Theoretical vibrational spectra and thermodynamics of organic semiconductive tetrathiafulvalene and its cation radical

Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 117 (2014) 315–322

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Theoretical vibrational spectra and thermodynamics of organic semiconductive tetrathiafulvalene and its cation radical V. Mukherjee a,⇑, N.P. Singh b a b

Physics, Sambalpur University Institute of Information Technology (SUIIT), Sambalpur, India Department of Physics, Udai Pratap Autonomous College, Varanasi, India

h i g h l i g h t s

g r a p h i c a l a b s t r a c t

 Optimized molecular structures of

PFV, TTF and TTF+ are presented.  Theoretical IR and Raman spectra of

these molecules are presented.  Vibrational canonical partition

function is calculated.  Thermodynamical parameters are

calculated.  Variation of partition function and

specific heat with temperature are presented.

a r t i c l e

i n f o

Article history: Received 1 May 2013 Received in revised form 20 July 2013 Accepted 31 July 2013 Available online 8 August 2013 Keywords: Organic conductors DFT IR and Raman spectra SQMFF Thermodynamics

a b s t r a c t s Molecular structure in optimum geometry and vibrational frequencies of pentafulvalene [bicyclopentyliden-2,4,20 ,40 -tetraene], tetrathiafulvalene [2,20 -bis(1,3-dithiolylidene)] and its cation are calculated. All the calculations are carried out by employing density functional theory incorporated with a suitable basis set. Normal coordinate analysis is also employed to scale the DFT calculated frequencies and to calculate potential energy distributions. The molecular structures and vibrational frequencies are compared for both the pentafulvalene and tetrathiafulvalene molecules. The effect upon geometry and vibrational frequencies of TTF due to charge transfer has also been studied. The vibrational partition function and hence, the thermodynamical properties, such as Helmholtz free energy, entropy, specific heat at constant volume and enthalpy are also calculated and compared for the title molecules. The reason of conductivity of tetrathiafulvalene has been tried to explain on the basis of molecular geometry and normal modes. Study of vibrational partition function exhibits that below 109 K, PFV starts to condense. Ó 2013 Elsevier B.V. All rights reserved.

Introduction An organic semiconductor is an organic material with semiconductor properties. Single molecules, short chain (oligomers) and organic polymers can be semiconductors. Semiconducting small molecules (aromatic hydrocarbons) include the polycyclic aromatic compounds like fulvalene derivatives, pentacene, anthracene, and rubrene. Polymeric organic semiconductors include ⇑ Corresponding author. Tel.: +91 9369050014. E-mail address: [email protected] (V. Mukherjee). 1386-1425/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.saa.2013.07.105

poly(3-hexylthiophene), poly(p-phenylene vinylene), as well as polyacetylene and its derivatives. There are two major overlapping classes of organic semiconductors. These are organic charge-transfer complexes and various linear-backbone conductive polymers derived from polyacetylene. Linear backbone organic semiconductors include polyacetylene itself and its derivatives. Charge-transfer complexes often exhibit similar conduction mechanisms to inorganic semiconductors. Such mechanisms arise from the presence of hole and electron conduction layers separated by a band gap. While such classic mechanisms are important locally, as with inorganic amorphous

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semiconductors, tunneling, localized states, mobility gaps, and phonon-assisted hopping also significantly contribute to conduction, particularly in polyacetylenes. Typical current carriers in organic semiconductors are holes and electrons in p-bonds. Almost all organic solids are insulators. But when their constituent molecules have p-conjugate systems, electrons can move via p-electron cloud overlaps, especially by hopping, tunneling and related mechanisms. Polycyclic aromatic hydrocarbons and phthalocyanine salt crystals are examples of this type of organic semiconductor. Mainly due to low mobility, even unpaired electrons may be stable in charge-transfer complexes. Such unpaired electrons can function as current carriers. This type of semiconductor is also obtained by pairing an electron donor molecule with an electron acceptor molecule. Fulvalene is a hydrocarbon obtained by formally cross conjugating two rings through a common exocyclic double bond. The name is derived from the similarly structured fulvenes which lack one ring. In general, the parent fulvalenes are very unstable, for instance, triafulvalene has never been synthesized. On the other hands stable fulvalenes can be obtained by proper substitution or benzannulation. Pentafulvalene (PFV) is the member of fulvalenes family consisting of two 5-membered rings, each with two double bonds. Although, it belongs to D2h point group of symmetry but however, it is very unstable and can be observed at very low temperature [1]. Tetrathiafulvalene (TTF), an organosulfur compound, is the sulfur substitution of PFV. TTF is also known as an organic semiconductor and studies on this heterocyclic compound contribute the development of molecular electronics. Bulk TTF itself has unremarkable electrical properties but however, distinct properties are associated with salts of its oxidized derivatives, such as salts derived from TTF+. The high electrical conductivity of TTF salts can be attributed to the several features, for instance, its planarity, which allow p–p stacking of its oxidized derivatives, its high symmetry, which promotes charge delocalization, thereby minimizing coulomb repulsion, and its ability to undergo oxidization at mid potential to give a stable cation radical. Wudl et al. first demonstrated that [TTF+]Cl was a semiconductor [2]. Subsequently, Ferraris et al. showed that the charge transfer salt [TTF]TCNQ is a narrow band gap semiconductor [3]. X-ray diffraction studies of [TTF]TCNQ revealed stacks of partially oxidized TTF molecules adjacent to anionic stacks of TCNQ molecules. This segregated stack motif was unexpected and responsible for the distinctive electrical properties, i.e., high and anisotropic electrical conductivity. Recently, Jaiswal et al. [4] have presented optimized geometry and vibrational frequencies of 1,3-dithiole-2-thione (DTT) and related compounds which are important precursors in the synthesis of TTF and its derivatives (organic p-donors). The IR and Raman spectra of TTF and TTF-d4 were reported earlier in which an assignment of the fundamental vibrational modes were presented only for planar modes [5]. However, vibrational spectroscopic studies of TTF and its several derivatives have been reported so far [6–13]. Our articles surveys reveal that the normal coordinates analysis (NCA) of TTF molecule has not been carried so far which is an important tool for mode assignment. In all the previous works vibrational frequencies of TTF were assigned to the corresponding normal modes using band positions, intensities and animations available in Gaussian program which may not be reliable hence, we are interested to present DFT and NCA calculations for TTF. Since TTF is a fulvalene derivative, therefore, we have included PFV in our study. In addition, TTF salts show more conducting nature rather TTF, therefore, we have also included TTF+ in our study. Therefore, our aim is to investigate optimum geometry and vibrational frequencies of PFV, TTF and TTF+ molecules. Moreover, we have also aimed to calculate vibrational canonical partition func-

tion and hence, some important thermodynamical parameters using statistical thermodynamics. Computational details The quantum chemical calculation has been performed using the B3LYP level of theory supplemented with the standard 631++G(d,p) basis set, using the Gaussian 03 program [14] to calculate optimized bond lengths, bond angles and vibrational frequencies with IR intensities and Raman scattering activities. The optimized geometries corresponding to the minimum on the potential energy surface have been obtained by solving self consistent field (SCF) equation iteratively. Harmonic vibrational frequencies have been calculated using analytic second order derivatives to confirm the convergence to minima on the potential surface and to evaluate the zero-point vibrational energies without imposing any molecular symmetry constraints. It is a well known fact that ab initio calculations tend to overestimate the vibrational frequencies with respect to the experimental ones. This is due to several reasons, for instance, the use of finite basis set, the incomplete implementation of the electronic correlation and the neglect of anharmonicity effects in the theoretical treatment. However, the calculated ab initio force field can be improved by using the scaled quantum mechanical force field (SQMFF) methodology. For subsequent normal coordinate analysis (NCA), the force field obtained in Cartesian coordinates and dipole derivatives with respect to atomic displacements were extracted from the archive section of the Gaussian 03 output and transformed to a suitably defined set of internal coordinates (the ‘‘natural coordinates’’) which are collected in Table 1 by means of a modified version of the MOLVIB program [15,16]. In present study, the scale factors are calculated using MOLVIB program and collected in Table 1. The vibrational canonical partition function is determined by multiplying the contribution from each of the normal modes. Assuming harmonic modes and choosing the zero of energy as the ground vibrational level for each mode, i.e., neglecting the zero point energy for each mode, the vibrational canonical partition function is defined as [17,18]:

Z vib ¼

Y i

1 i =kTÞ 1  expðhcm

ð1Þ

where i is the index representing the normal modes. The vibrational contribution to the specific heat, entropy, free energy and enthalpy are given by

C v;vib ¼ R

X ðhcm i =kTÞ2 expðhcm i =kTÞ i =kTÞ2 ½1  expðhcm

i

 X i =kT hcm i =kTÞg  logf1  expðhcm Svib ¼ R i =kTÞ  1g fexpðhcm i F v ;vib ¼ RT

X

i =kTÞg log f1  expðhcm

ð2Þ

ð3Þ

ð4Þ

i

hvib ¼ RT

X i

i =kT hcm i =kTÞ  1 expðhcm

ð5Þ

Results and discussions Molecular structure The optimized bond lengths and bond angles of the title molecules at the B3LYP/6–31++G(d,p) level along with the experimental values for TTF [19] are collected in Table 2. The optimized

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V. Mukherjee, N.P. Singh / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 117 (2014) 315–322 Table 1 Local symmetry coordinates and scale factors. S. no.

Parameters

Symmetry coordinatesa

Scale factorsb

Stretching 1 2–3

rCC1(exo-cyclic) rCC2 (ring)

R1 p1ffiffi ðR2 þ R3 Þ; p1ffiffi ðR2  R3 Þ 2 2

0.87473 0.87473

4–11

rCS

12–15

rCH

1 1 2 ðR4 þ R5 þ R6 þ R7 Þ; 2 ðR4 þ R5  R6  R7 Þ; 1 1 ðR þ R  R  R Þ; 4 6 5 7 2 ðR4 þ R7  R6  R5 Þ; 2 1 1 2 ðR8 þ R9 þ R10 þ R11 Þ; 2 ðR8 þ R9  R10  R11 Þ; 1 1 ðR þ R  R  R Þ; 8 10 9 11 2 ðR8 þ R11  R10  R9 Þ 2 1 1 1 2 ðR12 þ R13 þ R14 þ R15 Þ; 2 ðR12 þ R13  R14  R15 Þ; 2 ðR12

Bending 16–19

bCCS, bCSC, bSCS

20 21 22–25

bCC1 bCC2 bCCH

Wagging 26–29 30 31 Twisting 32–33 34–35 36 a b

0.99672 þ R14  R13  R15 Þ; 12 ðR12 þ R15  R13  R14 Þ

0.89976

þ R23  R24  R25 Þ R26 R27 1 1 1 1 2 ðR28 þ R29 þ R23 þ R31 Þ; 2 ðR28 þ R29  R30  R31 Þ; 2 ðR28 þ R29  R30  R31 Þ; 2 ðR28 þ R29  R30  R31 Þ

1.02281

xCH xCC1 xCC2

1 1 1 1 2 ðR32 þ R33 þ R34 þ R35 Þ; 2 ðR32 þ R33  R34  R35 Þ; 2 ðR32 þ R33  R34  R35 Þ; 2 ðR32 þ R33  R34  R35 Þ R36 R37

0.94093

sCC sCS sCC1 (exo-cyclic)

p1ffiffi ðR38 þ R39 Þ; p1ffiffi ðR38  R39 Þ 2 2 1 1 2 ðR40 þ R41  R42  R43 Þ; 2 ðR44

1.00473

p1ffiffi ðR16 þ R17 Þ; p1ffiffi ðR16  R17 Þ; 2 2 1 1 2 ðR18 þ R19  R20  R21 Þ; 2 ðR22

1.12674 1.12674 0.94093

1.12674 1.12674

1.00473

þ R45  R46  R47 Þ

R48

1.00473

symmetry coordinates are written in terms of internal coordinates and their definitions are given in Supplementary table S1. incorporated only seven different scale factor values.

molecular structures of PFV, TTF and TTF+ with atomic labeling are shown in Fig. 1. The theoretical bond lengths of TTF are found slightly higher than the corresponding experimental values except for C1@C6 [19]. The optimized bond length of C1@C6 is in good agreement with the experimental one. There is also a good agreement between theoretical and experimental values of most of the bond angles for TTF. PFV forms planar structure with D2h point group of symmetry while substitution(s) of four S atoms perturb the planarity of TTF in such a way that symmetry of TTF drops to C2v point group. The torsional angles C4AC2AS14AC1 and S14AC1AS13AC4 in TTF are nearly 6° and 10° respectively. In addition, optimization of TTF+ radical shows that TTF+ forms a planar structure similar to PFV, i.e., having D2h point group of symmetry, therefore, it is concluded that torsional perturbation produced by four S atoms

is balanced by a positive charge (+e) transfer by p-bond of exocyclic C@C. This C@C bond length is 1.366Å, 1.352 Å and 1.399 Å for PFV, TTF and TTF+ respectively, i.e., the substitutions of S atoms in TTF bring closer the two rings slightly as compare to PFV while in TTF+, this bond length shows single bond character which is the consequence of charge transfer. Each dithiolylidene ring in TTF has 7p electrons: 2 for each sulfur atom, 1 for each sp2 carbon atom. Thus, ionization converts each ring to an aromatic 6p-electron configuration, consequently leaving the central double bond essentially a single bond, as all p-electrons occupy ring orbitals. The cyclic C@C bond lengths is changed significantly in TTF and shortened by 0.14 Å as compared to PFV while this bond length is nearly same for TTF and TTF+. The CAS bond lengths show a significant change in TTF+ as compared to TTF and interestingly, all the eight CAS bond lengths are

Table 2 Optimized bond lengths (Å) and bond angles (°). S. no.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 a

Ref. [19].

Parameters

C1AC2/C1AS14 C1AC6/C1AS13 C1AC10/C1AC6 C2AC4/C2AS14 C4AC8/C2AC4 C6AC8/C4AS13 C2AH3 C4AH5/C2AH3 C6AH7 C8AH9/C4AH5 C2AC1AC6/S14AC1AS13 C1AC2AC4/C1AS14AC2 C2AC4AC8/S14AC2AC4 C4AC8AC6/C2AC4AS13 C8AC6AC1/C4AS13AC1 C2AC1AC10/S14AC1AC6 C4AC2AS14AC1 S14AC1AS13AC4 Potential energy (a.u.)

PFV

1.473 1.473 1.366 1.357 1.477 1.357 1.081 1.084 1.081 1.084 106.410 107.840 108.950 108.950 107.840 126.800 – – 385.830

TTF+

TTF a

Theo.

Exp.

1.787 1.787 1.352 1.763 1.339 1.763 – 1.083 – 1.083 113.740 94.640 117.960 117.960 94.640 123.130 6.120 9.920 1823.760

1.748 1.748 1.358 1.729 1.314 1.729 – – – – 114.2 94.50 118.0 – 94.50 – – –

1.748 1.744 1.399 1.741 1.348 1.741 – 1.084 – 1.084 114.540 95.520 117.210 117.210 95.520 122.730 0.000 0.000 1823.520

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Fig. 1. Optimized molecular structures: (a) PFV, (b) TTF (transverse view), (c) TTF (longitudinal view) and (d) TTF+ (longitudinal view).

nearly same in TTF+ which is not in TTF. In TTF, the theoretical bond length of those CAS bonds which are near to conjugation point is 1.787 Å while it is 1.763 Å for those CAS bonds which are relatively far from conjugation point whereas all the CAS bonds are nearly 1.74 Å in TTF+. The CAS bonds lengths in TTF are also found slightly larger than that in DTT [4]. The electrostatic potential energies of all three molecules are also calculated at same level of theory and these are listed at the last row of Table 2. The inspection of potential energy directly reveals that TTF is much more stable than PFV. Since the potential energy is calculated for isolated molecule, therefore, it is evident that PFV substance must have higher energy when lattice formation will take place, i.e., increase in entropy (disorder) and hence, result is less stability. However, TTF+ is slightly excited due to charge transfer and its excess energy is 150 kcal/mol than TTF. Vibrational dynamics The harmonic vibrational frequencies calculated for the PFV, TTF and TTF+ molecules at the B3LYP level using the triple split valence basis set along with diffuse and polarization functions, 631++G(d,p) are collected in Tables 3–5 respectively. The observed IR and Raman frequencies [6] for various modes of vibrations of TTF are also presented in same table for comparison reason. Comparison of the calculated frequencies with experimental values reveals the overestimation of the calculated vibrational modes due to neglect of anharmonicity in real system. However, inclusion of electron correlation in density functional theory to a certain extent makes the frequency values smaller. Reduction in the computed harmonic vibrations, though basis set sensitive are only marginal as observed in the DFT values using 6-31++G(d,p). Any way notwithstanding the level of calculations, it is customary to scale down the calculated harmonic frequencies in order to improve the agreement with the experiment and therefore, the calculated frequencies are scaled using NCA method implemented in MOLVIB 7.0 program [15,16]. The potential energy distributions (PEDs) are also calculated for conspicuous normal mode assignment. A brief discussion regarding the vibrational absorption and scattering profiles and normal modes analysis of the considered molecules are as followsVibrational absorption profile The calculated IR (absorption) spectra of PFV, TTF and TTF+ are depicted in Fig. 2. Absorption profile of PFV is much better than other two. TTF and TTF+ have nearly same profiles below 1800 cm1 while in higher wavenumber region, all the bands in TTF are very much weak and only one band (3254 cm1) is strong

enough in IR spectrum of TTF+. The bands at 1533 cm1, 648 cm1 and 701 cm1 in PFV, TTF and TTF+ respectively, are the strongest in the IR spectra. The PEDs reveal that the strongest band in PFV is due to the ring stretching mode while in both the TTF and TTF+, it is due to the CH wagging mode. However, the band at 780 cm1 due to the CH wagging in PFV is also showing strong IR intensity. Vibrational scattering profile The calculated Raman spectra of PFV, TTF and TTF+ are depicted in Fig. 3. The Gaussian (DFT) calculation provides Raman activity instead of Raman intensity which can be further converted into corresponding Raman intensity using empirical formula [20]. PFV has only one strong band at 1685 cm1 and others are relatively weak in its Raman spectrum. The PEDs of the mode of this frequency shows maximum contribution of the C@C (exocyclic) stretching vibration. Raman spectra of TTF and TTF+ show few strong bands along with the most strong band at 1583 cm1 and 1563 cm1 respectively. The scattering of these frequencies are contributed by C@C (exocyclic) stretching vibration in TTF and by C@C (ring) stretching vibration in TTF+. An interesting result is found for TTF and TTF+ that their IR spectra are somewhat same with a slight frequency shift but their Raman spectra show great discrepancy. In TTF, lower frequencies are relatively strong than the higher frequencies up to 1500 cm1 while in TTF+, frequencies below 150 cm1 are completely disappeared and only one band at 265 cm1 is strong enough in the far-IR region. Normal modes Our present calculations reveal that PFV, TTF and TTF+ belong to D2h, C2v and D2h point groups of symmetry respectively and hence, all the normal modes are distributed in corresponding species and the distributions are 9Ag + 3B1g + 4B2g + 8B3g + 4Au + 8B1u + 8B2u + 4B3u, 10A1 + 9A2 + 8B1 + 9B2 and 7Ag + 2B1g + 3B2g + 6B3g + 3Au + 6B1u + 6B2u + 3B3u respectively. These distributions are also shown in corresponding tables. There are three frequencies for TTF and two frequencies for TTF+ below 100 cm1. The normal mode having frequency 38 cm1 and 84 cm1 for TTF and TTF+ respectively, is the CAS twisting which looks like very similar to butterfly mode. The animation available in Gaussian 03 program [14] shows that when TTF vibrates in this mode, it gains its planarity at either extrema which is possible only when TTF is ionized (TTF+), therefore it may be concluded that in this mode TTF periodically losses and gains charge of one unit, i.e., a periodic motion of a charge of one unit is set up in lattice of TTF. Therefore, this mode has a good significance and may be responsible for conductivity in TTF. This mode mostly shows a blue

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319

Table 3 Normal mode assignment for PFV (D2h point group).

ma

IRb

Ramanc

Species

d

3264 3261 3258 3255 3233 3232 3222 3221 1685 1614 1610 1536 1533 1401 1387 1329 1328 1244 1146 1145 1116 1112 1105 1030 1007 954 943 938 932 925 903 835 806 803 791 776 730 729 659 608 572 522 444 399 249 159 121 102

0.0 10.66 13.33 0.0 0.0 16.73 10.22 0.0 0.0 0.0 0.18 0.0 169.65 78.25 0.0 2.56 0.0 0.0 0.04 0.08 0.0 35.75 0.0 70.58 0.0 1.14 0.0 0.0 0.13 0.0 0.0 38.97 0.0 1.73 0.0 171.78 0.0 0.0 0.0 34.65 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.54

363.64 0.0 0.0 25.73 391.85 0.0 0.0 211.39 1438.42 26.96 0.0 296.63 0.0 0.0 46.70 0.0 26.45 21.13 0.0 0.0 163.0 0.0 4.72 0.0 59.34 0.0 2.35 0.0 0.0 10.62 57.22 0.0 2.70 0.0 0.50 0.0 0.31 0.0 9.33 0.0 0.0 0.03 1.80 23.28 1.21 0.0 0.0 0.0

Ag B2u B1u B3g Ag B1u B2u B3g Ag B3g B2u Ag B1u B1u Ag B2u B3g B3g B2u B1u Ag B2u B3g B1u Ag B1u B1g Au B3u B2g Ag B1u B2g B2u B3g B3u B1g Au B2g B3u Au B1g B3g Ag B2g B2u Au B3u

99rCH 99rCH 99rCH 99rCH 99rCH 99rCH 99rCH 99rCH 70rCC1 + 16rCC2 + 6bCCH 65rCC2 + 27bCCH 67rCC2 + 27bCCH 81rCC2 + 13bCCH 74rCC2 + 19bCCH 68bCCH + 28rCC2 72bCCH + 19rCC2 81bCCH + 15rCC2 55bCCH + 32rCC2 42bCCH + 30rCC2 + 11bCC1 + 11bCC2 52bCCH + 41rCC2 71bCCH + 26rCC2 89bCCH + 8rCC2 49bCCH + 38rCC2 + 5bCCC1 + 5bCCC2 84bCCH + 14rCC2 68rCC2 + 29bCCH 80rCC2 + 15bCCH 58rCC2 + 32bCCH 66xCH + 17sCC2 + 16sCC1 66xCH + 17sCC2 + 17sCC1 586xCH + 25sCC2 + 18sCC1 59xCH + 24sCC2 + 17sCC1 42rCC2 + 26bCCH + 15bCCC2 + 15bCCC1 30bCCC1 + 30bCCC2 + 25bCCH + 6rCC2 49xCH + 25xCC1 + 11sCC2 + 10xCC1 + 6sCC1 26bCCC1 + 26bCCC2 + 25rCC2 + 23bCCH 26bCCC1 + 26bCCC2 + 24bCCH + 19rCC2 86xCH 65xCH + 20sCC2 + 15sCC1 64xCH + 22sCC2 + 13sCC1 51xCH + 25xCC1 + 10sCC2 + 10xCC2 34sCC2 + 30xCH + 18xCC1 + 11sCC1 + 7xCC2 59sCC2 + 20sCC1 + 15xCH + 5sCC 54sCC2 + 26xCH + 20sCC1 35bCC1 + 35bCC2 + 22rCC2 30rCC1 + 27rCC2 + 15bCCC1 + 15bCCC2 51sCC2 + 18sCC1 + 17xCC1 + 7xCH + 7xCC2 47bCC1 + 47bCC2 79sCC + 11xCH + 7sCC2 41sCC2 + 27xCC1 + 15sC11 + 11xCC2

PEDs

The abbreviations are: r–stretching, b–bending, x–wagging, s–twisting. a Gaussian calculated frequencies. b IR intensity in KM/mol. c Raman scattering activity in Å4/amu. d Main% contributions to the P.E.D. in sym. Coordinates (contributions below 5% are not considered).

shift in TTF derivatives [6]. Similarly, the normal modes having frequencies 82 cm1 and 48 cm1 for TTF and TTF+ respectively involve C@C bond (exocyclic) twisting, i.e., the relative twisting of two thiole rings. PFV absorbs at 121 cm1 due to this mode, i.e. substitutions of S atoms in TTF decreases the frequency of C@C twisting mode and further decrement is attributed by charge transfer in TTF+. TTF also shows degeneracy at 82 cm1 however, this normal mode is contributed by CAS twisting which looks like relative wagging of two thiole rings. The important and common mode in all three molecules is C@C (exocyclic) stretching mode. The frequency for this normal mode is 1685 cm1, 1583 cm1 and 1444 cm1 for PFV, TTF and TTF+ respectively. For PFV and TTF+, this normal mode shows pure C@C (exocyclic) stretching but for TTF, it is equally coupled by C@C (exocyclic) and C@C (ring) stretching vibrations. The red shift found in this normal mode from PFV to TTF+ is due to electronmolecular vibration (EMV) coupling which increases with the cou-

pling constant [21,22]. More recently, a normal mode assignment has also been presented for TTF without PEDs and the bands at 1616 cm1, 1592 cm1 and 1573 cm1 were assigned for three CAC stretching modes in which former was assigned for exocyclic C@C [6]. However, in present calculation the corresponding frequencies are 1626 cm1, 1602 cm1 and 1583 cm1 and PEDs reveal that the normal modes having frequencies 1626 cm1 and 1583 cm1 are strongly coupled by both the ring and exocyclic C@C stretching vibrations and the normal mode of the latter frequency shows comparatively maximum contribution of exocyclic C@C stretching vibration. The bands at 1666 cm1, 1651 cm1, 1588 cm1, 1581 cm1 and 1537 cm1 were assigned to have C@C stretching vibrations for C60-TTF dyad, bismethoxycarbonylTTF and bisbromomethyl-TTF [23]. All the bands except at 1537 cm1 show blue shift upon substitutions in TTF. There are eight CAS bonds in TTF and TTF+ but appreciable contributions of the CAS stretching vibrations can be found in more

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Table 4 Normal mode assignment for TTF (C2v point group).

ma

IRb

Ramanc

Scaled

3248 3248 3229 3229 1626 1602 1583 1288 1286 1124 1124 976 864 864 836 806 799 774 735 732 648 647 624 615 506 474 433 419 415 308 267 237 111 82 82 38

0.02 0.11 5.35 0.0 0.39 38.01 0.50 0.0 0.01 0.32 2.56 0.0 0.30 0.0 2.67 0.0 53.37 24.76 0.0 10.27 133.54 1.92 1.58 0.0 2.27 0.02 14.32 0.0 0.0 0.0 0.66 0.20 0.59 2.86 0.0 3.83

561.09 69.48 4.25 233.33 40.27 1.60 396.22 7.16 0.01 24.69 0.11 4.14 1.18 0.06 0.21 22.03 0.14 0.19 19.62 0.20 3.57 2.13 0.06 0.11 0.08 14.42 0.02 3.86 0.26 8.88 4.51 10.98 0.05 0.19 0.03 0.57

3081 3081 3063 3063 1541 1521 1501 1254 1250 1088 1088 1003 854 854 835 803 796 782 734 732 629 629 625 615 534 474 437 413 409 317 276 244 117 84 82 38

Exp.e 3082 3064

1528 1496 1254 1076

796 780 734 646 636

439

Species

f

A1 B2 B1 A2 A1 B2 A1 A2 B1 A1 B2 A2 B1 A2 B1 A2 B1 B2 A1 B2 A1 B2 B1 A2 B2 A1 B2 B1 A2 A2 A1 A1 B1 B2 A2 A1

99rCH 99rCH 100rCH 100rCH 40rCC1 + 39rCC2 + 7bCCH + 7rCS 78rCC2 + 13bCCH + 6rCS 55rCC1 + 29rCC2 + 8rCS 87bCCH + 10rCS 89bCCH + 9rCS 94bCCH + 6rCC2 93bCCH + 6rCC2 48rCS + 22bCC2 + 22bCC1 54sCC + 44xCH 54sCC + 44xCH 78rCS + 6bSCC + 5bCSC 50rCS + 33bSCC + 15bCCH 58rCS + 26bSCC + 14bCCH 64rCS + 19bSCS + 8bCSC 92rCS 92rCS 100xCH 97xCH 57rCS + 18bSCC + 18bCSC + 6bCCH 57rCS + 19bSCC + 16bCSC + 6bCCH 45xCC1 + 45xCC2 68rCS + 17bCSC + 6bSCC 32rCS + 29bCSC + 13bSCS + 7bSCC 40sCS + 35xCH + 25sCC 39sCS + 36xCH + 25sCC 51rCS + 21bCC1 + 21bCC2 31xCC1 + 31xCC2 + 15sCS + 10rCS + 6bCSC 19xCC1 + 19xCC1 + 18bSCS + 11sCS + 8rCC1 + 8rCS 49bCC1 + 49bCC1 85sCS + 5xCH 95sCC1 80sCS+7xCH

PEDs

The abbreviations are: r–stretching, b–bending, x–wagging, s–twisting. a Gaussian calculated frequencies. b IR intensity in KM/mol. c Raman scattering activity in Å4/amu. d Scaled frequencies using MOLVIB-7.0. e Taken from [6]. f Main% contributions to the P.E.D. in sym. Coordinates (contributions below 5% are not considered).

than eight normal modes having frequencies below 1000 cm1. However, the bands at 735 cm1 and 732 cm1 for TTF and at 836 cm1, 752 cm1 and 741 cm1 for TTF+ are contributed by pure CAS stretching vibrations. Rani and Yadav have also presented normal modes assignment for TTF but they assigned all the stretching modes of ring as ring stretching modes instead of the CAS and C@C stretching modes [6]. Some TTF derivatives show slight blue shift in one CAS stretching mode, however, most of the CAS normal modes have frequencies in agreement with the present assignment [21]. For C60-TTF dyad, one CAS stretching mode was assigned at 1188 cm1 and other below 700 cm1 [23]. Therefore, most of the CAS stretching modes shift towards lower wavenumber region and one mode shows blue shift upon substitution(s) in TTF. Thermodynamics The vibrational canonical partition function and some important thermodynamical parameters are calculated (at T = 300 K) for PFV, TTF and TTF+ using Eqs. (1)–(5)[17,18] and these are collected in Table 6. The thermodynamics of several TTF salts have been studied earlier [24,25]. The variation of vibrational partition function (Z) and specific heat (Cv) with temperature taking same vibrational frequencies at each time are also studied and the variations are shown in Fig. 4 and Figs. 5 and 6 (supplementary)

respectively. Since partition function plays the role of a normalizing constant and it encodes how the probabilities are portioned among the different microstates based on their individual energies [26], it can be concluded from Table 6 that there are much larger possibilities of distributions of TTF molecules in different vibrational energy levels than PFV and TTF+ at a given temperature. Since Z counts also the occupied energy states, at 300 K (room temperature) TTF have relatively much more occupied states than PFV and TTF+ and lesser vibrational states are accessible for PFV. The variation of Z with respect to temperature (Fig. 4) for all three molecules shows that the variation is linear up to 250 K, 75 K and 100 K and then there is an exponential growth for PFV, TTF and TTF+ respectively. From Eq. (1), it is clear that Z = 1 at T = 0 K, which is known as condensation. Clearly, Z = 1 represents that all the molecules are condensed to the ground state which occurs at absolute zero. However, some real systems show condensation (Z = 1) above absolute zero which is known as Bose–Einstein condensation. Normally, B–E condensation occurs at extreme low temperature which is also true for TTF and TTF+ (Z = 1 at 3 K and 4 K respectively) but interestingly, for PFV, condensation starts at 108 K as above this temperature Z P 2. As temperature decreases, Z decreases and it is 1.101, 1.043, 1.011, 1.001 and 1 at 50 K, 40 K, 30 K, 20 K and 10 K respectively. Therefore, all the molecules are

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321

Table 5 Normal mode assignment for TTF+ (D2h point group).

ma

IRb

Ramanc

Species

f

3254 3254 3238 3238 1563 1544 1444 1298 1294 1131 1131 1034 886 882 879 834 833 821 752 741 701 699 639 630 512 507 471 431 418 324 302 265 145 119 84 48

0.0 65.44 35.41 0.0 0.0 106.67 0.0 0.0 6.34 0.0 0.09 0.0 6.56 0.0 0.0 0.0 24.42 38.72 0.0 7.42 136.95 0.0 0.86 0.0 0.0 0.0 15.01 0.0 0.0 2.18 0.0 0.0 0.0 0.29 4.48 0.0

667.07 0.0 0.0 205.86 521.90 0.0 280.42 11.53 0.0 17.81 0.0 0.04 0.0 0.13 0.0 12.35 0.0 0.0 8.64 0.0 0.0 0.46 0.0 12.20 0.25 91.99 0.0 2.38 0.0 0.0 3.78 29.25 0.45 0.0 0.0 0.0

Ag B1u B2u B3g Ag B1u Ag Ag B1u B3g B2u B3g B2u B1g Au B3g B2u B1u Ag B1u B3u B2g B2u B3g B2g Ag B1u B1g Au B3u B3g Ag B2g B2u B3u Au

99rCH 99rCH 100rCH 100rCH 77rCC2 + 14bCCH + 5rCS 77rCC2 + 15bCCH + 5rCS 81rCC1 + 10rCS 87bCCH + 10rCS 90bCCH + 8rCS 92bCCH + 7rCC2 93 bCCH + 7rCC2 54rCS + 19bCC1 + 19bCC2 91rCS 51sCC + 46xCH 51sCC + 46xCH 55rCS + 30bSCC + 14bCCH 55rCS + 30bSCC + 14bCCH 66rCS + 18bSCS + 8bCSC 93rCS 93rCS 100xCH 99xCH 43rCS + 26bSCC + 22bCSC + 8bCCH 45rCS + 27bSCC + 19bCSC + 8bCCH 42xCC1 + 42xCC2 + 15sCS 70rCS + 16bSCS + 6bSCC 34bCSC + 33rCS + 15bSCS + 7bSCC 60sCS + 22xCH + 19sCC 60sCS + 21xCH + 19sCC 53sCS + 23xCC1 + 23xCC2 38rCS + 29bCC1 + 29bCC2 26bSCS + 27rCS + 20rCC1 + 20bCSC + 5bCC1 + 5bCC2 92sCS + 7xCH 49bCC1 + 49bCC2 56sCS + 19xCC1 + 19xCC2 + 6xCH 80sCC1 + 12sCS

PEDs

The abbreviations are: r–stretching, b–bending, x–wagging, s–twisting. Scaled frequencies using MOLVIB-7.0 e taken from a Gaussian calculated frequencies. b IR intensity in KM/mol. c Raman intensity in Å4/amu. f Main% contributions to the PED. in sym. Coordinates (contributions below 5% are not considered). d

Fig. 2. Theoretical IR spectra.

Fig. 3. Theoretical Raman spectra.

322

V. Mukherjee, N.P. Singh / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 117 (2014) 315–322

Table 6 Statistical thermodynamics (at T = 300 K). S. no.

Thermodynamics

PFV

TTF

TTF+

1 2 3 4 5 6 7

Partition function (Z) Entropy (S) (Cal/Mol-Kelvin) Specific heat (Cv) (Cal/Mol-Kelvin) Enthalpy (h) (kcal/Mol) Helmholtz free energy (Fv) (kcal/mol) Gibbs potential (G) Thermal energy (kcal/Mol)

35.692 17.416 25.077 3.114 2.134 1.720 93.403

999.757 28.709 30.277 4.514 4.106 3.512 55.779

384.236 25.838 29.233 4.223 3.535 2.941 56.151

Thermodynamics of selected molecules show very interesting result, especially, partition function and specific heat at low temperature of PFV show significant result. At low temperature very few vibrational states are accessible for PFV while TTF have much more accessible states at any temperature than TTF+ and PFV. Condensation of PFV in ground states is commenced at 108 K and complete condensation occurs at 10 K and Cv approaches to zero at 15 K. Acknowledgement The UGC (India) is gratefully acknowledged for the financial assistance through a research project. Prof. T. Sundius is also gratefully acknowledged to provide us his own program MOLVIB. Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.saa.2013.07.105. References

Fig. 4. Vibrational canonical partition function (Zvib) with temperature.

completely condensed at 10 K. This result may be significant as PFV exists at low temperature [1]. Fig. 5 (supplementary) shows the variation of specific heat (Cv) with temperature up to 50 K and Fig. 6 (supplementary) shows same in the temperature range 50–500 K of all three molecules. Variation of Cv with temperature is almost linear for all three molecules and at any temperature the inequality is given by, (Cv)TTF > (Cv)TTF+ > (Cv)PFV. Below 50 K, Cv profile is appreciably different for TTF and PFV and it is zero at 0 K and 15 K for TTF and PFV respectively. For TTF+, variation is quite similar to TTF with slightly lesser value at each point. Above 50 K, Cv profile of PFV approaches towards that of TTF and intersects nearly at 450 K. Then after the variation reverses and inequality is given by, (Cv)PFV > (Cv)TTF > (Cv)TTF+. The variation of Cv with temperature for PFV is also interesting as Cv approaches zero at 15 K which is an abnormal phenomena. Conclusions A theoretical study of molecular structure, vibrational frequencies and thermodynamics of PFV, TTF and its cation based upon DFT calculation are reported. PFV has higher symmetry (D2h) but substitutions of S atoms lowered the symmetry (C2v) of TTF but however, removal of one p electron from exocyclic C@C bond brings the symmetry of TTF+(D2h) identical to that of PFV. Despite of having large numbers of normal modes and higher symmetry, the absorption profile of both the TTF and TTF+ are very poor compared to that of PFV. Most of the normal modes are IR inactive for TTF and TTF+. Below 400 cm1, all the modes are Raman inactive for PFV while only on band at 265 cm1 is strongly appeared in Raman spectrum of TTF+ and few bands are appeared in Raman spectrum of TTF.

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