• Keine Ergebnisse gefunden

minor empirical modifications provide a reasonable way to do this

4.2 Comparison of model and experimental results

4.2 Comparison of model and experimental results

For the systems investigated in [9], model calculations were performed, the results of which are shown in Figure 4.3. The difference in solvation energy∆SEwas calculated as

∆SE(n) = VDE(NgnX)−VDE(X) (4.15)

from the experimental values ofVDE, the vertical detachment energy, i.e. the energy required to remove an electron from the anion. Thus, the difference in solvation en-ergies can be interpreted as the increase of the energy needed for the removal of an electron from the anion caused by the presence of the noble gas atoms in the cluster.

The theoretical counterpart is

∆SE(n) = Vneutralmin −Vanionmin +

i

1 2

ωneutraliωanioni (4.16)

whereVminis the depth of the potential energy well at (for the anionic cluster) or clos-est to (for the neutral cluster) the global energy minimum for the anionic cluster, and the sum represents the difference in zero point energies for the anion and the neutral cluster. Thus, ∆SE(n) with the X state as a reference corresponds to EAX(NgnX) in Figure 4.1.

The comparison of theory and experiment rests on the assumption that the electron detachment takes place mostly to the vibrational ground state of the neutral cluster. In other words, it is assumed that a minimum in the potential energy function of the neu-tral cluster exists for which the geometry of the cluster does not differ greatly from the anionic global minimum, such that the Franck–Condon factor for the 0-0 vibrational transition is the dominant one. This may well be a local minimum of the potential en-ergy function of the neutral state. Additionally, the experiment was usually not able to resolveX and I states. Noticing that obvious deviations are substantially greater than what would be expected to be introduced by either of these simplifications, however, they appear acceptable.

It should be noted that some changes in the parameters used have been made, resulting in values differing somewhat from those presented in [9]. The potentials and parameters used here are listed in Appendix C. All model results exhibit shortcomings when compared to the experimental values, which shall be analyzed in this section.

Beginning with the fluorine systems, it is obvious that only for the case of ArnF

Chapter 4. Interactions in weakly bound noble gas–halide clusters

4.2. Comparison of model and experimental results Figure 4.3:(facing page) Comparison of experimental and model results for the difference in solvation energy∆SEfor various halide–noble gas systems. “Bin. model” refers to calculations without many-body effects. e = 140.54 meV andranionm = 4.05 Å refer to changes in the Xe–Brbinary potential parameters (see text).

could a qualitative agreement be achieved. Of course, xenon and krypton are well-known to form compounds with fluorine, while compounds for argon with fluorine and hydrogen have been found only fairly recently[185], a fact that underscores the strength of the interaction between fluorine and these noble gases. The very short equilibrium distances of the corresponding anionic potentials lead to an exaggeration of the largest repulsive contribution, induction nonadditivity. As already pointed out elsewhere[3], an uncertainty in equilibrium distance in the binary potentials translates into an uncertainty in energy from all non-additive potential contributions.

Additionally, an uncertainty in the shape of the more distant part of the potential certainly has a detrimental effect on the accuracy of the energy from the second sol-vation shell onward. For instance, the quadrupole contribution to the Xe–F binary potential (MMSV or Morse-Morse-Switching-van der Waals-type) has obviously not been determined appropriately, while the quadrupole contributions in the Ar–F and Kr–F potentials appear exaggerated. In the case of the latter two, the outermost no-ble gas atoms (see Figure 4.5) are close to or in the range of the multipole part of the MMSV potential (i.e.rNgX >x2·rm) and indeed∆SEfor KrnF in the binary potential (Figure 4.3) level off much too strongly upon completion of the first shell of noble gas atoms (n > 6). However, it is obvious that strong deviations from the experimental values start much earlier: Even the values for clusters with only a single noble gas atom do not agree well with the experiment for XeF, and even more so for KrF, which is clearly due to a wrong well depth of the binary MMSV potential.

Figure 4.4 depicts the ratio of induction nonadditivity to the sum of all binary interactions between the halide anion and the surrounding noble gas atoms. The effect of the former starts out to be small for every combination of halide and noble gas and rises, to then level off as the first shell of noble gas atoms around the halide closes.

With respect to the total energy, this corresponds to a decrease in relative contribution of induction nonadditivity, as the contribution of the noble gas–noble gas interactions becomes dominant. Generally, the value for a cluster with only two noble gas atoms is below 0.1, except for Kr2F and Xe2F, where it is roughly 0.15 and 0.22, respectively.

Likewise, the upper limit for this ratio is generally about 0.25 to 0.3, while it is between 0.45 and 0.5 for KrnF and XenF. The upper limit of XenBr of 0.37 appears to be shared

Chapter 4. Interactions in weakly bound noble gas–halide clusters

1 5 10 15 20 25

0 0.1 0.2 0.3 0.4 0.5

n

Vindnonadd

iV RgiX

ArnF KrnF XenF KrnCl XenCl ArnBr KrnBr XenBr

KrnI

Figure 4.4:Ratio of induction nonadditivity to the sum of binary potential contributions be-tween the halide anion and all noble gas atoms as a function of cluster size.

by ArnF and seems to be still within the validity of the assumptions for induction nonadditivity, given that ∆SE(n) does not become erratic as in the case of XenF and KrnF after closure of the first solvent shell. A substantial contribution to the deviation from experimental values can thus certainly be attributed to overestimated induction nonadditivity in XenF and KrnF.

Another large deviation was found for XenBr-type clusters. Note that in the pre-sentation of the experimental data given in [9], these were in rather good agreement with the experimental values due to a change of the anionic potential well depth from 126.92 to 140.54 meV, as shown in Figure 4.3. Obviously, however, this is not a good correction as the binary potential should agree with the experimental value of XeBr (i.e. the case of a single interaction partner) and increasing the binding energy of the binary potential necessarily leads to worse agreement for all small clusters.

An increase in the anionic equilibrium distance, on the other hand, can have a similar effect in correcting the deviations from the experimental values, as also shown in Figure 4.3, by decreasing the mostly repulsive contributions of the non-additive potential contributions. Changes in this parameter leave the energy of the smallest cluster unaffected, but the slope of ∆SE for clusters with a closed first solvent shell obviously decreases too strongly. Ultimately, the given experimental data is not

suffi-4.2. Comparison of model and experimental results cient to determine which potential parameters require improvement and to what ex-tent, especially when considering that the binary potentials of the neutral species offer yet more parameters. It may, however, be assumed that parameters pertaining to the non-additive contributions to the potential energy, e.g. dipole and quadrupole polar-izabilities, are largely correct as this large deviation is not observable in other clusters containing either xenon or bromine. Similar problems appear to exist for the ArnF species, although to a much lesser degree.

For the remaining clusters, the greatest difficulty for the model appears to be to describe the closing of the first shell of noble gas atoms correctly. In KrnI, ArnBr, KrnBr, and KrnCl, the ∆SE value of the cluster n =14, 12, 13, and 13, respectively, exhibit an irregularly small increase in ∆SE. From the halide–noble gas distances shown in Figure 4.5, it can be inferred that these are due to some rearrangement within the not yet filled first solvation shell. For KrnBr and KrnCl, distances from the halide core have a larger spread in these instances, whereas in KrnI and ArnBr the spread in noble gas–halide distance is smaller in these cases than in the next larger and smaller clusters.

The most straightforward explanation seems to be that the equilibrium distances of the corresponding halide–noble gas potentials are insufficiently accurate.

Additionally, in many cases (especially KrnI, ArnBr, KrnBr, KrnCl) the slope of∆SE does not decrease after the completion of the first solvation shell as strongly as is the case for the experimental data. This indicates deficiencies in the long range part of the potential: most likely an overly attractive anionic potential, because it is the greatest contribution to impact on an increase of∆SE. This is true, although the binary noble gas interactions are the largest component of the total energy of the anion. For the computation of ∆SE these are indeed practically completely eliminated as they also exist, with almost identical magnitude, in the neutral clusters (see Figure 4.6). In other words: their significance extends mostly to the determination of the cluster geometry.

Geometries are of interest in particular with regard to the size of the first solvation shell. From the plot of distances in the various clusters (Figure 4.5), it is apparent that for KrnCl, KrnBr, XenCl, and XenBr, a tendency to form icosahedral structures is prevalent. In two systems, namely XenCl and XenBr, the icosahedron constitutes the inner shell of noble gas atoms as further atoms are added to the second shell. For XenBr even the start of a third shell can be seen. After it is energetically favorable for the first few noble gas atoms of the second shell to be located over the triangular faces of the icosahedron of the first shell, eventually forming a pentagon, it is then apparently more favorable to add the next xenon atom centered over that pentagon. It is thus also

Chapter 4. Interactions in weakly bound noble gas–halide clusters

1 5 10

3 5 7 9

ArnF

n rNgX

1 5 10

KrnF

n 1 5

XenF

n

1 5 10 15

3 5 7 9

KrnCl

n rNgX

1 5 10 15

XenCl

n

1 5 10 15

3 5 7 9

ArnBr

n rNgX

1 5 10 15

KrnBr

n 1 5 10 15 20 25

XenBr

n

1 5 10 15

3 5 7 9

KrnI

n rNgX

Figure 4.5:Halide–noble gas distances obtained from the model calculations for the respective anionic clusters.

4.2. Comparison of model and experimental results

1 5 10 15 20 25

2.5

2

1.5

1

0.5 0 0.5

n

e/eV

Xe–Xe (anion) Xe–Br(anion) induction nonadditivity (anion) exchange (anion)

dispersion multipole (anion) triple dipole (anion) Xe–Xe (neutral) Xe–Br (neutral) triple dipole (neutral)

Figure 4.6:Contributions to the total cluster solvation energy (SE) for the XenBr system (data for the neutral system is for theXstate; the unmodified potential was used for the anion).

on top of one of the tips of the icosahedron. This is a manifestation of the growing importance of xenon-xenon interactions versus xenon-bromide interactions as a result of increasing shielding of the attraction of the anion.

For KrnCl and KrnBr, the preference of an icosahedral geometry is noticeable from a substantially smaller spread in halide–noble gas distances, as compared to both smaller as well as larger clusters. In both cases, the icosahedron is subsequently dis-torted to enable the first solvation shell to accommodate two more noble gas atoms and eventually less symmetrical polyhedrons form the first solvation shell. Contrary to what was assessed earlier[9]about structures of clusters with an incomplete first sol-vent shell in these systems, they do not resemble a capped square antiprism forn =10, but ratherarachno[186]-type icosahedrons (i.e. icosahedrons with two apex atoms miss-ing).

In the cases of ArnBr and KrnI, shell closure occurs only with the 15th added noble gas atom, as the smaller ratio of van-der-Waals radii of noble gas and halide would

Chapter 4. Interactions in weakly bound noble gas–halide clusters lead to expect.

Marking the opposite end of the scale, fluorine clusters prefer much smaller sol-vation shells, with Ar8F being a square antiprism, of which subsequently (n = 9 and 10), caps are added to the squares and then the to the triangular faces (n > 11). Kr6F and Xe6F are both octahedral, but in both cases the addition of further noble gas atoms leads to distortion of the octahedron. While for KrnF (n > 6) subsequently added atoms are substantially farther from the halide, Xe8F is of square antiprismatic shape, although this is again distorted greatly in Xe9F.

This entire analysis of geometries, it should be noted, depends on the somewhat questionable (vide supra) accuracy of the equilibrium distances of the interaction po-tentials.

4.3 Conclusion

Improvements over the original work of Yourshawet al.[3]have been achieved by find-ing a concise analytic solution of the Lawrence and Apkarian-Hamiltonian[164] and the adoption of a hypertensor[177]-like treatment of induction nonadditivity. The lat-ter proved helpful for finding analytic derivatives of this energy contribution and thus avoiding the more costly numerical derivation.

While interesting insights into cluster geometries could be gleaned from model cal-culations, weaknesses of the underlying binary potentials were discovered by compar-ing the model results to experimental data. It seems that particularly the equilibrium distances of these potentials require greater accuracy, since many-body potential con-tributions are very sensitive to them. At the same time, the model may have general difficulties in describing larger clusters with a closed first solvent shell.

Bibliography

[1] Schade, M.; Moretto, A.; Crisma, M.; Toniolo, C. and Hamm, P.: Vibra-tional Energy Transport in Peptide Helices after Excitation of C–D Modes in Leu-d10. The Journal of Physical Chemistry B, 2009, 113(40), 13393–13397. DOI:

10.1021/jp906363a

[2] Hamm, P.; Ohline, S. M. and Zinth, W.: Vibrational cooling after ultrafast pho-toisomerization of azobenzene measured by femtosecond infrared spectroscopy.

The Journal of Chemical Physics,1997,106(2), 519–529. DOI:10.1063/1.473392

[3] Yourshaw, I.; Zhao, Y. and Neumark, D. M.: Many-body effects in weakly bound anion and neutral clusters: Zero electron kinetic energy spectroscopy and thresh-old photodetachment spectroscopy of ArnBr (n=2–9) and ArnI (n=2–19). The Journal of Chemical Physics,1996,105(2), 351–373. DOI:10.1063/1.471893

[4] Hirata, Y. and Mataga, N.: Picosecond Dye-Laser Photolysis Study of Diphe-nylcyclopropenone in Solution - Formation of the Electronically Excited States of Diphenylacetylene. Chemical Physics Letters, 1992, 193(4), 287–291. DOI:

10.1016/0009-2614(92)85669-2

[5] Nguyen, L. T.; De Proft, F.; Nguyen, M. T. and Geerlings, P.: Theoretical study of cyclopropenones and cyclopropenethiones: decomposition via intermedi-ates. Journal of the Chemical Society, Perkin Transactions 2, 2001, 6, 898–905. DOI:

10.1039/B100709M

[6] Vennekate, H.; Walter, A.; Fischer, D.; Schroeder, J. and Schwarzer, D.: Photode-carbonylation of Diphenylcyclopropenone — a Direct Pathway to Electronically Excited Diphenylacetylene? Zeitschrift für Physikalische Chemie, 2011, 225(9-10), 1089–1104. DOI:10.1524/zpch.2011.0164

[7] Schwarzer, D.; Kutne, P.; Schroder, C. and Troe, J.: Intramolecular vibrational en-ergy redistribution in bridged azulene-anthracene compounds: Ballistic enen-ergy

Bibliography

transport through molecular chains. The Journal of Chemical Physics,2004,121(4), 1754–1764. DOI:10.1063/1.1765092

[8] Lin, Z.; Zhang, N.; Jayawickramarajah, J. and Rubtsov, I. V.: Ballistic en-ergy transport along PEG chains: distance dependence of the transport ef-ficiency. Physical Chemistry Chemical Physics, 2012, 14, 10445–10454. DOI:

10.1039/C2CP40187H

[9] Kopczynski, M.: Femtosekunden Photodetachment- Photoelektronenspektroskopie an isolierten und massenselektierten Halogen-Edelgas-Clustern. PhD thesis, Georg-August-University,2010.

[10] Lenzer, T.; Furlanetto, M. R.; Pivonka, N. L. and Neumark, D. M.: Zero electron kinetic energy and threshold photodetachment spectroscopy of XenI clusters (n=2–14): Binding, many-body effects, and structures. The Journal of Chemical Physics,1999,110(14), 6714–6731. DOI:10.1063/1.478577

[11] Lenzer, T.; Yourshaw, I.; Furlanetto, M. R.; Pivonka, N. L. and Neumark, D. M.:

Characterization of ArnClclusters (n= 2–15) using zero electron kinetic energy and partially discriminated threshold photodetachment spectroscopy. The Jour-nal of Chemical Physics,2001,115(8), 3578–3589. DOI:10.1063/1.1388202

[12] Hamm, P.: Femtosecond IR Pump-Probe Spectroscopy of Nonlinear Energy Lo-calization in Protein Models and Model Proteins. Journal of Biological Physics, 2009, 35, 17–30. DOI:10.1007/s10867-009-9126-3

[13] Crim, F. F.: Bond-Selected Chemistry: Vibrational State Control of Photodissoci-ation and Bimolecular Reaction. The Journal of Physical Chemistry, 1996, 100(31), 12725–12734. DOI:10.1021/jp9604812

[14] Poloukhtine, A. and Popik, V.: Mechanism of the cyclopropenone decarbonyla-tion reacdecarbonyla-tion. A density funcdecarbonyla-tional theory and transient spectroscopy study. The Journal of Physical Chemistry A,2006,110(5), 1749–1757. DOI:10.1021/jp0563641

[15] Hamm, P.: Coherent effects in femtosecond infrared spectroscopy. Chemical Physics,1995,200(3), 415–429. DOI:10.1016/0301-0104(95)00262-6

[16] Reichardt, C.: Aufklärung des photoinduzierten Zerfallsmechanismus von aroma-tischen Peroxoestern mittels Femtosekunden-IR-Spektroskopie. PhD thesis, Georg-August-Universität Göttingen,2008.

Bibliography [17] Vennekate, H.: Untersuchung des photoinduzierten Zerfalls von Acetylbenzoyl- und Phthaloylperoxid mittels Femtosekunden-Infrarotspektroskopie. Diplomarbeit, Georg-August-Universität Göttingen,2008.

[18] Schäfer, T.: Untersuchung der Schwingungsenergierelaxation und Rotationsdynamik von assoziierten Flüssigkeiten über weite Dichte- und Temperaturbereiche. PhD thesis, Georg-August-Universität Göttingen,2009.

[19] Fischer, D.:Untersuchung der Dissoziation von Azido(cyclam-acetato)-Eisen(III)- hex-afluorophosphat nach UV-Anregung mit Infrarot-Femtosekundenspektroskopie. Bache-lor’s thesis, Georg-August-Universität Göttingen,2011.

[20] Auth, T.: Untersuchungen zur Orientierungsrelaxation von Azido(cyclam-acetato)-Eisen(III)- hexafluorophosphat in Acetonitril. Bachelor’s thesis, Georg-August-Universität Göttingen,2012.

[21] Hamm, P.; Kaindl, R. A. and Stenger, J.: Noise suppression in femtosec-ond mid-infrared light sources. Optics Letters, 2000, 25(24), 1798–1800. DOI:

10.1364/OL.25.001798

[22] Kaindl, R. A.; Wurm, M.; Reimann, K.; Hamm, P.; Weiner, A. M. and Woerner, M.:

Generation, shaping, and characterization of intense femtosecond pulses tunable from 3 to 20µm. Journal of the Optical Society of America B,2000,17(12), 2086–2094.

DOI:10.1364/JOSAB.17.002086

[23] National Instruments Corporation: LabView 8.2.1,2007.

[24] Hamm, P.; Lim, M. and Hochstrasser, R. M.: Structure of the Amide I Band of Peptides Measured by Femtosecond Nonlinear-Infrared Spectroscopy. The Jour-nal of Physical Chemistry B,1998,102(31), 6123–6138. DOI:10.1021/jp9813286

[25] Upitis, J. A. and Krol, A.: The Use of Diphenylcyclopropenone in the Treat-ment of Recalcitrant Warts. Journal of Cutaneous Medicine and Surgery,2002, 6(3), 214–217. DOI:10.1007/s10227-001-0050-9

[26] Sotiriadis, D.; Patsatsi, A.; Lazaridou, E.; Kastanis, A.; Vakirlis, E. and Chrysoma-llis, F.: Topical immunotherapy with diphenylcyclopropenone in the treatment of chronic extensive alopecia areata. Clinical and Experimental Dermatology, 2007, 32(1), 48–51. DOI:10.1111/j.1365-2230.2006.02256.x

Bibliography

[27] Grabowski, J. J.; Simon, J. D. and Peters, K. S.: Heat of formation of diphenyl-cyclopropenone by photoacoustic calorimetry. Journal of the American Chemical Society,1984,106(16), 4615–4616. DOI:10.1021/ja00328a052

[28] Fessenden, R. W.; Carton, P. M.; Shimamori, H. and Scaiano, J. C.: Measure-ment of the dipole moMeasure-ments of excited states and photochemical transients by microwave dielectric absorption. The Journal of Physical Chemistry, 1982, 86(19), 3803–3811. DOI:10.1021/j100216a020

[29] Potts, K. T. and Baum, J. S.: Chemistry of cyclopropenones. Chemical Reviews, 1974,74(2), 189–213. DOI:10.1021/cr60288a003

[30] Kandratsenka, A.; Schroeder, J.; Schwarzer, D. and Vikhrenko, V. S.: Molecu-lar dynamics modeling of cooling of vibrationally highly excited carbon diox-ide produced in the photodissociation of organic peroxdiox-ides in solution. Physical Chemistry Chemical Physics,2005,7(6), 1205–1213. DOI:10.1039/b414623a

[31] Kim, K.: The integrated intensity of the carbon monoxide fundamental band.

Journal of Quantitative Spectroscopy and Radiative Transfer, 1983, 30(5), 413–416.

DOI:10.1016/0022-4073(83)90104-8

[32] Ewing, G. E.: Infrared Spectra of Liquid and Solid Carbon Monoxide. The Journal of Chemical Physics,1962,37(10), 2250–2256. DOI:10.1063/1.1732994

[33] Fayer, D.: Ultrafast Infrared And Raman Spectroscopy. Practical spectroscopy: Tay-lor & Francis,2001. ISBN:978-0-8247-0451-3

[34] Hirata, Y.; Okada, T.; Mataga, N. and Nomoto, T.: Picosecond Time-Resolved Absorption-Spectrum Measurements of the Higher Excited Singlet-State of Diphenylacetylene in the Solution Phase. The Journal of Physical Chemistry,1992, 96(16), 6559–6563. DOI:10.1021/j100195a011

[35] Takeuchi, S. and Tahara, T.: Femtosecond absorption study of photodissocia-tion of diphenylcyclopropenone in soluphotodissocia-tion: Reacphotodissocia-tion dynamics and coherent nuclear motion. The Journal of Chemical Physics, 2004, 120(10), 4768–4776. DOI:

10.1063/1.1645778

[36] Ferrante, C.; Kensy, U. and Dick, B.: Does diphenylacetylene (tolan) fluoresce from its second excited singlet state? Semiempirical MO calculations and fluo-rescence quantum yield measurements. The Journal of Physical Chemistry, 1993, 97(51), 13457–13463. DOI:10.1021/j100153a008

Bibliography [37] Amatatsu, Y. and Hosokawa, M.: Theoretical Study on the Photochemical Behav-ior of Diphenylacetylene in the Low-Lying Excited States. The Journal of Physical Chemistry A,2004,108(46), 10238–10244. DOI:10.1021/jp047308n

[38] Kellerer, B.; Hacker, H. H. and Brandmüller, J.: On the Structure of Azoben-zene & Tolane in Solution: Raman spectra of AzobenAzoben-zene, AzobenAzoben-zene-d10, p-,p’-Azobenzene-d2, Azobenzene-15N=15N & Tolane. Indian Journal of Pure and Applied Physics,1971, 9, 903.

[39] Baranovi´c, G.; Colombo, L. and Skare, D.: A valence force field for pheny-lalkynes: Part II. Fundamental frequencies of phenylacetylene and tolane and molecular conformation of tolane in solution.Journal of Molecular Structure,1986, 147(3–4), 275–300. DOI:10.1016/0022-2860(86)80382-9

[40] Ishibashi, T. and Hamaguchi, H.: The central CC bond stretch frequencies and structure of S2and S1diphenylacetylene in solution studied by picosecond time-resolved CARS spectroscopy. Chemical Physics Letters,1997,264(5), 551–555. DOI:

10.1016/S0009-2614(96)01368-1

[41] Ishibashi, T. and Hamaguchi, H.: Structure and Dynamics of S2 and S1 Diphenylacetylene in Solution Studied by Picosecond Time-Resolved CARS Spectroscopy. The Journal of Physical Chemistry A, 1998,102(13), 2263–2269. DOI:

10.1021/jp972809c

[42] Ishibashi, T.; Okamoto, H. and Hamaguchi, H.: Picosecond transient infrared spectra and structure of S1 diphenylacetylene in solution. Chemical Physics Let-ters,2000,325(1–3), 212–218. DOI:10.1016/S0009-2614(00)00631-X

[43] Okuyama, K.; Hasegawa, T.; Ito, M. and Mikami, N.: Electronic spectra of tolane

[43] Okuyama, K.; Hasegawa, T.; Ito, M. and Mikami, N.: Electronic spectra of tolane