Journal of Nanomaterials
Volume 2017 (2017), Article ID 4360746, 10 pages
https://doi.org/10.1155/2017/4360746

Research Article

The IR Spectra, Molar Absorptivity, and Integrated Molar Absorptivity of the C₇₆-D₂ and C₈₄-D₂:22 Isomers

Tamara Jovanović,¹ Đuro Koruga,¹ and Branimir Jovančićević²

¹Department of Biomedical Engineering, Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Belgrade, Serbia
²Department of Applied Chemistry, Faculty of Chemistry, University of Belgrade, Studentski trg 12-16, 11000 Belgrade, Serbia

Correspondence should be addressed to Tamara Jovanović; tamara.jovanovic@sbb.rs

Received 4 February 2017; Revised 20 February 2017; Accepted 22 February 2017; Published 5 March 2017

Academic Editor: Xuping Sun

Copyright © 2017 Tamara Jovanović et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract.

The FT-IR spectra of the stable C₇₆ and C₈₄ isomers of D₂ symmetry, isolated by the new, advanced extraction and chromatographic methods and processes, were recorded by the KBr technique, over the relevant region from 400 to 2000 cm⁻¹, at room temperature. All the observed infrared bands are in excellent agreement with the semiempirical QCFF/PI, DFT, and TB potential calculations for these fullerenes, which is presented in this article, as the evidence of their validity. The molar absorptivity ε and the integrated molar absorptivity ψ of their IR absorption bands were determined and reported together with the relative intensities. Excellent agreement is found between the relative intensities of the main and characteristic absorption maxima calculated from and from the values in adequate integration ranges. These results are significant for the identification and quantitative determination of the C₇₆-D₂ and C₈₄-D₂:22 fullerenes, either in natural resources on Earth and in space or in artificially synthesized and biomaterials, electronic, optical, and biomedical devices, sensors, polymers, optical limiters, solar cells, organic field effect transistors, special lenses, diagnostic and therapeutic agents, pharmaceutical substances in biomedical engineering, and so forth.

1. Introduction

Fullerenes C₆₀ and C₇₀ were detected in a series of astrophysical objects and space environments [1–6], such as certain planetary [7, 8] and protoplanetary [9] nebulae, postasymptotic giant branch stars, young stellar objects [10], reflection nebulae [11], certain R-Coronae Borealis stars, and carbon rich stars [12–16], as well as in some resources on Earth [17, 18]. The identification and quantitative assessment of these molecules, both in natural and in artificially synthesized materials, were made possible by the measurement of their IR spectra, the dependence of these spectra on temperature, the molar absorptivity, and integrated molar absorptivity of their absorption bands [2–26].

It is expected that also higher fullerenes can be found in space, besides C₆₀ and C₇₀. Calculations [27] suggest that, on a per carbon atom basis [1], higher fullerenes are thermodynamically even more stable than C₆₀, C₇₀ [28], and from the hydrogenated derivatives fulleranes [17, 18, 29–31]. Their formation through coalescence of smaller fullerenes [32] and by laser ablation of carbon [17–19, 33, 34] also leads to the conclusion about their possible presence in nature.

For the qualitative detection of C₇₆ and C₈₄ fullerenes, the knowledge of the infrared band position and band widths, as well as the evolution of these parameters with temperature, is necessary. This need was fulfilled, for instance, by the previous works [1, 35–42] in the infrared spectroscopy of C₇₆ and C₈₄, whereas quantitative assessment of these fullerenes requires knowledge about intensities of their IR absorption bands, which is provided in the current work.

In the first phase of this research, the only stable C₇₆-D₂ isomer [43–45] and the most abundant, stable isomer of the higher fullerene C₈₄ with D₂ symmetry, C₈₄-D₂:22 [46–54], were isolated from carbon soot, by new and advanced chromatographic methods and processes [35–42], in comparison to previous methods for the separation of higher fullerenes under pressure [55–63]. Their IR (KBr) spectra were recorded over the entire relevant region, from 400 to 2000 cm⁻¹ in transparence mode [35–42], and in the absorption mode in this article.

A comparison of the experimentally observed vibrational frequencies in the IR absorption spectra of the isolated C₇₆-D₂ and C₈₄-D₂:22 samples [35, 38] with the semiempirical QCFF/PI, DFT, as well as TB potential theoretical calculations for these fullerenes [44, 45, 48–50], is presented in this article, indicating their validity.

In this work also, the molar extinction coefficients and the integrated molar extinction coefficients of their main and characteristic IR absorption bands were determined.

These data are important for the qualitative and quantitative determination of the C₇₆-D₂ and C₈₄-D₂:22 isomers, either in natural resources on Earth and in space or in artificially synthesized materials, electronic and optical devices, diagnostic and therapeutic agents for the applications in biomedical engineering, and so forth.

2. Experimental Methods

In the first phase of this research, C₆₀, C₇₀ [24–26], and the higher fullerenes, mainly C₇₆ and C₈₄ [35–42], were Soxhlet-extracted with a series of different and previously unapplied solvents or combinations of solvents from the samples of carbon soot, produced by electric arc (MER Corporation, Tucson, USA). The extraction procedures were performed until the complete disappearance of color in a Soxhlet extraction thimble. Solvents used were n-heptane, toluene, chlorobenzene, p-xylene, a mixture of o/m/p-xylene, and pyridine, as well as the successive use of toluene and chlorobenzene and p-xylene and pyridine. The yields, as well as the compositions of all the extracts, were determined by spectroscopic and chromatographic methods. The procedures for increases of fullerenes yields, as well as for additional selective extraction of higher order fullerenes, were found [24–26, 35–42].

In the second phase, C₆₀, C₇₀, and the higher fullerenes C₇₆ and C₈₄ (the only stable C₆₀-Ih, C₇₀-, and C₇₆-D₂ isomers of the first three mentioned fullerenes and the most abundant, stable C₈₄ isomer of D₂ symmetry) were chromatographically separated from the obtained soot extracts on the activated Al₂O₃ columns, by new and advanced methods [35–42].

The main difference and advancement of these methods [35–42], in comparison to previous methods under pressure [55–63], is the isolation of the purified stable isomers of the higher fullerenes C₇₆ and C₈₄ (the C₇₆-D₂ and C₈₄-D₂:22 isomers), successively after the basic fullerenes, in one phase of each of the processes, under atmospheric pressure and smaller flow of 1.5 mL/min, in increased milligrams yields. The other advantages of the developed methods [35, 42] are the use of significantly smaller amounts of the initial materials, as well as less expensive laboratory equipment. In these methods [35, 42], the entire materials and energy expense, the time spent on the purification processes, and environmental pollution were decreased, using smaller amounts of less toxic solvents. The yields and the purities of the isolated fullerenes were increased or maximized [35, 36, 39].

Purification of the higher fullerenes under pressure, on a preparative scale, either by flash chromatography or by HPLC, generally required larger amounts of the initial materials and repeated chromatographies, and the fullerenes were obtained in smaller yields [55–63].

In our new methods [35–42], the elution was performed continuously with several different original, defined gradients of solvents: from pure hexane or 5% toluene in hexane to pure toluene. The amounts of the initial materials used were as follows: fullerenes extracts, 10 mg, and finely granulated Al₂O₃, 50 g, activated for 2 h at 105°C, and eluent (1.5 to 1.75 L) per chromatographic separation [35–42]. Starting from 10 mg of the soluble soot extract, in average ca. 1 mg of C₇₆ and ca. 1 mg of C₈₄ were isolated in purified form per one chromatographic process, or up to few milligrams in some cases. The time spent on the purification processes was from 16.7 to 19.4 h [36, 39].

For comparison, using flash chromatography to separate fullerenes [55], on alumina, with hexane or 5% toluene in hexane as eluent, required about 50 times larger quantities of the initial materials, such as 500 mg of crude fullerenes extract, 2500 mg of alumina, and about 12.5 L of solvent for one chromatographic fraction, C₆₀, or 75 L for six chromatographic fullerene fractions, per one chromatography and the large size of columns. The entire time of this purification process, including repeated chromatographies, was 66 hours and purified higher fullerenes were obtained in lower yields. From the total amount of 2500 mg of toluene soluble soot extract, 12 mg of C₇₆ and 2 mg of C₈₄ were isolated.

From these data, it follows [36, 39] that 21 times larger amounts of the initial materials (extract, stationary phase, and solvent) and 2 times longer time are needed for obtaining 1 g of purified C₇₆, and 125 times larger amounts of the initial materials and 10 times longer time are required for obtaining 1 g of purified C₈₄ by the mentioned flash chromatography process [54], in comparison to our protocols [35–42].

In the previous method under pressure [57, 58], the purified basic and higher fullerenes were eluted according to their molecular weights on the monomeric ODS column, using large volumes of solvents, in comparison to our new methods [35–42]. Several tens of liters of a mixture of toluene and methanol (55 : 45, v/v) per chromatography were used, at a flow rate of 40 mL/min [57, 58]. In the new methods [35–42], under atmospheric pressure and smaller flow rate of 1.5 mL/min, significantly smaller volumes of solvents were used for the elution of the purified basic and higher fullerenes in one phase, 1.5 to 1.75 L per chromatography.

The IR spectra of all the chromatographically purified fractions of the basic and the higher fullerenes from this research, as well as of the obtained soot extracts, were previously recorded on a Perkin Elmer FT-IR 1725 X spectrometer by the KBr pellet technique, from 400 to 4000 cm⁻¹, at a resolution of 1 cm⁻¹, in the transparence mode [24–26, 36, 37, 39–42].

The IR spectra of the C₇₆-D₂ and C₈₄-D₂:22 samples, isolated by the new and advanced chromatographic methods [35–42], were also recorded on a Thermo Scientific FT-IR spectrometer Nicolet IR-6700, by the KB disk technique, in the range of 400–2000 cm⁻¹, at a resolution of 1 cm⁻¹, in the transparence mode [35, 38], as well as in the absorption mode in this article.

2.1. Measurement of the Molar Absorptivity and Integrated Molar Absorptivity of C₇₆-D₂ and C₈₄-D₂:22

Chromatographically isolated C₇₆-D₂ (0.249 mg) and C₈₄-D₂:22 (0.270 mg) were mixed with 70.8 mg and with 77.8 mg of KBr, respectively. The obtained powder was compressed at the 4 tons/cm² with the Perkin Elmer press.

The resulting pellets were placed in the FT-IR spectrometer. Measurements of the intensities (heights) of the absorption bands, as well as of the integrated band intensities of C₇₆-D₂ and C₈₄-D₂:22, with automatic subtraction of the baseline, were made possible through the OMNIC software from Thermo Scientific, dedicated to the FT-IR spectrometer. This software has also been recently used for the measurement of relative intensities of IR absorption bands of C₆₀ and C₇₀ [4].

The masses of the resulting pellets were 71.0 mg and 78.1 mg, and the percentages of carbon determined by the elemental analysis were 0.351 and 0.346. Their measured thicknesses () were 0.67 mm~0.07 cm and 0.74 mm~0.07 cm, the diameters () were 0.7 cm, and the half diameters () were 0.35 cm.

The volumes of the pellets () were determined from the abovementioned and parameters, by the equation . The obtained values of the volumes, as well as the thicknesses of pellets, were also confirmed using KBr density (2.753 g/cm³) [4] and the masses of pellets.

Concentrations () of fullerenes C₇₆ and C₈₄ in the pellets, as the number of moles per unit of volume, were calculated using the masses of C₇₆ and C₈₄ in the pellets, their molar masses of 912.76 g/mol and 1008.84 g/mol, and the volumes of pellets.

The ()⁻¹ values were determined for the C₇₆-D₂ and the C₈₄-D₂:22 samples in KBr pellets from the abovementioned experimental parameters. The ()⁻¹ value found for C₇₆-D₂ was 1409.7 L·cm⁻¹·mol⁻¹ and the ()⁻¹ value found for C₈₄-D₂:22 was 1436.0 L·cm⁻¹·mol⁻¹.

3. Results and Discussion

In the recent works [1, 35–42], the IR spectra of the higher fullerenes C₇₆ and C₈₄ and their stable isomers of D₂ symmetry have been studied. The dependence on temperature of the position and width of their infrared absorption bands has been determined [1, 35]. The molar extinction coefficients and integrated molar absorptivity of the infrared absorption spectra of C₆₀ and C₇₀, as well as of related hydrogenated derivatives, fulleranes, have also been recently determined [2–5]. However, neither the molar absorptivity nor the integrated band intensity of C₇₆-D₂ and C₈₄-D₂:22 has been reported.

Determination of molar absorptivity of the isolated higher fullerenes, in L·cm⁻¹·mol⁻¹, at a given wavenumber, , was achieved through (1), previously applied for C₆₀ and C₇₀, as well as for hydrogenated fullerenes [2–6, 64], according to Lambert and Beer law, using the absorbance read at a given wavenumber:

The determined values of ()⁻¹ for both the C₇₆-D₂ and the C₈₄-D₂:22 samples are reported in the Experimental Methods.

It was found that the peak height measurements that correspond to the absorbance are sensitive to changes in the resolution of the spectrometers used [2–6, 64]. The measurement of the integrated intensity that corresponds to the total area below a given absorption band is much less sensitive to instrumental resolution than the peak height measurement [2–6, 64].

Thus, the absorbance and the integrated band intensities in the obtained original IR spectra of the isolated C₇₆-D₂ and C₈₄-D₂:22 samples were determined using the OMNIC software of our spectrometer, in both cases subtracting automatically the baseline.

The integrated molar absorptivity of the C₇₆-D₂ and C₈₄-D₂:22 fullerenes, expressed in cm mol⁻¹ or 10⁻⁵ km mol⁻¹, was determined by (2), previously applied for the basic fullerenes, as well as for fulleranes [2–6, 64]:

In this equation, λ is the wavelength and is the molar absorptivity measured with a spectrometer with unlimited resolution, integrated over the whole band. In practice, by substituting (1) into (2), we get [2–6, 64]

The original, characteristic, representative IR spectrum of the isolated sample of the C₇₆-D₂ isomer is obtained in this article in the absorption mode, Figure 1, for determination of the molar absorptivity and integrated molar absorptivity of its absorption bands, which is important for the quantitative assessment of this fullerene and represents the main work of this article. It was previously provided in transparence mode, in supplemental material of our article [35], for the qualitative determination.

Figure 1: The IR spectrum of C₇₆-D₂ in a mode.

The main three, most intense, dominant C₇₆ maxima, registered in this research [35–42], appear at 967, 1082, and 1187 cm⁻¹, with some weak, distinct shoulders. Characteristic, sharp absorption bands unique to C₇₆ occur in the first relevant part at 893 and 823 cm⁻¹, with a neighboring shoulder at 792 cm⁻¹. Several other bands are present at 703 cm⁻¹ with a shoulder at 742 cm⁻¹, at 605 cm⁻¹ with the shoulders at 647 and 665 cm⁻¹, and at 484 cm⁻¹ with the shoulders at 538, 462, 456, and 426 cm⁻¹. Pronounced and intense bands are present in the higher frequency region at 1386 cm⁻¹ with the shoulders at 1397 and 1364 cm⁻¹, at 1493 cm⁻¹ with a neighboring shoulder band at 1462 cm⁻¹, as a doublet, and at 1735 cm⁻¹. Maximum at 1312 cm⁻¹ appears with the neighboring shoulders at 1273 and 1248 cm⁻¹, as a triplet. Complete absorption in this spectrum [35] is in agreement with the theoretical calculations for C₇₆-D₂, as well as for its dianion [44, 45].

In the previous articles [35, 37], a comparison of the experimentally observed absorption frequencies in the IR spectra of the chromatographically isolated C₇₆-D₂ samples, recorded on Perkin Elmer [37, 40–42] and on Thermo Scientific FT-IR spectrometer Nicolet IR-6700 at room temperature [35], with the semiempirical QCFF/PI theoretical calculations for this fullerene [35, 37, 40–42, 44], as well as with the IR spectra of C₇₆, recorded on three different temperatures between −180°C and +250°C [1, 35], was presented. On the basis of the obtained excellent agreement [35, 37, 40–42, 44], the validity of both the experimental results [35, 37, 40–42] and the mentioned theoretical calculations for C₇₆-D₂ [44] was indicated [35, 37, 44]. In the more recent article [35], a larger number of experimentally registered vibrational frequencies of C₇₆ were presented and theoretically confirmed [35, 44].

There is also a good agreement between the absorption bands in our infrared spectra at room temperature [35–42] and the recent spectra of C₇₆-D₂ at three different temperatures [1]. Only some smaller shifts, as well as some changes of their relative intensities with the temperature, were observed [1, 35].

In this article, a comparison of the experimentally obtained vibrational frequencies (cm⁻¹) in the IR absorption spectra of the chromatographically isolated C₇₆-D₂ samples (IR1-IR3), recorded from 400 to 2000 cm⁻¹, on a Thermo Scientific FT-IR spectrometer Nicolet IR-6700 [35], with the different theoretical calculations, by the QCFF/PI method (Calc. 1, from 286 to 1668 cm⁻¹) [44] and DFT method for C₇₆ (Calc. 2, from 206.7 to 1602.7 cm⁻¹) [45], as well as for (Calc. 3, from 195.7 to 1556.0 cm⁻¹) [45], is presented in Table 1. Excellent agreement is obtained between the experimental results [35] and all the aforementioned theoretical calculations for this fullerene [44, 45], as the evidence of their validity.

Table 1: Experimentally obtained vibrational frequencies (cm⁻¹) of C₇₆-D₂ [35] and theoretically calculated values between 400 and 2000 cm⁻¹ [44, 45].

IR
IR
IR
Calc.
Calc.
Calc.

1635.1
1631.4
1633.1
1635

1605.4

1607
1602.7

1581.6

1582
1581.4

1557.9

1556

1556.0

1551.5
1549

1555.7

1541.3
1541.6

1541.4

1493.8
1492.7
1493.4
1494
1489.7
1494.9

1461.8
1460.2
1461.1
1464
1463.9
1463.4

1397.0
1399.8
1398.7
1401

1400.5

1385.9
1385.4
1385.6
1388
1386.5
1390.7

1363.8
1363.1
1364.2
1369
1365.1
1366.0

1312.1
1311.4
1312.4
1312
1310.9
1309.4

1275.6

1275.7
1275.9

1273.1

1270
1274.0

1263.1

1259

1262.5

1248.4
1247.5
1247.6
1253
1249.4
1246.4

1210.5
1208.6

1208.7

1206.3

1204

1187.2
1185.0
1187.0
1189
1180.4
1189.2

1160.3

1161.6
1165
1157.7
1162.2

1121.9
1121.8
1122.0
1124
1126.1
1125.7

1100.9

1100

1101.5

1081.6
1081.8
1081.6
1079
1072.3
1090.3

1057.2
1056.4
1058
1054.7
1065.4

1028.6
1030.4

1027

1026.5

1024.2

1024.9

967.1
968.4
967.0
971
942.1
991.5

893.3
891.8
892.2
895
897.7
894.1

822.5
821.1
823.4
823
821.0
827.1

792.2
796.4

799
808.7
795.0

788.8
787
781.7
787.0

742.1

742.9
746
742.0
741.3

739.9

735
739.6
740.2

704.0
704.8
707
704.9
704.5

703.0

702.4
703.5

665.2
663.6

667
665.4
665.2

661.1
662

660.6

647.3
648.3
645.8
652
642.7
650.3

605.3
604.6
602.9
596

596.8

537.6
538.8

543
538.5
536.9

532.7
534
531.3
535.6

494.1

494
493.8
494.5

483.9

486.6
485
485.8
486.5

476.4

477
476.7
479.2

461.8

460.6
460

459.2

456.2

457
456.3
456.9

451.8

454
452.2
454.0

436.0

434.8
436.0

426.5
429.3

425.3

405.2
406
405.0
399.3

[35].

[44].

[45].

The IR spectra of all the chromatographically isolated samples of the C₇₆-D₂ isomer from this research, recorded on the two mentioned spectrometers, have similar properties. All the observed vibrational frequencies and the general pattern of these spectra [35–42] are in agreement with the semiempirical QCFF/PI [44] and DFT theoretical calculations for C₇₆-D₂ [45], as well as for its dianion C₇₆- [45].

The achieved agreement between our experimental results [35–42] and all the aforementioned theoretical predictions of the IR absorption frequencies of C₇₆-D₂ [44, 45], which is presented in this article in Table 1 and Figure 1 [35, 44, 45], is better in comparison to previous, partial experimental results for the obtained C₇₆ samples, from other separation processes, by other IR techniques [59–62].

It is important to mention that the obtained generally good correlation between the overall configuration of absorption and all the observed vibrational frequencies in our recent experimental IR spectra for the neutral C₇₆-D₂ [35–42] and the next obtained infrared multiphoton electron detachment (IR-MPED) spectrum of the unsolved gas phase dianion C₇₆- [45], as well as with the adequate most recent B3LYP/TZVP DFT calculations, presented in this article in Table 1, Figure 1 [35, 45], provides significant experimental evidence [35–42] that the dianionic molecule retains its overall symmetry (i.e., D₂ point group) with ¹A₁ ground state with respect to the neutral cage [45].

From the IR spectrum of C₇₆-D₂ in a mode, presented in Figure 1, the absorbance values , as well as the integrated absorbance values of the absorption bands, were determined using the OMNIC software.

The molar absorptivity , calculated according to (1), the integrated molar absorptivity , calculated according to (3), and the integration ranges of absorption bands of this fullerene are reported in Table 2.

Table 2: The relative intensities of the absorption bands of C₇₆-D₂ computed from and from the Ψ values in adequate integration ranges.

(cm⁻¹)
(L cm⁻¹ mol⁻¹)
Rel. int. []
Int. range (cm⁻¹)
(Km mol⁻¹)
Rel. int. []

1735.3
88.810
12.1
1770–1699
1.841
12.1

1493.8
286.167
39.1
1505–1451
5.947
39.1

1385.9
159.295
21.8
1397–1348
3.320
21.8

1312.1
119.824
16.4
1319–1242
2.504
16.5

1187.2
420.087
57.4
1227–1144
8.710
57.3

1081.6
434.184
59.3
1140–1005
9.029
59.3

967.1
731.629
100
997–925
15.212
100

893.3
101.498
13.9
912–850
2.136
14.0

822.5
87.401
11.9
850–772
1.818
11.9

703.0
54.978
7.5
763–680
1.135
7.5

605.3
54.273
7.4
674–596
1.147
7.5

483.9
109.956
15.0
550–418
2.285
15.0

It can also be seen from Table 2 that excellent agreement is found between the relative intensities of the main and characteristic absorption maxima of C₇₆-D₂ computed from and from the Ψ values, in adequate integration ranges, taking as 100 the most intense vibration mode of C₇₆-D₂ at the frequency of 967 cm⁻¹.

The original, characteristic, representative IR absorption spectrum of the isolated sample of the isomer C₈₄-D₂:22 is obtained in this article in the absorption mode, Figure 2, for determination of the molar absorptivity and integrated molar absorptivity of its absorption bands, which is important for its quantitative determination, as the main work of this article. It was previously provided in transparence mode [35], for qualitative determination.

Figure 2: The IR spectrum of C₈₄-D₂:22 in a mode.

A group of sharp, characteristic absorption bands is present between ca. 700 and 840 cm⁻¹ [35–42], at 711, 746, 779, and 843 cm⁻¹, followed by the bands at 635 and 473 cm⁻¹ in the first relevant part. Dominant and pronounced C₈₄-D₂:22 maxima appear in the higher frequency region, between ca. 1390 and 1120 cm⁻¹, as well as a group around 1600 cm⁻¹. The main, most intense band is present at 1385 cm⁻¹, followed by the bands at 1263 cm⁻¹ and 1122 cm⁻¹. Intense bands also appear at 1456–1465 cm⁻¹, 1599–1616 cm⁻¹, and 1731 cm⁻¹. The entire absorption in this spectrum [35] corresponds to the theoretical predictions for C₈₄-D₂:22 [48–50].

In the previous article [35], a comparison of the experimentally observed absorption frequencies in the IR spectra of the chromatographically isolated C₈₄-D₂:22 samples, recorded on a Thermo Scientific FT-IR spectrometer Nicolet IR-6700 at room temperature [35, 38], with the semiempirical QCFF/PI theoretical calculations for this fullerene [48], as well as with the IR spectra of C₈₄ (mixture of isomers), recorded on three different temperatures between −180°C and +250°C [1, 35], was presented. On the basis of the obtained excellent agreement [35, 38, 48], the validity of both the experimental results [35, 38] and the mentioned theoretical calculations [48] was indicated [35].

Most of the absorption maxima in our IR spectra of C₈₄-D₂:22 at room temperature [35–42] are also in good agreement with the recent IR spectra of C₈₄ (mixture of isomers) at different temperatures between −180°C and +250°C [1], as presented in the previous article [1, 35, 38]. However, significant changes of relative intensities of the main bands, as well as some shifts, were observed [1, 35].

In this article, a comparison of the experimentally obtained vibrational frequencies (cm⁻¹) in the IR absorption spectra, of the chromatographically isolated C₈₄-D₂:22 samples (IR1-IR3), recorded from 400 to 2000 cm⁻¹, on a Thermo Scientific FT- IR spectrometer Nicolet IR-6700 [35, 38], with the different theoretical calculations for this fullerene, by the QCFF/PI method (Calc. 1, from 179 to 1711 cm⁻¹) [48], DFT (Calc. 2, from 211 to 1674 cm⁻¹) [49], and TB potential method (Calc. 3, from 190 to 1726 cm⁻¹) [50], is presented in Table 3. Excellent agreement between the experimental results [35, 38] and the aforementioned theoretical calculations for this fullerene [48–50] provides the evidence of their validity.

Table 3: Experimentally obtained vibrational frequencies (cm⁻¹) of C₈₄-D₂:22 [35, 38] and theoretically calculated values between 400 and 2000 cm⁻¹ [48–50].

IR
IR
IR
Calc.
Calc.
Calc.

1731.1
1731.6
1734.9

1726

1684.5
1686.1
1688.8
1685

1671.5
1671.8

1667
1672
1671

1650.3
1650.9

1647
1652

1645.0

1646

1635.7

1638

1636

1634.3
1633.0

1628
1635

1615.7
1615.8

1613
1616
1612

1601.6
1602.3

1603

1598.7

1596

1600

1558.1
1558.5
1559.8
1564
1558
1561

1541.1
1541.0
1541.6
1544
1539
1541

1518.5

1522
1520
1518

1512.9

1512

1507.3
1506.0
1509.2
1501
1509
1500

1494.0
1491.5
1493.2
1492
1495
1490

1487.0

1486

1464.9
1463.7
1466
1465
1464

1456.4
1454.2

1461
1453
1448

1444.1

1446

1445

1433.4

1433
1439
1438

1403.3
1406
1403

1398.4
1399.8

1398
1395

1384.5
1384.6

1383
1384
1384

1377.1

1376

1339.8

1342.8
1340
1340
1339

1311.6

1311.2
1308

1313

1304.2
1303.3
1302
1307
1306

1289.8
1290

1290

1285.0
1284.1

1287
1283

1262.8
1263.8
1262.3
1272
1265
1265

1242.3

1241
1240
1244

1220.8

1219
1221
1222

1201.1
1207
1203
1201

1197.8

1195
1194
1196

1186.6

1187

1185

1157.7

1158
1161
1158

1169.7
1165
1170
1166

1138.2
1137.7

1146
1139
1141

1121.9
1122.0
1122.7
1129
1130
1133

1107.9

1104.9
1113

1094.5
1098.2

1099

1044.0

1041
1044
1038

973.2

975.5
973

938.5

937.1
941

889.6
896
896
895

884.2

884
880
882

1035.9

1036

1030.5
1029.4
1029
1030
1030

842.8
842.1
843.1
843
840
846

825.8

827
826
825

823.1

823

823

819.9
822

822

808.5

809
810

804.8
800.9

806

804

778.5
777.5
776.7
777
771
777

756.1
755
756
756

745.6
743.1

744
746

742.1
740
740

721.9
720
721
728

711.4
711.3

713
711
709

699.3
700.0
700.0
699
698
698

634.7
632.4
633.0
633
636
631

618.5
616.3
616.8
618
619
621

605.4

604

602.1

601

596.8

597.3

598
599

593.5

593

574.2

575.5
575

569.8

568
570
569

558.7

559.8
558

557

548.2
546.6

548

544.4

545

539.9

538.5
539

537

535.2
535.4
535
533
536

515.9
515.3
517.2
518
514
515

501.7
503.0
507
504

499.6

501
499
499

490.6
492.8

491
493

485.4
486.6
485.6
483
484
489

476.0
476.8
479

476

473.3

472
474
473

462.3
463.6
461.7
461
461
459

455.1
455.7
455.3
454
454
453

451.1
451.2
450.0
451
449
449

433.9
433.3

434

439.8

440
439

435.7

435.5
437
438
437

412.2

412.5

413

401.7
401.0
401.9
398

400

[35].

[38].

[48].

[49].

[50].

The IR spectra of all the chromatographically isolated samples of the isomer C₈₄-D₂:22 from this research, recorded on the mentioned spectrometers, have similar properties. All the observed vibrational frequencies and the overall appearance of these spectra [35–42] are in excellent agreement with the semiempirical QCFF/PI, DFT, and TB potential calculations for this fullerene [48–50].

The achieved agreement between our experimental results [35–42] and the aforementioned theoretical predictions for this molecule [48–50], which is presented in this article in Table 3 and Figure 2 [35, 38, 48–50], is better in comparison to previous experimental results for the obtained C₈₄ samples (partially separated isomers) from other separation processes, by other IR techniques [60–63]. This was also mentioned in the previous article [38].

From the IR spectrum of C₈₄-D₂:22 in a mode, presented in Figure 2, the absorbance values , as well as the integrated absorbance values of the absorption bands, were determined using the OMNIC software.

The molar absorptivity , as well as the integrated molar absorptivity , calculated according to (1) and (3), and the integration ranges of the absorption bands of this fullerene are presented in Table 4.

Table 4: The relative intensities of the absorption bands of C₈₄-D₂:22 calculated from and from the Ψ values in adequate integration ranges.

(cm⁻¹)
(L cm⁻¹ mol⁻¹)
Rel. int. []
Int. range (cm⁻¹)
(Km mol⁻¹)
Rel. int. []

1731.1
498.288
34.7
1753–1719
2.389
34.7

1598.7
344.637
24.0
1626–1572
1.657
24.1

1456.4
598.807
41.7
1475–1447
2.872
41.7

1384.5
1435.989
100
1392–1370
6.886
100

1262.8
483.928
33.7
1299–1232
2.328
33.8

1121.9
1102.810
76.8
1131–1102
5.277
76.7

842.8
542.804
37.8
850–836
2.628
38.2

825.8
173.755
12.1
833–813
0.788
11.5

778.5
422.181
29.4
784–768
1.966
28.6

745.6
409.257
28.5
751–722
1.913
27.8

711.4
413.565
28.8
717–705
2.032
29.5

699.3
113.443
7.9
705–682
0.541
7.9

634.7
150.779
10.5
642–613
0.722
10.5

473.3
163.703
11.4
479–459
0.758
11.0

Also in this case, as can be seen from Table 4, excellent agreement is found between the relative intensities of the main and characteristic absorption maxima of C₈₄-D₂:22 calculated from and from the values, in adequate integration ranges, taking as 100 the most intense vibration mode of C₈₄-D₂:22 at the frequency of 1385 cm⁻¹.

4. Conclusion

In this research, the stable C₇₆ and C₈₄ isomers of D₂ symmetry were isolated from carbon soot, by new and advanced chromatographic methods and processes [35–42]. The IR-KBr spectra of the isolated fullerenes were obtained over the entire fullerenes fingerprint region, 400–2000 cm⁻¹, on a Thermo Scientific FT-IR spectrometer, in transparence mode [35, 38], as well as in the absorption mode in this article.

Based on comparison of the experimentally observed infrared absorption frequencies of the isolated C₇₆-D₂ and C₈₄-D₂:22 samples [35, 38] with the semiempirical QCFF/PI, DFT, and TB potential calculations for these fullerenes [44, 45, 48–50] and the obtained excellent agreement [35, 38, 44, 45, 48–50], presented in this article, the validity of both the experimental results [35, 38] and all the mentioned theoretical calculations [44, 45, 48–50] is confirmed. These research results can be used for their qualitative determination.

The molar extinction coefficients and the integrated molar extinction coefficients of the IR absorption bands of the C₇₆-D₂ and C₈₄-D₂:22 isomers were determined at room temperature in KBr matrix. Excellent agreement is found between the relative intensities of the main and characteristic absorption maxima of these fullerenes calculated from the values and from the values in adequate integration ranges. These results can be used for their quantitative determination.

All the obtained data are important for the identification and quantitative assessment of the C₇₆-D₂ and C₈₄-D₂:22 isomers, either in natural resources on Earth and in space or in artificially synthesized materials, electronic and optical devices, such as polymers, composites, nanophotonic and biocompatible materials, optical limiters, sensors, special lenses with optical absorption properties closer to human eye light sensitivity, diagnostic and therapeutic agents, pharmaceutical substances, and biomaterials.

Conflicts of Interest

The authors declare that there are no conflicts of interest regarding the publication of this paper.

Acknowledgments

The authors are grateful to the Ministry of Education, Science and Technological Development of the Republic of Serbia and to the University of Belgrade for financial support of this research (Project III 45009).

References

F. Cataldo, Y. Hafez, and S. Iglesias-Groth, “FT-IR spectra of fullerenes C₇₆, C₇₈ and C₈₄ at temperatures between −180°C and +250°C,” Fullerenes Nanotubes and Carbon Nanostructures, vol. 22, no. 10, pp. 901–913, 2014.

F. Cataldo, S. Iglesias-Groth, and A. Manchado, “Low and high temperature infrared spectroscopy of C₆₀ and C₇₀ fullerenes,” Fullerenes Nanotubes and Carbon Nanostructures, vol. 18, no. 3, pp. 224–235, 2010.

S. Iglesias-Groth, F. Cataldo, and A. Manchado, “Infrared spectroscopy and integrated molar absorptivity of C₆₀ and C₇₀ fullerenes at extreme temperatures,” Monthly Notices of the Royal Astronomical Society, vol. 413, no. 1, pp. 213–222, 2011.

F. Cataldo, S. Iglesias-Groth, and A. Manchado, “On the molar extinction coefficient and integrated molar absorptivity of the infrared absorption spectra of C₆₀ and C₇₀ fullerenes,” Fullerenes, Nanotubes and Carbon Nanostructures, vol. 20, no. 3, pp. 191–199, 2012.

F. Cataldo, S. Iglesias-Groth, and A. Manchado, “Molar extinction coefficient of fullerenes and related hydrogenated derivatives 'fulleranes',” Proceedings of the International Astronomical Union, vol. 7, no. S283, pp. 324–325, 2011.

F. Cataldo, S. Iglesias-Groth, D. A. Garcia-Hernandez, and A. Manchado, “Determination of the integrated molar absorptivity and molar extinction coefficient of hydrogenated fullerenes,” Fullerenes Nanotubes and Carbon Nanostructures, vol. 21, no. 5, pp. 417–428, 2013.

J. Cami, J. Bernard-Salas, E. Peeters, and S. E. Malek, “Detection of C₆₀ and C₇₀ in a young planetary nebula,” Science, vol. 329, no. 5996, pp. 1180–1182, 2010.

D. A. García-Hernandez, S. Iglesias-Groth, J. A. Acosta-Pulido et al., “The formation of fullerenes: clues from new C60, C70, and (possible) planar C24 detections in magellanic cloud planetary nebulae,” Astrophysical Journal Letters, vol. 737, no. 2, article L30, 2011.

Y. Zhang and S. Kwok, “Detection of C₆₀ in the protoplanetary nebula IRAS 01005+7910,” The Astrophysical Journal, vol. 730, no. 2, article no. 126, 2011.

K. R. G. Roberts, K. T. Smith, and P. J. Sarre, “Detection of C60 in embedded young stellar objects, a Herbig Ae/Be star and an unusual post-asymptotic giant branch star,” Monthly Notices of the Royal Astronomical Society, vol. 421, no. 4, pp. 3277–3285, 2012.

K. Sellgren, M. W. Werner, J. G. Ingalls, J. D. T. Smith, T. M. Carleton, and C. Joblin, “Confirmation of C₆₀ in the reflection nebula NGC 7023,” EAS Publications Series, vol. 46, pp. 209–214, 2011.

D. A. García-Hernandez, N. K. Rao, and D. L. Lambert, “Are C₆₀ molecules detectable in circumstellar shells of R Coronae Borealis stars?” Astrophysical Journal, vol. 729, no. 2, article 126, 2011.

G. C. Clayton, D. M. Kelly, J. H. Lacy, I. R. Little-Marenin, P. A. Feldman, and P. F. Bernath, “A mid-infrared search for C₆₀ in R coronae borealis stars and IRC+10216,” Astronomical Journal, vol. 109, no. 5, pp. 2096–2103, 1995.

G. H. Herbig, “The search for interstellar C₆₀,” Astrophysical Journal, vol. 542, no. 1, pp. 334–343, 2000.

S. Iglesias-Groth, “Fullerenes and the 4430 Å diffuse interstellar band,” The Astrophysical Journal, vol. 661, no. 2, pp. L167–L170, 2007.

B. H. Foing and P. Ehrenfreund, “Detection of two interstellar absorption bands coincident with spectral features of C₆₀⁺,” Nature, vol. 369, no. 6478, pp. 296–298, 1994.

S. Hameroff, J. Withers, R. Loufty, M. Sundareshan, and D. Koruga, Fullerene C₆₀: History, Physics, Nanobiology, Nanotechnology, Elsevier Science Publishers, Amsterdam, The Netherlands, 1993.

A. Hirsch and M. Brettreich, “Chapter 14. Principles and perspectives of fullerene chemistry,” in Fullerenes: Chemistry and Reactions, vol. 48, pp. 1–48, 383–415, Wiley-VCH, Stuttgart, NY, USA, 2005.

W. Krätschmer, L. D. Lamb, K. Fostiropoulos, and D. R. Huffman, “Solid C₆₀: a new form of carbon,” Nature, vol. 347, no. 6291, pp. 354–358, 1990.

W. Krätschmer, K. Fostiropoulos, and D. R. Huffman, “The infrared and ultraviolet absorption spectra of laboratory-produced carbon dust: evidence for the presence of the C₆₀ molecule,” Chemical Physics Letters, vol. 170, no. 2-3, pp. 167–170, 1990.

D. M. Cox, S. Behal, M. Disko et al., “Characterization of C₆₀ and C₇₀ clusters,” Journal of the American Chemical Society, vol. 113, no. 8, pp. 2940–2944, 1991.

D. S. Bethune, G. Meijer, W. C. Tang et al., “Vibrational Raman and infrared spectra of chromatographically separated C₆₀ and C₇₀ fullerene clusters,” Chemical Physics Letters, vol. 179, no. 1-2, pp. 181–186, 1991.

J. P. Hare, T. J. Dennis, H. W. Kroto et al., “The IR spectra of fullerene-60 and -70,” Journal of the Chemical Society, Chemical Communications, no. 6, pp. 412–413, 1991.

T. Jovanovic, D. Koruga, B. Jovancicevic, and J. Simic-Krstic, “Modifications of fullerenes extractions and chromatographies with different solvents,” Fullerenes, Nanotubes and Carbon Nanostructures, vol. 11, no. 4, pp. 383–394, 2003.

T. Jovanović, D. Koruga, P. Polić, and G. Dević, “Extraction, separation and characterization of fullerenes from carbon soot,” Materials Science Forum, vol. 413, pp. 59–64, 2003.

T. Jovanovic, D. Koruga, B. Jovancicevic, and J. Simic-Krstic, “Improvement in separation of nanostructured carbon clusters C₆₀ and C₇₀,” International Journal of Nanoscience, vol. 2, no. 3, pp. 129–140, 2003.

J. Cioslowski, “Heats of formation of higher fullerenes from ab initio Hartree-Fock and correlation energy functional calculations,” Chemical Physics Letters, vol. 216, no. 3-6, pp. 389–393, 1993.

F. Cataldo, G. Strazzulla, and S. Iglesias-Groth, “Stability of C₆₀ and C₇₀ fullerenes toward corpuscular and γ radiation,” Monthly Notices of the Royal Astronomical Society, vol. 394, no. 2, pp. 615–623, 2009.

S. Iglesias-Groth, “Hydrogenated fulleranes and the anomalous microwave emission of the dark cloud LDN 1622,” Monthly Notices of the Royal Astronomical Society, vol. 368, no. 4, pp. 1925–1930, 2006.

F. Cataldo and S. Iglesias-Groth, “On the action of UV photons on hydrogenated fulleranes C₆₀H₃₆ and C₆₀D₃₆,” Monthly Notices of the Royal Astronomical Society, vol. 400, no. 1, pp. 291–298, 2009.

F. Cataldo and S. Iglesias-Groth, Eds., Fulleranes: The Hydrogenated Fullerenes, Springer, Berlin, Germany, 2009.

C. Yeretzian, K. Hansen, F. Diederichi, and R. L. Whetten, “Coalescence reactions of fullerenes,” Nature, vol. 359, no. 6390, pp. 44–47, 1992.

B. Kubler, E. Millon, J. J. Gaumet, and J. F. Muller, “Formation of high mass Cn clusters (n > 100) by laser ablation/desorption coupled with mass spectrometry,” Fullerene Science and Technology, vol. 4, no. 6, pp. 1247–1261, 1996.

F. Cataldo and Y. Keheyan, “On the mechanism of carbon clusters formation under laser irradiation. The case of diamond grains and solid C₆₀ fullerene,” Fullerenes Nanotubes and Carbon Nanostructures, vol. 10, no. 4, pp. 313–332, 2002.

T. Jovanović, D. Koruga, and B. Jovančićević, “Recent advances in IR and UV/VIS spectroscopic characterization of the C₇₆ and C₈₄ isomers of D₂ symmetry,” Journal of Nanomaterials, vol. 2014, Article ID 701312, 11 pages, 2014.

T. Jovanovic and D. Koruga, “Recent advances in chromatographic separation and spectroscopic characterization of the higher fullerenes C₇₆ and C₈₄,” Recent Patents on Nanotechnology, vol. 8, no. 1, pp. 62–75, 2014.

T. Jovanovic and D. Koruga, “The electronic structure and vibrational frequencies of the stable C₇₆ isomer of D₂ symmetry: theory and experiment,” Chemical Physics Letters, vol. 577, pp. 68–70, 2013.

T. Jovanovic, D. Koruga, and B. Jovancicevic, “The electronic structure and vibrational frequencies of the stable C₈₄ isomer of D₂ symmetry: theory and experiment,” Diamond and Related Materials, vol. 44, pp. 44–48, 2014.

T. Jovanovic, D. Koruga, and B. Jovancicevic, “Advances in chromatographic separation on Al₂O₃ and spectroscopic characterization of the higher fullerenes,” Fullerenes Nanotubes and Carbon Nanostructures, vol. 22, no. 4, pp. 384–396, 2014.

T. Jovanovic, D. Koruga, B. Jovancicevic, and J. Simic-Krstic, “Advancement of the process for extraction, chromatography and characterization of fullerenes,” Fullerenes, Nanotubes and Carbon Nanostructures, vol. 17, no. 2, pp. 135–150, 2009.

T. Jovanovic, D. Koruga, and B. Jovancicevic, “Isolation and characterization of the higher fullerenes from carbon soot,” Fullerenes Nanotubes and Carbon Nanostructures, vol. 19, no. 4, pp. 309–316, 2011.

T. Jovanovic, D. Koruga, B. Jovancicevic, V. Vajs, and G. Devic, “Comparative spectroscopic characterization of the basic and the higher fullerenes,” Fullerenes Nanotubes and Carbon Nanostructures, vol. 21, no. 1, pp. 64–74, 2013.

D. E. Manolopoulos, “Faraday communications. Proposal of a chiral structure for the fullerene C₇₆,” Journal of the Chemical Society, Faraday Transactions, vol. 87, no. 17, pp. 2861–2862, 1991.

G. Orlandi, F. Zerbetto, P. W. Fowler, and D. E. Manolopoulos, “The electronic structure and vibrational frequencies of the stable C₇₆ isomer of D₂ symmetry,” Chemical Physics Letters, vol. 208, no. 5-6, pp. 441–445, 1993.

O. Hampe, M. Neumaier, A. D. Boese, J. Lemaire, G. Niedner-Schatteburg, and M. M. Kappes, “Infrared multiphoton electron detachment spectroscopy of C₇₆²⁻,” Journal of Chemical Physics, vol. 131, no. 12, Article ID 124306, 2009.

D. E. Manolopoulos and P. W. Fowler, “Molecular graphs, point groups, and fullerenes,” The Journal of Chemical Physics, vol. 96, no. 10, pp. 7603–7614, 1992.

D. E. Manolopoulos, P. W. Fowler, R. Taylor, H. W. Kroto, and D. R. M. Walton, “Faraday communications. An end to the search for the ground state of C₈₄?” Journal of the Chemical Society, Faraday Transactions, vol. 88, no. 20, pp. 3117–3118, 1992.

F. Negri, G. Orlandi, and F. Zerbetto, “Prediction of the structure and the vibrational frequencies of a C₈₄ isomer of D₂ symmetry,” Chemical Physics Letters, vol. 189, no. 6, pp. 495–498, 1992.

H. F. Bettinger and G. E. Scuseria, “The infrared vibrational spectra of the two major C₈₄ isomers,” Chemical Physics Letters, vol. 332, no. 1-2, pp. 35–42, 2000.

B. L. Zhang, C. Z. Wang, and K. M. Ho, “Vibrational spectra of C₈₄ isomers,” Physical Review B, vol. 47, no. 3, pp. 1643–1646, 1993.

M. Hulman, T. Pichler, H. Kuzmany, F. Zerbetto, E. Yamamoto, and H. N. Shinohara, “Vibrational structure of C₈₄ and Sc₂@C₈₄ analyzed by IR spectroscopy,” Journal of Molecular Structure, vol. 408-409, pp. 359–362, 1997.

G. Von Helden, I. Holleman, M. Putter, A. J. A. Van Roij, and G. Meijer, “Infrared resonance enhanced multi-photon ionization spectroscopy of C₈₄,” Chemical Physics Letters, vol. 299, no. 2, pp. 171–176, 1999.

D. Bakowies, M. Kolb, W. Thiel, S. Richard, R. Ahlrichs, and M. M. Kappes, “Quantum-chemical study of C₈₄ fulleren isomers,” Chemical Physics Letters, vol. 200, no. 4, pp. 411–417, 1992.

T. Nishikawa, T. Kinoshita, S. Nanbu, and M. Aoyagi, “A theoretical study on vibrational spectra of C₈₄ fullerenes: results for C₂, D₂, and D2d isomers,” Journal of Molecular Structure: THEOCHEM, vol. 461-462, pp. 453–461, 1999.

F. Diederich, R. Ettl, Y. Rubin et al., “The higher fullerenes: isolation and characterization of C₇₆, C₈₄, C₉₀, C₉₄, and C₇₀O, an oxide of -C₇₀,” Science, vol. 252, no. 5005, pp. 548–551, 1991.

K. Jinno, H. Matsui, H. Ohta et al., “Separation and identification of higher fullerenes in soot extract by liquid chromatography-mass spectrometry,” Chromatographia, vol. 41, no. 5-6, pp. 353–360, 1995.

K. Jinno, Y. Sato, H. Nagashima, and K. Itoh, “Separation and identification of higher fullerenes by high-performance liquid chromatography coupled with electrospray ionization mass spectrometry,” Journal of Microcolumn Separations, vol. 10, no. 1, pp. 79–88, 1998.

K. Kikuchi, N. Nakahara, M. Honda et al., “Separation, detection, and UV/Visible absorption spectra of fullerenes; C₇₆, C₇₈, and C₈₄,” Chemistry Letters, vol. 20, no. 9, pp. 1607–1610, 1991.

K. Kikuchi, N. Nakahara, T. Wakabayashi et al., “Isolation and identification of fullerene family: C₇₆, C₇₈, C₈₂, C₈₄, C₉₀ and C₉₆,” Chemical Physics Letters, vol. 188, no. 3-4, pp. 177–180, 1992.

R. Ettl, I. Chao, F. Diederich, and R. L. Whetten, “Isolation of C₇₆, a chiral D₂ allotrope of carbon,” Nature, vol. 353, no. 6340, pp. 149–153, 1991.

R. H. Michel, H. Schreiber, R. Gierden et al., “Vibrational spectroscopy of purified C₇₆,” Berichte der Bunsengesellschaft fur Physikalische Chemie, vol. 98, no. 7, pp. 975–978, 1994.

A. G. Avent, D. Dubois, A. Pénicaud, and R. Taylor, “The minor isomers and IR spectrum of [84]fullerene,” Journal of the Chemical Society. Perkin Transactions 2, no. 10, pp. 1907–1910, 1997.

T. J. S. Dennis, M. Hulman, H. Kuzmany, and H. Shinohara, “Vibrational infrared spectra of the two major isomers of [84]fullerene: C₈₄{D₂(IV)} and C₈₄{D2d(II)},” Journal of Physical Chemistry B, vol. 104, no. 23, pp. 5411–5413, 2000.

N. B. Colthup, L. H. Daly, and S. E. Wiberley, Introduction to Infrared and Raman Spectroscopy, Academic Press, San Diego, Calif, USA, 3rd edition, 1990.