Vibronic analyses of the lowest singlet–singlet and singlet–triplet band systems of pyridazine

Chemical Physics 257 (2000) 1±20

www.elsevier.nl/locate/chemphys

Vibronic analyses of the lowest singlet±singlet and singlet±triplet band systems of pyridazine Gad Fischer a,*, Paul Wormell b b

a Department of Chemistry, The Faculties, Australian National University, Canberra, ACT 0200, Australia Centre for Biostructural and Biomolecular Research, University of Western Sydney, Hawkesbury, Richmond, NSW 2753, Australia

Received 17 March 2000

Abstract The ®rst singlet±singlet and singlet±triplet band systems of the absorption spectrum of pyridazine vapour are analysed using ab initio and vibronic coupling calculations. The lowest singlet±triplet absorption involves a comparatively unperturbed (p ,n) 3 B1 state, and contrasts with the highly perturbed singlet±singlet spectrum. The major source of vibronic perturbation in the singlet±singlet absorption is attributed to coupling between near-resonant (p ,n) 1 A2 and (p ,n) 1 B1 states, with the former being slightly lower in energy. Many features of this complex and unusual spectrum, and its associated single vibronic level ¯uorescence spectrum, can be explained using a simple vibronic model. This provides experimental support for recent relaxed CASPT2 and EOM-CCSD calculations, but contrasts with earlier assignments of the spectrum. Theory and experiment suggest that the spacing between the lowest A2 and B1 states is larger in the triplet manifold, leading to a simpler spectrum. Ó 2000 Published by Elsevier Science B.V. All rights reserved.

1. Introduction The resurgent computational interest in the diazabenzenes [1±12] makes it important for the electronic and vibrational properties of these compounds to be characterised experimentally, to test the range of theoretical predictions that are now available. This is particularly true for pyridazine (1,2-diazabenzene, Fig. 1), since the vibronic structure of the ®rst singlet±singlet absorption band has so far de®ed analysis. It is unusual that the most accessible absorption band of such a wellknown and spectroscopically signi®cant com* Corresponding author. Tel.: +61-2-6249-3043; fax: +61-26249-0760. E-mail address: gad.®[email protected] (G. Fischer).

pound is still poorly understood. The transition, which theory and experiment agree, is p n in character, has an origin in the vapour phase at 26 648.75 cmÿ1 [13,14]. Although the vapour spectrum was ®rst reported in 1949 [15], it has not been satisfactorily analysed despite much careful work during the succeeding ®ve decades; this indicates that the excited vibronic states are highly perturbed. The present paper suggests that these perturbations are attributable to strong vibronic coupling between the lowest-energy (p ,n) 1 B1 and (p ,n) 1 A2 states, which new calculations predict to be nearly degenerate, with the 1 A2 state slightly lower in energy. We propose a simple vibronic coupling scheme that uses the minimum number of adjustable parameters to model the principal features of the lowest singlet±singlet absorption and

0301-0104/00/$ - see front matter Ó 2000 Published by Elsevier Science B.V. All rights reserved. PII: S 0 3 0 1 - 0 1 0 4 ( 0 0 ) 0 0 1 3 7 - 3

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G. Fischer, P. Wormell / Chemical Physics 257 (2000) 1±20

Fig. 1. Structure and axis system for pyridazine.

¯uorescence spectra. Vibrational analyses are proposed for the singlet±singlet band system and the related but much simpler singlet±triplet system. The vapour absorption spectrum of pyridazine was ®rst reported by Halverson and Hirt [15], and several other studies have followed. The ®rst 3800 cmÿ1 of the ®rst singlet±singlet absorption spectrum is shown in Fig. 2, and the corresponding singlet±triplet absorption, which has previously been reported by Innes et al. [13], is shown in Fig. 3. The singlet±singlet spectrum is by far the more complicated. It contains a distinct origin, which we will call the 0 band, followed by strong bands at ‡373 and ‡534 cmÿ1 , then a series of about eight slightly weaker bands between 650 and 800 cmÿ1 . All bands are matrix dependent, notably the 373 cmÿ1 interval and the 650±800 cmÿ1 cluster of

bands, although there is little change in the 534 cmÿ1 interval for spectra of pyridazine in the vapour phase and in mixed crystals with benzene and cyclohexane [16]. The proliferation of matrix-dependent bands suggests that vibronic perturbations are active, involving one or more electronic states, which are not necessarily at higher energies. If this were the case, then the matrix dependence would arise from changes in the electronic energy gaps. The spectrum becomes increasingly dense and tangled at higher energies, but the ®rst 3000 cmÿ1 contains some discernible clusters of bands in which progressions of roughly 550 cmÿ1 are built on the 0 band, the 373 cmÿ1 band and the 650±800 cmÿ1 cluster of bands. The band spacings change at higher energies, but this pseudo-regularity in the spectrum (which has not, to our knowledge, been reported before) is consistent with our analysis of near-resonance vibronic coupling. A classic, and in some ways comparable, example of near-resonance vibronic coupling occurs for the lowest n and p p transitions of isoquinoline p [17,18]. Puzzling features, such as the complex vibronic structure, the irregular nature of the sequence structure, and the ambiguous isotope e€ect have been readily explained for this compound. The early study of pyridazine by Innes et al. [13] proposed that there is strong anharmonic coupling

Fig. 2. Vapour absorption spectrum for pyridazine: singlet±singlet absorption.

G. Fischer, P. Wormell / Chemical Physics 257 (2000) 1±20

3

Fig. 3. Vapour absorption spectrum for pyridazine: singlet±triplet absorption.

between the totally symmetric mode 6a (a1 symmetry, m6a in LordÕs notation [14], ground-state frequency 664 cmÿ1 ) and the overtone of an antisymmetric mode, thought to be mode 16b (b1 , ground state 370 cmÿ1 ). This interpretation, which required strong vibronic coupling with a second low-energy 1 B1 state [13], was discarded in a later paper [19] owing to rotational arguments and the single vibronic level ¯uorescence (SVLF) spectrum [20]. An alternative hypothesis was suggested by Ueda et al. [16], and Ransom and Innes [19]. These workers proposed that the second 1 B1 state is even closer to the ®rst than was previously thought, and indeed the two states are nearly degenerate. According to this proposal the 0 and 373 cmÿ1 bands are the electronic origins of the transitions to these two 1 B1 states. The di€erence in rotational constants for the two bands lent support to this model [19], as discussed below. The principal objection to this assignment of two nearresonant states is theoretical: molecular-orbital (MO) calculations, including our own, steadfastly refuse to place a second 1 B1 state near the ®rst. The predicted energy gaps are typically over 2.5 eV (20 000 cmÿ1 ), as shown in Tables 1 and 2. However, since these calculations also predict that a low-lying 1 A2 state occupies the position that

was formerly assigned to a second 1 B1 state, Zeng et al. [6] and the present workers have considered the possibility of strong coupling between the lowest 1 B1 and 1 A2 states. The 373 cmÿ1 interval varies in di€erent matrices [16] and in pyridazine clusters [21], but always remains closely associated with the 0 band; however, this is not an argument against the proposal of two near-degenerate states. The solvent e€ect for the ®rst observed band is not quantitatively large ± ‡89 cmÿ1 for cyclohexane, and ÿ178 cmÿ1 for benzene ± and may well be of this magnitude for both (p*,n) states. Thus, the spacing between the 1 A2 and 1 B1 states need not change substantially in di€erent molecular environments. No direct experimental evidence has been given for the predicted 1 A2 state, which would be electric-dipole forbidden and could only acquire appreciable absorption intensity through vibronic coupling with an allowed state. Palmer and Walker [2] reported some new experimental spectra for pyridazine, including near-threshold electron energy-loss (EEL) spectra. Their multireference, multi-root con®guration-interaction (MRDCI) calculations predicted that the lowest 1 B1 and 1 A2 states should be nearly degenerate, but no experimental evidence was found for the second state. Circular dichroism spectra of pyridazine

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G. Fischer, P. Wormell / Chemical Physics 257 (2000) 1±20

Table 1 Calculated vertical-excitation energies (in eV) for the lower-energy triplet and singlet states of pyridazine Excited states

1

Experimental [2] CNDO [25] CNDO/S-CIb MRDCI (DZ) [2] MRDCI (89 basis) [2] EOM-CCSD [7] EOM-CCSD(T) [7] MCLR (TZPD) [4] MCLR (TZ) [4] MCLR (TZP)c [4] SAC, SAC CI/4-31G [1] CASSCF [3] CASPT2 [3] EOM-CCSD(T) [10] STEOM-CCSD [10] CASSCF/6-31G*b CASPT2/6-31G*b

3.4 3.3 3.55 3.825 3.348 4.06 3.65 4.25 4.12 4.25 4.281 5.28 3.48 3.65 3.76 4.78 3.44

B1 (1)

1

A2

4.4 4.43 3.925 3.274 4.68 4.28

5.093 5.35 3.66 4.29 4.46 5.50 3.70

1

B1 (2)

1

B2

5.5±6 6.2 6.18 6.358 5.658 6.61 6.20 7.97 7.90 7.97

6.4 5.1 5.79 7.230 5.324 6.85 6.44 7.33 7.52 7.22

7.99 5.80 6.22 6.41

7.69 6.61 6.44 6.77

3

B1

3

A2

3

B2

4.0a

(2.9) 3.55 3.082

4.45 3.929

2.98 4.256

3.35 3.523

4.673

3.09 4.423

3.74 2.61

4.89 3.42

a

Feasible, but not yet secure, assignment. This work. c Benzene geometry. b

Table 2 Calculated transition energies (allowing for electronic relaxation, in eV) for the lower-energy triplet and singlet states of pyridazine Excited states

1

Experimental [14] EOM-CCSDa STEOM-CCSD [10] CIS/6-31G*a CASSCF/6-31+G*a CASSCF/6-31G*a CASPT2/6-31G*a

3.303 3.849 3.81 4.33b 4.39 4.44 3.09

B1 (1)

1

A2

1

B1 (2)

1

B2

3

B1

3

A2

3

B2

± 3.797

±

6.2

2.787 3.025

± 3.534

±

5.12c 4.32 4.37 2.98

8.35

6.73

2.78b

4.58c

3.22

7.89d

7.30 7.03

3.32 2.43

3.99 2.79

3.58 3.75

a

This work. Non-planar and zero-point corrected. c Planar and zero-point corrected. d State average of ground and ®rst two B1 states at CASSCF optimized geometry for ground state. b

have also been recorded [22±24] but they show no n transition. trace of a second p Zeng et al. [6] have proposed that the 373 cmÿ1 band may be attributed to 6b20 , i.e. two quanta of mode 6b (b2 , ground state 629 cmÿ1 ), built on a 1 B1 electronic origin. Indeed, our own CIS/6-31G* calculations predict a substantial lowering of this frequency in the 1 B1 state, presumably due to vibronic coupling with the nearby 1 A2 state, and further lowering may occur when other factors such as anharmonicity and electron correlation are considered [6]. However, this assignment presents some

diculties since it is not immediately clear why an overtone band should have comparable intensity to the 0 and 534 cmÿ1 bands, where 6a10 would become the obvious assignment for the latter band. Furthermore, it seems to con¯ict with the SVLF spectrum reported by Ueda et al. [16]. Indeed the SVLF spectrum, rather than exposing the vibronic character of the absorption spectrum, imposes further constraints on possible assignments, without clearly indicating what the actual assignment should be. Speci®cally, the SVLF spectra from the 0 and 373 cmÿ1 bands are very similar, consisting

G. Fischer, P. Wormell / Chemical Physics 257 (2000) 1±20

mainly of progressions in the totally symmetric 6a and 15 modes. If the strong 373 cmÿ1 band were attributable to 6b20 , then the SVLF spectrum should contain strong 6b20 and 6b22 bands; a similar argument was used by Ransom and Innes [19]. In contrast, the strong 534 cmÿ1 band has a di€erent SVLF spectrum, and this was used to support its 6a10 assignment. The strong band at 738 cmÿ1 was assigned to 9a10 on the basis of its ¯uorescence spectrum, while the SVLF spectra for the other bands in this region were complicated and could not be assigned by Ueda et al. These observations can be understood if the 1 B1 state is subject to near-resonance vibronic coupling. Ransom and Innes [19] point out that the 373 cmÿ1 interval increases to 374 cmÿ1 in pyridazine-d4 , and cite this as further evidence for a di€erent electronic state. We agree with their interpretation of two near-resonant electronic states, but propose that they are 1 A2 and 1 B1 , and that the 0 and 373 cmÿ1 bands are principally attributable to vibronic and electronic origins of the 1 A2 and 1 B1 states, respectively. As mentioned above, one argument that was used to support the earlier assignment to two neardegenerate 1 B1 states was the rotational contour analysis of the vapour spectrum; any new assignment must provide a credible explanation for this. Ransom and Innes [19] showed that the 0 and 373 cmÿ1 bands have di€erent pro®les ± this can be seen qualitatively in Fig. 2 ± and the large, negative inertial defect of the 373 cmÿ1 band requires an assignment to either (1) an antisymmetric vibration; (2) a second electronic transition, either the electronic origin of a second 1 B1 system or a vibronic origin of an expected 1 A2 system; or (3) a combination of both possibilities. The assignment to an 1 A2 state was rejected because it appeared to be inconsistent with the SVLF spectrum. We propose a fourth alternative, in which the 0 band is a vibronic origin of the 1 A2 state (although heavily mixed with 1 B1 character), and the 373 cmÿ1 band is the closest approximation to the 1 B1 origin. As discussed in Section 4.5 below, this is consistent with the observed inertial defect of the 373 cmÿ1 band. Our analysis of the ®rst singlet±singlet absorption band of pyridazine draws on our parallel analysis of the corresponding singlet±triplet ab-

5

sorption. In separate studies [26,27], we have recorded and analysed the lowest-energy singlet± triplet bands for the other diazines: pyrazine and pyrimidine. The principal aim of these studies was to determine the frequencies of non-totally symmetric modes for the lowest triplet states and, using vibronic arguments, to infer the approximate energies of some higher triplet states which have not been observed experimentally. Since the nontotally symmetric modes do not induce signi®cant intensity in the singlet±triplet absorption spectra, and cannot be seen directly, their frequencies are derived from sequence structure on the origin or other symmetry-allowed bands. For example, in pyrazine, the 411 sequence band occurs at ÿ461 cmÿ1 . Mode 4 has a ground-state frequency of 756 cmÿ1 , and hence its excited-state frequency is 295 cmÿ1 , compared to 517 cmÿ1 for the corresponding singlet state. Since this b2g mode couples the B3u and B1u excited states in both the triplet and singlet manifolds, the lower frequency suggests a smaller energy separation for these states in the triplet manifold. Similar arguments are expected to apply for pyridazine, but the singlet± triplet spectrum could also serve as a comparatively unperturbed model for the singlet±singlet spectrum. It was anticipated that comparisons between the two spectra, which involve orbitally similar excited states of di€erent spin multiplicity, would be instructive. As evidence for the expected similarity between the 1 B1 and 3 B1 states, we note the similarities between their unusual vapour-tocrystal blue shifts of 1702 and 1764 cmÿ1 , respectively [28]. Hochstrasser and Marzzacco [29,30] have reported part of the 4.2 K absorption spectrum of a pure pyridazine crystal. They observed a singlet± triplet absorption system with an origin at 24 251 cmÿ1 , followed by a stronger band at ‡225 cmÿ1 , which they assigned as a vibronic origin. Progressions in a 639 cmÿ1 mode are built on both of these origins. The 639 cmÿ1 interval appears in the vapour absorption spectrum, where it is assigned to mode 6a, but the 225 cmÿ1 band is not seen. A weak band seen by us at 212 cmÿ1 in the vapour is suspected to be a hot band. We note that the 6a frequency of 639 cmÿ1 (ground state 664 cmÿ1 ) is signi®cantly larger than the interval of 534 cmÿ1 in

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G. Fischer, P. Wormell / Chemical Physics 257 (2000) 1±20

the singlet±singlet system. The phonon structure built on the two crystal-state origins is markedly di€erent: the 24 251 cmÿ1 origin is followed by a sharp band at about ‡45 cmÿ1 , while the 225 cmÿ1 band has a broader feature centred on about ‡75 cmÿ1 . This suggests that the origin and 225 cmÿ1 bands might be assigned to molecules in two different sites. This would require the pyridazine unit cell to contain two inequivalent molecules at 4.2 K. However, the published crystal structure at 100 K reveals that all molecules have the same geometry [31]. It is conceivable that the pyridazine crystal at 4.2 K is in a di€erent crystal phase from the 100 K crystal on which the X-ray analysis was performed, but no other evidence exists that might test this possibility. The di€erence between the vapour and crystal spectra requires an explanation. The two most likely possibilities appear to be (1) site e€ects as described above; (2) vibronic interaction with another triplet state, where the energy gap between the interacting states changes signi®cantly for the vapour and crystal states. The calculated energies of the higher triplet states are discussed in Section 4.3 below, but even if a possible vibronic explanation were forthcoming, the di€erent phonon development for the two origin bands would still require explanation. Innes et al. [13] have analysed the stronger bands in the singlet±triplet vapour spectrum, notably the progression in 6a, but were unable to carry out a full analysis of the hot bands. We have recorded a more complete spectrum and, with the assistance of new calculations, have proposed further band assignments for both hot and cold bands, as set out in Section 4.3. As summarised in Tables 1 and 2, there have been several MO studies of the excited electronic states of pyridazine, including our own. Computational methods, such as the complete activespace self-consistent ®eld with second-order Mùller±Plesset correction (CASPT2) method have given good results for vertical-excitation energies of single-ring compounds such as benzene and the other azabenzenes, as well as the larger molecule naphthalene [32±34]. In a recent study of pyrazine, Weber and Reimers [11] have systematically considered the methods that are currently available

for calculating transition energies for molecules of this size. They concluded that the most reliable results were given by the ab initio CASPT2, equation-of-motion coupled-cluster with single and double excitations (EOM-CCSD, with a systematic improvement for EOM-CCSD(T) calculations, in which triple excitations are also considered) and density-functional B3LYP methods. In another recent study, Nooijen [10] concluded that good results can be obtained for the diazines from EOM-CCSD(T), similaritytransformed EOM-CCSD (STEOM-CCSD) and well-converged CASPT2 calculations. EOMCCSD calculations systematically overestimate the energies of (p*,n) states by 0.3 to 0.4 eV, but the computed ordering and energy spacings for the lower states should be suciently reliable for comparison with the present vibronic study. The con®guration interaction with single excitations (CIS) method [35,36] is less accurate than the CASPT2 or coupled-cluster methods, but is also less computationally expensive. It has been used successfully to study the electronic spectra of compounds, such as phthalazine, pyridine, benzene and 1,4,5,8-tetraazanaphthalene [5,35,37,38]. It allows the geometries of excited electronic states to be calculated, together with the frequencies of the associated normal vibrational modes; these quantities are particularly useful for studies of vibronic coupling between molecular states. Weber and Reimers [12] have shown that for pyrazine, the CIS method computes excited-state vibrational frequencies more reliably and economically than the complete active-space self-consistent ®eld (CASSCF) methods, although it is less reliable for vibronically active modes. In the present paper, we use both EOM-CCSD and CASPT2 methodologies for pyridazine, with the aim of answering some persistent questions about the excited electronic states of this compound. 2. Experimental Pyridazine (Fluka, purum grade) was puri®ed by distillation under reduced pressure. The singlet±triplet vapour absorption spectrum was measured in a six-metre multiple-re¯ection cell,

G. Fischer, P. Wormell / Chemical Physics 257 (2000) 1±20

with a path length of over 312 m, using a 450-W high-pressure xenon arc lamp as the light source. The cell was held at a temperature of about 75°C, with the end plates a few degrees hotter. The singlet±singlet absorption spectrum was obtained at room temperature using path lengths ranging from 12 to 72 m. All spectra were recorded photographically in the ®rst order of a 590 grooves per mm grating blazed at 400 nm, using a Jarrell-Ash 3.4-m grating spectrograph. Plates were traced using a Joyce-Loebl Mark IIIC scanning microdensitometer. 3. Calculations 3.1. Molecular-orbital and density-functional calculations Ab initio MO and density-functional calculations were carried out on pyridazine using the G A U S S I A N 9 4 and M O L P R O 9 8 . 1 programs [39±42] at the CIS/6-31G*, CASSCF/6-31G*, CASSCF/ 6-31+G*, CASPT2/6-31G* and B3LYP/6-31G* levels. The CASSCF (G A U S S I A N ) and CASPT2 (M O L P R O ) calculations used active spaces with four electrons in ®ve orbitals for the (p*,n) states (two n and three p*), and six electrons in six orbitals for the (p*,p) states (three p and three p*). CASPT2 energies were calculated for the corresponding CASSCF/6-31G* optimized geometries. EOM-CCSD [43] single-point energies were evaluated at the CASSCF-optimized structures for the ground state and the CASSCF excited states by ACES-II [44] using the 6-31G* basis set. The excited-state force constants and harmonic vibrational frequencies were obtained for the CIS/ 6-31G* calculations by analytic second di€erentiation of the energy with respect to nuclear displacements. Good results have been obtained by this method for other aza-aromatics [45], but since the calculations do not adequately account for electron correlation the theoretical vibrational frequencies must be multiplied by an empirical scaling factor. The values of 0.895 (for HF/6-31G* calculations) and 0.9613 (B3LYP/6-31G*) [46,47] have been found to give good ®ts with experiment for a range of other compounds in the ground

7

state. The CIS excited-state vibrational frequencies were scaled by a factor of 0.895, which has been found to work satisfactorily for other nitrogen heterocycles [5,38]. Harmonic vibrational frequencies were also determined analytically at the CASSCF level, but these were found to be less reliable than the scaled CIS frequencies; similar conclusions were reached by Weber and Reimers for pyrazine [12]. Geometry optimizations were carried out for pyridazine constrained to C2v symmetry. No imaginary frequencies were obtained for the ground state for any of the levels of theory used in this work. However, some imaginary frequencies were obtained for the (1) 1;3 B1 and (1) 1;3 A2 excited states (i.e., the lowest-energy states of these symmetries and multiplicities) at the CASSCF level, and for the (1) 1;3 B1 and (1) 1 A2 excited states at the CIS level, indicating that the C2v symmetry constraint was too restrictive. For the CIS calculations, relaxation of the C2v symmetry resulted in shallow double-minimum potentials for the singlet states, and a somewhat larger well depth for the 3 B1 state. The electronic transition energies quoted in Table 2 are for the optimized minima of the planar molecule; owing to electronic reorganisation, there are signi®cant di€erences between these values and the vertical-excitation energies in Table 1. Only for the 1;3 B1 states, where successful optimizations were carried out for the non-planar structures, were the transition energies calculated between the zero-point vibrational levels of the geometryoptimized ground and excited electronic states. The zero-point energies were multiplied by scaling factors of 0.9135 for the HF/6-31G* and CIS/ 6-31G* calculations [46,5]. The zero-point corrections slightly lower the transition energies, bringing them closer to the experimental values. The HF/6-31G* energy was used for the ground state of pyridazine, rather than the MP2/6-31G*, so that the energy di€erences involved pairs of calculations with comparable allowances for electron correlation. For comparison with the other listed energies, CNDO/S-CI calculations were carried out using the generalised I N D O - M R C I program of Reimers [6]. The optimized input geometry was calculated at the HF/6-31G* level.

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G. Fischer, P. Wormell / Chemical Physics 257 (2000) 1±20

Franck±Condon factors have been calculated for mode 6a in the singlet±singlet and singlet± triplet transitions from results of the CASSCF calculations: speci®cally, the structural di€erences between the combining states, and the form of the 6a normal coordinate [48]. Determinations of the displacement of the equilibrium positions (D, in dimensionless units) of the totally symmetric modes in electronic transitions have been used in simulations of the spectra of a number of molecules, including benzene [37]. For the 1 B1 state of pyridazine, the observed value of D appears to be in the range from 1.4 to 1.6, in agreement with these calculations. For the 3 B1 state, the observed value of D appears to be greater than 1.6 (predicted 1.32). 3.2. Vibronic coupling calculations As shown in Table 2, and discussed in Section 4.1 below, the ab initio calculations agree that the lowest 1 B1 and 1 A2 states are nearly degenerate, and the second excited 1 B1 state lies at a much higher energy. Accordingly, we propose a diabatic model in which the two lowest and near-degenerate excited states are vibronically coupled by mode 6b(b2 ), and moderated by the totally symmetric (a1 ) mode 6a. A complete and accurate vibronic model for pyridazine would be extremely complex, and would include most of the a1 and b2 modes, although the higher-energy modes would be expected to make relatively small contributions to the coupling. Also, the vibronic interactions with the ground and other excited electronic states would in¯uence the vibrational frequencies in the 1 B1 state. This model would be computationally very dicult, and would introduce a very large number of adjustable parameters, many of which would have to be estimated. Thus, a more complex model, although more accurate, would probably be less convincing when considered critically. We have therefore chosen the simplest model that gives a good semi-quantitative ®t with the observed absorption and SVLF spectra. It is restricted to the two lowest excited states and the 6a and 6b vibrations. Speci®cally, the model aims (1) to predict the presence of the 373 and 534 cmÿ1

bands in the absorption spectrum; (2) to explain why the SVLF spectra for the 0 and 373 cmÿ1 bands are very similar, while the spectrum for the 534 cmÿ1 is markedly di€erent; (3) to rationalise the solvent dependence of the 373 cmÿ1 band, which contrasts with the relative immobility of the 534 cmÿ1 band; (4) to attempt to explain the complexity of the spectrum beyond 534 cmÿ1 , while rationalising the presence of a progressionforming interval of roughly 550 cmÿ1 , and (5) to predict the deuterium isotope e€ect. We have included the totally symmetric 6a mode in the model since we believe that, as the two states are probably within 1000 cmÿ1 of each other, we cannot neglect the vibrational contribution to the energy gap between the vibronically coupled levels. Thus, we must include low-lying vibronic levels of b1 (i.e., B1  a1 , as well as A2  b2 ) symmetry in the calculation. For this reason, and because we are mainly concerned with the low-frequency part of the spectrum, we have considered only the lowest-frequency a1 and b2 modes, which are well separated from the higherfrequency modes of the same symmetry, and might conceivably contribute to the 373 and 534 cmÿ1 bands in the spectrum. In any case, strong coupling involving the higher-frequency b2 modes would not be expected to depress the frequencies of these modes signi®cantly; the e€ect should be concentrated on the lowest mode. In this study, the zero-order description corresponds to the energies and wavefunctions of the vibronic levels in the absence of the vibronic coupling. The input parameters for the calculation were the energy gap between the 1 A2 and 1 B1 states (DE12 ), the vibronic coupling constant (V), the vibrational frequencies for modes 6a and 6b (m6a and m6b ), and the vibrational overlap integrals (In;n0 ). The energy gap has been taken to be small owing to the various MO predictions, as summarised in Table 2, as well as the overwhelming evidence indicating near-resonance vibronic coupling. Furthermore, in order to account for the number of bands seen within the ®rst 1000 cmÿ1 ± a number far larger than the available number of fundamentals, combination bands and overtones of a1 symmetry associated with the B1 state ± we

G. Fischer, P. Wormell / Chemical Physics 257 (2000) 1±20

propose that the A2 state lies just below the B1 , and at least some of the bands in the 650±800 cmÿ1 region are attributable to b2 fundamentals with ground-state frequencies in the range 1000±1600 cmÿ1 . An energy gap of about 300±1000 cmÿ1 would allow this to occur, and this arrangement of electronic states would also provide an explanation for the proliferation of bands to higher frequencies. In an alternative model in which the 1 B1 state is lower, no obvious explanation can be found for the cluster of bands in the 650±800 cmÿ1 region, although the band at about 736 cmÿ1 has been attributed to 9a10 (a1 , ground state 1131 cmÿ1 ) on the basis of its SVLF spectrum. In our preferred model, a gap of 600 cmÿ1 was found to give a satisfactory explanation of the observed vapour absorption spectrum. This ®gure was chosen before it was found that the relaxed CASPT2 and EOM-CCSD calculations gave energy gaps of 890 and 420 cmÿ1 , respectively. This agreement, while very gratifying, is partly fortuitous, as these computational methods cannot reliably calculate energy gaps between states to 300 cmÿ1 (0:037 eV). However, they provide good computational support for our vibronic model. The vibronic coupling constant, V, is de®ned as the magnitude of the o€-diagonal element coupling the vibrationless level of the 1 B1 state with the one-quantum level (mode 6b), of the 1 A2 state. For the chosen energy gap (600 cmÿ1 ), it has been optimized to provide the best agreement with the observed spectra. Vibrational frequencies have also been optimized, with ground-state frequencies serving as a starting point. Part or all of the reduction in input frequencies from their groundstate values may be attributed to perturbations not included in the model; e.g. vibronic coupling with higher-energy electronic states. This was also seen to be the case for pyrazine [26,49]. The vibrational overlap integrals for mode 6a between the 1 A2 and 1 B1 states have been determined from the CASS-

9

CF(4,5)/6-31+G* calculations for the two states. They are analogous to the calculations of the Franck±Condon factors for the 6a progressions in the singlet and triplet spectra discussed above. A dimensionless shift, D, in the normal coordinate was determined. Using the calculated value of D, and assuming only that there is no change in vibrational frequency for 6a between the two states, the appropriate values of the overlap integrals were taken from the published tables [50]. By optimizing the input parameters in Table 3, satisfactory answers were obtained to points (1) to (5), as listed above. The results are, however, sensitive to the choice of vibrational overlap integrals, and they are constrained by the inclusion of only one a1 and one b2 mode in the model. An additional constraint in the model is that no distinction has been made between the vibrational frequencies of the two modes in the two coupled electronic states. Clearly, the simplicity of the model precludes it from providing exact agreement with all observations, but the general agreement provided by the model supports the proposed near degeneracy of the 1 A2 and 1 B1 states, and provides con®rmation for the assignment of the observed prominent bands to these two electronic states. The results of these vibronic coupling calculations are discussed in Section 4.4. Several alternative vibronic models were considered and superseded during this study. One of these was a three-state (1 B1 , 1 A2 and 1 B1 ), onemode (b2 ), model, with ®rst-order Herzberg±Teller coupling between the 1 B1 and 1 A2 states, and quadratic coupling between the ®rst two 1 B1 states through two quanta of 6b. Another model involved coupling of the two lowest 1 B1 states by a1 modes. Together, these two models could account for some of the observed spectral features. However, the energy gap between the two lowest 1 B1 states is relatively large: the EOM-CCSD(T) and CASPT2 vertical-excitation energies in Table 1

Table 3 Input parameters for vibronic coupling of the 1 B1 and 1 A2 states of pyridazine DE12 (cmÿ1 )

V (cmÿ1 )

m6a (a1 ) (cmÿ1 )

m6b (b2 ) (cmÿ1 )

D

p …mA2 =mB1 †

600

190

550

550

0.6

1.0

10

G. Fischer, P. Wormell / Chemical Physics 257 (2000) 1±20

give gaps of about 2.5 eV. This suggests that the perturbations induced by vibronic coupling with the second 1 B1 state are relatively small. More importantly, the dual coupling scheme could not account for some of the observations listed above, in particular (2), the similarity of the observed ¯uorescence from the origin and 373 cmÿ1 bands, in contrast with the SVLF spectrum from the 534 cmÿ1 band. This suggested that mode 6a should be explicitly included in the coupling scheme. Accordingly, the two models have been combined into one in which only the lowest-frequency a1 mode (6a) is retained, and the second 1 B1 state is neglected. Another alternative model might be based on vibronic coupling between the ®rst 1 B1 state and a 1 B2 state, possibly the observed state at about 6.2 eV [14], through mode 16a, (a2 , ground state 365 cmÿ1 ). EOM-CCSD(T) vertical-excitation energies [7] place the nearest 1 B2 state 2.8 eV above the 1 B1 state, and our relaxed CASPT2 calculations give an energy gap of 3.94 eV, suggesting that for vibronic coupling constants of less than 1000 cmÿ1 the vibronic interaction will be small. Consequently, the frequency of this mode will not decrease suf®ciently upon excitation to allow assignment of the 373 cmÿ1 band to 16a20 . We have preferred the twostate model described above, as the 1 A2 state lies much closer to the 1 B1 than does the 1 B2 , and the vibronic coupling constants can thus be much smaller. The situation is di€erent for the triplet states, where the calculations put the 3 B1 and 3 B2 states much closer: 1.32 eV (relaxed CASPT2, this work). Hence, mode 16a is expected to have a signi®cantly reduced frequency in the lowest triplet state. This is in accord with the observed frequencies of the 16a11 sequences in the triplet (ÿ192 cmÿ1 ) and singlet (ÿ19 cmÿ1 ) spectra. 4. Results 4.1. Calculated electronic energies Earlier workers have calculated vertical-excitation energies using a range of approaches; details of some spectroscopically important singlet and

triplet states are summarised in Table 1. Recent studies by Nooijen [10] and Weber and Reimers [11] suggest that the most accurate computational results for pyridazine are given by the various EOM-CCSD calculations, with the EOMCCSD(T) calculations being systematically better, and also the STEOM-CCSD [10] and CASPT2 calculations [3]. As expected, the EOM-CCSD(T) and CASPT2 vertical-excitation energies gave reasonable numerical agreement with the experimental band maximum of the lowest p n (presumably 1 B1 ) band system; other calculations, including the semiempirical CNDO/S-CI method, also gave satisfactory ®ts, but not all of these were expected to be systematically reliable for the higher excited states. The EOM-CCSD and STEOM-CCSD calculations slightly overestimated the 1 B1 energies, but were expected to give reliable orderings and energy spacings for the lowest 1 B1 and 1 A2 states. All of the more reliable methods, including EOMCCSD(T), predicted the 1 B1 state to be lower in energy than the 1 A2 ; the EOM-CCSD and EOM-CCSD(T) splittings were 0.62 and 0.63 eV, respectively. For the purpose of the present vibronic study, the most useful computed quantities are not vertical-excitation energies, which should be compared with Franck±Condon maxima of unperturbed band systems, but energies that allow for the reorganisation energy associated with relaxation of the excited-state geometry; these values can be compared with the observed band origins. This is particularly important in the present case, where the band origins of two interacting states appear to be nearly degenerate, and their relative energies are crucial to the analysis. The results of our relaxed CASSCF, CIS, CASPT2 and EOM-CCSD calculations are listed in Table 2, together with experimental adiabatic (0±0) transition energies, where these are available. As discussed above, CASPT2 and EOM-CCSD calculations should give reasonable results for the orderings and energy spacings of the lowest 1 B1 and 1 A2 states. Both types of calculation show that the 1 A2 state is lower, and the energy spacings are 0.11 eV (890 cmÿ1 , CASPT2) and 0.052 eV (420 cmÿ1 , EOM-CCSD). This is consistent with

G. Fischer, P. Wormell / Chemical Physics 257 (2000) 1±20

our vibronic analysis of the singlet±singlet vapour spectrum. The corresponding CASSCF calculations give similar results with two di€erent basis sets, 6-31G* and 6-31+G*, although the calculated energies are too high. The di€erent ordering of states for the vertical-excitation and relaxed calculations is due to the substantially di€erent reorganisation energies, 0.264 and 0.807 eV (EOM-CCSD), for the 1 B1 and 1 A2 states, respectively. In the triplet manifold the relaxed EOM-CCSD and CASPT2 calculations place the 3 B1 state below the 3 A2 , with energy gaps of 0.509 eV (4100 cmÿ1 ) and 0.36 eV (2900 cmÿ1 ), respectively. These gaps are signi®cantly larger than the singlet-state values, suggesting that vibronic interactions will be much weaker, for the vapour phase at least. As with the corresponding singlet states, the EOMCCSD reorganisation energy for the 3 A2 state is larger than that for the 3 B1 , but not enough to compensate for the larger vertical-excitation gap for the triplet states. The relaxed EOM-CCSD energy for the 3 B1 state is 0.238 eV higher than the experimental value; the CASPT2 energy is 0.357 eV lower than experiment. Our CASPT2 calculation places a 3 B2 state 1.32 eV above the 3 B1 ; the corresponding gap in the singlet manifold is 3.94 eV. When constrained to C2v symmetry, CIS/631G* vibrational-frequency calculations revealed one imaginary frequency for each state. The imaginary frequencies suggest that the constraint to C2v symmetry may be invalid. Nevertheless, the energy lowering upon removal of this constraint was small. The 1 B1 state optimized to a global minimum 0.06 eV lower, while the 1 A2 state for the molecule constrained to planarity, but initially distorted along the in-plane b2 mode, optimized to the 1 B1 state. Single-point energy determinations for the 1 A2 state showed the global minimum to be lower by about 0.05 eV. At the CIS/6-31G* level the separation between the 3 B1 and 3 A2 states was calculated to be much larger (1.80 eV) than for the corresponding singlet states (0.79 eV). On the other hand, the ®rst excited 3 B2 state was calculated (CIS 0.44 eV, MRDCI 1.32 eV [2]), and observed (1.1 eV [2]), to be much closer to the 3 B1 state. The lowest triplet

11

state also has a tendency to lose its planarity, both at the CIS and CASSCF levels, with a CIS calculated double-minimum potential of 0.3 eV along an a2 vibrational coordinate. The corresponding singlet frequency was also imaginary for C2v symmetry. 4.2. Calculated vibrational frequencies The ground- and excited-state vibrational frequencies for pyridazine are summarised in Table 4. For the ground-state frequencies, we have preferred the assignments of Martin and Van Alsenoy [51], whose B3LYP/cc-pVTZ density-functional calculations give a good ®t with experiment, and also those of Berces et al. [52], who used a Hartree±Fock (HF)/4-21G force ®eld adjusted using scaling factors taken from benzene. Billes et al. have proposed some alternative assignments [8] based on MP2/6-31G* and linear-combination of Gaussian-type orbital (LCGTO) density-functional calculations, but MP2 calculations of vibrational frequencies have been less reliable for some related molecules [53], and our scaled B3LYP/6-31G* calculations, which have performed satisfactorily for related compounds [53], agree well with those quoted in Refs. [51,52]. For excited-state vibrational frequencies Weber and Reimers [12] found that the CIS method appears to be more reliable than CASSCF for calculating excited-state vibrational frequencies of compounds, such as pyrazine; density-functional calculations also show promise, but are not yet feasible for molecules of this size. CIS calculations have been successfully used in analysing the electronic spectra of other aza-aromatic molecules [5,35,37,38]. We note that for pyridazine, the scaled CIS frequencies may not be accurate for b2 modes in the 1 B1 state if they are involved in strong vibronic coupling with the 1 A2 state. The strength of this coupling, and hence the frequencies of these modes, may be very sensitive to the energy gap between the states. Any inaccuracies in the calculated gap will therefore a€ect the predicted b2 frequencies and, of course, there are other potential discrepancies in this relatively simple computational method.

12

G. Fischer, P. Wormell / Chemical Physics 257 (2000) 1±20

Table 4 Comparison of ground- and excited-state vibrational frequencies (in cmÿ1 ) for pyridazine Mode numbera a1

b2

a2

b1

Ground state 1 A1

Excited state (p ,n) 1 B1 b

Excited state (p ,n) 3 B1

HF

B3LYP

Experiment

CIS C2v

CIS C2

Experiment

CIS C2v

CIS C2

Experiment

6a 1 15 9a 14 19b 8a 2 20b

660 950 1053 1100 1150 1462 1602 3033 3051

656 977 1058 1136 1157 1435 1562 3071 3094

664 963 1061 1131 1159 1446 1570 3052 3064

624 918 950 1138 1389 1432 1691 3045 3092

628 927 957 1134 1382 1413 1623 3043 3080

534

628 925 966 1143 1404 1449 1656 3047 3086

617 901 941 1175 1164 1392 1440 3046 3071

639 902 963 1114

6b 12 18a 3 19a 8b 7b 13

611 1019 1050 1292 1421 1605 3024 3042

608 1014 1049 1272 1396 1557 3066 3082

629 1012 1061 1283 1415 1563 3056 3085

317 786 851 1121 1301 1519 3031 3089

289 821 985 1135 1305 1544 3030 3077

424 805 985 1148 1322 1580 3033 3083

511 869 968 1122 1320 1535 3035 3067

509

16a 4 10b 5

389 750 943 1021

362 738 910 977

365 730 861 989

±c 526 779 954

278 584 795 951

346

±c 497 786 958

334 606 775 949

173

16b 10a 17b

401 763 980

363 736 940

370 760 963

372 738 939

401 733 935

461

359 741 943

165 716 936

564 817=830

969 736

1414

a

Ref. [14]. Ref. [51]. c Imaginary frequency. b

4.3. Analysis of the singlet±triplet absorption spectrum A microdensitometer trace of the singlet±triplet absorption spectrum is shown in Fig. 3, and a vibronic analysis is set out in Table 5. The original spectra show a large number of additional weak, but still distinct, bands that are not seen in Fig. 3, and have not been reported by Innes et al. [13]. The vapour spectrum is more complex than the 4.2 K crystal spectrum [29], owing to hot-band and sequence structure, but the strongest cold bands are similar in the two spectra, apart from the 225 cmÿ1 interval in the crystal spectrum, which we

have tentatively attributed to site structure (Section 1). The spectrum is dominated by a progression in mode 6a (a1 , 664 cmÿ1 in the ground state), which has a frequency of 639 cmÿ1 for both the pure-crystal and vapour spectra. Innes et al. [13] have suggested some assignments for the stronger features in the vapour spectrum, notably the progression in 6a, but experimental diculties prevented them from carrying out a detailed analysis of the hot bands. Our own spectrum shows more bands, and we have suggested some new assignments and revised some of the earlier ones on the basis of relative band intensities, experimental and theoretical ground-state frequencies, and CIS

G. Fischer, P. Wormell / Chemical Physics 257 (2000) 1±20 Table 5 1 Band assignments for the 3 B1 A1 p n band system of the vapour absorption spectrum of pyridazine m ÿ 22 488 (cmÿ1 )

Assignment

ÿ664 ÿ192 ÿ120 ÿ24 0 57 70 194 199 212

6a01

254 347 447 582 614 639 708 829 833 848 902 963 971 990 1086 1114 1279 1342 1414 1469 1490 1599 1609 1721 1920

16a11 6b11 6a11 000 …origin† 10a11 ? 10a11 ? 16b11 410 16a01 ? 410 16a01 6a20 1501 ? 6a10 16a22 16a20 6a10 16a11 111 6a10 6a21 6a10 6a10 10a11 ? 6a10 16b11 ? 6a10 16b11 ? 6a30 1501 ? 110 1510 6a10 6a20 9a10 6a20 6a20 8a10 6a20

16a20 16a11 10a11 ? 16b11

mexp: ÿ mass: (cmÿ1 ) ± ± ± 1 0 ± ± ± ÿ5 ÿ1 1 0 4 1 ± ÿ1 ÿ4 0 ÿ8 ± ± 4 0 ± 1 7=±6 ± ÿ3

6a10 1510

ÿ3

6a30 16a11 6a30

ÿ4 3

predictions of excited-state frequencies. In particular, we have identi®ed cold bands that are attributable to the totally symmetric 1, 15, 9a and 8a modes. The hot bands and sequence structure are expected to be derived from the lowest-frequency modes in the ground state, owing to their more favourable Boltzmann factors. These modes are as follows (Table 4): 16a (a2 , experimental value for ground state 365 cmÿ1 ), 16b (b1 , 370 cmÿ1 ), 6b (b2 , 629 cmÿ1 ), 6a (a1 , 664 cmÿ1 ), 4 (a2 , 730 cmÿ1 ), 10a (b1 , 760 cmÿ1 ), 10b (a2 , 861 cmÿ1 ), 1 (a1 , 963

13

cmÿ1 ), 17b (b1 , 963 cmÿ1 ) and 5 (a2 , 989 cmÿ1 ). All other modes have ground-state frequencies above 1000 cmÿ1 . The strong sequences, 16a11 and 16b11 are assigned to the hot bands at ÿ192 cmÿ1 and ‡194 cmÿ1 , respectively, on the basis of CIS predictions; we therefore concur with the assignments of Innes et al. [13]. We support the tentative assignment by Innes et al. that the band at about ÿ24 cmÿ1 is attributable to 6a11 , again on the basis of intensity and CIS predictions. A similar sequence band is seen at ÿ25 cmÿ1 on 6a10 . The hot band 6a01 is seen at ÿ664 cmÿ1 , in agreement with the measured ground-state frequency. The weak band at ÿ120 cmÿ1 is most likely 6b11 on intensity grounds, although 411 or even 10a11 is possible. CIS predictions for these three possibilities are ÿ187 (HF±CIS C2v ), ÿ253 and ÿ22 cmÿ1 . 6b11 seems the most likely, and we tentatively assign 10a11 to either of the weak bands at ‡57 or ‡70 cmÿ1 . No assignment is proposed for 411 as, apart from the four listed bands at ÿ664, ÿ192, ÿ120 and ÿ24 cmÿ1 , we do not see any bands with appreciable intensity that are substantially to the red of the origin. The assignments by Innes et al. of ‡212 cmÿ1 and ‡849 cmÿ1 as 6b10 16b01 and 6a10 6b10 16b01 are clearly incorrect, as the resulting vibrational symmetries are a2 , not a1 . Mode 16a (a2 , ground state 365 cmÿ1 ) shows a substantial decrease in frequency in the excited state. As suggested above, this could be evidence of vibronic coupling with a nearby 3 B2 (p ,p) state, which may have further implications for the spectrum. The original spectrum, and photographic prints taken from it, reveal a large number of weak but distinct bands: more than can be assigned on the basis of the known vibrational fundamentals. For example, there is a proliferation of weak bands around the origin. We propose that pyridazine in its triplet state exhibits vibronically induced Duschinsky mixing of a2 modes, brought about by vibronic coupling between the 3 B1 and 3 B2 states. This leads to a larger number of sequence and hot bands being seen than would be expected if there were no such mixing. For example, if the four a2 modes 16a, 4, 10b and 5 did not mix, only 16a11 , 411 , 10b11 and 511 would potentially carry intensity (subject, of course, to thermal considerations.) However, if the modes were

14

G. Fischer, P. Wormell / Chemical Physics 257 (2000) 1±20

scrambled, then there would be up to 16 possible transitions. Say, for example, that 16a and 4 were mixed in the excited state, producing two modes that we could call (16a/4) and (4/16a), then four 16a1 , (4/ transitions would be possible: (16a/4)1 16a1 , (16a/4)1 41 , (4/16a)1 41 , rather 16a)1 than just two: 16a11 and 411 . This situation would, however, make it harder to assign the hot bands and sequence bands, since there would be signi®cant e€ects on vibrational frequencies. Thus, a possible assignment for the band at +212 cmÿ1 is 410 16a01 . Modes 16b(b1 ) and 10a(b1 ) increase in frequency in the excited state; modes 6a(a1 ), 6b(b2 ), 16a(a2 ), and possibly 4(a2 ) decrease in frequency. A signi®cant feature of the singlet±triplet spectrum is the relatively small frequency shift of the progression-forming mode 6a, in contrast with the substantial shift for the singlet system. We take this as further indication that for the singlet system, the corresponding mode is a€ected by the strong coupling between the 1 B1 and 1 A2 states; in contrast, there is predicted to be a larger energy gap between the corresponding triplet states, leading to weaker coupling. 4.4. Vibronic coupling calculations The vibronic coupling calculations show that objectives (1)±(5) listed in Section 3.2 are largely met. In the calculated absorption spectrum, as summarised in Table 6, the ratio of absorption intensities of the ®rst three bands is in reasonable agreement with the observed spectrum, although the frequency of the third band, corresponding to

534 cmÿ1 in the observed spectrum, is too large. This is possibly a consequence of constraining the model to only one a1 mode, and also of not allowing the vibrational frequencies of modes 6a and 6b to vary between the electronic states. A lower calculated frequency could be obtained by using a lower input frequency for mode 6a. However, in such a semi-quantitative model such an intervention was not warranted: the two input frequencies were kept the same, and no distinction was made for both excited electronic states. A key outcome of the calculations is that the excited-state levels are heavily mixed in terms of the ground-state vibrational modes, and in terms of the two electronic states. Thus, the model calculations give excited-state wavefunctions for the low-lying vibrational levels, 0, 373 and 534 cmÿ1 , that contain signi®cant contributions from the 0, 2m6b , 4m6b , m6a , m6a ‡ 2m6b , and m6a ‡ 4m6b vibrational states associated with the 1 B1 state. They also contain signi®cant contributions from b1 (A2  b2 ) vibronic states deriving from the A2 state. Hence, the bands at 0, 373 and 534 cmÿ1 cannot be simply assigned to, e.g. the 1 B1 origin, 6b20 and 6a10 , respectively. More representative assignments, based on which state makes the largest contribution, are 6b(A2 ), 0(B1 ) and (6a ‡ 6b) (A2 ). For example, for the band at 0 the major contributors are ÿ0:51‰0…B1 †Š ÿ 0:17‰6b2 …B1 †Š ‡ 0:82‰6b…A2 †Š ‡ 0:06 ‰6b3 …A2 †Š. Table 7 compares the calculated and observed frequencies for molecules in the vapour phase and in a cyclohexane crystal [16]. In the vapour phase, the calculated frequencies for the ®rst two excitedstate vibrational bands are comparable to the ob-

Table 6 Calculated progressions in mode 6a for the singlet±singlet absorption spectrum of pyridazine vapour (relative intensities are in parentheses) Assignmenta 6b10

0(A2 ) 0(B1 ) 0(A2 ) 6a10 6b10 0(B1 ) 6a10 0(A2 ) 6a20 6b10 0(B1 ) 6a20 0(A2 ) 6a30 6b10 a

Abbreviation

Calculated (cmÿ1 )

Observed (cmÿ1 )

b(A2 ) 0(B1 ) ab(A2 ) a(B1 ) a2 b(A2 ) a2 (B1 ) a3 b(A2 )

0 376 643 918 1205 1447 1774

0 (1) 373 (1) 534 (1.9) 981 (1) 1087 (2) 1509 (1) 1614 (0.8)

Assignments refer to the largest contributor to the vibronic state.

(1) (1.7) (2.8) (1.5) (1.2) (0.8) (0.2)

G. Fischer, P. Wormell / Chemical Physics 257 (2000) 1±20

15

Table 7 Comparison of observed and calculated vibrational frequencies for pyridazine in the 1 B1 excited state, for molecules in the vapour phase and in a cyclohexane crystal (relative intensities are in parentheses) Observed (cmÿ1 )

Calculated (cmÿ1 )

Vapour

Cyclohexane

Di€erence

Vapour

Solvent

Di€erence

373 (1) 534 (1.9)

384 536

11 2

375.9 (1.7) 643.0 (2.8)

383.9 644.6

8 1.6

served values, and their intensities (in parentheses), scaled relative to the origin bands, are also in agreement. The solvent shift in the vibrational frequencies has been modelled by changing the energy separation of the two vibronically coupled states. In Table 7, the calculated solvent results are for a gap that has been increased by 100 cmÿ1 . Although agreement cannot be expected to be quantitative, since the energy gap in cyclohexane is unknown, the trend of the shifts is correct. Thus, the higher-frequency band is much less sensitive to solvent, in agreement with the much larger relative shift of the observed 373 cmÿ1 band. Deuteration of pyridazine led to almost no change in the 373 cmÿ1 interval but a large reduction in the 534 cmÿ1 interval [13]. This trend is also observed in our calculations, as shown in Table 8. In the SVLF of pyridazine [16], some fundamental questions have been raised by the spectra produced by excitation of the 0, 373 and 534 cmÿ1 vibronic levels. As discussed in Section 1 above, it was found puzzling that in ¯uorescence from the level at 373 cmÿ1 , whose possible assignment was 6b20 , the corresponding ground-state band, 6b02 , was not prominent. The answer is found in the extensive vibronic coupling between the 1 A2 and 1 B1 electronic states. These states are severely mixed, and according to our calculations the level at 376 cmÿ1 (calculated) contains only a small

contribution of 2m6b . Thus, 6b02 would not carry signi®cant intensity in the SVLF spectrum. The calculated and observed relative ¯uorescence intensities following excitation of the 0, 373 and 534 cmÿ1 bands are presented in Table 9. Although complete agreement with the observed intensities is not obtained, the important features are well represented. The calculated ¯uorescence from the 0 and 373 cmÿ1 levels is similar in so far as a progression in mode 6a is concerned, but di€erent from the ¯uorescence from 534 cmÿ1 , where all but the ®rst member of the 6a progression are very weak. As discussed above, bands corresponding to two quanta of 6b in the ground state are largely absent for the calculated ¯uorescence from 373 and 534 cmÿ1 , in agreement with the observed spectra. However, a 6b02 band is present in the calculated ¯uorescence from the 0 level, but not in the observed spectrum, indicating that there are some de®ciencies in the model. Obvious shortcomings in the model calculations that may explain these observations are noted above. In particular, they include the restriction to only one mode of each a2 and b2 symmetry. Furthermore, in the calculation of the ¯uorescence intensities, no allowance was made for possible Fermi resonance between two quanta of 6b and two quanta of 6a in the ground state, levels that are only separated by some 70 cmÿ1 .

Table 8 Comparison of observed and calculated vibrational frequencies for pyridazine-h4 and pyridazine-d4 in the 1 B1 excited state Observed (cmÿ1 )

Calculated (cmÿ1 )

-h4

-d4

Di€erence

-h4

-d4

Di€erence

373 534

374 496

1 ÿ38

375.9 643.0

374.2 623.2

ÿ1.7 ÿ19.8

16

G. Fischer, P. Wormell / Chemical Physics 257 (2000) 1±20

Table 9 Relative ¯uorescence intensities following excitation of the 0, 373 and 534 cmÿ1 levelsa

a

Ground frequency

Assignment

Calculated intensity

Observed intensity

0 665 1258 1330 1995

0!0 6a 2  6b 2  6a 3  6a

1.2 1.0 0.80 0.30 0.05

1.0 0 0.67 0.33

Assignment

Calculated intensity

Observed intensity

373 ! 0

0.60 1.0 0.24 0.57 0.15

1.0 0.05 0.87 0.39

Assignment

Calculated intensity

Observed intensity

534 ! 0

16 1.0 0.24 1.3 1.1

1.0 0.19 0.1 0.1

All frequencies are quoted in cmÿ1 .

A compressed tracing of the singlet±singlet spectrum (Fig. 2) shows that the band system becomes increasingly complicated above 1000 cmÿ1 , with considerable overlap between vibronic bands. The lower-energy regions of the spectrum are typical of vibronic coupling in the sparse regime [54], where the density of vibronic states in the overlapping electronic states is relatively low. The density increases at higher energies, leading to a rapid proliferation of bands as the spectrum enters the intermediate vibronic-coupling regime. In the pyridazine spectrum, vibronic coupling provides a mechanism whereby levels of b1 vibronic symmetry, associated with the dark A2 electronic state, can obtain allowed B1 electronic-state character, and thus become observable in the spectrum. Although no quantitative modelling has been undertaken for the higher vibronic states in the observed spectrum, since additional a1 and b2 modes would have to be included in the calculations, we propose that this mechanism can account for the proliferation of bands. One feature of this region of the spectrum that was already predicted by our simple vibronic model, as shown by the intervals listed in Table 6, is a progression-forming interval of approximately 550 cmÿ1 , which is presumed to be largely attributable to mode 6a. 4.5. Analysis of the singlet±singlet spectrum The absorption spectrum is marked by three well-resolved and prominent bands at 0, 373 and 534 cmÿ1 , followed by a rapid proliferation of bands at increasing frequencies, as shown in Fig. 2. Earlier studies have assumed the 0 band to be the electronic origin of a 1 B1 state; the assignments of

the 373 and 534 cmÿ1 bands have been a contentious issue, and no explanation has been advanced for the cluster of bands between 560 and 800 cmÿ1 . As discussed in Section 4.4, our vibronic analysis, based on near-resonant A2 and B1 states, can account for these features of the spectrum. 4.5.1. Origin (0) band There is general agreement that the band at 26 648.8 cmÿ1 is an electronic or vibronic origin [14]. Only hot bands are seen to lower frequencies ± we have not been able to identify a band that might correlate with the electric-dipole forbidden but magnetic-dipole allowed 1 A2 origin ± and our relaxed CASPT2 and EOM-CCSD calculations con®rm that the electronic origin of at least one excited state is near this frequency. The isotope e€ect (‡94 cmÿ1 , -d4 ) is small relative to the other diazines, 154 cmÿ1 for pyrazine and 116 cmÿ1 for pyrimidine [14], suggesting that for pyridazine the observed origin may be vibronic. As discussed above, our analysis suggests that the 0 and 373 cmÿ1 bands correspond to extensively mixed vibronic and electronic origins of the A2 and B1 states, respectively. In this respect, we are in agreement with the conclusions of Ueda et al. [16] and Ransom and Innes [19] that the absorption spectrum marks the presence of two nearresonant electronic states. However, the two states are severely scrambled, and it is the totally symmetric vibrational states that are seen for the B1 state, and vibronic states of b1 symmetry that obtain intensity through vibronic coupling, that are seen for the A2 state, rather than two B1 electronic states. As mentioned in Section 1, Ransom and Innes used the di€erent rotational contours of

G. Fischer, P. Wormell / Chemical Physics 257 (2000) 1±20

the 0 and 373 cmÿ1 bands as evidence that they were the electronic-origin bands of two di€erent 1 B1 states. They mentioned the possibility that the 373 cmÿ1 band might be a vibronic origin of an 1 A2 state, but rejected this suggestion owing to diculties with the SVLF spectrum. These diculties have now largely been overcome, and our analysis suggests that it is the 0 band that is the vibronic origin of the 1 A2 state, while the 373 cmÿ1 band is most closely identi®able with the 1 B1 origin. Despite this di€erence, our assignments are consistent with the rotational analysis by Ransom and Innes. A detailed analysis of the vapour spectrum is set out in Table 10; the higher temperature leads to greater complexity owing to hot-band and sequence structure, but the cold bands in the spectrum are readily identi®ed, at least in the initial region of the spectrum, and resemble those in the cold-vapour spectrum [16]. 4.5.2. Sequence and hot band structure The hot-band region to the red of the origin has been particularly useful. It shows well-developed hot-band and sequence structure, but is less congested and tangled than the higher-energy regions of the spectrum. The origin band shows a clear hot band at ÿ19 cmÿ1 , which we assign to 16a11 , supporting the tentative assignment by Innes et al. [13]; a comparable band is seen at ÿ19 cmÿ1 on the 6a01 hot band. The 373 and 534 cmÿ1 bands show similar features at ÿ22 and ÿ11 cmÿ1 , respectively, as does the 6a hot band (ÿ23 cmÿ1 ) associated with the 373 cmÿ1 band. Similar behaviour is seen for the 1511 (ÿ92 and ÿ83 cmÿ1 ), and 16b11 sequences (‡91 and ‡102 cmÿ1 ), on the origin and 373 cmÿ1 bands, respectively. We suggest that the di€erences in the sequence intervals and sequence band intensities re¯ect di€erences in the electronic character of the two vibronic states, and di€erent vibronic perturbations for the levels concerned. Since the vibronic coupling is considered to be near resonance, variations can arise from small di€erences in the energy separations of the coupled levels. We note that in the singlet±triplet spectrum 16a11 is assigned to the hot band at ±192 cmÿ1 on the basis of its intensity relative to the origin, and the CIS predictions.

17

Table 10 1 Band assignments for the 1 A2 =1 B1 A1 p n band system of the vapour absorption spectrum of pyridazine m ÿ 26 649 (cmÿ1 )

Assignment

ÿ1329 ÿ1140 ÿ1103 ÿ1064 ÿ1061 ÿ970 ÿ960 ÿ901 ÿ893 ÿ856 ÿ841 ÿ803 ÿ776 ÿ756 ÿ740 ÿ729 ÿ725 ÿ691 ÿ684 ÿ664 ÿ600 ÿ594 ÿ576 ÿ570 ÿ529 ÿ441 ÿ438 ÿ417 ÿ395 ÿ379 ÿ376 ÿ373 ÿ366 ÿ354 ÿ337 ÿ331 ÿ325 ÿ315 ÿ311 ÿ292 ÿ288 ÿ278 ÿ270 ÿ252 ÿ249 ÿ234 ÿ229 ÿ223 ÿ214 ÿ200 ÿ193 ÿ189

b(A2 ) 6a02

ÿ1

b(A2 ) 9a01

±

b(A2 ) 1501 b(A2 ) 101 0(B1 ) 6a02

± ± ÿ5

mexp: ÿ mass: (cmÿ1 )

b(A2 ) 6b22 ? b…A2 † ÿ 841 ‡ 16a11

ÿ11 4

b(A2 ) 6a12 ? b(A2 ) 6a01 1511 16a11 b…A2 † 6a01 1511 b…A2 † 16b02 0…B1 † 9a01 b…A2 † 16a02 0…B1 † 1501 b…A2 † 6a01 16a11 b…A2 † 6a01 0…B1 † 101 b…A2 † 6a01 16a11 16b11 b(A2 ) 6a01 16b11 ab(A2 ) 9a01 ab(A2 ) 1501 b(A2 ) 6b11 ? ab(A2 ) 101

ÿ9 ÿ1 0 ± 1 5 ÿ3 ÿ1 ± ÿ3 ÿ3 ÿ1 ÿ2 ± ÿ2

0(B1 ) 6a01 1511

4

0(B1 ) 16b02

1

0…B1 † 6a01 16a22 b…A2 † 1501 ‡ 736 0…B1 † 6a01 6a11 b…A2 † 1501 ‡ 755 0…B1 † 6a01 b…A2 † 1501 ‡ 776

ÿ4 0 ÿ5 ÿ5 ÿ1 ÿ3

b…A2 † 1501 ‡ 794 b…A2 † 101 ‡ 719

ÿ3 ÿ1

b…A2 † 101 ‡ 736 b…A2 † 6a11 1511 ?

0 ÿ7

b…A2 † 101 ‡ 755 0(B1 ) 6a01 16b11 b…A2 † 101 ‡ 776

1 0 1

18

G. Fischer, P. Wormell / Chemical Physics 257 (2000) 1±20

Table 10 (continued) ÿ1

m ÿ 26 649 (cm )

Assignment

ÿ176 ÿ159 ÿ129 ÿ113 ÿ92 ÿ36 ÿ19 0 55 74

b…A2 † 101 ‡ 794

91 111 130 164 200 229 290 305 328 351 373 388 433 475 497 523 534 546 548 579 596 649 655 664 672 704 710 719 736 755 776 789 794

b…A2 † 6a11 b…A2 † 1511 16a11 b…A2 † 1511 b(A2 ) 16a22 b(A2 ) 16a11 b(A2 ) b…A2 † 6a01 ‡ 719 b…A2 † 6a01 ‡ 736 b…A2 † 16a11 16b11 b…A2 † 16b11 b…A2 † 6a01 ‡ 755 b…A2 † 6a01 ‡ 776 b…A2 † 6a01 ‡ 794 b…A2 † 16b22 0…B1 † 6a11 0…B1 † 1511 b…A2 † 6a01 1510 0…B1 † 16a22 0…B1 † 16a11 0(B1 ) ab…A2 † 1511 0…B1 † 16b11 ab…A2 † 16a22 ab…A2 † 16a11 ab…A2 † or b…A2 † 6a10

mexp: ÿ mass: (cmÿ1 ) 0 1 ÿ2 ± ± ± ± 0 2 2 ± 0 ÿ1 0 18 ÿ14 9 0 ÿ9 ÿ3 ± ÿ9 11 1 8 ±

Hot band Hot band Hot band Hot band Hot band Hot band b(A2 ) 9a10

±

Hot band

Apart from the sequences discussed above, hot bands involving the modes 1, 6a, 9a and 15 are identi®ed in the spectrum and account for most of the vibrational structure seen to the red of the origin, and near the origin. Thus, the hot bands

some 300 cmÿ1 to the red of the origin are assigned to transitions, involving one quantum of mode 15 in the ground state, to the group of excited state levels extending from ‡719 to ‡794 cmÿ1 . 4.5.3. Excited vibrational structure It was pointed out above that some pseudoregularity can be detected in the spectrum, corresponding to the activity of groups of bands separated by an approximate 550 cmÿ1 interval. This feature of the spectrum is highly suggestive of the occurrence of accidental near resonances between discrete vibrational levels of each of the two vibronically coupled states. This is reminiscent of the sparse-level description in the theory of radiationless transitions [54], at least for levels in the ®rst 1000 cmÿ1 of the spectrum, and accordingly no line broadening is expected. Because our vibronic coupling model has been limited to the activity of only one b2 and one a1 mode, the model is unable to represent fully the spectrum at higher vibrational frequencies. Of the ®ve bands between 719 and 794 cmÿ1 only one has been identi®ed by SVLF to be largely 9a10 ; ¯uorescence from the others did not permit identi®cation. They must be signi®cantly mixed vibrational levels whose origin is the 1 A2 electronic state. In the (p , n) 1 B1 state most of the modes decrease in frequency, as would normally be expected, but several modes increase. The extent of these increases depends on the set of ground-state values that is considered, but similar results are found for phthalazine [5] and we believe that they are authentic. 5. Conclusions Ab initio CASPT2 and EOM-CCSD calculations are in agreement with an interpretation of the singlet±singlet spectrum that suggests the spectrum may be assigned to two near-resonant electronic states of 1 A2 and 1 B1 symmetries, with the former at slightly lower energy. Vibronic coupling calculations that involve one active mode (6b) and one totally symmetric mode (6a) are able to reproduce most features of the absorption and ¯uorescence spectra, and also the solvent and deuteration

G. Fischer, P. Wormell / Chemical Physics 257 (2000) 1±20

shifts. In contrast, the singlet±triplet spectrum assigned to a 3 B1 state is unperturbed, and analysis of the vibrational structure is relatively straightforward. The di€erence between the singlet±triplet and singlet±singlet spectra, and the solvent dependence of the singlet±singlet spectrum, can be rationalised in terms of di€erent spacings between the B1 and A2 states.

[15] [16] [17] [18] [19] [20] [21] [22] [23]

Acknowledgements Most of the ab initio calculations upon which part of this work is based were carried out using the Fujitsu VPP and the Silicon Graphics Power Challenge of the ANU Supercomputer Facility. We are grateful to Dr. J.R. Reimers for carrying out the EOM-CCSD calculations, and for giving us access to his INDO-MRCI program, and also to Drs. D. Rasmussen and D. Smith for helpful discussions. P.W. gratefully acknowledges the receipt of an Internal Research Grant from the University of Western Sydney, Hawkesbury. References [1] M. Terazima, S. Yamauchi, N. Hirota, O. Kitao, H. Nakatsuji, Chem. Phys. 107 (1986) 81. [2] M.H. Palmer, I.C. Walker, Chem. Phys. 157 (1991) 187. [3] M.P. F ulscher, K. Andersson, B.O. Roos, J. Phys. Chem. 96 (1992) 9204.  [4] S. Knuts, O. Vahtras, H. Agren, Theochem. 279 (1993) 249. [5] G. Fischer, P. Wormell, Chem. Phys. 198 (1995) 183. [6] J. Zeng, N.S. Hush, J.R. Reimers, J. Phys. Chem. 100 (1996) 9561. [7] J.E. Del Bene, J.D. Watts, R.J. Bartlett, J. Chem. Phys. 106 (1997) 6051. [8] F. Billes, H. Mikosch, S. Holly, Theochem. 423 (1998) 225. [9] C. Hannay, D. Du¯ot, J.-P. Flament, M.-J. HubinFranskin, J. Chem. Phys. 110 (1999) 5600. [10] M. Nooijen, Spectrochim. Acta Part A 55 (1999) 539. [11] P. Weber, J.R. Reimers, J. Phys. Chem. Part A 103 (1999) 9821. [12] P. Weber, J.R. Reimers, J. Phys. Chem. Part A 103 (1999) 9830. [13] K.K. Innes, W.C. Tincher, E.F. Pearson, J. Mol. Spectrosc. 36 (1970) 114. [14] K.K. Innes, I.G. Ross, W.R. Moomaw, J. Mol. Spectrosc. 132 (1988) 492.

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