electronically excited states play a prominent 
 role in many different 
 areas of chemical and condensed matter physics and organic chemistry . while nonadiabatic processes , such as irradiation induced dna damage 
 and repair mechanisms , are the hallmark of photochemical 
 and photobiological reactions , the fluorescent properties of excited 
 state systems are increasingly being employed as biomolecular probes . despite their obvious importance ,
a detailed investigation of the 
 excited state remains a challenge to experimentalists and theoreticians 
 alike .
recent developments in laser chemistry have afforded significant 
 advances in the study of light - induced dynamic phenomena .
however , due to the short excited state lifetime , 
 the information obtained from such experiments is limited to a very 
 small region of the excited state energy landscape .
for those systems 
 exhibiting longer excited state lifetimes , the interpretation of emission 
 spectra is complicated by the fact that a detailed configurational 
 representation of the experimental data requires knowledge of both 
 the excited state and ground state energy surfaces . from a theoretical 
 perspective
, the accurate and proper computation of the excited state 
 polyelectronic wave function is a decisive step to obtaining an accurate 
 representation of the photophysical properties of the system at hand . 
 in light of this , a variety of post - hartree  fock methods including 
 coupled cluster , configuration interaction , and multiconfigurational self - consistent field theory have been developed . in comparison to the ground state 
 analogue ,
a single slater determinant is no longer appropriate to 
 describe the excited state wave function , and a multiconfigurational 
 description is required . due to the intensive cpu time and large memory 
 requirements ,
the above methods are often limited to  static  
 single point energy calculations for small molecular systems .
the 
 advent of approximate density - functional theory ( dft)-based methods 
 for the calculation of the excited state wave function , such as restricted 
 open - shell kohn  sham ( roks ) theory 
 and , more recently , time - dependent dft , has facilitated the development of efficient excited - state ab initio molecular dynamics ( aimd ) simulations .
such aimd 
 simulations are readily employed to study the detailed molecular motions 
 of small isolated molecules and complex systems in the excited state . 
 nevertheless , despite the substantial increase in available computational 
 resources and the development of more efficient simulation algorithms , 
 such as the 
 well - known car 
parrinello approach , aimd simulations are generally limited to time - scales of tens to 
 hundreds of picoseconds .
this is often too short to fully sample the 
 ground and excited state surfaces .
recently , we implemented 
 the accelerated molecular dynamics method ( amd ) in the framework of ab initio molecular dynamics . accelerated ab initio molecular dynamics , a - aimd , 
 represents a highly efficient and robust 
 configurational space sampling method that allows for the study of 
 slow molecular motions and rare events .
a - aimd has successfully been 
 applied to study both slow conformational transitions and chemical 
 reactions in the ground state occurring on time scales 
 many orders of magnitude longer than those accessible using standard 
 aimd methods . in the present work
, we extend the application of a - aimd 
 to the study of excited state systems and their photophysical properties . 

we first demonstrate that a - aimd can be readily implemented as an 
 efficient tool for studying the excited state energy surface , identifying 
 both stable and metastable local energy minima and quantifying the 
 magnitude of the associated energy barriers that separate these states . 

we then demonstrate how the excited state a - aimd method can be used 
 to efficiently map out the photophysical topology of the system of 
 interest ( i.e. , characterizing the variation in the vertical de - excitation 
 energy gap as a function of the relevant internal degrees of freedom 
 of the system ) .
this information provides a detailed insight into 
 the photophysical properties of the system , allowing the prediction 
 of both excited state reactions and relaxation phenomena .
the 
 work presented in this paper is divided into two sections : 
 in the first section , we focus on systems exhibiting fast radiationless 
 decay processes , focusing on the identification of conical intersections 
 ( cis ) and extended crossing seams . in the second section ,
we demonstrate 
 how a - aimd can be used to describe the thermally averaged solvent 
 effect on the fluorescence spectra of molecular systems , most notably 
 making use of the enhanced configurational space sampling obtained 
 by a - aimd to accurately describe both the prominent features and line - shapes 
 of absorption and emission spectra .
a comprehensive account of the accelerated ab initio molecular dynamics ( a - aimd ) approach is available 
 in the literature , and we only provide a brief outline 
 of the essential details here . in the standard amd formalism , a continuous non - negative bias potential , v(r ) ,
is defined such that when the true 
 ( underlying ) potential of the system , v(r ) , lies below a certain , predefined threshold  boost  
 energy , eb , the simulation is performed 
 on a modified potential , v*(r ) = v(r ) + v(r ) , but when v(r )  eb , the simulation is performed on the true potential 
 [ v*(r ) = v(r ) ] .
the modified potential , v*(r ) , is related to the true potential , v(r ) , bias potential , v(r ) , and boost energy , eb , by1and the bias potential , v(r ) , is defined as:2 in the framework of aimd , the true potential , v(r ) , is defined as the density functional 
 energy .
the application of the bias potential results in a raising 
 and flattening of the pes , thus enhancing the exchange rate between 
 low energy states .
the extent of acceleration ( i.e. , how aggressively 
 we enhance the configurational space sampling ) is determined by the 
 choice of the boost energy , eb , and the 
 acceleration parameter , . configurational space sampling can 
 be enhanced by either increasing the boost energy or decreasing . 
 the reader is referred to ref ( 13 ) for more details . as the bias potential destabilizes low energy regions 
 of conformational space on the potential energy landscape , the population 
 statistics on the modified potential are inherently incorrect .
however , 
 as it is known at each step in the simulation exactly how much the 
 system is destabilized , one can readily retrieve the correct population 
 statistics by reweighting each point in the configuration space on 
 the modified potential by the strength of the boltzmann factor of 
 the bias energy , exp[v(r ) ] , at that particular point . as a result , a - aimd yields a canonical 
 average of an observable such that thermodynamic and other equilibrium 
 properties can be accurately determined . using the canonical 
 boltzmann reweighting formulism described above , representative free 
 energy surfaces for the system of interest
can be obtained as follows : 
 having defined an appropriate set of internal degrees of freedom ( see 
 the results and discussions section for specific 
 details ) , the configurational subspace is divided into bins , and the 
 structures collected across the a - aimd trajectories are allocated 
 to their respective bin ( j ) .
the effective population 
 statistic for each structure , i , is given by exp[v(i ) ] .
for each bin , the population statistics 
 are summed across all a - aimd trajectories to give an effective total 
 population in that bin , pop(j ) , and the free energy 
 surface , g(j ) , is obtained 
 as3where pop(j)max is the effective total population of the most populated bin . in the case of fd , we show that the ground and excited state free 
 energy surfaces obtained from the a - aimd simulations are directly 
 compared to a metadynamics reference 
 ( see the computational details section ) . having efficiently and exhaustively sampled the configurational space 
 of the molecular system of interest in the excited state , the photophysical 
 topology of the system was mapped out by identifying the appropriate 
 internal degrees of freedom and dividing this configurational subspace 
 into bins . each structure in the a - aimd simulations was then allocated 
 to a given bin . given the large number of structures obtained from 
 the a - aimd trajectories , 10 structures in each bin were randomly chosen , 
 and a ground state energy calculation was performed .
the vertical 
 de - excitation energy gap associated with each bin was then averaged 
 over the 10 representative structures .
the specific internal degrees 
 of freedom used for each system are defined explicitly in the results and discussions section .
all molecular 
 dynamics simulations were performed using an in - house modified version 
 of the aimd 3.13 package . in the case 
 of formaldimine ( fd ) ,
the system was placed at the center of an orthorhombic 
 box with side lengths ( 17.6  18.3  14.0 au ) .
similarly , for salicylidenaniline ( sa ) , the system was placed 
 at the center of a box with side lengths ( 22.9  35.6  
 14.0 au ) . in all ground state ( s0 )
simulations , 
 the electronic structure problem was solved with density functional 
 theory ( dft ) , and the restricted open - shell kohn  sham ( roks ) 
 method was implemented for simulations in the singlet ( s1 ) excited state . for all systems , the becke ( b ) exchange and lee , yang , parr correlation functional were employed .
core electrons were treated using 
 the norm - conserving pseudopotentials of troullier and martins , and 
 the valence orbitals were expanded in a plane - wave basis up to an 
 energy cutoff of 70 ry . in all ground and excited state ( accelerated 
 and nonaccelerated )
simulations , a fictitious mass of 400 au was ascribed 
 to the electronic degrees of freedom , and the coupled equations of 
 motion were solved using the velocity verlet algorithm with a time 
 step of 4 au .
all aimd simulations ( accelerated and nonaccelerated ) 
 were carried out at t = 300 k. standard aimd simulations 
 were performed using a nos  hoover chain thermostat on the ions , while in the case of the accelerated 
 aimd simulations , a nos  hoover thermostat was applied 
 to both the electronic and nuclear degrees of freedom . the ground 
 and
excited state metadynamics simulations 
 used for comparative analysis in the fd study ( see results and discussions ) were performed under exactly the 
 same physical conditions as the standard aimd simulations described 
 above .
the angular and torsional coordinates ( , ) were 
 employed as the collective variables .
metadynamics trajectories were 
 run for 1  000  000 md steps ( 100 ps ) and gaussian 
 hills with a half - width of 2.5 and a depth of 0.2 kcal / mol were 
 added every 200 md steps . before proceeding to the results and discussions section , it should be noted that there 
 are several limitations to 
 the method presented in this work : first , it is clear that the accuracy 
 of the relevant excited state free energy surfaces and photophysical 
 topologies , including the identified cis and extended conical intersection 
 seams , is strongly dependent on the integrity of the employed polyelectronic 
 wave function representation . in the present examples ,
we have used 
 the restricted open - shell kohn  sham ( roks ) method to describe 
 the excited state . the enhanced configurational space sampling afforded 
 by a - aimd
obviously does not have any effect on the accuracy of the 
 polyelectronic wave function representation , and , as in all cases 
 when using dft - based methods , it is important to validate the results 
 using more sophisticated post - hartree  fock methods ( see introduction ) .
indeed , we would like to point out 
 that for the two systems investigated here , fd and sa , the accuracy 
 of the roks approach has already been validated by comparison to more 
 sophisticated multireference configuration interaction methods .
second , the excited state a - aimd 
 trajectories presented here are strictly performed under adiabatic 
 conditions , and therefore explore the adiabatic excited 
 state energy surface . as a result , the excited state populations and 
 the corresponding free energies in the absence of relaxation are only 
 approximations that do not have a direct physical meaning .
in addition , 
 no direct information is obtained concerning the specific dynamic 
 processes that occur after vertical excitation that drive the system 
 toward the conical intersection .
nevertheless , a - aimd simulations 
 provide important information about the topology of the excited and 
 ground state surfaces and allow converged sampling of both surfaces . 

finally , it is also well - known that radiationless decay processes 
 occur not only close to the crossing seam , where the energy gap between 
 the intersecting states is small , but also in regions of configurational 
 space away from it . for these cases , a variety of theoretical approaches , such as the 
 method of fewest switches ( mfs ) , which 
 involve the calculation of a transition probability between the relevant 
 electronic states have been developed to address such relaxation mechanisms . 
 with specific regard to the msf approach ,
the transition probability 
 is strongly dependent on the temporal velocity of the wave function , 
 and as the evolution of the system in a - aimd occurs on a nonlinear 
 time scale , the application of such methods is beyond the scope of 
 the present study .
formaldimine ( fd ) , the smallest unprotonated 
 schiff base , is the prototypical system for studying cis  trans photoisomerization around a double 
 bond . the photophysical properties and
associated nonadiabatic photoisomerization 
 mechanism for this system have been rigorously studied using both 
 nonadiabatic ab initio md and high - level 
  static  multireference configuration interaction ( mrci ) 
 calculations . in the ground state ,
after vertical excitation to the lowest excited singlet 
 state , s1 , the system rapidly relaxes toward the local 
 energy minimum on the excited state pes and the n  h bond vector 
 twists out of the molecular plane .
on approaching the orthogonal twist 
 geometry , the system enters the ci region resulting in strong nonadiabatic 
 coupling between the s1 and s0 states .
after 
 a surface hop from the s1 to the s0 state , fd 
 returns to a planar geometry , leading either to the photoisomerized 
 product or to the regeneration of the reactant state ( see figure 1b ) .
the degrees of freedom ( 1,r1 ) and ( 2,r2 ) discussed in this work are indicated ( dihedral 
 angles highlighted in red ) .
( d ) scheme representing the photochemical 
 landscape of salicylideneaniline , including the esipt and the nonadiabatic 
 pathways . in order to study the configurational space sampling 
 properties 
 of fd ,
a multiple - copy ab initio md simulation strategy 
 was employed : after performing a standard geometry optimization and 
 equilibration procedure , five independent aimd simulations were performed 
 for 500  000 md steps ( the equivalent of 50 ps ) at 300 
 k in both the ground and excited state .
analysis of the resulting 
 trajectories revealed that the most significant variations in the 
 configurational geometry involved the h 
c = n  h 
 dihedral angle ,  , and the c = n  h angle , . 
 using these two internal degrees of freedom , the configurational space 
 sampling obtained from all five independent aimd simulations in the 
 ground and excited state are depicted in green in figure 2a and b , respectively .
notably , in both electronic states , 
 the configurational space sampling afforded by the standard aimd simulations 
 is rather limited : in the ground state , the h 
c = n  h 
 dihedral angle varies between 25 and + 25 and the c = n  h 
 angle varies between 100 and 125. these variations are the product 
 of local thermal fluctuations at 300 k about the geometry - optimized 
 structure with coordinates [ , ] = [ 0.0,111.36 ] .
the observed 
 thermal fluctuations in the excited state are slightly more pronounced 
 with the  angle varying by 40 and the  angle 
 varying by 20 about the geometry - optimized structure located 
 at [ , ] = [ 124.69,101.71 ] .
( a , b ) conformational 
 space sampled in formaldimine by standard 
 aimd ( green ) and a - aimd ( red ) simulations , on the ground ( left ) and 
 first singlet excited ( right ) electronic states .
( c , d ) free energy 
 surfaces derived from the conformational space sampled by a - aimd simulations 
 in a and b , respectively .
the standard aimd trajectories described above 
 served as the initiation 
 point for the accelerated ab initio md simulations . 
 using a fixed value for the acceleration parameter ,  = 0.01 
 au ,
a series of short [ 100  000 md step ] a - aimd simulations 
 were performed across a broad range of acceleration levels in both 
 the ground and excited state .
the acceleration level was controlled 
 by varying the boost energy , [ eb  v0 ] , where v0 is 
 the average density functional energy obtained from the standard aimd 
 simulations .
the choice of the acceleration level is exceedingly important : 
 if the acceleration level is too low , ostensibly no enhanced configurational 
 space sampling is observed .
in contrast , applying too high an acceleration 
 level results in a molecular explosion or dissociation of the system . 
 in the present case of fd , [ eb  v0 ]
the optimal acceleration levels for enhanced 
 configurational space sampling were found to be [ eb  v0 ] = 0.085 au 
 and [ eb  v0 ] = 0.060 au for the ground and excited state , respectively . 

these  optimal  acceleration levels afforded the most 
 efficient configurational space sampling , while not rendering dissociation 
 of the system .
once the optimal acceleration levels in the ground 
 and excited state had been determined , five independent a - aimd simulations 
 were performed for 500  000 md steps . the configurational 
 space sampling obtained from the five independent 
 a - aimd simulations in the ground and excited state
clearly , 
 the accelerated md simulations provide a much more complete and robust 
 description of the conformational space sampling properties of fd 
 compared to the standard aimd trajectories .
most importantly , in the 
 a - aimd simulations , we observe multiple   isomerization 
 events in both the ground and excited state .
interestingly , the a - aimd 
 simulations reveal significant differences in the specific adiabatic 
 isomerization pathways in the two electronic states : in the ground 
 state , as the  angle flips from 0 to 180 , 
 the c = n  h angle ,  , is seen to significantly increase . 
 at the orthogonal twist geometry (  = 90 )
, the c = n  h 
 angle adopts values between + 140 and + 170. by contrast , 
 in the excited state adiabatic isomerization process , the  
 angle adopts values between 90 and 140 at  = 0 .
the associated free energy surfaces in the ( , ) configurational 
 subspace ( see theory and computational details ) for the ground and excited state of fd are depicted in figure 2c and d , respectively .
the lowest free energy barrier 
 for adiabatic isomerization on the ground state surface was found 
 to be 0.052 au , and the associated transition state is located at 
 [ , ] = [ 100,150 ] .
similarly , in the s1 excited state , the lowest free energy barrier for isomerization 
 is 0.037 au , and the associated transition state is located at [ , ] 
 = .
the free energy barriers obtained from the a - aimd simulations 
 presented here are in excellent agreement with previous theoretical 
 and experimental studies , where the free energy of isomerization in 
 the s0 and s1 states was found to be 0.048 au 
 and 0.040 au , respectively . in order to provide 
 a reference to validate the a - aimd free energy 
 surfaces shown in figures 2c and d
, we performed 
 two metadynamics simulations using the 
  and  internal degrees of freedom as the collective 
 variables ( see theory and computational details ) .
the free energy surfaces for the ground and excited state obtained 
 from the metadynamics simulations are depicted in figure 2e and f , respectively .
clearly , the adiabatic free energy 
 surfaces provided by both methods are very similar , and the extent 
 of configurational space sampling obtained from the a - aimd and metadynamics 
 simulations is also similar .
this is an encouraging result when one 
 considers that in the accelerated molecular dynamics approach there 
 is no a priori definition of a reaction coordinate 
 or a set of collective variables .
the comparative analysis of 
 the present a - amd approach and the 
 more well - known metadynamics method clearly demonstrates that one 
 can obtain an accurate energetic description of the excited state 
 energy surface , which is both an important and necessary prerequisite 
 to acquiring a detailed picture of the photophysical topology of the 
 system .
the excited state free energy surface and associated population 
 statistics acquire much more significance when studying a system with 
 considerably longer excited state lifetimes , such as in the case of 
 the acetone - in - water system presented later in this paper .
the 
 efficiency of the configurational space sampling obtained from 
 the a - aimd simulations can be readily inferred from the magnitude 
 of the free energy barriers that are traversed during the simulations 
 of fd in the ground and excited state . according to transition state 
 theory ( tst ) ,
the predicted rate constant , k , for 
 a transition between two states separated by a free energy barrier , 
 g , is given by4where  is the transmission coefficient 
 and kb is the boltzmann constant .
as discussed 
 above , the free energy barrier for adiabatic isomerization of fd in 
 the ground state is 0.052 au . in the fast limit (  = 1 ) , the 
 tst predicted
rate constant for this process is therefore 1.62  
 10 s. given that a 50-ps 
 ground state a - aimd trajectory produces 45 isomerization 
 events , on average , in the a - aimd simulations , an isomerization event 
 is observed every 100  000 md steps ( 10 ps ) . in light 
 of this observation , the application of the bias potential enhances 
 the configurational space sampling rate by a factor of 10 . in order to map out the photophysical topology of fd ,
the 
 configurational 
 subspace ( , ) shown in figure 1b was divided into bins ; the vertical de - excitation energy gap across 
 the entire excited state configurational space was calculated ( see theory and computational details ) .
two large crossing 
 seam regions are clearly visible , located at [ 50 <  
 < 150 , 70 <  < 120 ] .
notably , outside of these 
 two regions , the vertical de - excitation energy gap significantly increases 
 to values on the order of 2030 kcal / mol .
closer inspection 
 of figure 3a reveals that there exists a considerable 
 amount of fine - structure on the vertical deactivation energy surface . 

this observation raises the important question as to whether this 
 fine structure is really a physical phenomenon of the system or whether 
 it is merely statistical noise invoked by the application of the bias 
 potential in the a - aimd simulations . in order to address this issue , 
 200 excited state structures along
the  coordinate were selected 
 from the a - aimd simulations with a fixed c = n  h angle ,  
 = 90 .
a partial geometry optimization procedure was performed for 
 each structure , in which the internal ( , ) coordinates 
 were constrained and the vertical de - excitation gap was then recalculated . 

figure 3b depicts the s1s0 energy profile along the  coordinate obtained from 
 the a - aimd structures collected  on - the - fly  and their 
 geometry - optimized counterparts .
the two resulting energy profiles 
 are remarkably similar , confirming the fact that small local molecular 
 distortions arising from the application of the bias potential in 
 the a - aimd simulations do not compromise the accuracy of the vertical 
 deactivation energy statistics . a very interesting feature in the 
 energy  gap profile depicted in figure 3b
is observed deep in the crossing seam region : between coordinates 
 [ 110 <  < 75 ] and again at [ 75 <
 
 < 110 ] , the vertical deactivation energy gap is seen to increase 
 by 2 kcal / mol .
this small variation in the energy gap is due 
 to a change in the pyramidalization angle about the c atom , which 
 reaches its maximum at a pyramidalization angle of 27. 
 this result is in agreement with a previous study by doltsinis et 
 al . , who observed a loss of degeneracy of the crossing seam at a pyramidalization 
 angle of 30. this result 
 provides additional validation to the degree of detail that can be 
 achieved in both the conformational space and free energy sampling , 
 otherwise not possible using standard md or single point electronic 
 calculations .
a second interesting feature shown in figure 3a and b is the observation of negative [ s1s0 ] energy gaps for a limited region of the a - amd - sampled 
 configurational space for fd .
such small negative energy gaps have 
 been observed previously and are invariably 
 the result of an error arising from the fact that the ground and excited 
 electronic state calculations are performed independently . as such
, 
 we would like to point out that these small artifacts are not a result 
 of the application of the a - amd biasing potential but rather a product 
 of the polyelectronic wave function representation employed in this 
 work .
( a ) variation in the energy gap [ s1s0 ] for formaldimine as a function of the internal coordinates  
 and  , obtained from single point calculations in randomly chosen 
 structures sampled across the a - aimd trajectory ( see theory and computational details ) .
the solid line indicates 
 the cut of the surface for which the direct relaxed difference has 
 been computed .
( b ) direct ( dashed line ) and relaxed 
 ( solid line ) s1s0 energy gap profiles 
 along the surface cut at  = 90. energies are expressed 
 in kcal / mol .
using our a - aimd approach on the fd system , 
 we were able to exhaustively investigate the photophysical properties 
 of the system and identify crossing seams from the data collected 
 in s1 at a higher sampling rate compared to standard aimd 
 approaches . in light of this successful initial study
the aromatic schiff base salicylideneaniline 
 ( sa ) represents a classic example of an excited state intramolecular 
 proton transfer ( esipt ) reaction .
the reactant and product forms of 
 sa , corresponding to the enol and cis - keto isomeric 
 forms , respectively , are connected by an esipt event after photoexcitation 
 to s1 , as shown in figure 1c . at 
 this point ,
the electronically excited cis - keto tautomer 
 can either undergo a cis  trans isomerization to form a trans - keto tautomer or 
 directly deactivate to s0 . despite this simple chemical 
 scheme ,
much controversy has arisen in the past 40 years concerning 
 the experimental determination of the time scale for the esipt process 
 in sa , with measurements ranging from 750 fs to less than 50 fs . the 
 reader is referred to ref ( 36 ) for an updated list of references on the sa studies .
sekiya 
 and collaborators proposed the presence of two nonadiabatic processes 
 competing with the proton transfer event : the first process involves a highly deformed enol conformation , 
 while the second relaxation mechanism is associated with the cis 
trans isomerization path of 
 the cis - keto tautomer , as depicted in figure 1d .
very recently ,  static  
 tddft calculations ( validated with high - level multiconfigurational ab initio calculations ) and quantum dynamical simulations 
 confirmed the presence of two ci regions associated with both the 
 enol and cis - keto states . in order to study the competition between the two relaxation 
 pathways on the excited state surface
, we performed a series of aimd 
 and a - aimd simulations similar to those described previously for fd . 

a standard geometry optimization and equilibration procedure was performed 
 on the enol tautomer in the excited state . the geometry optimization 
 led directly to the cis - keto tautomer of sa , indicating 
 that the enol state is not a stable species in s1 .
five 
 independent aimd simulations were performed for a total of 1  500  000 
 md steps ( 150 ps ) at 300 k on the cis - keto 
 tautomer in s1 .
the system remained in the cis - keto state during the simulations , and we were not able to observe 
 a reverse esipt event .
h atomic distance was seen to 
 fluctuate around the cis - keto geometry - optimized 
 value ( 2  ) in all the 150 ps trajectories , as 
 depicted in green in figure 4a .
the principal 
 geometrical fluctuations observed in the simulations can be described 
 by two independent variables : the c 
c = c  n dihedral 
 angle ( highlighted in red in figure 1c ) , 2 , which varies between 50 and + 50 degrees , and the 
 c = c bond distance , r2 , which varies 
 between 1.32 and 1.53  .
notably , although large amplitude vibrations 
 were seen along the 2 coordinate ( figure 4c ) , cis 
h distance of salicylideneaniline 
 during 150 ps of standard aimd ( green ) and a - aimd ( red ) simulations 
 in the s1 state .
( b , c ) conformational 
 space sampled in salicylideneaniline using standard aimd ( green ) and 
 a - aimd ( red ) simulations in the s1 state in the enol and cis - keto regions , respectively .
the intersection of the 
 solid lines indicates the location of the two mecps described in ref ( 36 ) . in order to improve the conformational space sampling , 
 a set of 
 short a - aimd simulations
were initiated . using a fixed value of  
 = 0.01 au for the acceleration parameter
, a series of 500  000 
 md - step a - aimd simulations were performed across a broad range of 
 acceleration levels for the cis - keto state in s1 , whereby [ eb  v0 ] was varied between 0.050 au and 0.200 au 
 in steps of 0.05 au .
the optimal acceleration level for enhanced configurational 
 space sampling was found to be [ eb  v0 ] = 0.150 au for the excited state .
this optimal 
 acceleration level was employed for five independent accelerated ab initio md simulations , each performed for a total of 
 1  500  000 md steps ( 150 ps ) .
the analysis 
 of our a - aimd simulations indicated that the configurational 
 space sampled within 150 ps covered both the cis - keto and the enol states .
h bond distance presented 
 large fluctuations during the first 100 ps , ranging between 1.2 and 
 5.5  .
after 110 ps , a reverse esipt event was observed , 
 which led to a decrease of the o 
a 
 difference of 10 kcal / mol between the enol and cis - keto regions in the excited state was estimated , which explains 
 why we did not observe a reverse esipt event during the standard aimd 
 simulations .
by contrast , however , the application of the bias potential 
 in the a - aimd simulations facilitated the observation of a reverse 
 esipt event after only 110 ps ( see figure 4a ) .
the newly formed enol tautomer remained stable for the last 40 
 ps of the simulation , affording both ample conformational and energy 
 statistics for the enol state .
as such , two chemically different but 
 relevant sections of the pes were successfully sampled from a single 
 molecular geometry . the configurational space sampled in the 
 enol region revealed significant 
 variations in both the c 
c = n  c dihedral angle 
 ( highlighted in red in figure 1c ) , 1 , and the c = n bond distance , r1 , which may be compared directly to the prominent 
 internal degrees of freedom identified for the cis - keto state [ 2 , r2 ] . 

interestingly , the rotation and stretching along double bonds in excited 
 electronic states has been previously proposed as a common feature 
 in nonadiabatic deactivation pathways for complex organic compounds .
the variation of these degrees of freedom sampled 
 in the five independent a - aimd simulations in the excited state are 
 depicted in red in figure 4b and c. as expected , 
 the accelerated md simulations provide considerably more exhaustive 
 configurational space sampling compared to their aimd counterparts . 
 in the a - aimd simulations ,
we observed multiple rotation events around 
 the dihedral angles 1 and 2 in 
 the enol and cis - keto regions , respectively , and 
 complete rotation events through 360 were observed in both cases . 

simultaneously , rather large fluctuations in the bond distances ( 1.221.67 
  for r1 and 1.231.75  
 for r2 ) were also observed .
the intersection 
 of the two straight lines depicted in figure 4b and c defines the coordinates for the two mecps described in a 
 previous study of sa .
these two mecps 
 are located at the coordinates ( 92 , 1.37 ) and ( 89 , 1.47 ) for the enol 
 and cis - keto regions , respectively .
notably , the 
 conformational space sampled in the standard aimd simulations for 
 the cis - keto state ( figure 4c ) does not include these coordinates , while the a - aimd simulations 
 readily encompass a considerably larger region of the configurational 
 subspace including the associated mecp coordinates .
the variation 
 in the underlying pes explored in our a - aimd simulations indicates 
 that the rotational barriers associated with the dihedral angles 1 and 2 are 16.75 and 18.03 kcal / mol , respectively . 
 as such
, the twisted conformations for both the enol and cis - keto tautomers are clearly inaccessible in the standard aimd simulations 
 but can be readily observed in the a - aimd trajectories .
the 
 vertical de - excitation energy gaps mapped across the entire 
 excited state configurational subspaces ( 1 , r1 ) and ( 2 , r2 ) for the enol and cis - keto tautomeric 
 states are depicted in figures 5a and b. two 
 large conical intersection regions are clearly visible on each plot , 
 located at [ 75 < 1 < 110 , 1.40 
 < r1 < 1.55 ] and [ 60 < 
 2 < 120 , 1.40 < r2 < 1.65 ] for the enol and cis - keto states , 
 respectively .
these results show that a complete characterization 
 of both crossing seams can be obtained from the a - aimd simulations , 
 even though they belong to very different regions of the pes .
( a , b ) variation 
 in the energy gap [ s1  s0 ] of salicylideneaniline , 
 in the enol and cis - keto regions , respectively .
the 
 surfaces are projected on the ( 1,r1 ) and ( 2,r2 ) subspaces and have been obtained from single 
 point calculations in randomly chosen structures sampled in the a - aimd 
 trajectories ( see theory and computational details ) .
the extended crossing seams present in the de - excitation 
 energy 
 maps ( figures 4 and 5 ) obtained from the a - aimd simulations clearly suggest that there 
 exist two competing radiationless relaxation decay processes which 
 completely describe the photophysical properties of sa after vertical 
 excitation : in the first of these relaxation decay mechanisms , the 
 vertical excitation energy initiates a spontaneous proton transfer 
 event which leads directly to the formation of the ( excited ) cis - keto state ( figure 1d ) , and a 
 subsequent rotation in 2 brings the system to the 
 extended conical intersection seam ( ci2 ) depicted in figure 5b , resulting in either a cis - keto 
 or trans - keto ground state photoisomerized product . 
 in a second competing relaxation mechanism , the vertical excitation 
 energy induces a rotation about the 1 dihedral angle 
 which breaks the hydrogen bond and results in the formation of a highly 
 twisted enol conformation . in the twisted enol state ,
the c = n 
 bond is weakened , and the r1 bond length 
 increases up to 1.67 ( see figure 4b ) , bringing 
 the system into the conical intersection region ( ci1 ) .
notably , the 
 correlation between the 1 and r1 coordinates assists the evolution of the enol tautomer 
 toward the extended ci seam , an observation that can not be ascertained 
 from the mecp result but is readily confirmed by the exhaustive configurational 
 space sampling provided by the a - aimd simulations .
the existence of 
 two competing radiationaless relaxation decay processes predicted 
 from this study readily explains the experimental observation that 
 the quantum yield of the cis / trans - keto products is lower than one would expect when only considering 
 a single nonadiabatic relaxation mechanism associated with the enol - to - cis - keto proton transfer event .
in this paper , we have performed excited 
 state accelerated ab initio molecular dynamics ( a - aimd ) 
 to explore the excited 
 state energy landscape and photophysical properties of a variety of 
 systems . in an initial case study on formaldamine , we have found that 
 a - aimd can be readily employed to enhance configurational space sampling 
 for the study of molecular systems in the excited state , crossing 
 energy barriers on the excited state energy landscape of up to 30 
 kcal / mol and affording a quantitative description of the excited state 
 free energy surface .
notably , in comparison to other popular enhanced 
 sampling methods that involve the specific definition of a reaction 
 coordinate , a - aimd does not require any a priori understanding 
 of the underlying free energy surface .
the method was subsequently 
 used to study the photophysical topologies of salicylideneaniline 
 ( sa ) .
it allowed the identification and characterization of conical 
 intersections ( cis ) and extended conical intersection seams and the 
 prediction of two different , competing radiationless decay processes . 
 for acetone in water
, we demonstrated that the enhanced configurational 
 space sampling obtained by a - aimd may be used to compute converged 
 absorption and emission spectra .
the a - aimd method is general and 
 may be implemented in combination with any methodological representation 
 of the polyelectronic wave function . given the rapid and sustained 
 increase in available computational resources , it may soon be possible 
 to combine a - aimd with more sophisticated post - hartree 
fock 
 representations of the polyelectronic wave function in order to efficiently 
 obtain an accurate and complete description of both ground and excited 
 state energy surfaces .
 in the present work , we employ excited state accelerated ab initio molecular dynamics ( a - aimd ) to efficiently study 
 the excited state energy landscape and photophysical topology of a 
 variety of molecular systems . in particular , 
 we focus on two important 
 challenges for the modeling of excited electronic states : ( i ) the 
 identification and characterization of conical intersections and crossing 
 seams , in order to predict different and often competing radiationless 
 decay mechanisms , and ( ii ) the description of the solvent effect on 
 the absorption and emission spectra of chemical species in solution . 
 in particular , using as examples the schiff bases formaldimine and 
 salicylidenaniline , we show that a - aimd can be readily employed to 
 explore the conformational space around crossing seams in molecular 
 systems with very different photochemistry . using acetone in water 
 as an example 
 , we demonstrate that the enhanced configurational space 
 sampling may be used to accurately and efficiently describe both the 
 prominent features and line - shapes of absorption and emission spectra . 