Temperature Variation of Ultralow Frequency Modes and Mean

Article pubs.acs.org/JPCA

Temperature Variation of Ultralow Frequency Modes and Mean Square Displacements in Solid Lasamide (Diuretic Drug) Studied by 35Cl-NQR, X‑ray and DFT/QTAIM Jolanta Natalia Latosińska,* Magdalena Latosińska, Jerzy Kasprzak, and Magdalena Tomczak Faculty of Physics, Adam Mickiewicz University, Umultowska 85, 61-614 Poznań, Poland

Jan Krzysztof Maurin National Medicines Institute, Chelmska 30/34, 00-750 Warsaw, Poland ́ National Centre for Nuclear Research, Andrzeja Sołtana 7, 05-400 Otwock-Swierk, Poland

ABSTRACT: The application of combined 35Cl-NQR/X-ray/DFT/QTAIM methods to study the temperature variation of anisotropic displacement parameters and ultralow frequency modes of anharmonic torsional vibrations in the solid state is illustrated on the example of 2,4-dichloro-5-sulfamolybenzoic acid (lasamide, DSBA) which is a diuretic and an intermediate in the synthesis of furosemide and thus its common impurity. The crystallographic structure of lasamide is solved by X-ray diffraction and refined to a final R-factor of 3.06% at room temperature. Lasamide is found to crystallize in the triclinic space group P-1, with two equivalent molecules in the unit cell a = 7.5984(3) Å, b = 8.3158(3) Å, c = 8.6892(3) Å; α = 81.212(3)°, β = 73.799(3)°, γ = 67.599(3)°. Its molecules form symmetric dimers linked by two short and linear intermolecular hydrogen bonds O−H···O (O−H···O = 2.648 Å and ∠OHO = 171.5°), which are further linked by weaker and longer intermolecular hydrogen bonds N−H···O (N−H···O = 2.965 Å and ∠NHO = 166.4°). Two 35Cl-NQR resonance frequencies, 36.899 and 37.129 MHz, revealed at room temperature are assigned to chlorine sites at the ortho and para positions, relative to the carboxyl functional group, respectively. The difference in C−Cl(1) and C−Cl(2) bond lengths only slightly affects the value of 35Cl-NQR frequencies, which results mainly from chemical inequivalence of chlorine atoms but also involvement in different intermolecular interactions pattern. The smooth decrease in both 35Cl-NQR frequencies with increasing temperature in the range of 77−300 K testifies to the averaging of EFG tensor at each chlorine site due to anharmonic torsional vibrations. Lasamide is thermally stable; no temperature-induced release of chlorine or decomposition of this compound is detected. The temperature dependence of ultralow frequency modes of anharmonic small-angle internal torsional vibrations averaging EFG tensor and mean square angle displacements at both chlorine sites is derived from the 35Cl-NQR temperature dependence. The frequencies of torsional vibrations higher for the para site than the ortho site are in good agreement with those obtained from thermal parameters obtained from X-ray studies. The mean square angle displacements are in good agreement with those estimated from X-ray data with the use of the TLS model. The detailed DFT/QTAIM analysis suggests that the interplay between different hydrogen bonds in adjacent molecules forming dimers is responsible for the differences in flexibility of the carboxyl and sulphonamide substituents as well as both C−Cl(1) and C−Cl(2) bonds. Three ultralow wavenumber modes of internal vibrations in Raman and IR spectra obtained at the B3LYP/6-311++G(d,p) level close to those obtained within the TLS model suggest that internal and external modes of vibrations are not well separated.

Received: July 13, 2012 Revised: September 27, 2012 Published: September 28, 2012 © 2012 American Chemical Society

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dx.doi.org/10.1021/jp306969u | J. Phys. Chem. A 2012, 116, 10344−10358

The Journal of Physical Chemistry A

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INTRODUCTION Nuclear quadrupole resonance (NQR) spectroscopy provides information on structural details on the interatomic spacing scale, which is complementary to that obtained by standard X-ray diffraction. Although the electron density distribution at the quadrupolar nucleus is fully experimentally determined by both X-ray and NQR, X-ray, whose spherically averaged pseudoatom electronic distributions are used, is sensitive to long-range periodic order, while NQR sensitivity, by contrast, is limited to short-range interactions. Thus NQR in addition to X-ray or neutron diffraction and NMR is recently considered as one of the most important methods to study three-dimensional patterns at the atomic level. It is well-known that X-ray diffraction studies yield information not only about all mean atomic positions, but also about the effects of atomic vibrations, i.e., isotropic or anisotropic atomic motions resulting from internal static or dynamic disorder, lattice defects, and vibrations (acoustic phonons).1 Standard X-ray refinement assumes that atomic motions are isotropic, harmonic, and independent of each other, but the real crystals are anharmonic and either expand (commonly) or shrink (rarely) on heating. A more recent approach allows estimation of anharmonic displacements from mean atomic positions, which provides information about dynamic processes in crystalline solids, their internal structural ordering, flexibility, and stability, as well as eliminates systematic errors (due to atomic motions) in the diffraction experiment.2 The atomic displacements of small-molecules can be described by six anisotropic displacement parameters (ADPs), which define the covariance matrix (U), one per each atom describing the motion of this atom about its mean position.3 The ADP parameters are usually difficult to interpret directly in chemical or physical terms of bonds or interactions, respectively, and their interpretation requires the transformation into modes of collective atomic displacements or frequencies, which is a rather complicated task, and thus nonstandard in structural analysis. The ADPs are composite quantities made up of a few small contributions brought by temperature-dependent mean square displacement (MSD) due to low-frequency motions, temperatureindependent MSDs due to high-frequency motions, disorder, and systematic errors, which cannot be distinguished using the onetemperature experiment but require the knowledge of temperature evolution of ADPs or complementary spectroscopic measurements. In general, the motion of a molecule consists of 3N − 6 internal vibrational modes, three modes of translations, and three modes of torsional vibrations (librations); an additional set of lowfrequency modes comes from the collective 3NM lattice vibrations, where N is the number of atoms in the unit cell and M is the number of unit cells in crystal, which are classified into acoustic and optical dispersion branches. In molecular crystals, internal and external modes of vibrations are considered to be well separated (interaction between internal and external vibrations is a secondorder effect3). However, if the coupling between internal and external modes of motion is strong, a rigorous separation can be impossible.4 The most important are external ultralow frequency modes (below 100 cm−1), which provide information of characteristic features of many materials. For example, they allow identification of folded acoustic and shear modes in multilayer superlattice structures of semiconductor devices,5 determination of the tube diameter in single and multiwall carbon nanotubes6,7 and discrimination of the polymorphs.8 These ultralow frequency vibrational modes are mainly manifested in inelastic neutron scattering (IS) and Raman scattering, which require complex and high cost equipment, but they also are an important source of averaging of electric field gradient (EFG) tensor manifested as

temperature variation of the experimentally measured temperature variation 35Cl-NQR frequency.9,10 It is well-known that the molecular vibrations in crystals, irrespective of their origins, induce changes in the electron density distribution, its symmetry, and orientation of the principal axes of EFG tensor. Nonetheless, typically only fundamental analysis within the Bayer model is performed, but the temperature variation of frequency of vibrational modes is rare,11,12 while displacement parameters have never been estimated. In this paper, the application of the 35Cl-NQR/X-ray/DFT/QTAIM combined studies for such a purpose is illustrated on the example of a sulfonamide diuretic: 2,4-dichloro-5-sulfamoylbenzoic acid (DSBA, or Lasamide; Figure 1). Lasamide, a sulfamoylbenzoic acid derivative,

Figure 1. The chemical structure of lasamide and the relevant atom numbering.

belongs to strong diuretics/antihypertensives and antiviral activity agents, but as a drug it is rather occasionally used, mainly in veterinary practice. However, it still remains an intermediate widely used in the pharmaceutical industry that is essential in the synthesis of a potent diuretic furosemide (FSE) in which lasamide condenses with furfurylamine.13 Thus lasamide is the most common and undesirable pharmaceutical impurity present in commonly used formulation of the furosemide containing drug Lasix14 (widely applied in the treatment of coronary heart diseases including edema, hypertension, hepatic cirrhosis, renal impairment, nephrotic syndrome, severe hypercalcemia, as well as cerebral/ pulmonary edema or anaphylactic shock15). According to a recent study, lasamide has been recognized as a highly hazardous agent that may lead to occupational asthma and rhinitis as well as allergic respiratory diseases.16 Although the influence of impurities on drug/intermediate properties and stability is one of the most important issues for the pharmaceutical industry, it has been rarely systematically studied. The impurities have been usually identified after synthesis by NMR, IR, MAS (lasamide17,18) and rarely by DSC. Often even their crystal structure also remains unresolved. Indeed, X-ray data of lasamide have never been published. The only crystallographic structure available19 is that obtained by a combination of neutronographic and X-ray study, according to which anhydrous lasamide crystallizes in the triclinic system, space group P-1, with two molecules in the unit cell and with the cell parameters a = 8.3223 Å, b = 8.6960 Å, c = 7.6062 Å, α = 106.204°, β = 112.386°, and γ = 81.227°. The quality of this structure is questionable, as evidenced at least by a significant deviation of the benzene ring from planarity and high inconsistency in the second moment.20 Although it was sufficient (after DFT refinement) to propose a relaxation mechanism, i.e., proton tunnelling as a low temperature mechanism and NH2 jumps as a high-temperature mechanism,20 the attempts to interpret the 35Cl-NQR spectra, which are more sensitive to structural details and intermolecular vibrations, have failed. The so-called characteristic ultralow part of the vibrational spectrum of lasamide has been never studied by any method. The aim of our paper is to show the usefulness of NQR in 10345



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where h is the Planck constant, k is the Boltzmann constant, ν0 is the NQR frequency at 0 K, T is temperature, AT is the moment of inertia, and f T is the frequency of torsional vibrations. In molecular crystals Raman spectra indicate a small variation in torsional frequency,22,23 therefore Brown24 assumed a linear temperature dependence of frequencies of torsional vibrations f(T) = f(0)(1 − gT). Thus, the Bayer model can be rewritten as quasiharmonic:

extension of the knowledge on the dynamics of the motion of atoms in crystals by delivering data complementary to those on ADPs obtained from X-ray study. Results of combined measurements by 35Cl-NQR, X-ray and DFT/QTAIM presented in this paper considerably expand and, on the other hand, confirm the conclusions derived from our earlier 1H NMR study20 and highlight the importance of the combination of experimental and theoretical techniques to get a sensitive method for investigation and interpretation of both structural features and molecular dynamics of solid drugs. NQR Theory. The 35Cl nucleus has spin I = 3/2 and therefore in zero magnetic field 35Cl exhibits two doubly degenerated nuclear quadrupole energy levels. Their energies depend on the nuclear quadrupole moment eQ and on the electric-fieldgradient (EFG) tensor Vik = ∂2V/∂xi∂xk, composed of the second derivatives of the electrostatic potential V with respect to the coordinates at the position of the nucleus. The symmetric traceless second rank EFG tensor has three principal values: VZZ = eq, VYY, and VXX (|VZZ| > |VYY| ≥ |VXX|), which are used to obtain two unique NQR parameters: the nuclear quadrupole coupling constant (e2Qqh−1) and asymmetry parameter (η), interrelated with the NQR frequencies (ν) through the following equation:21

ν=

e 2Qq 1 + η2 /3 2h

⎛ hfT (1 − gT ) ⎞ 3h 1 ⎟⎟ ν(T ) = ν0⎜⎜1 − coth 2kT 4π 2 AfT (1 − gT ) ⎝ ⎠ (4)

where g is the dimensionless factor describing anharmonicity, a product of the volume expansion coefficient, and the so-called Grueneisen parameter. The Tatsuzaki−Yokozawa11 model is a modification of eq 3 taking into account that the three modes of the internal torsional motions occur about the principal axes of the moment of inertia, which are not colinear with the principal directions of the EFG tensor. This approach results in the equation ⎛ 3h ν(T ) = ν0⎜⎜1 − π2 4 ⎝

(1)

However, Cl frequencies do not uniquely depend on the quadrupole coupling constant e2qQ/h but also on the asymmetry parameter η, but it is worth noting that for most organic compounds, including drugs, the value of η does not exceed 0.1. Thermal motions present in all crystals occur at frequencies much higher than those of NQR transitions, thus the EFG actually measured by NQR is time averaged over these motions. In the absence of phase transitions, the 35Cl-NQR frequency smoothly and slowly decreases with increasing temperature. The temperature factor is typically on the order of 10−4 1/K. The most important sources of averaging of the EFG tensor (1/ν)(dν/dT) are the fast torsional vibrations (librations). In general, librations of higher amplitudes are more effective in the process of averaging. The population of torsional levels varies with temperature and can be expressed equivalently as a change in the amplitude of the motions. Bayer’s theory9 assumes that the averaging of the EFG tensor by small and high frequency torsional motions is reflected in the NQR frequency according to

⎛ 3h ν(T ) = ν0⎜⎜1 − 4 π2 ⎝

(5)

∑ i

hf (1 − giT ) ⎤⎞ sin 2(αi) ⎡ ⎢coth i ⎥⎟⎟ ⎥⎦⎠ 2kT Ai fi (1 − giT ) ⎢⎣ (6)

where gi are dimensionless factors describing anharmonicity.

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EXPERIMENTAL SECTION Cl-NQR. A high-purity polycrystalline (powder) sample of lasamide (95%) was purchased from Sigma-Aldrich and used without any additional purification. The probe was sealed in a glass container to avoid hydration of the sample. The measurements were performed with the use of a homemade spectrometer equipped with a special NQR probe head developed at the Institute of Physics. The radiofrequency coil of the spectrometer including the glass ampule with the sample was placed in a Dewar vessel. The chromel-alumel thermocuple was used for the determination of temperature. The temperature was automatically controlled and stabilized to within 0.1 K. The 35Cl-NQR spectra of the compound were taken over the temperature range 77−300 K. NQR signals assigned to Cl nuclei were weak (S/N after 1000 accumulations was 3 and 5 for Cl(1) and Cl(2), respectively), and the resonant lines were wide, therefore the solid echo signal was measured. The optimized pulse length was about 13 μs. The accuracy of the 35Cl-NQR frequency determination was about 10 kHz.

(2)

where ν0 is the NQR frequency at 0 K, and θ is the root-meansquare angular displacement of the z-axis of EFG tensor from its equilibrium position. The asymmetry parameter η is neglected in this approach. The contribution of optical torsional vibrations can be interpreted with Bayer’s9 and Kushida’s10 models, employing the quantum oscillator formalism. This approach assumes that the averaging effect is caused exclusively by one mode of torsional vibrations, which occurs about the principal direction of the EFG tensor and leads to the following formula describing the temperature dependence of the 35Cl-NQR frequency: ⎛ hfT ⎤⎞ 3h ⎡ coth ν(T ) = ν0⎜⎜1 − ⎥⎟ ⎢ 2kT ⎦⎟⎠ 4π 2A TfT ⎣ ⎝

i

hf ⎤⎞ sin 2(αi) ⎡ ⎢coth i ⎥⎟⎟ Ai fi ⎣ 2kT ⎦⎠

where h is the Planck constant, k is the Boltzmann constant, T is temperature, ν0 is the NQR frequency at 0 K, αi is the angle between the z axis of the EFG tensor and the principal axes of the moment of inertia tensor, Ai is the principal moments of inertia tensor, f i is the frequency of torsional vibrations, and the summation runs over three modes of vibrations (i = x, y, z). A simplified version of this equation, the so-called two-mode approximation,12 consists only of two leading terms and thus is numerically convenient and widely used.25,26 In molecular crystals, when a linear temperature dependence of the frequencies of torsional vibrations is assumed, the threemode (i = x, y, z) quasiharmonic model can be rewritten as

35

⎛ 3 2 ⎞⎟ ν(T ) = ν0⎜1 − θ ⎝ ⎠ 2

∑

(3) 10346

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X-ray. X-ray structural studies of lasamide were performed at room temperature (RT) using an Xcalibur R single crystal diffractometer from Oxford Diffraction. Monochromated CuKα radiation was applied in experiments. A monocrystal of the studied compound was mounted on the goniometer, and reflections were collected up to a Bragg angle of 2θ ≤ 140°. The intensities of the reflections were corrected for Lorenzpolarization effects and for absorption and extinction. Structure was solved using direct methods from the SHELXS-98 program27 and then refined by application of SHELXL-98 software.28 The crystallographic data are given in Tables 1 and 2,

Table 2 (a) Atomic Coordinates (× 104) and Equivalent Isotropic Displacement Parameters (Å2 × 103) for La02-1absa x

Table 1. Crystal Data and Structure Refinement for La02-1abs identification code empirical formula formula weight temperature wavelength crystal system space group unit cell dimensions

volume Z density (calculated) absorption coefficient F(000) crystal size θ range for data collection index ranges reflections collected independent reflections completeness to θ = 70.96° absorption correction max. and min. transmission refinement method data/restraints/parameters goodness-of-fit on F2 final R indices [I > 2σ(I)] R indices (all data) extinction coefficient largest diff. peak and hole deposit no.

y

z

U(eq)

S(1) −290(1) −2384(1) 971(1) 31(1) Cl(1) −4124(1) −3286(1) 974(1) 51(1) Cl(2) −8895(1) 2197(1) 4309(1) 40(1) O(1) −144(2) −2689(2) −646(2) 40(1) O(2) 916(2) −1571(2) 1274(2) 45(1) O(3) −6609(2) 4337(2) 4408(2) 57(1) O(4) −3423(2) 3032(2) 4239(2) 52(1) N(1) 90(3) −4208(2) 1974(2) 45(1) C(1) −2749(2) −1033(2) 1809(2) 29(1) C(2) −4375(3) −1439(2) 1824(2) 33(1) C(3) −6246(3) −381(2) 2557(2) 35(1) C(4) −6509(2) 1078(2) 3298(2) 30(1) C(5) −4914(3) 1541(2) 3282(2) 29(1) C(6) −3045(3) 454(2) 2523(2) 30(1) C(7) −5056(3) 3096(2) 4040(2) 33(1) (b) Anisotropic Displacement Parameters (Å2 × 103) for La02-1absb

la02−1abs C7H5Cl2NO4S 270.08 293(2) K 1.54178 Å triclinic P-1 a = 7.5984(3) Å, α= 81.212(3)° b = 8.3158(3) Å, β = 73.799(3)° c = 8.6892(3) Å, γ = 67.599(3)° 486.79(3) Å3 2 1.843 Mg/m3 8.000 mm−1 272 0.4005 × 0.3056 × 0.1172 mm3 5.31 to 70.96° −9 ≤ h ≤ 9, −10 ≤ k ≤ 10, −9 ≤ l ≤ 10 8818 1855 [R(int) = 0.0291] 98.6% analytical 0.480 and 0.152 full-matrix least-squares on F2 1855/0/146 1.085 R1 = 0.0306, wR2 = 0.0877 R1 = 0.0311, wR2 = 0.0882 0.0171(16) 0.468 and −0.341 e·Å−3 CCDC 873842

U11

U22

U33

U23

U13

U12

S(1) 30(1) 26(1) 39(1) −14(1) −6(1) −8(1) Cl(1) 44(1) 41(1) 76(1) −30(1) −10(1) −18(1) Cl(2) 28(1) 42(1) 47(1) −13(1) −6(1) −7(1) O(1) 45(1) 36(1) 38(1) −13(1) −4(1) −14(1) O(2) 32(1) 40(1) 66(1) −24(1) −10(1) −12(1) O(3) 36(1) 39(1) 98(1) −38(1) −11(1) −5(1) O(4) 39(1) 40(1) 84(1) −32(1) −18(1) −9(1) N(1) 60(1) 27(1) 49(1) −10(1) −23(1) −7(1) C(1) 29(1) 25(1) 34(1) −9(1) −6(1) −8(1) C(2) 35(1) 28(1) 40(1) −11(1) −10(1) −12(1) C(3) 32(1) 35(1) 43(1) −8(1) −12(1) −14(1) C(4) 27(1) 30(1) 33(1) −6(1) −8(1) −7(1) C(5) 31(1) 24(1) 32(1) −7(1) −8(1) −9(1) C(6) 29(1) 27(1) 36(1) −8(1) −8(1) −11(1) C(7) 33(1) 28(1) 38(1) −11(1) −5(1) −9(1) (c) Hydrogen Coordinates (× 104) and Isotropic Displacement Parameters (Å2 × 10 3) for La02-1abs x H(4) H(1A) H(1B) H(3) H(6)

and the crystal packing of lasamide is shown in Figure 2. The structure has been deposited with Cambridge Structural Data Centre. The respective deposit number is shown in Table 1. DFT Calculations. Quantum chemical calculations were carried out within the GAUSSIAN03 code29 run on the CRAY supercomputer at the Supercomputer and Network Centre (PCSS) in Poznań, Poland. All calculations were performed within the Density Functional Theory (DFT) with the exchangecorrelation hybrid functional B3LYP (three-parameter exchange functional of Becke B330 combined with the Lee−Yang−Parr correlation functional LYP31) using the extended basis sets with polarization and diffuse functions 6-311++G(d,p). The components of the second-rank symmetric tensor of the EFG, qii (i = x, y, and z) obtained at the 6-311++G(d,p) level of theory, assuming the X-ray structures were used to calculate the principal components and axes orientations of the EFG tensor as well as the NQR parameters: nuclear quadrupole coupling constant

y

z

−3470(40) 3820(40) 4550(40) −100(40) −4990(40) 1620(30) 310(40) −4290(40) 2830(40) −7324 −652 2551 −1967 740 2497 (d) Hydrogen Bonds for La02-1abs [Å and °]

U(eq) 62 54 54 42 36

D−H···Ac

d(D-H)

d(H···A)

d(D···A)

∠(DHA)

N(1)-H(1A)···O(1)#1 C(3)−H(3)···O(2)#2 O(4)−H(4)···O(3)#3 N(1)-H(1B)···Cl(2)#4 N(1)-H(1B)···Cl(2)#5

0.84(3) 0.93 0.73(3) 0.80(3) 0.80(3)

2.15(3) 2.34 1.93(3) 2.91(3) 2.96(3)

2.965(2) 3.190(2) 2.648(2) 3.3028(19) 3.593(2)

166(3) 152.0 171(3) 113(2) 138(2)

a

U(eq) is defined as one third of the trace of the orthogonalized Uij tensor. bThe anisotropic displacement factor exponent takes the form: −2π2[h2a*2U11 + ... + 2hka*b* U12]. cSymmetry transformations used to generate equivalent atoms: #1 −x, −y−1, −z; #2 x−1, y, z; #3 −x−1, −y+1, −z+1; #4 x+1, y−1, z; #5 −x−1, −y, −z+1.

(e2Qqh−1), asymmetry parameter (η), and NQR frequency (v). A nuclear quadrupole moment for 35Cl equal to −8.165 fm2 was assumed.32 The vibrational frequencies and the infrared and Raman intensities were calculated after a very tight optimization of the geometry and scaled uniformly by a factor of 0.958, as 10347



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Figure 2. The crystal packing of lasamide.

proposed.33 The starting point for the geometry optimization was the experimental geometry. The harmonic vibrational frequencies and IR intensities were calculated from the elements of the force-constant matrix calculated under assumption of the equilibrium configuration (the gradient of the electronic energy with respect to nuclear coordinates vanishes). IR and Raman spectra were simulated using calculated intensities and fwhm assumed to be 30 cm−1 for each peak. A theoretical analysis of intermolecular interactions was performed within the Bader’s quantum theory of atoms in molecules (QTAIM).34 Within this approach, the net atomic charges were obtained by the integration of the charge distribution within properly defined atomic basins. Additionally, the electron density ρ(r) of a molecule treated as a scalar field was examined by analysis of its gradient vector field. Depending on the nature of the extremes (maxima, saddle points, or minima in the electron density) they are named as core-, bond-, ring-, and cage- critical points and denoted as NACP (nuclear attractor critical point) local maximum of electron density; BCP (bond critical point) minimum in the direction of the nucleus, but it is a maximum in another main direction; RCP (ring critical point) - minimum in two principal axes, and CCP (cage critical point) - local minimum of electron density, respectively. The kind of the extreme was determined with the help of a Hessian matrix composed of nine second-order derivatives of ρ(r). The Poincare−Hopf relationship35 was used as a consistency check. At each extreme point, the topological parametersthe electron density and its Laplacianwere calculated. In addition, the ellipticity of the bond, ε, the total electron energy density at BCP (HBCP), and its componentsthe local kinetic energy density (GBCP) and the local potential energy density (VBCP)and

hydrogen bonding energy EE according to Espinosa (EE = (1/2) VBCP)36 were calculated at each BCP.

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RESULTS AND DISCUSSION

Structure. The 35Cl-NQR spectrum of lasamide at 77 K reveals two Voight-shaped (convolution of Lorentzian and Gaussian) resonance lines at frequencies of 36.899 and 37.129 MHz at 77 K and 36.523 and 36.701 MHz at RT of noticeably different intensities, Figure 3. The presence of the two 35Cl-NQR resonance lines, one for each chemically inequivalent site in a molecule, suggests the lack of inequivalent molecules in the unit

Figure 3. The experimental 35Cl-NQR spectrum of lasamide obtained at RT by the solid echo technique (solid line: fit with Voight curve; correlation coefficient: 0.994). 10348



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Additionally, both chlorine atoms participate in weak intermolecular contacts: Cl(1) in N···Cl (RN(1)···Cl(1) = 3.561 Å) and three O···Cl (intramolecular: RO(1)···Cl(1) = 3.151 Å and intermolecular: RO(1′)···Cl(1) = 3.647 Å and RO(2′)···Cl(1) = 3.432 Å) and Cl(2) in three O···Cl (intermolecular: RO(3″)···Cl(2) = 3.546 Å, RO(4′)···Cl(2) = 3.257 Å; intramolecular: RCl(2)···O(3) = 2.946 Å), which binds Cl(1) with nitrogen and oxygen atoms from the sulphonamide group and Cl(2) with oxygen atoms from the carboxyl group. The electron densities at BCP, ρBCP(r), are 0.0049 au for N···Cl and 0.011, 0.037, and 0.0052 au for O···Cl (O(1)···Cl(1), O(1′)···Cl(1), and O(2)···Cl(1), respectively) while 0.0028, 0.0058, and 0.0138, a.u. for O···Cl (O(3″)···Cl(2), O(4′)···Cl(2), and O(3)···Cl(2), respectively), markedly lower than for the covalent bonds. The corresponding Laplacian values, Δρ, are positive and amount to 0.0161, 0.0403, 0.0138, and 0.0197 for N···Cl, O(1)···Cl(1), O(1′)···Cl(1), and O(2)···Cl(1), respectively, and 0.0128, 0.0231, and 0.0128 au for O(3″)···Cl(2), O(4′)···Cl(2), and Cl(2)···O(3), respectively. All contacts can be classified as pure closed shell, ρBCP > 0, ΔρBCP > 0, and |VBCP|/GBCP ≤ 1 (Table 3). The adjacent supramolecular synthons are linked into ribbons by two weak and long hydrogen bonds N(1)−H(1A)···O(1′) (RN(1)‑H(1A)···O(1′) = 2.965 Å and ∠NHO = 166.4°) determining the plane almost perpendicular (deviation is only 2°) to that with both carboxyl groups. The conformation of sulphonamide group with one SO bond lying in the plane of the benzene ring, while the orientation of the other one, making 128° with this plane, is close to that in 2-chlorobenzene-sulphonamide.42 The ribbons are linked by two O(3′)···Cl(2) and O(3″)···Cl(2) contacts (RO(3′)···Cl(2) = 2.946 Å and RO(3″)···Cl(2) = 3.546 Å) determining the plane slightly unparallel (deviation is 19°) to that with both carboxyl groups. As follows from a comparative analysis of BCPs and RCPs, two intermolecular N(1)H(1A)···O(1) hydrogen bonds and three interatomic contacts, O(1)···Cl(1), O(1′)···Cl(1), and N(1)···Cl(1), link the molecules in dimer only slightly weaker than two O(3)-H···O(4‴) hydrogen bonds; however, the O(3)−H···O(4‴) bond is much stronger than the N(1)−H(1A)···O(1) (Table 3). It is worth noting that the energies of interactions calculated using B3LYP/6-311++G** and atom−atom pair potentials (Table 3) are quite well correlated for dimers linked by O−H···O (−30 versus −25.8 kJ/mol), but distinct for dimers linked by N−H···O (−29 versus −41 kJ/mol). The large differences in the strength of the hydrogen bonds O−H···O and N−H···O (−30 versus −13 kJ/ mol) suggest the interplay between different hydrogen bonds in adjacent molecules creating dimers. This factor is responsible for the differences in flexibility of the carboxyl and sulphonamide substituents as well as both C−Cl(1) and C−Cl(2) bonds. The experimentally observed difference in bond lengths C−Cl(1) and C−Cl(2) is relatively small (∼0.002 Å) and only slightly affects the value of 35Cl-NQR frequencies. The relatively high difference in frequencies results mainly from chemical inequivalence of chlorine atoms caused by different electron withdrawing effects of −SO2NH2 and −COOH (at the 5 and 1 positions of the phenyl ring, respectively) and additionally from involvement in different intermolecular interaction patterns. Cl(1) in the p-position relative to the carboxyl group in the benzene ring forces the conformation of the sulphonamide group via S···O van der Waals contact of length 3.4 Å, while Cl(2) in the o-position links molecules in layers via intermolecular van der Waals N···Cl and Cl···O contacts. The assignment of two NQR frequencies to chlorine atoms, the one of the higher frequency to

cell. Indeed, as follows from the X-ray data collected at RT (Table 1), lasamide crystallizes with the P-1 space group, Z = 2, with cell parameters a = 7.5984(3) Å, b = 8.3158(3) Å, c = 8.6892(3) Å; α = 81.212(3)°, β = 73.799(3)°, anf γ = 67.599(3)°. In general, the hierarchy of structures in the crystals of lasamide (dimers-ribbons-layers) is reflected by the progressively weaker bonds. Thanks to the presence of carboxyl groups, lasamide forms symmetric dimers linked by two centrosymmetry-related intermolecular hydrogen bonds O−H···O (Figure 2, Table 2). A structural unit formed by these H-bonds can be termed supramolecular synthon.37 The bonds in the structural unit are short and linear (O−H···O = 2.648 Å and ∠OHO = 171.5°), similarly to those in FSE.13 Two intermolecular hydrogen bonds O−H···O should facilitate a concerted proton transfer, typical of the benzoic acids family, actually observed by 1H NMR in both compounds and widely discussed previously.20,38 As the carboxyl group is not coplanar with the benzene ring (∠CCCO angle = 18.2°), thus the plane with both OH···O bonds is also not coplanar with the plane containing benzene rings from adjacent molecules. Apart from O−H···O hydrogen bonds, the crystalline structure of lasamide contains a variety of intermolecular interactions including hydrogen bonds N−H···O, C−H···O, and N−H···Cl along with O···Cl and N···Cl contacts involving non-H atoms, which were revealed and described within the QTAIM approach (Table 3, Figure 4a). The values of electron densities at BCP, ρBCP(r), are 0.0260, 0.0145, and 0.0098 au for O−H···O, N−H···O, and C−H···O, respectively (typical range 0.001−0.035 au). The corresponding Laplacian values ΔρBCP(O−H···O), ΔρBCP(N−H···O), and ΔρBCP(C−H···O) are positive and reach 0.120, 0.066, and 0.041 au, respectively (a range typical of a hydrogen bond is 0.006−0.130 au). The ellipticity of O−H···O, N−H···O, and C−H···O bonds is 0.040, 0.166, and 0.006 au. The Koch and Popelier’s39 topological criteria required for HB allow their classification as hydrogen bonds. Recently, Espinosa40 proposed a classification of three kinds of atomic interactions: pure closed shell [CS, region I, ΔρBCP > 0, HBCP > 0], pure shared shell [SS, region III, ΔρBCP < 0, HBCP < 0], and transit closed shell [CS, region II, ΔρBCP > 0, HBCP < 0]. Very small values of ρ(r), small and positive values of Laplacian, relatively high values of ε, and nearly zero values of HBCP and values of |VBCP|/GBCP ≤ 1 classify O−H···O, N−H···O, and C−H···O interactions as the pure closed-shell (CS region I). Inside region I (pure CS), the bond degree parameter HBCP/ρBCP (Table 3a) indicates a softening degree (SD) per electrondensity unit at the BCP; the higher HBCP/ρBCP, the weaker the interaction and the greater the SD magnitude. It is worth noting that for O−H···O bonds, the H···O distance is 1.923 Å; for N−H···O bonds the H···O distance is 2.148 Å, and both are much shorter than 2.2 Å (Table 3) thus within the classification proposed by Jeffrey,41 the first two are considered to be moderate and partially covalent. For C−H···O and N−H···Cl bonds, the H···O and H···Cl distances are 2.339 and 2.910−2.970 Å; thus within the classification proposed by Jeffrey these bonds are weak and mainly electrostatic. The Laplacian ΔρBCP recovers the shell structure of atoms and allows tracing the effects of chemical bonding in the total charge density. The relief map of the Laplacian of electron density in the plane of intermolecular H-bonds for lasamide (Figure 4b) clearly exhibits maxima in the negative Laplacian on either side of the oxygen, nitrogen, and chlorine atoms, corresponding to the lone pair model. Moreover, they show the polarization of the oxygen/nitrogen lone-pair electrons toward hydrogen and differences in the polarization of the oxygen/nitrogen lone-pairs. 10349


R (X−H···Y) [Å]

R(Y···H) [Å]

R (X−H) [Å]

ρBCP [a.u.]

Δ(ρ BCP) [a.u.] ε [−] VBCP [H]

GBCP [H]

HBCP [H]

|VBCP/GBCP| [-] EE [kJ/mol] HBCP/ρBCP [H/e]

E Ca [kJ/mol]

aggregation

10350

a

0.0222 0.0064 0.0029 0.0010

Calculated according to ref 54.

ρ [a.u.]

ring critical point

C(1)−C(2)C(3)−C(4)−C(5)-C(6) C(7)−O(3)−H(4′)−O(4′)−C(7′)−O(3′)−H(4)−O(4) S(1)−O(1)−H(1A′)−N(1′)−S(1′)−O(1′)−N(1)−H(1A) Cl(2)O(3)Cl(2′)O(3′)

0.1608 0.0257 0.0145 0.0034

Δ(ρ) [a.u.]

−0.0251 −0.0047 −0.0020 −0.0004

VBCP [a.u.]

GBCP [a.u.] 0.0326 0.0056 0.0028 0.0006

HBCP [a.u.] 0.0076 0.0008 0.0008 0.0002

O(4′)···Cl(2) 3.257 0.0058 0.0231 0.1488 −0.0035 0.0047 0.0011 0.760 0.190 O(3″)···Cl(2) 3.546 0.0028 0.0128 0.2502 −0.0016 0.0024 0.0008 0.675 0.286 −5.7 O(3)···Cl(2) 2.946 0.0142 0.0535 0.0448 −0.0102 0.0118 0.0016 0.868 0.113 O(3)−H···O(4‴) 2.648 1.923 0.731 0.0260 0.1203 0.0398 −0.0231 0.0266 0.0035 0.869 −30.32 0.135 −25.8 dimer C(3)−H(3)···O(2) 3.190 2.339 0.930 0.0098 0.0405 0.0065 −0.0060 0.0080 0.0021 0.741 −7.88 0.214 −13.0 ribbon O(2)···Cl(1) 3.432 0.0052 0.0197 0.0616 −0.0030 0.0040 0.0010 0.760 0.192 ribbon O(1)···Cl(1) 3.151 0.0111 0.0403 5.3467 −0.0076 0.0088 0.0013 0.858 0.117 −41.0 dimer O(1′)···Cl(1) 3.647 0.0037 0.0138 0.1874 −0.0019 0.0027 0.0008 0.721 0.216 N(1)···Cl(1) 3.561 0.0049 0.0161 0.1025 −0.0025 0.0032 0.0008 0.757 0.163 N(1)H(1A)···O(1) 2.965 2.148 0.834 0.0145 0.0656 0.1167 −0.0101 0.0132 0.0032 0.761 −13.26 0.221 N(1)H(1B)···Cl(2′v) 3.303 2.910 0.800 0.0065 0.0276 0.4568 −0.0036 0.0052 0.0017 0.692 −4.73 0.262 −62.0 layer N(1)H(1B)···Cl(2v) 3.593 2.960 0.800 0.0046 0.0173 0.2202 −0.0023 0.0033 0.0010 0.697 −3.02 0.217 N(1)H(1B)···O 3.476 2.817 0.749 0.0039 0.0152 0.1905 −0.0024 0.0031 0.0007 0.774 −3.15 0.179 N(1)···O(2 v) 3.516 0.0032 0.0117 0.2495 −0.0019 0.0024 0.0005 0.792 0.156 Cl(2)···C(1 v) 3.542 0.0052 0.0162 0.5786 −0.0023 0.0032 0.0008 0.719 0.154 Cl(2)···O(3 v) 3.291 0.0053 0.0168 0.2193 −0.0029 0.0035 0.0007 0.829 0.132 C(4)···C(5 v) 3.573 0.0047 0.0129 2.7830 −0.0022 0.0027 0.0005 0.815 0.106 Cl(2)···O(3 v) 3.751 0.0035 0.0116 1.6634 −0.0017 0.0023 0.0006 0.739 0.171 (b) Topological Parameters of Electron Density for Lasamide (Selected RCPs): The Electron Density at RCP (ρ), Its Laplacian Δ(ρ), the Potential Electron Energy Density (VRCP), the Kinetic Electron Energy Density (GRCP), and the Total Electron Energy Density (HRCP) Calculated at the B3LYP/6-311++G(d,p) Level of Theory

bond critical point

(a) Topological Parameters of Electron Density for Lasamide (all BCPs): The Electron Density at BCP (ρ), Its Laplacian Δ(ρ), the Potential Electron Energy Density (VBCP), the Kinetic Electron Energy Density (GBCP), and the Total Electron Energy Density (HBCP), Bond Degree (HBCP/ρBCP), and Energy of Interactions (EE) Calculated at the B3LYP/6-311++G(d,p) Level of Theory; The Energy of Interactions Estimated within the Atom−Atom Pair-Potentials Approach (EC)

Table 3.

The Journal of Physical Chemistry A Article



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Figure 4. (a) Molecular graph of lasamide. Solid and dashed lines indicate the covalent bonds and interactions, respectively; large circles correspond to attractors, small ones correspond to critical points (red - RCP, green - BCP, blue - CCP). (b) Laplacian contour map of the hydrogen bond interactions (left) and atomic contacts (right) in lasamide (negative regions in red, positive regions in blue, neutral regions in green).

Table 4. The experimental and calculated by B3LYP/6-311++G** NQR frequencies, quadrupole coupling constants (QCC) and asymmetry parameters (η) for lasamide calculated B3LYP/6-311++G** ν [MHz], e2qQ/h [MHz], η [−] experimental ν [MHz]

X-ray

optimized

site

77 [K]

RT

monomer

dimer O−H···O

dimer N−H···O

tetramer O−H···O

monomer

dimer O−H···O

dimer N−H···O

Cl(2)

37.129

36.701

Cl(1)

36.899

36.523

36.618 72.869 0.233 35.314 70.628 0.174

36.720 72.795 0.231 35.522 70.679 0.176

36.776 72.885 0.235 35.781 71.205 0.174

36.786 72.859 0.243 35.546 70.732 0.175

37.276 73.880 0.221 35.957 71.639 0.146

36.684 72.680 0.234 35.846 71.380 0.152

36.332 72.663 0.239 35.855 71.709 0.162

B3LYP/6-311++G(d,p) computations performed assuming the monomer and tetramer constructed on the basis of crystalline structure (Table 4). The lower frequency assigned to Cl(1) in lasamide is underestimated, while the higher frequency assigned to the Cl(2) site in lasamide and those for 1,3-dichlorobenzene are well reproduced. The asymmetry parameters for both sites are clearly distinct (0.145 for Cl(1) versus 0.243 for Cl(2)) and

Cl(2) (RC−Cl(2) = 1.732 Å) and the one of the lower frequency to Cl(1) (RC−Cl(1) = 1.728 Å), was made on the basis of a comparison with the experimental data for 4-chlorobenzoic acid,43 2-chlorobenzoic acid,44 2,4-dichlorobenzoic acid,45,46 2-chlorobenzenesulphonamide,47 4-chlorobenzene-sulphonamide,48 monochlorobenzene,43,49 1,3-dichlorobenzene43 and furosemide.50 The above assignment was also confirmed by 10351



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are listed in Table 5. It is evident that neither the main axes of librations nor translations are parallel to the z-axis of the EFG tensor. The MSAD of the principal z-axis of EFG in this direction evaluated from the L tensor using eq 7 with L is 0.0059 rad2 and 0.0018 rad2 (i.e., 19.5°2 and 5.9°2) for Cl(1) and Cl(2), respectively. The averaged value is 0.0035 rad2 (i.e., 11.5°2). The MSAD of the EFG z-axis evaluated from the translation tensor calculated using eq 7 with T is 0.0274 Å2 and 0.0269 Å2 for Cl(1) and Cl(2), respectively. The normal-mode frequencies calculated assuming that the observed T,L,S, which reflect the potential around the molecule, were correctly approximated within the TLS formalism and are 29.1, 30.5, 34.9, 36.7, 47.9, and 63.9 cm−1. Detailed inspection of the matrix of ΔA,B at RT (Table 5) revealed the relatively rigid parts of the molecule and indicated the motion of N(1) relative to Cl(1) and carbon atoms in the benzene ring due to −NH2 jumps (indeed revealed in 1H NMR studies) and the motion of Cl(2) relative to O(3) and O(4), which in fact describe torsions of the −COOH group about 3.9° relative to the benzene ring (unrevealed in 1H NMR studies).20 However, the presence of −COOH torsions in structurally related unsubstituted benzoic acid has been recently reported in IR studies.51

relatively high in comparison to those for 1,3-dichlorobenzene (0.097), which suggests the important role of intermolecular interactions, as well as those linking molecules from neighboring layers or dynamical effects. Additionally, 35Cl-NQR resonance lines differ in shape, line width, and integral intensity not only at RT but in the whole 77−300 K temperature range. The much higher temperature variations in full width at half-maximum (FWHM) for Cl(1) than Cl(2) and different slope of ν(T) (Figure 5) dependence indicate the different flexibilities of both C−Cl bonds.

■

MOLECULAR DYNAMICS The temperature variation of NQR frequencies and line shape in the range 77−300 K is shown in Figure 5. The number of resonance lines was constant, and the integral intensity ratio of both NQR resonance lines was approximately constant in the whole range 77−300 K. The smooth and slow decrease in 35 Cl-NQR frequencies with increasing temperature from 77 to 300 K (Figure 5) confirms no phase transition during the data collection. The global temperature coefficients 1/νQ(dνQ/dT) take the mean values of −4.546 × 10−5 1/K and −4.807 × 10−5 1/K for the chlorine atoms at Cl(2) and Cl(1), respectively. In general, they indicate the close character of temperature variations, i.e., quite similar temperature sensitivity of both sites. Negative temperature coefficient of NQR frequencies suggests that the averaging effect on the EFG results mainly from small amplitude torsional oscillations and can be interpreted within the Bayer-Kushida or the Brown model. The plots in Figure 5 present the result of the fit with eqs 1 and 6, while Table 6 lists the values of the physical parameters obtained from this fit. The correlation coefficient and standard deviation are close and thus not much helpful in choosing the best model. Much more adequate criterion is a comparison of physical parameters, the moment of inertia, and frequency of torsional vibrations, with the expected values. The principal values of the moment of inertia tensor calculated on the basis of the X-ray structure of lasamide are Ixx = 1205 × 10−47, Iyy= 2776 × 10−47, and Izz = 2231 × 10−47 kgm2, while the angles that the principal axes make with the z-axis of the EFG tensor are 26.5°, 64.2°, and 95.6° and 40.5°, 49.5°, and 90.9° for Cl(2) and Cl(1), respectively. It is evident that the principal axes of the moment of the inertia tensors and the EFG tensor do not coincide at the Cl(2) and Cl(1) sites, and thus the effective moment of inertia is lower. However, even under this assumption, the moment of inertia obtained from the fit is highly underestimated. The frequencies of ultralow modes of torsional vibrations, which should be typically about 40−60 cm−1 are overestimated (Table 6). Such a discrepancy suggests that the simple Bray model is unsatisfactory. Moreover, in the high temperature limit according to the Bayer model, ν should be a

Figure 5. The temperature variation of the experimentally measured temperature variation 35Cl-NQR frequency for lasamide in the range 77−300 K.

This observation is also supported by the refined equivalent isotropic displacement parameters 0.051 and 0.040 Å2 at RT for Cl(1) and Cl(2), respectively. Typically, thermal ellipsoids for heavy atoms are nearly spherical, but for lasamide, the anisotropy at chlorine sites is relatively high: the asymmetry parameter of the U tensor is 0.67 and 0.49 for Cl(1) and Cl(2), respectively, or, using the ratio of minimum and maximum eigenvalues of U, 0.35 and 0.12 for Cl(1) and Cl(2), respectively. This makes a clear indication about the different degrees of anisotropy of thermal motions, which should result in more or less differing degrees of averaging of EFG tensors at each chlorine site in the whole temperature range. The MSDs in the direction of the principal z-axis of the EFG tensor can be calculated according to the formula

θ 2 = nT Un

(7)

where n is the vector describing the direction. The MSD values (in the Cartesian coordinate system) are 0.0190 and 0.0271 Å2 for Cl(1) and Cl(2), respectively. The MSD of carbon atoms C(2) and C(4), bonded to chlorine atoms Cl(1) and Cl(2), respectively, are 0.0195 and 0.0266 Å2. The mean square angular displacement (MSAD) of the principal z-axis of the EFG tensor calculated using eq 7 is 0.0040 and 0.0012 Å2 for Cl(1) and Cl(2), respectively. Small R factor justifies assuming the lasamide molecule as a rigid body undergoing translation/libration/screw (TLS) vibrational motion. The tensor components are L, T, and S; eigenvectors and eigenvalues of L and T expressed in the Cartesian crystal system calculated according to the THMA formalism4 as well as the angles between eigenvectors of L or T and principal z-axis of EFG tensor 10352



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Table 5. (a) The Components of T,L,S Tensors for La02-1abs L

T 2

2

L11 L12 L13 L22 L23 L33

[rad ]

[° ]

0.00206 (0.00027) −0.00211 (0.00016) −0.00120 (0.00011) 0.00520 (0.00034) 0.00290 (0.00022) 0.00290 (0.00016)

6.777 (0.877) −6.922 (0.510) −3.936 (0.356) 17.082 (1.128) 9.532 (0.712) 9.528 (0.517)

S 2

[Å ] T11 T12 T13 T22 T23 T33

[rad Å]

0.05064 (0.00184) −0.00960 (0.00111) 0.02302 (0.00210) 0.03183 (0.00153) −0.01477 (0.00133) 0.05657 (0.00264)

S11 S12 S13 S21 S22 S23 S31 S32 S33

0.00398 (0.00036) 0.00144 (0.00061) 0.00390 (0.00057) −0.01107 (0.00073) 0.00331 (0.00047) −0.01224 (0.00100) −0.00591 (0.00050) 0.00363 (0.00041) −0.00729 (0.00063)

(b) The ΔAB Matrix of 104·MSD for La02-1abs atom S(1) Cl(1) Cl(2) O(1) O(2) O(3) O(4) N(1) C(1) C(2) C(3) C(4) C(5) C(6)

C(7) 34 34 −23 −28 −55 −2 7 −30 18 29 5 −22 16 −17

C(6) 51 26 18 0 −34 17 −8 −10 15 10 5 14 3

C(5) 34 18 24 −30 −35 −1 10 −62 18 13 4 0

C(4) 2 26 −4 −63 −58 40 28 −141 0 −1 −2

C(3) 40 52 50 −16 −13 33 0 −131 13 12

C(2) 52 6 21 −11 25 −10 −20 −100 3

C(1)

N(1)

O(4)

O(3)

O(2)

O(1)

Cl(2)

Cl(1)

3 30 −4 −42 −13 −19 −18 −60

5 40 154 −5 7 44 −15

75 27 −3 50 7 9

37 16 −45 3 −43

4 −32 58 −7

18 −27 65

7 5

42

g factor estimated from this model (Table 6) indicates that anharmonicity and temperature variations of torsional vibration are not negligible. The opposite approach allows the use of the simple Bayer’s model for determination of the anharmonicity of vibrations. The temperature variation of the frequencies of torsional vibrations of the two modes calculated from eq 4 treated as an implicit nonlinear equation, with f i(T) as variables for both chlorine atoms, is shown in Figure 6. The solid lines in this figure were plotted using f i(T) = f i(0)(1 − giT), where f i(0) and gi are parameters from the fit. In general, the variation of torsional frequencies for Cl(2) is smaller than for Cl(1) and less far from linear, especially in the low temperature range. Additionally, the discrepancy between two modes of vibrations for Cl(1) is significantly larger than that for Cl(2), which reflects the higher rigidity of the Cl(2) bond. This is a consequence of two factors: participation in stronger van der Waals interactions and different rigidity of both substituents −COOH and −SO2NH2. Cl(2) participates in a longer bond than Cl(1), but, in contrast to Cl(1), it is strongly bonded by two hydrogen bonds, which is reflected by half the MSAD of the z-axis of the EFG tensor from its equilibrium position for Cl(2) in comparison to that for Cl(1). The temperature variation of the mode corresponding to the motion about the axis perpendicular to the benzene ring, f YY, is smaller than the mode corresponding to the motion about the axis in the plane of the ring making an angle of 114° with the C− Cl bond, f XX. This is a consequence of the intermolecular interactions pattern: contacts linking Cl(2) lying in plane of the benzene ring, and hydrogen bond lying out of this plane. In general, the decrease in vibration frequencies indicates a reduction in the strength of interactions between atoms and

linear function of T: ⎞ ⎛ 3k ⎟⎟ ν(T → ∞) = ν0⎜⎜1 − T 2π 2A TfT 2 ⎠ ⎝

(8)

while in a low temperature limit it should be constant: ⎛ 3h ⎞⎟ ν(T → 0) = ν0⎜⎜1 − ⎟ 4π 2A TfT ⎠ ⎝

(9)

but in fact the temperature dependence (Figure 5) is a nonlinear function of T in any region, which is clearly indicated by the character of dν/dT shown in the inset. The change in slope of dν(T)/dT observed in the low-temperature region and above 270 K is associated with the onset of an extra motion, which affects the resonant nucleus. Thus it is evident that additional factors contribute to ν(T), e.g., anharmonicity, vibrations with larger frequencies, disorder, or systematic errors. Several anharmonic models (the so-called improved Bayer’s models) using linear or even square temperature dependence of the frequencies of torsional vibrations have been tested. Some results are listed in Table 6. The best fitting results were obtained not only using polynomial-type models but also a mixed model taking into account torsional averaging, excitations of torsional vibrations, and reorientation, but the unphysical parameters of this fit discredit it. The plot in Figure 5 presents the results of the fit for both chlorine sites performed using a modified Tatsuzaki−Yokozawa model (eq 6) and assuming two modes of anharmonic vibrations. The moments of inertia were assumed, and the weights to incorporate measured variation into the fitting were used. The relatively high value of the 10353



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Table 6. The Parameters Obtained from the Fit Using Equations of Different Models site Cl(1)

model a,e

eq 3 eq 5b,e

37.105 37.105

eq 5b,d,e

37.034

eq 6b

37.003

eq 6c

37.011

eq 6c,d

36.961

eq 6b,d

36.992

ν(T) = a−1T−1 + a0+ a1T ν(T) = a0 + a1T + a2T2 ν(T) = a−1T−1 + a0+ a1T + a2T2 ν(T) = a0 + a1T + a2T2 + a3T3 ν(T) = a−1T−1 + a0+ a1T + a2T2 + a3T3 Cl(2) eq 3a,e eq 5b,e

a

a1 10−3 a0 (a) a2 10−6 a3 10− a‑1 [MHz] [MHz/K] [MHz/K2] [MHz/K3] [MHz K] b [MHz]

37.036 36.991 36.838 37.038 36.887 37.271 37.271

eq 5b,d,e

37.432

eq 6b

37.219

eq 6b,d

37.223

eq 6c

37.219

ν(T) = a−1T−1 + a0+ a1T ν(T) = a0 + a1T + a2T2 ν(T) = a−1T−1 + a0+ a1T + a2T2 ν(T) = a0 + a1T + a2T2 + a3T3 ν(T) = a−1T−1 + a0+ a1T + a2T2 + a3T3

37.254 37.217 37.107 37.271 37.584

0.0024 0.0024 0.0024 0.00099 0.00094 0.00017 0.000937 0.000904 0.000217 0.000465 0.000472 0.000595

−1.67 −1.160 −2.403 −2.077 −7.023

−1.303 −2.968 3.956 −1.202

96.36 96.41 96.31 31.55 29.87 32.33 30.61 38.43 38.88 18.73 43.51 39.25 36.23 53.28 50.44

133.94 134.02 133.88 43.86 41.52 44.94 42.54 53.42 54.04 26.04 60.48 54.56 50.36 74.06 70.12

g [−]

0.000402 0 0.0005253 0 0.0003125 0.0269 0.0009 9 × 10−6 0.000401

5.588

0.000371 0.000254 0.000199 −1.400 −0.562 −1.771 5.089 16.401

fT [cm−1]

−7.396 91.988 23.777

0.00327 0.001637 0.001637 0.00091 0.00062 0.000633 0.000442 0.000104

−1.792 −1.526 −0.869 −2.524 −5.453

c [K]

5.517 −99.262 −253.426 −11.572

66.13 66.53 65.72 32.65 23.92 27.09 25.53 29.93 21.99 19.22 31.69 32.68

91.92 92.48 91.36 45.38 33.24 37.66 35.49 41.6 30.6 26.72 44.05 45.43

4 × 10‑.09 0.0004

1 × 10−5 0.00071 0.00058

s [kHz]

r2

4.5 4.7

0.9985 0.9985

6.1

0.9967

3.1

0.9994

3.7

0.9994

1.4

0.9999

3.1

0.9992

6.6 2.9 1.4 1.3 1.2 4.5 4.8

0.9968 0.9994 0.9999 0.9999 0.9999 0.9986 0.9986

1.6

0.9998

4.3

0.9990

3.3

0.9991

4.5

0.9992

4.8 3.2 2.6 2.1 1.6

0.9983 0.9992 0.9995 0.9997 0.9998

One mode. bTwo modes. cThree modes. dMoment of inertia assumed. eNo anharmonicity.

expansion of the molecular crystal of lasamide with increasing temperature. The temperature dependence of both modes revealed the influence of different kinds of effects in three different temperature regions: low T < 150 K (proton transfer region in 1H NMR), middle 150 < T < 270 K, and high T > 270 K (NH2 jumps region in 1H NMR). It is difficult to judge whether the frequencies of vibrations are satisfactorily reproduced because the experimental IR and Raman spectra of lasamide in ultralow wavenumber region are not available. However, the frequencies of vibrations are close to those obtained on the basis of X-ray data and Kushida approximation: 30 and 45 cm−1 for Cl(2) and Cl(1), respectively; Tatsuzaki-Yokozawa derived approximation: 37 and 35, 29 and 40 cm−1 for Cl(1) and Cl(2), respectively; as well as those reported for 2,6-dichlorophenol (38 and 40 cm−1),52 but also close to those obtained within the TLS approach for translations and librations. A single molecule of lasamide has 60 degrees of vibrational freedom: six correspond to external modes of vibrations (three translations and three librations, which the molecule undergoes as a rigid body) and the other 54 correspond

to internal vibrations. A good quality prediction of the frequencies of internal vibrations modes active in Raman and IR spectra have been obtained fully theoretically at the B3LYP/ 6-311++G(d,p) level under the assumption of an optimized molecule of lasamide. The nonplanar structure of the monomer and dimers obtained during optimization is consistent with the X-ray data. The result of structure optimization is very good: RMS error does not exceed 9 × 10−3 Å. However, it should be mentioned that the bond length optimized by DFT is overestimated due to the solid-state effect, but the one measured is underestimated due to the limitations in the determination of proton positions. In fact, the experimental C−H and N−H bond lengths are shorter than optimized (0.93 versus 1.08 Å and 1.013 versus 0.834 Å, respectively). The frequencies of the internal normal modes (harmonic vibrations) cover the range from 28 to 3770 cm−1 (27 to 3573 cm−1 after scaling) (Figure 7a). In dimers, the intramonomer modes are doubled, and additionally six intermonomer modes appear, thus this range is a bit wider 6− 3777 cm−1 (6−3618 cm−1 after scaling) for the −NH2SO2 dimer and 3−3633 cm−1 (3−3423 cm−1 after scaling) for the −COOH 10354



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Figure 7. The experimental/calculated (a) IR and (b) Raman spectra of lasamide (monomer, two kinds of dimers linked by OH···O and NH···O).

2500−2600 cm−1, which is characteristic of carboxyl acids. For monomer and −COOH dimer, a characteristic sharp peak near 3500 cm−1 and 3000 cm−1, respectively, is predicted by DFT. In the IR KBr spectrum of lasamide, the carbonyl stretching frequency assigned to the dimer is found near 1700 cm−1, i.e., it is slightly shifted in comparison to those calculated for monomer and −COOH dimer. Although the N−H stretching band is typically less sensitive to hydrogen bonding than O−H band, in lasamide the presence of the hydrogen bonded dimers linked by primary amine from the sulfamoyl group makes the N−H stretching band unusually strong in the range of 3400 to 3500 cm−1. Strong also are the in-plane NH2 scissoring bands in the range 1550−1650 cm−1 and the out-of-plane wagging in 650− 900 cm−1. In general, the correlation between the experimental IR KBr53 and the theoretically calculated IR spectra is high (Figure 7a). Three ultralow wavenumber modes of internal vibrations 29, 47, and 56 cm−1 (28, 45, 54 cm−1 after scaling) for monomer are close to those obtained within the TLS model (29.1, 30.5, 34.9, 36.7, 47.9, and 63.9 cm−1), which suggests that the internal and external modes of vibrations are not well separated. The lowest mode of 29 cm−1 describes the twisting motion of the carboxyl group, while two modes at 47 and 56 cm−1 are assigned to the in-plane and out-of-plane bending torsional vibrations of the

Figure 6. Temperature variation of (a) ultralow frequency modes (points - implicit solution of eq 2; solid lines - from the fit with eq 6). (b) First derivatives of ultralow frequency modes. (c) Nonlinear contribution to ultralow frequency modes.

dimer. The presence of the hydrogen bonded dimers linked by a carboxyl group in solid lasamide is associated with two characteristic infrared stretching bands in the IR KBr spectrum. The O−H stretching absorption in the 2500−3300 cm−1 range is very strong and broad with small peaks in the range 10355



Article

sulphonamide group (τCCSO, τCCSN). In dimers, the ultralow wavenumber modes of internal vibrations are downshifted in comparison to the monomer and additional intermonomer modes, which come from butterfly motions, intermonomer torsions, tilting, and displacements appear in low-frequency part of IR or Raman spectra (Figure 7b). The ultralow frequency part of the IR/Raman spectra consist of 3, 10, and 12 modes for the monomer and −NH2SO2 and −COOH dimers, respectively. The temperature variation of MSAD of the z-axis of the EFG tensor can be derived from eq 1, which can be rewritten in a simple form: ⎛ 3 ν(T ) = ν0⎜⎜1 − 2 ⎝

∑ i

⎞ θi2 ⎟⎟ ⎠

(10)

where ν0 is the NQR frequency at 0 K and θ is the MSAD of the ith axis of EFG tensor (i = x, y, z) from its equilibrium position being a result of the i-mode of vibrations. The simplified, numerically more convenient version of this equation, the socalled two-mode approximation, was used for the estimation of the temperature variation of MSAD of the z-axis of EFG tensor in two perpendicular directions x and y, which is shown in Figure 8a. Much higher displacements at Cl(1) than at Cl(2) are in a good agreement with those calculated from ADPs at RT. The increase in the mean-square amplitudes of motion with temperature indicates the reduction in the strength of interactions between the atoms, which is a clear indication of crystal expansion. The temperature dependence of MSAD is at first sight linear, but a more detailed investigation of temperature variation of first derivatives (Figure 8b) revealed that ADP's increase is no longer linear with temperature. The division into the three different temperature regionslow T < 150 K, middle 150 K < T < 270 K, and high T > 270 Kis evident. At sufficiently high temperatures, MSAD is a linear function of temperature, i.e., it is well approximated by the harmonic oscillator model, while in low temperatures it extrapolates to higher or lower but negative values at 0 K, which is a clear indication of anharmonicity of vibrations. Both low-frequency modes reach almost purely classical behavior but only in the middle range of temperatures. The disturbances to linearity of the temperature dependence of MSAD and torsional frequencies in the low temperature region are mainly connected with concerted proton transfer OH···O, while those in high temperature are connected with conformational motion −NH2 jumps20 (Figures 6c and 8c). The proton jumps in acid dimers should be manifested by equalization of the lengths of CO and C−O bonds and disorder of hydrogen position or its position between two oxygen atoms. In this structure, the positions of hydrogen atoms from the carbonyl and thioamide groups were refined but not their temperature factors. No dynamical disorder of hydrogen atoms at room temperature was noted, while the CO bond was significantly longer (1.234 Å) than expected (1.226 Å,55) and that of the C−O bond (1.280 Å) is significantly shorter (1.305 Å,55) than expected. The fluctuations of the anharmonic parts of frequencies of torsional vibrations and MSAD are evident (Figures 6c and 8c). The librational motion and the internal motion were considered independent as a first approximation, but it is evident that the internal vibrations are superimposed on the overall librational motion of the molecule. The MSAD and torsional frequencies calculated from the temperature dependence of NQR frequency point to a much faster averaging of EFG tensor in low and high temperatures than expected for a rigid body.

Figure 8. The temperature variation of (a) MSADs and (b) the first derivatives of MSADs (points - implicit solution of eq 2; solid lines from the fit with eq 6).

■

CONCLUSIONS

(1) Lasamide crystallizes in the P-1 space group, with Z = 2 and cell parameters a = 7.5984(3), b = 8.3158(3), c = 8.6892(3) Å; α = 81.212(3), β = 73.799(3), and γ = 67.599(3)°. The anisotropy at chlorine sites is relatively

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(2)

(3)

(4)

(5)

(6)

(7)

(8)

■

high, which makes a clear and valuable indication of the different degrees of anisotropy of thermal vibrations. The difference in C−Cl(1) and C−Cl(2) bond lengths only slightly affects the value of 35Cl-NQR frequencies, which results mainly from chemical inequivalence of chlorine atoms but also involvement in different intermolecular interactions pattern. The underestimation of the lower frequency calculated at the B3LYP/6-311++G(d,p) level and assigned to Cl(1) suggests the important role of intermolecular interactions as well as dynamical effects. The DFT/QTAIM analysis suggests that the interplay between different hydrogen bonds in adjacent molecules making dimers is responsible for the differences in the flexibility of the carboxyl and sulphonamide substituents as well as of both C−Cl(1) and C−Cl(2) bonds. The 35Cl-NQR frequency smoothly and slowly decreases with increasing temperature, which indicates that lasamide in the solid state is stable. No evidence of phase transitions, release of chlorine, or thermal decomposition was detected. A temperature dependence of frequency of ultralow modes of anharmonic small-angle internal torsional vibrations, averaging EFG tensor, and MSADs at both chlorine sites Cl(1) and Cl(2) (para and ortho relative to the carboxyl functional group) from the 35Cl-NQR temperature are revealed. The discrepancy between two modes of vibrations for Cl(1) is significantly greater than for Cl(2), which reflects the higher rigidity of Cl(2) bond. This is related to the influence of two factors: participation in different numbers of intermolecular interactions and the different rigidity of both substituents −COOH and −SO2NH2. Three ultralow wavenumber modes of internal vibrations 29, 47, and 56 cm−1 (28, 45, 54 cm−1 after scaling) for monomer obtained at the B3LYP/6-311+ +G(d,p) level are close to those obtained within the TLS model (29.1, 30.5, 34.9, 36.7, 47.9, and 63.9 cm−1), which suggests that the internal and external modes of vibrations are not well separated. The MSADs derived from the temperature dependence of the 35Cl-NQR frequency are in a good agreement with those estimated from X-ray data with the use of the TLS model. The temperature dependence of energy of both modes revealed the influence of different effects in three different temperature regions: low T < 150 K (proton transfer region in NMR), middle 150 < T < 270 K, and high T > 270 K (NH2 jumps region in NMR). Within the temperature range accessible to the experiment, the low-frequency modes reached mixed behavior. A deviation from the classical behavior near 270 K indicates contributions to MSAD from the onset of the conformational NH2 jumps. The decrease in the torsional frequencies and increase in the mean-square amplitudes of motion with temperature indicate the reduction in the strength of interactions between atoms, which is a clear indication of crystal expansion. A study of a temperature dependence of the 35Cl-NQR frequency seems to be a good source of valuable, although indirect, information about mean atomic displacements and changes in the intermolecular interactions pattern due to thermally induced vibrations or molecular movements.

Article

AUTHOR INFORMATION

Corresponding Author

*Mailing address: Faculty of Physics, Adam Mickiewicz University, 61-614 Poznań, Poland. Tel.: +48-61-8295277. Fax: +48-61-8257758. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS Generous allotment of computer time from the Poznan Supercomputing and Networking Centre (PCSS) in Poznań, Poland is gratefully acknowledged.

■

REFERENCES

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Temperature Variation of Ultralow Frequency Modes and Mean

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