Stergios Piligkos
email: piligkos@kiku.dk

Ib Laursen

Axel Morgenstjerne

Høgni Weihe
email: weihe@kiku.dk

Sign and Magnitudes of Spin Hamiltonian Parameters for Mn 2+ Impurities in Calcite. A Multi-and Low-Frequency EPR Study

Keywords: EPR spectroscopy, calcite, dolomite, marble, spin Hamiltonian

L-, S-, and X-band powder EPR spectra and an L-band single-crystal spectrum of Mn 2+ impurities in calcite are analysed by fitting of full spectral traces to a theoretical model. This analysis gives as parameters the traditional spin Hamiltonian parameters reflecting the three-fold symmetry of the cation lattice site as well as parameters determining the bandshape and width of the resonances. The three frequencies give a consistent description of the system. For this spin system it is shown that the relative sign of the axial zero-field splitting parameter D and the hyperfine coupling constant A may be safely determined at L-band.

Introduction

The EPR spectrum of Mn 2+ ions present as an impurity in calcite, i.e. CaCO 3 which crystallises in the space group R 3c belonging to the trigonal crystal system, has for more than half a century [1] been a challenge for EPR spectroscopists. The Mn 2+ ion in this lattice has a high-spin 3d 5 electronic configuration resulting in an orbitally non-degenerate S = 5 2 ground state. The Mn 2+ ion is coordinated to 6 oxide ligands from the carbonate anions resulting in a ligand field of S 6 symmetry. In addition, the 55 Mn nucleus has a nuclear spin of I = 5 2 . This results in spectra exhibiting fine as well as hyperfine structure, resulting from the three-fold site symmetry and the electron-nucleus interaction, respectively. In the past, the parameters in the 1.997 < g ⊥ < 2.0018 2.001 < g < 2.004 2.00 < g N < 3.31 (2) where the parameters, except the g factors, are all in units of 10 -4 cm -1 .

Evidently, the numerical values of A ⊥ , A , g and g ⊥ are found to lie within fairly narrow ranges. These values were, in most cases, extracted from the experimental spectra by using formulae from perturbation theory to various orders. Very recently, this subject was critically reviwed by ref [16], which introduced six (!) different methods to extract D and A values from the powder spectrum. To the best of our knowledge, the studies performed so far have all been performed at X-band frequencies, i.e. at 9-10 GHz, and at such relatively high frequencies the magnitude, not the sign, of the parameters A = (A ⊥ ≈ A ), and D, by and large, determine the overall appearence of the spectrum; the remaining parameters being less important. The following three sign combinations of the hyperfine coupling constant A and the axial zero-field splitting parameter D have been reported in the earlier literature: (D<0,A<0) [3,7,16], (D>0,A<0) [8,9,10,11,12], and (D>0,A>0) [1,5] . Only two of the papers [3,12] cited above seem to have acknowledged that only one sign combination of the values of A and D can possibly be correct. A sad detail is, however, that these authors disagree.

In this contribution we present experimental EPR spectra of powder samples of Mn 2+ impurities in calcite recorded at 9.450, 3.866 and 1.1078 GHz, as well as a single-crystal spectrum obtained at 3.002 GHz. These spectra clearly allow us to, first, distinguish between the two possible relative-sign situations A×D > 0 or A×D < 0. Based on the fact that the nuclear g N factor of 55 Mn is positive we are, finally, in the position of determining the absolute signs of A and D.

Results and Discussion

An X-band powder spectrum of CaCO 3 :Mn 2+ is shown in Figure 1. The X-band spectrum has been discussed in depth the last five decades, or so, and we will not repeat this discussion here. Every line and shoulder has been assigned to specific transitions within the 36 energy levels of this spin system. The correctness of these assignments depends, of course, on whether or not the right sign of A is chosen. Of importance for this work, however, is the large variation of more than an order of magnitude in bandwiths of the numerous lines in the spectrum. The narrowest derivative-like lines have a peak-to-peak widths of less than 1 G whereas some of the weaker absorptionlike lines have a full widths in half height in excess of 10 G.

Initially, the X-band spectrum was modelled with eqn (1) without the last three nuclear terms. This, already, resulted in good agreement yielding the residual designated as "b" in Figure 1. The very systematic appearence of this residual, especially at field values associated with the lines marked with an "f" in Figure 1 prompted for the nuclear terms to be present in the operator. These lines correspond to the 10 possible transitions within the ± 1 2 Kramers doublet having ∆M = 1 and ∆m = ±1, i. e. the nuclear quantum number changes, and as a consequence these lines are sensitive to the nuclear parameters, i. e. the nuclear Zeeman effect and the quadrupole interaction. Inclusion of these terms in the Hamiltonian changed the fit from being just good to being absolutely excellent, see the residual designated as "c" in Figure 1, the computed spectrum is virtually identical with the experimental one.

The spin Hamiltonian parameters together with the bandwidth and bandshape parameters were extracted directly from the full spectrum by minimising the squared residuals as outlined in the Appendix. From the Xband spectrum we extracted the following spin Hamiltonian parameters:

g ⊥ = 2.00123(2), g = 2.00131(5), A ⊥ = -88.23(1) • 10 -4 cm -1 , A = -87.60(4)•10 -4 cm -1 , D = -76.0(2)•10 -4 cm -1 , B 0 4 = -0.047(3)•10 -4 cm -1 , B 3 4 = 1.12(5) • 10 -4 cm -1 , g N = +1.38(5) cm -1 , P D = -0.176(12) • 10 -4 cm -1 , P E = 0.13(5) • 10 -4 cm -1 .
Here, the digit(s) in parentheses is the estimated standard deviation on the last digit(s) as given by the Levenberg-Marquard A noteworthy exception to this agreement is the nuclear g N factor which is found outside the previously determined range, see eqs (2). The value found by us is, within one standard deviation, identical to that reported for the 55 Mn nucleus, namely g N = +1.3844 .

In order to account for the bandwidth and bandshape the following parameters were introduced and determined: (5). The parameters w x , w y , and w z are the components of an anisotropic linewidth common for all energy level pairs, and the a parameter describes the lorentzian/gaussian composition of the line shape, see the Appendix. The parameters σ D accounts for the fact that the Mn 2+ centers are not all situated exactly in the same environment in the crystals. The result is that the spin Hamiltonian parameter D has not a sharp value but is somehow distributed around a mean value; the mean value being the value reported above. We have assumed that this distribution is gaussian having a width of σ D . It was necessary to also introduce a small spread in the rhombic spin Hamiltonian parameter E, i.e. the coefficient multiplying the spin operator term ( Ŝ2

w x = w y = 0.89(2) • 10 -4 cm -1 , w z = 1.01(5) • 10 -4 cm -1 , σ D = 1.1(6) • 10 -4 cm -1 , σ E = 2.8(6) • 10 -4 cm -1 , a = 0.87
x -Ŝ2 y ). The mean value of the parameter E is zero but due to crystal imperfections, the Mn 2+ ions are not situated at sites having strict S 6 symmetry. We note in passing, that a similar situation was found for

∆(+)[Cr(chxn) 3 λλλ] 3+ doped into ∆(+)[Rh(chxn) 3 λλλ](NO 3 ) 3 •3H 2 O (chxn = 1,2-diamino-cyclohexane) which
also crystallises in a uniaxial space group with the cation ion on a three-fold axis [19]. We tried to introduce spreads in the other parameters of eqn (1); this did not improve the fits significantly, and therefore we have chosen σ D and σ E as the only bandwidth broadening parameters. The correctness of the parameter values, as extracted from the X-band powder spectrum, may now be verified by recording spectra at lower frequencies. Powder spectra at S and L band frequencies are shown in Figures 2 and3, respectively. The powder used in Figures 1,2, and 3 was from the same calcite single crystal. Fitting these spectra to the same model as used above resulted in essentially the same parameter values with two exeptions. (1) The nuclear g N factor becomes badly determined at low magnetic fields; this is expected since the energetic consequence of this term is small at lower fields.

(2) The bandwidth parameters obtained from the S and L band spectra were higher, reflecting that these spectra were recorded with a slightly too large modulation amplitude. The computed spectra are also shown in Figures 2 and3. The agreement is good. We tried to change the sign of one of the parameters D or A. In the case of the S band spectrum, Figure 2, this gave a spectrum clearly different from that shown. In the case of the L band spectrum, Figure 3, this sign change resulted in a computed spectrum bearing no resemblence, at all, with the experimental spectrum. From the comparison of the experimental and computed L band spectra we can conclude that D and A have the same sign. The reason for this clear conclusion may be inferred from Figures 4 and5 which shows the energy level diagram at low magnetic fields for two different sign combinations. At low magnetic fields the two situations result in qualitatively very different energy level diagrams.

At L and S band, the microwave quantum is small compared to the splittings at zero magnetic field, see Figures 4 and5. Therefore, the spectra depend dramatically on the sign combination, especially in the low-field end.

The acid test performed in order to verify our parameter values is shown in Figure 6, which shows a single-crystal spectrum recorded at 3 GHz on a home-built instrument. See the caption of Figure 6 details. The spectrum exhibits very uniform linewidths varying between 1.0 and 1.6 Gauss. This indicates a crystal of higher quality than that used for the powder spectra. Likewise, this indicates the use of a too large modulation amplitude which we had to choose in order to reduce the noise in, and the acquisition time of, the spectrum. At least 110 lines can be counted in the experimental spectrum. A computed spectrum obtained by using the above spin Hamiltonian parameters is shown as the lower trace in Figure 6. The line positions in the computed spectrum deviate on average by 0.4 Gauss, and for no line more than the bandwidth, from the the corresponding lines in the experimental spectrum. This agreement is acceptable taking into account that there is some uncertainty in the orientation of the crystal. The whole spectrum, and especially the number and placement of the very weak lowfield lines, is very sensitive to the relative signs of A and D, as well as to the remaining spin Hamiltonian parameters.

In summary, we have demonstrated here that magnitudes and signs of the spin Hamiltonian parameters may be obtained from low-frequency EPR spectra at room temperature. The X-band spectrum indicates that the D and A parameters have the same sign. This was verified by the lower-frequency spectra. By making use of the fact that the nuclear g N factor is positive, we conclude that the parameters D and A are both negative as only this sign combination of g N , D, and A reproduces all spectra. Hence, we agree with reference [3], which discussed these matters based on temperature variations of low-temperature, presumably X-band, spectra, but without showing the experimental data.

Our discussion of the subject might be of importance for the field of archeometry which currently makes use of the CaCO 3 :Mn 2+ X-band EPR spectrum as a probe for the provenance of marble blocks used in ancient and(c) with all the terms of eqn (1). The vertical scale is the same for all plots. The lines on each side of the "f"-s correspond to the transitions

| -1 2 , m → | 1 2 , m ± 1 .

B/G

A Computations

The parameters of eqn (1) were extracted from the experimental spectra by standard χ 2 minimization

χ 2 = i [y exp,i (B i ) -y calc,i (B i ; q)] 2 σ 2 i ( 3
)
making use of the Leuvenberg-Marquardt algorithm [17]. y exp,i and y calc,i is the experimental and calculated intensity, respectively, obtained for the i-th field value B i . q designates the parameters to be extracted from the spectrum. σ i is the experimental uncertainty of the i-th experimental intensity.

In our computations, this factor is composed of two terms

σ 2 i = σ 2 n + ∂y i ∂B 2 σ 2 B ( 4
)
where σ n is the noise level common to all field points and σ B is the field uncertainty taken to be constant (0.1 G) in the field interval.

At each field value the contribution to the derivative spectrum from any pair of energy levels a, b is computed as the field derivative of y = (P ab p a -P ba p b ) × f (hν, ∆ ab , Γ) .

(5)

Here, P ab and P ba is the transition probability for the upward and downward transition, respectively. p a and p b is the thermal population of level a and b, respectively. f () is a bandshape function with the energy equivalent of the microwave radiation, the energy separation between levels a and b, and a bandwidth as arguments, respectively.

In order to introduce some flexibility into the bandshape we use as band-

w 2 ab = w 2 x l 2 x + w 2 y l 2 y + w 2 z l 2 z + i ∂∆ ab ∂q 2 σ 2 q i , ( 7
)
where w x , w y , and w z are common residual bandwidths for all energy level pairs, and l x , l y , and l z are direction cosines of the magnetic field vector with respect to the molecular coordinate system. The terms in the summation account for that the parameters do not have sharp values but rather may be distributed around a mean value. The form eqn (7) assumes that this parameter distribution is gaussian with a width of σ q i . We are well aware of that eqn ( 7) is only correct bandwidth to use if the bandshape itself as well as parameter distribution are both gaussian. For a bandshape described by eqn (6), eqn (7) should be modified. However, such a modification would not alter the qualitative outcome of using eqn (7), namely that transitions involving energy levels being more or less sensitive to the parameter q i will become broad and narrow, respectively.

16

Page

Introduction

The EPR spectrum of Mn 2+ ions present as an impurity in calcite, i.e. CaCO 3 which crystallises in the space group R 3c belonging to the trigonal crystal system, has for more than half a century [1] been a challenge for EPR spectroscopists. The Mn 2+ ion in this lattice has a high-spin 3d 5 electronic configuration resulting in an orbitally non-degenerate S = 5 2 ground state. The Mn 2+ ion is coordinated to 6 oxide ligands from the carbonate anions resulting in a ligand field of S 6 symmetry. In addition, the 55 Mn nucleus has a nuclear spin of I = 5 2 . This results in spectra exhibiting fine as well as hyperfine structure, resulting from the three-fold site symmetry and the electron-nucleus interaction, respectively. In the past, the parameters in the

Ĥ = µ B g ⊥ ( Ŝx B x + Ŝy B y ) + µ B g z Ŝz B z + A ⊥ ( Ŝx Îx + Ŝy Îy ) + A Ŝz Îz +D Ŝ2 z - 1 3 S(S + 1) + B 0 4 Ô0 4 + B 3 4 Ô3 4 +P D Î2 z - 1 3 I(I + 1) + P E ( Î2 x -Î2 y ) -µ N g N Îx B x + Îy B y + Îz B z , (1)
|P E | = 0.069 1.997 < g ⊥ < 2.0018 2.001 < g < 2.004 2.00 < g N < 3.31 (2)
where the parameters, except the g factors, are all in units of 10 To the best of our knowledge, the studies performed so far have all been performed at X-band frequencies, i.e. at 9-10 GHz, and at such relatively high frequencies the magnitude, not the sign, of the parameters A = (A ⊥ ≈ A ), and D, by and large, determine the overall appearence of the spectrum; the remaining parameters being less important. The following three sign combinations of the hyperfine coupling constant A and the axial zero-field splitting parameter D have been reported in the earlier literature: (D<0,A<0) [3,7,16], (D>0,A<0) [8,9,10,11,12], and (D>0,A>0) [1,5] . Only two of the papers [3,12] cited above seem to have acknowledged that only one sign combination of the values of A and D can possibly be correct. A sad detail is, however, that these authors disagree.

In this contribution we present experimental EPR spectra of powder samples of Mn 2+ impurities in calcite recorded at 9.450, 3.866 and 1.1078 GHz, as well as a single-crystal spectrum obtained at 3.002 GHz. These spectra clearly allow us to, first, distinguish between the two possible relative-sign situations A×D > 0 or A×D < 0. Based on the fact that the nuclear g N factor of 55 Mn is positive we are, finally, in the position of determining the absolute signs of A and D.

Results and Discussion

An X-band powder spectrum of CaCO 3 :Mn 2+ is shown in Figure 1. The X-band spectrum has been discussed in depth the last five decades, or so, and we will not repeat this discussion here. Every line and shoulder has been assigned to specific transitions within the 36 energy levels of this spin system. The correctness of these assignments depends, of course, on whether or not the right sign of A is chosen. Of importance for this work, however, is Initially, the X-band spectrum was modelled with eqn (1) without the last three nuclear terms. This, already, resulted in good agreement yielding the residual designated as "b" in Figure 1. The very systematic appearence of this residual, especially at field values associated with the lines marked with an "f" in Figure 1 prompted for the nuclear terms to be present in the operator. These lines correspond to the 10 possible transitions within the ± 1 2 Kramers doublet having ∆M = 1 and ∆m = ±1, i. e. the nuclear quantum number changes, and as a consequence these lines are sensitive to the nuclear parameters, i. e. the nuclear Zeeman effect and the quadrupole interaction. Inclusion of these terms in the Hamiltonian changed the fit from being just good to being absolutely excellent, see the residual designated as "c" in Figure 1, the computed spectrum is virtually identical with the experimental one.

The spin Hamiltonian parameters together with the bandwidth and bandshape parameters were extracted directly from the full spectrum by minimising the squared residuals as outlined in the Appendix. From the Xband spectrum we extracted the following spin Hamiltonian parameters:

g ⊥ = 2.00123(2), g = 2.00131(5), A ⊥ = -88.23(1) • 10 -4 cm -1 , A = -87.60(4)•10 -4 cm -1 , D = -76.0(2)•10 -4 cm -1 , B 0 4 = -0.047(3)•10 -4 cm -1 , B 3 4 = 1.12(5) • 10 -4 cm -1 , g N = +1
.38(5) cm -1 , P D = -0.176(12) • 10 -4 cm -1 , P E = 0.13(5) • 10 -4 cm -1 . Here, the digit(s) in parentheses is the estimated standard deviation on the last digit(s) as given by the Levenberg-Marquard A noteworthy exception to this agreement is the nuclear g N factor which is found outside the previously determined range, see eqs (2). The value found by us is, within one standard deviation, identical to that reported for the 55 Mn nucleus, namely g N = +1.3844 .

In order to account for the bandwidth and bandshape the following parameters were introduced and determined: (5). The parameters w x , w y , and w z are the components of an anisotropic linewidth common for all energy level pairs, and the a parameter describes the lorentzian/gaussian composition of the line shape, see the Appendix. The parameters σ D accounts for the fact that the Mn 2+ centers are not all situated exactly in the same environment in the crystals. The result is that the spin Hamiltonian parameter D has not a sharp value but is somehow distributed around a mean value; the mean value being the value reported above. We have assumed that this distribution is gaussian having a width of σ D . It was necessary to also introduce a small spread in the rhombic spin Hamiltonian parameter E, i.e. the coefficient multiplying the spin operator term ( Ŝ2

w x = w y = 0.89(2) • 10 -4 cm -1 , w z = 1.01(5) • 10 -4 cm -1 , σ D = 1.1(6) • 10 -4 cm -1 , σ E = 2.8(6) • 10 -4 cm -1 , a = 0.87
x -Ŝ2 y ). The mean value of the parameter E is zero but due to crystal imperfections, the Mn 2+ ions are not situated at sites having strict S 6 symmetry. We note in passing, that a similar situation was found for The correctness of the parameter values, as extracted from the X-band powder spectrum, may now be verified by recording spectra at lower frequencies. Powder spectra at S and L band frequencies are shown in Figures 2 and3, respectively. The powder used in Figures 1,2, and 3 was from the same calcite single crystal. Fitting these spectra to the same model as used above resulted in essentially the same parameter values with two exeptions. (1) The nuclear g N factor becomes badly determined at low magnetic fields; this is expected since the energetic consequence of this term is small at lower fields.

∆(+)[Cr(chxn) 3 λλλ] 3+ doped into ∆(+)[Rh(chxn) 3 λλλ](NO 3 ) 3 •3H 2 O (chxn = 1,2-diamino-cyclohexane) which
(2) The bandwidth parameters obtained from the S and L band spectra were higher, reflecting that these spectra were recorded with a slightly too large modulation amplitude. The computed spectra are also shown in Figures 2 and3. The agreement is good. We tried to change the sign of one of the parameters D or A. In the case of the S band spectrum, Figure 2, this gave a spectrum clearly different from that shown. In the case of the L band spectrum, Figure 3, this sign change resulted in a computed spectrum bearing no resemblence, at all, with the experimental spectrum. From the comparison of the experimental and computed L band spectra we can conclude that D and A have the same sign. The reason for this clear conclusion may be inferred from Figures 4 and5 which shows the energy level diagram at low magnetic fields for two different sign combinations. At low magnetic fields the two situations result in qualitatively very different energy level diagrams.

At L and S band, the microwave quantum is small compared to the splittings at zero magnetic field, see Figures 4 and5. Therefore, the spectra depend dramatically on the sign combination, especially in the low-field end.

The acid test performed in order to verify our parameter values is shown in Figure 6, which shows a single-crystal spectrum recorded at 3 GHz on a home-built instrument. See the caption of Figure 6 details. The spectrum exhibits very uniform linewidths varying between 1.0 and 1.6 Gauss. This indicates a crystal of higher quality than that used for the powder spectra. Likewise, this indicates the use of a too large modulation amplitude which we had to choose in order to reduce the noise in, and the acquisition time of, the spectrum. At least 110 lines can be counted in the experimental spectrum. A computed spectrum obtained by using the above spin Hamiltonian parameters is shown as the lower trace in Figure 6. The line positions in the computed spectrum deviate on average by 0.4 Gauss, and for no line more than the bandwidth, from the the corresponding lines in the experimental spectrum. This agreement is acceptable taking into account that there is some uncertainty in the orientation of the crystal. The whole spectrum, and especially the number and placement of the very weak lowfield lines, is very sensitive to the relative signs of A and D, as well as to the remaining spin Hamiltonian parameters.

In summary, we have demonstrated here that magnitudes and signs of the spin Hamiltonian parameters may be obtained from low-frequency EPR spectra at room temperature. The X-band spectrum indicates that the D and A parameters have the same sign. This was verified by the lower-frequency spectra. By making use of the fact that the nuclear g N factor is positive, we conclude that the parameters D and A are both negative as only this sign combination of g N , D, and A reproduces all spectra. Hence, we agree with reference [3], which discussed these matters based on temperature variations of low-temperature, presumably X-band, spectra, but without showing the experimental data.

Our discussion of the subject might be of importance for the field of archeometry which currently makes use of the CaCO 3 :Mn 2+ X-band EPR spectrum as a probe for the provenance of marble blocks used in ancient and(c) with all the terms of eqn (1). The vertical scale is the same for all plots. The lines on each side of the "f"-s correspond to the transitions

| -1 2 , m → | 1 2 , m ± 1 .
B/G 3600 3400 3200 3000

A Computations

The parameters of eqn (1) were extracted from the experimental spectra by standard χ 2 minimization

χ 2 = i [y exp,i (B i ) -y calc,i (B i ; q)] 2 σ 2 i ( 3
)
making use of the Leuvenberg-Marquardt algorithm [17]. y exp,i and y calc,i is the experimental and calculated intensity, respectively, obtained for the i-th field value B i . q designates the parameters to be extracted from the spectrum. σ i is the experimental uncertainty of the i-th experimental intensity.

In our computations, this factor is composed of two terms

σ 2 i = σ 2 n + ∂y i ∂B 2 σ 2 B ( 4
)
where σ n is the noise level common to all field points and σ B is the field uncertainty taken to be constant (0.1 G) in the field interval.

At each field value the contribution to the derivative spectrum from any pair of energy levels a, b is computed as the field derivative of y = (P ab p a -P ba p b ) × f (hν, ∆ ab , Γ) .

Here, P ab and P ba is the transition probability for the upward and downward transition, respectively. p a and p b is the thermal population of level a and b, respectively. f () is a bandshape function with the energy equivalent of the microwave radiation, the energy separation between levels a and b, and a bandwidth as arguments, respectively.

In order to introduce some flexibility into the bandshape we use as band-

where w x , w y , and w z are common residual bandwidths for all energy level pairs, and l x , l y , and l z are direction cosines of the magnetic field vector with respect to the molecular coordinate system. The terms in the summation account for that the parameters do not have sharp values but rather may be distributed around a mean value. The form eqn (7) assumes that this parameter distribution is gaussian with a width of σ q i . We are well aware of that eqn ( 7) is only correct bandwidth to use if the bandshape itself as well as parameter distribution are both gaussian. For a bandshape described by eqn (6), eqn (7) should be modified. However, such a modification would not alter the qualitative outcome of using eqn (7), namely that transitions involving energy levels being more or less sensitive to the parameter q i will become broad and narrow, respectively.

16

Page

7 74. 9 < 4 0

 794 [2] eqn(1) have been determined.Ĥ = µ B g ⊥ ( Ŝx B x + Ŝy B y ) + µ B g z Ŝz B z + A ⊥ ( Ŝx Îx + Ŝy Îy ) + A Ŝz Îz +D Ŝ2 z -+ 1) + P E ( Î2 x -Î2 y ) -µ N g N Îx B x + Îy B y + Îz B z , (1) where the first line accounts for the electronic Zeeman and the electron nucleus hyperfine interaction. The middle lines model the effect of the ligand field, and the bottom line accounts for the nuclear quadrupole term and the nuclear Zeeman interaction. Over the last 50 years, the following parameter values and ranges have been determined 87.0 < |A ⊥ | ≈ A < 88.|D| < 76.< |P D | < 0.467 |P E | = 0.069

4 Page

 4 fitting routine[17]. Most of the parameter values agree well with the ab-found by previous investigators and reproduced in eqn(2).

5

 5

for relevant experimental 6 Page

 6

Figure 1 :

 1 Figure 1: Experimental and calculated X-band spectrum of CaCO 3 :Mn 2+ are shown together as the traces desinated as "a". The experimental spectrum was obtained at room temperature with ν = 9.450 GHz. The lower traces show the difference y obs -y calc (b) without the terms with P D , P E , and g N ,

Figure 2 :Figure 3 :Figure 4 :Figure 5 :Figure 6 :

 23456 Figure 2: Experimental and calculated room-temperature S-band spectrum of CaCO 3 :Mn 2+ . The experimental spectrum (noisy trace) was obtained at room temperature with ν = 3.8660 GHz.

  shape function a popular approximation to the Voigt profile [20], namely a linear compination of a Lorentzian L and a Gaussian G lineshape with common bandwidth and centre f = aL + (1 -a)G . Finally, to account for the different bandwidth of the numerous lines in the spectra we model the bandwidth for the transition involving energy levels a and b as

1 Page

 1 [2] eqn(1) have been determined.

7 74. 9 < 4 0

 794 where the first line accounts for the electronic Zeeman and the electron nucleus hyperfine interaction. The middle lines model the effect of the ligand field, and the bottom line accounts for the nuclear quadrupole term and the nuclear Zeeman interaction. Over the last 50 years, the following parameter values and ranges have been determined 87.0 < |A ⊥ | ≈ A < 88.|D| < 76.< |P D | < 0.467

3 Page

 3 of more than an order of magnitude in bandwiths of the numerous lines in the spectrum. The narrowest derivative-like lines have a peak-to-peak widths of less than 1 G whereas some of the weaker absorptionlike lines have a full widths in half height in excess of 10 G.

4 Page

 4 fitting routine[17]. Most of the parameter values agree well with the ab-found by previous investigators and reproduced in eqn(2).

5 Page

 5 also crystallises in a uniaxial space group with the cation ion on a three-fold axis[19]. We tried to introduce spreads in the other parameters of eqn (1); this did not improve the fits significantly, and therefore we have chosen σ D and σ E as the only bandwidth broadening parameters.

for relevant experimental 6 Page

 6

7 Page

 7 around the Mediterranean bassin. One of the important parameters in this context is the calcite:dolomite ratio being characteristic for a specific location. This ratio cannot be obtained from the spectra unless the spectra are correctly modelled.

Figure 1 :

 1 Figure 1: Experimental and calculated X-band spectrum of CaCO 3 :Mn 2+ are shown together as the traces desinated as "a". The experimental spectrum was obtained at room temperature with ν = 9.450 GHz. The lower traces show the difference y obsy calc (b) without the terms with P D , P E , and g N ,

Figure 2 :Figure 3 :Figure 4 :Figure 5 :Figure 6 :

 23456 Figure 2: Experimental and calculated room-temperature S-band spectrum of CaCO 3 :Mn 2+ . The experimental spectrum (noisy trace) was obtained at room temperature with ν = 3.8660 GHz.

and b as w 2 ab = w 2 x l 2 x + w 2 y l 2 y + w 2 z l 2

 2222 shape function a popular approximation to the Voigt profile [20], namely a linear compination of a Lorentzian L and a Gaussian G lineshape with common bandwidth and centre f = aL + (1a)G .Finally, to account for the different bandwidth of the numerous lines in the spectra we model the bandwidth for the transition involving energy levels a

[ 20 ]

 20 Bruce, S. D.; Higinbotham, J.; Marshall, I.; Beswich, P. H. J. Magn. Reson. 2000, 142, ://mc.manuscriptcentral.com/tandf/://mc.manuscriptcentral.com/tandf/://mc.manuscriptcentral.com/tandf/://mc.manuscriptcentral.com/tandf/://mc.manuscriptcentral.com/tandf/://mc.manuscriptcentral.com/tandf/tmph Molecular Physics

17 of 44 URL

  Duliu, O. G.; Dinescu, L. C.; Skliros, D. J. Trace Microprobe Tech.Sign and Magnitudes of Spin HamiltonianParameters for Mn 2+ Impurities in Calcite.A Multi-and Low-Frequency EPR Study.

	Page 19 of 44	Molecular Physics Molecular Physics
	[14] 1999, 17, 165-175
	[15] Attanasio, D.; Platania, R. J. Magn. Reson. 2000, 144, 322-329
	F o r P e e r R e v i e w O n l F r P e R e v i e n l y l O n O w Reson. 2000, 142, 57-63 w e i v e R r e r e e versity Press 1988 P merical Recipes in C: The art of scientific computing Cambridge Uni-o [16] Garribba, E.; Micera, Giovanni. Magn. Res. Chem. 2006, 44, 11-19 [17] Preuss, W. H.; Flannery, B. P.; Teukolsky, S. A.; Vetterling, W. T. Nu-F Stergios Piligkos * 1 , Ib Laursen 2 , Axel Morgenstjerne 2 and o r Høgni Weihe * 1
		y y
		18

: http://mc.manuscriptcentral.com/tandf/tmph [18] Mabbs, F E.; Collison, D. Electron Paramagnetic Resonance of d Transition Metal Compounds, Elsevier 1992 [19] Klitgaard, S. K.; Galsbøl, F; Weihe, H. Spectrochimica Acta 2006, A63, 836-839 [20] Bruce, S. D.; Higinbotham, J.; Marshall, I.; Beswich, P. H. J. Magn. URL: http://mc.manuscriptcentral.com/tandf/tmph 1 Department of Chemistry, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen, Denmark 2 Quantum Protein Centre, Technical University of Denmark, Building 309, DK-2800 Lyngby, Denmark

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  [14] Duliu, O. G.; Dinescu, L. C.; Skliros, D. J. Trace Microprobe Tech.1999, 17, 165-175 [15] Attanasio, D.; Platania, R. J. Magn. Reson. 2000, 144, 322-329 [16] Garribba, E.; Micera, Giovanni. Magn. Res. Chem. 2006, 44, 11-19 [17] Preuss, W. H.; Flannery, B. P.; Teukolsky, S. A.; Vetterling, W. T. Numerical Recipes in C: The art of scientific computing Cambridge University Press 1988 [18] Mabbs, F E.; Collison, D. Electron Paramagnetic Resonance of d Transition Metal Compounds, Elsevier 1992 [19] Klitgaard, S. K.; Galsbøl, F; Weihe, H. Spectrochimica Acta 2006, A63,

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Acknowledgements

EPSRC EPR National service at the University of Manchester for use of the spectrometers. We are grateful to Ole Johnsen, National Geological Museum in Copenhagen, for providing us the high quality calcite crystal used for the 3 GHz single-crystal experiment.

8

Acknowledgements


Vincent ; Boudon
email: vincent.boudon@u-bourgogne.fr

Pierre Asselin

Pascale Soulard

Jet-cooled

Keywords: Tetracarbonyl, FTIR spectroscopy, Supersonic jet, Spherical-top, Rovibrational analysis Tetracarbonyl, FTIR spectroscopy, Supersonic jet, Spherical-top, Rovibrational analysis, Tensorial formalism, Semi-classical analysis

Introduction

Four transition-metal carbonyls are spherical-top molecules. Three are octahedral: Cr(CO) 6 [1], Mo(CO) 6 [2] and W(CO) 6 [3], while one is tetrahedral, namely Ni(CO) 4 . Some years ago, the nickel hexacarbonyl infrared-active C-O stretch fundamental (ν 5 ) was investigated at high-resolution using a supersonic expansion jet by Davies and co-workers [4,5]. A similar work was performed recently on non-tetrahedral C and O isotopic substitutions by Martinez and Morse [6].

The papers of Davies et al., however, only report on harmonic frequencies and rotational constants. No other rovibrational constant (Coriolis coupling, tetrahedral splitting, . . . ) was determined. Moreover, in Ref. [5], rotational constants on both the ground and v 5 = 1 states are simultaneously fitted, while the Coriolis constant is fixed to zero. For a triply degenerate fundamental of a spherical-top, this is not correct, because there is necessarily a non-zero (even if it is small) Coriolis constant. It is not possible to determine it simultaneously with the ground and excited state rotational constants using only excited state data. The access to precise values of Coriolis constants can also be very useful to derive internuclear distances by taking advantage of real B 0 values determined for at least two tetrahedral isotopologues in the case of Ni(CO) 4 .

We have thus decided to reinvestigate this band thanks to a new jet-cooled FTIR spectrum. For the analysis, we use here the electron-diffraction value for the ground state rotational constant B 0 and we fit the excited state rovibrational constants up to order 3. The Coriolis constant is shown to be small, but somewhat larger than in the case of Mo(CO) 6 [2] and W(CO) 6 [3]. Although it is very small, we show that the tetrahedral splitting can be observed and the corresponding parameters can be determined. We also discuss briefly the semi-classical description of the rovibrational energy levels, as it was done (although in a more detailed way since this was a particular case) for Mo(CO) 6 in Ref. [7].

F

Experiment

The low pressure supersonic jet-FTIR spectrometer set-up at LADIR has been described in details elsewhere [2]. Briefly, Ni(CO) 4 obtained from Strem (> 98 % purity) is seeded in argon at about 20 % by bubbling the rare gas through the liquid metal carbonyl into a constantly cooled bath maintained at about -60 • C. The 1 mol.h -1 flow rate of the Ni(CO) 4 /Ar gas mixture is expanded at a stagnation pressure of 80 mbar through a 0.74 mm circular nozzle into a vacuum chamber evacuated at a background pressure of 10 -3 mbar by a 18 m 3 .h -1 Varian four stage oil diffusion pump backed by a 400 m 3 .h -1 roots pump (Edwards 500 H) and a 60 m 3 .h -1 rotary vane pump (Leybold D60). The supersonic expansion is finally probed by the 16-pass arrangement of the IR beam issued from a Bruker IFS 120 HR interferometer and then focused on a InSb detector equipped with a narrow bandpass filter centered around the C-O stretching region (1950-2100 cm -1 ). A typical jet spectrum of the ν 5 stretching band of Ni(CO) 4 represents the Fourier transform of 10 coadded interferograms recorded at 0.006 cm -1 resolution. Particularly concentrated Ni(CO) 4 /Ar mixtures have been used in the present work to obtain a higher rotational temperature T r (25 K from our rovibrational band contour simulations) which enables to observe higher J transitions containing tetrahedral splitting information. The theoretical model described below to develop the Hamiltonian operator is based on the tensorial formalism and vibrational extrapolation methods used in Dijon. These methods have already been explained for example in Ref. [START_REF] Champion | Spectroscopy of the Earth's atmosphere and interstellar medium[END_REF]. We only recall here the basic principles and their application to the case of a tetrahedral molecule.

If we consider an X(YZ) 4 molecule for which the vibrational levels are grouped in a series of polyads designed by P k (k = 0, . . . , n), P 0 being the ground state (GS), the Hamiltonian operator can be put in the following form (after performing some contact transformations) :

H = H {P0≡GS} + H {P1} + . . . + H {Pk} + . . . + H {Pn-1} + H {Pn} . ( 1
)
Terms like H {Pk} contain rovibrational operators which have no matrix elements within the P k >k basis sets. The effective Hamiltonian for polyad P n is obtained by projecting H in the P n Hilbert subspace, i.e.

H <Pn> = P <Pn> HP <Pn> = H <Pn> {GS} + H <Pn> {P1} + . . . + H <Pn> {Pk} + . . . + H <Pn> {Pn-1} + H <Pn> {Pn} . ( 2
)
The different terms are written in the form

H {Pk} = all indexes t Ω(K,nΓ)ΓvΓ v {s}{s } β ε V Ωv(ΓvΓ v )Γ {s}{s } ⊗ R Ω(K,nΓ) (A1) . ( 3
)
In this equation, the t

Ω(K,nΓ)ΓvΓ v {s}{s }
are the parameters to be determined, while ε V

Ωv(ΓvΓ v )Γ {s}{s }
and R Ω(K,nΓ) are vibrational and rotational operators of respective degree Ω v and Ω. Their construction is described in Ref. [START_REF] Champion | Spectroscopy of the Earth's atmosphere and interstellar medium[END_REF]. Again, the vibrational operators only have matrix elements within the P k ≤k basis sets. β is a factor that allows the scalar terms (Γ = A 1 ) to match the usual terms like B 0 J 2 , etc. The order of each individual term is Ω + Ω v -2. Such a Hamiltonian development scheme enables the treatment of any polyad system. In this work however, since we only consider an isolated fundamental band, we will use only the two following effective Hamiltonians :

• The ground state (GS) effective Hamiltonian,

H <GS> = H <GS> {GS} . ( 4
)
• The ν 5 C-O stretch fundamental effective Hamiltonian,

H <ν5> = H <ν5> {GS} + H <ν5> {ν5} . (5)
A dipole moment operator is developed in the same way (see for instance [START_REF] Champion | Spectroscopy of the Earth's atmosphere and interstellar medium[END_REF] for details about its construction).

We use here a vibrational basis restricted to the ν 5 mode:

Ψ (Cv ) v = Ψ (l5=1,F2) v5=1 , (6)
i.e. we use a harmonic oscillator wavefunction for a triply degenerate fundamental with vibrational angular momentum l 5 . The Hamiltonian and dipole moment matrix elements are calculated in the coupled rovibrational basis

Ψ (Cv) v ⊗ Ψ (J,nCr) r (C) , (7)
Ψ (J,nCr) r
being a rotational wavefunction with angular momentum J, rotational symmetry species C r and multiplicity index n (see [START_REF] Champion | Spectroscopy of the Earth's atmosphere and interstellar medium[END_REF]) and C the overall symmetry species (C = C v ⊗ C r ).

Analysis

The ground state rotational constants of Ni(CO) 4 are not known in detail. We thus expand H <GS> up to order zero only, which implies only one parameter, that is the ground-state rotational constant t 2(0,0A1)A1A1 {000000000F2}{000000000A1 } = B 0 . If we use the electron diffraction bond lengths of Hedberg et al. [8], namely r Ni-C = 1.838(2) Å and r C=O = 1.141(2) Å, we can calculate an approximate B 0 value. We get:

B 0 = 3 32πc m C r 2 Ni-C + m O (r Ni-C + r C=O ) 2 0.0346 cm -1 . ( 8
)
H <ν5> is expanded up to order 3. By using the band center of Davies et. al. [4,5] and moving by hand the Coriolis constant term t

1(1,0F1)F2F2
{000010000F2 }{000010000F2 } , we could make some preliminary assignments and fit the scalar terms (those with Γ = A 1 ).

To go further, we noticed that the high J lines, which in fact correspond to clusters of many lines, are slightly asymmetric. We attributed this to a small tetrahedral splitting due to the t

3(1,0F1)F2F2 {000010000F2 }{000010000F2 }
anisotropic Coriolis term. By moving this value by hand, we could assign some lines to peak positions obtained by fitting Gaussian shapes to the experimental data, as illustrated on Figure 1.

[Insert Figure 1 It is then possible to fit 6 effective Hamiltonian parameters. The results are given in Table 1. Since the Q branch is too congested to be experimentally resolved, no Q line could be assigned. As it is usual in this case, for an unperturbed triply degenerate fundamental of a spherical-top, the t

2(2,0E)F2F2 {000010000F2 }{000010000F2 } and t 2(2,0F2)F2F2
{000010000F2 }{000010000F2 } parameters cannot be fitted simultaneously. Thus it is necessary to fix one of them. But the value to which it is fixed has a strong influence on the Q branch shape. We thus chose to move t 2(2,0F2)F2F2 {000010000F2}{000010000F2 } by hand (and fit the other parameters) until this shape was consistent with the experimental spectrum. Then, we kept the value obtained in this way.

Figure 2 shows an overview of the experimental spectrum, compared to the simulation. One distinguishes somewhat intense broad bands on the low wavenumber side of the Q branch. According to the work of Davies et al. [5] these features are assignable to the Q branches of hot bands starting from two low frequency C-Ni-C bending vibrations, namely ν 4 (62 cm -1 ) and ν 8 (79 cm -1 ). The intensity ratio, of about respectively 18 % and 12 % between these hot bands and the ν 5 fundamental band provides an estimate of the vibrational temperature (T v ) in the jet, that is about 50 K. The important difference observed between T v and T r originates in the more efficient rotational relaxation in the supersonic expansion. Figure 3 displays a small portion of the R branch from the same experimental spectrum.

[Insert Figure 2 Concerning transition intensities, the dipole moment operator has been expanded up to order 1. Since no absolute measurement of the line strengths is available, the order zero parameter (which is the dipole moment derivative relative to the ν 5 mode) was simply set to one. In order to match the experimental relative intensity ratio between P and R lines, we used the first order parameter (which is a so-called Herman-Wallis factor). This one was set to the value given in Table 1.

Discussion

As a first remark, although we have used here natural abundance nickel which contains five different isotopes ( 58 Ni: 68.077 %, 60 Ni: 26.223 %, 61 Ni:1.140 %, 62 Ni: 3.634 %, 64 Ni: 0.926 %), we observe no isotopic shift. This is usual for carbonyl molecules, for which the C-O stretch modes are not affected by isotopic substitutions of the metal atom [2,3].

Another interesting point is related to the comparison of the value of the Coriolis parameter between different carbonyls. We can calculate an approximate value of the ζ 5 Coriolis constant, that is

ζ 5 t 1(1,0F1)F2F2 {000010000F2 }{000010000F2 } 3 √ 2B 0 -0.032. ( 9
)
This value is somewhat larger than that reported by Hedberg et al. [8] (-0.02), but the order of magnitude is consistent. Such a value is small, but it is one order of magnitude larger than is the case of the ν 6 C-O stretch fundamental of octahedral hexacarbonyls like Mo(CO) 6 (ζ 6 -0.0044 [2]) and W(CO) 6 (ζ 6 0.0023 [3]). Thus, we do not expect here the same striking level exchange phenomena as those observed in Mo(CO) 6 [7] since a larger Coriolis constant better separates the branches.

We can notice that the value of B 0 given in Table II of Ref. [5] is in fact an effective value, (since it was fitted without the Coriolis term). With our ζ 5 value obtained above, we get B 0 0.03462 cm -1 , which is very close to the electron-diffraction value and this fully justifies our initial approximation.

B 0 B 0 (1 -ζ 5 ) 0.0357213cm -1 , (10)
To illustrate the effect of the Coriolis constant, the calculated reduced energy levels for the ν 5 band are displayed on Figure 5. The reduced energy levels are obtained by subtracting the scalar term, i.e.,

E red = E - Ω t Ω(0,0A1)A1A1 {000000000}{000000000} (J(J + 1)) Ω/2 = E -B 0 J(J + 1) + D 0 J 2 (J + 1) 2 -. . . ( 11
)
We remark that the levels are distributed among three well separated branches even for low J values. This is not the case for Mo(CO) 6 because the Coriolis constant is one order of magnitude smaller. On the same Figure, we plotted the semiclassical energy curves obtained in the same way as in Ref. [7]. Let us simply recall that in this model, the quantum description of the vibrational part of the Hamiltonian is combined with the classical description of the rotational degrees of freedom. Using the vibrational basis functions

{|v 5x , v 5y , v 5z } = {|1, 0, 0 , |0, 1, 0 , |0, 0, 1 } , ( 12
)
we get the following matrix of the effective Hamiltonian :

H = ⎛ ⎝ H 11 H * 21 H * 31 H 21 H 22 H * 32 H 31 H 32 H 33 ⎞ ⎠ , ( 13
)
where the different terms are expressed in terms of the rotational angular momentum components (J x , J y , J z ). Detailed expressions can be found in Ref. [7]. The rotational operators J x , J y , and J z are then converted to classical dynamical variables (J x , J y , J z ) = J (sin θ cos φ, sin θ sin φ, cos θ), (14) where angles φ and θ define the axis of rotation and J is the constant amplitude of the classical angular momentum,

J = J(J + 1). ( 15
)
The angles (θ, φ) are the coordinates on the classical phase space for the rotational motion, called rotational phase sphere [11][12][13][14]. Diagonalization of matrix ( 13) for a given value of J and for each direction (θ, φ) gives three eigenvalues E J k (θ, φ) (k = -1, 0 and +1) which represent three classical rotational energy surfaces defined as functions on the rotational phase sphere. We are particularly interested in the values of E J k (θ, φ) for stationary axes of rotation. Principal stationary axes of any T d spherical-top molecule are its symmetry axes C 4 , C 3 , and C 2 . The T d group has several axes of each kind equivalent by symmetry and naturally the value of E J k for each of the equivalent axes is the same. More precisely, equivalent by symmetry points (θ, φ) form an orbit of equivalent points on the rotational phase sphere. The principal axes are always stationary, and moreover, axes C 4 and C 3 should be stable for any generic Hamiltonian. This means that generically functions E J k have a nondegenerate maximum, a minimum, or a saddle at the corresponding points on the phase sphere for any J. These points form critical orbits [15] with local symmetry C 2 , C 3 , and C 4 . The C 4 and C 3 points can either be a maximum or a minimum, while the C 2 point can also be a saddle. To calculate E J k we choose one representative in each critical orbit indicated in Table 2. Simple analytical expressions can be found for the energies on the critical orbits by diagonalizing the matrix (13) and are given in Ref. [7].

[ Insert Table 2 The curves on Figure 5 perfectly match the quantum energy levels in each branch and never cross, confirming that there is no level exchange between the branches in this case. In other words, we find again the usual splitting of the F 2 vibrational states into three components (corresponding to the three eigenvalues E J k defined above) with effective quantum numbers R = J -1, J, J + 1. There is almost no mixing between these components.

[Insert Figure 5

about here.] 6 Conclusion

This work constitutes the first detailed analysis of the ν 5 C-O stretch fundamental of Ni(CO) 4 , including the Coriolis constant and non-scalar terms that induce tetrahedral splitting. We have also shown that, contrary to spherical-top hexacarbonyls Mo(CO) 6 and W(CO) 6 , tetrahedral Ni(CO) 4 has a C-O stretch fundamental with a standard Coriolis structure.

The present analysis was performed thanks to the STDS set of programs [16] that implements the Dijon tensorial formalism methods [START_REF] Champion | Spectroscopy of the Earth's atmosphere and interstellar medium[END_REF]17]

  FTIR spectroscopy and analysis of the ν 5 C-O stretch fundamental of Ni(CO) 4 3

  FTIR spectroscopy and analysis of the ν 5 C-O stretch fundamental of Ni(CO) 4

Figure 1 .Figure 2 .

 12 Figure 1. Tetrahedral splitting for high J values in the R branch of the ν 5 band of Ni( 12 C 16 O) 4 ; arrows indicate how assignments were made; vertical sticks show the calculated individual transitions

Figure 3 .

 3 Figure 3. Detail in the R branch of the ν 5 band of Ni( 12 C 16 O) 4 , compared to the simulation.

Figure 4 .

 4 Figure 4. Observed-calculated wavenumbers for the ν 5 band of Ni( 12 C 16 O) 4 .

  Fig.5

  3 and ν 4 ), one triply-degenerate mode with F 1 symmetry (ν 9 ) and 4 triply-degenerate modes with F 2 symmetry (ν 5 , ν 6 , ν 7 and ν 8 ). Only F 2 fundamentals are infrared active. ν 5 corresponds to a C-O stretch mode.Since both the 12 C and16 O atoms have a zero nuclear spin, the spin statistical weights of Ni( 12 C 16 O) 4 are such that only levels with A 1 or A 2 rovibrational symmetry species are allowed (in this work, we only considered this main isotopologue, the others being not observed under the present experimental conditions).

3 Theory

Ni(CO) 4 possesses nine normal modes of vibration

[8]

: 2 non-degenerate modes with A 1 symmetry (ν 1 and ν 2 ), 2 doubly-degenerate modes with E symmetry (ν

  about here.]

	October 4, 2007 17:9 Molecular Physics paper
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	October 4, 2007 17:9 Molecular Physics paper
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Table 1 .

 1 and which is freely available at the URL http://icb.u-bourgogne.fr/OMR/SMA/SHTDS/. Effective Hamiltonian and dipole moment parameters.

	F o r
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	y

a Fixed parameter (see text).

Table 2 .

 2 Stationary rotation axes of a tetrahedral molecule.

	Axis	[Jx, Jy, Jz]	( θ, φ)	N u m b e r
	C 4 C 3 C 2	[0, 0, 1] [1, 1, 1]/ √ [1, 1, 0]/ √	3 2	(0, 0) (arctan √ 2, π/4) ( π/2, π/4)	3 4 6

  12 C 16 O) 4 .Figure 5. Calculated reduced energy levels and semiclassical energy curves (see text) for the ν 5 band of Ni( 12 C 16 O) 4 .

	October 4, 2007 17:9 Molecular Physics paper October 4, 2007 17:9 Molecular Physics paper October 4, 2007 17:9 Molecular Physics paper October 4, 2007 17:9 Molecular
	Page 11 of 19			Molecular Physics Molecular Physics Molecular Physics	Page 12 of 19
	10 12			FIGURES FIGURES FIGURES	11
					Fig. 1 Fig. 2 Fig. 3
	current
	peak	0.10
		0.10	Experiment Experiment	: Experimental points : Gaussian peaks
		0.4 0.08			: Fit with Gaussians
			R(46)	R(47)	R(48)
	Absorbance Absorbance Absorbance	F o r P 0.05 0.00 Simulation F o r P 0.2 0.0 Simulation, T = 25 K F o r P 0.06 0.04 0.02 F o r P	: Simulated spectrum : Calculated stick spectrum Experiment
		0.00		e e r e e r e e r e e r	Simulation, T = 25 K
			2058 2064.6	R e v i e 2064.65 2064.60 R R R Wavenumber / cm -1 e v i e 2062 2060 Wavenumber / cm -1 e v i e 2065.2 2065.0 2064.8 2064.55 e Wavenumber / cm -1 v i e	2064	2064.70 2066 2065.4
					w w w w
					O n l O n l O n l O n l
					y y y y

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Acknowledgments

Support from the Région Bourgogne for the computer equipment of the Institut Carnot de Bourgogne is gratefully acknowledged. We also wish to thank the SpecMo network of the CNRS.