FT-IR, FT-Raman spectra and ab- initio DFT vibrational analysis of 2-chloro-5- aminopyridine

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1 Indian Journal of Pure & Applied Physics Vol. 45, December 2007, pp FT-IR, FT-Raman spectra and ab- initio DFT vibrational analysis of 2-chloro-5- aminopyridine N Sundaraganesan a, B Dominic Joshua b, M Rajamoorthy c & C H Gangadhar a a Department of Physics, Annamalai University, Annamalai Nagar b Department of Physics, Sri Aravindar Arts and Science College, Akasampet, Vanur Dt c Sri Paramakalyani College, PG Department of Physics, Alwarkurichi Received 3 March 2006 ; revised 14 February 2007 ; accepted 18 September 2007 The FT-IR and FT-Raman spectra of 2-chloro-5-aminopyridine (CAP) have been recorded in the region cm -1 and cm -1, respectively. The optimized geometry, frequency and intensity of the vibrational bands of CAP were obtained by the ab- initio and DFT levels of theory with complete relaxation in the potential energy surface using 6-31G(d,p) and G(2df,2p) basis sets. The harmonic vibrational frequencies were calculated and the scaled values have been compared with experimental FT-IR and FT-Raman spectra. A detailed interpretation of the vibrational spectra of this compound has been made on the basis of the calculated potential energy distribution (PED). The observed and the calculated frequencies are found to be in good agreement. The experimental spectra also coincide satisfactorily with those of theoretically constructed bar type spectrograms. Keywords: FT-IR spectra, FT-Raman spectra, Ab- initio, DFT,2-chloro-5-aminopyridine, Vibrational analysis IPC Code: G 01 J 3/28 1 Introduction Aminopyridine and its derivative are currently finding increasing applications for several reasons. At the outset, they represent a group of compounds used as reagents in analytical chemistry. Secondly, some of them show anesthetic properties and are used as drugs for certain brain disease. In spite of these physiological applications and the consequent interest in their qualitative and quantitative characterisation in aqueous solution, the quantum mechanical calculations of these compounds have not been thoroughly investigated. In recent years, the ab- initio and density functional theory (DFT) has become a powerful tool in the investigation of molecular structure and vibrational spectra. The purpose of the present study is to perform calculations for 2-chloro-5-aminopyridine at the HF and B3LYP level of theories using different basis sets. Knowledge of both the molecular structure and infrared spectra of these molecule is very important for the investigation of inter- and intra-molecular interactions using vibrational spectroscopic method. Sasaki et al 1. recorded infrared and Raman spectra for iodine dichlorides and iodine dibromides of 2-, 3- and 4-amino pyridines in solids and they have also address: sundaraganesan_n2003@yahoo.co.in measured pyridine Raman spectra in methanol solutions. Sanyal et al 2. attempted to interpret the infrared spectrum of 3-amino-2-chloropyridine without giving complete assignments. The vibrational spectra of 3-amino-2-chloropyridine was reinvestigated by Settu 3. The vibrational spectra of substituted pyridine have been the subject of several investigations 4-6. IR and Raman spectroscopy is an efficient method to probe electronic and geometric structure of molecules, and has been used widely in studying the structural consequences, such as in-plane or out-of-plane structure of pyridine 7. The philosophy of computational methods of vibrational spectroscopy 8-10 changed significantly after the introduction of scaled quantum mechanical calculations (SQM). Literature survey reveals that to the best of our knowledge, no ab- initio HF/DFT frequency calculations for 2-chloro-5-aminopyridine (CAP) have been reported so far. Therefore, the present investigation is undertaken to study the vibrational spectra of this molecule completely and to identify the various normal modes with greater wave number accuracy. Ab- intio HF and density functional theory (DFT) calculations have been performed to support our wave number assignments.

2 970 INDIAN J PURE & APPL PHYS, VOL. 45, DECEMBER Experimental Details The compound 2-chloro-5-aminopyridine (CAP) in solid form was purchased from Sigma-Aldrich Chemical Company, USA and used as such without further purification to record FT-IR and FT-Raman spectra. A Bruker IFS 66V Fourier transform (FT) IR spectrometer was used to record the spectra. An FRA 106 Raman module was used as an accessory for the FT-Raman measurements. The instrument has a resolution ~2-3 cm -1. Multi-tasking OPUS software on a PC/AT 486 computer was used for processes such as signal averaging, signal enhancement and base line corrections. An air cooled diode pumped Nd-YAG laser operated at 1064 nm and with the laser output maintained at 200 mw was used for Raman spectral measurements. The spectra were recorded in the range cm -1. For IR measurements, a globar source was used and the spectra were recorded over the range cm -1. The sample for this measurement was finely ground and mixed with KBr. This mixture was then pressed under vacuum at high pressure to obtain a transparent disc, which was then placed in the sample compartment. In the FT-IR mode the detector was a pyroelectric device incorporating deuterium triglycine sulphate (DTGS) in a temperature-resistant alkali metal halide window. The spectral measurements were carried out in Sophisticated Analytical Instrumentation Facility (SAIF), IIT, Chennai. The experimental FT-IR and FT-Raman spectra along with structure of molecules are shown in Figs 1-3. Theoretically predicted infrared spectra with their scaled frequencies using scale factors for each mode are shown in Figs 4 and 5. Fig. 1 FT-IR spectrum of 2-chloro-5-aminopyridine Fig. 2 FT-Raman spectrum of 2-chloro-5-aminopyridine Fig. 3 Numbering system adopted in this study (2-chloro-5- aminopyridine) 3 Computational Details The entire calculations were performed at Hartree- Fock (HF) and B3LYP levels on a Pentium IV/1.6 GHz personal computer 11 using Gaussian 03W program package, invoking gradient geometry optimization 12. Initial geometry generated from standard geometrical parameters was minimized without any constraint in the potential energy surface at Hartree-Fock level, adopting the standard 6-31G(d,p) basis set. This geometry was then reoptimized again at HF level, adding polarization functions 2d and 1f diffuse function on heavy atoms and 2p functions on the hydrogen atoms, in addition

3 SUNDARAGANESAN et al.: FT-IR, FT-RAMAN SPECTRA AND DFT VIBRATIONAL ANALYSIS 971 to triple split valence basis set [6-311+G(2df,2p)], for better description of polar bonds of amino and chloro groups. The optimized structural parameters were used in the vibrational frequency calculations at the HF and DFT levels to characterize all stationary points as minima. Then, vibrationally averaged nuclear positions of CAP were used for harmonic vibrational frequency calculations resulting in IR and Raman frequencies together with intensities and Raman depolarization ratios. We have utilized the gradient corrected density functional theory 13 (DFT) with the three-parameter hybrid functional 14 (B3) for the exchange part and the Lee-Yang-Parr (LYP) correlation function 15, accepted as a cost-effective approach, for the computation of molecular structure, vibrational frequencies and energies of optimized structures. Vibrational frequencies computed at DFT level have been adjudicated to be more reliable than those obtained by the computationally demanding Moller-Plesset perturbation methods. Density functional theory offers electron correlation frequently comparable to second-order Moller-Plesset theory (MP2). Finally, the calculated normal mode vibrational frequencies provide thermodynamic properties also through the principle of statistical mechanics. By combining the results of the GAUSSVIEW program 16 with symmetry considerations, vibrational frequency assignments were made with a high degree of accuracy. There is always some ambiguity in defining internal coordination. However, the defined coordinate, form a complete set and matches quite Table 1 Geometrical parameters optimized in 2-chloro-5-aminopyridine (CAP), Bond length (Å), angle ( ) Parameters HF B3LYP 6-31G(d,p) G(2df,2p) 6-31G(d,p) G(2df,2p) Bond length (Å) C1-C C1-H C1-N C2-C C2-N C2-Cl C3-C C3-H C4-C C4-H C5-N N11-H N11-H Bond angle ( ) C5-C1-H C5-C1-N H6-C1-N C3-C2-N C3-C2-Cl N9-C2-Cl C2-C3-C C2-C3-H C4-C3-H C3-C4-C C3-C4-H C5-C4-H C1-C5-C C1-C5-N C4-C5-N C1-N9-C C5-N11-H C5-N11-H H12-N11-H

4 972 INDIAN J PURE & APPL PHYS, VOL. 45, DECEMBER 2007 Table 2 Experimental FTIR and FT-Raman frequencies and assignments for 2-chloro-5-aminopyridine (cm -1 ) Species FT-IR frequency Vibrational FT-Raman frequency and intensity assignments and intensity A 3317 w N-H symmetric stretching A 3191 m (2 1590) 3194 w A C-H stretching 3083 m A 1640 w C-C stretching A NH 2 scissoring 1611 vs A 1590 w C-C stretching A 1574 m C-C stretching 1575 w A C-C stretching 1485 w A 1465 vs C=N stretching A 1411 s C-N stretching 1410 w A C-C stretching 1316 w A 1278 w C-NH 2 stretching A C-H in-plane bending 1142 w A 1128 w C-H in-plane bending 1120 m A 1100 w C-H in-plane bending A 1090 w NH 2 twisting A 1016 m C-H out-of-plane bending A 886 m C-H out-of-plane bending A /A 860 vw ring breathing 864 s 830 vs C-H out-of-plane bending/ A C-N in-plane bending A 700 w C-C out-of-plane bending A 650 w C-Cl stretching 652 ms A 634 m C-C out-of-plane bending A 512 m C-C in-plane bending A C-Cl in-plane bending 438 w A C-NH 2 in-plane bending 407 ms A C-Cl out-of-plane bending 162 w NH 2 torsion 118 vs vs - very strong; s - strong; w - weak; ms - medium strong, s stretching. well with the motions observed using the GAUSSVIEW program. 4 Results and Discussion 4.1 Molecular geometry The labelling of atoms in 2-chloro-5-aminopyridine is given in Fig 3. The optimized geometrical parameters (bond length and angles) by HF, DFT/B3LYP with 6-31G(d,p) and G(2df,2p) as the basis sets are presented in Table Vibrational assignments According to the theoretical calculations, CAP has a planar structure of C s point group symmetry. The molecule has 13 atoms and 33 normal modes of fundamental vibration which span the irreduciable representations: 23 A (planar) and 10 A (nonplanar). All the 33 fundamental vibrations are active in both IR and Raman. The assignments are presented in Table 1, for several of phenyl ring modes are obvious and require no further discussion. A brief analysis is given for the substituents in the present work. The harmonic vibrational frequencies calculated for CAP at HF and B3LYP levels using the triple split valence basis sets along with diffuse and polarization functions, 6-31G(d,p) and G(2df,2p) have been presented in Tables 3-6. The observed IR and Raman frequencies for various modes of vibrations are presented in Table 1. The last column of Table 6 shows the detailed vibrational assignment obtained from the calculated potential energy distribution (PED). Comparison of the frequencies calculated at HF and B3LYP with the experimental values (Table 1) reveals the overestimation of the calculated vibrational modes due to neglect of anharmonicity in real system. Inclusion of electron correlation in density functional theory to a certain extend makes the frequency values smaller in comparison with the

5 SUNDARAGANESAN et al.: FT-IR, FT-RAMAN SPECTRA AND DFT VIBRATIONAL ANALYSIS 973 Table 3 Vibrational wavenumbers obtained for 2-chloro-5-aminopyridine (CAP) at HF/6-31G (d,p) [harmonic frequency (cm -1 ), IR intensities (Km mol -1 ), Raman scattering activities (Å 4 amu -1 ), Raman depolarization ratio and reduced masses (amu), force constants (m dyne Å -1 )] Mode Wavenumber IR intensity Raman intensity Depolarization Red Force number unscaled scaled Abs Rel Abs Rel ratios mass constants HF frequency data. Reduction in the computed harmonic vibrations, though basis set sensitive are only marginal as observed in the DFT values using 6-31G(d,p) and G(2df,2p). It is customary to scale down the calculated harmonic frequencies in order to improve the agreement with the experiment. Vibrational frequencies calculated at B3LYP level 17 were scaled by 0.96, and those calculated at HF level were scaled 18 by The stick spectra of CAP at HF and B3LYP levels using 6-31G(d,p) and G(2df,2p) are shown in Figs 4 and C-H vibrations Since CAP is a disubstituted aromatic system, it has two adjacent and one isolated C-H moieties. The expected three C-H stretching vibrations correspond to mode nos, 29, 30 and 31. The scaled vibration, of mode nos. 29, 30 and 31 (Tables 3-6) corresponds to stretching modes of C 3 -H, C 4 -H and C 6 -H units. The vibrations (mode nos 29-31) assigned to aromatic C-H stretch 19 in the region are in agreement with experimental assignment The C-H inplane bending vibrations assigned in the region cm -1 (mode nos19-20 and 22) even though found to be contaminated by C-N and C-NH 2 stretching are in the range found in the literature 15,21, while the experimental observations are at cm -1. The calculated frequencies cm -1 (mode nos 13, 15-16) for the C-H out-of-plane bending falls in the IR/Raman values of cm C=N, C-N vibrations The identification of C=N and C-N vibrations is a very difficult task, since the mixing of several bands are possible in this region. Silverstein 20 assigned C-N stretching absorption in the region cm -1 for

6 974 INDIAN J PURE & APPL PHYS, VOL. 45, DECEMBER 2007 Table 4 Vibrational wavenumbers obtained for 2-chloro-5-aminopyridine (CAP) at HF/6-311+G(2df,2p) [harmonic frequency (cm -1 ), IR intensities (Km mol -1 ), Raman scattering activities (Å 4 amu -1 ), Raman depolarization ratio and reduced masses (amu), force constants (m dyne Å -1 )] Mode Wavenumber IR intensity Raman intensity Depolarization Red Force number unscaled scaled Abs Rel Abs Rel Ratios mass Constants Fig. 4 Comparison of corrected frequencies in cm -1 normalised IR intensities at each level of calculations considered Fig. 5 Comparison of corrected frequencies in cm -1 normalised IR intensities at each level of calculations considered

7 SUNDARAGANESAN et al.: FT-IR, FT-RAMAN SPECTRA AND DFT VIBRATIONAL ANALYSIS 975 Table 5 Vibrational wavenumbers obtained for 2-chloro-5-aminopyridine (CAP) at B3LYP/6-31G(d,p) [harmonic frequency (cm -1 ), IR intensities (Km mol -1 ), Raman scattering activities (Å 4 amu -1 ), Raman depolarization ratio and reduced masses (amu), force constants (m dyne Å -1 )] Mode Wavenumber IR intensity Raman intensity Depolarization Red Force number unscaled scaled Abs Rel Abs Rel Ratios mass Constants aromatic amines. In benzamide, the band observed at 1368 cm -1 is assigned to be due to C-N stretching 22. In benzotrizole, the C-N stretching bands are found to be present at 1382 cm -1 and 1307 cm -1. In the present work, the frequencies observed as very strong bands at 1465 and 1411 cm -1 in FT-IR spectrum have been assigned to C=N and C-N stretching vibrations, respectively. The theoretically computed values of C=N and C-N stretching vibrations also falls in the region cm -1. These vibrations are almost mixed up with C-C stretching and C-H in-plane bending vibrations. 4.5 C-NH 2 vibrations The scaled -NH 2 symmetric and asymmetric stretches in the range cm -1 (mode nos. 32,33) are in agreement with experimental values of 3317 cm -1. The asymmetric vibration calculated at 3526 cm -1 is missing in both IR and Raman. The computed NH 2 scissoring vibration at 1596 cm -1 (mode no 28) is in excellent agreement with the expected characteristic value 23,24, 1600 cm -1. This is also very good agreement with recorded Raman value of 1611 cm -1. The IR stretching mode 1278 cm -1 corresponding to C-NH 2 moiety was calculated to be 1262 cm -1 (mode no 22). The C-NH 2 out-of-plane and in-plane bending vibrations at 251 and 394 cm -1, respectively are also in good agreement with the assignment in the experimental data. The NH 2 wagging computed at 525 cm -1 is missing in both IR and Raman spectra. The NH 2 twisting vibration calculated to be 1041 cm -1 is in very good agreement

8 976 INDIAN J PURE & APPL PHYS, VOL. 45, DECEMBER 2007 Table 6 Vibrational wavenumbers obtained for 2-chloro-5-aminopyridine (CAP) at B3LYP/6-311+G(2df,2p) [harmonic frequency (cm -1 ), IR intensities (Km mol -1 ), Raman scattering activities (Å 4 amu -1 ), Raman depolarization ratio and reduced masses (amu), force constants (m dyne Å -1 )] Mode Wavenumber IR intensity Raman intensity Depolarization Red Force Assignments (PED) number unscaled scaled Abs Rel Abs Rel ratios mass constants γ C-NH 2 (54) + γ CCl (21) γ C-NH 2 (21) + γ CCl (24) τ ΝΗ 2 (66) t NH 2 (52) + β CCC (39) ν CCl (78) + β C-NH 2 (12) β CNH 2 (54) + β CCl (37) β CCC (59) + β CH (30) + β CN (16) ω NH 2 (61) + γ CCC (20) ω ΝΗ 2 (43) + γ CCC (26) β CCC (61) + β CH (24) ν CCl (68) + ν CH (18) β CN (71) + β CCC (16) γ CH (67) β CCC (88) γ CH (71) γ CH (59) β CCC (74) + β CH (16) t NH 2 (44) ν CN (56) + ν CC (20) + β CH (19) β CH (66) + β CCC (24) ν CN (70) + ν CC (19) ν C-NH 2 (51) + β CH (20) β CH (56) + β CN (19) ν CN (68) + β CC (2) + β CH (11) ν CC (79) + ν CN (10) ν CC (80) + β CCC (12) δ NH 2 (46) + β CC (21) + β CN (16) δ NH 2 (51) ν CH (96) ν CH (93) ν CH (90) ν S NH 2 (96) ν as NH 2 (95) v stretching; ν s -sym. stretching; ν as -asym. stretching; β in-plane-bending; γ -out-of-plane bending; δ-scissoring; ω -wagging; ρ - rocking; t - twisting; τ - torsion. with recorded value of 1090 cm -1 in IR spectrum. It should be emphasized that the wave number calculated by the B3LYP/6-311+G(2df,2p) method for the NH 2 torsion mode at 276 cm -1 is not in agreement with experimental observation of Raman value of 118 cm C=C vibrations The C=C aromatic stretch, known as semicircle stretching, predicted at 1552 cm -1 is in excellent agreement with experimental observations of both in IR and Raman spectra. The ring-breathing mode at 852 cm -1 (unscaled value, mode no. 14) coincides satisfactorily with the very strong Raman band 25 at 864 cm -1. The theoretically calculated C-C-C out-ofplane and in-plane bending modes have been found to be consistant with the recorded spectral values. 4.7 C-Cl vibrations The vibrations belonging to the bond between the ring and the halogen atom are worth to discuss here, since mixing of vibrations are possible due to the lowering of molecular symmetry and the presence of heavy atoms on the periphery of the molecule 26. In the earlier vibrational studies of 3-chloro-2-, 2-chloro-6-, 4-chloro-2- and 5-chloro-2- methyl anilines are observed cm -1 for the ν(c-cl) bands 27,28. Mooney 29,30 assigned vibrations of C-X group (X=Cl,

9 SUNDARAGANESAN et al.: FT-IR, FT-RAMAN SPECTRA AND DFT VIBRATIONAL ANALYSIS 977 Table 7 Theoretically computed energies (a.u.), zero point vibrational energies (kcal mol -1 ), rotational constants (GHz), entropies (cal mol -1 K -1 ) and dipole moment (Debyes) for CAP. HF B3LYP Parameters 6-31G(d,p) G(2df,2p) 6-31G(d,p) G(2df,2p) Total energy Zero-point energy Rotational constants Entropy Total Translational Rotational Vibrational Dipole moment Br, I) in the frequency range cm -1. The ring halogen stretching mode were observed as strong Raman and weak to medium IR bands at cm - 1 range for chlorine. As expected in our studies, the bands at 650 and 652 cm -1 are assigned to C-Cl stretching vibration, respectively. The theoretical wave number of C-Cl stretching vibration coupled with ring deformation vibration (mode no11), 633 cm - 1 coincides exactly with experimental observation. The C-Cl in-plane bending and out-of plane bending vibrations are assigned to the Raman bands at 438 and 162 cm -1, respectively. This is in agreement with the literature data The force constant values computed at HF and DFT level of theories at various basis set have been collected in Tables 3-6. These force constant values on comparison with related molecule 7,31 are found to deviate approximately by one unit. 5 Other Molecular Properties Several calculated thermodynamic parameters are presented in Table 7. Scale factors have been recommended 32 for an accurate prediction in determining the zero-point vibration energies (ZPVE), and the entropy, S vib (T). The variations in the ZPVE seem to be insignificant. The total energies are found to decrease with the increase of the basis set dimension. The changes in the total entropy of CAP at room temperature at different basis set are only marginal. 6 Infrared Intensities The calculated intensities for the title molecule are also shown in Tables 3-6. The intensities calculated for the some of the modes qualitatively match the experimental ones very well. In some cases, B3LYP method predicts IR intensities lower than HF method does, and in some cases such as ν s NH 2, ν as NH 2, ν CH and δ ΝΗ 2 both methods obtain the comparable intensities. 7 Conclusion Attempts have been made in the present work for the proper frequency assignments for the compound CAP from the FT-IR and FT-Raman spectra. The equilibrium geometries and harmonic frequencies of CAP were determined and analysed both at HF and DFT level of theories utilizing 6-31G(d,p) and G(2df,2p) basis sets, giving allowance for the lone pairs through diffuse functions. The difference between the observed and scaled wave number values of the most of the fundamental is very small. Any discrepancy noted between the observed and the calculated frequencies is due to the fact that the calculations have been actually done on a single molecule in the gaseous state contrary to the experimental values recorded in the presence of intermolecular interactions. Therefore, the assignments made at higher levels of theory with only reasonable deviations from the experimental values, seem to be correct. References 1 Sasaki K, Kuwano & Aida K, J Inorg Nucl Chem, 43 (1981) Sanyal N K, Srivastava S L & Ananda Devi, Indian J Pure Appl Phys, 21 (1983) Settu K, Ph.D. Thesis, Vibrational spectra and assignments of some polyatomic molecules Pondicherry University, 1993.

10 978 INDIAN J PURE & APPL PHYS, VOL. 45, DECEMBER Topacle A & Bayari S, Spectrochim Acta, part A, 57 (2001) Medhi R N, Barman R, Medhi K C & Jois S S, Spectrochim Acta, part A, 56 (2000) Lopez Tocon I, Woolley M S, Otero J C & Marcos J J, J Mol Struct, 470 (1998) Krishnakumar V & John Xavier R, Spectrochimica Acta, part A, 61 (2005) Fogarasi G, Puley P & Durrg J R (Ed.), Vibrational Spectra and Structure: Vol. 14 Elsevier, Amsterdam (1985) chapter 3 p Pulay P & Schaefar H F III (Ed.), Application of Electronic Structure Theory, Modern Theoretical Chemistry: Vol. 4 (Plenum, New York), (1997) p Panchenko Y N, J Mol Struct, 567 (2001) Frisch M J, Trucks G W, Schlegel H B, Scuseria G E, et al., Gaussian Inc, Wallingford CT (2004). 12 Schlegel H B, J Comput Chem, 3 (1982) Hohenberg P & Kohn W, Phys Rev, 136 (1964) B Becke A D, J Chem Phys, 98 (1993) Lee C, Yang W & Parr R G, Phys Rev, B 37 (1988) Frisch A, Nielson A B & Holder A J, GAUSSVIEW User Manual, Gaussian Inc, Pittsburgh PA (2000). 17 Pople J A, Schlegel H B, Krishnan R, Defrees D J, Binkley J S, Frisch M J, Whiteside R A, Hout R H & Hehre W J, Int J Quantum Chem Quantum Chem Symp 15 (1981) Pople J A, Scolt A P, Wong M W & Radom L, Isr J Chem, 33 (1993) Rastogi K, Palafox M A, Tanwar R P & Mittal L, Spectrochim Acta A, 58 (2002) Silverstein M, Clayton Basseler G & Morill C, Spectrometric Identification of Organic Commpounds: (Wiley New York), Becke A D, J Phys Chem, 98 (1993) Shanmugam R & Sathyanarayana D, Spectrochim. Acta A, 40 (1984) Yadav R A & Sing I S, Indian J Pure & Appl Phys, 23 (1985) Wiberg K B & Shrake A, Spectrochim Acta A, 29 (1973) Sing N P & Yadav R A, Indian J Phys, B 75 (4) (2001) Bakiler M, Maslov I V & Akyiiz S, J Mol Struct, 475 (1999) Zierkiewiez W, Michalska D & Zeegers-Huyskens Th, J Phys Chem A, 104 (2000) Varsanyi G, Assignments for Vibrational Spectra of Seven hundred Benzene Derivatives: Vols1 &2 Adam Hilger (1974). 29 Mooney E F, Spectrochim Acta, 20 (1964) Mooney E F, Spectrochim Acta, 19 (1963) Prystupa D A, Anderson A & Torrie B H, J Raman Spectrosc, 25 (1994) Alcolea Palafox M, Int J Quant Chem, 77 (2000) 661.