Chem. F’hys.Letters 43’(1976)’ 524. [9] J.hl..Leclercq and C,Mijoule, to be published. [IO1 J. Del Bene and H.H. Jaffi, J. Chem: Phys. 48 (1968) 1807;48 (1968)4050;49 (1968) i221;53 (1969) 1126. [ 111 G. Henbcrg, Molecular spectra and molecular structure, Vol. 3. Electronic spectra and elkctronlc structure of polyatomic molecules (Van Nostrand, Princeton, 1966); J.W. Sidman, Chem. Rev. 58 (1958) 689:
[ 121S.P.McClynn,T. Azumi and M.‘Kinoshita,Molecular spectroscopyof the triplet state (Prentice-Hall,Englewvood Cliffs, 1969). 1131 R.S. Beck& Theory and interpretation of fluorescence and phosphorescence (V&y--Interscience, New York, 1969). [ 141 H.M. Chang, H.H. Jaff; and C.A. hlasmanidls, J. Phys. Chem. 79 (1975) 1109. [ 151 CA. Masmanidis, H.H.Jaffi and R.L. Ellis, J. Phys. Chem. 79 (1975) 2052. (16:. V.E. DiGiorgio and C.W. Robinson, J. Chem. Phys. 31 (1959) 1678. [ 171 K. Inuzuka, Bull. Chem. Sot. Japan 33 (1960) 678. [IS] J. Olmsted III and M.A. El Sayed, J. Mol. Spectry. 40 (1971) 71. [I91 M.A. Souto and CT. L.m,Chem. Phys. 17 (1976) 129. [ 201LX. Sutton, ed., Tables of interatomic distances and configuration in molecules and ions, Suppl. 1956-1959 (Chemical Society, London, 1965). [Zl] T. Tokuhiro. B.R. Appleman, G. Fraenkef, P.K. Pearson and C.W. Rem, J. Chem. Phys. 57 (1972) 20. [22] A.D. Cohen and C. Reid, J. Chem. Phys. 24 (1956) 85. (231 J.C.D. Brand, J. Chem. Sot (1956) 858. [24] G.W. Robinson, Can. J. Phys. 34 (1956) 699. (251 R.H. Staleqi, L.B. Harding, W.A. Goddard III and J.L. Beauchamp, Chem. Phys. Letters 36 (1975) 589. [26] R.J. Buenker and S.D. Peyerimhoff, J. Chem. Phys. 53 (1970) 1368; S-D. Peyerimhoff, R.J. Buenker, W.E. Kammer and H. Hsu, Chem. Phys. Letters 8 (197l) 129. [27] T. Yonezawa, H. Kcto and H. Kato, J. Mol. Spectry. 24 (1967) 500. (281 R.L. Ellis, R. Squire and H-H. Jaffe’,J. Chem. Phys. 55 (1971) 3499. [29] P- Yvan, Mol. Phys. 31 (1976) 451. [30] D.R. Keamsand W.A. Case, J. Am. Chem. Sot. 88 (1966) 5087. I31 ] W.D. Chandler and L. Goodman, J. Mol. Spectry. 37 (1971) 33. 1321 W-T. Naff, R.N. Compton and C.D. Cooper, J. Chem. Phys. 57 (1972) 1303. [33] J.C.D. Brand and D-G.Williamson, Discussions Faraday sot. 35 (1963) x4. t341 EJ. Balr, W. Goetz and D.A. Ramsay, Can. J. Phys. 49 (1971) 2710. [3S] R.F. Borkman arid D.R. KEms, J. Chem. Phys. 44 (1966) 94s. 1361 W.D. Chandler and L. Goodman, 3. Mol. Spectry. 36 (1970) 141.
J. Leclercq et aL/Tr@let states. If
[37] H.H. Brongersma, Ph.D. Thesis, University of Leyden, The Netherlands (1968). [38] W.M.St. John III, R.C. EstIer and J.P.Doeting, J. Chem. Phys. 61(1974) 763. (391 L.W. Johnson, HJ. Maria and S.P. McGlynn, J. Chem. Phys. 54 (1971) 3823. (401 H. Basch, M.B. Robin and HA. Kueblet, J. Chem. Phys. 49 (1968) 5007; S.D. Peyerimhoff and R.J. Buenker, J. Chem. Phys. 50 (1969) 1846. 1411 R.S. Mulliken, 3. Cbem. Phys. 23 (1955) 1997. (421 K.K. Innes, J.P. Byrne and LG. Ross, I. Mol. Spectry. 22 (19671 125. [43] D.F. Evans, J. Chem. Sot. (1957) 3885. [44] R.J. Hoover and hi. Kasha, J. Am. Chem. Sot. 91(1969) 6508. 1451 S. Japar and D.A. Ramsay, l.Chem. Phys. 58 (1973) 5832. [46] E.H. van Veen and FL. Plantenga, Chem. Phys. Letters
30 (1975) 28. [47] M.N. pisanias, LG. Christophorou, LG. Carter and D.L. McCorkle,J. Chem. Phys. 58 (1973) 2110. [48] L. Goodman and R.W. Harrell, I. Chem. Phys. 30 (1959) 1131. (491 T. Yonaawa, H. Kito and H. Kate, Theoret. Chim. Acta 13 (1969) 125. [SO] S.-Y. Chen and R.M. Hed~es,‘lbeoret. Chim. Acta 31 (1973) 275. [SlI H.H. Jaff;, CA. Masmaimdis,H.M. Chang and R.L. Ellis, I. Chem. Phys. 60 (1974) 1696; H.H. Jaff& H.M. Chang and CA. Mesmaaidis,~. Comp. Phys. 14 (1974) 180. [52] R.M. Hochstrasser and C. Marzzacco, J. Chem. Phys. 46 (1967) 4155. 1531 t. Goodman, J. MoLSpectry. 6 (1961) 109; L. Goodman and V.C. Krishna, J. Chem. Plrys. 37 (1962) 2721; Rev. Mod. Phys. 35 (1963) 541,735. (541 L. Vanquickenborne and S.P. McCIynn, J. Chem. Phys. 45 (1966) 4755.
243
[SSj L. Goodman and M. Kasha, I. Mol. Spectry. 2 (1958) 58. [56] R. Shimada, Spectrochim. Acta 17 (1961) 14. [S7] M.A. El-Sayed and G.W. Robiison, J. Chem. Phys. 34 (1961) 1840; 3.5(1961) 1896;Mol.Phys.4 (1961) 273. [SS] V.G. Krishna and L. Coociman, J. Am. Chem. Sot. 83 (1961) 2042; J. Chem. Phys. 36 (1962) 2217. [591 B. Jarnattona and 6. Goodman, J. Chem. Phys. 40 (1964) 2042. [60] L.M. Logan and I.G. Ros. J. Chem. Phys 43 (1965) 2903. [611 R.M. Hochstrasser and C. Marzzacco, I. Chem. Phys. 49 (1968) 971. (6.21 R.M. Kochstrasser and T.-S. Lin, Symp. Faraday Sot. 3 (1969) 100. [63] L. Seamans, A. Moscowitz. R.E. Lider, G. Barth, E. BunnenbergandC. Djerassi,Chem. Phys. 13 (1976) 135. (641 R. Shiiada, Spectrochim. Acta 17 (1961) 30. 16.51K.K. Innes, W.C.Tincherand E.F. Pearson, J. Mol. Spcctry. 36 (I970) 114. (661 M. Hackmeyer and J.L. Whitten, J. Chem. Phys. 54 (1971) 3739. [67] W.R. Wadt and W.A. Goddard III, J. Am. Chern. Sot. 97 (1975) 2034; W.R. Wadt, W.A. Goddard III andT.H. Dunning Jr., 1. Chem. Phys. 65 (1976) 438. [68] BJ. Cohen and L. Goodman, 3. Chem. Phys. 46 (1967) 713. [69] W.R. Hall, Chem. Phys. Letters 37 (1976) 335. (701 R.M. Hochstrasser and AX. ZewiI, I. Chem. Phys. 55 (1971) 5291. 1711 E.R. Bernstein and R.E.Smalley, J. Chem, Phys. 58 (1973) 2197;Chem. Phys. 2 (1973) 321. [721 D.T. Livak and K.K. Innes, J. Mol. Spcctry. 39 (i9?1) 11s. [731 J.R. McDonald and L.E. Bms, J. Chem. Phys. 59 (1973) 4966. [74] R.M. Hochstrasser and D.S. King, Chem. Phys. 5 (1974) 439.
AVARIATIONAtPLUSPER~RBATIONALCALCULATIONOFTRlPLETSTATES OFPOLYATOMICMOLECULE$H.ALtPHATICCARBONYLSAND AZABENZENES J.LECLERCQ,P.YVAN Laboratoire d’optique Appfiquge.kale Polytechnique. 75230 ParisCeder 05, Frame
and J.M. LECLERCQ Centrede Mkanique
OndulatoireAppliquie,
75019 Paris,Fmnce
Received31 August 1976 Revisedmanuscript received 24 January 1977
The two lowest triplet states of some aliphatic carbonyls(fonnaldehyde, formic acid, acetaldehyde, acetic acid,acnldehyde, acrylicacid and acetone) and the lower triplet states of the six knownazabenzenesare described by: (i) a SCFcalctliationin the open-shellone-operator for&ii of Roothaan using semi-empiricaIZDOparametrizations;(ii) a treatment of the electronic correlation of the SCF states by a second-order perturbation expansion. The orctiator strengths of the lowest energy tripletsinglet transitions are investigatedfor eachcompound. Spinandspatial symmetry-adapted functions are used in these cakulations.
1. Introduction In a previous paper [I] (hereafter Teferred to as I), we briefly specified the self-consistent field equations for any non-multiconfigurational triplet state with two open shells in the one-operator formalism of Roothaan [2,3] with the onIy hypothesis of a set of zero clifferential overlap (ZDO) basis functions. Then the outline of a treatment of the eIectronic correlation energy of these SCF triplet states by a second-order perturbation expansion was presented [4]. Besides,as trial applications of this work, we reported conformational analyses ofthe me&stable triplet state of some compounds using the CNDO/Zparametrization [S] . Other applications were developed successfuIly elsewhere [6--91. In this paper, we present and discuss: (i) in section 2, an investigation of the two lowest. triplet-singIet transitions of some aliphatic carbonyls, in the outline of the CNDO/Sparametrization [lo] ; further, distinct descriptions of the vertical and O-O T, + So transitions, using the CNDO/2parametrization are reported;
(ii) in section 3,aninvestigation in the CNDOjS parametrization of the lower triplet-singlet transitions of the six known azabenzenes. Although the aliphatic carbonyls which we have investigated and the azabenzenes are not large compounds (ab initio calculations have been carried out for some of them), we have considered them because they are among the most studied systems both experimentally and theoretically. ExceUent reviews of the general re-; levant literature have been reported [I I-131. Besides, most of these compounds were investigated by Jaffe; et al. [14,15, and references therein] in the outline bf the CNDO/Sparametrization, both by VO-Cl calculations (S&F S, molecular orbitals; configuration interaction restricted to the lowest singly-excited contigurations with respect to the SCF S, contiguration) and by direct self-consistent field calculations of triplet stat& (without eIectronic correIation energy calculations). In addition, we have computed the oscillator strengths fof the Tj + S, transitions for the lowest nn* and m* triplet states. These calculations have been carried out
234
J. Leclixq et a!./Ttipietstates. II
with the usual one-electron one-center approximation of the spin-orbit hamiltonian (for instance, see ref[7]). After various trial calculations, we may point out that refinements of the wavefunctions beyond a threshold of accuracy do not introduce significant alterations of the/(Tj f So) values. Taking into account this fact, to overcome the difficulty which follows from the non-orthogonality of the SCF molecular orbit& of distinct states, the matrix elements of the spinorbit hamiltonian have been derived from wavefunctions issued from extended VO-CI CNDO/S calculations (SCF So MO, CI extended to doubly-excited configurations). Spin and spatial symmetry-adapted functions are used in all these investigations.
2. The lowest nn* and nf
triplet states of some
aliphaticcarbonyls The carbonyl compounds present very interesting tests of our methodology. Firstly, they contain both x and lone-pair electrons. Secondly, experimental studiesof formaldehyde [16], acraldehyde [ 171, benzaldehyde [I81 and acetophenone [I91 reported an elongation of about 0.1 A of the C=O bond length from S, to St or T, states. The previous study I lets us hope to account for this one significant difference which other Investigations show to be essential for a correct evaluationof the spin dipole-dipole contnbution to the zero-field-splitting parameters of the me&table triplet state of aromatic carbonyl compounds such as benzaldehyde [8] and benzophenone [9]. ; In this section, the T, + So and Tz f So transitions )f formaldehyde, formic acid, acetaldehyde, acetic sid, tram-acraldehyde (trans.acrolein, trans-propenal), crylic acid and acetone are obtained In the outline of he CNDO/S parametrization, which is the adequate ;DO parametrization for theoretical spectroscopic tudies of such compounds. For these investigations of +e vertical Ti + So transitions, we have proceeded with be ground state experimental geometries reported by tton 1201 and the axes conventions are shown in . 1. However,this parametrization is inadequate to tribe the alteration of geometry and we hav: atpted to characterize the vertical and the 0-O T, + transitions in the outline of the CND0/2 paramePization (it is well established that this parametrization
I
2
0
-I-.. II
/YY
R
R’
Fig. 1. Ives conventions for the aliphatic carbonyls: fomaldehyde and formic acid (RsH, R’=H,OH), acetaldehyde and acctic acid (R&Ha, R’=H,OH), acraldehyde and acrylic acid (R=CHt=CH-, R’=H,OH), acetone (R=R’=CHs).
is inadequate for the investigation of the higher states). For these latter investigations, we have assumed for the Ti state the theoretical values of the C=O bondlength reported in I. Moreover, we have computed the oscillator strengths of the T, f So and T2 + So transitions. Such computations have been carried out before for the nrr* triplet states and the qualitative (if not quantitative) interpretation is unambiguous, but this is not true for the m* triplet states (for instance, see the following discussion for formaldehyde). In the computation of the electric dipole moments of the singlet-singlet and triplettriplet transitions, the two-center integrals Qs(A), n 2~,03)),
where u Ex,y,z and A and B (#A) stand for carbon or oxygen atom of the carbonyl group, were taken into account in addition to the one-center integrals. On the other hand, trial computations of the matrix elements of the spin-orbit hamiltonian, using the values of the two-center integrals (2s(A), ‘Bxl’3B2p,,(B)L - - .>Qp,(A), &Jr;
2~#3)),
.--9
reported by Tokuhiro et ai. [21], have shown that the introduction of these integrals leads to modifications of the values of oscillator strengths of the triplet-singlet transitions less than 5%. Consequently, these latter Integrals have been neglected. 2.1. Fommldehyde The T1 + So transition in formaldehyde with origin (O-O band) at = 3.12 eV is known for a long time [22 -241. From trapped-electronspectra, the vertical tm-
J. Leclercq et al./Tdplet states. II
235
and the oxygen atoms of the carbonyl group, is necessitions T, + So and T, (3A,) +- So are found at 3.75 sary because the ratio of the one-center to the twoand 6.20 eV, respectively [25]. center integrals is less than two while the coefficients Many theoretical investigations of the electronic which arise from LCAO expansions are of similar order. structure of this compound have been carried out. The Hence, the x component of the electric dipole moassignments of the vertical lower singlet-singlet and ment for the S3 4 S, transition is -0.1464 eB (leading triplet-singlet transitions have been defmite for many years but, as far as we know, the change of geometry be- tof(T, + So) z 1.5 X 10W7)from atomic-polarization tween the ground and excited states has been onIy inves- caIcul&ons and -0.0366 eA from atomic-plus valencepolarization calculations. Our valuef& + So) = 13.0 tigated by Buenker and Peyerimhoff [26]. Our values X IO-‘, twenty times weaker than f(T1 + So), is conissued from caIculations with CNDO/S parametrization sistent with the estimation reported by Becker (ref. are consistent with the ab initio investigations. The SCF [13] ,p. 161). values for the vertical Ti + So transitions are even better, the semi-empirical parametrization taking a certain 2.2. Acetaldehyde, acraidehyde mid acetone amount of correIation into account. The CNW2 investigation is more significant. The values, resulting Our energy for the vertical T, -+ So transition, alfrom SCF calcrdations plus perturbation treatment, of though always improved by correlation treatment, the vertical and the O-O T1 +S, transitions (3.85 and corresponds rather to the O-O band than to the vertical 3.03 eV) are in good agreement with experimental data transition itself (this is true also for the values reported (3.75 and 3.12 eV). Unfortunately, this parametrizaby Jaffe et al. [14] for acraIdehyde and acetone, see tion is inadequate for the description of the higher exconclusion).The energy of the vertical Tz 4 So transicited states because of the undue mixing of (Tand R tion is in agreement with the experimental data for aceorbit&. taldehyde and acetone (see table 1). For these two Many theoretical studies of the spin-orbit coupling compounds, the correlation treatment improves the SCF in the 3& + So (IA,) transition have been reported value in a significant manner. On the other hand, the [27-29,151. Our valuefiT + So) = 2.5 x 10-7, tbou$l energies of the O-O and vertical T, + So transitions smaller than the estimation of DiGiorgio and Robinson issued from CNDO/Z calculations are in good agreement [16], is consistent with the values obtained by Yonezawa et al. [27] (6.7 X IO-‘/) and Jaffe et al. [28] with the experimental data. In particular, it may be pointed out that the differential correlation effect for (2.4 X 10e7). Tire study of the oscillator strength of the T, + So transition is more significant. Kearns and acetone is very important. Our vahref(T1 + So) = 3.3 X lo-’ for acetone is Case [30] have previously reported an estimation f(TZ + So) = 1.3 X 10-9, taking only into considerain agreement with the estimation issued from the extion the coupling between the S, and T2 states. Inperimental data: r? = 0.4 ms and 4, = 0.03 in rigid deed, our study shows that the $A1 (T,) state is chiefly ether-IPA at 77 K, while @lC= 1.0 +O.l [35]. For perturbed by the lowest ‘B, (S3) state and not by the this molecule, as for acetaldehyde and acraldehyde, S1 state. Besides, it must be pointed out that the calthe met&able triplet state is chiefly perturbed (via the culated value off(T2 + So) for such compounds is spin-orbit interaction) by the fust excited Inn* state proportional to the oscillator strengths of the singletand the T1 + So transition is polarized in the molecular singlet or triplet-triplet rr* + n and rr* + D transitions. plane, along or nearly along the C=O bond. On the These oscillator strengths are zero jn any ZDO approxiother hand, the f(T2 + So) values are of the same order mation for planar molecules. The introduction of atomof magnitude and consistent with the estimation of ic polarization, i.e. the integrals (2s (A), u 2p,(A)), Becker [ 131. where u zx,y, z and A stands for the carbon or oxygen atom of the carbonyl group, leads to overestimated 2.3. Fomic, acetic and amylic acids values for these oscillator strengths for such compounds which are in fact nearly-diatomic systems. The.introThe O-O band of the S, (mr*) + S, transition is duction of valence polaiization, i.e. the integrals (2s(A), located at x 5.0 eV for formic and acetic acids [ 1 l] u 2p,(B)1, where A and B (#A) stand for the carbon instead of 3.49 and 3.56 eV for formaldehyde and ace-
J. Lectercq et at./Trt@tetstates. II
‘236 Table 1
Thetwo triplet-singlet transitions of some carbonyl compounds (t: vertical transition TjtSo;O-0:
0-O band of the Tj-
So
transitions) Compound
State
Trans.
E(Ti>- E(So) (eV)
SCFa) formaldehyde
3A* 3AI
formic acid
3**.
aA’ accetaldehyde
acetic acid
3A”
3A’ 3A” 3 t
A
acraldehyde
3hrP
3Al acrylic acid
3
A
.*
accfone 3A,
t
3.02
o-o t t
6.26
O-O t t
5.38
o-o t t o-o t t o-o t t o-o t t o-o t
3.70
3.00
SCF f 3.65 2.88 4.06 3.39 3.54 2.52
6.09 3.65
3.24 6.69 4.03 5.71 3.22
3.96
2.98 2.03
3.20
3.64 2.52
3.21
2.91 5.69
3.85 3.03
3.15 2.43
exp.
3.75 [25] 3.12 [22-241 6.20 1251
4.34 3.67 4.02 3.06
3.15 c) -3.10 1311 6.40 c)
4.58
10’
talc. b)
WLp.
2.5 (z)
al2.0 [ 161
0.13 (x) 15.0 (2 >y) 0.24 (x1 2.3 (z %y) 0.07 (xl 13.0 (z > Jg
3.80
3.16
3.28
‘)
6.48 3.94
5.43 2.10
A&*)
f(Tj+$)X
5.75 2.78
3.10 3.79 3.29 3.17 3.17
0.49 (x) 10.0 (z > ,I)
4.05 3.01 [3394]
0.06 (x) 15.0 (z %y)
4.63 3.55 4.13 3.42
6.09
4.15 d) ==3.50[35,363 6.25 d)
0.30 (x) 3.3 (2)
2.8-4.2 e,
0.02 (x)
a) WithCNDO/Sparametrization (on the left) and with CNDO/2 parametrization (on the right). b)x,y andz stand for the theoretical polarization of the T- +-+ So transitions (fig. 1 shows the axes conventions). ‘) TI *Se: 3.8eV [321,3.75eV [251;T2 *So:635 eV’[32],6.40 eV [25]. d)T1 +-S1,:4.15eV [3732,25],4.16 eV 1381-T , 2 +S,-,: 6.25eV [37,25],5.88 eV [38],6.3 eV [32]. e, From vaIues of rp and+ for the TI -L Se transition (see text).
taldehyde, respectively:Unfortunately, few experimental and theoretical data about the triplet states of these compounds are available from the literature. McGlynn et al. [39] report for formic and acetic acids a phosphorescence from a state they assumed to have TV* character when the theoretical investigations of Basch et al., Peyerimhoff and Buenker [40] and Jaff6 et al. [10,14] locate the 3nn’ state of formic acidlower than the 37rir*one. Our results are consistent with these latter studies. However, we have not carried out conformational analyses for the 3mr* state and we do not rule out the possibility of an important change in the equilibrium
geometry of this state. It may be pointed out that the oscillator strengths of the triplet-singlet transitions, specially the 3~n* t- So ones, are increased in a significant manner with respect $0 the aldehydes ones. Moreover, for these carboxylic acidsas well as for the
aldehydes,the introduction of the two-center integrals in the electric-dipole-momentcalculationsis shownto be essential.
3. The lower triplet states of azabenzenes Fig. 2 shows the geometries that we have assumed
J. Leclercq et al.lTriplet states. Ii
Pyridine’
Pyr imidine
Pyrazine
237
Table 2 The labelling of n, P and P* SE molecular orbit& of ezaknspecies, in ground state
zenes, according to group-theoretical
CNDO/S calculations
D 2h
Compound
Labels of n orbitals
pyridine
n: 7al
pyrazine
n_
s-Triazine
Lables of n* o:bitals
C2”
: 3b,u
n+ : 4ag Pyridarine
Lables of 51orbitals
b
s-Tetrazintb
pyrimidine
n+ n_
: 7al : 5b2
.nl : lb3, r2 : lb2g 7r3 : lblg ‘il : lb1 ail : laz 7r3 : 2b1
pyridazine
n+
: 7al
n_ : Sb2
CP”
%h
D2h
sym-triazine
nl
: 3ai
n2 : 4e” Fig. 2. Geometries and axes conventions for the azabenzenes. Unless different values are specified, all C-C bond lengths are
equal to 1.38 A, all C-H bond lengths are equal to 1.08 A and all angles are equal to 120’. (a) Idealized geometry with all C-C bond lengths equal to 1.40 A; (b) see ref. [ 201.
sym-tetrizine
nt
: la’;
~1~: .le”
na
: 46
?Tj :
nl
: 3bzu : 3bm
rrl : lb3u f2 : lblg n3 : lbzg
n2
n3 :4a
g
le”
nz,: 2bag for these compounds. The axes were labelled according to Mull&en’s conventions [41] and the review of Innes et al. [42]. Table 2 specifies the labelling of the SCF
n, n and n* molecular orbitals, according to grouptheoretical species, in ground state CNDO/S calculations. It allows an easy correspondence between our labelling in table 3 and the more usual ones [21]. In table 3, we report the energies of the lower triplet states (CNDO/S parametrization), with respect to the corresponding ground state energies (vertical transitions). As examples, table 4 shows the detailed contributions to AE(2) of the symmetry-adapted functions for the metastable triplet state of pyridazlne and table 5 summarizes the second-order perturbation treatment of the electronic correlation for some states. The inclusion of all the symmetry-adapted functions into the perturbation expansion is justified once again (the results of
columns four and five of table 5 show that the.totaI contributions of functions such as lSE~211> 0.01 eV is always < 30% of A@‘)_
3.1. Fyridine Evans [43] has observed triplet-singlet absorption bands and located a triplet level at 3.67 eV. He suggested that this state is rrrr* and the lowest one. Contrary to this assignment, Hoover and Kasha [44] predicted that the lowest triplet state must have nrr* character and lies about 3.50 eV above the ground state. In a more recent paper, Japar and Ramsay [45] assign two weak bands at * 3.68 eV to a triplet-singlet mr* transition, similar to the 3400 A band system of benzene (a distinct band system is observed between 3.87 and 4.13 eV but no de&rite assignment can yet be made). On the other hand, some electron-impact investigations [46; 47, and references therein] and several semi-empirical calculations 48-511 have been reported. Our “SCF + AE Q)” results for the three lowest
3h 3B2g
pyrazinc
Al
I
I A2
3El ‘A’;
?A’;
3
% jA2 % 3A* 3B2 3AI 3gr
pyridczinc
sym-trinzinc
3BI 3Az 3h 3Az 3A* 3B*
pyrimidinc
-3
301 3A1 % 3AI jSZ
pyridinc
3Au 3h” 3BzU 3%~ 3B*U
stntcc)
Compound
2.97 3.38
3.89 3.89 5.92
4.05 3.52 4.93
2n*
+ 2e”
5.58
5.17
5.11
3 2e”
4c’
lc”
4.72
+ 2c” A 2e”
le”
4.31
4.65
4.61
4e’
-t 2e”
-+ 2e”
-+
lc”
4c’
la2
4.59
4.47
4.44
4.61
4.74
4.06
4.94
4.84
3.59 [62,70]
0.01 (2j
1.5oF>y)
4.82
-t 2a2, Ia2 -c3b,
2bl
4.37
5.97 5.02
+ 3bl
2bl
1.9(x =y>z) 0.06 (x)
0.53 tj. 2)
4.81
3.01--3.206)
I
4.55
4.14
2bI -+2a2
+3bl,
la2
3.20
4.6R
4.45
4.42
1.1 f_!Jax) [Gl]
2.6 (x)
-3.70
1.2 (v > 2)
1.2 (VI 2.2 (x)
0.0
1.4 (2)
0.95 (x)
1.2 (z)
talc.
4.01
3.43-3.58C)
3.22-=3.50d)
3.68 143,453
n3.50 144)
cxp.
3.94
3.31
4.04
a&) -
fO;.'SO)X IO'
3.70
3.59 4.75
3.57 4.70
32a2 + 3bl, 7~11 --r2az
5bz
5bz
4.18
4.35
+ 232
2bl
7a1
2bI
4.78
-r2i2,2b,-+3b,
la2
4.73
4.65
-r3b,,7q-c2a2
4.22
4.53
4.13
-e 2az
5bz
5%
3.85
4.22 4.74
4.88
lblg * 2bm
lbng -, 2bm
5.39
4.67
3.90
+2az,5bl-r3b,
4.78
3.65 3.76
6.04
lbzg -, Ia,
+3bi,lazh2az
4.22 4.25
3.89
3.49
4.76
3.56
4.40
4.14
3.75
4.25
4.84
+3b,
3.84 4,lO
3.92 3.65
3.31 5.02
4ag + 2b3u 3bm + 2b3, -+ la, 43g lb,g -, la,
la2
2bi
la2
-+2n2,2bl-+3bl *2a2 * 3bl, Ia23 2a2 2bl
3.63
3.61
SW *
SCP
3.99
vo-Cl
f:‘(Tj) - fi(So) (cV) c,
7aI -+3b,
Leading confiyrntions b,
. -p--
Table 3 ?11elower triplet stntcs of aznbcnzcncs (CNDO/Sparamctrlzation)
-
0.01 - 0.12h)
cxp.
:
.,
12
:
..’
.
‘.
.'
J. Leclercq et
@/Trip&t states. II
239
triplet states are: 3B, at 3.63 eV, 3AI at 3.84 eV and 3 B2 at 4.10 eV (it may be pointed out that our lowest SCF state is 3 B, as in the studies of Gaffe et al. [ 14,5 11). These values are totally consistentwith those of Chen
and Hedges[SO] and are not in disagreementwith the photoabsorption data [43-45]. However,the precision of our calculationsbeing 2 0.15 eV at least for each state, we must conclude that no definite assignment may be suggested for the lowest triplet state of pyridine. In fact, the smali spacing between the two lowest nrr* and rrrr* triplet states we obtained (consistent with previous work [49,50]) would indicate large vibromc coupling between these states as suggested for instance by Hochstrasser and Marzzacco 1521 for pyridazine. Because of ‘the lack of any experimental data, our values~(3Bl(nn*)+So)= 1.2X 10e7 andf(3A,(nlr*)
+ So) = 0.95 X 10m7can only be comparedwith other theoretical values [49,51,53,54]. For the first transition, the agreement is good. For the second transition, our value is consistent with that of Vanquickenborne and McClynn [54] but somewhat different from those reported by Yonezawa et al. [49] and by Jaffe et al. [51]. This may be explained by the gag we obtained between the energies of the perturbed AI state and of the most perturbing state, the lowest ‘B, state. 3.2. i’?zedinzines: pyrazine, pyrimidine a& pyrihzine Most of the authors agree with the nrr* character of the lowest triplet state of the diazines [55-651. Our results for this state are in fairly quantitative agreement with experimental data for pyrirnidie and pyridazine. For pyrazine, our “SCF + A@J” value (2.97 eV) is somewhat smaller than the experimental value (see table 3) but better than the values reported by YoneZaWa et ti. [49] (2.65 eV) and by Chen and Hedge
[50] (2.82 eV) in similar calculations and this failure is probably due to an insufficiency of semi-empirical parametrizationsrather than specificcharactersof our investigations.Our value (4.04 eV) for the lowest 3B1u (nn*) =+So vertical transition is consistent with the ab initio values reported by Hackmeyer and Whitten [66] (4.11 eV) and by Wadt and Goddard [67] (4.07 eV). However, the outstanding point of our investigation consists in the obtained values for the other mr* transitions:Indeed, we Iocate a 3B, (n-a:) + S,-,transition at 3 38 eV and a 3Au (n+nz) ES,-, transition at 3.49 eV. Evenin takmginto account an error of0.3-0.5 eV for
J.Leclercq et affTriplet states. II
240
Table4 Mailed contributions to A!+‘) of the spin and spatial symmetry-adapted functions for the metastable triplet state of pyridasine class a)
Contributions > 0.0 1 eV b,
AUthe contributions
number
number
$“*)6E$%)
m
-t”C!
0
0.0
k
-rmC)
0
0.0
k
+u
p.IJ+l k, m k,.nt k, k k. k
+ %t -tn,v
3 0 3 1
k,
1
.k,m kk k, 1 k, l k 1
--‘“,” *WV
*u,u
+P*P+l +u,t +u.t -rm,u
‘V,”
-+u,r
total
0 3 4 1 0 10 0 3
0.0 -0.1098 -0.1997 -0.04 29 0.0 -0.2324 0.0 -0.0417
7 5 165 10 90 60 98 168 18 1410 882 1641 1008 15012
28
-0.8394
20574
-0.0894 0.0 -0.1088
-0.0147
ZJ&$)(eV) 0.0 0.0
-0.122 -0.006 -0.136 -0.029 -0.025 -0.211 -0.232 -0.269 -0.040 -0.814 -0.097 -1.376 -3.357
3, Weuse the indices k, I for the closed-shell orbitals, m, n for the two open-shell orbitals (ttt = p orp + 1, n = p + 1 orp, respectively) and u, I for the virtual orbitak b, Contributions of the functionsJ such as j6E 5“1 z 0.01 eV, where 6.Ep'= - ~~IHlO~/[~~lHIJ~-~OIH(O~j;z$@standsfor the summation on these functions while ZJ stands for the summationon all the functions. c, BriUouin’stheoremis fubilled for these classes. these vertical-excitationenergies
[in accord&e
with
the lowest 3 Bg, (n+n,*) + So investigation] our cakulations indicate that it seems plausible that the adiabatic energies of the lowest 3 B and 3Au states are in the % range 3.540 eV, just below or just above the adia-
batic energy of the ‘%u state. The spin-orbit interaction is spatial-symmetry forbidden between the ‘B3,, and 3B2, states but allowed between the ‘B3u and 3A,, states and the matrix element of the spin-orbit hamiltonian (H&I is (1B,uIH,,13Au)= 0.6 cm” while
Table 5 Second-order perturbation energy AS(‘) for some triplet states of azabenzenes. (All values are in ev) Compound
pyridine pyrazine pyrimidine pyridazine sym-triaziie sym-tetrazine
‘1 See footnote b) of table 4.
State
3Bt (7ar 3bt) 3&u (lbtg la”) ‘Ba (2bt 2aa) ‘BI (Sbz 2~4 3E” (4e’ 2e”) 3Bz~ (lbzglau)
Contributions Z 0.01 eV a) number
Zy.‘)6$)
A.!+)
(OlH)O)
25 28 19 28 25 23
-0.77 -0.90 -0.36 -0.84 -0.71 -0.45
-3.57 -3.01 -2.66 -3.36 -3.33 -2.40
-343237 -3565.81 -3553.99 -3616.47 -3646.08 -3738.75
J, Leclercq et al./Triplet states. II
~1B3,1H,,13B,U~=6.6 cm-l. Consequently, the 3Au state seems a second plausible origin of the perturbations observed in the lB3,, bands, which might be important if the adiabatic energies of the two states are very close. For pyrazine, our valuef(T1 + So) = 1.4 X 1K7 is consistent with the limits reported by Jamattona and Goodman 1591: f= l-10 X I@. Forpyrimidine, taking into account the experimental value for pyrazine [59] AT, + So) may be estimated equal to 0.04 0.50 X lo-’ from the work of Hochstrasser and Lin [62] . On the other hand, Shimada 1641 measured a radiative lifetime TV% 10 ms for the metastable triplet state, leading tof(T1 + So) = 4 X 10e7 from the values rePorted by Cohen and Goodman [68]. of$ and& For the three diazines, our values agree with the other theoretical calculations [l&49,53,69]. 3.3. Sym-ttizine and sym-tetrazine For sym-triazine, our SCF cakulations (in a oneconfiguration scheme) with the 4e’ (n) and 2e” (n”) So SCF MO as trial open-shell MO, lead to four degenerate solutions. Because of the one-contiguration approach, these solutions are not A’;, A’; and E” symmetry-adapted functions. They are physically equivalent (the C, and C, operations of the D3n group lead from one to the others.) In the same way, the SCF calculations with the le” (rr) and 2e” (jr*) So SCF MO as trial open-shell MO lead to four degenerate solutions which are not A;, Aa and E’ symmetry-adapted functions. Ibe two distinct manifolds (a 3nrr* one and a 3rrrr* one) issued from these calculations are reported in table 3 as 3E” (mr*) and 3A; (ma*) but in fact each degenerate solution is a linear combination of symmetry-adapted functions (A’;, A’; and E” for the first manifold, A;, A; and E’ for the second). Though our investigation of the triplet states of symtriazine is only a first approach, the “SCF + AIZ(2)yy energy for the vertical transition 3E” (3A’;, 3Ai) f-S, (4.06 eV) is consistent with the experimental data (O-O band located at 3.59 eV 162,701). Indeed, it is obvious that the breakdown of the degeneracy by an improved approach, will lead to, an energy somewhat smaller for the vertical T, 4 So transition’(from VOCI calculations, T, has a E” character Our value f(T, + So) = I .5 X lo- $*is larger than the experimental value equal to 0.01 - 0.12 X 1O‘7 from
241
ref. [62], taking into account +he results of ref. (591. However, this value is an estimation only and, on the other hand, it is essential to keep in mind that the oscillator strength is an observable more sensitive to the breakdown of a degeneracy than the energy. For the 3A; (nn*) + S,, transition, we obtainf= 1 X IO-‘. Via the spin-orbit interaction, the 3A’r state is chiefly perturbed by the lowest ’ E” (nrr*) states. The results for sym-tetrazine show our treatment of the electronic correlation to be remarkablysuccessful. Our “SCF t A.$*)” energy for the lowest vertical 3 B,, (mr*) + So transition is equal to I .87 eV, in fairly quantitative agreement with the experimental data (O-O band located at 1.65-1.75 eV [72,74], absorption system extending to = 2.20 eV 174)) while the VO-CI value (291 ev) and tbe SCF value (3.22 eV) are in poor agreement. Our value f(T1 -+ So) =‘4.3 X lo-’ is practically consistent with the estimation of McDonald and Brus [73] . For the lowest 3 B,, (II?T*) + S, transition, the order of magnitude seems correct. On thetther hand, it is interesting to point out that the lowest 5 (nn”) state is chiefly perturbed by the first ‘B3e (nrr ) state [(3AelHsoI lB,J = -5.8 cm-’ via the interaction between the 2b3, (n,) and 4an (n3) MO] ; this perturbation leads to a polarization of the lowest 3Aa -+ S, transition perpendicular to the molecular plane.
4. Conclusion To recapitulate the discussion developed above, we may point out: (i) for non_multiconfigurationaI triplet states, the SCF values are equivalent to the results obtained by VO-CI calculations; (ii) in any case, except for the T, + S,, transition of formaldehyde, the treatment of the correlation energy improves the CNDOlS results (for instance, see the me&table triplet state of the three diazines and sym-tetrazine), in spite of the fact that such semi-empirical parametrization takes this correlation energy into account; (iii) for the CND0/2 investigations, the improvement due to the treabnent of the correlation energy is sometimes spectacular: = 0.5 eV for the O-O T, + So transition of acetaldehyde, * 1.0 eV for the O-O and vertical T, + So transitions of acraldehyde and acetone.
242.
‘J. Leckrcq et a/./Triplet states. II
However, we must point out that our treatment &nnot’remedy the intrinsic weak points of the semiempirical parametrizations. Thus, the VO-CI CNDO/S result for the vertical S1 +.SO transition of formaldehyde is 3.4 eV [lo] while the exqimental values for the O-O and vertical transitions are = 3.5 and 4.1 eV, respectiveIy. This failure leads to too small values inall the CNDO/S investigations of the vertical T, + So transitions of the carbonyl compounds. The necessity of an elaborate treatment of the correlation energies for correct predictions of the transition energies has already been pointed out for an initio calculations. The results of this work support this remark for semi-empirical ZDO calculations. However, an adaptation of the usual parametrizations (CNDO/2 and CNDOIS) to these treatments of the correlation energies seems necessary. We think that it would be more adviiable to substitute the use of rigorous ZDO basis functions sets in calculations. This point of view will be d&Cussedin the other papers of this series. On the other hand, the outstanding points of the calculations of the oscillator strengths reported in sections 2 and 3 are: the necessity of the introduction of some two-center integrals to obtain credible values for the lowest 3m* -+ S, transitions of the carbonyl compounds; the same magnitudes of the oscillator strengths of the 3nn* C- So and the ‘ns” + So transitions of the azabenzenes.
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