268
Ecotoxicological Issues
These results can be explained by the assumption that the frontier HOMO and
LUMO orbital condition the lowest excited states of the molecule [11]. Larger
energy gaps result in larger energy differences between the ground state and
excited states of the same microstate multiplicity. This explains the correlations
found [9] between the HOMO-LUMO gap and spectroscopic parameters of the
excited states, and justified our assumption that the ground state HOMO-LUMO
gap could be an electronic index of absorbed energy.
The advantage of ground state calculations is that of computing speed, because
excited state modeling is often prohibitively computer intensive.
3
PHOTO-TOXICITY OF PAHS AND THEIR EXCITED
STATE ELECTRONIC STRUCTURE
The relation of the HOMO-LUMO gap of the PAHs to the energies of the excited
states is due to the fact that the quantum mechanical theory of response to a
perturbation in a chemical system depends on this gap. The perturbations of
electronic structure are usually modeled by mixing excited-state wave functions
with the ground-state functions. The coefficient weighing these mixed wave
functions is inversely proportional to the energy difference between the states.
Therefore, according to the principle of maximum hardness, hard molecules (with
larger HOMO-LUMO gap) should less readily undergo changes in electronic
structure than soft molecules.
We found [12] the energy convergence procedures of MOPAC6 for optimizing
geometries of the excited states to be much too time-consuming (each structure
requiring many hours of CPU-time on the EPA Cray). On the other hand, lSCF
calculations without optimized structures for individual microstates yielded energy
values for excited states which did not correlate with the observed spectroscopic
data.
As a computing compromise, we chose the first MOPAC6 option to perform only
geometry optimization of the excited states. To mimic the energy of the excited
states, we assumed that the optimized geometry of the excited states described an
average molecular geometry of all microstates taken into account in the
calculations. Finally, the lSCF calculations using these optimized structures did
provide electronic indices which mimicked the energies of the excited states.
Although the HOMO-LUMO gap does not have physical meaning for the excited
states because of the multiplicity of the microstates, the principle of maximum
hardness [13] sug§ests that the computed "HOMO-LUMO gap" [denoted as
(H 0 M 0 -L UM 0) ] of these hypothetical structures might be an appropriate
stability estimate, assuming the optimized geometry of excited states is an average
geometry of all microstates.
This hypothesis was supported [12] by much better correlations found between
(HOMO-LUMO)* gap of the excited states and their observed energies from
spectroscopic data than the QSARs found for ground state structures. Further, the
models for the triplet state energies were significantly better than those for the
singlet states, probably because of the greater stability of the former.
Ecotoxicological Issues
These results can be explained by the assumption that the frontier HOMO and
LUMO orbital condition the lowest excited states of the molecule [11]. Larger
energy gaps result in larger energy differences between the ground state and
excited states of the same microstate multiplicity. This explains the correlations
found [9] between the HOMO-LUMO gap and spectroscopic parameters of the
excited states, and justified our assumption that the ground state HOMO-LUMO
gap could be an electronic index of absorbed energy.
The advantage of ground state calculations is that of computing speed, because
excited state modeling is often prohibitively computer intensive.
3
PHOTO-TOXICITY OF PAHS AND THEIR EXCITED
STATE ELECTRONIC STRUCTURE
The relation of the HOMO-LUMO gap of the PAHs to the energies of the excited
states is due to the fact that the quantum mechanical theory of response to a
perturbation in a chemical system depends on this gap. The perturbations of
electronic structure are usually modeled by mixing excited-state wave functions
with the ground-state functions. The coefficient weighing these mixed wave
functions is inversely proportional to the energy difference between the states.
Therefore, according to the principle of maximum hardness, hard molecules (with
larger HOMO-LUMO gap) should less readily undergo changes in electronic
structure than soft molecules.
We found [12] the energy convergence procedures of MOPAC6 for optimizing
geometries of the excited states to be much too time-consuming (each structure
requiring many hours of CPU-time on the EPA Cray). On the other hand, lSCF
calculations without optimized structures for individual microstates yielded energy
values for excited states which did not correlate with the observed spectroscopic
data.
As a computing compromise, we chose the first MOPAC6 option to perform only
geometry optimization of the excited states. To mimic the energy of the excited
states, we assumed that the optimized geometry of the excited states described an
average molecular geometry of all microstates taken into account in the
calculations. Finally, the lSCF calculations using these optimized structures did
provide electronic indices which mimicked the energies of the excited states.
Although the HOMO-LUMO gap does not have physical meaning for the excited
states because of the multiplicity of the microstates, the principle of maximum
hardness [13] sug§ests that the computed "HOMO-LUMO gap" [denoted as
(H 0 M 0 -L UM 0) ] of these hypothetical structures might be an appropriate
stability estimate, assuming the optimized geometry of excited states is an average
geometry of all microstates.
This hypothesis was supported [12] by much better correlations found between
(HOMO-LUMO)* gap of the excited states and their observed energies from
spectroscopic data than the QSARs found for ground state structures. Further, the
models for the triplet state energies were significantly better than those for the
singlet states, probably because of the greater stability of the former.