the 
 response of a molecule to an applied electromagnetic field 
 is strongly modified by the nearby presence of metal nanoparticles 
 ( nps ) or nanostructures . the resulting effects define the field of molecular plasmonics(1 ) and include 
 many striking phenomena such as surface enhanced raman scattering 
 ( sers ) , surface enhanced infrared absorption ( seira ) , and metal enhanced 
 fluorescence . several theoretical models have been proposed through 
 the years to understand such phenomena , some of which exploit a quantum - chemical 
 description of the molecule . for these models , the nearby nanostructure 
 is typically too large to be routinely treated by quantum - chemistry 
 ( qm ) methods as well . presently , metal nps of up to around 1000 atoms , 
 i.e. , a few nanometers in diameter , can be described by qm methods , but they are much smaller than many nps of practical interest . to 
 tackle this limitation , and taking into account the good quality that 
 a classical electromagnetic ( em ) description gives of the optical 
 properties of the np , in the past different groups devised multiscale 
 methods that keep the quantum - mechanical description of the molecule 
 but include the np as a classical object , either as a continuous dielectric or as a collection of polarizable ( and chargeable ) atoms . most of these models treat the applied electric field , and 
 the 
 corresponding molecule + np response , in the frequency domain , i.e. , 
 assuming a monochromatic sinusoidal em perturbation acting on the 
 system . while this is , in principle , a very general approach ( any 
 time - dependent em field can be fourier - decomposed in a superposition 
 of sinusoidal monochromatic fields ) , it is not the only one . a fully 
 real - time description of optical phenomena involving molecules is 
 also possible , i.e. , a numerical approach that solves the time - dependent 
 schrdinger equation ( or the time - dependent kohn  sham 
 equation for time - dependent density functional theory , tddft , approaches ) 
 for the molecule in the presence of a time - dependent field . such a 
 real - time description is quite suitable when one wants to simulate 
 the interaction of molecules with short light pulses ( that span many 
 frequencies ) such as those employed in ultrafast spectroscopies , also 
 in the presence of plasmonic nanostructures . finally , a real - time description also offers 
 an alternative way to interpret optical phenomena involving molecules , 
 that may disclose more clearly the physics taking place in the system . on the down side , a real - time description typically 
 requires large computational efforts if fine features in a spectra 
 should be solved , and many of the analysis that are straightforward 
 in the frequency domain ( e.g. , orbital excitations contributing to 
 a given transition ; inspection of the transition density ) require 
 extra steps . in this work we shall present an evolution of the 
 polarizable continuum 
 model ( pcm)-inspired approach that has 
 been developed in the past to treat optical properties of molecules 
 close to a metal np to the real - time domain . 
 in that model , fock / time - dependent 
 hartree  fock ( hf / tdhf ) and then 
 by dft / tddft and zindo , and was coupled to a classical dielectric description of 
 the metal np employing an empirical frequency - dependent dielectric 
 constant corrected for quantum - size effects . the boundary element method ( bem ) was used to solve the quasi - static 
 electromagnetic problem needed to write the effective hamiltonian 
 for the molecule close to the np . many phenomena were treated with 
 this model , such as sers , seira , metal - enhanced fluorescence , and excitation 
 energy transfer ( eet ) close to a np . the optical phenomena 
 that will be considered here are the light absorption of the molecule  np 
 system , with the goal to extend the method to a range of phenomena 
 in the near future . in the field of quantum - chemical models 
 for molecules close to 
 nps the approach that we are proposing 
 here differs from previous ones in two main aspects . the first is 
 the choice of the quantum - mechanical method for the molecule . all 
 the cited works exploit real - time tddft ( rt - tddft ) . here , for the 
 molecule we shall instead solve the time - dependent schrdinger 
 equation projected on a finite basis of multielectronic states , obtained 
 by configuration interaction ( td ci approach ) . the second difference 
 is that previous works used the finite difference time domain ( fdtd ) 
 method for the np polarization , while here we shall exploit bem ( in 
 the quasi - static limit ) . the choice of a wave function based 
 method ( ci ) instead of rt - tddft 
 is motivated by the qualitative artifacts that plague the current 
 versions of rt - tddft when the molecular state departs substantially 
 from the ground state . for example , the behavior in response to a 
 light pulse that should take most of the population to a given excited 
 state is unsound with respect to the pulse parameter , and rabi oscillations are not properly described . the cause of these artifacts is believed to be the adiabatic 
 approximation , i.e. , the assumption that the exchange - correlation 
 ( xc ) potential at a given time depends only on the density at that 
 time rather than on all the previous instants . therefore , although rt - tddft will likely become in the future as 
 accurate in the study of electronic dynamics as dft and tddft are 
 now for ground and excited state properties , at present , such artifacts 
 make it difficult to correctly assign the physical origin of features 
 observed in the electronic dynamics of a molecule close to a metal 
 np . td ci offers the simplest theoretical framework to bypass these 
 problems and has been already applied to the investigation of multielectronic 
 dynamics for molecules in the gas phase . here , we shall limit ourselves 
 to the simplest ci method , ci singles ( cis ) . although cis is known 
 to have a limited accuracy in terms of excitation energies , it provides qualitatively correct behaviors 
 also for charge transfer states , and can be systematically improved 
 ( e.g. , the cis(d ) correction has already been used in a td context ) . the classical electromagnetic description of the np via bem 
 is 
 an alternative approach to fdtd . , bem has some computational advantages when coupled to a molecule 
 described with a localized basis set , that will be discussed in the 
 theoretical section . bem is most naturally a technique applied in 
 the frequency domain , and it needs to be translated to the time domain 
 to be directly coupled to td ci . we have recently investigated the 
 electronic dynamics of molecules in solution by a novel extension 
 to the time domain of the pcm implicit solvation approach . to this aim , we have developed equations of motion ( eoms ) for the 
 apparent charges that describe the evolution of time - dependent solvent 
 polarization . such eoms are able to describe the delayed solvent response 
 coded in the debye dielectric constant . formally , the electrostatic 
 problem involved in pcm and in a quasi - static bem description of a 
 molecule close to a continuous metal np is the same . as such , the eom method developed in ref ( 42 ) can be extended to nps 
 as well , as anticipated in that work . however , the debye dielectric 
 constant used there is not appropriate for metal nps . lorentz 
 dielectric function , and adopt a numerical 
 approach consistent with such eoms . the real - time td ci coupled with 
 eom bem evolution is implemented in the stand - alone homemade software 
 wavet that is interfaced with a local version of the widespread quantum - chemistry 
 code gamess . the article is organized 
 as follows : in section 
 2 , we shall present the theoretical basis of the current approach , 
 including the derivation of the eom for the np apparent charges that 
 originates from the drude  lorentz dielectric function . then , 
 in section 3 , we shall apply this theory to 
 study the absorption spectrum of a molecule close to a complex - shaped 
 metal np . finally , we shall draw the conclusions and discuss the development 
 perspectives of this modeling approach . the basic features of the model we are using for a molecule close 
 to a np have already been described elsewhere . here the np is 
 described as a continuous dielectric with a complex shape and characterized , 
 in the present work , by a drude  lorentz dielectric function 
 ():1the metal 
 np is polarized both by the externally 
 applied , incident time - dependent electric field einc(r,t ) and 
 by the time - dependent em field originated by the time - varying electronic 
 charge density of the molecule . in turn , these two polarizations create 
 time - dependent electric fields ( sometimes dubbed reflected field eref(r,t ) and image or polarization field epol(r,t ) , respectively ) that act on the molecule . in the quasi - static limit ( i.e. , in the 
 limit of electric field wavelength much larger than the np ) , such electric fields are locally associated 
 with time - dependent electrostatic potentials ( vref(r,t ) and vpol(r,t ) ) that satisfy proper quasi - static poisson equations and the electrostatic 
 boundary conditions at the np surface . following 
 standard integral equation theory and the boundary elements method 
 ( ief - bem ) , each of these electrostatic potentials ( reflected and image ) 
 can be written as originated by a proper set of point charges ( qref(t ) and qpol(t ) ) located in representative points on 
 the np surface . the molecule is 
 described by an effective hamiltonian (t ) that includes the electromagnetic interaction 
 with the incident field einc(r,t ) , the reflected field eref(r,t ) , and the polarization field epol(r,t ) . the 
 first is included in the usual dipole approximation ; the second and 
 the third interactions are instead written exploiting the charges qref(t ) and qpol(t):2here ,  is the hamiltonian of the isolated 
 molecule ,   is the 
 dipole operator , einc(rm , t ) is evaluated in 
 the molecular center of charge rm , and v is a vector operator representing 
 the electrostatic potential of the solute at the representative points 
 on the np surface where the apparent charges qref(t ) and qpol(t ) are also located . notably , qpol(t ) depends on the electrostatic potential originated by 
 the molecule v(t ) at all 
 the previous instants t < t , giving rise to a nonlinear and nonlocal - in - time evolution problem . in the next subsection , we shall focus 
 on the calculations of qref(t ) and qpol(t ) for a np described 
 by the drude lorentz 
 dielectric constant . following previous 
 works , in the frequency domain , qpol( ) and qref( ) are 
 calculated from the electrostatic potential produced by the molecular 
 charge density on the np discretized surface ( v( ) ) 
 and the potential associated with the incident field vinc(r ) = reinc(rm, ) , respectively , as follows:3where q( ) is the response 
 matrix in the frequency domain:4a is a diagonal matrix with elements 
 equal to the tessera areas ; s and d are 
 the representative matrices of the calderon s projectors:5si are the representative points on the nanoparticle surface 
 and nj are unit 
 vectors normal to the j - th tessera and pointing outward . the generalization to the time domain of eq 3 is straightforward ( for the sake of brevity , 
 we focus here on qpol and v only ; 
 the equations are identical for the pair qref and vinc):6with charges and potentials defined in the 
 time domain and q(t  t ) being the kernel ( or memory ) matrix that determines 
 the nonequilibrium response of the np in the time domain , obtained 
 by fourier - transforming q( ) . following the route 
 presented in ref ( 42 ) , we rewrite the q(t t ) matrix in terms of a diagonal representation:789where the matrices t and  are built by the eigenvectors and the eigenvalues , 
 respectively , of the symmetric matrix 1/2(sdas + sads ) 
  sdas ( the identity is exact for the corresponding integral operators ) . lorentz 
 dielectric function eq 1 , kii( ) in eq 8 can be written as10we compute then the 
 fourier transform11to obtain 
 the following form of the diagonal 
 kernel function:12with1314(t the equations 
 for the apparent charges are then obtained by substituting in eq 7 the expression of the 
 diagonal kernel function kii(t  t ) given 
 in eq 12 . time of eq 7 , and use them to eliminate the 
 convolution integral from the definition of qpol(t ) , similarly to what was done in ref ( 42 ) . this leads to the eom:151617and analogously for the reflected field charges:18with kf being the diagonal matrix defined 
 before in eq 10 and k still diagonal and with elements defined 
 by19the form of eqs 15 and 18 is clearly 
 that of ( coupled ) forced damped harmonic oscillators (  =   res2x + f ) . the squared frequencies 
 of the oscillators are those given in eq 19 and depend on two quantities : one is the 
 lorentz resonance frequency 0 characteristic of 
 the material making up the np , the other ( kf , ii ) is a purely geometric term 
 that is related to the shape of the np and the various excitations 
 it can sustain . we have already discussed the possible values of ii for a spherical np in ref ( 42 ) . based on those results , 
 we find that for a spherical metal np described by a drude dielectric 
 constant ( i.e. , 0 = 0 and a = p2 in eq 1 , where p is the plasma frequency ) , the squared frequencies 
 of the plasmonic modes ( i.e. , k,ii ) are20i.e . , 
 the well - known frequencies of the multipolar 
 plasmons of a spherical particle . from a practical point of 
 view , numerically integrating the eom eq 15 requires some care . here we exploit the velocity  verlet scheme 
 proposed in ref ( 53 ) , second - order accurate in the numerical integration step dt . the theory of td 
 ci in the presence of a solvent with a delayed response has been recently 
 developed . the equivalent td ci theory 
 for a molecule coupled to a metal np is very similar , and will be 
 only briefly summarized here . the state vector |(t) of the molecule satisfies the time - dependent 
 nonlinear schrdinger equation21approximated 
 solutions can be obtained by 
 writing |(t) as a linear combination 
 with time - dependent coefficients ci(t ) of a reference ground state |0 and a finite set of excited states |i22by using eq 22 , the time - dependent schrdinger equation , eq 21 , becomes23where the hamiltonian 
 matrix h has elements:24we choose a reference state given by the hartee fock 
 determinant |0 = |hf for the molecule 
 equilibrated with the np described as a perfect ( and charge neutral ) 
 conductor , and we use as the excited states |i ( with i > 0 ) those obtained from 
 a configuration interaction expansion limited to single excitations 
 ( cis ) . such cis excited states |i and the corresponding energies are obtained here by solving , 
 in the subspace of the single excited determinants |ia = |hf (  and  are electron creation 
 and annihilation operators , respectively ) , the time - independent schrdinger 
 equation for the molecular solute in the presence of the fixed hartee fock 
 polarization charges:25with this choice , the elements of 
 the hamiltonian 
 matrix in eq 2 become26where qpol(t ) , ij , and vij are defined by272829qpol(t ) in eq 27 and qref(t ) in eq 26 are obtained by the eom approach described 
 in the previous section . numerically , eq 23 is solved by a simple euler method at the 
 first order , using the same dt as for the apparent charge eoms . we close this section 
 by remarking that , within the present bem 
 approach , the electrostatic potentials vij in eq 26 have to be calculated only for points on the np surface . 
 in a fdtd approach , they would be needed on a volume including the 
 np , making the calculation rather cumbersome . the geometry 
 of the licn molecule used in the calculations is the one of ref ( 36 ) ( lic and cn bond lengths 
 of 1.949 and 1.147  , respectively ) . we have used a drude dielectric 
 function ( i.e. , 0 = 0 ) with parameters for silver : plasma frequency p = 0.332 au = 9.03 ev ( a = p2 ) and  = 1.515  10 au = 4.123  
 10 ev . no interband transition is included in 
 the dielectric constant ; therefore , the np absorption spectra are 
 not directly comparable to silver np experimental ones . the calculations 
 of the hf and cis states in the presence of the np , their energies 
 ( at frozen np dielectric response ) , the expectation values and transition 
 integrals of the dipole moment , and the electrostatic potential operators 
 are performed using the 6 - 31g(d ) basis set exploiting a locally modified version of the gamess code . only the first 15 excited states are kept in the hamiltonian . the 
 coupled propagation of the wave function of the molecule , the polarization , 
 and reflected field charges is performed using wave - t , a homemade 
 code . the time step of the propagation simulations is dt = 4.838 as ( 0.2 au ) . for the calculations with the spherical np , 
 240 tesseras were used ; in those with the elongated np , the number 
 of tesseras was 472 ( tests with 676 and 850 tesseras were also done ) . we could perform 10.9 ( 7.4 ) ps / day of simulation on a intel xeon e5 - 2650 
 core and 472 ( 676 ) tesseras ( no parallelization of the code was attempted ) . to test our approach , we present the results of the simulations 
 for the induced dipole of the np in two cases where an analytical 
 result is available , i.e. ( i ) a spherical np subject to a monochromatic 
 time - dependent electric field and ( ii ) a spherical np interacting 
 with a static dipole placed at a large distance . ( i ) the analytical 
 expression for the induced dipole moment of the np ( n ) generated by a monochromatic time - dependent electric field 
 is the following:30where a is the radius of 
 the np , einc is the complex amplitude 
 of the incident field ,  is a unit vector defining its 
 direction , and (inc ) is the dielectric function 
 evaluated at the frequency inc . in figure 1 we compare the profile of 
 n(t ) obtained from the 
 eom bem simulation31with the analytical 
 one , eq 30 , in the case 
 of a sinusoidal external 
 field with maximum amplitude of 10 au and a 2.5-nm - radius 
 np . si are the 
 positions of the tessera representative points . during the simulation , 
 the incident electric field is slowly turned on by modulating the 
 sinusoidal form with a linear function between t = 
 0 fs and t = 120 fs . the frequency of the external 
 field is inc = 0.26 au = 7.1 ev . simulation profiles of 
 the x - component of n for 
 a spherical np with a radius of 2.5 nm . the labels  sim  
 and  anl  refer to the results of the simulation and 
 to the analytical profile , eq 30 , respectively . ( ii ) when a spherical np is polarized by a static dipole 
 at large 
 distance , n may be evaluated by taking the t  0 limit in eq 30 and considering , as an incident field , the electric 
 field generated by the nonpolarizable dipole moment at the center 
 of the np . in a simulation we model such a limiting case by placing 
 the molecule far away from the np and by freezing its charge density 
 as it was in vacuum . the value of |n| computed 
 for a system s configuration where the center of the np is 
 placed at a distance of 25 nm from the center of charge of the molecule 
 is 9.4184  10 d. the direction of the molecular 
 dipole is perpendicular to the line joining the center of the molecule 
 and the np ( the np is the same used in the previous test ) . taking 
 into account that the magnitude of the dipole moment of licn in vacuum 
 is 9.425 d , the difference between the calculated and the analytical 
 values is less than 0.1% . these simple tests back up the numerical 
 accuracy of the model . 
 in the next section we discuss the results obtained from 
 eom bem td cis simulations of a licn  np system where the metal 
 np is build as the union of two intersecting spheres , each with radius 
 5 nm and having centers displaced 4 nm along the x direction . the licn molecule is also placed along x , with the n atom closest to the np and at 4  from its surface . the surface of the np is divided in tesseras that are smaller closer 
 to the molecule ( see figure 2 ) . we compute the frequency - dependent linear polarizability 
 tensors ( x ) from the fourier 
 transforms of the induced dipole signals for the molecule ( x = m ) , 
 the np ( x = n ) , and the entire system ( x = s ) . the elements of x may be written as follows32here j and k refer to two of the three directions in cartesian 
 space , einc , k( ) 
 is the component 
 of the fourier transform of the perturbing field along k , x , j(t ) = x , j(t )  x , j(0 ) is the component of the induced dipole 
 profile along j , and m is a damping 
 constant that allows modeling a finite lifetime for the excited states 
 ( m = 2000 au = 48.38 fs ) . a narrow gaussian pulse at t = 0 , mimicking a -pulse , 
 directed along the x axis is used to perturb the 
 system within the linear regime . the perturbing field has a width 
 of 48.38 as and a maximum intensity of 10 au . the imaginary part of x , xx( ) 
 is proportional to the absorption cross section . in figure 3 we compare such imaginary parts for the molecular polarizabilities 
 in vacuum , and close to the np . two simulations have been performed 
 to address the effect of the np polarization on the molecular properties , 
 one with the np polarization frozen at its equilibrium value before 
 the action of the perturbation ( qpol(t ) = qref(t ) = 0 ;  np frozen  in figure 3 ) , and one with the full propagation of both 
 the np and molecule electronic dynamics as detailed in section 2 (  full  in figure 3 ) . the effect of the equilibrium polarization 
 of the np manifests as a blue - shift on the molecule excitation energies 
 in the gas phase . this is reasonable , since the dipole moments in 
 the excited states corresponding to these excitations are lower than 
 in the ground state , and therefore , they are less stabilized by the 
 np presence . in addition to this , accounting for the full time - dependent 
 np polarization results in a further , but smaller , blue - shift of the 
 molecular excitations and a strong enhancement of the peak intensities 
 ( see the inset in figure 3 ) . the new peaks at a frequency lower than 7 ev are reminiscent 
 of the np absorption . they can be negative , as the physical requirement 
 of a positive absorption ( starting from the ground state ) refers to 
 the overall ( molecule + np ) system . in figure 4 we report the imaginary parts of the np 
 and system polarizabilities for the simulation with the full propagation 
 of the system degrees of freedom . because of the difference in size 
 between the np and the molecule , the responses have different orders 
 of magnitude and the effect of the molecule on the np response is 
 not detectable . side ( left ) and front ( right ) views of the np used in section 3.2 . the long axis of the np is directed 
 along x. the np surface is divided in 472 tesseras , 
 refined in the region closer to the molecule . imaginary part of m , xx plotted 
 as a function of frequency for ( i ) a simulation of the molecule in 
 vacuum ( vacuum ) , ( ii ) a simulation with the np polarization frozen 
 at its equilibrium value when no perturbation is acting on the system 
 ( np frozen ) , and ( iii ) a simulation with the full propagation of the 
 molecule and np degrees of freedom ( full  see section 2 ) . imaginary parts of s , xx ( s ) 
 and n , xx ( n ) plotted as a function 
 of frequency for a simulation where the full propagation of a molecule 
 and np degrees of freedom is performed ( see section 
 2 ) . finally in figure 5 we compare the profiles of the imaginary 
 part of n , xx for the nanoparticle 
 in vacuo calculated ( i ) using eq 32 and ( ii ) directly in 
 the frequency domain . we close this section by remarking that the results , in general , will 
 depend on the accuracy of the nanoparticle tessellation . this is discussed 
 in the supporting information , where it 
 is shown that increasing the number of tesseras from 472 to 676 can 
 shift the nanoparticle peaks by 0.10.2 ev and that peak intensities 
 can also change . in practical applications where specific experiments 
 are targeted , it is therefore necessary to check the convergence of 
 the numerical results with the tesselation . imaginary part of n , xx as a 
 function of the frequency calculated using eq 32 ( time ) and directly in the frequency domain 
 ( freq ) . in this work , we have presented a real - time 
 methodology to study 
 the electronic dynamics of a molecule close to a metal np , based on 
 a polyelectronic ( td ci ) description of the molecule and a eom bem 
 treatment of the molecule  metal np electromagnetic coupling 
 ( in the quasi - static limit ) . we have then applied this approach to 
 study the light absorption by a drude metal np plus molecule system . the present work represents an initial step to provide a comprehensive 
 modeling of the real - time dynamics of molecules close to metal nps , 
 that will require developments in various directions . for what regards 
 the molecule , the quality of the wave function approach used here 
 can be improved by obtaining the necessary quantities ( excitation 
 energies , dipole and electrostatic potential matrix elements ) via 
 methods more accurate than cis , that can be coded in richly featured 
 and flexible quantum - chemistry software such as gamess . the coupling 
 with rt - tddft , notwithstanding its current drawbacks related to the 
 adiabatic approximation , is also important to benefit from the advantageous 
 accuracy vs computational cost balance of such a method . moreover , 
 here , the molecular nuclei have been frozen , which is suitable if 
 only the electronic dynamics is of interest . the study of several 
 other phenomena , ranging from vibrational spectroscopy to photochemistry , 
 requires such an assumption to be relaxed . on the side of the 
 np description , there are some extensions that 
 are relatively straightforward , such as to consider more complex dielectric 
 functions that involve a sum of drude  lorentz terms . with this 
 kind of ( ) , one can reproduce quite faithfully empirical 
 permittivities that also account for interband transitions ( disregarded 
 here ) , as done in fdtd approaches . corrections for the limited mean 
 free - path of the electrons in the confining np can be included . np response ( that are included , for example , 
 in proper nonlocal dielectric functions ) may also be included at different levels in a ief bem approach . in perspective , a supermolecular description of the molecule + np 
 system may also be envisaged , where part of the np is treated quantum - mechanically 
 together with the molecule . here we have exploited the quasi - static approximation , that becomes 
 less and less accurate for increasing np size . bem can be extended to a full electromagnetic description 
 as well , that is still compatible with coupling with 
 a quantum - chemistry molecule . finally , 
 we have neglected here the possible presence of a solvent / dielectric 
 matrix , that can be included as an additional dielectric ( with its 
 own time - dependent response ) hosting the molecule in a cavity , as 
 done previously in the frequency domain . in conclusion , the development presented here represents a 
 promising 
 starting point to investigate the optical properties of molecules 
 close to metal nps , that is amenable to various developments currently 
 ongoing in our group .
the 
 optical properties of molecules close to plasmonic nanostructures 
 greatly differ from their isolated molecule counterparts . to theoretically 
 investigate such systems from a quantum - chemistry perspective , one 
 has to take into account that the plasmonic nanostructure ( e.g. , a 
 metal nanoparticle 
 np ) is often too large to be treated atomistically . 
 therefore , a multiscale description , where the molecule is treated 
 by an ab initio approach and the metal np by a lower level description , 
 is needed . here 
 we present an extension of one such multiscale model 
 [ corni , s. ; tomasi , j. j. 
 chem . 
 phys.2001 , 114 , 3739 ] , originally inspired by the polarizable 
 continuum model , to a real - time description of the electronic dynamics 
 of the molecule and of the np . 
 in particular , we adopt a time - dependent 
 configuration interaction ( td ci ) approach for the molecule , the metal 
 np is described as a continuous dielectric of complex shape characterized 
 by a drude  lorentz dielectric function , and the molecule 
 np 
 electromagnetic coupling is treated by an equation - of - motion ( eom ) 
 extension of the quasi - static boundary element method ( bem ) . 
 the model 
 includes the effects of both the mutual molecule 
 np time - dependent 
 polarization and the modification of the probing electromagnetic field 
 due to the plasmonic resonances of the np . 
 finally , such an approach 
 is applied to the investigation of the light absorption of a model 
 chromophore , licn , in the presence of a metal  np of complex 
 shape .