The vibrational structure of the oxygen K-shell spectra in acenaphthenequinones: An ab initio study

1

The vibrational structure of the oxygen K-shell

spectra in acenaphthenequinones : an ab initio

study

Denis Duflot*, Jean-Pierre Flament

Laboratoire de Physique des Lasers, Atomes et Molécules (PhLAM), UMR CNRS 8523,

Université Lille1 Sciences et Technologies, F-59655 Villeneuve d'Ascq Cedex, France

* email : [email protected], tel : +33 3 20 43 49 80, fax : +33 3 20 43 40 84

2

ABSTRACT

The vibrational structure of the K-shell O1s * of acenaphthenequinone C12H6O2

and its halogenated compound C12H2Br2Cl2O2 has been simulated using an entirely ab initio

approach. For both molecules, analysis of the calculated Franck-Condon factors confirm

without ambiguity that, contrary to initial claims, the C-H stretching modes are not modified

in the core states and are not excited. For C12H6O2, the vibrational fine structure appears to be

mainly due to three modes, involving C=O* asymmetric stretch and in-plane ring

deformation modes, due to the symmetry breaking of the core state. For C12H2Br2Cl2O2, the

vibrational excitation arises essentially from the C=O* asymmetric stretch, with numerous

secondary peaks arising from hot and combination bands. For both molecules, these bands

are probably responsible of the asymmetry deduced in the experimental fits using a unique

Morse potential and initially assigned to anharmonic effects.

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I. INTRODUCTION

In the past few years, the oxygen K-edge NEXAFS spectrum of condensed

acenaphthenequinone C12H6O2 (ANQ) has been the subject of several experimental studies

1,2. The first band, assigned to the sole O1s * transition, showed not well resolved fine

features due to vibrational excitation. The gas phase spectrum has only been shown in the

Elettra synchrotron facility journal 3. This gas phase spectrum has essentially the same

vibrational features but more easily distinguished. By fitting these features with the

anharmonic Franck-Condon factors progression of a single Morse potential, the authors of 1,2

found an energy spacing of 200 meV. Using an empirical relation 4, this mode was initially

assigned to a C-H stretching mode, rather than to a C=O stretching mode, although this

interpretation was already debated among the authors 2. More recently, the authors have

measured the same oxygen O1s * transition band in the halogenated molecule

C12H2Br2Cl2O2 (Br2Cl2-ANQ) 5. The energy spacing deduced from the fit was found to be the

same, leading to the conclusion that C-H stretching modes were not involved. This

conclusion was supported by ab initio calculations of the core state geometry based on the

Z+1 approximation.

In order to determine without ambiguity which modes are excited in the core

excitation of these molecules, it is necessary to calculate theoretically the vibrational

structure of the band. This is the subject of the present work, where we use a purely ab initio

approach. It should be kept in mind that our goal is not to fit the observed spectra, in contrast

to aforementioned studies, but to get qualitative insight on the processes at work.

4

II. COMPUTATIONAL DETAILS

In order to obtain similar accuracy, both ground state and core excited states should

be calculated at the same level of theory. For core states, it is not easy to use the standard

correlated methods employed for ground states, due to the possible variational collapse of the

energy. For these reasons, both states were calculated at the Hartree-Fock level. The core

states were obtained using the ROHF-GVB method 6, implemented in the GAMESS-US

program 7. For hydrogen, carbon and oxygen atoms, the atomic basis set employed is the TZP

taken from Dunning 8. This basis has natively double zeta character on the 1s shells, in

contrast to more recent ones, leading to a better description of core states. An all-electron

TZP basis was also used for chlorine 9, containing one d polarization function (d = 0.619).

For bromine, the small-core energy consistent relativistic pseudo-potential designed by

Peterson et al. 10 was employed for the 10 inner electrons, together with the corresponding cc-

pVTZ-PP (10s11p9d)/[5s4p3d] basis set.

The ground states geometries were optimized in the C2v symmetry group. For core

states, two possible pictures may be used : the delocalised one, which keeps the C2v symmetry

of the molecule, and the localised one, where the symmetry is reduced to Cs. This is due to

the well-known dynamical localization of the core hole in polyatomic molecules 11. In the

present work, this localization effect was assumed. The symmetry was reduced accordingly

and Z+1 (equivalent core) MO’s were used as a guess for the ROHF-GVB calculation.

Harmonic frequencies were obtained analytically at the RHF and ROHF-GVB

levels for ground and core states, respectively. It is expected that the values will be about

10% too large when compared to experiment. Indeed, the recommended scaling factor at the

HF/TZP level is 0.9047 12. However, for the purpose of the present work, unscaled

frequencies were used in the Franck-Condon factors calculations. In order to study possible

5

anharmonicity effects, anharmonic frequencies were calculated at the VSCF level 13 using

GAMESS-US. The QFF approximation 14 was used with 1D couplings (324 points) and 2D

couplings (17496 points).

Vibrational Franck-Codon factors (FCF) were calculated first in the linear coupling

approximation, using our local implementation 15 of the Domcke-Cederbaum model 16. We

recall that in this approximation, the excited state is supposed to have the same vibrational

frequencies as the ground state, and a shifted geometry. The evaluation of the FCF only

requires the gradient of the excitation energy at the ground state geometry (the vector). In a

second step, the “true” FCF were obtained using the core state frequencies, via the

ezSpectrum code 17. In this case, Duschinsky rotations 18 between the ground and the core

states vibrations are taken into account. For both models, hot and combinations bands were

taken into account and the Boltzmann factor for room temperature was included. The spectra

were obtained using Gaussian profiles. In the following, the core excited oxygen atom will be

designated as O*.

III. RESULTS AND DISCUSSION

A. Acenaphtenequinone

To the best of our knowledge, there is no available experimental determination of the

geometry of ANQ in the gas phase (see ref. 19 for the crystal structure). This geometry was

however calculated by Sinha et al. 20 at the B3LYP/6-311++G(3d,2p) level. Our own

RHF/TZP bond lengths are shown on Fig. 1.a. When compared to DFT results, the RHF

values are slightly shorter, due to the lack of correlation effect. The corresponding

frequencies are compared to previous works in Table II. Only the modes relevant for our

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purpose are shown in this table. It appears that unscaled values are 10% too large with respect

to experiment. The anharmonic values, obtained with 2D-coupling methods, are smaller than

the harmonic ones. Interestingly, the anharmonic C=O stretches are only 1% smaller than the

harmonic values. The remaining difference between harmonic and experimental frequencies

are due to correlation effects.

The ROHF-GVB vertical core excitation energy Ev is calculated at 530.87 eV, i.e.

slightly above the valued deduced from experiment (530.14 eV for gas phase, Table I). This

discrepancy is typical of a SCF-type calculation. And indeed, our value is very similar to

the theoretical result of 530.78 eV previously obtained with the IVO method implemented in

the GSCF3 21 program (see table V in 2). For comparison, using a delocalised picture, the

energy obtained by exciting the b2 and a1 oxygen 1s MO’s is much larger : 542.734 eV.

These MO’s, as well as the two core excited states, are almost perfectly degenerate. As

pointed out by Schulte and Cederbaum 22, this is related to the large distance (~ 2.9 Å)

between the two oxygen atoms. Consequently, the optimised geometries of the two

delocalised core states are virtually indiscernible. The localised ROHF-GVB geometry of the

core states is shown in Fig. 1.b. The C=O* bond length is clearly longer (1.303 Å), consistent

with the promotion of the core electron to the * orbital. The five-member ring is distorted

while, on the other hand, the six-member rings are less affected. Especially, the C-H bond

lengths are not modified. The calculated adiabatic energy Ea (using unscaled harmonic ZPE

correction) of the core state is 530.08 eV. Using the anharmonic ZPE does not affect the

result significatively. This value is slightly too large when compared to the experimental

estimated value (529.00 eV, Table I). However, assuming that correlation effects are similar

for ground and core geometries, the Ev - Ea should be more reliable. The theoretical value of

0.79 eV may be compared to the three different values obtained for ANQ (0.72, 1.10 and 1.14

eV, Table I), which show the difficulty to identify the 0-0 band origin in the experiment.

7

These geometry changes between ground and core states are also reflected in the calculated

harmonic frequencies showed in table III : while the C-H stretching modes are identical to

those of the ground state, the C=O* stretching mode is reduced by ~19 % , while the other

C=O mode in almost unaffected (~4 %). This reduction leads to an unscaled value of 1645

cm-1, i.e. about 0.2 eV. Interestingly, this value corresponds to those of the vibrational

progression deduced from the fit of the experimental spectra (table I). As pointed out in 5, for

O1s *(C=O) core excited CO and H2CO, there is a reduction of about 37% of the C=O*

stretching when compared to ground state. The same reduction is also obtained for the O1s

*(C=O) state of acetic acid23. However, for this latter case and for formaldehyde24, the core

state geometry is pyramidalized, which is not the case for ANQ.

The calculated spectrum of the vibrational structure of core-excited ANQ using the

linear coupling approximation is displayed in Fig. 2.a. Because the four lowest lying modes

are below the typical kT value at room temperature (about 0.025 eV), a large number of hot

bands are populated. However, the spectrum seems dominated by a single progression of

~0.25 eV. In fact, it corresponds to the excitation of the two C=O stretching modes (and their

combination). Indeed, these modes are nearly degenerate in the ground state (47 and 48 in

table II). The 0.25 eV spacing is too large when compared to the value 0.2 eV deduced from

the fits, because the linear coupling approximation supposes that the excited state has the

same frequencies as the ground state. Consequently, when compared to experiment 1-3,5, the

peaks are too much separated, but the general shape of the band is well reproduced. The

secondary progressions in the simulated spectrum (0.05 to 0.14 eV) are mainly due the

excitation of five a1 modes corresponding to the in-plane deformation of the ring and

hydrogen bending movements. On the other hand, the calculations confirm without ambiguity

that the C-H stretching modes are not excited at all, contrary to initial claims 1,2. This rules

8

out the empirical formula used by Turner 4 to deduce the ground state frequency from the

excited state frequency and the Ev – Ea value.

The same spectrum, taking into account Duschinsky rotations, is shown in Fig. 2.b.

Only peaks with an intensity larger than 0.00001 were used. The general shape is very similar

to the first one. Because the excited state frequencies are slightly different from ground state,

hot bands peaks are not any more degenerate with the v=0 peaks. In order to identify clearly

which modes are involved, the calculations were reproduced without hot bands and a limiting

threshold for the Franck-Condon factors. The result is shown in table III. The main

conclusion is that several modes are excited upon core excitation : in addition to the C=O*

stretching mode (44), three modes (43, 42, 39) corresponding to in-plane deformation of the

ring and hydrogen bending movements are excited. Moreover, they have similar frequencies,

especially 44 and 43. Analysis of the modes shows that mode 44 has some in-plan hydrogen

bending character. Similarly, the three other modes have some C=O* stretching contribution,

especially 43. As can be seen in fig. 3, the quasi-degenracy of the two main modes 44 and

43 explains why the experimental data can apparently be fitted by a single mode, as was

done previously 1-3,5.

Another conclusion drawn from the fit of the experimental spectrum by a single

Morse potential is the degree of anharmonicity of about 2-3 meV, i.e. ~1% (table I). As can

be seen in table III, the calculated anharmonicity for the C-H stretching modes is indeed

about 1%. However, these modes are not excited in the core state. On the other hand, the four

main modes of fig. 3 show a very small anharmonicity (a few tens of wavenumbers, table

III). Especially, the calculated anharmonic C=O* is nearly identical to the harmonic value :

1622 cm-1 instead of 1645 cm-1. More likely, the uneven spacing of the vibrational peaks seen

in the experimental fit may be due to the quasi-degeneracy of modes 44 and 43, combined

to the huge number of peaks, especially hot bands. This is illustrated in Fig. 2 : the positions

9

of the stick peaks does not correspond necessarily to the maximum of the Gaussian

convolution and can cause the illusion of anharmonicity.

B. Halogenated acenaphtenequinone

The information on Br2Cl2-ANQ is even scarcer than for ANQ. The calculated

RHF/TZP geometry is shown in Fig. 4.a and the calculated frequencies in table IV. Except

for the lower values of C-Cl and C-Br stretching modes, they are very similar to ANQ,

especially the C=O and C-H stretching modes. There are no experimental values available,

but harmonic frequencies were calculated at the BP/6-31G* level in 5 (table IV). When

compared to these results, the RHF values are overestimated by ~15%, as in ANQ. 1D

anharmonic frequencies are very close to harmonic values.

The SCF vertical core excitation energy is predicted to be 530.78 eV, i.e 0.70 eV

above the proposed experimental value (Table I). The delocalised value is 542.66 eV. The

unscaled harmonic ZPE-corrected adiabatic value is 530.02 eV. As for ANQ, the Ev - Ea

difference (0.76 eV) is very close to that obtained from the fit (0.69 eV from Table I). The

ROHF/TZP optimised geometry of the core state is shown in Fig. 4.b. The structural changes

are very similar to the ANQ case, and consist essentially in a weakened C=O* bond length

and a slight distortion from C2v to Cs symmetry. The corresponding frequencies are given in

table IV. As for ANQ, upon O1s * excitation, the frequency (2034 cm-1) of the

asymmetric C=O stretching mode is reduced by 19%.

The simulated vibrational structure of core excited Br2Cl2-ANQ is shown in Fig. 5. In

Fig. 5.a, the linear coupling approximation was used, while the Duschinsky effect spectrum is

displayed in Fig 5.b. It should be noticed that the calculations of Fig 5.a do not include hot

bands, because of limitations of the linear coupling program. Indeed, in Br2Cl2-ANQ, hot

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bands play a role even larger than in ANQ, since 10 of the 54 modes are below the kT value

at room temperature.

The analysis of the Fig 5.a spectrum shows assignments very similar to the ANQ case

: the main excitation is due to the two quasi-degenerate C=O stretching modes, with

contributions of in-plane ring deformation modes. The spacing of the main progression (0.25

eV) is therefore too large when compared to the value deduced from experiment (0.186 eV,

table I). When Duschinsky rotations are taken into account (Fig. 5.b), the main progression is

still present, with a spacing of about 0.2 eV, in agreement with experiment. Although the

same FWHM (239 meV) was used in both Fig. 5.a and 5.b, this reduced spacing gives a

spectrum which looks like the experimental one 5. Because the core state frequencies are

slightly different from the ground state ones, hot bands are not degenerate with the v=0 peaks

and are slightly shifted.

As for ANQ, in order to determine which modes are responsible for the main

progression, hot bands were removed from the simulation. The result is shown in Fig. 6.a.

The result is qualitatively different from the ANQ case : only the C=O* stretching mode 48

has large Franck-Condon factors. The ring deformation/hydrogen bending modes (39, 43,

and47) and the second C=O mode (52) only appear as combination bands with 48 but with

rather low intensities. Moreover, in contrast to the ANQ case, mode 48 is almost a pure

C=O* stretching mode with no contribution from the movement of other atoms in the

molecule. Similarly, modes involving Br and Cl atoms are not excited, because of the larger

mass of these atoms. Thus, for Br2Cl2-ANQ, it would seem more justified to simulate the

vibrational structure with only one mode. However, it is not possible to ignore the numerous

hot bands. This can be seen in Fig. 6.b where the sole 48 progression is shown with all the

corresponding hot bands. This figure emphasizes the major role played by hot bands in the

11

vibrational excitation. Moreover, these hot bands are probably responsible of the slight

anharmonicity (2.4 meV or 1.2 %, table I) deduced from the fit of the experimental data.

IV. CONCLUSION

In the present work, we have used a simple but entirely ab initio approach to obtain

insight on the vibrational structure of the core states of ANQ and Br2Cl2-ANQ. The main

conclusions are the following :

- When compared to the ground state frequency, the C=O* stretching frequency

corresponding to the core excited oxygen is lowered by about 19% due to the

weakening of the C=O bond upon excitation to the * orbital. The calculations

confirm that this mode cannot be assigned to a C-H stretching mode.

- For ANQ, this C=O* stretching mode has significant contribution from in-plane

carbon ring deformation and bending movements of the hydrogen atoms. At least two

other modes show this kind of mixing and lead to significant Franck-Condon factors.

This is consistent with the C2v to Cs symmetry breaking of the core excited molecule.

Therefore, as initially stated, the localized excitation of the oxygen 1s orbital has

repercussions on the whole molecule. Because these three modes have very similar

frequencies, the experimental spectrum can be accurately fitted by a single

progression of ~0.2 eV.

- For Br2Cl2-ANQ, the situation is qualitatively different since only the almost pure

C=O* stretching mode leads to significant Franck-Condon intensities. However,

because this molecule has numerous low frequency modes, hot bands contribute

significatively to the spectrum.

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- Anharmonic effects appear to be very small, especially for the C=O* stretching mode.

The apparent anharmonicity deduced from the experimental fits is likely due to the

large number of hot and combination bands in the calculated spectra. This raises the

question of how many free parameters should be included in a fit for a molecule with

54 vibrational modes.

The main drawback of the calculations is the lack of correlation effects, responsible

for an overestimation of the calculated frequencies. However, inclusion of such effects should

not modify the validity of the present conclusions.

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Table I. Main results of experimental fits of the experimental NEXAFS spectra (eV)

Ea Ev Ev - Ea h’ h’ (meV)

Br2Cl2-ANQa 529.39 530.08 0.69 0.186 2.4

ANQa 529.35 530.07 0.72 0.193 2.5

ANQb 528.98 530.08 1.10 0.200 2.6

ANQ (gas phase)c 529.00 530.14 1.14 0.200 3.2

a Ref. 5

b Ref. 1

c Ref. 3

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Table II. Calculated and observed frequencies of the highest lying modes of ANQ ground state (cm-1)

RHF a

TZP

RHF b

TZP

RHF c

TZP

RHF d

TZP

B3LYP e

6-311++G(3d,2p)

Exp.

FTIR e

Exp.

Raman e

Exp.

FTIR f

Exp.

Raman g

a1 54 3362 (3042) 3340 (3022) 3255 (2945) 3221 (2914) 3194 (3091) - 3086 3065 3056 C-H sym. Str.

b2 53 3361 (3041) 3396 (3072) 3241 (2932) 3227 (2919) 3194 (3091) - 3086 3078 3075 C-H asym. Str.

a1 52 3349 (3030) 3365 (3044) 3244 (2935) 3210 (2904) 3182 (3080) - 3086 C-H sym. Str.

b2 51 3348 (3029) 3370 (3049) 3240 (2931) 3227 (2919) 3182 (3080) - 3086 3028 3030 C-H asym. Str.

a1 50 3332 (3014) 3357 (3037) 3213 (2907) 3200 (2895) 3168 (3066) 3051 3075 C-H sym. Str.

b2 49 3330 (3013) 3367 (3046) 3203 (2898) 3187 (2883) 3166 (3064) 3051 3075 2938 - C-H asym. Str.

a1 48 2037 (1843) 2031 (1837) 2013 (1821) 2007 (1816) 1817 (1759) - 1745 1780 1780 C=O sym. Str.

b2 47 2034 (1840) 2045 (1850) 2008 (1817) 2004 (1813) 1798 (1740) 1705 1725 1737 1735 C=O asym. Str.

a This work. Harmonic values. Scaled (0.9047) values in parentheses.

b This work. Anharmonic values (unscaled), 1D-coupling. Scaled (0.9047) values in parentheses.

c This work. Anharmonic VSCF values (unscaled), 2D-coupling. Scaled (0.9047) values in parentheses.

15

d This work. Anharmonic PT2-VSCF values (unscaled), 2D-coupling. Scaled (0.9047) values in parentheses.

e Ref. 20. Scaled (0.9679) values in parentheses.

f Sigma-Aldrich values quoted in Ref. 20

g Ref. 25 (solid phase)

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Table III. Calculated frequencies of the relevant modes of ANQ O1s * excited state (cm-1)

Cs GVB a

TZP

GVB b

TZP

GVB c

TZP

GVB d

TZP

a’ 54 3362 (3042) 3324 (3007) 3228 (2920) 3215 (2909) C-H Str.

a’ 53 3361 (3041) 3331 (3014) 3230 (2922) 3221 (2914) C-H Str.

a’ 52 3348 (3029) 3364 (3043) 3240 (2931) 3197 (2892) C-H Str.

a’ 51 3347 (3028) 3369 (3048) 3238 (2929) 3220 (2913) C-H Str.

a’ 50 3331 (3014) 3372 (3051) 3199 (2894) 3187 (2883) C-H Str.

a’ 49 3330 (3013) 3367 (3046) 3194 (2890) 3181 2878) C-H Str.

a’ 48 1960 (1773) 1946 (1761) 1933 (1749) 1933 (1749) C=O Str.

a’ 44 1645 (1488) 1645 (1488) 1622 (1467) 1621 (1467) C=O* Str./ HCC in-plane bend/ Ring deformation

a’ 43 1626 (1471) 1628 (1472) 1606 (1453) 1604 (1451) HCC in-plane bend/ Ring deformation / C=O* Str.

17



a This work. Localized core hole. Harmonic values. Scaled (0.9047) values in parentheses.

b This work. Anharmonic values, 1D-coupling. Scaled (0.9047) values in parentheses.

c This work. Anharmonic VSCF values (unscaled), 2D-coupling. Scaled (0.9047) values in parentheses.

d This work. Anharmonic PT2-VSCF values (unscaled), 2D-coupling. Scaled (0.9047) values in parentheses.

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Table IV. Calculated frequencies of the highest lying modes of Br2Cl2-ANQ ground state

(cm-1)

RHF a

TZP

RHF b

TZP

BP c

6-31G*

a1 3391 (3068) 3343 (3024) 3154 C-H sym. Str.

b2 3391 (3068) 3455 (3126) 3154 C-H asym. Str.

a1 2048 (1853) 2041 (1846) 1766 C=O sym. Str.

b2 2044 (1849) 2055 (1859) 1734 C=O asym. Str.

a1 1775 (1606) 1775 (1606) C-C ring Str.

b2 1768 (1600) 1770 (1601) C-C ring Str./C-H bend

a1 1744 (1578) 1746 (1580) C-C ring Str./C-H bend



a1 1508 (1364) 1511 (1367) C-C ring Str./C-H bend

…

a1 1099 (994) 1100 (995) C-Cl sym. Str.

b2 1008 (912) 1008 (912) C-Cl asym. Str.

a1 960 (869) 960 (869) C-Br sym. Str.

b2 754 (682) 755 (683) C-Br asym. Str.

a This work. Harmonic values. Scaled (0.9047) values in parentheses.


c Ref. 5

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Table V. Calculated frequencies of the highest lying modes of Br2Cl2-ANQ O1s *

excited state (cm-1)

Cs GVB a

TZP

GVB b

TZP

a’ 54 3390 (3067) 3308 (2993) C-H sym. Str.

a’ 53 3389 (3066) 3310 (2995) C-H asym. Str.

a’ 52 1969 (1781) 1954 (1768) C=O Str.

a’ 51 1771 (1602) 1773 (1602) HCC in-plane bend/ Ring deformation



a’ 48 1655 (1497) 1653 (1495) C=O* Str.




a This work. Localized core hole. Harmonic values. Scaled (0.9047) values in parentheses.


20

REFERENCES

1 A. Schöll, D. Hubner, T. Schmidt, S. G. Urquhart, R. Fink, and E. Umbach, Chem. Phys. Lett. 392, 297 (2004).

2 A. Schöll, Y. Zou, D. Huebner, S. G. Urquhart, T. Schmidt, R. Fink, and E. Umbach, J. Chem. Phys. 123, 044509 (2005).

3 R. Fink, D. Hübner, A. Schöll, E. Umbach, K. C. Prince, R. Richter, M. Coreno, and M. Alagia, Elletra Highlights, 51 (2002-2003).

4 D. W. Turner, C. Baker, A. D. Baker, and C. R. Brundle, Molecular Photoelectron Spectroscopy. (Wiley, London, 1970).

5 N. Schmidt, T. Clark, S. G. Urquhart, and R. H. Fink, J. Chem. Phys. 135, 144301 (2011).

6 G. Chaban, M. W. Schmidt, and M. S. Gordon, Theor. Chem. Acc. 97, 88 (1997). 7 M. W. Schmidt, K. K. Baldridge, J. A. Boatz, S. T. Elbert, M. S. Gordon, J. H.

Jensen, S. Koseki, N. Matsunaga, K. A. Nguyen, S. Su, T. L. Windus, M. Dupuis, and J. A. Montgomery Jr, J. Comp. Chem. 14, 1347 (1993).

8 T. H. Dunning Jr., J. Chem. Phys. 55, 716 (1971). 9 A. McLean, J. Chem. Phys. 72, 5639 (1980). 10 K. Peterson, D. Figgen, E. Goll, H. Stoll, and M. Dolg, J. Chem. Phys. 119, 11113

(2003). 11 R. F. Fink, S. L. Sorensen, A. N. de Brito, A. Ausmees, and S. Svensson, J. Chem.

Phys. 112, 6666 (2000); L. S. Cederbaum and W. Domcke, J. Chem. Phys. 66, 5084 (1977); N. V. Dobrodey, H. Köppel, and L. S. Cederbaum, Phys. Rev. A 60, 1988 (1999).

12 S. G. Andrade, L. s. C. S. GonÃ§alves, and F. E. Jorge, J. Mol Struct. (THEOCHEM) 864, 20 (2008).

13 R. B. Gerber and J. O. Jung, in Computational Molecular Spectroscopy, edited by P. R. B. P.Jensen (Wiley and Sons, Chichester, 2000), pp. 365; G. Chaban, J. Chem. Phys. 111, 1823 (1999).

14 K. Yagi, J. Chem. Phys. 121, 1383 (2004). 15 J. P. Dognon, C. Pouchan, A. Dargelos, and J. P. Flament, Chem. Phys. Lett. 109, 492

(1984); J.-P. Flament, Université de Paris-Sud, 1981. 16 L. S. Cederbaum and W. Domcke, J. Chem. Phys. 64, 603 (1976); W. Domcke and L.

S. Cederbaum, J. Chem. Phys. 64, 612 (1976); H. Köppel, W. Domcke , and L. S. Cederbaum, Adv. Chem. Phys. 57, 59 (1984).

17 V. A. Mozhayskiy and A. I. Krylov, ezSpectrum, http://iopenshell.usc.edu/downloads 18 F. Duschinsky, Acta Physicochim. USSR 7, 551 (1937). 19 T. C. W. Mak and J. Trotter, Act. Cryst. 16, 811 (1963). 20 L. Sinha, O. Prasad, V. Narayan, and R. K. Srivastava, J. Mol Struct. (THEOCHEM)

958, 33. 21 N. Kosugi and H. Kuroda, Chem. Phys. Lett. 74, 490 (1980). 22 H. D. Schulte and L. S. Cederbaum, J. Chem. Phys. 103, 698 (1995). 23 D. Duflot, J.-P. Flament, A. Giuliani, J. Heinesch, and M.-J. Hubin-Franskin, Int. J.

Mass Spec. 277, 70 (2008). 24 A. B. Trofimov, E. V. Gromov, T. E. Moskovskaya, and J. Schirmer, J. Chem. Phys.

113, 6716 (2000). 25 S. Nath Singh, M. G. Jayswal, and R. S. Singh, Current Sci. 36, 624 (1967).

21

22

Figure 1. (a) Calculated geometry (RHF/TZP) of ANQ. (b) Calculated geometry (ROHF/TZP) of core excited ANQ. Distances in Å

and angles in °. The black square indicates the core excited atom.

23

Figure 2. Vibrational structure of core excited ANQ. (a) in the linear coupling approximation, 156 meV FWHM (b) with Duschinsky

rotations. Blue : 156 meV FWHM Green : 218 meV FWHM.

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Figure 3. :Most important modes involved in core excited ANQ.

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Figure 4. (a) Calculated geometry (RHF/TZP) of Br2Cl2-ANQ. (b) Calculated geometry (ROHF/TZP) of core excited Br2Cl2-ANQ.

Distances in Å and angles in °. The black square indicates the core excited atom.

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Figure 5. Vibrational structure of core excited Br2Cl2-ANQ (FWHM = 239 meV). (a) in the linear coupling approximation (b) with

Duschinsky rotations.

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Figure 6. (a) Most important modes involved in core excited Br2Cl2-ANQ. (b) Hot bands for mode 48.

Documents

The vibrational structure of the oxygen K-shell spectra in acenaphthenequinones: An ab initio study