6417
J. Phys. Chem. 1995, 99, 6417-6423
Combining Molecular Mechanics with Quantum Treatments for Large Conjugated Hydrocarbons. 2. A Geometry-Dependent Heisenberg Hamiltonian Gabin Trebow," Daniel Maynau, and Jean Paul Malrieu I.R.S.A.M.C.,Luboratoire de Physique Quantique, Unit6 associ6e au C.N.R.S. (U.A. 505), Universit6 Paul Sabatier, 31 062 Toulouse Cedex, France Received: August 8, 1994; In Final Form: January 26, 1995@
A new algorithm, coupling mechanic molecular 0 potentials with a previously derived nonempirical Heisenberg Hamiltonian for the n electrons, is presented. It makes possible a direct and efficient geometry optimization of any neutral state (in the sense of valence bond theory) for large-size conjugated hydrocarbons with reduced computational effort. The method is tested on planar and twisted conformers of various conjugated systems. The predicted geometries and energy barriers are in good agreement with experimental data and refined ab initio calculations. The potential energy surfaces of the stilbene molecule in its lowest SO and TI states are studied as a function of the torsional angles around the ethylenic C-C and the C-phenyl bonds.
I. Introduction Most monoelectronic methods such as SCF calculations give rather reliable results for the ground-state geometries of hydrocarbons, despite nonnegligible configuration interaction (CI) effects. But even if significant progresses in the algorithms and in computers (for a striking illustration of the improved efficiency of ab initio calculations, see for instance the performances of the TURBOMOLE package') have been obtained, ab initio is still a difficult way to address even moderately large molecules. The determination of excited-state geometries and energies is much more difficult since it requires CI descriptions of the excited state. Performing CI calculations requires a large amount of computational effort at both the integral transformation level (which is proportional to p,N being the dimension of the atomic orbital basis set) and the matrix diagonalization step. Our aim, in this series of work, of which the present paper is the third member, is to develop new algorithms,* leading to valuable descriptions of the wave functions of conjugated molecules in various electronic states at a very low cost. .Following the direction proposed by Karplus et al.3,4some years ago, a partition of the total energy into an additive o part and a quantum mechanically calculated n part is used. Taking benefit of the well-known n-n separability, we write
The HUMM model may be used for the study of cationszb and eventually anions of conjugated hydrocarbons, but it would be useless for the excited states of neutral systems since it does not discriminate between triplet and singlet states. For these problems, and more precisely for the neutral states (in the VB sense) of conjugated molecules, we can use the nonempirical magnetic (or Heisenberg) Hamiltonian, derived some years ago by our gr0up.~3'O This model, which used the eigensolutions of an analytical Hamiltonian, is well suited for ground states, triplet states, and some low lying singlet states, i.e. those which may be considered as essentially neutral in their valence bond decomposition. The method has proved to give reliable results for the ground-state conformationsl03' or for the excited-state geometries and energiesI2-l3of a large series of molecules. The ionic states (in the VB sense), for which the transition from the ground state is dipolarly allowed, are not accessible from the present Hamiltonian.
11. Method
The Heisenberg Hamiltonian is not popular in chemistry, where it is essentially used for the rationalization of the magnetic properties of diradicals, either organic or more frequently organometallic. This Hamiltonian works on the basis of an N-electronic function built from products of atomic orbitals, as in the valence bond approach. But it only considers the neutral VB determinants. For a half-filled band problem of 2n n electrons on 2n sites (conjugated carbons), in the neutral where E, is the sum of local interatomic potentials (according determinants each atom bears only one electron in a 2pn atomic to the localizability of the o electrons), orbital. If one has n a spin and n /3 spin electrons, the number corresponding to all possible spin of such determinants is E, = c V i j distributions. These determinants are localized and have almost ij negligible direct interaction, but the effect of the electronic delocalization, i.e. of the interaction with ionic VB structures, and E, is calculated through a n-only Hamiltonian. may be translated through effective spin-coupling between In the preceding pape3a we studied the ground state of neutral adjacent atoms i andj, Le. negative effective exchange integrals molecules using a geometry-dependentHuckel Hamiltonian. We go. The amplitude of these effective exchanges depends on the checked the pertinence of the Huckel molecular mechanics distance ri, between atom i and j and on the angle (between scheme (hereafter labeled as HUMM) and the accuracy of its the p, orbitals), and the function gij(ro,€Jo)has been extracted results for both the ground-state potential energy surface and IR or Raman spectra. These were found to be as a c c ~ r a t e * ~ . ~ from a careful study of the potential energy surface of the simplest conjugated hydrocarbon, i.e. ethylene, as explained as those calculated with the well-known and largely used MM, below. The long step of this method is the research of the methods.6-s relevant eigenvalues of the c,-dimensional Hamiltonian, so that the present method is limited to 20 carbon atoms. The Abstract published in Advance ACS Abstracts, April 1, 1995.
cn,
+
@
0022-365419512099-6417$09.00/0 0 1995 American Chemical Society
6418 J. Phys. Chem., Vol. 99, No. 17, 1995
Treboux et al.
TABLE 1: Twist Angles and Internal Rotational Barrier Heights of Biphenyl from Experiments in the Gas Phase and from Calculations" thermodynamic data Raman spectra ED data EAS extended Huckel CND012 PCILO HF/double- 5 HF/STO-3G HF/6-31G HF/6-3 lG* HF/6-3 1G* * MP2/6-3lG*/l HF/6-3lG* MP3/6-31G*// HF/6-31G* MP4(SDQ)/6-31G*// HF/6-31G* HUMM HEIMM a
31 32 17, 18 19 20 21 22 23 24 25 26 29 30 27 28 28 16 16 16 16
1-2 1.4 1.4(0.5)
1-2 1.4 1.6 (0.5)
5.5 12.46 4.9 1.8 2.1 0.7 1.2 3.76 3.2 2.05 3.17 3.23 3.28 3.34 3.33 3.84
0.9 0.23 0.0 1.6 3.6 2.2 4.5 2.26 2.2 2.40 1.62 1.65 1.48 1.54 1.51 1.72
16
3.45
1.73
16
3.47
1.58
2.8 2.67
1.o 2.63
2 this work
44.4(1.2) 40-43 50 66 90 42 35 20-40 32 42 43.8 38.63 45.4 1 44.74 46.13 45.63 46.26
44.1 50.0
Angles in degrees; energies in kcal/mol. Equilibium twist angles.
advantage of the method is that it takes into account the correlation effects, neglected in monoelectronic pictures, and that the neutral excited states are treated with the same accuracy as the ground state, while MO approaches are hardly balanced, the single-determinantal description being relevant only for the closed shell ground state. The Heisenberg Hamiltonian has the form
~ e "= "
C
[ R ~ gij(ai+aj+a,ai - +ai +aj+aj- ai -
ij bonded
+
ai+aj +aj- ai - ai +ai+a,%-)]
In the previous version, Rij is a scalar function characterizing the (5 bond force field and the repulsion between the n electrons with parallel spins, and gv is the effective exchange between bonded atoms i and j . Let us comment on the extraction of the parameters R and g. For a two-center problem, Le. for ethylene, the (S, = 0) problem reduces to a 2 x 2 matrix and the two basic quantities R and g are immediately obtained: 1151
If one knows the potential surface of the lowest singlet and triplet states, the parameters R and g may be obtained as functions of the geometric conformation. In the previous modeling, they were obtained as functions of the interatomic distance T between atoms i a n d j and of the torsion around the i-j bond. The potential energy surface of the ethylene ground and lowest triplet states had been obtained through an ab initio calculation (SCF d t f d polarization), followed by CI level calculations. The R(r,@ and g(r,8) functions have been fitted in a polynomial expansion as a function of r for each value of 8. Another representation of R(r,O) and g(r,8) functions is needed in our program since we want to introduce other
TABLE 2: Calculated Geometric Parameters for the Twisted, Coplanar, and Perpendicular Conformers of
Biphenyla
distances, anglesb
exP ED ( r g )
HF/6-31G**C HEIMM
c1-C1' Cl-C2 C2-C3 c3-c4 C2-H2 C3-H3 C4-H4 C2-C1 -C6 C1 -C2-C3 c2-c3-c4 c3-c4-c5 C1 -C2-H2 C2-C3-H3 C3-C4-H4
Twisted Conformer 1.492 1.456 1.509 (82) 1.393 1.399 1.406 (82) 1.384 1.395 1.397 (83) 1.385 1.395 1.398 (83) 1.076 1.103 1.102 (24) 1.076 1.103 1.102 (24) 1.076 1.103 1.102 (24) 118.4 118.5 119.4 (82) 120.8 121.0 119.9 (82) 120.2 120.0 120.9 (83) 119.5 119.6 119.0 (84) 119.6 120.0 119.8 119.7 120.1 119.8 120.3 120.2 120.5
c1-C1' Cl-C2 C2-C3 c3-c4 C2-H2 C3-H3 C4-H4 C2-Cl-C6 Cl-C2-C3 c2-c3-c4 c3-c4-c5 Cl-C2-H2 C2-C3-H3 C3-C4-H4
Coplanar Conformer 1.501 1.465 1.396 1.407 1.384 1.395 1.383 1.393 1.072 1.099 1.076 1.103 1.076 1.103 116.8 113.7 121.7 123.9 120.5 120.2 118.8 118.2 120.7 121.4 119.3 120.3 120.6 119.4
c1-Cl' Cl-C2 C2-C3 c3-c4 C2-H2 C3-H3 C4-H4 C2-Cl-C6 c 1 -c2-c3 c2-c3-c4 c3-c4-c5 Cl-C2-H2 C2-C3-H3 C3-C4-H4
Perpendicular Conformer 1.499 1.468 1.391 1.396 1.386 1.395 1.385 1.395 1.076 1.102 1.076 1.103 1.076 1.103 118.7 119.7 120.7 120.2 120.2 120.0 119.6 120.0 119.4 119.8 119.7 120.0 120.2 120.0
X-ray
1.497 (19) 1.398 (18) 1.387 (18) 1.379 (19) 0.980 (18) 0.990 (18) 1.000 (18) 117.4 (18) 121.2 (17) 120.4 (17) 119.5 (18) 118.7 (85) 119.5 (85) 120.3
Distances in angstroms; angles in degrees. The numbering of atoms is shown in Figure 9. Reference 16.
parameters in the u potential and to take into account steric interactions between nonbonded atoms. All geometrical deformations are taken into account, and the full geometrical optimization must be performed. Then continuous functions R and g are necessary. Let us change the orthogonal valence bond basis, composed of two neutral determinants, 12 and 72, and two ionic determinants, l i and 22, into a symmetry-adapted basis (12 - i 2 ) / f i and (17 22)/&, which are singlets of gerade symmetry, (12 12)/&, which is a triplet, and the ungerade singlet (17 - 22)/& The energy of the ground state is obtained by diagonalizing the matrix
+
+
(12 - i 2 p h K
2F
where the zero of energy is that of the neutral single determinant,
J. Phys. Chem., Vol. 99, No. 17, 1995 6419
Geometry-Dependent Heisenberg Hamiltonian
K is the exchange integral K12, AENIis the positive energy difference of the diagonal elements, and F is the extradiagonal element F12 of the Fock operator. The energy of the triplet state is -K and 2g =
-
4.69
a
W
-0.691
p\,
A
+ &53)
(-f%I
- 2K
2
It is reasonable to assume the following conformational dependance of the integrals and energy differences: I"
t
= a(r)
F = F(r,O) cos 8 = p ( r ) cos 8
K = K ( r ) cos2 8 - C ( r ) So that our four parameters a(r), P(r), K(r), and C(r) can be determined from the values of g(r) for 8 = 0", 30°, 45", and 90" given in ref 11. For the o potential, we wanted to take benefit of our molecular mechanics potential previously defined in ref 2. In this work the ?t energy was calculated from a geometry-dependent Huckel Hamiltonian. Since the n energy is now calculated differently, the V,, o potential had to be revised by adding a new term R'(r,8> such that Ea-,(ethylene) = R' VMM- 2g where Ea-! is the ab initio ground-state energy of ethylene. We note that, in a physical range of r, we obtain never more than a few percent deviation between our continuous definition of R(r,8)and g(r,8> and those used in previous formu1ation.",l2 One should remark also that on the basis of the proposals of refs 9 and 10, Robb and co-workers have recently developed a molecular mechanics valence bond (MM-VB) algorithmI4 which was successfully used in photochemistry studies (see, for instance, ref 15). The target of their algorithm is the study of photochemical processes involving bond breakings, creation of o bonds from ?t electrons, and vice versa, and modelization covers a domain of conformations (in particular strong carbon pyramidalization) which are not in the scope of the present work. The present method essentially intends to study conformations and spectroscopic features, including relaxation and vibrational properties in ground and excited states. Our molecular mechanics potential is certainly more precise for conjugated conformations but is only valid in this domain and would be unable to follow the photochemical events studied by Robb and co-workers.
+
+
111. Results
The superiority of the present HEIMM program over the previous n Heisenberg version consists of an improved modelization of the o part of the molecule. In polyene studies,I0," these improvements result in tiny changes and the previous algorithm was already Our algorithm appears superior wherever an interplay between steric and ?t effects occurs; biphenyl for instance, where n conjugation between phenyl rings stabilizes the planar conformer, is a typical target for our program. Due to the wide amount of theoretical and experimental studies available for this system, it is a good test for the accuracy of our model. Biphenyl. This molecule appears to be close to the maximum size manageable with an ab initio method with large basis sets and CI levels. Optimized geometries of ground-state biphenyl have been calculated at the Hartree-Fock level with 6-31G* and 6-31G** basis sets by Tsuzuki et a1.I6 The intemal rotational barrier heights at 0" ( A E o ) and at 90" (&?go) have been addressed by the same authors at the HF and the MP4-
0
18
36
90
72
54
PHI-PHI diedral angle (degree) Figure 1. Adiabatic ground state of biphenyl, dependance on the interphenyl dihedral angle.
3 -0.595
,
I
T I I I l
I
o I I I
I
1
1
1 I
I
I
I
3
v
LLI
-0.605
1 t
-0.61
1
-0.615
1
1
,/
7
/
/
/
j
,
3
/
i -0625
1 "
0
, I I # I
"""'"'''
IS
36
54
12
90
PHI-PHI diedral anale (degree)
Figure 2. Adiabatic lowest triplet state of biphenyl, dependance on the interphenyl dihedral angle.
(SDQ)/6-3lG* levels. This calculation appears to be of the best quality until now. We report our work in regard to several calculations and experimental for both energetical (Table 1) and geometrical (Table 2) considerations. The amplitude of the twist angle is rather correct (50' instead of 45"), and the barrier height is somewhat too large with respect to experiment but lower than the ab initio value for the planar barrier. The triplet excited states are not known to date. We report potential curves obtained with variation of the 4-4 dihedral angle (hereafter noted 8) for both the adiabatic ground state (Figure 1) and the adiabatic first excited triplet state (Figure 2), relaxing all geometrical parameters except 8. We examine in Figures 3 and 4 the energetic relaxation occurring in both the two lowest triplet states. The lowest triplet state is found to be planar, with a barrier height of 13.4 kcal mol-' for the twisted conformation. The vertical SO-TI absorption would be 2.4 eV, while the vertical emission from TIto SOwould be' 1.8 eV and the adiabatic transition would take place at 2.1 eV. The vertical T I - T ~absorption is calculated to lie at 1.4 eV. It is worth discussing the behavior of the excited potential surface near 90". In this twisted conformation the electronic interaction between the two rings is very small (cf. the small amplitude of
Treboux et al.
6420 J. Phys. Chem., Vol. 99, No. 17, 1995
w
-0.58 -0.6
4.62
I
'.- ... '..
..
4
... ..... .............. .." ...
--'..
/ /
/
c
/
4
'**-.*--
1- with triplet localisation 2- without trlplet locallsation
c3
- 4.59s
I
~
I
I
I
1
1
1
1
I
2
w
-0.6
-0.605
-0.64
-0.66
-0.61
4.68 4.615
-0.7 0
36
18
54
12
90
anale (degree) Figure 3. Energy of the lowest triplet state TIof biphenyl as a function of interphenyl dihedral angle and full optimization of the other geometrical parameters for TI and energies of SOand Tz states for the same geometries. PHI-PHI diedral
1-
Z' -0.58 I
W
._... ..... ... .- ...
50
.- .....2
-
-0.64
-0.66 -0.68
-..-
, 5-5'
...-_ .
...--.
_,r.__.-
i
-9.5
Q)
v
w
36
54
72 PHI-PHI diedral angle (degree)
90
E"""""""'S
-10
-10.5
B-6
-11
-0.7 1s
so
Figure 5. Energy of the lowest state of biphenyl (1) with triplet localization and (2) without triplet localization.
7
I
-
70
60
PHI-PHI diedral angle (degree) 5'-B
/
0
I 40
..... ......
-0.6
-0.62
-0.62
I
/
90
Figure 4. Ground singlet and two lowest triplet states of biphenyl as a function of interphenyl dihedral angle with full geometry relaxation of each state.
-11.5 -12
I ' ' ' the g parameter for 8 = 90"), and the two diabatic configurations -1z.j r 3B~-'B2 and ' B I - ~ B ~where , B1 and B2 are the left and right 0 22.5 45 61.5 90 benzene rings, have a very small interaction. In such a condition C C dihedral angle (degree) 7 1 one lowers the energy by breaking the symmetry and relaxing Figure 6. Energy of the ground state of styrene as a function of the one of the benzene rings to fit its triplet optimal conformation, torsion angle around ethylenic C=C and position of the lowest triplet while the other adopts the geometry of the singlet ground state. state for the optimized conformation of the ground state. As pictured in Figure 5 , the symmetry breaking takes place near previous Heisenberg calculations), it is possible that the 8 = 80". This is a typical example of electronic localization vibrational levels are delocalized in the two symmetric wells. and symmetry breaking in a region where electronic coupling The calculated barrier for 8 = 90" is of reasonable magnitude. becomes small. Another interesting point addressable in this molecule conStyrene. The same competition-steric repulsion versus n cerns the electronic events occurring during the cis-trans conjugation occurs in this molecule. Although many experiisomerization path corresponding to the rotation around the mental and theoretical studies conceming the equilibrium geometry and the torsional coordinate have been r e p ~ r t e d , ~ ~ - ~ ' double bond (C,=Cs, see Figure 9). Several mechanisms have been proposed on theoretical grounds to interpret the cis-trans the results, summarized in Table 3, are still controversial. For isomerization of styrene. Bruni et aL5* suggested that the the ground state our model exhibits a double-well potential photoisomerization of styrene might proceed through a methylsurface, as obtained through the HF level, which is in disagreebenzyl+ (M-Bf) ionic twisted intermediate, the funnel of which ment with experimental data. However, the energy difference induces an avoided crossing with the surface of the vertical between the twisted minimum energy conformer and the planar excited state. Bendazoli et first performed ab initio conformer is calculated at about 0.1 kcal mol-', which is close calculations and reported that the twisted excited states resulted to the value reported5' at the MP4 level, the more sophisticated in the prediction of a twisted singlet excited diradical M'B'* correlated level reached until now. With such a low barrier, lying much below the ionic one. Using minimal basis sets, the due to nonbonded interactions (and therefore absent from the I
4
5
Geometry-Dependent Heisenberg Hamiltonian
f Y
-19A
J. Phys. Chem., Vol. 99, No. 17,1995 6421
c
Lrl
TABLE 3: Twist Angles and Internal Rotational Barrier Heights of Styrene &' AEn AEqn ref Raman 36 0 0.0 1.78 0 0.0 3.27 fluorescence 37 fluorescence and Raman 0 0.0 3.06 38 microwave spectroscopy 0 0.0 3.29 39 HF/minimal basis set 0 0.0 3.9 48
/
-19.9
-20.4
t
0
HF/STO-3G HF/4-21G HF/4-3 1 G HF/6-3 1G HF/6-31G*< HF/6-31G*d MP2/6-31G*//HF/6-3lG*d MP3/6-31G*//HF/6-3lG*d MP4(SDQ)/6-3 1G//HF/6-3lGd HEIMM Jj
90 13s diedd angle (dcgrce)
I so
Figure 7. Energy of the ground state and lowest triplet state of stilbene as a function of the torsion angle around ethylenic C=C, with full geometry relaxation of each state.
c
-19.5
this work
0 24 18 0 15 15 (15) (15) (15) 19
1c
0.0 0.38 0.12 0.0 0.004 0.04 0.14 0.11 0.10 0.11
3.89 2.29 2.81 3.13 2.85 2.88 2.61 2.60 2.48 3.43
a Angles in degrees; energies in kcal/mol. Equilibrium twist angles. Geometries were optimized under the constraint that the phenyl ring and the vinyl group maintain planarity. Geometries were fully optimized without any constraint.
H5
H6
-1
I
3
Y
c!
49 49 49 50 51 51 51 51 51
Biphenyl
ii '
I I H2
HI
-19.7
Styrene
I
r -19.9 7r
-
CS
[
-?0.3
I
0
I
$5
I
90
I
135
1 130
die0ra.l i n g l e (degretl
Figure 8. Adiabatic lowest triplet state of stilbene as a function of the torsion angle around ethylenic C=C.
ionic and diradical excited states of the twisted styrene molecule have been calculated through extended CI. The lowest excited state is found to be a diradical, so that photoisomerization should not involve the ionic state.54 Our modeling leads to a result (cf. Figure 6) similar to that of the previous Heisenberg algorithm. We have not reported the tiny deviations between the present results and those of ref 13. The lowest triplet state is confirmed to have two minima for 8 = 0" and 8 = 90" with a barrier of 2.5 kcal mol-' for 8 = 38". Stilbene. In Table 4, we report the results of geometry optimization of the SO. The well-established80181experimental geometries and some calculated conformations reported by Langkilde et al.79from largely used methods, a semiempirical QCFFPI Hamiltonian and a ROHF ab initio method using the 6-31G basis set, permit us to check the accuracy of our modeling, which gives a small torsion around the double bonds of the bridge for the E isomer. For the Z isomer a torsion of the bridge double bond takes place, but the calculation certainly exaggerates its amplitude, due to an overestimation of the repulsion between the H atoms in very close position.8 The calculated potential energy difference between (Z) and ( E ) is
c4
I
Figure 9. Numbering of atoms in biphenyl, styrene, and stilbene.
4.4 kcal mol-', in good agreement with the estimate of Saltiel et aL7* (4.6 kcal mol-') in benzene and with the ab initio estimate of Wolf et aLE2(5.7 kcal mol-'). The rotational barrier (Figure 7) has been calculated with a full geometrical relaxation of the transition state, and we find a barrier height of 37 kcal mol-'. It corresponds to the rotation of the central bond, and it is somewhat smaller than the experimental activation energy for the cis-trans thermal isomerization (42.8 kcal Stilbene (1,2-diphenylethylene) is widely used as a model in studies of C=C double-bond isomerization. The E Z (trans cis) photoisomerization of stilbene has been reviewed in detai1.53-56Structure and dynamics on both SI^^-^^ and T171-79 excited potential energy surfaces (PES) have been studied in a number of papers. In this paper we compare ours with previous calculations on stilbene ground and excited triplet states. The vertical absorption energy to the TIstate are calculated to be 45.5 and 58.5 kcal mol-' in (E)- and @)-stilbene, respectively, to be compared with experimental data76of 51.0 and 55.5 kcal mol-'. The main features of the triplet TI potential energy surface (Figure 8) are in perfect agreement with the qualitative proposals of Saltiel et aL7' The relaxation energy from the planar E form to the planar triplet optimal geometry would produce an energy lowering of 8.4 kcal mol-', but the corresponding geometry which appears in Table 5 (where it may be compared with recent ab initio HF/6-31G and semiempirical
-
-
6422 J. Phys. Chem., Vol. 99, No. 17, 1995
Treboux et al.
TABLE 4: Structural Parameters of (E)- and (Z)-Stilbene in the Ground State Soo exP ref distances, anglesb HF/6-31G' QCFFIPI' HEIMM Ce-Ce Ce-Cph Cph-C1 Cl-C2 C2-C3 c3-c4 c4-c5 C5-Cph Ce-Ce-Cph Cph-Ce-Ce-Cph C1-Cph-Ce-Ce
1.332 1.475 1.396 1.386 1.386 1.389 1.384 1.397 126.5 0.0 17.2
Ce-Ce Ce-Cph Cph-C1 Cl-C2 C2-C3 c3-c4 c4-c5 C5-Cph Ce-Ce-Cph Cph-Ce-Ce-Cph C1-Cph-Ce-Ce
1.332 1.482 1.395 1.386 1.387 1.388 1.386 1.395 129.6 5.0 43.0
E Isomer 1.359 1.477 1.421 1.405 1.406 1.406 1.404 1.422 124.6 0.0 0.0
1.363 1.449 1.404 1.395 1.394 1.394 1.395 1.404 127.1 0.0 15.2
80
ref 81
1.33 1.47 1.394 1.394 1.394 1.394 1.394 1.394 129
