photochromic molecules 
 from the spiropyran family are reversibly 
 switched between the spiro form ( sp ) , displaying absorption only in 
 the uv region , and the merocyanine form ( mc ) , absorbing light also 
 in the visible region , using light of appropriate wavelengths . although the color change is the most widely 
 recognized feature for spiropyrans and photoswitches in general , it 
 is by no means the only property that changes upon isomerization . additional examples are the redox energies , molecular structure , and charge distribution , to mention a few . altogether , the light - induced 
 changes in these and other properties have been harnessed for applications 
 in , for example , the photocontrol of biological functions , bioimaging , optical signal processing , and photoswitching in general , as well as in chemosensing . in many of these situations , aqueous media is required and , hence , 
 also spiropyran derivatives that are readily dissolved in water . as 
 the spiropyran backbone per se has very poor water solubility , covalent 
 attachment of solubilizing groups , or supramolecular complex formation 
 with water - soluble hosts our approach has been to covalently attach positively charged alkylamino- 
 or amidine groups to the spiropyran photoswitch . these compounds have 
 been studied in the contexts of photo- and ph controlled dna - binding , photoinduced cytotoxicity , membrane 
 interactions , and supramolecular complex 
 formation . owing to the potential applicability 
 in diverse fields , the ring - opening mechanism , conformational 
 distribution , and photochemical properties of various derivatives have also been addressed by theoretical investigations . although the spiropyrans represent a very versatile class of photochromic 
 compounds with several promising candidates for future use in biological 
 applications , the behavior in aqueous media is relatively unexplored . 
 here , we present a comprehensive model of all processes relevant for 
 the interconversions between the different species ( sp , mc , and the 
 respective protonated forms ) including the thermal and photoinduced 
 isomerization processes , as well as the undesired hydrolysis reaction . 
 to support experiments , the hydrolytic degradation of the mc form 
 was also investigated by theoretical calculations , using both quantum 
 mechanics ( qm ) and combined quantum mechanics / molecular mechanics 
 ( qm / mm ) models employing density functional theory . these addressed 
 several mechanisms for both the protonated and the nonprotonated forms 
 of the molecule and also the effect of water on the barrier heights , 
 with final energies obtained at the b3lyp/6 - 311++g(2d,2p ) level of 
 theory . we hope that the results from this study will be of help to 
 others in the design of spiropyran derivatives for various applications 
 where aqueous media is a requirement . the synthesis of 1,2,4 , and 6(7 ) have been described earlier , whereas the synthesis 
 of 3 and 5 are outlined in the supporting information . the ring - opened forms 
 ( mc and mch ) were prepared by heating the sp isomer in 
 an aqueous solution at ph 1 until the sample was fully converted to 
 the mch form ( ca . 5 min ) . for mc , the sph form was 
 prepared by dissolving sp in aqueous solution followed by acidification 
 with conc . the absorption 
 measurements 
 were carried out on a carybio 50 uv / vis spectrometer equipped with 
 a varian pcb 1500 water peltier system thermostat for temperature 
 control . the visible light was generated by a 500 w xe lamp equipped with a 
 hot mirror ( a = 1.8 at 900 nm ) to reduce the ir intensity 
 and suitable optical filters . for quantum yield determinations , an 
 interference filter in the visible region was used ( see supporting information for details ) . the uv light 
 was generated by a uvp lamp model uvgl-25 ( 254 nm , 700 w / cm ) . the time - based absorption measurements at ph 410 
 were performed in buffered solutions with 10 mm na2hpo4/nah2po4 set to the respective ph . at 
 ph 3 and lower , all quantum chemical calculations 
 were performed using the gaussian 09 software package . to address the reaction mechanism of hydrolysis , 
 two models were used . the reaction steps of the minimum energy path 
 and the alternative reaction paths were addressed using a smaller 
 qm model which included the initial merocyanine and one explicit water 
 molecule ( qm(1w ) ) ( see figure s6 in the supporting 
 information ) . all the minima and transition states ( tss ) for 
 qm(1w ) were optimized using becke s three parameter parr 
 correlation functional ( b3lyp ) with the 
 6 - 31+g(d , p ) basis set . this model considered solvent effects of water 
 using the integral equation formalism for the polarizable continuum 
 solvent model ( iefpcm ) . to investigate 
 potential effects of explicit water molecules on the barrier heights 
 of the most important tss , an oniom ( our own n - layered integrated 
 molecular orbital and molecular mechanics ) integrated qm / mm method model was used , in which six water molecules 
 and the merocyanine were included in the qm layer , surrounded by a 
 40  box of explicit water molecules in a b3lyp/6 - 31g(d):amber 
 setup ( oniom(6w ) ) . to ensure the relaxation of water equilibrated 
 around mc , the final oniom(6w ) model initially , the qm / mm model was fully minimized with only the mc molecule 
 included in the qm layer . this was followed by an optimization with 
 the water molecule closest to ca ( for labeling of atoms , 
 see scheme 1 ) included in the qm layer , and 
 all water molecules farther than 15  from the mc molecule being 
 frozen . finally , five additional water molecules were chosen ( the 
 five closest to the ca atom ) , resulting in three above 
 and three below the plane of the merocyanine molecule ( see figure 
 s6 in the supporting information ) . this 
 way , the potential stabilizing contribution of water molecules from 
 both sides of the mc molecule could be followed . for the qm layer 
 atoms , charges were determined using the merz  singh kollman 
 scheme on the qm(1w ) model , and for the 
 remaining five water molecules the charges were determined after initial 
 minimization . our focus was on the mc reactant state 
 and on the three critical tss , tsi , tsii , and tsiii , which were subject to further calculations . all critical points obtained for qm(1w ) , and the above selected 
 ones for oniom(6w ) , were followed by second derivative calculations 
 at the same level of theory as optimizations were performed . these 
 were used to determine the nature of the optimized critical point 
 ( minimum or ts ) , to obtain both zero point energies and thermal contributions 
 to the energy , and entropy contributions to free energies within the 
 harmonic approximation . in the case of qm(1w ) , for iii and tsiv the initial reactant consists practically 
 of two molecules coordinated 
 only by one small group from each , which resulted in convergence problems 
 with the molecular fragments rotating around the intermolecular axis . therefore , convergence was achieved by constraining the relative orientation 
 of the fragments for the above two critical points . this led to an 
 additional imaginary vibrational frequency for both calculations , 
 not related to the reaction coordinate . due to the small magnitudes , 
 2i cm and 12i cm , respectively , the final energy values are 
 not significantly affected . tsiii and the ts between 
 the ttt and the ttc conformers of 
 mch could not be located with the solvent model . therefore , 
 these two tss were optimized at the same level of theory as the other 
 critical points in the gas phase , followed by a single point calculation 
 which considered solvent effects . for the two product states ( iv and hp ) , the transformations between different 
 coordination relative to each other were not considered . the transition 
 state htsi starting from the ttc conformer 
 of mch was obtained using the loose convergence criteria 
 as implemented in the gaussian 09 software package . electronic 
 energies were also calculated using point energy calculations 
 at the b3lyp/6 - 311++g(2d,2p ) and b3lyp/6 - 311++g(2d,2p):amber level 
 of theory for qm(1w ) and oniom(6w ) , respectively . for qm(1w ) critical 
 points iii , tsiv , iv , and hp consist of two separate molecules coordinated to each other , 
 why the single point energy calculations with higher basis set also 
 serve the purpose of minimizing potential effects of basis set superposition 
 errors observed with smaller basis sets . for more details , 
 see section  theoretical calculations  in the supporting information . the primary objective of this work has been to investigate in detail 
 the various thermal , acido- and photochromic processes for the spiropyran 
 derivatives shown in figure 1 . compounds 14 have a nitro substituent in the 6-position 
 of the benzopyran moiety ( c6 , see scheme 1 for labeling of relevant atoms discussed in the text ) . these 
 compounds differ in the number of methylene units in the aminoalkyl - derived 
  tail  attached to the indoline nitrogen ni ( three or five ) , as well as the number of methyl groups on the amino 
 nitrogen na ( two or three ) . compounds 5 and 6 are equipped with a quaternary amine via a propyl tail and 
 come with an aldehyde and a cyano group on c6 , respectively . the main reason for using different substituents on the benzopyran 
 ring was to vary the pka - value of the 
 phenolic oh group of the protonated mc isomer ( mch , see 
 scheme 1 ) . a more 
 electron withdrawing substituent is expected to stabilize the negatively 
 charged oxygen oph of the nonprotonated mc isomer and , 
 hence , decrease the pka - value . moreover , the variation of the substituents 
 at both the benzopyran ring and the indoline nitrogen ni effects several other thermal and photoinduced processes , as will 
 be described in detail below . in the following sections , the experimental 
 results ( spectra , kinetic traces , etc . ) will be shown only for 1 , whereas the corresponding data for 26 is collected in the supporting information . structures of the closed spiro ( sp ) forms of the spiropyran derivatives 
 studied in this work . scheme 1 shows 
 the relevant forms of 1 and the corresponding interconversion 
 pathways . the spectra of the respective forms are shown in figure 2 ( see figure s1 in the supporting 
 information for corresponding spectra of 26 ) . framed : labelling of relevant 
 atoms discussed in the text . the sp isomer 
 is converted to the mc isomer by uv - light exposure , 
 and the reverse reaction is triggered by visible light . in the dark , 
 the two isomers are interconverted by thermal processes . as opposed 
 to organic solvents , where the thermal equilibrium is shifted to virtually 
 100% sp , the rate constants for the thermal isomerization processes 
 sp  mc and mc  sp ( ko and kc in scheme 2 ) are comparable 
 in aqueous solution . absorption spectra of 1sp (  ) , 1sph (  ) , 1mc (  ) , 1mch (  ) , and hp (  ) . at ph below 
 ca . this is due to the highly polar nature of water 
 which stabilizes 
 the zwitterionic mc form . it has also been suggested that hydrogen 
 bonding contributes to the mc form stabilization . upon acidification , protonation of the mc phenolate 
 oxygen oph leads to the formation of mch . here , the pka - value of this form is referred 
 to as pka . while this form 
 is readily converted 
 to sp using visible light , the corresponding thermal conversion is 
 not observed . moreover , we suggest that the mch isomer 
 is stable also to hydrolytic degradation ( vide infra ) . upon further acidification , also the sp isomer is protonated . we assign this species to sph , where the indoline nitrogen 
 ni of the sp isomer is protonated , with a pka - value referred to herein as pka . this form displays 
 neither thermal nor photoinduced isomerizations , i.e. , it can only 
 be interconverted to the other forms after deprotonation to the sp 
 isomer . it is obvious that the substituent 
 on c6 influences pka , whereas it has no effect on pka . the ability to tune the pka - value by the choice of substituent has been proven useful 
 in many situations , including the ph - controlled dna - binding observed 
 in our laboratory . furthermore , pka for 16 are significantly lower compared to spiropyran derivatives 
 without a positively charged functionality attached to the indoline 
 nitrogen ni . for example , pka of 1 , 2 , 5 , and 6 are almost two units lower compared to spiropyran derivatives 
 with a methyl group attached to ni ( 0.4 versus 2.3 ) . as sph can not be converted to mc / mch by neither thermal nor photoinduced processes , this implies 
 that the ph range over which 16 maintain 
 their photochromic properties is significantly broadened . finally , 
 one of the limiting factors for the application of spiropyrans 
 in aqueous medium is the hydrolytic instability of the mc form . hydrolysis has been proposed to be initiated 
 by nucleophilic attack at the ene - iminium cation , followed by a retro - aldol 
 reaction yielding fischer s base and salicylaldehyde as hydrolysis 
 products ( hp ) . here , we suggest that the nonprotonated mc isomer is 
 the only form that is susceptible to hydrolysis and that water is 
 the major nucleophile involved in the reaction . scheme 2 summarizes the kinetic 
 model with the respective rate constants for the thermal processes 
 and the pka - values for the protonated 
 forms . the sections below 
 are organized as follows : first , the thermal 
 processes ( isomerization reactions and hydrolysis ) at ph 7 will be 
 described together with the photoinduced isomerization reactions . 
 at ph 7 , none of the protonated species are formed , i.e. , the involved 
 components are sp , mc , and hp . second , the corresponding results at 
 different ph will be presented for a selection of the derivatives . our main objective in the design of 16 was to investigate the influence from the substituent on c6 in the benzopyran ring . the results from ph 59 suggest that 
 water is the nucleophile in the hydrolysis reaction , rather than oh . in the ph - interval 01 , the equilibrium mc / mch is shifted to nearly 100% mch and the hydrolysis 
 reaction is virtually halted . hence , our kinetic model in this ph 
 range contains sph , sp , and mch . based on 
 these results . finally , we present computational results , which addressed 
 the hydrolysis mechanism in aqueous media for both the mc and the 
 mch forms that further strengthen the above notion . figure 3 shows the time - dependent absorbance of 1mc reflecting the thermal interconversions of the dissolved sp and 
 the mc forms together with the subsequent hydrolysis of mc . as the pka - values of the sph and the mch forms of 1 were determined 
 to 0.4 and 3.7 , respectively , the concentrations of the protonated 
 forms are negligible at ph 7 ( see table 1 for 
 the pka - values of derivatives 16 ) . hence , our kinetic model at this ph includes 
 the species sp , mc , and hp . , the kinetic model 
 shown in eq 1 was used to describe the kinetics 
 at ph 7.1 kinetic absorption trace of 1mc at 25 c 
 monitored 
 at 512 nm reflecting the thermal interconversions between sp , mc , 
 and hp according to eq 1 . the solid line is 
 the fitted trace using the biexponential expression in eq 2 . inset : absorption spectrum recorded at t = 12000 min , clearly showing the residual absorption of 1mc centered at 512 nm . this kinetic model gives rise to a biexponential rate expression 
 for the concentrations of all involved species . thus , the kinetic trace was fitted according to eq 2.2here , krise reflects 
 the rise time of the initial part of the kinetic trace in figure 3 , whereas kdecay is 
 the rate constant of the subsequent decay . if ko + kc  kh + k  h , krise would have been the sum of ko and kc and , hence , the rise would 
 reflect the rate of the thermal equilibrium establishment between 
 sp and mc . here , this assumption is not valid , and the analytic rate 
 expressions for [ sp ] , [ mc ] , and [ hp ] derived using the laplace transform 
 method were used ( see supporting information for the derived rate expressions ) . it is obvious that 
 there are large variations in both the ratio ko / kc as well as 
 the sum ko + kc between the different derivatives , which in turn manifest itself 
 in differences in the hypothetical thermal equilibrium position [ mc]/[sp ] 
 and the time required to reach it . 80% mc at thermal equilibrium , whereas the corresponding number 
 for 6 is only 14% . depending on the application , both 
 situations may be desired ( visible - light activation to the sp form 
 versus uv activation to the mc form ) . as for minimizing the effect 
 of the hydrolytic degradation , a thermal equilibrium position enriched 
 in sp is preferred , as the concentration of the hydrolyzable mc isomer 
 is kept at a minimum . the quantum yields of the photoinduced isomerization 
 processes and the photostationary distributions ( psd ) are also collected 
 in table 1 . the resistance toward photodegradation no detectable decomposition was observed after 10 cycles ( see figure 
 s5 in the supporting information ) . isomerization quantum yield for 
 the process sp  mc using 254 nm uv - light . isomerization quantum yield for 
 the process mc  sp using visible light centered at 503 nm . photostationary distribution 
 [ mc]/[sp ] 
 after the application of 254 nm uv - light . the experiments and the 
 data analysis procedure at ph 7 described above were performed also 
 at ph 510 . figure 4 shows the ph dependence 
 of the rate constants ko , kc , kh , and k the extracted rate constants reflect the kinetic model 
 shown in eq . 1 , i.e. , none of the protonated 
 species sph or mch were considered . for 1 , this is a good approximation over the entire ph interval 
 510 as pka = 3.7 
 for this derivative , and hence , less than 5% exists as mch at ph 5 . for 5 and 6 , this implies 
 that around 25% mch is present at ph 5 , why the data is 
 only shown between ph 6 and ph 10 . ph dependence of the thermal rate constants ko ( a ) , kc ( b ) , kh ( c ) , and k  h ( d ) . data shown for 1 (  ) , 5 (  ) , 
 and 6 (  ) . the rate constants for thermal opening and closing 
 ( ko and kc in figure 4a , b ) show no significant variations 
 with ph . this 
 is true also for the rate constant of hydrolysis mc  hp ( kh in figure 4c ) up to 
 ph 9 , whereas an increase by a factor of ca . 2 this strongly suggests that water is the major 
 nucleophile in the hydrolysis reaction in the ph - independent interval 
 up to ph 9 , whereas the corresponding attack by oh is the rate determining step at higher ph . the data for the corresponding condensation reaction ( reverse hydrolysis , k  h in figure 4d ) shows that the process experiences a rate increase when going 
 from ph 8 to ph 7 . we will , however , not analyze the condensation 
 reactions in the sections below , but instead focus on the hydrolysis 
 reaction . the rate constants displayed in figure 4 are tabulated in table s1 in the supporting 
 information . at ph 
 significantly below 
 pka ( see scheme 2 and table 1 ) the mc / mch equilibrium is shifted to virtually only mch . hence , sp was dissolved at the respective ph and the rise in the absorbance 
 of mch was monitored as a function of time . the results 
 for 1 at ph 0 and ph 1 are shown in figure 5 . thermal formation of 1mch from 1sp via 1mc at ph 0 ( dashed line ) and ph 1 ( solid line ) . the slower rise observed at ph 0 reflects the lower concentration 
 of the thermally isomerizable sp form . from the  rise and stay  behavior it is obvious 
 that 
 the hydrolysis reaction is virtually halted at ph 0 and ph 1 . therefore , 
 the kinetic model in this ph regime is described by eq 3.3 in this ph region , however , the [ mc]/[mch ] equilibrium 
 is shifted to virtually 100% mch . hence , the kinetic situation 
 reduces to a model including only 
 sph , sp , and mch according to eq 4.4the kinetic traces were fitted to a monoexponential 
 rate expression according to eq 5.5the equilibrium establishment between sp and 
 sph is extremely fast compared to ko . hence , the apparent rate constant of thermal 
 opening , krise , is described by eq 6.6as pka for sph ( pka , see table 1 ) is known for all derivatives , the rate constant ko is easily extracted from the experimentally 
 fitted krise . the ko - values at ph 0 and 1 were found to be : 4.0  10 min and 3.4  10 min for 1 , 1.3  10 min and 2.0  10 min for 5 , and 5.0  10 min and 5.3  10 min for 6 . these values agree very well 
 with the corresponding values at ph 5 to ph 10 shown in figure 4a . the fact that the rate constant of thermal opening 
 sp  mc is virtually ph independent between ph 0 and 10 clearly 
 shows that there is no direct accelerated acid induced opening sp 
  mch , but that mch is formed via thermal 
 opening sp  mc followed by protonation of mc . furthermore , 
 no hydrolysis is seen over 8000 min at ph 0 and 1 . if oh would have been the nucleophile involved 
 in the rate determining step , the halted hydrolysis could have been 
 explained by the low oh concentration at these 
 ph values . this is highly unlikely , however , as the rate of hydrolysis 
 does not vary significantly with the oh concentration 
 between ph 5 and 9 . thus , we suggest that mch is not susceptible 
 to hydrolysis . this notion will be further supported by computational 
 means ( vide infra ) . at ph 24 , 
 a full kinetic model including all species and processes shown in 
 scheme 2 has to be applied . we could not find 
 the analytic expression for this kinetic situation by the laplace 
 transformation method . instead we used the experimental rate constants 
 derived at ph 5 and the respective pka - values to simulate the concentration profiles versus time for all 
 relevant species by numerical means . these concentration profiles 
 were compared with the experimentally recorded absorption traces of 
 mc and mch at ph 24 . while the experimentally 
 obtained values of ko and kc at ph 5 together with pka and pka were 
 used in the simulations , the values of kh and k  h were slightly adjusted 
 for each ph - value to improve the goodness of fit ( the experimental 
 values at ph 5 , kh = 1.8  10 min , k h = 6.6  10 min , were 
 varied in the intervals 1.8  10 min  2.6  10 min and 0  6.6  10 min , respectively ) . note that these adjustments are no 
 larger than the variations in the experimentally obtained values of kh and k  h between ph 5 and ph 10 . the results for 1 are shown 
 in figure 6 and the corresponding data for 5 and 6 is shown in figure s4 in the supporting information . the results clearly show 
 that the kinetic model holds also at ph values where the interconversions 
 between all five species have to be taken into account . experimentally 
 recorded absorbance traces for 1mc and 1mch at 25 c at ph 2 ( dash - dot , recorded 
 at 410 nm , mch ) , ph 3 ( dashed , recorded at 410 nm , mc 
 and mch ) , and ph 4 ( dotted , recorded at 512 nm , mc ) . the 
 corresponding normalized traces derived from a simulation using the 
 kinetic model in scheme 2 and the rate constants 
 at ph 5 are also shown ( solid lines ) . note that kh and k  h were slightly 
 adjusted from the values determined at ph 5 ( see text for details ) . to support 
 experiments , the mechanism of hydrolysis of the mc isomer the reaction steps were explored 
 using a qm model with one explicit water molecule considered , referred 
 to herein as qm(1w ) , whereas the effect of solvent molecules on the 
 barrier height was also addressed with a larger oniom model . here , six water molecules were included in the 
 qm layer , further surrounded by water molecules treated by mm ( oniom(6w ) ) . fortunately , in recent years several theoretical studies have focused 
 on various spectral properties of the sp  mc conversion mechanism 
 of spiropyrans and related derivatives , which greatly helped in selecting 
 the optimal models and the applied theoretical method . have analyzed in detail the effect of several density functionals 
 and continuum solvent models on relative energies of different conformers . based on these results and on previous tests 
 on hydrolysis reactions using mller plesset ( mp2 ) calculations 
 as a reference , geometry optimizations for the 
 qm(1w ) model were performed at the b3lyp/6 - 31+g(d , p ) level of theory 
 with solvent effects of water considered by the iefpcm model . final energies were obtained from point energy 
 calculations at the b3lyp/6 - 311++g(2d,2p ) level . prior 
 to addressing the reaction steps , the initial  reactant  
 conformer of mc was selected based on considering the four different 
 relative orientations of the p - nitro - phenolate and 
 the indolenium groups . based on previous results and on our analysis ( see supporting 
 information ) , we concluded that the ttc conformer 
 is the major initial reactant and , hence , was used in the calculations . the initial ttc conformer was optimized with four 
 alternative water positions close to ca and the lowest 
 energy conformer was selected to be the reactant state ( mc ) as shown in figure 7 . a similar analysis 
 was performed for the protonated form , mch , where the 
 energetic distribution of the conformers showed that the ttt conformer is somewhat more stable than the ttc conformer . however , the two conformers are separated by only a low energy transition 
 state ( ts ) as detailed in the supporting information , why we addressed the reaction paths starting from both ttc and ttt conformers for mch . selected critical points along the minimum energy path starting 
 from the ttc conformer with the nucleophilic water 
 molecule coordinated on the molecule ( mc ) . the obtained 
 critical points were qualitatively the same for the qm(1w ) and oniom(6w ) 
 models . relevant distances of the atoms participating in the hydrolysis 
 are displayed for the qm(1w ) and in parentheses for the oniom(6w ) 
 with values in ngstrms . for more details , see tables 3 and 4 , and figures s6 and 
 s7 in the supporting information . to determine the most likely minimum 
 energy pathway of the reaction these include two different paths starting from the neutral form , 
 mc , and also two paths starting from the protonated form , mch . the energy profile of the reaction was compared with the 
 free energy values derived back from the experimental rate constants 
 of hydrolysis shown in table 2 using classical 
 transition state theory . out of the reaction 
 pathways mentioned above , those which resulted in unlikely high energy 
 values for tss or for intermediate structures see the experimental section , and  theoretical calculations  
 in the supporting information . the structure of the hydrolysis products 
 shows that the nucleophilic attack of the water molecule takes place 
 on the double - bond between the nitro - phenolate and the indolenium 
 fragments , with the water oxygen ( o ) coupling to carbon 
 atom ca ( for labeling of the atoms see scheme 1 and scheme 3 ) . accordingly , 
 in the initial reactant state mc , for both qm(1w ) and 
 oniom(6w ) models , the water molecule is coordinated on the phenolate 
 oxygen oph close to the central ca cb double bond as shown in figure 7 and 
 figure s7 in the supporting information . the reaction in qm(1w ) then proceeds via the first transition state 
 ( tsi ) with a barrier of 26.5 kcal / mol into the first 
 intermediate ( i ) , in which oph becomes protonated 
 and the oh group from the water molecule ( o  h ) 
 forms a bond with ca . judging from the structure of the 
 hydrolysis products , the protons from the two oh groups eventually 
 have to transfer to the opposite carbon , cb , which will 
 finally result in a methyl group on the indolenium fragment . from 
 intermediate i , the overall reaction could in principle 
 proceed with a double proton transfer , where o h 
 protonates cb , together with simultaneous o protonation by oph  h ( see scheme 3 ) . however , the corresponding ts energy shown in figure 8 is above 40 kcal / mol , which renders this reaction 
 path very unlikely . instead , the structure of intermediate i allows for a direct protonation of cb from oph h , with a barrier height of 28.9 kcal / mol at tsii ( see table 3 and figures 7 and 8) . from this point , intermediate ii , the reaction proceeds with the breakup of the bond between 
 ca and cb via tsiii , with g = 26.5 kcal / mol . in intermediate iii although at this point 
 the proton is still bonded to the oxygen , the extended conjugation 
 with the ring system renders the molecule in a planar conformation . finally the protonation of cb takes place with a small 
 barrier from iii ( 19.4 kcal / mol ) through tsiv ( 20.7 kcal / mol ) , and the hydrolysis products are formed ( iv and hp ) . considering reaction energetics of the minimum 
 energy path , there are three tss : tsi , tsii , and tsiii , which have similar relative energies where 
 the highest barrier corresponds to the transfer of the first proton 
 to cb from oph ( tsii ) with a free 
 energy of 27.2 and 28.9 kcal / mol at the b3lyp/6 - 31+g(d , p ) and b3lyp/6 - 311++g(2d,2p ) 
 levels of theory , respectively . considering the reactant and the product 
 states , mc and hp , the small relative energy 
 difference , 0.6 and 0.3 kcal / mol for the b3lyp/6 - 31+g(d , p ) 
 and b3lyp/6 - 311++g(2d,2p ) levels , respectively , are in line with the 
 ratios of kh and k  h displayed in table 2 . this 
 is also in accordance with other similar hydrolysis reactions , where 
 reversibility was observed . cb bond at tsiii , there are two molecular fragments , and the following 
 steps in the reaction involve a shallow ts in our investigation . consequently , 
 the formation of the final two hydrolysis product molecules could 
 in principle also be achieved by proton transfers with other solvent 
 molecules that the present quantum chemical calculations do not consider . reaction 
 profile for hydrolysis of energy values for the minimum energy pathway via 
 the phenolate mediated proton transfer ( solid line ) , and the reaction 
 pathway with direct protonation ( dashed line ) were obtained considering 
 solvent effects of water at the iefpcm - b3lyp/6 - 31+g(d , p ) level of 
 theory . to address the effects of further 
 explicit water molecules on the 
 barrier height with a different approach , the initial mc form and 
 the three high energy tss were also investigated in the oniom(6w ) 
 model . despite major differences in the qm(1w ) and oniom(6w ) models , 
 the main structural parameters of the optimized mc , tsi and tsii critical points are very similar 
 as seen in figure 7 . the largest difference can be observed for tsiii , where the distance between 
 ca and cb is 2.22  and 2.08  for 
 the qm(1w ) and oniom(6w ) models , respectively . using iefpcm solvent model for water . using the iefpcm - b3lyp/6 - 31+g(d , 
 p ) structure and iefpcm solvent model for water . tsiii structure was 
 obtained in the gas phase at the b3lyp/6 - 31+g(d , p ) level of theory . in terms of energetics , the 
 oniom(6w ) free energy barrier heights 
 are all lower than the values for the corresponding tss in qm(1w ) . 
 when the e values presented in table 4 are compared for tsi and tsii , it is seen that they are similar for the two models . thus , the 
 lower free energies arise from the more favorable relative entropy 
 terms and also from some smaller extra stabilization by the surrounding 
 water molecules . however , in the case of tsiii the final 
 energies are significantly lower for the oniom(6w ) than for the qm(1w ) 
 model . to understand the underlying reasons for this difference , we 
 have analyzed the components of the oniom energies , which is briefly 
 discussed here . the electronic relative energy of only the qm layer 
 is 31.3 kcal / mol for tsiii at the b3lyp/6 - 311++g(2d,2p ) 
 level , which is 18.6 kcal / mol from the total oniom e of 13.3 kcal / mol obtained with the b3lyp/6 - 311++g(2d,2p):amber 
 setup shown in table 4 . this clearly shows 
 that the different tsiii geometry with 2.08  cacb distance in the oniom(6w ) 
 compared to the 2.22  as obtained for the qm(1w ) has no substantial 
 effect on the barrier height . the excess stabilization of tsiii in the oniom(6w ) model is rather caused by the favorable contributions 
 of the water molecules in the mm layer : the coulomb and the van der 
 waals terms are , respectively , 9.8 and 8.7 kcal / mol more favorable 
 in tsiii compared to mc . the relative 
 energies were obtained 
 at the iefpcm - b3lyp/6 - 311++g(2d,2p)//iefpcm - b3lyp/6 - 31+g(d , p ) level 
 of theory . the relative 
 energies were obtained 
 with b3lyp/6 - 311++g(2d,2p):amber setup calculated on b3lyp/6 - 31g(d):amber 
 structures . the major difference arising from considering explicit 
 water molecules is that for the qm(1w ) model there are three high 
 energy tss , while for the oniom(6w ) model there is only one ts found 
 with higher energy : tsii . for both models this is the 
 highest ts with a 28.9 and 24.0 kcal / mol barrier height for the qm(1w ) 
 and oniom(6w ) models , respectively . although further refinement of 
 the energy values , e.g. , by investigating several qm / mm water configurations 
 or by obtaining conformational entropy contributions using md sampling 
 is beyond our scope , the obtained values can be used for a qualitative 
 comparison with the experimental rates . free energy values can be 
 derived back from the experimental rate constants kh displayed in table 2 using classical 
 transition state theory . these are 2324 kcal / mol , 
 which is in close agreement with the theoretical values . to consider further paths 
 for hydrolysis , we have also investigated the protonated form mch using the qm(1w ) model starting from both of its two lowest 
 energy conformers , ttc and ttt ( see 
 figure s8 , table s2 and text in the supporting 
 information ) . in the reactant form , referred to as mch , the oph h group is clearly less 
 prone to accept a proton from the nucleophilic water molecule . to 
 test this reaction path , we have obtained in principle the protonated 
 form of the first intermediate , hialt ( see 
 figure s8 in the supporting information ) . here h2 , and the remaining oh from the water 
 molecule forms a bond with ca . the relative energy of this 
 intermediate is very high , 58.4 kcal / mol for ttc , 
 and for ttt we could not even locate this critical 
 point as calculations converged back to the reactant state . in an 
 alternative pathway , the reaction could start with the addition of 
 water directly to the central ca cb double - bond , 
 with oh forming a bond with ca , and 
 h coupling to cb . however , this reaction path 
 is also much higher than any critical point along the reaction observed 
 for mc , as the corresponding ts has a relative energy of 49.9 and 
 48.5 kcal / mol for the ttc and ttt conformers , respectively . the very high energy critical points observed 
 for the hydrolysis paths of mch are clearly a consequence 
 of either the protonation per se , or the fact that 
 a direct addition of water to the central ca the similarity of the results 
 obtained for ttc and ttt demonstrates 
 that a change in the initial mch conformation for this 
 reaction would not alter the energetics significantly . furthermore , 
 considering the structure of the hydrolysis products hp , the initial 
 addition of water can not take place in any alternative way , which 
 is why we conclude that mch is not susceptible to hydrolysis . the nomenclature of the different conformers in 
 the reactant state mc is based on the cis or trans position of the central three bonds , here 
 shown for the lowest energy conformer , ttc . we have investigated 
 the behavior of six spiropyran derivatives 
 in aqueous solution between ph 0 and 10 . the following conclusions 
 can be drawn : ( i ) the substitution pattern influences 
 substantially the rates of the thermal isomerization processes as 
 well as the pka - values for the protonated 
 forms of sp and mc ( sph and mch ) . interestingly , 
 the pka of sph is decreased 
 by as much as 2 units by the attachment of positively charged 
 amino groups to the indoline nitrogen via alkyl linkers . this allows 
 for photoinduced isomerizations between the sp and the mc forms over 
 a wider ph range . ( ii ) the apparent rate of hydrolysis of the mc isomer varies significantly with the 
 substitution pattern . this , however , is a result of the differences 
 in the thermal equilibrium positions [ mc]/[sp ] , whereas the intrinsic 
 rate constant of hydrolysis is virtually the same for all derivatives . ( iii ) the rate constant of hydrolysis does not vary 
 significantly between ph 5 and 9 , clearly suggesting that water is 
 the nucleophile in this ph range . ( iv ) the nonprotonated 
 mc isomer is the only form that is susceptible to hydrolysis . this 
 is due to the key role of the phenolate oxygen , acting as a base by 
 accepting a proton from the nucleophilic water , and later transferring 
 it to the farther carbon , cb . as a consequence , the hydrolytic 
 degradation is halted at ph values where mch is the dominating 
 open form .