MAGNESIUM PHOTOIONIZATION |
377 |
(3p4s). The phaseshifts of the unperturbed STOCOS states plotted in this figure (points) have been calculated by fitting their asymptotic behaviour, but nearly identical results have been obtained by the single-channel K-matrix step. Only this last technique has been employed for the GTO basis; the calculated phaseshifts (circles) agree closely with the STOCOS results and demonstrate the ability of our method to obtain these quantities from moderately diffuse bases. The difference in the phase- shifts for the K-matrix states in the GTO and STOCOS calculations is partially due to the different wave energy of the resonance (about 0.002 lower with the STOCOS basis).
The s–wave contribution to the photoionization from the level is plotted in figure 3 and shows a quite satisfactory gauge invariance. Its peak value is in excellent agreement with that yielded by our previous STOCOS calculations, 346 Mb (3).
4.Conclusions
It may be concluded that a method based on the K-matrix technique may be conveniently adapted to calculate the continuum properties using variational basis functions that are accurate only inside the ”molecular region”. This means that the calculations may be carried out upon GTO bases, which allow the extension of the
proposed method to molecular systems, as already checked for |
(13). |
Acknowledgment
One of the authors (R.M.) gratefully acknowledges the financial help of the Progetto
Finalizzato Chimica Fine of the CNR.
References
1.P.W. Langhoff and C.T. Corcoran, J. Chem. Phys. 61, 146 (1974); I. Cacelli, V. Carravetta, R. Moccia and A. Rizzo, J. Phys. Chem. 92, 979 (1988); I. Cacelli, V. Carravetta, R. Moccia and A. Rizzo, J. Chem. Phys. 89, 7301 (1988)
2.I. Cacelli, R. Moccia and V. Carravetta, Chem. Phys. 90, 313 (1984); I. Cacelli,
V. Carravetta, A. Rizzo and R. Moccia, Physics Reports 205, 283 (1991)
3.R. Moccia and P. Spizzo, J. Phys. B21, 1121, 1133 and 1145 (1988), Phys. Rev.
A39, 3855 (1989)
4.R. Moccia and P. Spizzo, Phys. Rev. A43, 2199 (1991) and references therein
5.R. Moccia and P. Spizzo, J. Phys. B23, 3557 (1990); Il Nuovo Cimento 13D, 757 (1991)
6.R. Moccia and P. Spizzo, Can. J. Chem. 70, 513 (1992)
7.U. Fano, Phys. Rev. 124, 1866 (1961)
8.I. Cacelli, V. Carravetta and R. Moccia, J. Chem. Phys. 85, 7038 (1986)
9.R.G. Newton, Scattering Theory of Waves and Particles, Springer-Verlag, New York, 1982
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10.S. Bashkin and J.O. Stoner, Atomic Energy Levels and Grotrian Diagrams,
North Holland, Amsterdam, 1975
11.C.J. Mitchell, J. Phys. B8, 25 (1975); L. Lundin, B. Engman, J. Hilke and I.
Martinson, Phys. Scr. 8, 274 (1973); F.M. Kelly and M.S. Mathur, Can. J.
Phys. 56, 1122 (1978)
12.D.J. Bradley, C.H. Dugan, P. Ewart and A.F. Purdie, Phys. Rev. A13, 1416
(1976); R.E. Bonanno, C.W. Clark and T.B. Lucatorto, Phys. Rev. A34, 2082 (1986)
13.I. Cacelli, R. Moccia and A. Rizzo, J. Chem. Phys. (in press)
Investigation of Photochemical Paths by a Combined Theoretical and Experimental Approach
F. MOMICCHIOLI, I. BARALDI, A. CARNEVALI and G. PONTERINI
Dipartimento di Chimica, Università di Modena, Via Campi 183, I-41100, Modena, Italy
1. Introduction
The attempt to set the wide field of photochemical reactivity within the framework of quantum chemical methods is relativity recent, if one considers what has occured in other fields like, for instance, electronic molecular spectroscopy. In the common view, the origin of theoretical photochemistry dates back to two papers, published in 1972, which first provided a general description of biradical-like species by elucidating their electronic structure in terms of the basic 3x3 CI model [1], and bringing to light their role in organic photochemistry [2]. From then on Salem, Michl and others, starting essentially from analysis of state correlation diagrams, have introduced several new theoretical concepts, such as avoided crossing, funnel, twisted intramolecular charge transfer (TICT) state, etc., which are now currently used to rationalize a variety of photophysical and photochimical behaviours (for comprehensive descriptions, see ref. [3-6]). By accurate calculations on simple model systems [4,5], the above mentioned concepts have been shown to have fairly general validity, so they can be seen as real supports for the modern theory of organic photochemistry.
On the other hand, when dealing with photochemistry of large molecules in dense media
(e.g organic dyes in liquid solution) the application of the above interpretative framework faces two serious problems. The first one is that construction of potential energy surfaces of the ground state (S0) and some low-lying electronic excited states (at least ) cannot be fulfilled by the same ab initio extended-CI procedures used for the model compounds. Thus, one should have resort to all-valence-electron NDO (neglect of differential overlap) methods which yet, in their current formulations, have proved more or less inadequate to build ground and excited state potential surfaces, particularly along paths leading to conformational rearrangements or formation of photoreaction intermediates
(radical-like structures) (for detailed analysis, see ref. [7-10]. The second problem comes from the fact that the potential surfaces for the isolated molecule, even if they were rightly calculated, are in principle poorly representative of the photochemical behaviour in solution phase where energy minima and barriers may be substantially affected by solvent polarity and viscosity [6, 11-16].
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Y. Ellinger and M. Defranceschi (eds.), Strategies and Applications in Quantum Chemistry, 379–399.
© 1996 Kluwer Academic Publishers. Printed in the Netherlands.
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Starting from such considerations, during the last decade we have searched for an |
effective approach to the theoretical |
understanding of the condensed-phase |
photochemistry of large organic molecules. Our study had two major components:
1) formulation of a new model Hamiltonian of the all-valence-electron type capable of providing, in the case where it is adequately solved, qualitatively correct descriptions of the reaction paths in both the ground and lowest excited states, and 2) implementation of photophysical and photochemical measurements devised to minimize the degree of arbitrariness inherent in any comparison between the results of molecular quantummechanical calculations and the experimental observations in condensed phase. As for point 1), our studies led us to publish in the early 1980s two modified INDO-based methods, namely C INDO [9] (limited to prediction of ground state properties) and CS INDO [10] (capable of reliably handling both ground and excited state properties), subsequently applied to the study of electronic spectra and cis-trans (ground and excited state) isomerizations in a variety of conjugated systems: diarylethylenes [17-20], polyphenyls [21], binaphthyls [22,23], cyanines [24,25], diphenylmethane dyes [26], donor-acceptor-type stilbene derivatives [27,28], etc. . Point 2) was fulfilled by setting up in our laboratory a complete equipment for both stationary and time-resolved nanosecond spectroscopy as well as by access to picosecond spectroscopic apparatuses of external laboratories.
The remainder of the present article is divided into two parts. The first one reviews the main points of our combined theoretical-experimental approach. The second one reports an application of it to the study of the mechanism and dynamics of trans-cis photoisomerization of bisdimethylaminopentamethine cyanine (BMPC)#1.
2. Combining theory and experiment
2.1.CONSTRUCTION OF MOLECULAR WAVEFUNCTIONS AND POTENTIAL SURFACES: THE CS INDO MODEL
CS INDO [10] (as well as the parent C INDO [9]) shares the same basic idea as the PCILO scheme [29,30]: to exploit the conceptual and computational advantages of using a basis set of hybrid atomic orbitals (AOs) directed along, or nearly, the chemical bonds.
In the PCILO scheme the hybrid AOs, determined according to Del Re's method [31], are used to construct a basis of molecular orbitals (MOs) localized on the bonds and lone pairs, and from this to build a configuration basis set constituted by a fully localized determinant, representing the chemical formula, and the excited configurations obtained by utilizing the antibonding orbitals. On this basis, two different perturbative
CI procedures were developed in successive times for the ground state [29,30] and the excited states [32,33]. In short, the early one is a perturbation expansion up to the third order for the fully localized determinant, taken as the zeroth order ground state wavefunction. As is well known [34], the CNDO version of such PCILO scheme
#1 This study starts from previous work carried out by three of us (F.M., I.B., G.P.) in collaboration with Bcrthier [24,25], and may be considered as the logical pursuance of it.
PHOTOCHEMICAL PATHS BY A COMBINED THEORETICAL AND EXPERIMENTAL APPROACH |
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overcomes, at least partly, the most striking failures of the ordinary CNDO-SCF procedure as far as the conformational predictions are concerned. The PCILO-CNDO method for the excited states, as proposed by Langlet and Malrieu [32,33], is based on a second-order perturbation treatment of multiconfigurational zeroth-order wavefunctions determined by variational CI on a proper basis of local single excitations. A similar procedure, using the CIPSI method [35] for a better choice of the zeroth-order wavefunctions, was applied to study cis-trans photoisomerism in styrene [36] and s- trans-1,3-pentadiene [37] and emphasized the usefulness of the excitonic scheme in interpreting photoreaction mechanisms.
In conclusion, from the scanty reported applications the CIPSI-PCILO-CNDO procedure stands as an interesting investigation tool in photochemistry. However, with especial reference to large conjugated systems, the PCILO-CNDO scheme has some limitations arising from both the very model (e.g. arbitrariness sometimes arising in the choice of the zeroth-order localized structure [30,38]) and the CNDO parametrization (e.g. underestimation of the internal rotation barriers [9,34] and, at the same time, large overestimation of transition energies [30,36,37]), the latter defects being retained at the INDO level of approximation [39].
Thus, we resolved to reconsider the delocalized NDO-type MO-SCF techniques and explore the possibility, if any, of decidedly improving their predictive capabilities through the use of hybridised AO basis sets. It is well known that the main defect of CNDO and INDO SCF procedures, making them hardly usable to predict conformations and rotational barriers of conjugated molecules [9,34,40], is an anomalous stabilization
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of geometries with perpendicular arrangement of |
subsystems. This failure originates in |
a large overestimation of |
(hyperconjugative) interactions [7-9] which is traceable in |
turn to the fact that CNDO-INDO methods adopt |
averaged |
, bonding parameters (i.e. |
depending only on the nature of atoms A and B) in order to satisfy all invariance
conditions [41]. In |
fact, the use of averaged |
parameters causes |
inadequate |
differentiation of the |
resonance integrals |
corresponding to |
the various |
types of interactions |
occurring in conjugated systems. Of course, the |
correct differentiation might be approximately restored by introducing specific screening constants , but the realization of this simple idea requires the characters of the interactions to be unequivocally identifiable in any context. In planar geometries,
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the belonging of the basis AOs to |
or |
systems is fixed by symmetry, so proper |
screenings can be introduced for |
and |
interactions using pure Slater orbitals (e.g. |
with |
orbitals forming the system), as is done, for instance, in CNDO/S [42] and |
INDO/S [43] methods. However, in out-of-plane twisted conformations the use of pure
Slater orbitals does not make it possible to discriminate between |
and |
symmetries |
(now definable only within each |
planar subsystem), and hence |
the CNDO-INDO/S |
procedure for the evaluation of |
integrals becomes ineffective. On the other hand, by |
switching from the usual STO valence set to a set of hybrid AOs retaining |
or (local) |
symmetry in both planar and non-planar geometries, the resonance integrals can be
382 |
F. MOMICCHIOLI ET AL. |
made to correspond to chemically well-defined interactions and can therefore be specifically reparametrized according to a formula like
where |
is the overlap integral between the hybrid orbitals |
(atom A) and |
; (atom |
B) and |
is a screening factor depending on the nature |
of the involved |
hybrids. |
There is ample evidence [9,17,44] that the INDO SCF procedure transformed according to this scheme (C INDO) can provide predictions comparable to those of minimal-basis- set ab initio SCF calculations for conformations and rotational barriers of conjugated molecules in the ground state.
Starting from the C INDO scheme, in a second step we derived a new version of the method (CS INDO, where C and S stand for conformations and spectra) [10] capable of correctly handling electronic spectra and excited state potential surfaces, yet preserving the quality of the C INDO predictions as far as the ground state properties are concerned. The relevant changes incorporated into CS INDO are: 1) re-modelling of the
screening effects for |
integrals, 2) scaling down of the electron repulsion integrals |
according to one of the current "spectroscopic" parametrizations (e.g. Pariser-Parr, Ohno-Klopman, Mataga-Nishimoto), 3) use of a new formula for core-core repulsions
) self-fitting the adopted |
parametric function. Moreover, rather extended - |
properly selected CIs are performed as needed for a correct excited state treatment.
At the present stage of development [45] the essential steps of the CS INDO CI procedure can be summarized as follows:
1) A basis set of hybrid ,having or n character, is prepared by the Slater s,p valence set according to the maximum overlap criterion [31,46]. An extension to d orbitals is in progress.
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2) The selection of the screening factors for |
integrals is made assuming |
and |
obtaining |
the |
best values of |
by fitting rotational barriers, |
transition |
energies |
and |
transition energies, respectively. The remaing factors |
are |
then deduced by a simple proportionality criterion. It being understood that ' |
is kept |
equal to one ("pivot" parameter) the optimized values of the other screening factors are slightly dependent on the adopted CI scheme (see point 4). The introduction of three extra-parameters related to chemically distinct interactions and controlling distinct molecular properties, is the main feature of the CS INDO method.
3)Apart from minor exceptions all other parameters are given the same values as in standard INDO (electroneguivities, Slater-Condon parameters, bonding parameters) or CNDO/S (one-centre repulsion integrals) methods. Two-centre repulsion integrals are usually evaluted by the Ohno-Klopman formula.
4)With reference to our main target (large conjugated molecules), CI calculations are expanded on the subspace of the configurations generated within a restricted MO basis
set encompassing all and |
type orbitals which, in CS INDO, are easily identifiable in |
non-planar conformations, too. From this common starting point CI calculations are
PHOTOCHEMICAL PATHS BY A COMBINED THEORETICAL AND EXPERIMENTAL APPROACH |
383 |
performed by purely variational or mixed variational-perturbative (CIPSI-type [35,47]) approaches. In both cases a rather limited number of representative configurations (e.g. the monoexcited configurations "localized" on the characteristic chromophores) form a privileged reference set for the construction of the CI matrix.
The results of the above cited applications [18-28,45] have clearly shown that CS INDO method is fairly successful in combining equally satisfactory predictions of electronic spectra and potential surfaces (especially along internal rotation pathways) of conjugated molecules, a goal never reached by other NDO-type procedures. CS INDO shares, at least partly, the interpretative advantages of the CIPSI-PCILO-CNDO procedure [32,33,36,37], coming from using the same hybrid AO basis sets, but improves its predictive capabilities as far as spectroscopic and photochemical properties are concerned.
The advantages of CS INDO with respect to all other NDO-type procedures derive, in summary, from the resonance integrals being made to depend on the nature (in the chemical sense) of the interacting orbitals. This implies, in principle, loss of the hybridizational invariance [41], but the practical disadvantages are slight since in general the hybridization is nearly determined by the molecular structure and, when ambiguity arises (e.g. with nonbonding hybrids of heteroatoms), hybridization may well be fixed according to an energetic criterion [44]. A more serious deficiency of CS
INDO, inherent in the INDO approximations, concerns the description of those
Coulombic interactions where the angular dependence plays an important role (e.g. lonepair interactions). This defect, due to the use of spherically averaged two-centre electron-repulsion integrals (required to preserve rotational invariance), could be partly overcome by switching to the NDDO level of approximation [48,49], but the benefit would not balance the difficulty of working out a complete re-parametrization of
NDDO for the excited states.
From the foregoing considerations, taken as a whole, the CS INDO CI method appears to be a suitable tool to try to explore ground and excited state potential surfaces of large conjugated molecules. On the other hand, such systems are commonly studied in solution, so one must face the extra problem of the possible solvent effects (see next section) on the mechanism and dynamics of photochemical processes. Of course, no effects of the solvent viscosity can be explicitly treated within the framework of the electronic theory of photochemistry. However, leaving aside specific solute-solvent interactions, the dielectric solvent effects can be conveniently evaluated by theoretical models treating the solvent as a continuum, essentially the reaction field and the virtual charge (solvaton) models [3]. Quantum chemical SCF treatments incorporating the dielectric effects of the solvent have been developed for both models [50-52]. Such direct quantum chemical approaches are certainly advisable for studies limited to the ground state, but they are hardly practicable in photochemistry where the solvent effects on the ground state and some lowest excited states are to be evaluated at the same time. Thus we limit ourselves to calculating state by state the solvation energy of a solute molecule using its electrical properties as obtained in the isolated-molecule approximation. Following the conclusions of a recent study [27], where the two
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F. MOMICCHIOLI ET AL. |
continuum models have been comparatively tested, we evaluate |
according to the |
solvaton model which, after Hedrich et al. [53], can be conveniently expressed as:
where |
is the static dielectric constant of the solvent, |
is an average effective atomic |
radius, |
is the distance between the centres of the atoms A and B, and QA (QB)is the |
net charge on the atom A (B) derived from the CI treatment of the isolated molecule. As pointed out in ref. [27], this "microscopic" model is superior to the "macroscopic" ones based on the global dipole moment of the solute, since it is able to take into account local solute-solvent interactions. This is especially important in large molecules, where high local net charges may well occur in spite of a small global dipole moment.
2.2.PRODUCTION OF SELECTED PHOTOPHYSICAL AND PHOTOCHEMICAL DATA
As said above, our theoretical tools are especially effective for studying photoisomerizations (in a generalized sense) of conjugated non-rigid systems. Such processes usually involve large amplitude motions of rather bulky groups, so that coupling of these motions with solvent drag is often strong. Furthermore, in many cases, marked changes of the electrical properties, related to separation or localization of charge, take place along the reaction coordinate (e.g. sudden-polarization [54] and TICT-formation [6] phenomena). As a consequence, coulombic interactions with solvent molecules may deeply affect the potential governing the internal motion of a solute molecule. A fruitful experimental approach should provide selected and organized experimental information on both the spectroscopy of the species and the dynamic of the processes involved in the photoisomerization.
This purpose is achieved in our laboratory carrying out photostationary (steady-state fluorometry and photolysis) and time-resolved (time-correlated fluorescence singlephoton counting, laser or conventional flash photolysis) experiments, at variable temperature and in solvents with different polarities and viscosities. The results may consist as well in the absorption and emission spectra of a number of transients (e.g. triplets and photoisomers) as in lifetimes, quantum yields and rate constants. The analysis of the temperature dependences of the latter affords the preexponential factors
(A) and activation energies of the processes under study in the solvent employed.
The repetition of the variable temperature measurements in several solvents of very different dielectric constants, yet similar and low viscosities, will make the "pure" medium-polarity effects on the kinetic parameters emerge and will help to check the validity of a theoretical model [55] as well as to verify the reliability of the calculated solvation energies. However, in order that a more quantitative check of the calculated potential barriers may be possible, activation energies must be cleared of the contributions arising from solvent frictional effects. Such "intramolecular" (but for
electrostatic solute-solvent interactions) activation energies are obtained as the slopes of
PHOTOCHEMICAL PATHS BY A COMBINED THEORETICAL AND EXPERIMENTAL APPROACH |
385 |
isoviscosity plots made with data measured in a series of homologous solvents. Within a certain accuracy, the procedure itself provides a check of the reasonableness of the assumptions on which it rests [16].
Steady-state experiments can also be designed within the same kind of strategy. As an example, we can cite recent works [25,45], where the results of a quantitative analysis of the resolved absorption spectra of a number of trans and cis isomers of cyanine dyes were compared with calculated oscillator strengths and transition energies so as to propose the identification of the observed phototropic species as well defined cis isomers.
Starting from the results of such a theoretical-spectroscopic investigation on BMPC [25], in the next section we report a typical application of the above outlined approach, in which kinetic measurements as functions of the solvent properties have been prompted by theoretical considerations and the experimental results are used in turn to analyse critically the calculated potential energy curves.
3.An example: the trans cis photochemical and cis trans thermal back isomerization of BMPC
Photoisomerism of BMPC (Scheme 1) has already been investigated by us [25] through the comparison between the calculated spectra of the trans and the two mono-cis (2-3 and 3- 4 cis) isomers, on the one hand, and the experimentally resolved spectra of the
stable and photochemically produced forms, on the other. It was concluded that irradiation of the stable (all-trans) form results in the formation of a single isomer with
cis-planar structure and, by considerations on the intensity relations between . |
and |
(cis peak) transitions, the phototropic species was assigned as the 3-4 cis isomer. Both these findings appeared to be in agreement with the predictions of an early theoretical study based on simple MO correlation diagrams as well as on explicit potential-energy curve (CS INDO CI) calculations [24] for unsubstituted pentamethine cyanine (PC). Ref.s [24,25], taken together, disproved previous theoretical interpretations [56,57] according to which cyanine photoisomers should correspond to twisted ground state conformations (resulting from a 90°-rotation around one of the C-C bonds) strongly stabilized by electrostatic solute-solvent interactions. In view of such a striking interpretative contrast, and considering that calculations of ref. [24] had been carried out for a model system (PC) neglecting any solvent effect, we decided to tackle
