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Ultrafast dynamics of surfaceadsorbed conjugated molecules
S. Yu. Kotkov, V. N. Zadkov, B. A. Grishanin Department of Physics, Moscow State University, Moscow 119899, Russia

V. D. Vachev and I H. Frederick Department of Chemistry, University of Nevada, Reno, Nevada 89557-0020

ABSTRACT A detailed computer examination of the excited state dynami of stilbene, both isolated in the gas phase and physisorbed on an inert surface is presented. It is discussed how the surface affects stilbene's dynamics in comparison with the isolated molecule case.

1. INTRODUCTION
In many cases, the design of photochromic materials, organic conductors, and nano-switches centers upon a fundamentel understanding of conjugated ir-systems and their physical properties and chemical transformations. The present paper is focused on a detailed examination of the excited state dynamics of conjugated molecules, both isolated in the gas phase and physisorbed on an inert surface. By obtaining a fundamental understanding of the dynamical processes

such systems can undergo in both environments, we hope to gain insight into not only how desired isomerization channels might be enhanced and controlled, but also how a surface can influence a photoisomerization process. The general strategy used in all of our investigations can be outlined as follows. First, an empirical BornOppenheimer Potential Energy Surface (PES) is constructed for the isolated molecular system of interest using a combination of spectroscopic fItting techniques, ab initio information about the molecular structure, and standard molecular modeling force fields. If necessary, surfaces for both the ground electronic state and one more excited electronic states are constructed. The interaction of the system with a radiation field is then simulated to determine the non-stationary state that is prepared by an ultrafast (i. e. femtosecond) laser pulse using a semidassical algorithm developed previously.13 Finally, the molecular dynamics of that non-stationary state is determined numerically using classical molecular dynamics algorithms. As an extension of the approach we have successfully applied to the ultrafast dynamics of isolated photoexcited polyatomic molecules, we have also theoretically investigated optically driven nonthermal surface reactions. Here, we simulate a single molecule's dynamics on a surface, and focus on cases involving only "physical interaction? in the molecule--surface system, that is, when there is no chemisorption. In the case of- stilbene, for example, we model the molecule-surface interaction using only van der Waals.-type interactions. In this way, we can simply extend the molecular modeling empirical potential surfaces used previously by adding pairwise atom-atom interactions between the molecule and the atoms that constitute the surface. In the presence of an applied intense laser field, there also exists induced-dipole-image-dipole interaction between the molecules and the substrate.4 We treat these field-induced interactions as an "electromagnetic" interaction in the dynamics simulations. Again, because of the size of the system, extensions of our semiclassical expressions for ultrashort pulse excitation can be used to model this process and all dynamica can be simulated using the classical molecular dynamics method. In this work we are only concerned with the regular van der Waals interactions as perturbations on the isolated molecule, and answers are given to the following questions: (i) How do adsorbed molecule's spectra compare to the spectra obtained in supersonic jet experiments? (ii) What are the differences in adsorbed molecule's dynamics (isomerization time, IVR rates, etc.) in comparison with the isolated molecule's dynamics? To answer these questions, we considered a stilbene molecule on the surface of a graphite lattice. Neglecting collective interactions we represent the lattice potential as a sum of potentials due to individual C-atoms. To describe the molecule--lattice interaction we used the same force constants which were adopted earlier for stilbene Molecular Mechanics (MM) potentiaL3 Here we restrict the graphite lattice model to a single surface layer, in order to minimize the calculation time. After that we have investigated what initial equilibrium configurations of a molecule relative to

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the surface are possible. Next, for these equilibrium configurations we have calculated the absorption spectra of tran&stilbene on the surface and compared it with the one predicted for an isolated molecule within the same calculation scheme and the same MM parameters. Finally, we have performed a series of dynamics calculations and obtained dynamic trajectories both for an isolated and surface-adsorbed ci,-stilbene molecule excited with a 100 fs Gaussian laser pulse with 4000 cm1 excs vibrational energy.3 Here we are interestedjust in the cis-tranisomerization channel and do not take into accxunt the interaction responsible for CIS-DHP isomerization.3

2. EQUILIBRIUM STATE OF STILBENE ON A GRAPHITE LATTICE
Due to the assumption that the molecule of interest has no chemical bonds with the surface, we can reasonably describe their interaction potential with the well-known formula for van der Waals (nonbonded) interactions. These are calculated for all pairs of atoms (i, i) using a Hill type potential5 involving two parameters for each atom: one is the van der Waals' radius of the atom, and the other is an energy scale factor. The function representing the potential consists of attractive term varying as r6, which represents dipole/induced dipole interaction, and repulsive term which is exponential. A latent problem with this type of function is that at small atom distances the potential turns over and becomes strongly attractive. To prevent this from becoming a factor in the present study, especially in finding the equilibrium configuration of the molecule on the surface, an exponential repulsion term is fit to the potential function at the inflection point so that the potential and its first derivative are continuous
( I [--2.25/r + 8.28 x iO exp(--r/O.O736)J ,
r u=.:)14

if

r
(1)

V exp(--.kr),

otherwise.

Here I is proportional to the depth of the potential and depends on the identity of the two atoms; and ri = where s is sum of the van der Waals radii for atoms i and j, and r = r1 91. The total potential is
Utot = Urnoi + 111nt,

(2)

where Urnoi 15 juSt the MM potential of an isolated stilbene molecule including nonbonded interactions and U1,t is a molecule-lattice interaction potential introduced for each pair of atoms belonging to the molecule and the surface respectively with the use of Eq. (1). Both for Urnoi and U parameters we used the values obtained previously.3 There are no additional parameters except the geometrical size of the layer's cell. We used the computer program of Ref. 2 modified by changing the potential to the total one introduced by Eq. (2) for the PES of a surface adsorbed molecule. We begin our calculations with an investigation of the possible equilibrium states ofthe molecule on the lattice, with the molecule being in the ground electronic state. To obtain the equilibrium configurations we calculate dynamical trajectories in the lattice's potential and introduce velocity damping in the equations of motion. The initial conditions are chosen to correspond to the initial separation between a molecule and the surface 5 A. The molecule's potential energy depends most strongly on the orientation angle of the molecular plane with respect to the layer's plane. Three trajectories corresponding to the parallel (o 0°), perpendicular (4o 9O) and intermediate (4o 45°) initial orientation are presented in Fig. 1 through the time-potential energy dependences. In each case, the final states have nearly the same potential energy and correspond to the same equilibrium state that is characterized by a parallel orientation 4ј) = O. For 4o Qo orientations there exists a kind of intermediate equilibrium with non-zero angle 4 for which two major dynamical time scales exist, one corresponding to a movement perpendicular to the surface and another corresponding to rotation around the equilibrium parallel state. The direction of a molecule with respect to the axes of the surface's cell is also significant but, due to the relatively large dimensionality of stilbene with respect to the cell's period, the corresponding potential energy dependence is weak. Its minimization requires much more calculation time than we had and prevented us therefore from a complete minimization (in the minimization procedure we have used a damping time Tr = 1.0 Ps).

3. CALCULATION OF THE ABSORPTION SPECTRUM OF SURFACE-ADSORBED
cis-STILBENE
For systems with a few degrees of freedom an exact (numerically) fully quantum treatment is feasible. More complicated systems like a polyatomic molecule on surface require the introduction of statistical methods. Here we use the density

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I
I
0
2000 4000 6000

8O

Time, fs
Figure 1: Calculation of the equilibrium state of cis-stilbene molecule on the surface. Time dependence of the molecule's potential energy. Damping rate is equal to 1 ps, 4 is an orientation angle with respect to the surface.
matrix formalism69 which allQws the introduction of nonessential "bath" degrees of freedom, carrying out of thermal averagings and mixed quantum and classical description of different degrees of freedom. For example, the essential object in this study is the molecule and the surface is providing a "bath" of interactions. Utilizing the interaction representation7 for the molecular system interacting with a laser field, the density matrix of the excited state is given by1

i3 =

frj2

j

-- j dTldT2EL(Tl)E(T2) exp[--Я(t -- s)]j5('r) exp[7(t )1,

(3)

where we have used second order with respect to the field perturbation expansion and the Condon approximation for the electronic transition dipole moment, dee. In this equation EL(rk) is the complex wavefunction of the laser field,

'r='r2--r1;

s=('r2+ri)/2;

3(r)

=

exp(--7r/2) exp(7tgr/2)3' exp(7Igr/2) exp(--Я'r/2),

(4)

and 3gT S the density matrix of the ground equilibrium state with temperature T. When the evolution of the density matrix is performed for the time scales of interest we obtain the absorption spectrum by averaging the final density matrix. In addition we obtain the average values and the distribution of the coordinates and momenta which can be used for further MD simulations of the excited state dynamics. In order to obtain analytical results we further invoke the harmonic approximation for the molecule. If we consider a harmonic polyatomic molecule with two adiabatic electronic states Ig) and le) and N vibrational degrees of freedom, we can write the Hainiltonian (in the absence of an electromagnetic field and electronic relaxation) as 11 = Ig)fl(gI + ehwge + lie)(eI, (5) with

74=,;(j;2В;2_1),
and where

(6)

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Here, Wge S the electronic transition frequency between the lowest vibronic states of g) and je) (0-0 transition), and

we label ground-state quantities by a double prime and excited-state quantities by a single prime. In Eqs. (5,6) ' and ij denote the dimensionless normal mode momentum and position vectors, respectively, on the excited state. Likewise, f" and j" represent dimensionless normal mode momentum and position vectors on the ground state. These vectors can be related to the dimensioned Cartesian displacement and momentum coordinates, (r, p), using the normal mode transformation for mass-weighted coordinates on the ground state. This gives (in matrix notation)

p
where

..-,l

=.w .V.M I
1
ii--1/2

--1/2

h112

·p ,

q

-"

i1/2 =c; .V.M' ·r,
1 112

(7)

d' and M are diagonal matrices whose elements are the normal mode frequencies and atomic masses, respectively, and V is the diagonalizing unitary transformation matrix that relates the Cartesian displacements, r, to the mass-weighted normal mode coordinates, Q", that is,
Q"=V.M1'2.r ,

P"=VM"2p.

(8)

We discard the six zero-frequency normal modes arising from translation and rotation to obtain (3N 6) normal mode coordinates. In Eq. (6), S is the Dushinsky rotation matrix which allows the ground and excited state normal coordinates to be different. If the normal modes in the ground and the electronically excited states are identical, the Dushinsky transformation matrix is diagonal, that is,

sij

= ()

(9)

and the transformation between the normal coordinates is

Q'=Q"+D .
where

(10)

in Eq. (6) is the dimensionless displacement between the equilibrium configurations of the two electronic
I
1/2

states. Its components D, are re1ted to D, by

L1=(t)

D, .

(11)

With the harmonic Harniltonian defined with Eq. 5, Eq. 4 determines a generalized Gaussian density matrix and using standard techniques for calculation of averages, analytical expressions can be obtained for the quantities of interest. The absorption (excitation) or 0 dispersed fluorescence spectfa (0° denotes the vibrationless excited electronic state) of the molecule are calculated in the dipole and Condon approximation using the following formula

for the transition probability:'3

P() = (/4)

J drf(r) exp[i(ii. c&ge)rJ(r),

(12)

where f('r) = dsi4(s -- -i-/2)i4(s + 'r/2) is the laser pulse autocorrelation function; 11L = ELdge/h is the R.abi
frequency; x('r) is the linear response function given by'3
,, . --

f

PeTJ

--

det[sinh(hw"/kT)/(sis2)]
det1/2(ci/cd' + c2/cd)det1/2 (c1ci" + c2cd)

x exp[_DT (cud' + C2/d4/) . D],

(13)

s1 = sinh[cd'(h/kT -- iT)], = sinh(ЭiJr/2), c2 = coth(icdT/2). c1 = coth[cd'(h/kT -- ir)/2}, Here the matrices d' and ci are diagonal when the Dushinsky rotation matrix is also diagonal, in accordance with
Eq. (9). Eqs. (12,13) provide the quantum expression for the one-photon transition probability in terms of the ground
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SPIE


and excited state frequency matrices, the displacements of the two surfaces andthe temperature, which is the complete set of parameters characterizing a harmonic molecule. The general procedure for computing the electronic.vibrational spectra is as follows. First, the ground and excited states of the molecule are defined in the Born-Oppenheimer approximation using empirical MM approach and Eq. 2. The frequency matrices w" and d, and the vector of displacements D are calculated using standard routines for normal mode analysis. Then, the temperature is given and the function x(r)is calculated using Eq. (13) for N points (N is set to an exact power of 2 for the use of a FFT routine--typically N = 8192) with time increments ir = [(N -- where is the spectral resolution of the calculation. A standard FFT routine is used to obtain the absorption spectrum via Eq. (12). The calculated results for the absorption spectra obtained both for isolated and surface-adsorbed tiuna-stilbene molecule are presented in Fig. 2. The spectrum of the surface-adsorbed molecule at T=5° K is as sharp as the spectrum of isolated molecule. We investigated the structure of the spectrum as a function of the distance between the surface and the molecule introducing a scaling coefficient e. This provides us with the correlation between the lines of the isolated and surface-adsorbed species. The equilibrium structure of a molecule on the surface, obtained in Sec. 3, is described by = 1 and the case of infinitely large distance (isolated molecule) between a molecule and the surface is described by e =0. The correspondence between the spectral lines of isolated and surface-adsorbed trans-stilbene is also presented in Fig. 2. It shows that the corresponding frequencies of an adsorbed molecule are shifted to the violet edge due to the additional interaction with the surface.

w

.--

0
0

0
0
0
500
1000 1500

2000

o)-ci, cni'
Figure 2: Calculated absorption spectra of (a) isolated and (b) surface-adsorbed t,unsstilbene.

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4. DYNAMICS OF PHOTOEXCITED SURFACE-ADSORBED CL-STEBENE
The excited state dynamics of ciasti1bene was modeled using an ensemble of classical trajectories. For the averaged normal coordinates after the excitation, we have

= Q + JP(T)LQ(T)dT/P(wL)i

(14)

where Q is the minimum energy configuration on the excited electronic state je); p(-r) is the time-density expression,

dP()/dr (see Eq. (12)); and AQ(r) is the (dynamical) displacement vector corresponding to time interval 'r and

given by'3

iQ(r) = TXQ/5(T) _1 1s2'(ci/w" + c2/w')1D .

(15)

On average the momenta are not changed during the excitation because the Harniltonians flg and 7-1 are displaced from each other only in coordinate space, and not in momentum space. The main innovation presented here is the use of the results for harmonic potentials to generate a method for creating quasiclassical initial conditions that simulate the nonstationary state prepared by an ultrashort pulse for a molecule at finite (non-zero) temperature. The initial conditions for the trajectory calculations were chosen to reflect the quantum state prepared by excitation of a vibrationally cold harmonic molecule using an ultrashort laser pulse. Using the empirical PES of the surface adsorbed molecule for the ground and excited states, the frequency matrices and displacements were calculated for all 72 normal modes. Then excitation with a 100 fs Gaussian laser pulse with 4000 cm1 excess vibrational energy was modeled in the way similar to Ref. 3. Here we present the calculation results for the dynami on the excited electronic surface. Typical trajectories are presented in Fig. 3. They show that an adsorbed molecule moves to the twisted state about 2 times faster than an isolated one. The corresponding average time to achieve the 90° twisted configuration is rp '-'14O is; whereas, in the case of an isolated molecule it is s28O is. Thus, under similar excitation conditions, the surface--molecule interaction accelerates the isomerization process relative to that in the isolated molecule. Finally, the dynarnic of one of the two phenyl rings' twist angles q$(CphlCeCeCph2) iS presented in Fig. 3, (c). As in an isolated molecule the phenyl ring undergoes torsional rotation, however, in adsorbed stilbene it undergoes additional adjustments so as to achieve a final state nearly parallel to the surface.

5. CONCLUSIONS
Using harmonic approximation of the PES and the calculation methods of Refs. (1--3), we have calculated the absorption spectra and photoinduced dynamics of surface-adsorbed tinns.stilbene molecule. Although just the simplest model of a molecule-surface interaction with a graphite lattice was used, we expect that the correspondence between the spectra lines of an isolated molecule and adsorbed one, revealed in our calculations, is qualitatively cxrrect. Using the MM method we have also calculated the isomerization dynamics of a photoexcited surface-adsorbed cis-stilbene molecule and discovered that it proceeds ''2 times faster than in case of isolated stilbene. The average time for the transition to the 900 twisted configuration is equal to '14O fs. An analysis of the calculated trajectories shows that the influence of a graphite lattice does not relax the ability to undergo cis-tmns photoisomerization. We are also able now to modify our calculations in order to take into account specific lattice vibrations. That will enable us to describe dynamical interplay between a molecule and the lattice and provide the calculated spectra including the influence of interaction of molecule vibrations with surface phonons. The computer simulation undertaken in this work shows that such a generalization is possible with use of the available cxmputer resources.

6. ACKNOWLEDGMENTS
This work was partially supported by the NATO grant No. HTECH.CRG 941231 (to J.H.F.) and the 1SF grants No. MS9000 and MS9300 (to V.N.Z).

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I 60

(a)

00 0 0

120

Isolated molecule Molecule on a surface

0 0
0

80

40

0
0 200 400 600 800 1000

time, fs
(I)

0,

0) 0, ·0

0
CS

time, fs
14

C-)

time, fs
Figure 3: Time dependence of (a) torsional angle O(CphCeCeCph), (b) bending angle a(C5C6C7) and (c) phenyl twist angle 4(CphlCeCeCph2) calculated along a representative single MD trajectory cis-stilbene (±1800 angles are geometreically identical).

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REFERENCES
1. B.A.Grisharnn, V.D.Vachev, V.N.Zadkov, Mol. Cryst. Liq. Cryst., Vol. 3, pp.
375--386

(1992).

2. V.D.Vachev, J.H.Frederick, B.A.Grishanin, V.N.Zadkov, N.I.Koroteev, Chem. Phys. Lett., Vol. 215, pp. 306-- 314 (1993).

3. V. D. Vachev, J. H. Frederick, B. A. Grishanin, V. N. Zadkov, N. I. Koroteev, J. Phys. Chem., Vol. 99,
pp. 5247--5263 (1995).

4. P. Ye, Y. R. Shen, Phys. Rev., Vol. B28, No. 8, pp.4288--4294 (1983).

5. T. L. Hill, J. Chem. Phys., Vol. 16, pp. 399-404 (1948).
6. U. Fano, Rev. Mod. Phys., Vol. 29, pp. 74--93 (1957).
7. R. P. Feynman, Phys. Rev., Vol. 84, pp. 108--128 (1951).

8. L. E. Fried, S. Mukamel, Adv. Chem. Phys., Vol. 84, pp.

435--516

(1993).

9. S. Mukamel, Annu. Rev. Phys. Chem., Vol. 41, pp.

647--681

(1990).

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