Документ взят из кэша поисковой машины. Адрес оригинального документа : http://qilab.phys.msu.ru/papers/SPIE-1921-391-401(1993).pdf Дата изменения: Mon Feb 4 18:39:33 2008 Дата индексирования: Mon Oct 1 20:00:49 2012 Кодировка:

MD Investigations of Photoinduced Transformations in Organic Molecules

Boris A. Grishanin, Valentin D. Vahev, and Victor N. Zadkov International Laser Center, Moscow State University, 1 19899 Moscow, Russia

1. ABSTRACT
A computer simulation procedure is developed for modeling intramolecular dynamics in polyatomic molecules. Electronic-vibrational excitation by ultrashort laser pulses (20 fs - 1 ps) is treated explicitly using quantum theory in harmonic approximation. MD simulation is used for studying the excited state dynamics. Stilbene photoinduced isomerization is modeled. Model potential energy surfaces (PES) for the ground and first excited singlet states are obtained using experimental absorption spectra in supersonic jet. Using a symmetrical along the torsional coordinate PES, it is shown that cis-stilbene undergoes the first stage of the isomerization reaction, i. e. transition to the twisted configuration, much faster than Lrans-stilbene, only due to the specific conformational properties.

2. INTRODUCTION
Many important processes in polyatomic molecules take place in excited electronic states or use them as transition states. Between these are photoinduced isomerization of retinal systems and photosynthetic bacteria, electron transfer in biological, interfacial, or electrochemical systems, vibrational relaxation in liquids, and photodissociation. These processes occur typically on pico- and subpicosecond timescales, and recent advances in generation of ultrashort and broadly tunable laser pulses are highly promising for experimental studies of the basic mechanisms realized in Nature.'4 Such investigations are important also in the search of new materials for nonlinear optics, electro-optics and molecular electronics. The complexity of the objects under consideration, however, makes difficult a direct interpretation of the data obtained from different laser spectroscopy methods in both time and frequency domains. Thus, appropriate approximations and computer simulation methods are necessary.
Molecular Dynamics (MD) is a computer-based technique for modeling gases, liquids and solids on microscopic scales of distance and time, and is therefore an ideal technique for studying molecular behavior in many physical processes.57 The method is based on the assumption that atomic motions are governed by classical mechanics provided some appropriate multidimensional force-field is used. Limitations of the method are well known. A fundamental one results from the basic assumptions of the method, namely, quantum-mechanical behavior is neglected and a single potential energy surface is assumed to govern the motion. The quantum nature of vibrational and electronic motion, however, is important and must generally be accounted for. Other problems are connected with practical difficulties in constructing accurate force-field, including large number of atoms, integrating over long times, or achieving accurate statistical sampling. All of these depend on the efficiency of the computational procedure and models used. A general formulation of the problem and the approach used can be understood from Figure 1. A molecule

being initially in a ground electronic state 1) after irradiation is excited to an upper electronic level 2). The initial state of the molecule after excitation depends on the two potential energy surfaces (PES) and laser pulse characteristics such as laser frequency, time duration and coherence length. The laser pulse duration r should be
compared with the vibrational period r of the molecule. For instance, ultrashort laser pulse, r, <
0-8194-11 54-X/93/$4.00

SPIE Vol. 1921 Laser Spectroscopy of Biomolecules (1992)! 391


initial state distributioi

12>

L) 1>
initial ground state distribution

x

Figure 1. MD simulation of electronically excited polyatomic molecules. The excitation by ultrashort laser pulses is treated explicitly, using quantum harmonic theory. MD simulation is used for modeling the excited state dynamics.

Most often the experimental situation corresponds to the intermediate case with vibrational frequencies in the range of 20 cm1--3500 cm1 and excitation by laser pulse in the range of 20 fs1 ps. Elsewhere,9"° we
have considered this intermediate case and presented a quantum harmonic theory of the one-photon electronicvibrational excitation. The basic results of this previous study are as follows. The transition probability is given
by

P(WL) =

(/4)

f f(r) exp[i(WL _ wi2)r](r)dr 7

(1)

where f(r) = u(s -- T/2)tL(S + r/2)ds is the laser pulse autocorrelation function, Q = ELd12/h is the Rabi frequency, w12 is the frequency of the electronic transition; x(r) is analytical function of the frequency matrices w1 and w2, the deviations L ofthe energy minima along each vibrational coordinate, and temperature (see Eqs. (5--6) in Ref. 10). After averaging the displacements of nuclei coordinates over the laser pulse one obtains
Xq X2 + fP(T)X(T)dT/P(WL)
,

f

(2)

where Xq 5 a 3N-dimensional vector of the averaged coordinates after excitation; x2 is 3N-coordinate vector of the energy minima point of 12), p(T) is the time density of transition probability dP(WL)/dT (see Eq. (1)), zx(T) is the displacement relative to x2 at the moment of time r (see Eqs. (7--8) in Ref. 10). For the average momenta
0. The absorption (excitation) spectrum or 00 dispersed fluorescence spectrum (00 denotes the vibrationless excited electronic state) are calculated using Eq. (1), in which the integration is carried over a time period larger than all vibrational periods. In Sec. 3 we use the available absorption spectrum of stilbene molecule obtained in supersonic jets for precise determination of characteristics of 12 active normal modes (we use only modes well identified in the experimental spectrum). In doing so the PES are determined in harmonic approximation which may be useful in aJ)J)licatiomIs such a.s ultrafast excitation or early stage dynamics.
we have Pq

392 / SPIE Vol. 1921 Laser Spectroscopy of Biomolecules (1992)


In Sec. 4 the PES are determined in a more general way by Molecular Mechanics (MM) potential energy functions. The correspondent parameters are calculated so as to ensure good agreement between calculated and experimental spectra. In Sec. 5 MD simulation results on the excited state PES (in the full 3N-dimensional coordinate space) are reported. Using Eq. (2), MD trajectories are calculated with initial conditions given by the
centers of weight of the wave packet. The dynamical behavior of Lrans-- and cis--stilbene are compared.

3. SPECTRA CALCULATION AND NORMAL MODES CHARACTERISTICS
In harmonic approximation the molecule is considered as a set of 3N --6 independent harmonic oscillators or normal modes (N is the number ofatoms). Ifone neglects anharmonicities and Dushinski rotation each vibrational degree of freedom can be described by its frequencies in the ground and excited state, and by the displacement z between

the minima of the two states. Actually, in the absorption spectrum only a small number of modes with sufficient values of L appear with sufficient intensity and are usually called optically active modes.
Using Eq. (1), Eqs. (5--6) in Ref. 10 and the developed computer procedure we simulate irans-stilbene supersonic

j(t absorption spectrum using the characteristics of 12 optically active normal modes. Their frequencies in the ground and first excited singlet state are known from supersonic-jets experimental spectra (see Tables 2 and 3 in Ref. 11). The simulation consists in varying the displacements along each mode until the relevant calculated intensities agree well with the experimentally obtained ones. The final result is presented in Figure 2 and Table 1. The simulation is straightforward, not surprisingly as the normal modes are independent, and the precision of the calculated characteristics is mainly determined by the precision of the experimental spectrum. This is also due to the effectiveness of the computational procedure allowing for a large number of iterations. A spectrum calculation takes of about 4 mm with spectral resolution of 1 crn on a 33 MHz i486-based computer. This is 3N -- 6 dimensional calculation (N = 26), though for only 12 modes 0. In a similar calculation Shan et al determined the characteristics of 17 anthracene modes,12 using a more general but not so efficient computational procedure. The obtained normal mode characteristics may be used for constructing the molecular Hamiltonian in applications where the harmonic approximation is valid, for instance in consideration of ultra.short pulsed laser excitation and early stage dynamics.

0

0

0

6

500 iobo 1560 WLWOo (cm-i)

2000

Figure 2. The absorption spectrum of jet-:ooled trans-stilbene molecule calculated using 12 active modes (see Table 1). The calculation was made using Eq. (1) (see Eqs. (5-6) in
Ref. 10)

SPIE Vol. 1921 Laser Spectroscopy of Biomolecules (1992) / 393


Table 1. \'ibrational frequencies and dimentionless displacements of 12 active modes of trarzs-stilbcnc. is the calculated absorption intensity. The corresponding experimental values (see Table 2 in Ref. 11) are given iii Parentheses.

I

w0, crn1
0 204 290 624 870 1006 1072 1031 1340 1495 1584 1607 1654

w1, cin1
0 197.6

L
1.21

I, a. u.
78.5 (79) 30.0 (30) 10.0 (10) 16.9 (17) 25.8 (26) 4.9 (5) 10.3 (10.6) 6.8 (7.5) 1.8 (1.7) 3.0 (3.5) 1.7 (1.9) 2.2 (2.3)

280.3
590.7 850

972.7 1069.8 1249.3 1332.4 1464 1548.4 1553 1637.8

0.75 0.32 0.56 0.70 0.26 0.38 0.34 0.12 0.20 0.16 0.17

4. USING OF MOLECULAR MECHANICS METHOD FOR CALCULATION OF THE GROUND AND EXCITED STATES' POTENTIAL ENERGY SURFACES
In many applications harmonic approximation is not adequate and a more general determination of the PES is necessary. As an example, in this section we determine the PES of the ground and the electronically excited states of stilbene molecule by means of the Molecular Mechanics (MM) potential energy functions. MM functions have been developed and parameterized on the basis of structural and thermodynamic experimental data. In this work, with the example of stilbene molecule, we parameterize our force field using the absorption spectrum obtained in
supersonic jet experiments.11 We use the following MM potential energy functions:'3

U(rl,...,rN)=Ub+Uva+Utor+Uvw,

(3)

where Ub, Uva, and Utor are contributions due to deviations of chemical bonds lengths, valence and torsional (dihedral) angles from their equilibrium values, respectively, U being the contribution due to Van-der-Waals interactions.
Deformations of chemical bonds lead to increase of the energy:

Ub 0.5>kb(b

-- b0)2 ,

(4)

where the sum is taken over all bonds. For every bond (i,j) its equilibrium length b0 and stretching force constant -- i is the current bond length. kb are known; b = The deviations of valence angles from their equilibrium values coo lead to the following increase in energy:

Uva0.5koo)2 ,
where are the beiicling angle force constants, and the sum is taken over all valence angles. 1h1( potelitials of (lihedral (torsional) angles 0 are taken in tiLe following form:
394 1 SPIE Vol. 1 92 1 Laser Spectroscopy of Biomolecules (1992)

(5)


UtorO.5>V9[1_COS(flO)J .

(6)

Here for every kind of torsional angles one has to set the values of force constant V0 and potential multiplicity n. Van-der-Waals (nonbonded) interactions are calculated for all pairs of atoms (ii) which do not belong to the same chemical bond or the same valence angle:

Uvw = >i: f[--2.25/R6 + 8.28 x iO exp(--R/O0736)} ,
and

(7)

where I is the force constant; R r/s, s is sum of Van-der-Waals radii determined by the types of atoms i, j,
bond lengths, valence angles and Van-der-Waals radii are well known'3 and may be used directly. The transferability of the force constants has been proved for a large number of molecules. For dynamic investigations, however, the force constants should be adjusted additionally, as well as the equilibrium bond lengths and valence angles of the excited molecule. Using the standard technique we calculate the frequency matrix of the ground state and vary the force constants of the MM PES (4--7) until a good fit to the available experimental data is obtained. As a result we can characterize entirely the ground PES and with the finally accepted parameters the calculated frequencies correspond to the experimental values (see Tables 1--3 in Ref. 11) with deviations less than

r=J All the equilibrium
--

10 cm1.
For the excited state we accept the same potential energy functions as that for the ground state and look for the changes of the parameters accounting for the absorption and 00 dispersed fluorescence spectrum. Spectra are calculated using Eq. (1). rFle main features of the spectra are determined by the normal modes deviations of the two terms La = (x2 -- x1) and the differences of the frequency matrices and w2 or, correspondingly, by the changes of the parameters of the MM PES. Spectra are most sensitive to changes in the equilibrium bond lengths. As a rule, bond lengths increase in an excited state. However, in stilbene, delocalization of the double bond results in stretching of the ethylene bond CeCe and compression of Cephflyl bond in the excited state compared to their lengths in the ground state. In our calculations we also find out that changes in bond lengths larger then 0.01 A lead to highly congested unresolved spectra, while it is known from the experiment that the spectra consist of well-resolved lines. Consequently, we used an iterative procedure for calculating the parameters of the excited PES, varying their values in thus obtained limits. The finally accepted parameters are given in Table 2 and the calculated spectrum is shown in Figure 3. It fits well the experimental data from Ref. 11, showing the same trends for the dominant peaks and a similar background.

100

0
0

75

25
0

_____________________________
0

500

1000
.41QQ

1500

2000

( --4-"L

(Cm-I)

Figure 3. The calculated absorption spectrum of jet-cooled trans-stilbene. The calculation was made using Eq. (1) and potential energy surfaces determined by Molecular Mechanics
method using Eqs. (4---7) and parameters given in 'Fable 2; woo is the vibrationless electronic transition frequency.

SPIE Vol. 1921 Laser Spectroscopy of Biomolecules (1992) / 395


Table 2. Parameters of MM PES (see Eqs. . Figure 3.

(4--7))

used in calculation of the absorption spectrum presented in

Parameters for bond stretching potentials

Ground state
Bond

Excited state
b0

c--c C--H Ce Ce

CCe C--Il

kb (kcal/rnol x A2) 993.7 725.6 1150.0 818.0 725.6

k
(kcal/mol x A2 )

b
(A)
1.397 1.113 1.343 1.451 1.114

(A)
1.397 1.113 1.338 1.458 1.113

893.0 725.0 750.0 1100.0 720.0

Parameters for angle deformation potentials

Ground state
Angle
Wo

Excited state
(deg)
120 120 120 120 120

C--C--C
C--

C--C--H

CCeC C--
Ce H -- Ce

C

--

Ce

Ce Ce

(kcal/mol x deg2 ) 0.0016 0.0014 0.0010 0.0012 0.0014 0.0015

k (kcal/mol x deg2 ) 0.0013 0.0011 0.0008

(deg)
120.1 120.4 121.3 120.0 121.7 120.8

00010
0.0008 0.0009

120

Parameters for torsional potentials

Ground state
Bond
k9

Excited state

n

k

n
-2

C--

CCe

C

(kcal/mol)
3.0 3.0

-2
-1

(kcal/mol) 3.0 3.1

Parameters for Van-der-\Vaals potentials

I
Atom(s)
C--C C--H H--il

Rd
(A)

(kcal/mol)
0.107 0.067 0.042

-- --
--

C
II

-- --

1.7 1.2

396 1 SPIE Vol. 1 92 1 Laser Spectroscopy of Biomolecules (1992)


5. MD SIMULATIONS OF EXCITED STATE DYNAMICS

5.1. General scheme
.A general scheme of the computer experiments which are possible with the developed simulation programs is presented in Figure 4. Using a standard MM program or self-made minimization procedure and the expression for the force field one obtains the equilibrium molecular structure. Then, as it has been described in Sect. 4, using Eq. (1) it is possible to calculate the force field parameters in accordance with the available experimental data. We note, however, that the computer simulation is not straightforward. The spectrum is determined by the characteristics of the normal modes (see Sect. 3) while in the simulation one varies the force field parameters. For a certain force field it may be not possible to obtain appropriate parameters.
Molecular Structure

MM Potential Energy Functions and Parameters

4

Absorption/Emission Spectra Calculations

I
Comparison with Experimental Data
I

Potential Energy Surfaces

of the Ground and Excited States
Simulation of Excitation by Ultrashort Laser Pulse: Characteristics of the Initial Excited State (excitation energy distribution between normal modes; average coordinate values and delocalization)

MD Trajectories: X(t), V(t)

]

I

Emode(t) in the initial basis

Fourier Spectra of Emode(t)

Figure 4. Gcnera scheme of computer experiments on photoinduced excited statedynamics.

having determined the PES of the ground and excited states one uses the standard technique for obtaining
the cigenvalues and vectors for the matrices of the potential energy second derivatives. The eigeiivalues determine the frequency matrices, while the eigen vectors determine the basis for transformation of Cartesian coordinates
SPIE Vol. 1921 Laser Spectroscopy of Biomo!ecules (1992) / 397


to normal coordinates. Using this initial basis and calculated MD trajectories it is possible to monitor the time evolution of the energy in all vibrational modes. The Fourier spectra of these time-dependencies reveal the typical frequencies of the energy exchange between the normal modes. For calculating MD trajectories in the excited state the initial coordinates should be determined by using the calculated average (over the excitation pulse duration) coordinates (Eq.(2)) and their delocalization ztx (Eq. (8) in Ref. 10). We have used this procedure for modeling ultrashort pulsed laser excitation (a number of modes with sufficient L-s excited simultaneously) or SVL excitation and study of the processes of intramolecular vibrational energy
redistribution (IVR) in anthracene (C14H10) and p-difluorobenzene (C6F2H4).'4

5.2. MD study of the photoinduced stilbene isomerization
Stilbene (1,2-diphenylethylene) has been studied extensively as a model system for isomerization dynamics. The two conformers, ft'ans and cis, are divided by a 46 kcalxmol1 potential barrier in the ground electronic state. In the first excited singlet state, however, only a small barrier of about 3.3 kcalxmol' is known to exist (as found from supersonic jet experiments) , not far away along the torsional coordinate. Ground state equilibrium geometries of the two conformers are shown in Figure 5, and the torsional dependences for the ground and excited states are shown in Figure 6. Typical isomerization times vary from 200 ps to ' 10 ps in vapors and different solvents, depending, also, on the excitation wavelength. The times of cis-stilbene isomerization are much less (of about 1 -- 2 ps) and using of a barrierless PES or very small barrier to isomerization is accepted.'518 The information deduced from experiments is, however, related to an effective PES, because after a certain amount of energy is transferred to the molecule, the latter undergoes the transition. Here we will use the MM PES determined in Sec. 4. The torsional dependence (see Eq. (6)) along the C6C7C8C9 torsional angle in this model would coincide with a quantum chemical calculation in which only this angle is varied, all other parameters being constant. Performing the calculation described in Sec. 4 we ensure that the harmonic

part of our PES is in accordance with the experimental data. The anharmonic part of the potentials may be proved only by means of explicit dynamic calculations. We point out, however, that the anharmonic part of the potential is not determined only by Eqs. (6--7). Although, the other two potentials, Eqs. (4--5) are a harmonic approximation with respect to internal coordinates, they contribute to anharmonic terms due to the nonlinear relation between internal and normal coordinates. An estimation using 3-th and 4-th order derivation matrices shows a reasonable anharmonic part of the potentials. In previous studies'9 we found that in the isomerization
reaction only small changes of the bond lengths (less than 5 %) and of the valence angles (less than 8 %) occur. Consequently, a reasonable model is to use the calculated parameters for the whole time of the reaction and to determine additionally only the energy dependence on the torsional coordinate. We used the following expression for ethylenic bond contribution in the excited PES (see Figure 6):
Ueth
where 0 is the torsional 00 = 90° . Parameters Vi
V1 sin2(20) -- V2 cos2(O -- Oo)
,

(8)

angle corresponding to twisting of the molecule around the double ethylenic bond, and and V2 determine the local barrier of isomerization (region A in Figure 6) and the deeper potential well around the twisted geometry (region B in Figure 6). We use V2 = 8 kcalx mol ' and different values of V1 in this way modeling different values of the local barrier E1 and its position along the torsional coordinate Oi (see Figure 6b). This simple analytical function enables for modeling of a barrierless potential (with V1 =0), a fiat local potential (for instance, with V1 = 2 kcalxmol' the potential is fiat with accuracy of 0.001 kcalxmol' over 8° , see Table 3), and with small local barrier (see Figure 6b and Table 3). To perform a MD study of the excited state dynamics we simulate molecule excitation by ultrashort 40 fs laser pulse with frequency exceeding the frequency of the vibrationless transition by 3000 cm . Using Eq. (2) we calculated the coordinates averaged over the time of excitation and use them as a starting point for the MD trajectory. For integration of the equations of motion we use 4-tb order Runge-Kutta algorithm with adaptive stepsize control ensuring conservation of the total energy within an accuracy of 2 %. Along the obtained MDtrajectories we calculate the torsional angle (C6C7C8C9). Typical dependencies of the torsional angle on time are shown in Figure 7 for the two conformers. One and the same PES determined by Eqs. (3--8) was used, under one and the same excitation. Nevertheless, the dynamic behavior of the two conformers is different. The cis-stilbene molecule undergoes transition to the twisted conformation much faster than irans-stilbene. The results for different values of the local barrier and its position along the torsional coordinate are shown in Table 3 (all other parameters

398

/ SPIE Vol. 1921 Laser Spectroscopy of Biomolecules (1992)


of the PES retained values given in Table 2). Most likely, the different dynamic behavior is due to the strong
Van-der-Waals interactions between atoms C6, C14, H15, and 1121 in cis-stilbene (see Figure 5).

Figure 5. Ground state equilibrium geometries of travis- (left) and cis-stilbene (right).

100 0
C)

(a)

A

B 94 92
E1

(b)

80 60 40 20

--

88
84

C)

0 0 45 90

torsional angle(degr.)

135 180

0

i9

60

120

180

Torsional angle, degrees

Figure 6. The potential energy surfaces for the ground and excited electronic states of stilbene as a function of ethylene torsional coordinate (a) and the torsional potential for the excited state (b, see Eq. (8)). The local barrier E1 and its position 9 along the torsional angle are determined by parameters Vj and V in Eq. (8).

6. CONCLUSION
Frequency- and time-resolved absorption/emission spectra recorded in supersonic jets contain a large amount of information about the potential energy surfaces of the ground and electronically excited states, and about the
purely intramolecular photoinduced dynamics. Previously, using the first order perturbation theory for the quantum density matrix and local quadratic approximation of the PES near the ground state equilibrium coordinates we have found out exact expression for the one-photon quantum transition probability P(w), giving its dependence on the frequency matrices and the normal modes' displacements of the both electronic terms (see Eq. (1)). If, then, one uses any appropriate way of determining the PES, spectra calculation ba.sed on these equations can be used for adjusting the parameters of the PES. Otherwise, ifonly experimental spectra are available, the frequency matrices are determined to some extent and the dimensionless normal modes displacements can be calculated in a computer simulation (Sec. 4). We determined the PES by means of the MM potential energy functions. They are relatively siInI)le and widely used in structural studies of organic molecules. \\Te have shown that the MM potential energy

SPIE Vol. 1921 Laser Spectroscopy of Biomolecules (1992) / 399


functions can also be used successfully for dynamical studies and some of the parameters can be determined. After the PES or equivalently (in harmonic approximation) the frequency matrices and the dimensionless displacements of normal modes are determined, some characteristics of the excited state can be calculated and used for an accurate MD or wave packet analysis of the molecule's dynamics after excitation. As a first guess, the coordinates Xq averaged over the pulse duration (see Eq. (2)) may be used as initial conditions for the equations excitation should be done.
120
t,.J

of motion. For a more precise quantitative results, a statistical averaging of the delocalization x during the

C)

(a)

C) C)

170 150 130 110 90 70

(b)

C) C)

100

tO
C)

C)

80 60 40
20

C)

tO

tO
CC

a
CC
CO

cC

a

0

a 0
CIC

0

0

0

0

1

2

3

4

5

0

100

200

300

time, ps

time, fs

Figure 7. Typical dependences on time of the torsional angle C6C7C8C9 (see Figure 5), calculated along MD
trajectories for trczrzs--stilbene (a) and cis-stilbene (b). The potential energy surfaces are determined by Eqs. (3--8) and Table 2. In Eq. (8) V1 = 2.9 kcalxmol' , V2 = 8 kcalxmol1 . The initial coordinates for MD trajectories are calculated using Eq. (2), simulating molecule excitation by 40 fs Gaussian laser pulse with excess vibrational energy

E = 3000 cm1.
Table 3. Trans. and cis-stilbene dynamics on the excited PES (3N-dimensional). The time for reaching the twisted conformation depends on the parameters of the ethylene torsional potential
(see Eq. (8)). All other parameters, Eqs. (4--7), are kept as in Table 2.

Torsional potential parameters
V1 V2
E1

stilbene

trans
(kcal/mol)
0 2

cis
(fs)

(kcal/mol)
8

(degr.)

(kcal/mol)

'rgc (fs)

2.5 2.8
2.9 3.1 3.3 3.5

8 8
8 8
8 8 8

0.000 8.667 20.000 23.333
24.667
26.00

0.00 0.00 0.10

112

37 52 65 78
86

0.23
0.28 0.39 0.51

302 1087 3282
4221

6889
10554
15318

102 189
1889

27.333 28.667

0.64

We have presented a general scheme of the computer experiments, which can made with the developed molecular sinitilation )aCkageS (see Sec. 5.1). Our results on the excited state dynamics of stilbene show that the (lilferent dynamic behavior of the Iraus-- and cs--stilbene can be accounted for by the specific conformational interactions 400
/ SPIE Vol. 1921 Laser Spectroscopy of Biomolecules (1992)


rather than by an asymmetry of the PES along the torsional coordinate.

7. ACKNOWLEDGEMENTS
We wish to express our gratitude to the late Professor Sergei Akhmanov who initiated this work, for his support and valuable discussions. We are grateful to Dr. A. Makarov and Prof. N. Koroteev for many helpful and stimulating discussions.

8. REFERENCES
1. Akhmanov S. A., Vysloukh V. A., Chirkin A. S., Opiics offemiosecond laser pulses, AlP, 1992. 2. Mathies R. A., Cruz C. H. B., Pollard W. T., Shank C. V., "Direct observation of the femtosecond excited state cis-irans isomerization in rhodopsin" , Science, 240, pp. 777--780, 1988.

3. Dexheimer S. L., Wang Q.,
61--66, 1992.
4.

Peteanu

L. A., Pollard W. T., Mathies R. A., Shank C. V., "Femtosecond

impulsive excitation on nonstationary vibrational states in bacteriorhodopsin" ,Chem. Phys. Lett. , 188, pp. Schoenlein A. M., Peteanu L. A., Mathies R. A., Shank C. V., Science, 254, p. 3412, 1991. 5. Molecular dynamics simulations of staisiical mechanical systems, N. Holland, Amsterdam, 1986. 6. Levine R. D., Bernstein R. B., Molecular reaciion dynamics and chemical reaciviiy, Oxford Univ. Press,
1987.
7.

8.
9.
10.
11.

12.

13.

Compuier simulaiion siudies in Condensed Mafler Physics, Landau D. P., Mon K. K., and Schutter H. B. (Editors), Springer, 1990 Felker P. M., Zewail A. H., "Picosecond time-resolved dynamics of vibrational energy redistribution and coherence in beam-isolated molecules" , Adv. Chem. Phys., 70, pp. 265--364, 1988. Grishanin B. A., Vachev V. D., Zadkov V. N., "On the theory and MD simulation of one-photon electronic excitation of polyatomic molecules" , Proc. SPIE, 1402, pp. 44--52, 1991 Grishanin B. A., Vachev V. D., Zadkov V. N., "Computer simulation of the conformational switching induced by ultra short laser pulse" , Nonlinear Optics, (to be published), 1992. Syage J. A., Feller P. M., Zewail A. H., "Picosecond dynamics and photoisomerization ofstilbene in supersonic beams. I. Spectra and modes assignments" , J. Chem. Phys., 81, pp. 4685--4705, 1984. Shan K., Yan Y. J., Mukamel S., "Intra-molecular dephasing and vibrational redistribution in the dispersed fluorescence of ultracold molecules: application to anthracene" , J. Chem. Phys., 87, pp. 2021--2035, 1987. Vinter J, Davis A, Saunders M., "Strategic approaches to drug design" , J. Comp. Aided Mol. Design, 1,
pp. 31--51, 1987.

14. Vachev V. D., Grishanin B. A., Zadkov V.N., "MD study of pulsed laser excitation of electronic transitions in polyatomic molecules" , Izv. Akad. Nauk, Ser. Fiz., 56, pp. 16--26, 1992. 15. Abrash S., Repinec S., Hochstrasser R. M., "The viscosity dependence and reaction coordinate for isomerization of cis-stilbene" , J. Chem. Phys., 93, pp. 1041--1053, 1990. 1 6 . Todd D . , Jean J ., Rosenthal S . , Ruggiero A . J . , Yang D . , Fleming G . , "Fluorescence up conversion study of cis-stilbene isomerization", J. Chem. Phys., 93, pp. 8658--8668, 1990. 17. Petek H., Yoshihara K., Fujiwara Y., Frey J. G., "Isomerization of cis-stilbene in rare-gas clusters: direct measurements of rans-stilbene formation rates on a picosecond time scale", J. Opt. Soc. Am. B, 7, pp. 1540--
1544, 1990.

18. Frederick J. H., Fujiwara Y., Pen J. H., Yoshihara K., Petek H., "Models for stilbene photoisomerization: experimental and theoretical studies of the excited state dynamics of 1,2-diphenylcycloalkenes", J. Phys. Chem., 95, pp. 2845-2858, 1991. 19. Vachev V. D., Zadkov V. N., "Molecular Dynamics of stilbene molecule under laser excitation", Proc. SPIE, 1403, pp. 487--496, 1991.

SP!E Vol. 1921 Laser Spectroscopy of Biomolecules (1992) / 401