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Inelastic neutron scattering and DFT study of potassium hydrogen phthalate
Journal of Molecular Structure 967 (2010) 89–93
Contents lists available at ScienceDirect
Journal of Molecular Structure journal homepage: www.elsevier.com/locate/molstruc
Inelastic neutron scattering and DFT study of potassium hydrogen phthalate Mariana Derzsi a,b,*, Daniele Colognesi c a
Institute of Inorganic Chemistry, Slovak Academy of Sciences, Dúbravská cesta 9, SK-845 36 Bratislava, Slovak Republic _ Interdisciplinary Centre for Mathematical and Computational Modeling, The University of Warsaw, Zwirki i Wigury 93, 02-089 Warsaw, Poland c Istituto dei Sistemi Complessi, Consiglio Nazionale delle Ricerche, via Madonna del Piano 10, 50019 Sesto Fiorentino (FI), Italy b
a r t i c l e
i n f o
Article history: Received 28 October 2009 Received in revised form 19 December 2009 Accepted 21 December 2009 Available online 11 January 2010 Keywords: Potassium hydrogen phthalate Inelastic neutron scattering Density functional theory Hydrogen bond
a b s t r a c t Inelastic neutron scattering and solid state quantum chemistry calculations are applied to investigate the lattice vibrations in crystalline potassium hydrogen phthalate containing very short intermolecular OAH O hydrogen bond (2.529 Å). The inelastic neutron scattering spectrum is interpreted in the energy range 30–3500 cm1 using the density function theory approach within the harmonic approximation. The one-dimensional potential of the proton moving along the short OAH O bond is mapped and a considerable contribution of anharmonicity (about 24%) to the antisymmetric OHO stretching vibration is calculated. Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction Potassium hydrogen phthalate ðC8 H5 O4 K; K-H-pht, hereafter) has a wide range of applications in many research fields. It is commonly used as a primary standard for acid–base titrations and for calibrating pH-meters [1], for monochromators and analyzers in the field of X-ray spectroscopy and for electro-optic modulators [2]. Additionally, it is employed as substrate for the deposition of thin films of organic nonlinear optical materials [3]. K-H-pht crystallizes in the orthorhombic structure ðPca21 , a ¼ 9:546ð2Þ Å, b ¼ 13:201ð3Þ Å, c ¼ 6:405ð2Þ ÅÞ with four formula units in the unit cell. It exhibits one short, strong intermolecular OAH O hydrogen bond (2.528(8) Å) [4] which links neighboring hydrogen phthalate molecules into zigzag chains (Fig. 1). Up to date, several studies have been done concerning the vibrational properties of the title compound [3,5–11]. Unfortunately, one finds huge discrepancies between vibrational spectra reported so far for various samples of K-H-pht. In this study we use theoretical methods to rationalize the vibrational features of K-H-pht with particular emphasis on the oscillations of the hydrogen atoms available from the inelastic neutron scattering (INS) technique, and we compare our findings to the previously published spectroscopic data. The INS spectra of K-H-pht and of its deuterated version K-D-pht have been reported by Colognesi
et al. [12], while demonstrating the high resolution of the TOSCA-I spectrometer. Here we provide the full assignment of the INS spectrum in the range 30–3500 cm1, based on the normal coordinate analysis in the solid state using the density functional theory (DFT) method. Such a combined INS/DFT approach has been successfully applied in the past to several crystals of hydrogen bonded systems [13–17] but not to K-H-pht [18]. Additionally, one-dimensional potential of the proton moving along the short hydrogen bond is mapped in the current work, suggesting a large anharmonicity of the antisymmetric OHO stretching vibration. 2. Neutron scattering experiment Neutron scattering measurements on K-H-pht and K-D-pht were both carried out using the TOSCA-I [19] inelastic spectrometer of the ISIS pulsed neutron source (Rutherford Appleton Laboratory, Chilton, Didcot, UK). TOSCA-I was a crystal analyzer inversegeometry spectrometer, where the final neutron energy was selected by a set of pyrolitic graphite crystals placed in back-scattering (at about 136° with respect to the incident beam). The INS data of K-H-pht were collected at 20 K. Details of the measurements are given in Ref. [12]. 3. Calculation details
* Corresponding author. Address: Interdisciplinary Centre for Mathematical and _ Computational Modeling, The University of Warsaw, Zwirki i Wigury 93, 02-089 Warsaw, Poland. Tel.: +48 22 55 40 825. E-mail address: [email protected] (M. Derzsi). 0022-2860/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.molstruc.2009.12.044
Fixed-volume crystal DFT calculations were performed with VASP [20–23], using the experimental unit cell (Z ¼ 4) taken from the single-crystal neutron diffraction refinement at 30 K [4]. The
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M. Derzsi, D. Colognesi / Journal of Molecular Structure 967 (2010) 89–93
Fig. 1. Structure of K-H-pht projected on the ac-plane (left) and phthalate ions linked into a zig–zag chain by short OAH O hydrogen bonds (right). Large blue balls represent potassium atoms, small red balls oxygen and small gray balls carbon atoms. Hydrogen atoms are omitted for clarity. (For interpretation of color mentioned in this figure the reader is referred to the web version of the article.)
Perdew–Wang 91 (PW91) functional was employed, with the exchange and correlation effects handled within the Generalized Gradient Approximation (GGA) [24]. The interactions between ions and electrons were described by the Projector Augmented Wave (PAW) method [25,26] and the atomic pseudo-potentials [27]. For the electronic and ionic optimization the conjugate gradient algorithm was used. The energy cut-off for the plane wave basis set was 500 eV. The Brillouin-zone sampling was restricted to one k point. No symmetry restrictions were applied during the geometry optimization and the force constant calculation. The optimization stopped when all the forces on the individual atoms were smaller than 2 104 eV=Å. Vibrational normal modes were calculated from the Hessian within the harmonic approximation. The Hessian was constructed from single-point energy calculations on 6n structures generated from the optimized structure by displacing each of the n atoms in the cell along the Cartesian directions x; y; z by 0:02 Å. Each pair of single-point energy calculations was used to evaluate the force constants [28]. The INS spectrum was calculated from normal modes using the aCLIMAX 4.0.1 code [29], while the graphical package MOLEKEL [30] was used for visualizing molecular geometry and analyzing individual normal modes. The geometry of the optimized structure was analyzed using PLATON [31].
Table 2 Experimental [35] and calculated geometry of the O1AH1 O4i hydrogen bond (Å, °). Symmetry code: (i) 3/2 x, y, z 1/2.
Exp. Calc.
O1AH1
H1 O4i
O1 O4i
O1AH1 O4i
1.07(15) 1.063
1.456(16) 1.446
2.528(8) 2.509
174.6(13) 177.8
tion of the proton. In the structure of K-H-pht, H is present in four CH groups and in one OH group. The hydroxyl group can be easily deuterated leading to K-D-pht, and the INS spectrum of K-D-pht thus reveals CH vibrations only (Fig. 2). In the region below 1700 cm1, the spectrum of K-H-pht contains well localized peaks, characteristic of fundamental vibrations emerging on the top a broad band, which is mainly due to the first overtones (Fig. 2). A broad band centered at 3050 cm1 originating from CAH stretching vibrations is the only considerably intense feature above 1700 cm1. In the following, the internal OHO and phthalate vibrations, as well as the librational motions are discussed in Sections 4.1–4.3, respectively. We devote a special subsection, namely 4.4 to the comparison of our calculations to the previously published spectroscopic data,
4. Results and discussion Calculated bond distances, angles and torsional angles are in good agreement with the experimentally determined values (Table 1). Noticeably, our calculations correctly reproduce the asymmetry observed in the bond lengths of the carboxylic groups and the geometry of the short OAH O hydrogen bond (Table 2). The INS spectrum of K-H-pht can be considered as a pure hydrogen spectrum since the scattering cross-sections of carbon, oxygen and potassium are negligible in comparison with the large incoherent scattering cross-sec-
Table 1 Selected experimental [35] and theoretically calculated bond distances, bond angles and torsional angles (Å, °).
C7AO1 C7AO2 C8AO3 C8AO4 O3AC8AO4 O2AC7AO1 C3AC2AC8AO4 C6AC1AC7AO2
X-ray (100 K)
Neutron (30 K)
Calc.
1.3168(16) 1.2296(16) 1.2486(15) 1.2769(16) 124.61(11) 124.80(12) 103.51(13) 147.60(13)
1.309(9) 1.241(8) 1.237(8) 1.281(7) 124.6(6) 125.1(6) 104.6(6) 146.9(6)
1.321 1.243 1.257 1.286 123.6 124.5 103.3 147.2
Fig. 2. The INS spectra of K-H-pht (top black) and K-D-pht (middle blue) measured at 20 K shown together with the calculated INS spectrum and calculated contribution from the first overtones (bottom, red and gray, respectively) in the 30– 3500 cm1 range. The experimental spectra are vertically shifted for clarity. (For interpretation of color mentioned in this figure the reader is referred to the web version of the article.)
M. Derzsi, D. Colognesi / Journal of Molecular Structure 967 (2010) 89–93
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focusing on the antisymmetric OHO stretching vibration and contribution of anharmonicity to it. 4.1. OHO vibrations The highest frequency antisymmetric stretching OHO mode is predicted to appear in the INS spectrum as a well localized peak centered at 2196 cm1. However, no such peak is observed in the experimental INS spectrum (Fig. 2). The absence of this band in the INS spectrum is primarily due to low cross-section of the hydrogen bonded protons, since they have to compete against the overtones of the much stronger CH system. The OHO stretching is further suppressed by the impact of phonon wings. These wings spread the, already weak, fundamental OHO stretching mode into broad combination bands. Additionally, the impact of phonon wings on the INS spectrum is strongly affected by the magnitude of the neutron momentum transfer, being the highest at higher energies, just where the OHO stretch is expected. Vibrations containing some share of the proton motion along the OAH O bond are also predicted to appear in the frequency range 270–550 cm1 (Fig. 3). At these low frequencies, however, they do not form localized modes, but are rather weak components of the complex movements of the phthalate ions. Since the hydrogen bond is formed between the carboxyl and carbonyl groups, their in-plane (ip) and out-of-plane (op) deformations naturally induce a deformation of the hydrogen bond. While at low frequencies (<550 cm1 Þ, they cause mainly a stretching of the hydrogen bond, at higher frequencies up to 850 cm1 the bending of the hydrogen bond, d(OHO), is mostly observed. These motions are additionally coupled with ip and op deformations of the benzene ring. The only d(OHO) mode independent of the phthalate ion vibrations is calculated at 1196 cm1 (Fig. 3, top). In this mode, the hydrogen atom is moving perpendicular to the hydrogen bond and out of the carboxyl plane. Interestingly, the hydrogen exhibits here an extremely large displacement vector, while the motions of all the remaining atoms are negligible. For this reason the d(OHO)op mode can be easily identified at 1113 cm1 in the experimental spectrum of K-H-pht while it is obviously absent in the spectrum of K-D-pht (Fig. 3, top). Such OHO out-of-plane vibrations are reported to be very sensitive to molecular interactions [32]. This high sensitivity is probably the reason for the discrepancy between the experimentally and theoretically determined position of this mode, its frequency being overestimated by as much as 7% in the DFT calculations. The OHO vibrations, in which the proton vibrates in the carboxyl plane, d(OHO)-ip, with a large displacement vector, are predicted to appear in the frequency range 1250–1500 cm1 mixed with the d(CH)-ip vibrations. Indeed, we can identify two strong peaks (1264 and 1431 cm1) in the experimental spectrum of KH-pht (Fig. 3); the former band being broadened by, while the intensity of the latter one being raised by the contribution of the d(OHO)-ip vibration. 4.2. Phthalate CH vibrations Most of the intensity in the INS spectrum of K-H-pht is due to the CH hydrogen atoms moving in the plane, d(CH)-ip, (1000– 1500 cm1) or out-of-the plane of the benzene ring, d(CH)-ip, (700–1000 cm1), and due to the riding motion of the hydrogen atoms on the phthalate ion during its deformational movement (300–700 cm1) (Fig. 3, top and Table 3). Similarly to the case of the CH vibrations, the hydrogen riding on the benzene in-plane deformations shows up at frequencies higher than that of the hydrogen riding on the benzene out-of-plane deformations (647 and 686 cm1 vs. five intense peaks between 300 and 600 cm1 in the experimental K-H-pht spectrum). On the other hand, the in-plane riding modes are predicted to yield less intense peaks
Fig. 3. In each plot: INS spectrum of K-H-pht (top black curve) and K-D-pht (middle blue curve) measured at 20 K, together with the calculated partial INS spectra of the OH hydrogen atoms (bottom thick green curve) and of the CH ones (bottom thin red curve) in the range 300–1700 cm1 (top plot) and 30–300 cm1 (bottom plot). The experimental spectra are vertically shifted for clarity. (For interpretation of color mentioned in this figure the reader is referred to the web version of the article.)
than the out-of-plane riding ones. The most intense peak appearing in the experimental spectrum at 1145 cm1 is assigned to a pure d(CH)-ip vibration. Naturally, the highest frequency CH modes are the stretching vibrations appearing in the experimental K-Hpht spectrum as a broad band centered at 3050 cm1 (Fig. 2). Our DFT calculations overestimate this value by 3% only (3135 cm1). 4.3. Librations According to our calculations, in the INS spectrum of K-H-pht there is a clear borderline between the internal deformations of individual (benzene, ACOOH, ACO2) groups and their librations at 300 cm1. The peaks appearing in the experimental INS spectrum in the region 150–300 cm1 can be assigned mainly to the librations of the ACOOH group and benzene ring. The out-of plane librations of the entire phthalate ion are predicted to appear in the spectrum in the range 30–150 cm1 together with two peaks (at 140 and 68 cm1) due to the in-plane librations of the phthalate ion. The lowest frequency peak measured at 42 cm1 has been as-
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Table 3 Assignment of the vibration modes in a phthalate ion as observed in the measured INS spectrum of K-H-pht, and obtained from the solid state DFT (zone-center) calculations in the range 300–3500 cm1. For assignment of the vibrations of the benzene ring, we use the Varsanyis notation for the 2,3-Di-’heavy’ subsistent pattern of benzene [36] with short explanation of the corresponding mode given in square brackets. In case of the CCC-deformational modes, the INS intensity is due to H-riding motion. m = stretch, d = bend, ip = in-plane, op = out-of-plane. INS 3050 1431 1264 1145 1113 1078 1029 984 960 885 811 786 767 720 686 647 582 549 406 364 336
DFT 3135 1438 1261 1154 1196 1076 1042 992 957 882 795 783 754 709 686 645 578 547 406 365 335
Assignment
m(CH) d(COH)-ip and d(CH)-ip 3 [d(CH)-ip] and d(OH)-ip 9b [d(CH)-ip] d(COH)-op 12 [d(CCC)-ip] 1 [benzene breathing] 5 [d(CH)-op] 17b [d(CH)-op] 17a [d(CH)-op] d(CH)-op d(CH)-op d(CH)-op 4 [d(CCC)-op] 6b [d(CCC)-ip] 6b [d(CCC)-ip] 16a [d(CCC)-op] 16a 16b [d(CCC)-op] 16b d(CCC)-op
signed to the phthalate libration together with translational motion of the phthalate ion (lattice mode) (Fig. 3, bottom and Table 4).
IR-Raman spectra of commercial anhydrous K-H-pht contained in the Aldrich library of commercial products [33], showing no IR absorption above 3200 cm1. The IR spectrum shows the presence of three strong absorption bands in the 2800–3000 cm1 region corresponding to the CH stretches, with their Raman-active counterparts shifted to slightly higher wavenumbers (3000– 3100 cm1). In addition, two weak bands appear in the IR spectrum at ca. 2480 cm1 and 2630 cm1 probably corresponding to overtones and combination modes. Most importantly, a very broad band (1750–2200 cm1) of moderate intensity centered at 1920 cm1 can be detected in the IR spectrum; we assign this band to the antisymmetric stretching mode of the strong OHO hydrogen bond. The experimental wavenumber is by 13% lower than the value obtained from our calculations (2196 cm1) owing to the harmonic approximation applied to our frequency calculations. In order to evaluate the contribution of anharmonicity, we have mapped the one-dimensional proton potential along the strong OAH O bond. A one-dimensional Schrödinger equation was then solved using the FGH1D (Fourier Grid Hamiltonian method) code [34], where 42 points in the OAH bond range 0.5–2 Å have been employed to build the potential. A highly asymmetric but still single-well potential was obtained (Fig. 4), justifying the previous suggestions by Harte et al. [35]. Our 1D model of the OHO potential energy well leads to an OHO stretching at 1629 cm1. Thus, anharmonicity downshifts the frequency considerably, by about 24% with respect to the corresponding harmonic value. The OHO band approaches closely the region of bending modes and their intense overtones, opening the possibility of coupling with them. Indeed the smearing of the OH stretch across wide range of frequencies (1750–2200 cm1) is observed in the IR spectrum of commercial anhydrous K-H-phthalate.
4.4. Where to search for the antisymmetric OHO stretching vibration? The OHO stretching mode which appears in the calculated spectrum at 2196 cm1 cannot be identified in the experimental INS spectrum, because of its low intensity and impact of phonon wings. The IR and Raman studies published so far are inconsistent in its assignment. In the first study focusing on the internal vibrations of K-H-pht done by Orel et al. [5], the authors assign the OH stretching vibration to three broad IR bands near 2000, 2450 and 2700 cm1. However, the reported IR spectra either show no traces of the strong CH stretching bands or shows very strong and broad IR absorption band extending up to 3600 cm1, suggesting that the samples contained a substantial amount of water. The same problem appears in the most recent IR study by Meenakshisundaram et al. [10]. In another study by Marvin et al. [3], the Raman band assigned by these authors to the OH stretching frequency decrease its wavenumberpffiffiupon deuteration by factor of only 1.04–1.13 ffi rather than by k ¼ 1:41, as typical for the H-to-D substitution. Geetha et al. [7] contributed to the controversy by assigning the OH stretches at 3750 and 3650 cm1 and the hydrogen bond stretching at 3415 cm1. Because of the above mentioned inconsistencies that we fond in the previous studies, we have decided to compare our results to the
5. Conclusions Using the combined INS/DFT approach, we have investigated the low temperature vibrational spectrum of K-H-pht. The K-Hpht and K-D-pht INS spectra provided information on the motions of hydrogen atoms at 20 K. Theoretical DFT approach was used to reconstruct and interpret the entire experimental INS spectrum of K-H-pht in the range 30–3500 cm1. The theoretical model of the crystal structure of K-H-pht agreed very well with the one obtained from the low temperature neutron diffraction data. The calculated INS spectrum is in excellent agreement with the experimental one. The antisymmetric OHO stretching mode is
Table 4 List of librational modes in a phthalate ion as observed in the measured INS spectrum of K-H-pht, and as obtained from the solid state DFT (zone-center) calculations. INS
DFT
Assignment
271, 225, 207 188, 170, 150
271, 226, 209 194, 178, 151
Benzene lib., COOH lib.
140, 126, 115 106, 92, 88, 85 81, 68, 65, 54
139, 125, 118 109, 99, 94, 85 80, 66, 61, 49
Phthalate lib.
42
39
Phthalate lib. + trans.
Fig. 4. Calculated one-dimensional potential felt by the H1 hydrogen moving along the O1AH1 O40 hydrogen bond.
M. Derzsi, D. Colognesi / Journal of Molecular Structure 967 (2010) 89–93
the only important vibration which could not be localized in the experimental INS spectrum of K-H-pht due to its low intensity and impact of phonon wings. The band assigned to this mode falls across a very broad range of frequencies (1750–2200 cm1) in the IR spectrum. Indeed, the DFT calculations predict the harmonic antisymmetric OHO stretching mode at 2196 cm1. However, highly asymmetric single-well 1D potential is obtained for the proton motion along the OAH O bond, leading to anharmonic frequency of 1629 cm1. Thus, harmonic and anharmonic calculated frequencies nicely encompass the range corresponding to the experimentally observed unusually broad IR absorption band. Acknowledgement This study was partially supported by the Slovak Grant Agency VEGA under the contract No. 2/0150/09. M.D. acknowledge Wojciech Grochala and Lˇubomír Smrcˇok for valuable discussions and Piotr Leszczyn´ski for help with the literature. References [1] D.A. Skoog, D.M. West, F.J. Holler, S.R. Crouch, Fundamentals of Analytical Chemistry, Brooks/Cole-Thomson Learning, Belmont, CA, 2004. [2] N. Kejalakshmy, K. Srinivasan, J. Phys. D: Appl. Phys. 36 (2003) 1778. [3] B.N. Mavrin, M.V. Koldaeva, R.M. Zakalyukin, T.N. Turskaya, Opt. Spectrosc. 100 (2006) 862. [4] Available from:
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[10] S.P. Meenakshisundaram, S. Parthiban, G. Madhurambal, S.C. Mojumdar, J. Therm. Anal. Calorim. 94 (2008) 21. [11] G. Vasudevan, P. AnbuSrinivasan, G. Madhurambal, S.C. Mojumdar, J. Therm. Anal. Calorim. 96 (2009) 99. [12] D. Colognesi, M. Celli, F. Cilloco, R.J. Newport, S.F. Parker, V. Rossi-Albertini, F. Sacchetti, J. Tomkinson, M. Zoppi, Appl. Phys. A 74 (2002) 64. [13] M.R. Johnson, K. Parlinski, I. Natkaniec, B.S. Hudson, Chem. Phys. 291 (2003) 53. [14] J.A. Ciezak, S.F. Trevino, J. Phys. Chem. A 110 (2006) 5149. [15] K. Holderna-Natkaniec, I. Natkaniec, W. Kasperkowiak, E. Sciesinska, J. Sciesinski, E. Mikuli, J. Mol. Struct. 790 (2006) 94. [16] M. Sládkovicˇová, Lˇ. Smrcˇok, P. Mach, D. Tunega, A. Kolesnikov, Chem. Phys. 340 (2007) 245. [17] M. Sládkovicˇová, Lˇ. Smrcˇok, P. Mach, D. Tunega, A.J. Ramírez Cuesta, J. Mol. Struct. 874 (2008) 108. [18] The authors of Ref. [7] report some calculated frequencies, but it is unclear which theoretical method was applied, whether harmonic approximation was used or not. [19] Z.A. Bowden, M. Celli, F. Cilloco, D. Colognesi, R.J. Newport, S.F. Parker, F.P. Ricci, V. Rossi-Albertini, F. Sacchetti, J. Tomkinson, M. Zoppi, Physica B 276– 278 (2000) 98. [20] G. Kresse, J. Furthmüller, Comput. Math. Sci. 6 (1996) 15. [21] G. Kresse, J. Hafner, Phys. Rev. B 47 (1993) 558. [22] G. Kresse, J. Hafner, Phys. Rev. B 49 (1994) 251. [23] G. Kresse, J. Furthmüller, Phys. Rev. B 54 (1996) 11169. [24] J.P. Perdew, Y. Wang, Phys. Rev. B 45 (1992) 13244. [25] P.E. Blöchl, Phys. Rev. B 50 (1994) 17953. [26] G. Kresse, D. Joubert, Phys. Rev. B 59 (1999) 1758. [27] G. Kresse, J. Hafner, J. Phys. Condens. Matter 6 (1994) 8245. [28] J. Hafner, J. Mol. Struct. 651–653 (2003) 3. [29] A.J. Ramirez-Cuesta, Comput. Phys. Commun. 157 (2004) 3. [30] S. Portmann, H.P. Luthi, Chimia 54 (2000) 766. [31] A.L. Spek, PLATON, A Multipurpose Crystallographic Tool, Utrecht University, The Netherlands, 2002. Available from:. [32] V. Videnova-Adrabin´ska, J. Baran, H. Ratajczak, J. Mol. Struct. 145 (1986) 33. [33] Spectra for product No. 96148 (Fluka) obtained through on Dec 7, 2009. Available from: . [34] G.G. Balint-Kurti, C.C. Martson, J. Chem. Phys. 91 (6) (1989) 3571. [35] S.M. Harte, A. Parkin, A. Goete, Ch.C. Wilson, J. Mol. Struct. 741 (2005) 93. [36] G. Varsányi, Vibrational Spectra of Benzene Derivatives, Academic Press, New York, 1969.
Contents lists available at ScienceDirect
Journal of Molecular Structure journal homepage: www.elsevier.com/locate/molstruc
Inelastic neutron scattering and DFT study of potassium hydrogen phthalate Mariana Derzsi a,b,*, Daniele Colognesi c a
Institute of Inorganic Chemistry, Slovak Academy of Sciences, Dúbravská cesta 9, SK-845 36 Bratislava, Slovak Republic _ Interdisciplinary Centre for Mathematical and Computational Modeling, The University of Warsaw, Zwirki i Wigury 93, 02-089 Warsaw, Poland c Istituto dei Sistemi Complessi, Consiglio Nazionale delle Ricerche, via Madonna del Piano 10, 50019 Sesto Fiorentino (FI), Italy b
a r t i c l e
i n f o
Article history: Received 28 October 2009 Received in revised form 19 December 2009 Accepted 21 December 2009 Available online 11 January 2010 Keywords: Potassium hydrogen phthalate Inelastic neutron scattering Density functional theory Hydrogen bond
a b s t r a c t Inelastic neutron scattering and solid state quantum chemistry calculations are applied to investigate the lattice vibrations in crystalline potassium hydrogen phthalate containing very short intermolecular OAH O hydrogen bond (2.529 Å). The inelastic neutron scattering spectrum is interpreted in the energy range 30–3500 cm1 using the density function theory approach within the harmonic approximation. The one-dimensional potential of the proton moving along the short OAH O bond is mapped and a considerable contribution of anharmonicity (about 24%) to the antisymmetric OHO stretching vibration is calculated. Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction Potassium hydrogen phthalate ðC8 H5 O4 K; K-H-pht, hereafter) has a wide range of applications in many research fields. It is commonly used as a primary standard for acid–base titrations and for calibrating pH-meters [1], for monochromators and analyzers in the field of X-ray spectroscopy and for electro-optic modulators [2]. Additionally, it is employed as substrate for the deposition of thin films of organic nonlinear optical materials [3]. K-H-pht crystallizes in the orthorhombic structure ðPca21 , a ¼ 9:546ð2Þ Å, b ¼ 13:201ð3Þ Å, c ¼ 6:405ð2Þ ÅÞ with four formula units in the unit cell. It exhibits one short, strong intermolecular OAH O hydrogen bond (2.528(8) Å) [4] which links neighboring hydrogen phthalate molecules into zigzag chains (Fig. 1). Up to date, several studies have been done concerning the vibrational properties of the title compound [3,5–11]. Unfortunately, one finds huge discrepancies between vibrational spectra reported so far for various samples of K-H-pht. In this study we use theoretical methods to rationalize the vibrational features of K-H-pht with particular emphasis on the oscillations of the hydrogen atoms available from the inelastic neutron scattering (INS) technique, and we compare our findings to the previously published spectroscopic data. The INS spectra of K-H-pht and of its deuterated version K-D-pht have been reported by Colognesi
et al. [12], while demonstrating the high resolution of the TOSCA-I spectrometer. Here we provide the full assignment of the INS spectrum in the range 30–3500 cm1, based on the normal coordinate analysis in the solid state using the density functional theory (DFT) method. Such a combined INS/DFT approach has been successfully applied in the past to several crystals of hydrogen bonded systems [13–17] but not to K-H-pht [18]. Additionally, one-dimensional potential of the proton moving along the short hydrogen bond is mapped in the current work, suggesting a large anharmonicity of the antisymmetric OHO stretching vibration. 2. Neutron scattering experiment Neutron scattering measurements on K-H-pht and K-D-pht were both carried out using the TOSCA-I [19] inelastic spectrometer of the ISIS pulsed neutron source (Rutherford Appleton Laboratory, Chilton, Didcot, UK). TOSCA-I was a crystal analyzer inversegeometry spectrometer, where the final neutron energy was selected by a set of pyrolitic graphite crystals placed in back-scattering (at about 136° with respect to the incident beam). The INS data of K-H-pht were collected at 20 K. Details of the measurements are given in Ref. [12]. 3. Calculation details
* Corresponding author. Address: Interdisciplinary Centre for Mathematical and _ Computational Modeling, The University of Warsaw, Zwirki i Wigury 93, 02-089 Warsaw, Poland. Tel.: +48 22 55 40 825. E-mail address: [email protected] (M. Derzsi). 0022-2860/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.molstruc.2009.12.044
Fixed-volume crystal DFT calculations were performed with VASP [20–23], using the experimental unit cell (Z ¼ 4) taken from the single-crystal neutron diffraction refinement at 30 K [4]. The
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M. Derzsi, D. Colognesi / Journal of Molecular Structure 967 (2010) 89–93
Fig. 1. Structure of K-H-pht projected on the ac-plane (left) and phthalate ions linked into a zig–zag chain by short OAH O hydrogen bonds (right). Large blue balls represent potassium atoms, small red balls oxygen and small gray balls carbon atoms. Hydrogen atoms are omitted for clarity. (For interpretation of color mentioned in this figure the reader is referred to the web version of the article.)
Perdew–Wang 91 (PW91) functional was employed, with the exchange and correlation effects handled within the Generalized Gradient Approximation (GGA) [24]. The interactions between ions and electrons were described by the Projector Augmented Wave (PAW) method [25,26] and the atomic pseudo-potentials [27]. For the electronic and ionic optimization the conjugate gradient algorithm was used. The energy cut-off for the plane wave basis set was 500 eV. The Brillouin-zone sampling was restricted to one k point. No symmetry restrictions were applied during the geometry optimization and the force constant calculation. The optimization stopped when all the forces on the individual atoms were smaller than 2 104 eV=Å. Vibrational normal modes were calculated from the Hessian within the harmonic approximation. The Hessian was constructed from single-point energy calculations on 6n structures generated from the optimized structure by displacing each of the n atoms in the cell along the Cartesian directions x; y; z by 0:02 Å. Each pair of single-point energy calculations was used to evaluate the force constants [28]. The INS spectrum was calculated from normal modes using the aCLIMAX 4.0.1 code [29], while the graphical package MOLEKEL [30] was used for visualizing molecular geometry and analyzing individual normal modes. The geometry of the optimized structure was analyzed using PLATON [31].
Table 2 Experimental [35] and calculated geometry of the O1AH1 O4i hydrogen bond (Å, °). Symmetry code: (i) 3/2 x, y, z 1/2.
Exp. Calc.
O1AH1
H1 O4i
O1 O4i
O1AH1 O4i
1.07(15) 1.063
1.456(16) 1.446
2.528(8) 2.509
174.6(13) 177.8
tion of the proton. In the structure of K-H-pht, H is present in four CH groups and in one OH group. The hydroxyl group can be easily deuterated leading to K-D-pht, and the INS spectrum of K-D-pht thus reveals CH vibrations only (Fig. 2). In the region below 1700 cm1, the spectrum of K-H-pht contains well localized peaks, characteristic of fundamental vibrations emerging on the top a broad band, which is mainly due to the first overtones (Fig. 2). A broad band centered at 3050 cm1 originating from CAH stretching vibrations is the only considerably intense feature above 1700 cm1. In the following, the internal OHO and phthalate vibrations, as well as the librational motions are discussed in Sections 4.1–4.3, respectively. We devote a special subsection, namely 4.4 to the comparison of our calculations to the previously published spectroscopic data,
4. Results and discussion Calculated bond distances, angles and torsional angles are in good agreement with the experimentally determined values (Table 1). Noticeably, our calculations correctly reproduce the asymmetry observed in the bond lengths of the carboxylic groups and the geometry of the short OAH O hydrogen bond (Table 2). The INS spectrum of K-H-pht can be considered as a pure hydrogen spectrum since the scattering cross-sections of carbon, oxygen and potassium are negligible in comparison with the large incoherent scattering cross-sec-
Table 1 Selected experimental [35] and theoretically calculated bond distances, bond angles and torsional angles (Å, °).
C7AO1 C7AO2 C8AO3 C8AO4 O3AC8AO4 O2AC7AO1 C3AC2AC8AO4 C6AC1AC7AO2
X-ray (100 K)
Neutron (30 K)
Calc.
1.3168(16) 1.2296(16) 1.2486(15) 1.2769(16) 124.61(11) 124.80(12) 103.51(13) 147.60(13)
1.309(9) 1.241(8) 1.237(8) 1.281(7) 124.6(6) 125.1(6) 104.6(6) 146.9(6)
1.321 1.243 1.257 1.286 123.6 124.5 103.3 147.2
Fig. 2. The INS spectra of K-H-pht (top black) and K-D-pht (middle blue) measured at 20 K shown together with the calculated INS spectrum and calculated contribution from the first overtones (bottom, red and gray, respectively) in the 30– 3500 cm1 range. The experimental spectra are vertically shifted for clarity. (For interpretation of color mentioned in this figure the reader is referred to the web version of the article.)
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focusing on the antisymmetric OHO stretching vibration and contribution of anharmonicity to it. 4.1. OHO vibrations The highest frequency antisymmetric stretching OHO mode is predicted to appear in the INS spectrum as a well localized peak centered at 2196 cm1. However, no such peak is observed in the experimental INS spectrum (Fig. 2). The absence of this band in the INS spectrum is primarily due to low cross-section of the hydrogen bonded protons, since they have to compete against the overtones of the much stronger CH system. The OHO stretching is further suppressed by the impact of phonon wings. These wings spread the, already weak, fundamental OHO stretching mode into broad combination bands. Additionally, the impact of phonon wings on the INS spectrum is strongly affected by the magnitude of the neutron momentum transfer, being the highest at higher energies, just where the OHO stretch is expected. Vibrations containing some share of the proton motion along the OAH O bond are also predicted to appear in the frequency range 270–550 cm1 (Fig. 3). At these low frequencies, however, they do not form localized modes, but are rather weak components of the complex movements of the phthalate ions. Since the hydrogen bond is formed between the carboxyl and carbonyl groups, their in-plane (ip) and out-of-plane (op) deformations naturally induce a deformation of the hydrogen bond. While at low frequencies (<550 cm1 Þ, they cause mainly a stretching of the hydrogen bond, at higher frequencies up to 850 cm1 the bending of the hydrogen bond, d(OHO), is mostly observed. These motions are additionally coupled with ip and op deformations of the benzene ring. The only d(OHO) mode independent of the phthalate ion vibrations is calculated at 1196 cm1 (Fig. 3, top). In this mode, the hydrogen atom is moving perpendicular to the hydrogen bond and out of the carboxyl plane. Interestingly, the hydrogen exhibits here an extremely large displacement vector, while the motions of all the remaining atoms are negligible. For this reason the d(OHO)op mode can be easily identified at 1113 cm1 in the experimental spectrum of K-H-pht while it is obviously absent in the spectrum of K-D-pht (Fig. 3, top). Such OHO out-of-plane vibrations are reported to be very sensitive to molecular interactions [32]. This high sensitivity is probably the reason for the discrepancy between the experimentally and theoretically determined position of this mode, its frequency being overestimated by as much as 7% in the DFT calculations. The OHO vibrations, in which the proton vibrates in the carboxyl plane, d(OHO)-ip, with a large displacement vector, are predicted to appear in the frequency range 1250–1500 cm1 mixed with the d(CH)-ip vibrations. Indeed, we can identify two strong peaks (1264 and 1431 cm1) in the experimental spectrum of KH-pht (Fig. 3); the former band being broadened by, while the intensity of the latter one being raised by the contribution of the d(OHO)-ip vibration. 4.2. Phthalate CH vibrations Most of the intensity in the INS spectrum of K-H-pht is due to the CH hydrogen atoms moving in the plane, d(CH)-ip, (1000– 1500 cm1) or out-of-the plane of the benzene ring, d(CH)-ip, (700–1000 cm1), and due to the riding motion of the hydrogen atoms on the phthalate ion during its deformational movement (300–700 cm1) (Fig. 3, top and Table 3). Similarly to the case of the CH vibrations, the hydrogen riding on the benzene in-plane deformations shows up at frequencies higher than that of the hydrogen riding on the benzene out-of-plane deformations (647 and 686 cm1 vs. five intense peaks between 300 and 600 cm1 in the experimental K-H-pht spectrum). On the other hand, the in-plane riding modes are predicted to yield less intense peaks
Fig. 3. In each plot: INS spectrum of K-H-pht (top black curve) and K-D-pht (middle blue curve) measured at 20 K, together with the calculated partial INS spectra of the OH hydrogen atoms (bottom thick green curve) and of the CH ones (bottom thin red curve) in the range 300–1700 cm1 (top plot) and 30–300 cm1 (bottom plot). The experimental spectra are vertically shifted for clarity. (For interpretation of color mentioned in this figure the reader is referred to the web version of the article.)
than the out-of-plane riding ones. The most intense peak appearing in the experimental spectrum at 1145 cm1 is assigned to a pure d(CH)-ip vibration. Naturally, the highest frequency CH modes are the stretching vibrations appearing in the experimental K-Hpht spectrum as a broad band centered at 3050 cm1 (Fig. 2). Our DFT calculations overestimate this value by 3% only (3135 cm1). 4.3. Librations According to our calculations, in the INS spectrum of K-H-pht there is a clear borderline between the internal deformations of individual (benzene, ACOOH, ACO2) groups and their librations at 300 cm1. The peaks appearing in the experimental INS spectrum in the region 150–300 cm1 can be assigned mainly to the librations of the ACOOH group and benzene ring. The out-of plane librations of the entire phthalate ion are predicted to appear in the spectrum in the range 30–150 cm1 together with two peaks (at 140 and 68 cm1) due to the in-plane librations of the phthalate ion. The lowest frequency peak measured at 42 cm1 has been as-
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Table 3 Assignment of the vibration modes in a phthalate ion as observed in the measured INS spectrum of K-H-pht, and obtained from the solid state DFT (zone-center) calculations in the range 300–3500 cm1. For assignment of the vibrations of the benzene ring, we use the Varsanyis notation for the 2,3-Di-’heavy’ subsistent pattern of benzene [36] with short explanation of the corresponding mode given in square brackets. In case of the CCC-deformational modes, the INS intensity is due to H-riding motion. m = stretch, d = bend, ip = in-plane, op = out-of-plane. INS 3050 1431 1264 1145 1113 1078 1029 984 960 885 811 786 767 720 686 647 582 549 406 364 336
DFT 3135 1438 1261 1154 1196 1076 1042 992 957 882 795 783 754 709 686 645 578 547 406 365 335
Assignment
m(CH) d(COH)-ip and d(CH)-ip 3 [d(CH)-ip] and d(OH)-ip 9b [d(CH)-ip] d(COH)-op 12 [d(CCC)-ip] 1 [benzene breathing] 5 [d(CH)-op] 17b [d(CH)-op] 17a [d(CH)-op] d(CH)-op d(CH)-op d(CH)-op 4 [d(CCC)-op] 6b [d(CCC)-ip] 6b [d(CCC)-ip] 16a [d(CCC)-op] 16a 16b [d(CCC)-op] 16b d(CCC)-op
signed to the phthalate libration together with translational motion of the phthalate ion (lattice mode) (Fig. 3, bottom and Table 4).
IR-Raman spectra of commercial anhydrous K-H-pht contained in the Aldrich library of commercial products [33], showing no IR absorption above 3200 cm1. The IR spectrum shows the presence of three strong absorption bands in the 2800–3000 cm1 region corresponding to the CH stretches, with their Raman-active counterparts shifted to slightly higher wavenumbers (3000– 3100 cm1). In addition, two weak bands appear in the IR spectrum at ca. 2480 cm1 and 2630 cm1 probably corresponding to overtones and combination modes. Most importantly, a very broad band (1750–2200 cm1) of moderate intensity centered at 1920 cm1 can be detected in the IR spectrum; we assign this band to the antisymmetric stretching mode of the strong OHO hydrogen bond. The experimental wavenumber is by 13% lower than the value obtained from our calculations (2196 cm1) owing to the harmonic approximation applied to our frequency calculations. In order to evaluate the contribution of anharmonicity, we have mapped the one-dimensional proton potential along the strong OAH O bond. A one-dimensional Schrödinger equation was then solved using the FGH1D (Fourier Grid Hamiltonian method) code [34], where 42 points in the OAH bond range 0.5–2 Å have been employed to build the potential. A highly asymmetric but still single-well potential was obtained (Fig. 4), justifying the previous suggestions by Harte et al. [35]. Our 1D model of the OHO potential energy well leads to an OHO stretching at 1629 cm1. Thus, anharmonicity downshifts the frequency considerably, by about 24% with respect to the corresponding harmonic value. The OHO band approaches closely the region of bending modes and their intense overtones, opening the possibility of coupling with them. Indeed the smearing of the OH stretch across wide range of frequencies (1750–2200 cm1) is observed in the IR spectrum of commercial anhydrous K-H-phthalate.
4.4. Where to search for the antisymmetric OHO stretching vibration? The OHO stretching mode which appears in the calculated spectrum at 2196 cm1 cannot be identified in the experimental INS spectrum, because of its low intensity and impact of phonon wings. The IR and Raman studies published so far are inconsistent in its assignment. In the first study focusing on the internal vibrations of K-H-pht done by Orel et al. [5], the authors assign the OH stretching vibration to three broad IR bands near 2000, 2450 and 2700 cm1. However, the reported IR spectra either show no traces of the strong CH stretching bands or shows very strong and broad IR absorption band extending up to 3600 cm1, suggesting that the samples contained a substantial amount of water. The same problem appears in the most recent IR study by Meenakshisundaram et al. [10]. In another study by Marvin et al. [3], the Raman band assigned by these authors to the OH stretching frequency decrease its wavenumberpffiffiupon deuteration by factor of only 1.04–1.13 ffi rather than by k ¼ 1:41, as typical for the H-to-D substitution. Geetha et al. [7] contributed to the controversy by assigning the OH stretches at 3750 and 3650 cm1 and the hydrogen bond stretching at 3415 cm1. Because of the above mentioned inconsistencies that we fond in the previous studies, we have decided to compare our results to the
5. Conclusions Using the combined INS/DFT approach, we have investigated the low temperature vibrational spectrum of K-H-pht. The K-Hpht and K-D-pht INS spectra provided information on the motions of hydrogen atoms at 20 K. Theoretical DFT approach was used to reconstruct and interpret the entire experimental INS spectrum of K-H-pht in the range 30–3500 cm1. The theoretical model of the crystal structure of K-H-pht agreed very well with the one obtained from the low temperature neutron diffraction data. The calculated INS spectrum is in excellent agreement with the experimental one. The antisymmetric OHO stretching mode is
Table 4 List of librational modes in a phthalate ion as observed in the measured INS spectrum of K-H-pht, and as obtained from the solid state DFT (zone-center) calculations. INS
DFT
Assignment
271, 225, 207 188, 170, 150
271, 226, 209 194, 178, 151
Benzene lib., COOH lib.
140, 126, 115 106, 92, 88, 85 81, 68, 65, 54
139, 125, 118 109, 99, 94, 85 80, 66, 61, 49
Phthalate lib.
42
39
Phthalate lib. + trans.
Fig. 4. Calculated one-dimensional potential felt by the H1 hydrogen moving along the O1AH1 O40 hydrogen bond.
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the only important vibration which could not be localized in the experimental INS spectrum of K-H-pht due to its low intensity and impact of phonon wings. The band assigned to this mode falls across a very broad range of frequencies (1750–2200 cm1) in the IR spectrum. Indeed, the DFT calculations predict the harmonic antisymmetric OHO stretching mode at 2196 cm1. However, highly asymmetric single-well 1D potential is obtained for the proton motion along the OAH O bond, leading to anharmonic frequency of 1629 cm1. Thus, harmonic and anharmonic calculated frequencies nicely encompass the range corresponding to the experimentally observed unusually broad IR absorption band. Acknowledgement This study was partially supported by the Slovak Grant Agency VEGA under the contract No. 2/0150/09. M.D. acknowledge Wojciech Grochala and Lˇubomír Smrcˇok for valuable discussions and Piotr Leszczyn´ski for help with the literature. References [1] D.A. Skoog, D.M. West, F.J. Holler, S.R. Crouch, Fundamentals of Analytical Chemistry, Brooks/Cole-Thomson Learning, Belmont, CA, 2004. [2] N. Kejalakshmy, K. Srinivasan, J. Phys. D: Appl. Phys. 36 (2003) 1778. [3] B.N. Mavrin, M.V. Koldaeva, R.M. Zakalyukin, T.N. Turskaya, Opt. Spectrosc. 100 (2006) 862. [4] Available from:
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