acceptor 
 systems such as substituted benzenes reveals many interesting processes 
 occurring in electronically excited states .
particularly , dual fluorescence 
 of 4-(n , n - dimethylamino)benzonitrile 
 ( dmabn ) in polar solution , consisting of an emission from the lb state and an  anomalous  red - shifted 
 emission from the la state has attracted considerable attention .
the lb state is usually characterized to be local excitation ( le ) 
 and the la state as charge - transfer ( ct ) state . 

the position and intensity of the red - shifted band show a marked dependence 
 on solvent polarity .
this property was interpreted as an indication 
 for a large dipole moment of the emitting state and hence for its 
 charge - transfer character .
in contrast to solution , in the gas phase , 
 the emission spectrum of dmabn consists of a single local excitation 
 ( le ) fluorescence band s1(lb ) , and 
 evidence for a le  ict process in dmabn was not found . the structural and electronic nature of the red - shifted emission 
 band of dmabn
the most widely accepted concept is based on the twisted 
 intramolecular charge - transfer ( tict ) model in which the torsion 
 of the dimethylamino group around the cn bond to the phenyl ring induces 
 a charge transfer in which the former group acts as electron donor 
 and the benzonitrile moiety as the electron acceptor .
alternatively , 
 a ct process has been suggested to occur at planar dmabn structures 
 ( pict model ) where the vibronic interaction in the franck  condon 
 region is the important factor for the formation of the ct state .
the third model to be mentioned here is the rehybridized ict ( rict ) 
 model representing a bent *cn state . even though it was not considered a viable alternative 
 to the tict model for dmabn originally , in later work the main features
have been taken up as the origin of a 
 new state involved in the electron - transfer dynamics .
based on the models listed above , the structural 
 and dynamical 
 aspects of the ict in dmabn have been widely investigated from an 
 experimental as well as from a computational point of view .
the absorption spectrum of dmabn in the gas phase consists of a 
 main band with a maximum at 4.57 ev attributed to s2(la , ct ) and a weak absorption with a lower - energy shoulder with 
 a band maximum given at 4.13 ev attributed to the s1(lb , le ) state .
the 
 ultrafast photodynamics of dmabn starting in the bright s2(la ) state has been investigated by fuss et 
 al . by means of femtosecond pump 
probe 
 experiments in the gas phase using nonresonant multiphoton ionization 
 as a probe process .
the main mechanistic result deduced from this 
 investigation is the ultrafast relaxation ( 68 fs ) to the ct and lb - type s1 states .
after equilibration within 1 ps , 
 the molecule relaxes further within 90 ps to a lower excited triplet 
 state and then decomposes within 300 ps .
it was also shown that the 
 passage through the conical intersection involves strong geometrical 
 distortions which were related to a twist coordinate .
. led to a similar analysis of the photodynamics 
 indicating also a broadening of the rotational contour above an excess 
 energy of 600 cm .
this fact was ascribed in ref ( 18 ) to the conversion of the 
 initially excited lb state to the higher - lying ct state 
 with an activation barrier of 600 cm .
quantum 
 chemical calculations exploring the torsional potential 
 within the tict model performed at configuration interaction with 
 singles ( cis ) , complete active space self - consistent field ( casscf ) , 
 and cas perturbation theory to second order ( caspt2 ) by sobolewski 
 et al .
show that the former two methods 
 do not provide a correct description of the torsional behavior of 
 the le and ct states , e.g. , the casscf approach does not lead to a 
 crossing between the two states at 45. caspt2 calculations 
 have been also performed by serrano - andres et al . in this work , the effect of the torsional mode in the tict 
 model and the wagging mode of the dimethylamino group have been compared 
 with respect to the charge transfer required by the dependence of 
 the second fluorescence band on polar solvents .
it was shown that 
 in contrast to the torsional mode , the wagging mode was unable to 
 lead to the required significant charge separation , thus favoring 
 the tict model for the explanation of the experimental findings .
a 
 similar conclusion has been reached by mennucci et al . based on multireference perturbation configuration 
 interaction ( cipsi ) .
full geometry optimizations of the le and ct 
 states have been reported by rappoport and furche based on time - dependent density functional theory ( td - dft ) 
 and by khn and httig using 
 the approximate coupled - cluster singles - and - doubles method cc2 .
both 
 studies also investigate the change in force constants and vibrational 
 frequencies of the le and ct states as compared to the ground state 
 and find good agreement with picosecond time - resolved infrared ( ir ) 
 and resonance raman spectra . according to these studies , the le state has a c2 symmetric minimum . in the cc2 calculations , three coordinates 

contribute to the reaction path from le to ict : the twisting motion 
 of the dimethylamino group , the just - mentioned pyramidalization of 
 the ring carbon atom , and quinoidalization modes of the ring .
both 
 td - dft and cc2 support the assumption that the torsional mode stabilizes 
 the ct state and is a major driving force of the photodynamics .
the investigation by gmez et al . was dedicated to the description of the s2/s1 intersection seam and its connection to the internal conversion 
 process .
it was found that the torsion of the n(ch3)2 group is not included in the two coordinates describing the 
 intersection seam .
the first consists of a nonadiabatic reaction path , 
 evolving after vertical excitation to s2 via the transient 
 s2-pict structure toward the crossing seam . depending on 
 the actual torsional angle
, a wide range of the seam can be accessed 
 where internal conversion to s1 can occur . on the basis 
 of the fact that the minimum of the intersection seam has a planar 
 structure ,
the other pathway possesses adiabatic character and 
 connects the le and tict structures on the s1 state with 
 an energy barrier of 18 kcal / mol from the side of the le structure . 

recent nonadiabatic photodynamics simulations based on the algebraic diagrammatic construction method to second 
 order ( adc(2 ) ) show a picture which is in good 
 agreement with the findings of gmez et al .
the transition from the s2 to the s1 state is extremely fast ( 8.5 fs ) and does not include the n(ch3)2 twisting motion .
population of the tict state 
 occurs primarily via equilibration from the le state as already suggested 
 in ref ( 22 ) based on 
 time - correlated single - photon counting experiments .
the idea 
 of the rict structure has been taken up in tddft / bp86 
 calculation by zgierski and lim . by variation 
 of the c(ph)cn angle in dmabn , a 1a( * ) 
 state is found , located at 120 and 3.28 ev above the 
 ground state .
this state is characterized by the charge transfer from 
 an aromatic  orbital to a  * orbital of the cyano group . 

subsequent tddft / b3lyp calculations resulted 
 in an energy of 4.20 ev for that state , a value which compares somewhat 
 better with caspt2 results of 4.50 ev and 4.92 ev .
transient excited - state absorption ( esa ) 
 of dmabn measured in n - hexane and in acetonitrile ( an ) plays an important part in analyzing the 
 role of the ict for 
 the dual fluorescence mechanism .
in hexane , a uniform decrease of 
 all absorption bands is observed and no indication for an ict state 
 is found . in acetonitrile , the situation is different
. a decrease 
 of the bands at 360 and 680 nm assigned to le absorption combined 
 with an increase of the ict band at 320 nm is found .
both the appearance 
 of the ict band and the decrease of the bands assigned to the le state 
 occur with the same lifetime of 4 ps .
the character of the 680 nm 
 band has been reassigned to a * * 
 transition based on the absence of  * 
 transitions with significant oscillator strength starting from the 
 lb state computed at the tddft level and the observed blue 
 shift of the 680 nm band with increasing probe delay times .
the latter 
 observation compares well with the charge - transfer character of the 
  * state .
the just - mentioned reassignment led to the 
 proposition of a *-mediated ict mechanism where a reaction 
 sequence of  *   *  ict 
 structures is proposed .
however , it should 
 be mentioned that caspt2 calculations were reported which , in contrast to the just - mentioned tddft investigations , 
 give excitation energies for the le state which are in good agreement 
 with the experimentally observed bands so that from that point of 
 view a  * state need not be invoked for the assignment 
 of the 680 nm band .
the differences in the nanosecond decay 
 time between the transient 
 absorption of the tict state ( 4.8 ns ) and the fluorescence 
 decay of the ict ( 2.9 ns ) in an led to the conclusion 
 that these two states are not identical .
combined casscf and caspt2 
 calculations reported in ref ( 38 ) indicated the existence of a partially twisted ict ( ptict ) 
 structure with a twisting angle of 53. the fluorescence with 
 the decay time of 2.9 ns was uniquely assigned to originate from the 
 ptict structure . in view of the still existing different interpretations 
 and structural 
 models for the explanation of the dual fluorescence of dmabn , the 
 purpose of the present study is to perform a detailed survey of the 
 excited - state mechanism of ict using multireference methods which can simultaneously describe the energy 
 surfaces of the le and ct states and their nonadiabatic crossing regions 
 and are capable of full optimization of excited - state geometries and 
 conical intersections .
special emphasis is given to the calculation 
 of solvent effects in the excited state using a polarizable continuum 
 model based on the conductor - like screening model ( cosmo ) .
the question of dual fluorescence 
 of dmabn in that solvent and the role of the  * state 
 were addressed as well .
because in this case conical intersections 
 need not be considered and a multitude of excited states had to be 
 computed which would increase the effort of mr calculations significantly , 
 we decided to use for that purpose a more straightforward approach , 
 the aforementioned adc(2 ) method in combination with the recently 
 developed methods for excited - state solvation within cosmo .
the geometry optimization of dmabn in the ground state was performed 
 at second order mller 
plesset perturbation theory ( mp2 ) using the split valence polarization basis ( svp).c2v symmetry was used with c2 along the z axis and the benzene ring located in the yz plane .
the calculations on electronically excited states were performed 
 using the complete active space self - consistent field ( casscf ) method 
 and multireference configuration interaction with single excitations 
 ( mr - cis ) and with single and double excitations ( mr - cisd ) , accounting 
 for dynamic electron correlation effects . the active space chosen 
 for the casscf wave functions was a cas(10,9 ) consisting of 10 electrons 
 in 9 active  and  * orbitals .
the active space comprises 
 the  bonding and antibonding orbitals of the benzonitrile and 
 of the amino n atom . in the casscf calculations ,
a state - averaging 
 ( sa ) procedure was adopted with equal weights for the lowest three 
 singlet states ( sa-3 ) .
based on the molecular orbitals computed at 
 the sa-3-casscf(10,9 ) level , mrci calculations were performed with 
 an mr - cis reference space composed of 10 electrons in 9 orbitals ( mr - cis(10,9 ) ) , 
 of 8 electrons in 7 orbitals ( mr - cis(8,7 ) ) , and with a mr - cisd reference 
 space composed of 6 electrons in 5 orbitals ( mr - cisd(6,5 ) . in all 
 cases , the 11 1s orbitals on the carbon and nitrogen atoms were kept 
 frozen .
the orbital occupation scheme of the different reference wave 
 functions are collected in table s1 of the supporting 
 information .
size - extensivity corrections were taken into account 
 in single - point calculations according to pople et al .
geometry optimizations and the determination of the 
 minima on the crossing seam ( mxs ) have been performed with the ( 10s6p3d)/[3s2p1d ] 
 basis for n and c and ( 7s)/[2s ] for h. the extended basis [ 4s3p2d ] 
 for n and c atoms was also applied in selected cases . the first basis 
 set is termed ano - dz , and the second one ano - tz .
dipole moments and 
 population analysis data were computed at the mr - cis level for gas 
 phase and solution .
three states are included in the state - averaging 
 procedure ( sa-3 ) : 
 the ground state and the two low - lying singlet excited states le and 
 ct .
the twisting (  ) and wagging (  ) angles of the amino 
 group of dmabn were chosen as reaction coordinates to construct energy 
 curves and energy surfaces for the s1 and s2 states .
the twisting coordinate was defined as  = ( 1 + 2)/2 , and the wagging coordinate as  
 = ( 1  2)/2 , where 1 and 2 are the torsional angles c2c1n1c6 and c2c1n1c6 , respectively ( figure 1 ) .
solvent effects were taken into account 
 in single - point calculations by means of the conductor - like screening 
 model .
nonequilibrium and equilibrium versions 
 were used for the excited states in solution for mrci as described 
 in refs ( 58 and 59 ) . for a discussion 
 concerning the excited - state adc(2)-cosmo calculations , see ref ( 39 ) .
condon 
 excitations and fluorescent transitions were treated at the nonequilibrium 
 level , whereas for the reaction paths the equilibrium approach was 
 used . in the latter case
optimized geometries of dmabn in the ground state ( c2v symmetry ) ( a ) , in the s1(le ) state ( c2 ) ( b ) , in the ct 
 state 
 ( c1 ) ( c ) , in the s2/s1 mxs ( c2 ) ( d ) at the mrcis ( 8,7)/ano - dz 
 level , and in the  * state ( cs ) ( e ) at the adc(2)/tzvp level . for the ground - state 
 structure , the mrcis ( 8,7)/ano - dz results are given in roman type
, 
 mp2/svp data are presented in bold , and the experimental data in italic .
geometries of le and ct stationary 
 points , and the mxs between 
 those two states were optimized at the mr - cis level using analytic 
 mr - ci gradients and nonadiabatic coupling vectors .
mr - cis second derivatives of the energy were computed numerically 
 using analytically calculated first derivatives .
all other calculations have been carried out with the program system 
 columbus using its parallel version .
to 
 assess the accuracy 
 of the different multireference approaches used , the two low - lying 
 vertical excitation energies of dmabn were computed at casscf , mrcis , 
 and mrcisd levels of theory using the ano - dz and ano - tz basis sets 
 and compared to the experimental gas phase data ( table 1 ) .
it should be noted that the absorption maximum (s2,abs ) in the gas phase comes directly from 
 the experimental spectrum , whereas the (s1,abs ) is hidden under the strong s2 absorption 
 and its value was obtained after extrapolation .
the ( 10,9 ) , ( 8,7 ) , and ( 6,5 ) reference spaces were tested 
 in mr - cis and mr - cisd calculations .
total energy of b2(le ) state : 455.6544360 
 au , calculated with the ano - dz 
 basis set ( atomic natural orbital ( ano ) basis set - ( 10s6p3d)/[3s2p1d ] 
 basis for n and c and ( 7s)/[2s ] for h ) and pople correction ( + p ) .
total energy of a1(ct ) state : 455.6332238 au calculated with the 
 ano - dz 
 basis set and pople correction ( + p ) . at all computational levels , the transition to the s1(b2 ) state possesses a small oscillator strength . 

it involves mainly a homo(namino , ncyano , cph)lumo+1(cph ) transition with dominant 
 local excitation character .
it is due to a homo(namino , ncyano , cph)lumo(ncyano , cph,,namino ) transition which possesses partial charge - transfer 
 character .
the orbitals , involved in the transitions above are plotted 
 in figure s1a of the supporting information .
the casscf calculation overestimates the energy of the s2(a1 ) state by 1.4 ev as compared to the experimental 
 value , similar to the results reported in refs ( 8 and 28 ) .
the single excitation correction produces 
 an energy decrease of s2(a1 ) by 
 1 ev , whereas the energy of the s1(b2 ) state is not changed . reducing the reference cas from 
 ( 10,9 ) to ( 8,7 )
leads to an increase of the s1(b2 ) and s2(a1 ) energies 
 by 0.10.3 ev .
the single and double excitations calculations 
 ( mr - cisd(6,5)+p and mr - cisd(8,7)+p ) do not improve the excitation 
 energies and even lead to their slight increase .
the extended basis 
 set , ano - tz , changes the energies of both excited states only slightly . 

higher - order excitations using the pople correction lower the absorption 
 energies significantly , bringing them into quite good agreement with 
 experimental values .
the calculated (s1/s2 ) gaps computed at the mrcis(8,7)+p and mrcisd(6,5)+p levels agree 
 well with the experimental data ( table 1 ) . 
 among the methods tested
, the mrcis(8,7)+p / ano - dz provides the best 
 approach with respect to experimental s1 and s2 vertical excitation energies ( both excited states are overestimated 
 by about 0.3 ev ) and reproduces the (s1/s2 ) gap of 0.57 ev very well . in view of the good performance of the 
 mrcis(8,7)+p / ano - dz level and
because of considerations of computational 
 efficiency , all calculated transition energies presented below were 
 performed with this approach .
next , the optimized geometries 
 in the franck  condon ( fc ) region 
 are discussed ( figure 1a  c ) .
the optimized 
 geometries of s2/s1 mxs state and the  * 
 state , discussed in the following sections , are given in figure 1d , e .
the mp2/svp calculations for the s0 geometry yield a minimum at cs symmetry 
 ( i.e. ,  = 0.0 ) and a wagging angle of  = 10.2. 
 the experimental  and  angles obtained from x - ray diffraction 
 measurements ( at 253 k ) are 0.0 and 7.7 , respectively .
microwave spectroscopic measurements in the 
 gas phase lead to a  angle of about 15. the mp2 calculations reproduce well the amino c1n1 and c4c5 bond 
 lengths (  = 0.0050.007  ) , whereas the calculated 
 phenyl c  c and cyano c5n2 bond 
 lengths are longer by 0.020.03  as compared 
 to the crystallographic data . the c2v symmetry structure (  =  = 0 ) 
 is only slightly higher in energy by 0.06 kcal / mol than the cs structure .
the ground - state dmabn structure 
 was also calculated with the mrcis(8,7 ) method ( figure 1a ) ; the bond distances are comparable with the mp2 bond distances 
 (  up to 0.007  ) .
it should be noted that the mrcis(8,7 ) 
 method reproduces better the cyano c5n2 bond length ( 1.157  versus 1.145  exptl ) , whereas with 
 mp2/svp and cc2/tzvpp it is too large 
 by 0.035  .
the phenyl moiety shows a quinoidal distortion along 
 the long molecular axis ( i.e. , shortened c2c3 , c2c3 bond 
 lengths ) .
the c  namino bond distance ( calcd , 1.372 
  ( mp2 ) ; exptl , 1.365  ) is shorter than a normal single 
 c  n bond ( 1.46  ) because of the resonance between the dimethylamino part and the 
 adjacent benzene ring . around the franck 
the le geometry 
 was optimized without symmetry constraint at the mrcis(8,7)/ano - dz 
 level .
the optimized le geometry reveals a twisting angle  
 of 13.9 , a wagging angle  of 0 , and out - of - plane 
 benzene h atoms ( dihedral hcch angle , 5 ) ( figure 1b ) .
the calculated  and  values can 
 be compared to the experimental ones of  = 30 ;  
 = 0 obtained by microwave spectroscopy ;  = 30 by time - of - flight mass spectroscopy ;  = 26 by resonant enhanced two - photon 
 ionization ; and  = 25 ,  
 = 3 by rotationally resolved fluorescence spectra .
it should be noted that the potential energy 
 curve of the le state with regard to the twisting coordinate appears 
 quite shallow in the region of 030 ( see below ) , allowing 
 the twisting angle to vary largely .
the le geometry is characterized 
 by an elongation of the phenyl c1c2 and 
 c2c3 bond lengths by 0.017 and 0.036 
  , respectively , and by slight variations of the c5n2 , c2n1 , and c4c5 bond lengths ( up to 0.008  ) as 
 compared to the ground state .
the cc2/tzvpp calculations of dmabn 
 ( c2 ) show similar  and  
 values of 19 and 0 , respectively , and similar trends in 
 bond length changes .
the intense ultraviolet 
 ( uv ) absorption due to the s2 state is assigned to the 
 ct state with a large dipole moment in the fc region . in the fc region , 

the s2(ct ) geometry is not stable . instead , the ct state 
 twists around the c1n1 bond and shows 
 a minimum ( then in the s1 state ) at a twisting angle of 
 90.2 and a wagging angle of 0.8. selected structural data 
 are given in figure 1c .
the small deviations 
 from 90 and 0 are not considered to be significant and 
 are due to the shallow energy surface in this region of angles .
the 
 optimized ct geometry is characterized by significant quinoidal distortions 
 ( i.e. , shortened c2c3 and c2c3 bond lengths ) as compared to the ground 
 state and also to the le structure .
the most significant geometrical 
 change was found for the c1n1amino bond , 
 which elongates by 0.06  , facilitating rotation around c 
the c4c5 bond is shortened by 
 0.02  , whereas the cn bond is slightly stretched 
 by 0.01  as compared to the s0 geometry .
bond length 
 changes have been estimated experimentally by comparing the vibrational 
 frequencies in the ct state to those in the ground state .
numerous 
 efforts were made to measure the vibrational frequencies of dmabn 
 in the ct state by picosecond ir , picosecond 
 time - resolved resonance raman spectroscopies and femtosecond stimulated raman spectra .
the elongation of the c  namino and c  ncyano bonds in the ct state was confirmed by these experimental 
 studies , supporting the tict structure in which the -conjugation 
 including the c  namino bond is broken . for comparison , 

the ct geometry obtained by cc2/tzvp calculations showed a saddle point structure with a twisting angle at 
 90 , a wagging angle of 0 , and an out - of - plane angle at 
 41. the bond length changes ( s0 to ct ) calculated 
 by cc2 and mrcis(8,7 ) methods follow the same trend .
the calculated 
 vertical excitation energies , minimum - to - minimum 
 and vertical fluorescence energies in the gas phase and in an solution 
 are presented in table 2 .
position of 00 transition 
 ( approximation ) ; the result in ref ( 27 ) was used .
laser - induced fluorescence ( lif ) 
 excitation spectrum in the gas phase , ref ( 45 ) .
the 
 calculated oscillator strength for the vertical excitation 
 to the s2(ct ) state is large and will dominate the absorption 
 intensity in comparison to the s1(le ) state .
going from 
 gas phase to an solution the experimental absorption energy decreases 
 from 4.57 to 4.24 ev , resulting in a decrease of the e(s1s2 ) energy gap from 0.44 ev ( gas ) to 0.38 ev ( an ) . 
 in accordance with the experiment , the calculations in an solution 
 showed a decrease of the vertical excitation energy of the s2 state ( 4.90 ev ( gas ) to 4.75 ev ( an ) ) and of the e(s1,s2 ) energy gap from 0.58 ev ( gas ) 
 to 0.41 ev ( an ) ( table 2 ) .
a similar trend 
 of the solvent effects ( aprotic and protic solvent ) was predicted 
 from the average solvent electrostatic potential from molecular dynamics 
 ( asep / md ) calculations of the dmabn uv / vis spectra .
the energy diagrams of the le  tict process 
 for dmabn in 
 the gas phase and an solution are compared in figure 2 .
le / ct energy diagram ( ev ) of dmabn in vacuum ( black ) and acetonitrile 
 ( red ) calculated at the mrcis(8,7)+p / ano - dz level .
the calculated e for the le  tict 
 reaction in the gas phase is positive ( 0.16 ev ) in keeping with the 
 positive formation enthalpy ( 0.05 ev ) , determined by extrapolation 
 from plots of h vs the solvent polarity parameter . in line with the experiment ,
caspt2 calculations 
 have predicted a positive e of 0.41 kcal / mol 
 ( 0.02 ev ) for a twisted ict and of 7.10 kcal / mol ( 0.31 ev ) for a planar 
 ict .
the experimental and calculated 
 endothermic reaction le  ict of dmabn in the gas phase is 
 in line with the absence of dual fluorescence in the gas phase .
the 
 cc2/svp calculations , however , have predicted 
 a small exothermic gas - phase le  ict reaction of dmabn ( e= 1.84 kcal / mol/0.08 ev ) .
this result was 
 corrected by using higher - order coupled cluster single and double 
 excitations with noniterative triple - corrected excitation energy ( ccsdr(3 ) ) 
 calculations , which shifted the ict level to higher energy by 0.2 
 ev relative to the le level . in 
 an solution ,
the e for the reaction 
 le  ict calculated at the mrcis(8,7)+p / ano - dz level is negative 
 ( 0.25 ev ) , which is consistent with the experimental exothermic 
 reaction ( e = 0.28 ev ) .
the exothermic le  ict reaction is in 
 accordance with the ict producing dual fluorescence in an solution . finally , dmabn relaxes into s0 via fluorescence emission 
 from s1 .
the emission energy at the le geometry is 3.93 
 ev in the gas phase and 3.94 ev in an .
the experiment predicts a somewhat 
 larger solvent effect on le emission energies : 3.68 ev in the gas 
 phase and 3.44 ev in an .
the an solvent stabilizes the ct structure significantly 
 more than the le structure leading to a negative energy of the le 
  ct reaction ( figure 2 ) .
the calculated 
 emission energy of 3.27 ev for the optimized tict structure in the 
 gas phase shows good agreement with the experimental ict emission 
 energy of 3.55 ev for dmabn in the gas phase ( extrapolated from solvent 
 series ) .
both experimental and calculated 
 ict emission transitions of dmabn in an are found at lower energies , 
 2.52 and 2.77 ev , respectively .
the an 
 solvent produces greater stabilization of the ict structure and hence 
 a red - shift of the emission maximum for dmabn in the tict state .
similar 
 results were obtained recently from adc(2)/cosmo calculations and from asep / md calculations . in table 3 ,
the mrcis(8,7)/ano - dz 
 dipole 
 moments of the gs , le , and ct states are compared to the experimental 
 values and to those obtained in other calculations . 

the mp2/svp optimized 
 ground - state geometry of dmabn in c2v symmetry (  ,  = 0 ) was taken 
 as starting point for computing potential energy curves along the 
 twisting angle ( rotation around the c1n1 bond ;  = 0 , 15 , 30 , 45 , 48 , 49 , 50 , 60 , 75 , 90 ) and 
 the two - dimensional potential energy surfaces in both the twisting 
 and wagging (  = 0 , 5 , 10 , 15 , 20 ) coordinates in the 
 gas phase and an solution .
the shape of the most important mos can 
 be found in figures s1a , b and s2a , b of the supporting 
 information .
rigid potential energy curves along the twisting angle 
  
 ( the wagging angle  is fixed at 0 ) ( a ) and charge transfer , qring+cn ( e ) ( b ) for the two 
 lowest singlet excited states of dmabn in the gas phase at the mrcis(8,7)+p / ano - dz 
 level .
energies are given relative to the s0 energy of 
 the ground - state minimum at c2v symmetry (  ,  = 0 ) .
inspection of the potential energy curve along the twisting 
 path 
 ( figure 3a ) shows the two minima in the s1 state : the le state at the nontwisted geometry (  = 
 0 ) and the ct state at the perpendicular twisted geometry (  
 = 90 ) of dmabn .
the energy of the nontwisted geometry is lower 
 by 0.27 ev as compared to s1 at twisted dmabn .
potential energy 
 surfaces along the twisting (  ) and wagging 
 (  ) coordinates of the two lowest singlet excited states of 
 dmabn in the gas phase at the mrcis(8,7)+p / ano - dz level . as shown in figure 3a , with 
 the increase 
 of the twisting angle , the s1 and s2 states 
 cross at 50. inspecting the calculated fragment charge 
 of the phenyl ring plus cn group , qring+cn , computed from a mulliken population analysis , illustrates charge transfer in the s2 state 
 that is only slightly larger than that in the s1 state 
 for the nontwisted form ( figure 3b ) . along 
 the twisting
coordinate between 0 and 48 , the charge - transfer 
 character of the s2(ct ) state progressively increases by 
 0.1 e : the charge qring+cn decreases from 0.3 e to 0.4 e ( the main contribution belongs to the acceptor ( a ) phenyl 
 charge ) , whereas concomitantly the charge of the donor ( d ) amino group 
 increases from + 0.3 e to + 0.4 e. 
 at a twisting angle of 50 , the character between the 
 two states is abruptly exchanged because of the intersection of the 
 two states .
after the intersection the state characters are ct for 
 s1 and le for s2 . along the twisting
coordinate 
 from 50 to 90 , the energy of the s1(ct ) state 
 decreases with the increase of its charge transfer ( figure 3 ) . the large dipole moment and large charge separation 

figure 4 displays the s1 and s2 energy surfaces in the torsion and wagging coordinates .
it 
 can be seen that altering the wagging angle does not lift this degeneracy 
 significantly .
the calculated potential energy curves , the fragment 
 charge qring+cn , and energy surfaces of 
 dmabn in an 
 ( equilibrium solvation conditions ) are plotted in figures 5a , b and 6 , respectively . 
 for comparison , the nonequilibrium solvent calculations of the potential 
 energy curves and surfaces of dmabn were also calculated .
they are 
 presented in the supporting information ( figure s3 and figure s4 ) .
the computed potential energy curves 
 and surfaces are very similar in both solvation cases .
potential energy curves 
 along the twisting angle  ( the wagging 
 angle  is fixed at 0 ) ( a ) and charge transfer , qring+cn ( e ) ( b ) , of the two 
 lowest singlet excited states of dmabn in acetonitrile for equilibrium 
 solvent conditions at the mrcis(8,7)+p / ano - dz level . in an ,
the s1 and s2 energy 
 curves resemble 
 those in the gas phase up to  = 50 , only the energy gap , 
 (s1/s2 ) , is smaller for an solvation . 

the s1 energy curve in an shows also two minima as in the 
 gas phase , but unlike the gas - phase curves the lower energy minimum 
 appears at the twisted ( 90 ) dmabn form ( by 0.46 ev ) . 

there is a quite strong stabilization of the s1 ( ct ) state 
 at  = 90 , but the gap to the s0 state remains 
 still quite large ( 2.9 ev ) .
potential energy surfaces along the twisting 
 (  ) and wagging 
 (  ) coordinates of the two lowest singlet excited states of 
 dmabn in acetonitrile for equilibrium conditions at the mrcis(8,7)+p / ano - dz 
 level . to illustrate the stabilization 
 of the tict state in solution , 
 the fragment charge qring+cn for s0 , s1 , and s2 state
inspection 
 of the charge transfer in the s1 and s2 states 
 for the gas phase ( figure 3b ) and solution 
 ( figure 5b ) for the nontwisted dmabn form shows 
 a slight solvent effect on the charge separation .
the small difference 
 in charge transfer for the s1 and s2 states 
 found in the gas phase disappears in solution . on the other hand , 

the solvent causes a somewhat larger charge separation ( 0.09 e ( gas ) , 0.13 e ( an ) ) in the nontwisted 
 ground - state form .
along the twisting coordinates between 0 and 55 , the charge 
 transfer of the s2(ct ) state progressively increases , following 
 the trend found in the gas phase .
the calculations predict a somewhat 
 larger charge separation in solution for the s2(ct ) state 
 ( increases by 0.2 e. from 0 to 50 
 twisting ) ; the charge of the donor ( d ) amino group increases within 
 the above - mentioned torsion range from + 0.3 e to 
 + 0.5 e ( and the qring+cn charge decreases from 0.3 e to 0.5 e accordingly , figure 5b ) , whereas 
 in the gas phase , qamino and qring+cn charges are changed by only 0.1 e within that range of the twist angle .
it should be noted that the 
 charge transfer gets larger in solution ( compared to the gas phase ) 
 primarily at twisting above 30. the fragment charge of the s1(le ) state is hardly increased ( up to 0.05 e ) by the solvent effect in the twisting range of 0 to 50. at a twisting angle of 50 , the character between 
 the two states is exchanged ( figure 5a ) in 
 analogy to the situation described for the gas phase .
the fragment 
 charge separation for the twisted ( 90 ) dmabn structure in solution 
 remains larger by 0.1 e ( going from 0 
 to 90 twist angle , qring+cn decreases 
 by 0.31 e ( an ) versus 0.25 e ( gas ) ) . 

after the intersection , the s2 state obtains le character 
 and its charge separation abruptly tends to zero and the s2(le ) state loses practically any charge - transfer character . in the 
 gas phase
. the larger 
 charge separation of the s1(ct ) state in solution as compared 
 to that in the gas phase agrees with its larger stabilization in polar 
 solvent and with the fact that the minimum of the s1(tict ) 
 state is lower in energy than that of the s1(le ) state . in an solution , the s1 and s2 energy curves 
 intersect at approximately the same twisting angle of 50 
 as in the gas phase ; therefore , the s2/s1-mxs 
 appears to be quite independent of the environment polarity .
a survey 
 of the s1 and s2 energy surfaces of dmabn in 
 the gas phase and an ( figures 4 and 6 ) shows that the wagging coordinate does not strongly 
 affect the e(s1s2 ) energy 
 difference in the s1/s2 crossing region and 
 could play only a small role in assisting the twisting intracharge 
 transfer mechanism .
g- and h - vectors for the mxs 
 between 
 s2 and s1 computed at the mrcis(8,7)/ano - dz 
 level in the gas phase . in figure 7 , the energy gradient difference 
 vector g and the nonadiabatic coupling vector h characterizing the branching space of the intersection cone are displayed for the mxs structure between s2 and s1 ( figure 1d ) .
these 
 two vectors describe bond - stretch motions within the benzene ring 
 and with the two substituents but do not contain the twisting angle 
 . thus , in agreement with the calculations of gmez 
 et al . and kochman et al .
we find that this coordinate is not part of 
 the branching space and thus will not participate in the nonadiabatic 
 transfer from s2 to s1 .
the g - vector 
 shows modes along the quinoidal c2/c3 and c2/c3 coordinates as suggested in 
 ref ( 27 ) . as already discussed 
 in the introduction , an alternative deactivation 
 path via a rehybridized ict ( rict ) in a bent *cn state
was suggested a long time ago and has been 
 taken up recently emphasizing the importance of this state for the 
 deactivation processes in dmabn ( see ref ( 38 ) and references therein ) . to compare with the 
 twisting pathway described in the previous section , adc(2 )
calculations 
 have been performed along the c4c5n2 angle ( see figure 1 ) similar to the investigations 
 reported in ref ( 36 ) .
rigid potential energy curves along the ccn angle for the lowest 
 singlet excited states of dmabn under cs symmetry restriction ( a ) in the gas phase and ( b ) in an solution 
 at the adc(2)/tzvp level .
starting point is the mp2/svp optimized 
 ground - state geometry of dmabn ( c2v , ccn = 180 ) .
optimized geometries of le , mxs , 
 tict structures at mrcis ( 8,7)/ano - dz level and of  * 
 structure at adc(2)/tzvp level were used .
figure 8a shows the potential 
 curves under cs symmetry restriction for 
 several excited states 
 in the gas phase in dependence of the ccn angle .
most of the curves 
 increase in energy when starting at the linear geometry at 180 , 
 only the  * is stabilized , similar to the findings in 
 refs ( 8 and 36 ) . in spite of the 
 significant stabilization of this state , it still is located 1 
 ev above the le minimum ( table 4 ) .
this fact 
 led to the conclusion that at least in the gas phase this state would 
 not contribute significantly to the deactivation dynamics in dmabn . moreover ,
analysis of the hessian matrix showed 
 several imaginary frequencies related to out - of - plane modes .
starting 
 a geometry optimization from a slightly out - of - plane distorted geometry 
 led to the le minimum structure .
thus , at least in the gas phase the 
  * state does not correspond to a stable structure at 
 the adc(2 ) level . in an solution ( figure 8b ) , 
 because of the large dipole moment of the  * state ( 15.9 
 d ) , polar solvation stabilizes this state significantly with respect 
 to the two lowest  * states .
table 4 shows that at the energy minimum ( in the one - dimensional potential 
 energy curve ) the  * state is even a little lower than 
 the le state .
thus , the  * state is energetically accessible 
 in comparison to the absorption energy of the bright s2 state ( table 1 ) .
condon 
 factors for the transition between the ground and  * 
 states will certainly not favor this transition because of the strong 
 bending of the ccn group in the latter state in comparison to the 
 linear arrangement in the ground state .
the discussion 
 of the photodynamical deactivation model orients itself on the following 
 observations reported in this work .
a minimum on the crossing seam 
 between the le and ct states ( s1/s2 ) has been 
 located at mrcis level as a twisted structure ( figure 1d ) as postulated in the tict model . in agreement with the 
 results obtained from casscf calculations by gmez et al . and 
 kochman et al . , it is found that the twisting 
 motion is not included in the branching space but characterizes the 
 intersection seam . as a consequence , the seam will be accessible via 
 a wider range of twisting angles .
condon point in s2 to 
 the twisted ct minimum on the s1 surface ( rigid torsion , 
 figure 3 , gas phase ) .
two minima have been 
 located on the s1 surface , a quasi - planar le structure 
 and an orthogonal ct structure ( panels b and c of figure 1 , respectively ) .
the  * state is energetically 
 too high to play a significant role in the gas phase dynamics .
starting 
 from the bright s2 state , the photodynamics will be driven 
 by the twisting around the cn bond between the phenyl ring and the 
 dimethylamino group because of the energetic stabilization of that 
 state .
however , the nonadiabatic transition to the s1 state 
 is determined by planar intraring coordinates and not by the torsion . 

in fact , the recent surface hopping study by kochman et al . has shown that such a decay should occur at 
 very early stages of the photodynamics , a fact which is also supported 
 by the characterization of the branching space of the conical intersection 
 between s2/s1 computed at the mrcis level .
the 
 equilibration between the le and tict states will occur on the s1 surface . in polar ( acetonitrile )
solution , the shape 
 of the twisting potential curves is the same as in the gas phase ( rigid 
 torsion , figure 5 ) .
condon point to the mxs is slightly flatter 
 as compared to the gas phase ; only the path from the mxs to the tict 
 minimum is steeper . because the evolution of the charge transfer , qring+cn , in the gas phase and in an solution 
 is quite similar for torsion angles up to the intersection ,
it is 
 expected that the qualitative character of the branching space will 
 not change and that also in solution it will be determined by intraring 
 vibrations and not by the torsional motion .
thus , it is quite likely 
 that also in polar solution the initial dynamics will primarily proceed 
 as in the gas phase and that the major fraction of the nonadiabatic 
 decay will lead to the le state from which equilibration with the 
 tict will occur .
because of the enhanced stability of the latter state 
 in polar solution as compared to the gas phase case , the tict state 
 will be predominantly populated .
the strong stabilization of 
 the  * state in an solution 
 has already been noted ( figure 8) , leading 
 to a possible contribution to the photodynamics , as emphasized in 
 refs ( 11,3638 , and 83 ) .
however , starting with the photodynamics 
 in the franck  condon point , ccn bending of the nitrile group 
 leads to a destabilization of the s1 and s2  * 
 states so that at least in the initial phase of the dynamics , population 
 of the  * state by this mode can not be expected .
as described 
 in the previous paragraph , similar to the gas phase , the photodynamics 
 will start in the s2 state with a twisting of the n(ch3)2 group and a rapid decay to the le structure . 
 because of the comparable stability of the le and  * 
 structures in an , participation of the latter structure in the later 
 phases of the photodynamics is possible . from our static calculations 

it is difficult to predict to which extent the ccn bending motion 
 will be actually activated . in any case , the final structure ( in addition 
 to the le minimum ) in the excited state should be the tict structure . in our mrcis calculations and also in the adc(2 )
no additional 
 partially twisted ( ptict ) minimum was found in contrast to the casscf 
 optimizations performed by coto et al .
in fact , the twisting angle of 53.4 reported in this 
 latter work coincides almost exactly with the twisting found for the 
 mxs ( figure 1d ) , and figure 5 shows a barrierless reaction path on s1 to the 
 tict structure .
thus , a ptict structure stable over the time of several 
 nanoseconds , as required by the proposal suggested in ref ( 38 ) ( that this structure is 
 the source of fluorescence ) , does not seem likely according to our 
 findings .
the mechanism leading 
 to dual fluorescence of dmabn in the gas 
 phase and in acetonitrile solution has been addressed using two computational 
 methods : ( i ) the multireference configuration interaction with single 
 excitations ( mrcis ) and ( ii ) the second - order algebraic diagrammatic 
 construction ( adc(2 ) ) method .
solvent effects have been based on the 
 conductor - like screening model in both approaches .
the mrcis 
 calculations show that the main absorption proceeds to 
 the s2 state possessing a charge - transfer ( ct ) character 
 somewhat larger than that of the s1 state . in the gas phase 
 as well as in an solution the excited s2(ct ) state structure 

coordinate the s2 state is stabilized , crossing the s1 state at 50 in the minimum on the crossing 
 seam ( mxs ) .
it is important to note that in agreement with the findings 
 of gmez et al .
the twisting angle 
 is not part of the intersection space , which makes the intersection 
 seam accessible for a larger range of twisting angles .
this result 
 is also well in line with the results of recent nonadiabatic dynamics 
 simulations which show a very fast deactivation 
 from s2 to s1 within 8.5 fs at practically planar 
 geometries .
the calculated fragment charge qring+cn in the gas phase and in solution are used to describe 
 the character changes of both states at the conical intersection . 

the larger charge separation found for the 
 twisted dmabn ( tict ) structure explains the enhanced stabilization 
 of the s1(tict ) state in polar solvent and hence the lower 
 energy minimum of s1(ct ) state in comparison to the s1(le ) state .
the adc(2 ) calculations have been used primarily 
 to investigate 
 the role of the ccn bent  * state .
the results show that 
 for the gas phase this state is energetically too high and should 
 not participate substantially in the photodynamics starting from s2 . in an solution this state
the initial dynamics starting in the s2( * ) 
 state will begin with the ( ch3)2n twisting or , 
 as outlined in ref ( 27 ) , also by pyramidalization of the carbon ring atom next to the nitrogen . 
 the ccn bending , however , would lead to an initial destabilization 
 of the  * states . nevertheless , in polar solution , because 
 of the comparable stability of the le and planar  * states , 
 the latter state could play a role in a later phase of the dynamics . 

finally , dmabn should either arrive in the s1(le ) or s1(tict ) structures from which fluorescence can occur . because 
 of the close structural similarity of the ptict structure with the 
 mxs structure , the former does not appear to be sufficiently stable 
 to act as the origin of fluorescence with a lifetime of 2.9 ns .
future 
 work is certainly needed to shed more light on the question of whether 
 the two different transient lifetimes found for absorption ( 4.8 ns ) 
 and fluorescence ( 2.9 ns ) really point 
 to the presence of two independent ict structures or whether an explanation 
 based on one ict structure can be found .
 the 
 structural processes leading to dual fluorescence of 4-(dimethylamino)benzonitrile 
 in the gas phase and in acetonitrile solvent were investigated using 
 a combination of multireference configuration interaction ( mrci ) and 
 the second - order algebraic diagrammatic construction ( adc(2 ) ) methods . 
 
 solvent effects were included on the basis of the conductor - like screening 
 model . 
 the mrci method was used for computing the nonadiabatic interaction 
 between the two lowest excited  * states ( s2(la , ct ) and s1(lb , le ) ) and the 
 corresponding minimum on the crossing seam ( mxs ) whereas the adc(2 ) 
 calculations were dedicated to assessing the role of the  * 
 state . 
 the mxs structure was found to have a twisting angle of 50. 
 the branching space does not contain the twisting motion of the dimethylamino 
 group and thus is not directly involved in the deactivation process 
 from s2 to s1 . 
 polar solvent effects are not 
 found to have a significant influence on this situation . applying cs symmetry restrictions , the adc(2 ) 
 calculations 
 show that ccn bending leads to a strong stabilization and to significant 
 charge transfer ( ct ) . nevertheless , this structure is not a minimum 
 but converts to the local excitation ( le ) structure on releasing the 
 symmetry constraint . 
 these findings suggest that the main role in 
 the dynamics is played by the nonadiabatic interaction of the le and 
 ct states and that the main source for the dual fluorescence is the 
 twisted internal charge - transfer state in addition to the le state . 
Introduction
Computational Details
Results and Discussion
Conclusions