Vibration Energy Accumulation and Redistribution in Organic Molecules Irradiated by Infrared Photons - De Gruyter
←
→
Page content transcription
If your browser does not render page correctly, please read the page content below
Vibration Energy Accumulation and Redistribution in Organic Molecules
Irradiated by Infrared Photons
Hartmut Jungclas, Anna M. Popova, Viacheslav V. Komarov, Lothar Schmidt, and
Alexander Zulauf
Fachbereich Chemie, Philipps-Universität, D-35032 Marburg, Germany
Reprint requests to Prof. Dr. H. J.; E-mail: jungclas@staff.uni-marburg.de
Z. Naturforsch. 62a, 324 – 330 (2007); received February 5, 2007
A theoretical approach to the dissociation and low-energy electronic excitation of polyatomic or-
ganic molecules with donor and acceptor substructures is suggested. The donor hydrocarbon molecu-
lar substructures can serve as antennas for low-energy infrared (IR)-photon absorption, which coher-
ently induce collective vibrational excitations (excimols). Due to dipole-dipole interactions, the accu-
mulated energy can transit to the molecular acceptors: dipole-type trap-bonds or molecular parts with
π -electron orbits. The analytical expressions for the probability functions of molecular fragmentation
and electronic excitation induced by IR-multiphoton absorption are derived. The vibrational energy
accumulation and redistribution in the molecules of diphenylalkanes irradiated by infrared photons
are considered from the presented point of view. – PACS numbers: 30.00 – 34.10 – 36.40
Key words: Organic Molecules; Energy Accumulation.
1. Introduction to the acceptor parts of the same molecule, causing var-
ious molecular transformations.
The infrared (IR)-multiphoton-induced excitation
and the following transformations of a single organic 2. Alkanes as Antennas for Mid-IR Radiation and
molecule have been extensively studied in the last few Molecular Energy Donors
decades [1 – 7], since these processes are able to give
valuable information about the intermolecular energy As it was shown by us earlier [22 – 23], hydrocar-
redistribution and molecular transformation. In a few bon chains in single organic molecules can serve as
series of experiments it has been shown that the prob- antennas for external IR-photons. A band of collective
ability and the duration of the photon-induced pro- low-energy vibrational states can arise in (CH2 )n , due
cesses in molecules irradiated by mid-IR-photons sig- to the relatively high dipole moment of the CH-bonds
nificantly depend on the radiation fluence and fre- and the small distance between them of about 1.5 Å
quency as well as on the topological and spectral prop- in the chain. The state in the band with the lowest en-
erties of the considered molecules [8 – 21]. ergy Eex = 0.07 eV and the lifetime τex = 5 · 10−11 s
This explains the necessity to develop a suitable is called excimol [24]. An excimol can travel from one
theoretical approach to the mentioned nonstatistical CH-dipole to the neighbour dipole along the antenna
femtosecond processes in organic molecules consist- due to the resonant dipole-dipole interaction between
ing of a few substructures with different topological the CH-valence bonds in the time interval τtr = 10−14 s
and spectral properties. without energy loss and phase change. As a result, N
In this paper we present a theoretical model for the excimols can be excited in one antenna dipole, where
multiphoton-induced vibration energy accumulation N = τex /τtr . Thus, the excitation process of M effec-
and transformation in large organic molecules consist- tive dipoles takes place, if M = N · Mr , and Mr is the
ing of donor-acceptor-type substructures. We consider real number of CH-dipoles in the antenna.
molecules in which the donor is a hydrocarbon chain In the excimol model [25], due to the large unhar-
(CH2 )n serving as an antenna for mid-IR-photons. The monicity of the CH-dipoles, which we consider as os-
intramolecular vibrational energy accumulated in the cillators, the excimols can not concentrate in one CH-
donor can be transferred through a dipole-dipole valve bond, and there is no interaction between the excimols
0932–0784 / 07 / 0500–0324 $ 06.00
c 2007 Verlag der Zeitschrift für Naturforschung, Tübingen · http://znaturforsch.comH. Jungclas et al. · Vibration Energy Accumulation in Organic Molecules 325
in the antenna. Then we can define a probability of Mr oscillators is depending resonantly on the radiation
independent excitation of K excimols in M effective flux F. Then, the accumulation of a certain amount of
dipoles in an antenna by the relation excimol energy in an oscillator chain with Mr 1 is
a double resonance process, since its probability de-
1 (K − MP01)2 pends resonantly on the field frequency and radiation
PMK = exp − , flux.
2π MP01(1 − P01) 2MP01(1 − P01)
(1)
3. Molecular Substructures as Acceptors of
where P01 is the probability of resonant excitation of Excimol Energy
one excimol in a CH-dipole during τex . The probability
The acceptors in a single polyatomic organic
of one excimol excitation per time unit, calculated in
molecule can be either valence bonds of dipole-type,
the dipole approximation, has the form
the so-called trap-bonds, or electronic trap-bonds,
2 which define low-energy π -π ∗ excitation of some
4π 2 eD0
P̃01 = M12 J, (2) molecular parts with π -electron orbits. If the electronic
3h̄c r0 trap-bonds or acceptors of composite molecules are not
where eD0 is a parameter of the CH-dipole of the cor- directly joined together but separated by the donor sub-
responding chain. structure, then it is allowed to assume that the absorp-
Equation (2) contains J = 2F/∆E, where F is the ra- tion spectrum of each acceptor is not influenced by the
diation flux. M1 is a matrix element of the dipole transi- presence of another one.
tion, ∆E is the energy width of the radiation flux with Let us consider the donor-acceptor interaction in the
the frequency ωex . r0 and r are equilibrium and vari- mentioned molecule, which is a dipole-dipole interac-
able CH-dipole lengths. tion. The vibration energy transfer is defined by the
The energy E(K) of K excimols accumulated in the interaction potential WB between K identical antenna
antenna can transfer radiationless to the acceptor due dipoles and one acceptor dipole. The function WB has
to dipole-dipole interaction. The number of excimols the form
accumulated in the antenna depends linearly on the in- K
tensity of external IR-radiation with the frequency ωex . WB = ∑ wiB with
This statement follows from the properties of the func- i=1
(4)
tion PMK , which reaches its maximum by the condition
e 2 D0 DB ri RB
wiB = ΦiB (ϑi , ϑiB ) 3 .
K = M · P01. (3) r0 R0 LiB
The number of excimols K, as it follows from (3), Here LiB is the distance between the origin of the
depends linearly on P01 , and P01 in turn depends lin- dipole moment D i = eD0r i /r0 of any CH-bond in the
early on the value F. Therefore K depends linearly on chain and the origin of the trap-bond’s dipole moment
F, i. e. the accumulated excimol energy E(K) = K · Eex D B = eDBR B /R0 .
depends linearly on the radiation flux F. This result ex- The function ΦiB (ϑi , ϑB ) = cos ϑix cos ϑBx +
plains the experimental data of the work [26], where cos ϑiy cos ϑBy − 2 cos ϑiz cos ϑBz in (4) takes into ac-
it was observed, that the number of absorbed photons count the position of the trap-bond’s dipole moment
in organic molecules with hydrocarbon chains depends relative to the position of any CH-dipole moment in
linearly on the radiation flux. the antenna. The angles ϑi and ϑB define the direction
Thus for the excitation of a definite number K of of r i and R B in a coordinate system, where axis OZ
excimols in the antenna with fixed M, a certain value of coincides with the vector L iB .
radiation flux is required, and this value is smaller than The value of the potential wiB strongly depends on
the value of the flux, which is needed for the excitation the distance LiB and the angle function ΦiB (ϑi , ϑB ).
of one dipole with P01 = 1. The potential wiB reaches its maximum when LiB has
The relation (1) shows that the probability PMK for a its smallest value. This minimum of LiB is the distance
fixed energy E(K) = K · Eex corresponding to a num- L1B = L between the trap-bond dipole DB and the near-
ber K of accumulated excimols in the antenna with est dipole D 1 in the antenna.326 H. Jungclas et al. · Vibration Energy Accumulation in Organic Molecules
A necessary condition for a bond to act as a trap- We propose that the energy of all K excited dipoles
bond is that the excimol transition time along the an- is transmitted via dipole i = 1 to the trap-bond. The
tenna to dipole D 1 is much shorter than the excimol value L in (5) is a distance between the antenna’s
transition time from dipole D 1 to the trap-bond. This dipole D 1 and the dipole D B . In the model, the trap-
makes it possible to assume that the excimols accu- bond B is defined and handled as a vibrational quan-
mulated in an antenna can transit practically simulta- tum oscillator with the ground state energy εB0 =
neously and coherently from the antenna dipole D 1 to h̄ωB0 /2, corresponding to the oscillator wave function
the trap-bond. Thus, we can conclude that the energy ϕB0 (RB ) with αB = (h̄/2µB ωB0 )1/2 and reduced mass
E(K) of K accumulated excimols transits coherently µB . If dissociation of the oscillator bond B occurs,
from the antenna to the trap-bond as one photon with the fragments (the products of this dissociation) move
the energy E(K). apart with a relative kinetic energy Eq = h̄2 q2 /2µB
In our model the number of trap-bonds, which are with q = p/h̄, where p is the value of the relative mo-
dissociated in a molecule by an IR-radiation pulse, is mentum of the molecular fragments.
limited by the number of excimols which can be ac- The analytical expression (5) for the probability of
cumulated in the molecular antenna substructures dur- trap-bond dissociation allows to analyze its depen-
ing irradiation time, because the maximum of the ac- dence on the variables and molecular parameters.
cumulated excimol energy can not be less than the
sum of dissociation energies of these trap-bonds. The 5. Molecular Electronic Excitation by Multiphoton
maximum amount of energy, which can be transmitted Absorption
to a trap-bond, is the sum of excimol energy quanta
E(K) = Kmax · Eex with Kmax = M accumulated in the
adjacent antenna. Let us consider the excimol energy transition to
the electronic trap-bond induced by the energy poten-
Since the potential WB defines the probability for the
tial (4). The probability function Pel per time unit of π -
transition of vibrational energy from the antenna to the
electron excitation of acceptor B induced by the tran-
acceptor, we can consider it as an energy valve driven
sition of excimol energy E(K) from the hydrocarbon
by the potential parameters. For example, as it follows
antenna can be calculated by perturbation theory with
from (4), according to the property of the function Φ1B ,
the result
if the dipole D 1 is perpendicular to the dipole momen-
tum of some trap-bond, then the excimol energy is not 2
2π PMK P01 2 2e2 D0 Del
able to transit to this bond. Pel = K M1 Mel
h̄ E(K) r0 R0
(6)
4. Molecular Fragmentation by Multiphoton 2 1
· Φ1,el (ϑ1 , ϑel ) 6 ,
Absorption R1
In agreement with the excimol theory suggested by where R1 is the distance between the antenna dipole
us earlier [22], the excimol energy accumulated in the D 1 and the dipole D B , Mel is a matrix element of the π -
antenna happens to be high enough to excite a trap- π ∗ transition in the considered acceptor. Equation (6)
bond up to its dissociation. When E(K) exceeds the is valid if E(K) = εel∗ − εel0 , i. e. the excimol energy
dissociation energy Ed (B) of a trap-bond B, it can be is equal to the electronic excitation energy of the ac-
cleaved. ceptor. Therefore, molecular electronic excitation in-
The dissociation probability per time unit Pf for a duced by mid-IR-multiple photon absorption occurs,
certain trap-bond can be calculated on the basis of the when a proper number K of the accumulated excimols
perturbation theory [25] with the result appears during the IR-radiation pulse period. The func-
tion Pel depends resonantly on the frequency of the ex-
Pf = PMK P01 P, where ternal mid-IR-photons. As in the case of the molecular
√ 2 fragmentation, the probability function Pel of molec-
2 π 2 2e2 D0 DB
P= K M1 Φ1B (ϑ1 , ϑB ) (5)
ular electronic excitation has a maximum value when
h̄Eq r0 R0 the relation K = M · P01 is fulfilled. This last relation
q3 αB5 exp(−q2 αB2 ) determines a connection between the electronic excita-
· . tion energy and the value of the radiation flux for the
L6H. Jungclas et al. · Vibration Energy Accumulation in Organic Molecules 327
Fig. 1. The calculated excimol num-
ber K versus flux F for diphenyl-
alkanes. The curves 1, 2, 3 cor-
respond to molecular hydrocarbon
antennas with the dipole numbers
Mr = 6; 10; 20.
maximum of Pel . We note, that the probability function with an intensity less than 106 J/cm2 s leads to accu-
Pel has the same properties as the function Pf presented mulation of the vibration energy E(K) by excitation of
above. K excimols in the antenna with Mr ≈ 20 CH-dipoles.
Analysis of the analytical expressions for Pf and The number of excited excimols during the excimol
Pel as functions of K shows, that these functions have lifetime depends on the radiation intensity F, and on
resonant behaviour, when K · Eex = Ed and K · Eex = the real dipole number Mr in the antenna.
εel∗ − εel0 , correspondingly. Another important property We calculated the number of excimols K excited in
of these probabilities is, that since the excimol accumu- the hydrocarbon antenna versus the radiation intensity
lation depends resonantly on the IR-flux, the consid- for Mr = 6; 10; 20. The result of the calculation is pre-
ered processes are essentially resonant processes ver- sented in Figure 1. One can see, that excitation of a
sus the IR-flux, and consequently have a threshold be- fixed number of excimols occurs by an intensity value
haviour. reciprocal to the number of real dipoles in the antenna.
As is known, the energy of 3.5 eV (K = 50 exci-
6. Model Calculations for Diphenylalkanes mols) is needed to dissociate a C-C bond [27]. The
energy of 4.42 eV (K = 64 excimols) is needed for
The model outlined above of the processes initi- the electronic π -π ∗ transition in the phenyl group [28].
ated in polyatomic organic molecules by action of mid- Then, a variety of processes can be induced in diphen-
IR-photons was applied to diphenylalkane molecules ylalkane molecules by IR-radiation with the resonance
[C6 H5 -(CH2 )n -C6 H5 , for n > 2]. The donor substruc- frequency ω = ωex , when the radiation intensity is in-
tures (CH2 )n in these molecules are antennas for pho- creased or when the number of accumulated excimols
tons with an energy equal to the excimol energy Eex = in the antenna increases (K = 50; 64; 100; 114; 128):
0.07 eV. The vibration energy of K excimols accumu- one C-C trap-bond dissociation; electronic excitation
lated within τex = 5 · 10−11 s in the antenna can transit of one phenyl group; two simultaneous C-C bond
radiationless to the acceptor consisting of two valence dissociations; simultaneously one C-C bond dissoci-
bonds C-C, which connect the alkyl group with the ation and electronic excitation of one phenyl group;
phenyl groups acting as electronic trap-bonds. Reso- and finally electronic excitation of two phenyl groups.
nant absorption of photons from an IR-radiation pulse By using (5) and (6), we calculated the dissociation
with a frequency equal to the excimol frequency and and electronic excitation probabilities of the diphenyl328 H. Jungclas et al. · Vibration Energy Accumulation in Organic Molecules
Fig. 2. The dissociation probability function Pf
versus flux F for diphenylalkanes, calculated by
(5) with the parameters: K = 50; D0 /r0 = 0.7;
DB /R0 = 0.7; L = 0.5 Å; Φ1B = 0.9; M1 =
2 · 10−9 cm. The plots (a), (b), (c) correspond
to molecular hydrocarbon antennas with the
dipole numbers 10, 20, 100.
molecule versus the intensity of the radiation flux, tak- with donor-acceptor substructures led to the develop-
ing into account the processes mentioned above. The ment of a nonstatistical model for the vibration en-
results of the calculations for Mr = 10; 20; and 100 are ergy accumulation and redistribution in the consid-
presented in the Figs. 2 and 3. ered molecules. By using the excimol theory, analyti-
As one can see from the figures, the considered pro- cal expressions were obtained for the probability func-
cesses are super fast and occur in different intensity tions of molecular fragmentation and electronic ex-
intervals with respect to the number of dipoles in the citation activated by collected excimol energy. The
molecular antenna. following consequences of this model were estab-
lished.
7. Conclusions
The probability functions Pf and Pel of both con-
The theoretical approach presented in this article sidered processes depend resonantly on the frequency
to IR-multiphoton absorption by organic molecules ωR of the external IR-radiation. The value ωR must beH. Jungclas et al. · Vibration Energy Accumulation in Organic Molecules 329
Fig. 3. The electronic excitation probability
function Pel versus flux F for diphenylalkanes,
calculated by (6) with the parameters: K = 64;
D0 /r0 = 0.7; Del /r0 = 1; R1 = 2.72; Mel2 =
8 · 10−17 cm2 . The plots (a), (b), (c) corre-
spond to molecular hydrocarbon antennas with
the dipole numbers 10, 20, 100.
equal to the excimol frequency in the molecular hydro- Moreover, trap-bonds of a particular molecule with dif-
carbon antenna. ferent dissociation energies break at different radiation
In addition, the probability functions Pf and Pel de- fluencies. It also can be concluded that the probability
pend resonantly on the energy E(K) of the excimols of a specific low-energy π -π ∗ transition in an unsat-
accumulated in an antenna. The energy E(K) must be urated hydrocarbon substructure has a maximum at a
equal either to the value of the trap-bond’s dissociation certain radiation flux.
energy in the case of molecular fragmentation, or to the The analytical expressions for the fragmentation
value of the energy Eel in the case of electronic exci- and π -electron excitation probabilities of organic
tation (π -π ∗). Since the probability to accumulate the molecules induced by multiple IR-photons demon-
energy E(K) in the antenna depends resonantly on the strate the strong dependence of these processes on the
IR-flux, the probabilities Pf and Pel also depend res- number Mr of dipoles in antennas, because the proba-
onantly on the IR-flux like the functions PMK and P01 . bility to accumulate K excimols in the antenna reaches330 H. Jungclas et al. · Vibration Energy Accumulation in Organic Molecules
the maximum when the relation K = Mr · P01 is ful- spondingly, then the considered processes are forbid-
filled. Therefore, the radiation flux, which is needed for den, i. e. there exists a dipole valve between molecu-
the excitation of K excimols in the antenna with maxi- lar antenna and the rest of the molecule. The energy
mum probability is reciprocal to the number Mr . Thus, transmission from the antenna to the rest of molecule
organic molecules with antennas containing a big num- in this case strongly depends on the orientation of the
ber of identical dipoles can be fragmented or electron- antenna dipoles relative to the orientation of the trap-
ically excited by a much lower IR-radiation flux than bond dipole.
molecules with short antennas only. The probability functions Pf and Pel depend on
The probability functions Pf and Pel are very sen- L−6 −6
B and Lel , correspondingly. This strong dependence
sitive to the molecular structure parameters and the shows, that molecular fragmentation or π -electron ex-
functions Φ (ϑ1 ϑB ) and Φ (ϑ1 ϑel ), correspondingly. citation occurs in the trap-bond which is closest to the
These parameters define angles between the direction antenna.
of the dipole moment of the biatomic groups in the an- The resonance dependence of the fragmentation on
tenna and the direction of the dipole moment DB of a the field frequency and intensity opens the possibility
trap-bond or the dipole moment D el related to the π - to control the molecular fragmentation and the lumi-
electron. If the moments D B or D el are perpendicular nescence processes experimentally to a certain extent
to the moment D 0 and to the vectors L B or L el , corre- by the parameters of the external radiation.
[1] P. A. Schulz, A. S. Sudbø, D. I. Krajnovich, H. S. [16] P. A. Schulz, A. S. Sudbø, E. R. Grant, Y. R. Shen, and
Kwok, Y. R. Shen, and Y. T. Lee, Annu. Rev. Phys. Y. T. Lee, J. Chem. Phys. 72, 4985 (1980).
Chem. 30, 379 (1979). [17] J. L. Stephenson, Jr., M. M. Booth, J. A. Shalosky, J. R.
[2] M. Quack, Annu. Rev. Phys. Chem. 41, 839 (1990). Eyler, and R. A. Yost, J. Am. Soc. Mass Spectrom. 5,
[3] F. F. Crim, Annu. Rev. Phys. Chem. 44, 397 (1993). 886 (1994).
[4] D. J. Nesbitt, Annu. Rev. Phys. Chem. 45, 367 (1994). [18] J. D. Williams, R. G. Cooks, J. E. P. Syka, P. H. Hem-
[5] B. J. Schwartz, Annu. Rev. Phys. Chem. 54, 141 berger, and N. S. Nogar, J. Am. Soc. Mass Spectrom.
(2003). 4, 792 (1993).
[6] Y.-P. Lee, Annu. Rev. Phys. Chem. 54, 215 (2003). [19] S. E. Van Bramer, P. L. Ross, and M. V. Johnston,
[7] D. J. Nesbitt and R. W. Field, J. Phys. Chem. 100, J. Am. Soc. Mass Spectrom. 4, 65 (1993).
12735 (1996). [20] P. F. Bente, F. W. McLafferty, D. J. McAdoo, and
[8] K. L. Kompa, H. Lamprecht, H. Schröder, A. A. Puret- C. Lifshitz, J. Phys. Chem. 79, 713 (1975).
zky, and V. V. Tyakht, J. Chem. Phys. 84, 2020 (1986). [21] P. J. McKeown and M. V. Johnston, J. Am. Soc. Mass
[9] M. H. Yu, M. R. Levy, and C. Wittig, J. Chem. Phys. Spectrom. 2, 103 (1991).
72, 3789 (1980). [22] L. Schmidt, A. M. Popova, V. V. Komarov, and
[10] C. N. Plum and P. L. Houston, Chem. Phys. 45, 159 H. Jungclas, Z. Naturforsch. 51a, 1144 (1996).
(1980). [23] H. Jungclas, A. Wieghaus, L. Schmidt, A. M. Popova,
[11] E. Stone, K. J. Gillig, B. Ruotolo, K. Fuhrer, M. Gonin, and V. V. Komarov, J. Am. Soc. Mass Spectrom. 10,
A. Schultz, and D. H. Russell, Anal. Chem. 73, 2233 471 (1999).
(2001). [24] V. V. Komarov, L. Schmidt, H.-W. Fritsch, and H. Jung-
[12] L. Windhorn, J. S. Yeston, T. Witte, W. Fuß, clas, Computational Mater. Sci. 2, 427 (1994).
M. Motzkus, D. Proch, K.-L. Kompa, and C. B. Moore, [25] H. Jungclas, L. Schmidt, V. V. Komarov, A. M. Popova,
J. Chem. Phys. 119, 641 (2003). and I. O. Stureiko, Z. Naturforsch. 57a, 270 (2002).
[13] T. Witte, T. Hornung, L. Windhorn, D. Proch, R. de [26] N. Presser, J. R. Barker, and R. J. Gordon, J. Chem.
Vivie-Riedle, M. Motzkus, and K. L. Kompa, J. Chem. Phys. 78, 2163 (1983).
Phys. 118, 2021 (2003). [27] A. A. Radzig and B. M. Smirnov, Reference Data on
[14] J. C. Stephenson and D. S. King, J. Chem. Phys. 69, Atoms, Molecules and Ions, Springer Verlag, Berlin
1485 (1978). 1985.
[15] T. A. Watson, M. Mangir, C. Wittig, and M. R. Levy, J. [28] F. Hirayama, J. Chem. Phys. 42, 3163 (1965).
Phys. Chem. 85, 754 (1981).You can also read
