the natural pyrethrin insecticides have the desirable environmental properties of being both non - toxic to mammals and non - persistent . chrysanthemic acid [ 2 , 2-dimethyl-3-(2-methyl-1-propenyl ) ] is one of the products from pyrethrin photodecomposition and is widely used as the acidic part of synthetic pyrethroidin insecticides [ 4 - 9 ] . the photochemical degradation of the acid components of pyrethrins has been examined in numerous studies . and ueda and matsui   found that carbons 1 and 2 ( scheme 1 ) of the main cyclopropane group are cleaved , subsequently leading to the formation of a diradical according to elliot and janes . the photochemistry of simple cyclopropanes has been examined by several workers [ 13 - 18 ] and the fundamental photochemical transformations are generally observed . for instance , the photodegradation of pyrethrins in sunlight is rapid and results in the isomerization of the side - chains , photooxidation to a variety of carboxylic acids , and isomerization of the cyclopropane acids . the main objective of this project was to carry out a theoretical study to determine the reaction mechanism of the decomposition of chrysanthemic acid . this investigation may improve our knowledge about the potential energy surface ( pes ) of these important compounds . we explored the potential energy surfaces of the ground state and the lowest singlet and triplet excited states and the interplay between them . dft calculations have been used successfully in calculating transition structures   and the reaction parameters of various reactions , such as pericyclic rearrangements , cycloadditions   and bimolecular snreactions . in the present work , we use the density functional ( dft ) approach to undertake a theoretical investigation of the mechanism of photochemical decomposition of cha . more specifically , we calculate structures and relative energies of reactant , products , intermediate and transition states involved in all the three suggested pathways ( cis - trans isomerization , rearrangement , fragmentation ) . for a more complete study we also carried out the effect of solvent on the pes using the polarizable continuum model ( pcm ) . all calculations were performed with the gaussian03w   program , running on a pentium iv personal computer . we used restricted and unrestricted b3lyp gradient corrected exchange - correlation functional   in combination with the 6 - 311+g * * basis set [ 25 - 27 ] . in our computational investigation , we determined the location of the minima and transition structures of the singlet state surfaces . for equilibrium geometries and transition states , we carried out irc calculations to confirm that the transition stats connect to right minima . zero - point vibrational energy corrections ( zpve ) were estimated at the same theory level at which optimization was carried out and etotal was calculated as eopt ( optimization energy at equilibrium geometry ) + zpve . basis set superposition error ( bsse ) corrections   were used to obtain more reasonable total energies in fragmentation reaction ( pathway 3 ) . subsequently , the polarizable continuum model ( pcm )   was applied considering water , ethanol , and cyclohexane as solvents (  = 78.3553 , 24.852 , and 2.0165 , respectively ) . all calculations were performed with the gaussian03w   program , running on a pentium iv personal computer . we used restricted and unrestricted b3lyp gradient corrected exchange - correlation functional   in combination with the 6 - 311+g * * basis set [ 25 - 27 ] . in our computational investigation , we determined the location of the minima and transition structures of the singlet state surfaces . for equilibrium geometries and transition states , we carried out irc calculations to confirm that the transition stats connect to right minima . zero - point vibrational energy corrections ( zpve ) were estimated at the same theory level at which optimization was carried out and etotal was calculated as eopt ( optimization energy at equilibrium geometry ) + zpve . basis set superposition error ( bsse ) corrections   were used to obtain more reasonable total energies in fragmentation reaction ( pathway 3 ) . subsequently , the polarizable continuum model ( pcm )   was applied considering water , ethanol , and cyclohexane as solvents (  = 78.3553 , 24.852 , and 2.0165 , respectively ) . three pathways are possible for the decomposition reaction of chrysanthemic acid , as described in an introduction and as displayed in chart 1 : trans - cis isomerization ( p1-p3 ) , fragmentation , cleavage of the 1 , 3 and 1 , 2 bonds ( p1-p5 ) and rearrangement ( p2-p4 ) . this project was designed to explore the pes for the photodecomposition of chrysanthemum acid , which is a major product from the decomposition of pyrethrine pesticides . to reduce the time necessary for calculations , we replaced the methyl groups in cha with hydrogen atoms . atom labels for trans - chrysanthemic acid . to investigate the cis - trans isomerization mechanism of cha ( p1-p3 ) , the potential energy profile was generated by scanning the c12-c1-c3-c8 (  ) angle ( figure 1 ) from 0 to 180 in the s0 state . the different conformations located during the cis - trans isomerization of cha are displayed in figure 2 . the values of c12-c1-c3-c8 dihedral angles are 150.0 and 2.72 for p1 and p3 isomers , respectively . these results show that the two branched groups of cha are approximately in a plane in the cis form ( additional file 1 ) . by inspection figure 2 , one trans conformer associated with the dihedral angle c12-c1-c3-c8 = 180 is less stable than cis form , p1 by ~ 10 kcal / mol . however , the energy difference between the two minimum isomers ( p1 and p3 ) is only 0.577 kcal / mol . the potential curve calculated at the b3lyp/6 - 311+g * * level of theory possesses minima at  = 2.72 and 150 in the cis and trans isomers , respectively . the structure with  = 60 is predicted to be a transition state with an imaginary frequency of i1130.91 cm . no significant differences were found in all of the other geometrical parameters between the two isomers ( cis and trans ) , as shown in figure 3 . the optimized geometries of the reactants , transition state and products are shown in figure 3 . a more detailed and comparative analysis of the geometric parameters for the p1-p3 reaction revealed that a drastic geometric reorganization occurs from p1 to the transition state ( ts ) . the c1-c2 distance decreases from 1.539  in p1 to 1.492  in ts . the c3-c2 and c3-c1 distances increase from 1.512  and 1.499  in p1 to 1.531  and 1.518  in ts , respectively . the average total lengths of the three c - c bonds in the ring are exactly the same ( 1.515  ) , indicating that the ring does not open during rotation about the c12-c1-c3-c8 dihedral angle . these results indicate that the cis and trans forms of cha are found in similar proportions , in accordance with previous experimental observations . potential energy profiles along the rotation around the c12-c1-c3-c8 dihedral angle and some optimized structures ( angles and relative energies are given in angles and kcal / mol , respectively ) . geometries of the stationary points for the first suggested pathway ( p1-p3 ) ; distances are given in  . the rearrangement of cha ( p1 ) to produce lactone ( p4 ) was investigated using the b3lyp/6 - 311+g * * level of theory . our computations predict that the pathway of the rearrangement of cha occurs in stepwise mechanism . as shown in figure 4 , the potential energy surface of rearrangement process contains two transition states and diradical intermediate . the electronic energies , the electronic energies plus the corresponding zero - point vibrational energy ( zpve ) corrections , and relative energies for all the species are reported in table 1 and take the corresponding reactant as a reference . all calculations are carried for all species in potential energy surface for rearrangement process using the restricted and unrestricted b3lyp/6 - 311+g * * level . the relative energies in figure 4 indicate that the rearrangement pathway for cha is endothermic reaction where the product is at 16.8 kcal / mol above reactant . the closed - shell first transition structure on this process , ts1 , is located 1.4 kcal / mol below the second transition state ts2 . according to the relative energies for the stationary points listed in figure 5 , the forward and back activation barriers are 47.5 and 32.1 kcal / mol , respectively . the previous studies on the rearangment of vinylcyclopropane have reported   that only one transition state is located . the activation barrier in this studied had about 46.9 kcal / mol compared to 47.5 kcal / mol in our study . this result indicates that an influence of the carboxylic group on the activation energy of the rearrangement path is little . the energy difference between the final product and the intermediate species is 24.10 kcal / mol from dft calculations . when focused on the overall energetic of the reaction p1-p4 , it is evident that the reaction depends on the energetic balance due to the cleavage of a c1-c3 bond in the starting reactant p1and accompanied by the formation of a c3- o bond in the rearranged carbon centered diradical intermediate . this path is started with cleavage c1-c3 bond in trans conformation p1 with decreasing others c - c bonds except the terminal ch = ch2 . figure 5 displays the main geometrical parameters of the equilibrium and transition structures for the formation of lactone optimized at the b3lyp level with the basis set described above . the negative charge of oxygen atom in the carbonyl group increases from ts1 ( additional file 2 ) with -0.343 to reach -0.351 in ts2 . also , the positive charge on c1 in ts1 and ts2 is 0.286 and 0.315 , respectively . these values mean that the formation bond during this pathway occurs easily between oxygen of carbonyl group and c1 than other carbon atoms . in conclusion , the rearrangement in the cha followed the same route as that in the vinylcyclopropane with the slightly lowered potential barrier . the calculated relative energies in kcal / mol of the rearrangement of cha at the b3lyp/6 - 311+g * * level . calculated energies of the stationary points of rearrangement of cha ( p1-p4 ) . bond lengths and milliken charge distribution for optimized structures of the stationary points located for the rearrangement reactions ( p1-p4 ) . therefore , the most important channel for cha decomposition channels is the decomposition to carbene product via ts3 , the third pathway is the fragmentation , which gives a carbene compound ( p1-p5 ) via c1-c2 and c1-c3 bond cleavage , was also investigated with the b3lyp/6 - 311+g * * level of theory . the total energy of the conformations along the potential surface increases with cleavage of the c1-c2 bond , followed by cleavage of the c1-c3 bond to produce the products , as shown in figure 6 . inspection of the data in figure 6 reveals an increased dihedral angle c2-c1-c3-c12 and decreased c3-c1 bond length in ts2 , indicating that the reaction appears to be concerted . however , figures 7 and 8 show a noticeable shortening of the c2-c3 bond along the fragmentation pathway . the fragmentation process occurs after two steps of successive conformational changes via two transition states , ts2 and ts3 . calculations of the harmonic vibrational frequencies ( imaginary frequencies ) revealed that ts2 and ts3 are true transition states and identified the atoms undergoing the main displacement in the transition structure . because it is too endothermic , this fragmentation process ( p1-p5 ) is less favorable to proceed than the other two pathways . the high endothermicity of the third pathway prevents fragmentation because it is even higher than the energy barrier for the more feasible pathway through ts3 ( 47.5 kcal / mol ) , as shown in figure 7 . this required energy is significant when compared to the more feasible pathway , as shown in figure 4 ( 1.445 kcal / mol endothermic ) . the potential energy surface diagram of the fragmentation process via c1-c2 cleavage ( p1-p5 ) . a standard b3lyp hybrid functional was consistently employed for both geometry optimizations and td - dft calculations . we used the td - dft/6 - 311+g * * method to determine if the reactions occur in the ground or an excited state . if this energy is small , then the reaction probably occurs in the excited state . in further details about the electronic structure , we characterized the low - lying three singlet excited states within the current td - dft calculations as in table 2 . all excited states represent the p - p * and n - p * intramolecular charge transfer ( ct ) transitions . the first and second peaks originate from mixing orbitals , homo and homo-1 to lumo . the first intense peak , dominantly describable with homo-1 - lumo excitation , has large f of 0.195 ( additional file 3 ) . the homo is mainly delocalized on whole molecule whereas the homo-1 is located on carboxylic moiety , depicted in figure 9 . homo-1 - lumo excitation therefore leads to intramolecular ct from vinyl moiety to carboxylic moiety , as illustrated in figure 9 where the electron density increases mainly in the vinyl moiety and decreases in the carboxylic moiety . the third transition originates from homo-1 ( mainly distributed on carboxylic moiety ) to lumo with moderate f of 0.037 . by inspection of the fmo correlation diagram of p1 as depicted in figure 9 , the homo is stabilized than the lumo , which lead to the gap energy is high . the electron density is littler on c1-c3 bond in the ring this means that this bond is easy to break . our results showed that the promotion of an electron requires a large amount of energy relative to the activation energy and the energy of the reaction . the excitation energy of p1 is 136.46 kcal / mole ( table 2 ) , which is larger than the value of barrier of the three studied pathways . these results suggest that all of the studied reactions take place in their ground state rather than in an excited state . calculated low - energy singlet excitation energies , wavelengths , and oscillator strengths ( f ) for cha ( p1 ) using td - b3lyp/6 - 311 g * * level . frontier molecular orbital picture ( fmo )   ( homo , homo-1 , lumo ) of cha ( p1 ) we investigated the solvent effect using single - point scrf calculations on optimized structures . we used an scrf method with a polarizable continuum model ( pcm ) at the b3lyp/6 - 311+g * * level ( additional file 4 ) . the effect of different dielectric constants on the pes of the decomposition of cha was performed using three solvents ( water = 78.3553 , ethanol = 24.852 and cyclohexane = 2.0165 ) . the solvent effect on the pes for the reaction decomposition of cha at the dft level of theory the solvation energies in kcal / mol of the studied species in pes using pcm at the b3lyp/6 - 311+g * * level .   the solvent does not affect the ordering stability of the potential energy surface species . however , the solvents increase the stability of all of the reaction species with increasing dielectric constants . to investigate the cis - trans isomerization mechanism of cha ( p1-p3 ) , the potential energy profile was generated by scanning the c12-c1-c3-c8 (  ) angle ( figure 1 ) from 0 to 180 in the s0 state . the different conformations located during the cis - trans isomerization of cha are displayed in figure 2 . the values of c12-c1-c3-c8 dihedral angles are 150.0 and 2.72 for p1 and p3 isomers , respectively . these results show that the two branched groups of cha are approximately in a plane in the cis form ( additional file 1 ) . by inspection figure 2 , one trans conformer associated with the dihedral angle c12-c1-c3-c8 = 180 is less stable than cis form , p1 by ~ 10 kcal / mol . however , the energy difference between the two minimum isomers ( p1 and p3 ) is only 0.577 kcal / mol . the potential curve calculated at the b3lyp/6 - 311+g * * level of theory possesses minima at  = 2.72 and 150 in the cis and trans isomers , respectively . the structure with  = 60 is predicted to be a transition state with an imaginary frequency of i1130.91 cm . no significant differences were found in all of the other geometrical parameters between the two isomers ( cis and trans ) , as shown in figure 3 . the optimized geometries of the reactants , transition state and products are shown in figure 3 . a more detailed and comparative analysis of the geometric parameters for the p1-p3 reaction revealed that a drastic geometric reorganization occurs from p1 to the transition state ( ts ) . the c1-c2 distance decreases from 1.539  in p1 to 1.492  in ts . the c3-c2 and c3-c1 distances increase from 1.512  and 1.499  in p1 to 1.531  and 1.518  in ts , respectively . the average total lengths of the three c - c bonds in the ring are exactly the same ( 1.515  ) , indicating that the ring does not open during rotation about the c12-c1-c3-c8 dihedral angle . these results indicate that the cis and trans forms of cha are found in similar proportions , in accordance with previous experimental observations . potential energy profiles along the rotation around the c12-c1-c3-c8 dihedral angle and some optimized structures ( angles and relative energies are given in angles and kcal / mol , respectively ) . geometries of the stationary points for the first suggested pathway ( p1-p3 ) ; distances are given in  . the rearrangement of cha ( p1 ) to produce lactone ( p4 ) was investigated using the b3lyp/6 - 311+g * * level of theory . our computations predict that the pathway of the rearrangement of cha occurs in stepwise mechanism . as shown in figure 4 , the potential energy surface of rearrangement process contains two transition states and diradical intermediate . the electronic energies , the electronic energies plus the corresponding zero - point vibrational energy ( zpve ) corrections , and relative energies for all the species are reported in table 1 and take the corresponding reactant as a reference . all calculations are carried for all species in potential energy surface for rearrangement process using the restricted and unrestricted b3lyp/6 - 311+g * * level . the relative energies in figure 4 indicate that the rearrangement pathway for cha is endothermic reaction where the product is at 16.8 kcal / mol above reactant . the closed - shell first transition structure on this process , ts1 , is located 1.4 kcal / mol below the second transition state ts2 . according to the relative energies for the stationary points listed in figure 5 , the forward and back activation barriers are 47.5 and 32.1 kcal / mol , respectively . the previous studies on the rearangment of vinylcyclopropane have reported   that only one transition state is located . the activation barrier in this studied had about 46.9 kcal / mol compared to 47.5 kcal / mol in our study . this result indicates that an influence of the carboxylic group on the activation energy of the rearrangement path is little . the energy difference between the final product and the intermediate species is 24.10 kcal / mol from dft calculations . when focused on the overall energetic of the reaction p1-p4 , it is evident that the reaction depends on the energetic balance due to the cleavage of a c1-c3 bond in the starting reactant p1and accompanied by the formation of a c3- o bond in the rearranged carbon centered diradical intermediate . this path is started with cleavage c1-c3 bond in trans conformation p1 with decreasing others c - c bonds except the terminal ch = ch2 . figure 5 displays the main geometrical parameters of the equilibrium and transition structures for the formation of lactone optimized at the b3lyp level with the basis set described above . the negative charge of oxygen atom in the carbonyl group increases from ts1 ( additional file 2 ) with -0.343 to reach -0.351 in ts2 . also , the positive charge on c1 in ts1 and ts2 is 0.286 and 0.315 , respectively . these values mean that the formation bond during this pathway occurs easily between oxygen of carbonyl group and c1 than other carbon atoms . in conclusion , the rearrangement in the cha followed the same route as that in the vinylcyclopropane with the slightly lowered potential barrier . the calculated relative energies in kcal / mol of the rearrangement of cha at the b3lyp/6 - 311+g * * level . calculated energies of the stationary points of rearrangement of cha ( p1-p4 ) . bond lengths and milliken charge distribution for optimized structures of the stationary points located for the rearrangement reactions ( p1-p4 ) . therefore , the most important channel for cha decomposition channels is the decomposition to carbene product via ts3 , the third pathway is the fragmentation , which gives a carbene compound ( p1-p5 ) via c1-c2 and c1-c3 bond cleavage , was also investigated with the b3lyp/6 - 311+g * * level of theory . the total energy of the conformations along the potential surface increases with cleavage of the c1-c2 bond , followed by cleavage of the c1-c3 bond to produce the products , as shown in figure 6 . inspection of the data in figure 6 reveals an increased dihedral angle c2-c1-c3-c12 and decreased c3-c1 bond length in ts2 , indicating that the reaction appears to be concerted . the c2-c3 bond is the same in the two transition states . however , figures 7 and 8 show a noticeable shortening of the c2-c3 bond along the fragmentation pathway . the fragmentation process occurs after two steps of successive conformational changes via two transition states , ts2 and ts3 . calculations of the harmonic vibrational frequencies ( imaginary frequencies ) revealed that ts2 and ts3 are true transition states and identified the atoms undergoing the main displacement in the transition structure . because it is too endothermic , this fragmentation process ( p1-p5 ) is less favorable to proceed than the other two pathways . the high endothermicity of the third pathway prevents fragmentation because it is even higher than the energy barrier for the more feasible pathway through ts3 ( 47.5 kcal / mol ) , as shown in figure 7 . this required energy is significant when compared to the more feasible pathway , as shown in figure 4 ( 1.445 kcal / mol endothermic ) . the potential energy surface diagram of the fragmentation process via c1-c2 cleavage ( p1-p5 ) . a standard b3lyp hybrid functional was consistently employed for both geometry optimizations and td - dft calculations . we used the td - dft/6 - 311+g * * method to determine if the reactions occur in the ground or an excited state . if this energy is small , then the reaction probably occurs in the excited state . in further details about the electronic structure , we characterized the low - lying three singlet excited states within the current td - dft calculations as in table 2 . all excited states represent the p - p * and n - p * intramolecular charge transfer ( ct ) transitions . the first and second peaks originate from mixing orbitals , homo and homo-1 to lumo . the first intense peak , dominantly describable with homo-1 - lumo excitation , has large f of 0.195 ( additional file 3 ) . the homo is mainly delocalized on whole molecule whereas the homo-1 is located on carboxylic moiety , depicted in figure 9 . homo-1 - lumo excitation therefore leads to intramolecular ct from vinyl moiety to carboxylic moiety , as illustrated in figure 9 where the electron density increases mainly in the vinyl moiety and decreases in the carboxylic moiety . the third transition originates from homo-1 ( mainly distributed on carboxylic moiety ) to lumo with moderate f of 0.037 . by inspection of the fmo correlation diagram of p1 as depicted in figure 9 , the homo is stabilized than the lumo , which lead to the gap energy is high . the electron density is littler on c1-c3 bond in the ring this means that this bond is easy to break . our results showed that the promotion of an electron requires a large amount of energy relative to the activation energy and the energy of the reaction . the excitation energy of p1 is 136.46 kcal / mole ( table 2 ) , which is larger than the value of barrier of the three studied pathways . these results suggest that all of the studied reactions take place in their ground state rather than in an excited state . calculated low - energy singlet excitation energies , wavelengths , and oscillator strengths ( f ) for cha ( p1 ) using td - b3lyp/6 - 311 g * * level . frontier molecular orbital picture ( fmo )   ( homo , homo-1 , lumo ) of cha ( p1 ) we used an scrf method with a polarizable continuum model ( pcm ) at the b3lyp/6 - 311+g * * level ( additional file 4 ) . the effect of different dielectric constants on the pes of the decomposition of cha was performed using three solvents ( water = 78.3553 , ethanol = 24.852 and cyclohexane = 2.0165 ) . the solvent effect on the pes for the reaction decomposition of cha at the dft level of theory the solvation energies in kcal / mol of the studied species in pes using pcm at the b3lyp/6 - 311+g * * level . . however , the solvents increase the stability of all of the reaction species with increasing dielectric constants . potential energy surface ( pes ) for three channels of decomposition of cha ( p1 ) were studied in the gas phase at the b3lyp/6 - 311+g * * level of theory . the solvent effect on pes , we conclude the following . 1 - the calculations rationalize and verify all experimental facts . the b3lyp/6 - 311+g**level of theory provides a reasonable way to investigate the decomposition channels of chrysanthemic acid . 2 - cis - trans isomerization pathway is energetically favorable than the fragmentation and rearrangement pathways . 3 - the solvent effect does not affect the shape of the potential energy surfaces . in other words , the solvent effect on the reaction is small and tends to stabilize all of the isomers . p1-opt . output optimized of p1 structure . p1-tddft . output uv absorption calculation using tddft method for p1 . this project was funded by the deanship of scientific research ( dsr ) king abdulaziz university , jeddah , under grant no .