The structure, vibrational spectra and nonlinear optical properties of the l -lysine × tartaric acid complex—Theoretical studies

Spectrochimica Acta Part A 64 (2006) 6–23

The structure, vibrational spectra and nonlinear optical properties of the l-lysine × tartaric acid complex—Theoretical studies M. Drozd ∗ , M.K. Marchewka Institute of Low Temperature and Structure Research of the Polish Academy of Sciences, Ok´olna 2 Str., Wrocław 50-422, Poland Received 22 April 2005; received in revised form 15 June 2005; accepted 21 June 2005

Abstract The room temperature X-ray studies of l-lysine × tartaric acid complex are not unambiguous. The disorder of three atoms of carbon in l-lysine molecule is observed. These X-ray studies are ambiguous. The theoretical geometry study performed by DFT methods explain the most doubts which are connected with crystallographic measurements. The theoretical vibrational frequencies and potential energy distribution (PED) of l-lysine × tartaric acid were calculated by B3LYP method. The calculated frequencies were compared with experimental measured IR spectra. The complete assignment of the bands has been made on the basis of the calculated PED. The restricted Hartee–Fock (RHF) methods were used for calculation of the hyperpolarizability for investigated compound. The theoretical results are compared with experimental value of β. © 2005 Elsevier B.V. All rights reserved. Keywords: l-Lysine; Tartaric acid; DFT; B3LYP; RHF; Time-dependent HF; Nonlinear optics; Hydrogen bond; PED

1. Introduction Due to modern society’s demand for improved telecommunications and data processing, photonics – the use of light to acquire, store, process and transmit data – has become an active field of research. The design of devices that utilize photons instead of electrons in the transmission of information has created a need for new materials with unique optical properties [1]. Of particular interest are materials possessing nonlinear optical (NLO) susceptibility [2]. Molecules with symmetry close to three-fold rotational (oclupolar molecules) can exhibit non-zero β (second-order nonlinear optical coefficient), despite being non-polar [3]. A number of molecules as well as molecular ions of D3h (or C3 or D3 ) symmetry have been shown to display promising properties [4]. In addition to molecules with a two-dimensional character of β, a few 3D octupolar molecules have been investigated, also. ∗

Corresponding author. Tel.: +48 71 343 5021; fax: +48 71 3441029. E-mail address: [email protected] (M. Drozd).

1386-1425/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.saa.2005.06.033

Contemporary trends in investigation of new compounds with NLO properties focus attention on designing of new crystal organic cations and inorganic or organic ions. Among nonlinear optical crystals, organic salts occupy an intermediate position between molecular organic compounds with covalent bonds and inorganic compounds with mainly ionic bonds [5,6]. The salts of protonated amino acids are representatives of an important class of such compound, interest in which has recently increased following the discovery of promising nonlinear optical properties in crystal of l-arginine phosphate monohydrate (LAP) [7–11]. One possible class of organic salts of amino acids is iodates [12]. The iodates [13] of arginine and lysine, bis(hydrogeniodate) of arginine and tris(hydrogeniodate) of lysine has been discovered and display nonlinear optical properties. Some complexes of the amino acids with simple organic and inorganic salts appear to be promising for optical second harmonic generation (SHG). The crystals display interesting physical and chemical properties, exhibiting phase transitions with ferroelectric, antiferroelectric and ferroelastic behavior

M. Drozd, M.K. Marchewka / Spectrochimica Acta Part A 64 (2006) 6–23

as well as phases with commensurate and incommensurate superstructures [14,15]. In this paper, we report the results of theoretical calculations for new molecular complex: l-lysine with tartaric acid (C5 H9 (NH2 )2 COOH × (CH(OH)COOH)2 ; 1:1). This compound exhibits two phase transitions above room temperature connected with disordering of carbon atoms in l-lysine molecule. The existence of commensurate phase is proved. According to X-ray studies, the clear-cut determination of crystallographic structure seems to be very difficult. Our DFT studies focused on theoretical approximation of geometry should be helpful in future X-ray studies. The full potential energy distribution (PED) analysis and assignment of all characteristic bands is performed. Comparison with experimental spectra of adequate crystal was made. This part of work will be helpful in design of new chemical complexes with detailed specific expectations. Furthermore, the time-dependent Hartee–Fock calculation of NLO properties and dipole moments of the investigated complex are performed and discussed with experimental values of β, because l-lysine × tartaric acid crystal belongs to non-cetrosymmetric crystallographic system.

2. Experimental 2.1. Vibrational measurements The FTIR powder spectra were measured as nujol suspensions using a Bruker IFS-88 spectrometer with a resolution 2 cm−1 . The resolution was 2 cm−1 . For elimination of the side lobes that result after truncating the interferogram with a boxcar function the Norton–Beer weak apodization function was used. The samples were put between KBr and NaCl windows. 2.2. X-ray measurements A few samples were examined but all selected crystals were twinned. The crystal was mounted on a KUMA DIFFRACTION single crystal diffractometer equipped with a two-dimensional area CCD detector. The Mo K␣ graphite monochromated radiation and the ω scan with ω = 0.75◦ for one image were used for data collection. The 960 images for six different runs covered 95% of the Ewald sphere. The lattice parameters were calculated for 150 reflections obtained from 30 images for 10 runs with different orientations in reciprocal space. From all collected reflections (number unique 1424) only the ones were selected, which belonged to the single domain (number unique 1006). The cutting of the number of reflections drastically decreased the number of reflections per number of the variables (5), but the crystal structure seems to be determined correctly. It was solved by a direct method and subsequent difference Fourier syntheses SHELXTL PLUS program system [16]. The struc-

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ture refinement by a full matrix least squares method on (Fo2 ) was done using SHELXL97 [17]. Anisotropic thermal displacement parameters were used for all non-hydrogen atoms. The co-ordinates of H-atoms were found from a geometric analysis of the crystal structure. 2.3. Theoretical The optimized equilibrium structure for l-lysine × tartaric acid has been calculated by the DFT/B3LYP RHF method. The 6-311++G(d,p) basis set have been employed. The harmonic frequencies and infrared intensities were calculated by the density functional triply parameter hybrid model (DFT/B3LYP). The 6-311++G(d,p) basis set was used. The normal coordinate analyses have been carried out for l-lysine × tartaric acid according to the procedure described and recommended by Fogarasi and Pulay [18]. The frequencies of NH, OH and CO stretching vibrations involved in hydrogen bond network were scaled by 0.92. This scaling factor is smaller than that recently reported for the A–H stretching force constants [19]. The other harmonic frequencies were scaled by the factor of 0.983 determined in previous studies of similar organic systems [20]. The calculated potential energy distribution for l-lysine × tartaric acid has enabled us to make detailed band assignment in infrared spectra. The nonlinear optical response of an isolated molecule in an electric field Ei (ω) can be presented as a Taylor series expansion of the total dipole moment, µt , induced by the field: µt = µ0 + αij Ei + βijk Ei Ej + · · · where α is the linear polarizability, µ0 the permanent dipole moment and βijk are the first hyperpolarizability tensor components. The NLO response of the material in molecular state can be determined by computation and by measuring it experimentally. The values obtained by different methods may be different, therefore it is necessary to give an exact definition [21]. In this paper, we will consider only the frequency doubling process, i.e., β = β(−2ω, ω, ω), and define in a molecule fixed coordinates: 1
βi = βiii (βikk + βkik + βkki ) 3 ki k

where i = x, y or z  βV = βx2 + βy2 + βz2 For calculation of the first hyperpolarizability by quantum chemical methods at RHF ab initio level of theory with 6311++G(d,p) basis set was chosen. All calculation was performed with the GAMESS [22] program, version from 12 December 2003 (R2) compiled under Linux operating system. This job was executed on PC Cluster consisting of one server node with two 32-bit Intel Xeon processors running at 1.8 GHz and 3 GB RAM, 20 com-

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M. Drozd, M.K. Marchewka / Spectrochimica Acta Part A 64 (2006) 6–23

puting nodes with dual 32-bit Intel Xeon processors running at 2.8 GHz and 2 GB RAM, 9 computing nodes with dual 32-bit Intel Xeon processors running at 1.7 GHz and 1 GB RAM.

3. Results 3.1. Geometry The numbering of atoms and optimized geometrical parameters of l-lysine × tartaric acid are presented in Fig. 1 and Table 1. The hypothetical packing of crystallographic unit cell by molecule of this compound with theoretical geometry is presented in Fig. 2. Figs. 3 and 4 show the geometry of one formal molecule of investigated crystal obtained from

X-ray studies. The experimental values of bonds distances and angles are collected in Table 2. 3.1.1. Tartaric acid molecule According to crystallographic room temperature studies three carbon atoms are disordered. This disorder is observed on the C(4*), C(2*) and C(1*) (symbol (*) indicates the atoms in real molecule) atoms in tartaric acid molecule. The C(5*)–C(41*) and C(5*)–C(42*) bonds are equal to 1.44 ˚ respectively. Similar differences are observed and 1.70 A, for two bonds C(41*)–C(3*) and C(42*)–C(3*) (1.53 and ˚ In the case of C(3*)–C(21*) and C(3*)–C(22*) dis1.29 A). ˚ tances the experimental lengths are equal to 1.44 and 1.59 A, respectively. The other two distances (C(21*)–C(11*) and ˚ It is interC(22*)–C(12*)) are equal, practically (1.59 A). esting that in theoretical calculation performed for this case

Fig. 1. The numbering of atoms in calculated molecule l-lysine with tartaric acid.

M. Drozd, M.K. Marchewka / Spectrochimica Acta Part A 64 (2006) 6–23

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Fig. 2. Hypothetical packing of real X-ray crystal cell by l-lysine × tartaric acid complex.

the C–C distances are very similar. All distances are in the ˚ These results strongly suggest that in real range 1.53–1.54 A. carbon chain of tartaric acid molecule the only tree atoms of carbon (C(41*), C(21*) and C(12*) or C(11*)) should be present. This assumption was made on the basis of analysis of length of carbon–carbon distances. Choosing of shorter experimental bonds seems to be more adequate (in theoretical calculation, the length of distances is longer than in real experiment). According to these results, the disordering of two carbon atoms (C(4*) and C(2*)) can be questionable. Additional analysis of C–N distances reveal that the C(12*)–N(8*) and C(11*)–N(8*) experimental distances are dramatically ˚ respectively). The comparison different (1.53 and 1.45 A, ˚ with theoretical results (C(1)–N(8) length is equal to 1.49 A) suggest strongly that the C(11*)–N(8*) (shorter distance) chemical bond should be realized. On the basis of theoretical approach seems to be clear that C(11*) atom should be present in real structure, only. According to this consideration, the X-ray studies should be revised. The assumption about disorder of three carbon atoms in structure with many of hydrogen bonds with different distances is artificial and may be result of imperfection of measured crystal. For C(5)–N(9) (in real molecule C(5*)–N(9*)) distance, the good agreement between experiment and calculation was noticed. In real crys-

˚ and in DFT approach is a tal, this distance is equal to 1.45 A ˚ little bigger (1.49 A). Other characteristic distances in tartaric acid molecule are C–O distances. In real crystal, these lengths are equal ˚ (C(6*)–O(7*)) and 1.26 A ˚ (C(6*)–O(10*)). These to 1.24 A results suggest strongly that first chemical bond has a character of double chemical bond whereas for second one the single character is expected. These differences in length of two C–O bonds are visible better in DFT approach. In this case, the ˚ than C(6)–O(10) bond (single bond) is much longer (1.34 A) ˚ the C(6)–O(7) distance (double bond) with distance 1.20 A. These differences between experimental and theoretical values are expected. In theoretical approach, the length of single bond (C(6)–O(10) is determinate by interaction between oxygen atom and hydrogen H(24)). In real X-ray experiment, the huge problems with determination of position of this proton are observed. Some problems are noticed when the distances of C–H and N–H are taken into account. The all calculated C–H ˚ In experdistances are very similar and equal to ca. 1.095 A. imental results the differences are observed. These lengths ˚ Comparison of are included in the range of 0.87–1.14 A. experimental and theoretical results confirm that the distances are longer in DFT approach (excepting the C(4*)–H(30*)

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M. Drozd, M.K. Marchewka / Spectrochimica Acta Part A 64 (2006) 6–23

Fig. 3. One formal molecule of investigated crystal (X-ray data). In tartaric acid molecule three carbon atoms (C(4*), C(2*) and C(1*)) are disordered.

Fig. 4. The crystal structure and hydrogen bonds network in investigated crystal (the X-ray experimental data).

M. Drozd, M.K. Marchewka / Spectrochimica Acta Part A 64 (2006) 6–23 Table 1 The calculated distances and angles

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Table 2 The experimental (X-ray) distances and angles

Distance

˚ Value (A)

Angle

Value (◦ )

Distance

˚ Value (A)

Angle

Value (◦ )

C1–C2 C1–H26 C1–H27 C1–N8 C2–C3 C2–H28 C2–H36 C3–C4 C3–H29 C3–H37 C4–C5 C4–H30 C4–H38 C5–C6 C5–H31 C5–N9 C6–O7 C6–O10 C12–C13 C12–O17 C13–C14 C13–H21 C13–O18 C14–C15 C14–H23 C14–O19 C15–O16 C15–O20 N8–H25 N8–H39 N8–O11 N9–H32 N9–H33 O10–H24 O11–C12 O11–H40 O18–H22 O19–H35 O20–H34

1.53 1.10 1.09 1.49 1.54 1.10 1.09 1.54 1.09 1.09 1.54 1.09 1.10 1.54 1.10 1.49 1.20 1.34 1.53 1.21 1.57 1.09 1.40 1.53 1.09 1.40 1.20 1.35 1.02 1.02 2.68 1.02 1.02 0.97 1.33 1.03 0.97 0.97 0.98

C1–C2–C3 C1–C2–H28 C1–C2–H36 C1–N8–H25 C1–N8–H39 C1–N8–O11 C2–C1–N8 C2–C3–C4 C2–C3–H29 C2–C3–H37 C3–C4–C5 C3–C4–H30 C3–C4–H38 C4–C5–C6 C4–C5–H31 C4–C5–N9 C5–C6–O7 C5–C6–O10 C5–N9–H32 C5–N9–H33 C6–O10–H24 C12–C13–C14 C12–C13–H21 C12–C13–O18 C12–O11–H40 C13–C14–C15 C13–C14–H23 C13–C14–O19 C13–O18–H22 C14–C15–O16 C14–C15–O20 C14–O19–H35 C15–O20–H34 N8–C1–H26 N8–C1–H27 N8–O11–C12 O11–C12–C13 O11–C12–O17

113.23 108.49 108.84 110.42 109.61 119.33 111.49 114.00 109.29 108.40 113.81 110.04 109.98 111.46 108.21 113.90 122.42 115.60 109.77 108.67 107.66 109.20 107.55 111.58 113.09 110.26 108.49 110.60 107.26 121.68 116.53 106.60 113.05 110.69 107.53 116.68 111.44 125.21

C(12*)–O(11*) C(12*)–C(13*) C(13*)–H(21*) C(13*)–O(18*) H(22*)–O(18*) C(13*)–C(14*) H(23*)–C(14*) C(14*)–O(19*) C(14*)–C(15*) C(15*)–O(20*) H(34*)–O(20*) C(15*)–O(16*) H(25*)–N(8*) N(8*)–H(39*) N(9*)–H(32*) H(22a*)–C(22*) C(2*)–H(28*) C(42*)–H(42a*) H(39*)–N(8*) N(8*)–C(12*) N(8*)–C(1*) H(38*)–C(4*) H(12a*)–C(12*) H(33*)–N(9*) H(33*)–N(9*) C(5*)–N(9*) C(22*)–H(22b*) C(22*)–C(3*) H(36*)–C(2*) C(2*)–C(1*) C(2*)–C(3*) C(42*)–H(42b*) H(12b*)–C(12*) C(4*)–C(3*) C(4*)–C(5*) C(4*)–H(30*) C(1*)–H(26*) C(1*)–H(27*) C(5*)–H(31*) C(3*)–H(37*) C(3*)–H(29*) C(5*)–C(6*) C(6*)–O(10*) C(6*)–O(7*) H(35*)–O(19*) O(17*)–C(12*) C(42*)–C(5*) C(42*)–C(3*) C(22*)–C(12*)

1.24 1.52 1.00 1.40 0.97 1.53 0.93 1.42 1.51 1.31 1.02 1.22 0.97 0.84 1.02 1.09 0.96 0.97 0.85 1.53 1.45 0.99 1.00 0.90 0.94 1.45 0.99 1.59 0.87 1.59 1.44 1.08 0.94 1.53 1.44 1.14 0.94 0.92 0.89 1.05 1.04 1.52 1.24 1.26 1.16 1.28 1.70 1.29 0.97

O(11*)–C(12*)–C(13*) O(11*)–C(12*)–O(17*) H(21*)–C(13*)–C(12*) O(18*)–C(13*)–C(12*) C(12*)–C(13*)–C(14*) O(17*)–C(12*)–C(13*) H(21*)–C(13*)–O(18*) H(21*)–C(13*)–C(14*) H(22*)–O(18*)–C(13*) O(18*)–C(13*)–C(14*) H(23*)–C(14*)–C(13*) O(19*)–C(14*)–C(13*) C(15*)–C(14*)–C(13*) H(23*)–C(14*)–O(19*) H(23*)–C(14*)–C(15*) O(19*)–C(14*)–C(15*) H(35*)–O(19*)–C(14*) O(20*)–C(15*)–C(14*) O(16*)–C(15*)–C(14*) H(34*)–O(20*)–C(15*) O(16*)–C(15*)–O(20*) H(39*)–N(8*)–H(25*) H(39*)–N(8*)–H(25*) H(25*)–N(8*)–C12 H(25*)–N(8*)–C(1*) H(39*)–N(8*)–H(39*) H(39*)–N(8*)–C12 H(39*)–N(8*)–C(1*) H(33*)–N(9*)–H(32*) H(33*)–N(9*)–H(32*) H(32*)–N(9*)–C(5*) H(22b*)–C(22*)–H(22a*) H(22a*)–C(22*)–C(3*) H(22a*)–C(22*)–C(3*) H(36*)–C(2*)–H(28*) H(28*)–C(2*)–C(1*) H(28*)–C(2*)–C(3*) H(42a*)–C(42*)–H(42b*) H(42a*)–C(42*)–C(5*) H(42a*)–C(42*)–C(3*) H(39*)–N(8*)–C(12*) H(39*)–N(8*)–C(1*) C(1*)–N(8*)–C(12*) H(12a*)–C(12*)–N(8*) H(12b*)–C(12*)–N(8*) C(22*)–C(12*)–N(8*) N(8*)–C(1*)–C(2*) H(26*)–C(1*)–N(8*) H(27*)–C(1*)–N(8*) H(38*)–C(4*)–C(3*) H(38*)–C(4*)–C(5*) H(38*)–C(4*)–H(30*) H(12b*)–C(12*)–H(12a*) C(22*)–C(12*)–H(12a*) H(33*)–N(9*)–H(33*) H(33*)–N(9*)–C(5*) H(33*)–N(9*)–C(5*) C(4*)–C(5*)–N(9*) H(31*)–C(5*)–N(9*) N(9*)–C(5*)–C(6*) N(9*)–C(5*)–C42 H(22b*)–C(22*)–C(3*) C(12*)–C(22*)–H(22b*)

119.08 123.68 108.12 115.49 108.15 117.22 110.34 101.58 108.09 112.18 112.94 110.73 111.02 102.87 109.63 109.33 85.88 113.20 122.53 110.86 124.24 104.81 115.53 111.96 105.76 96.73 94.37 124.93 105.79 112.42 112.81 115.90 102.76 107.28 99.37 126.21 108.22 119.93 107.93 106.18 126.16 109.49 31.39 104.60 113.34 138.23 111.23 100.34 115.48 106.32 107.55 123.01 106.36 76.31 102.56 107.68 114.54 124.38 111.26 110.96 91.80 108.34 77.02

˚ which is longer in experiment). Of course, distance 1.14 A the comparison of two results: experimental and theoretical seems to be very difficult. According to X-ray studies, the proton position may be determined from difference map or by geometric parameters. These ways give different results. ˚ (C(2*)–H(28*)) The experimental distances equal to 0.87 A ˚ (C(5*)–H(31*)) are dramatically short. and 0.89 A On the other hand, the similarity of all calculated distances seems to be strange, but the calculated medium distances (ca. ˚ are acceptable. 1.095 A) Similar doubts are expected when the N–H distances are described. Almost all theoretical distances N–H are practi˚ but in both NH3 groups (of N(8) and cally equal to 1.02 A, N(9) nitrogen atoms) the only two protons are connected by these bonds with nitrogen atoms. Two protons H(40) and H(34) are involved in hydrogen bond and the N–H distance is much longer (the nitrogen atoms play the acceptors role, practically). This picture is not observed from the crystal-

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M. Drozd, M.K. Marchewka / Spectrochimica Acta Part A 64 (2006) 6–23

Table 2 (Continued ) Distance

˚ Value (A)

Angle

Value (◦ )

C(2*)–C(3*)–C(22*) C(4*)–C(3*)–C(22*) H(37*)–C(3*)–C(22*) H(29*)–C(3*)–C(22*) C42–C(3*)–C(22*) C(12*)–C(22*)–C(3*) H(36*)–C(2*)–C(1*) H(36*)–C(2*)–C(3*) C(3*)–C(2*)–C(1*) H(26*)–C(1*)–C(2*) H(27*)–C(1*)–C(2*) C(2*)–C(3*)–C(4*) H(37*)–C(3*)–C(2*) H(29*)–C(3*)–C(2*) C(42*)–C(3*)–C(2*) H(42b*)–C(42*)–C(5*) H(42b*)–C(42*)–C(3*) H(12b*)–C(12*)–C(22*) C(5*)–C(4*)–C(3*) H(30*)–C(4*)–C(3*) H(37*)–C(3*)–C(4*) H(29*)–C(3*)–C(4*) C(42*)–C(3*)–C(4*) H(30*)–C(4*)–C(5*) H(31*)–C(5*)–C(4*) C(4*)–C(5*)–C(6*) C(4*)–C(5*)–C(42*) H(27*)–C(1*)–H(26*) H(31*)–C(5*)–C(6*) H(31*)–C(5*)–C(42*) H(29*)–C(3*)–H(37*) H(37*)–C(3*)–C(42*) H(29*)–C(3*)–C(42*) O(10*)–C(6*)–C(5*) O(7*)–C(6*)–C(5*) C(6*)–C(5*)–C(42*) O(10*)–C(6*)–O(7*) C(3*)–C(42*)–C(5*)

32.93 140.27 105.37 103.26 120.39 143.15 76.80 111.19 123.37 84.27 126.11 113.67 73.07 117.66 125.30 114.88 93.16 105.97 115.54 101.30 57.28 115.34 50.70 103.60 78.79 113.41 45.19 111.41 114.10 120.97 104.53 106.80 115.09 117.29 116.62 105.56 125.88 113.78

lographic experiment. All protons in both NH3 groups are connected with nitrogen atoms, only. The N–H distances are ˚ The experidifferent and include in the range 0.84–1.02 A. mental values are shorter. 3.1.2. l-Lysine molecule The carbon chain in l-lysine molecule is shorter than in the tartaric acid. Only four atoms C(12*), C(13*), C(14*) and C(15*) are in the skeleton of this molecule. Two external carbon atoms are involved in hydroxycarboxylic group. Two experimental distances (C(12*)–C(13*) and ˚ The C(13*)–C(14*)) are very similar and equal to 1.52 A. ˚ In theothird bond C(14*)–C(15*) is a little shorter (1.51 A). retical approach, this relationship is disturbed. Two chemical bonds C(12)–C(13) and C(14)–C(15) are very similar and ˚ respectively, whereas the disequal to 1.527 and 1.532 A, ˚ It should be tance C(13)–C(14) is much longer (1.572 A). emphasized that the theoretical results seems to be better, because the C(13) and C(15) atoms involve in COOH groups. The distance C(13)–C(14) (these atoms are connected with

other carbon atoms, only) should be much different than two other. It is interesting that this calculated C–C distance is longer than in tartaric acid molecule. It suggests strongly that length of C–C bond is correlated with carbon chain length. In theoretical approach to the C–O distances of COOH groups, the clear differences in length between single (C–O) and double (C O) bonds are observed. For both carboxylic ˚ groups, the C O bonds length are similar and equal to 1.21 A ˚ (C(15)–O(16)). The single bonds (C(12)–O(17)) and 1.20 A ˚ (C(12)–O(11)) C–O are much longer and equal to 1.33 A ˚ (C(15)–O(20)). The same situation is noticed and 1.35 A in experimental results, but in this case the differences are smaller. The C(12*)–O(11*) and C(15*)–O(16*) bonds ˚ respectively. The longer are equal to 1.24 and 1.22 A, ˚ (C(12*)–O(17*)) and 1.31 A ˚ bonds distances are 1.28 A (C(15*)–O(20*)). It is characteristic that in the case of these C O bonds the calculated distances are smaller than that experimental, in contrary to the lengths of C–O single bonds. Good agreement between experiment and theoretical calculation is observed for C–O bonds for COH group situated in l-lysine chain. For both C(13)–O(18) and C(14)–O(19) ˚ bonds this distance is equal, practically (1.397 and 1.399 A, respectively). Very similar situation is observed in X-ray ˚ (C(13*)–O(18*)) data. These distances are equal to 1.401 A ˚ (C(14*)–O(19*)). Of course, in the case of and 1.421 A these C–O distances, the main relationship between experiment and theory is disturbed. The calculated bonds lengths are a little shorter than that obtained from crystallographic studies. According to theoretical and experimental values of C–O distances (these distances are longer than for COOH group) the single character of these bonds is more clearly expressed. Similar situation as in the case of tartaric acid molecule is observed when C–H distances are analyzed. The calculated lengths are a little bigger than that experimental. The ˚ C(13)–H(21) and C(14)–H(23) distances are equal to 1.09 A, ˚ respecwhereas the experimental values are 1.00 and 0.93 A, tively. Contrary results are noticed for O–H bonds in the COH groups. The calculated by DFT method results are ˚ (O(18)–H(22)) and 0.970 A ˚ very similar and equal to 0.968 A (O(19)–H(35)). The experimental values are bigger and equal ˚ (O(18*)–H(22*)) and 1.162 A ˚ (O(19*)–H(35*)), to 0.974 A but when the calculated and experimental results of C–H and O–H lengths are compared, the same doubts as in the case of tartaric acid molecule should be respected. 3.1.3. Hydrogen bonds The experimental values of nine hydrogen bonds are collected in Table 3. These distances are in the range ˚ The shortest hydrogen bond is observed 2.54–3.03 A. for O(20*)–H···O(17*) atoms, whereas for three atoms N(9*)–H···O(19*) this distance is the longest. In the theoretical approach, only four hydrogen bonds is noticed. In theoretical structure of investigated com-

M. Drozd, M.K. Marchewka / Spectrochimica Acta Part A 64 (2006) 6–23 Table 3 The experimental hydrogen bonds distances in investigated crystal ˚ D–H (A)

H···A ˚ (A)

D···A ˚ (A)

∠(DHA) (◦ )

1.02(2) 0.97(2) 1.16(2) 0.85(2) 0.97(2) 0.90(2) 0.90(2) 1.02(2) 0.94(2)

1.53(2) 1.83(2) 2.15(2) 2.03(2) 1.97(2) 2.38(2) 2.41(2) 1.85(2) 2.19(2)

2.542(2) 2.738(2) 3.012(2) 2.848(2) 2.862(2) 2.828(2) 2.702(2) 2.838(2) 3.033(2)

170.0(2) 153.9(2) 128.1(2) 160.6(2) 151.2(2) 110.8(2) 99.0(2) 162.3(2) 148.8(2)

O(20*)–H···O(17*)A $3 O(18*)–H···O(11*) $2 O(19*)–H···O(18*) N(8*)–H···O(17*)A $1 N(8*)–H···O(7*) $5 N(9*)–H···O(11*) $3 N(9*)–H···O(10*) N(9*)–H···O(16*)D $6 N(9*)–H···O(19*) $7

Symmetry codes: $1 −X, Y + 0.5, −Z; $2 X − 1, Y, Z; $3 X, Y, Z + 1; $5 X, Y, Z − 1; $6 X + 1, Y, Z; $7 X + 1, Y, Z + 1.

plex one hydrogen bond O–H···O is observed. Three atoms O(10)–H(24)···O(20) are involved in this bond. According to theoretical calculations, the length of this hydro˚ Surprisingly the three gen bond is equal to 3.693 A. other hydrogen bonds (NHO) are shorter. The shortest ˚ O(11)–H(40)···N(8) hydrogen bond is equal to 2.683 A, ˚ whereas the medium O(20)–H(34)···N(9) is 2.997 A. The ˚ This longest distance N(9)–H(32)···O(11) is equal to 3.180 A. inversion in lengths of investigated distances is very strange and will be object of our studies in future. Of course, the considerated geometry is different than experimental and simple comparison of these two methods is difficult. The restrictions of DFT method and studies performed on the one molecule only, seem to be main obstacle in these comparisons. It is clear that for these detailed theoretical studies for real crystal, the huge power of computers is needed and special programs for calculation in solid crystalline phase have to be used. 3.2. Lowdin population analysis The results of calculations of the natural charges of llysine × tartaric acid complex by Lowdin method are presented in Table 4. The total charge of investigated complex is equal to 0. According to our calculation, the negative charge in investigated molecule is de-localized between nitrogen, oxygen and carbon atoms. The two nitrogen atoms of amine group (N(8) and N(9)) have the smallest negative charge (−0.2085e and −0.2533e, respectively). It is interesting that a little bigger charge for nitrogen atom is noticed for atom which is connected with C(5) carbon atom (the C(5) atom is the third of l-lysine carbon chain, whereas smaller negative charge is noticed for N(8) atom which is the first one in these chain. The all oxygen atoms have negative charges. Very similar negative charges are noticed for two oxygen atoms O(18) and O(19) (ca. −0.17e) which are involved in COH groups of tartaric acid. Surprisingly, the similar charges are observed for two oxygen atoms (O(11) and O(17)) localized in COOH group of tartaric acid. This value is equal to ca. −0.20e. One

13

of these oxygen atoms is connected with hydrogen H(40) and C(12) carbon atoms whereas the other makes the typical chemical bond with C(12) atom, only. For other COOH group in tartaric acid the huge differences of the calculated charges are noticed. For the O(20) atom the charge is equal to −0.1139e, whereas for O(16) atom this value is −0.165e. Much more differences are observed in the case of hydroxycarboxylic group in l-lysine molecule. In this group, the O(7) atom has charge −0.180e. The calculated charge for second atom (O(10)) is much smaller and equal to −0.083e. In both cases of this hydroxycarboxylic group, the smaller charge is observed for oxygen atom connected with hydrogen atom. A little more complicated situation is observed when the charges of carbon atoms are considered. For three atoms of l-lysine chain (C(2), C(3) and C(4)) the charges are very similar and equal to ca. −0.16e. For two carbon atoms C(5) and C(1) which are connected in this chain with nitrogen atoms the charges are a little smaller and equal to ca. −0.1e. Much smaller charges are noticed for two carbon atoms of tartaric acid chain (C(13) and C(14)). In this case, the carbon atoms are connected with oxygen atoms. The calculated values of charges are for two atoms similar and equal to ca. −0.05e. According to our calculations, the three carbon atoms (C(6), C(12) and C(15)) have positive charges. The values of calculated charges are included in the range of 0.013–0.021e. Such results are expected because the three carbon atoms are involved in hydroxylcarboxyl groups. For this group very characteristic is, that positive charge is located on the carbon atom, whereas the negative charge is expected for oxygen atoms. For the hydrogen atoms, the differences in calculated charge are relatively smaller. The very similar values of positive charges are observed for hydrogen atoms connected with nitrogen atoms of amine groups. For the tree atoms (H(25), H(33) and H(39)), the calculated charge is practically equal (ca. 0.14e). Surprisingly, the charge of H(32) atom which is involved in hydrogen bond is very similar as calculated for other hydrogen atoms of amine groups. In this case, the more differences in values of calculated charges are expected. The biggest values of charge are noticed for two atoms (H(22) and H(35)) connected with oxygen atoms in hydroxyl groups of tartaric acid. The calculated values are equal to 0.169e. For hydrogen atoms of hydroxylcarboxyl groups (H(40), H(24) and H(34)) the values of charges are different. For first atom, the charge is equal to 0.147e, whereas for atom H(24) this value is bigger (0.157e). The smallest value is noticed for third hydrogen atom (0.139e). For hydrogen atoms connected with carbon atoms in tartaric acid and l-lysine molecules the calculated charges values are in the range 0.126–0.090e. The highest values are noticed for H(31), H(21), H(23) and H(30) atoms. In contrary the smallest charge are observed for H(28), H(26) and H(37) atoms. It should be emphasized that in the case of our calculations the values of charges obtained by Mulliken method seems to be wrong. The much better results are observed when the Lowdin method was used.

14

M. Drozd, M.K. Marchewka / Spectrochimica Acta Part A 64 (2006) 6–23

Table 4 The Lowdin charges calculated for l-lysine with tartaric acid

Atom

Charge (e)

1C 2C 3C 4C 5C 6C 7O 8N 9N 10O 11O 12C 13C 14C 15C 16O 17O 18O 19O 20O 21H 22H 23H 24H 25H 26H 27H 28H 29H 30H 31H 32H 33H 34H 35H 36H 37H 38H 39H 40H

−0.111026 −0.165509 −0.173242 −0.158738 −0.092567 0.013306 −0.180357 −0.208582 −0.253262 −0.083562 −0.207509 0.017084 −0.053872 −0.061349 0.020739 −0.164732 −0.191777 −0.173906 −0.178897 −0.113953 0.121381 0.169466 0.117144 0.157369 0.144588 0.090025 0.10385 0.096135 0.110768 0.111608 0.126242 0.142627 0.143141 0.138817 0.168585 0.096228 0.094058 0.100193 0.142392 0.147091

M. Drozd, M.K. Marchewka / Spectrochimica Acta Part A 64 (2006) 6–23 Table 5 The dipole moment (µ), first and second hyperpolarizability (β and γ), of l-lysine × tartaric acid complex µx µy µz µ α βxxx βyxx βzxx βxxy βyxy βzxy βxxz βyxz βzxz βxyy βyyy βzyy βxyz βyyz βzyz βxzz βyzz βzzz βx βy βz βVEC

6.454 −6.211 3.887 9.764 1.312 −0.308 0.200 −0.064 0.200 −0.295 0.067 −0.066 0.068 −0.103 −0.297 −0.028 −0.140 0.070 −0.142 0.051 −0.106 0.050 −0.488 −2.123 0.666 −2.082 3.047

γ xxxx γ yyyy γ zzzz γ xxyy γ xxzz γ yyxx γ yyzz γ zzxx γ zzyy γ

18.08 15.97 10.55 5.23 3.43 5.22 4.40 3.40 4.37 14.13

Dipole moment (µ) in Debay. α(0; 0), β(−2ω; ω, ω) (10−30 esu); γ(−3ω; ω, ω, ω) (10−36 esu). The moment of inertia: Ixx = 1449.034, Iyy = 2182.617, ˚ 2 ). Izz = 3264.047 (amu A

3.3. Hyperpolarizability calculation The dipole moment, µ, isotropic polarizability, α, and first hyperpolarizability, β, are collected in Table 5. All theoretical results are given in the molecular internal coordinate system represented by (x, y, z) whereby the indices x, y and z refer to the three axes corresponding to the components of moment of inertia in increasing order (Ixx = 14449, Iyy = 2182 ˚ 2 ]). and Izz = 3264 [amu A The calculated dipole moment is equal to 9.764 D. The highest value of dipole moment is observed for component µx . In this direction, this value is equal to 6.454 D. For directions y and z, these values are equal to −6.211 and 3.887 D, respectively. The calculated polarizability, α, is equal to 1.312 × 10−30 esu. This value is similar as obtained for organic compound (for example, paraaminonitropyridine N-oxide the calculated polarizability is equal to 0.83 × 10−30 esu [23]), but for other calculation of compound with NLO properties the higher value of polarizability was noticed [4]. The calculated (at fundamental wavelength of 1064 nm) value of β vector part for l-lysine × tartaric acid molecule is equal to 3.047 × 10−30 esu. It should be noticed that experimental value observed for investigated crystal is much bigger and equal to 34% of β for KDP crystal [24] (1.063 × 10−9 esu). This effect (smaller value of calculated

15

hyperpolarizability than experimental one) was observed [25] but in the case of our work these differences are very big. It is important to note that the theoretical method used here (TDHF) does not include the electron correlation effect, which has been found in a number of cases as considerably influencing the NLO coefficient [26]. Additionally, recent experimental measurements and theoretical analyses reveal [27] that in the low frequency limit, electron–phonon coupling contribution to the optical nonlinearity may become quite important. This inclusion of vibronic terms in the calculation of NLO coefficients may become necessary for agreement with experiment [25]. It should be emphasized that similar type of coupling between the high frequency hydrogen stretching vibration and low frequency phonons is described [28] in crystals with hydrogen bonds. The hyperpolarizability, β, is dominated by the longitudinal components of βzzz , βxxx , βxyy , βyxy , βxxy and βyxx . Domination of particular components indicates a substantial de-localization of charge in this direction. In directions of βzxz , βxzz , βzyy and βyyz the values of components are medium, relatively. In other directions, the particular components are practically equal to 0. Of course, the ab initio time-dependent Hartee–Fock calculations strongly depend on calculation method and basis set used, but the theoretical values may be compared with experimental one. In the case of l-lysine × tartaric acid complex, these differences between theoretical and experimental values are huge, but theoretical calculations seem to be more helpful in determination of particular components of hyperpolarizability tensor than in establishing of real values of β. On the basis of our combined theoretical and experimental studies, it is clear that this compound seems to be promising material in perspective of NLO research. The average value of second hyperpolarizability, γ, is equal to 14.13 × 10−36 esu. The large values of γ are obtained for diagonal directions: xxxx, yyyy and zzzz ((18.08–10.55) × 10−36 esu). In non-diagonal directions these γ factors are smaller and include in the range (5.23–3.40) × 10−36 esu. This obtained value of second hyperpolarizability is relatively larger when compared to pnitroaniline (PNA). The calculated values of PNA are equal to 8.6 × 10−36 esu (γ xxxx ) and 1.88 × 10−36 esu (γ). 3.4. Vibrational spectra and their assignment The factor group analysis for investigated crystal is presented in Table 6. Table 7 shows the experimental and theoretical frequencies and intensities and PED for investigated molecule. Fig. 5 presents the experimental and the calculated IR spectra. The theoretical results indicate that l-lysine × tartaric acid molecule has a C1 symmetry. The factor group analyses show that in infrared and Raman spectra both modes A and B should be observed. The 42A and 42B modes are expected for llysine molecule and 66A + 66B modes should be active in

16

M. Drozd, M.K. Marchewka / Spectrochimica Acta Part A 64 (2006) 6–23

Fig. 5. The experimental and calculated IR spectra of investigated compound.

the case of tartaric acid molecule. Additionally, the 5A + 4B translational and 6A + 6B librational modes are active. It should be noticed that in PED analysis one imaginary frequency is observed. Imaginary frequencies appear at transition states. The normal mode of an imaginary frequency represents the transition vector of that state. Sometimes the imaginary vibrational frequencies can be observed when the no adequate calculation method is used [29]. In our case (very

complex basis set in calculation was used), one obtained negative frequency suggests strongly that the nearest stationary state of real crystal structure is obtained. 3.4.1. C–C vibrations The PED studies of the theoretical spectrum show that the bands originating from stretching C–C vibrations should be observed in wide spectral range. The bands noticed at 1085,

M. Drozd, M.K. Marchewka / Spectrochimica Acta Part A 64 (2006) 6–23 Table 6 Factor group analysis for investigated crystal C2

Lattice modes A

T

L

A B

1 2

5 4

6 6

l-Lysine internal modes

Tartaric acid internal modes

Activity

42 42

66 66

R, IR R, IR

A: acoustic, L: librational, T: translational, R: Raman activity, IR: infrared activity.

1077, 1068, 1012, 1003, 954, 926, 883, 875 and 859 cm−1 were assigned to these type of vibrations. The experimental counterparts of these bands are observed at 1075, 1043, 1027, 948, 937, 911, 889 and 865 cm−1 . Of course, in PED calculation, the most bands are complex, but in four cases (954, 926, 883 and 875 cm−1 ) the bands derived from C–C stretching vibrations are “pure”. At 781 cm−1 (in theoretical approximation) the band was noticed and assigned to in-plane deformation C–C groups, but the percentage participation of these type of vibrations in described band is estimated as 22%. The theoretical calculated intensity of this band is medium (36 km/mol). On the basis the PED analysis and the band observed in experimental spectrum at 778 cm−1 was assigned to this type of vibrations. Of course, the other out-of-plane deformations of the carbon skeleton participate partially in the bands noticed at 359, 327, 318, 284, 234, 184, 163, 151, 118, 102, 92, 86, 79 and 72 cm−1 , but comparison of these values with experimental data and verification of theoretical approach in this spectral range is very difficult. 3.4.2. C–H vibrations According to PED analysis the bands observed in theoretical spectrum at 3061, 3029, 3015, 3010 and 2981 cm−1 were assigned to antisymmetric stretching vibrations of C–H bonds. As derive from the symmetric stretching bonds were recognized the bands noticed at 2979, 2974, 2972, 2964, 2955 and 2933 cm−1 . It should be emphasized that PED analysis in the case of stretching vibrations of C–H groups is unambiguous. According to these studies, the all C–H stretching vibrations are not mixed with other types of vibrations. On the other hand, the differences between calculated frequencies of antisymmetric and symmetric bands should be considerate. In our calculation, these differences are typical and include in the range of 80–40 cm−1 . More disturbing is detailed analysis of calculated intensities for these bands. The intensities of bands originating from antisymmetric stretching vibrations are comparable with intensities of bands derived from symmetric stretching vibrations. Usually, in experimental spectra the intensities of bands connected with antisymmetric vibrations in IR spectrum are bigger than symmetric counterpart. The in-plane deformations (δ) of C–H groups are noticed on the PED analysis at 1493, 1484, 1469, 1463, 1456, 1419, 1409 and 1401 cm−1 . These values of calculated frequencies

17

are typical and in very good agreement with experimental data. In the case of this type of vibrations, the percentage participation in the PED (for vibrations in the range 1493–1401 cm−1 ) is very high, but these bands should be considerate as slightly mixed. Bands at 1382, 1360, 1339, 1324, 1320, 1306, 1301, 1267, 1258, 1250, 1239, 1206, 1194, 1183, 1138 and 1291 cm−1 were assigned to rocking type vibrations of C–H bands. It should be emphasized that only one band (1360 cm−1 ) was noticed as “pure”. The PED analysis shows that in these bands the other vibrations participate, also. The bands noticed at 830 and 711 cm−1 were assigned to out-of-plane deformation type of vibration (ω) of C–H groups. In these bands, the pronounced participation of other types of vibrations is observed. Of course, the comparison of these obtained frequencies with experimental value is impossible because the experimental spectrum was measured as nujol mulls. 3.4.3. C–O vibrations The bands originating from stretching vibrations of carbonyl groups are very characteristic and easy to observe. It is clear that the band arising from typical C O␯as vibration is observed in the range of 1750–1650 cm−1 . At lower frequencies the band, which can be assigned to antisymmetric stretching vibration of COO− group where the bond C–O has mixed character (this bond is between single and double bond), is observed. Of course, when the proton of COOH group is involved in hydrogen bond (in real crystal) the frequencies of ␯as CO are different than that calculated for one molecule. In the case of these bands, the other scaling factor should be used (scaling factor equal to 0.92 was used by us). On the basis of PED calculation the bands at 1685, 1680 and 1638 cm−1 were assigned to antisymmetric stretching vibration of C O group. In experimental spectrum these bands were found at 1704 and 1648 cm−1 . The noticed frequencies are typical for this class of compounds. The more complicated situation is observed for bands arising from ␯s vibration of COOH group. During PED analysis, these bands are observed in wide spectral range, namely at 1206, 1183, 1167, 1160, 1138, 1107 and 1097 cm−1 . Only two last bands have “pure” character, whereas the other are strongly mixed. The “pure” bands are the strongest. The experimental counterparts of these bands are found at 1290, 1267, 1253, 1219, 1170 and 1155 cm−1 . The intensities of these bands in real IR spectrum are medium. The bands originating from deformation vibration of COOH group are noticed on the basis of PED analysis at 824, 806, 745, 734 and 675 cm−1 . The other bands at 609, 592, 570, 529, 515 and 448 cm−1 should be assigned to deformation vibration of this group, too. The counterparts of these bands in experimental spectrum are observed at 812, 793, 778, 652, 627, 596, 557 and 515 cm−1 . It is interesting that in most cases (taking into account PED) these bands are not mixed. According to PED calculation, the typical bands arising from out-of-plane deformation vibrations of COOH are

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M. Drozd, M.K. Marchewka / Spectrochimica Acta Part A 64 (2006) 6–23

Table 7 The experimental and theoretical frequencies and intensities, PED analysis of investigated compound Scaled theoretical frequency 3482 3444 3404 3266 3241 3195 3192 3173 3061 3029 3015 3010 2981 2979 2974 2972 2964 2955 2932

2415

Theoretical intensity (km/mol) 72 106 166 11 68 9 743 97 15 27 14 8 39 39 9 16 28 26 19

Experimental frequency

Relative experimental intensity

3326 3245 3165

0.7 0.78 0.79

2958N 2921N 2871N 2855N 2727 2668 2527 2361

0.57 0.53 0.46 0.28 0.26 0.33 0.73 0.81 0.87

2544

PED %

Assignment

O18–H22 100% O19–H35 100% O10–H24 100% N8–H25 72%, N8–H39 28% N9–H33 62%, N9–H32 36% N8–H39 71%, N8–H25 27% O20–H34 85% N9–H32 56%, N9–H33 29%, O20–H34 13% C3–H37 81%, C3–H29 15% C1–H27 88% C3–H29 48%, C4–H30 25%, C3–H37 18% C4–H30 61%, C3–H29 32% C2–H36 75%, C1–H26 15% C13–H21 87%, C14–H23 13% C14–H23 87%, C13–H21 13% C5–H31 90%, C4–H38 10% C1–H26 75%, C2–H36 11% C4–H38 77%, C4–H30 11%, C5–H31 10% C2–H28 85%, C2–H36 12%

␯OH ␯OH ␯OH ␯as NH3 ␯N–H···O ␯N–H···O ␯OH(hydrogen bond) ␯s NH3 , ␯OH ␯as CH ␯as CH ␯as CH ␯as CH ␯as CH ␯s CH ␯s CH ␯s CH ␯s CH ␯s CH ␯s CH

O11–H40 98%

1685 1680 1649

177 482 36

2340 1940 1704 1611 1648

1638 1623

397 27

1583

0.85

1506

0.84

1493

24

1484

9

1469 1463

35 21

1456 1419 1409

3 8 13

1401 1393 1382 1360

35 22 19 4

1377N 1368N

1339

36

1344

1324

125

1320

200

1329

0.78

1316 1306

365 11

1313

0.79

1466N 1456N 1417

0.83

0.77

C6–O7 77%, C15–O16 9% C15–O16 77%, C6–O7 9% C5–N9–H32 29%, C4–C5–N9–H32 26%, C4–C5–N9–H33 23%, C5–N9–H33 21% C12–O17 85% C2–C1–N8–H25 27%, C2–C1–N8–H39 25%, C1–N8–H39 25%, C1–N8–H25 23% C1–C2–C3–H29 30%, C1–C2–C3–H37 27%, C12–O11–H40 13.%, C2–C3–H29 9% O11–N8–C1–H26 34%, O11–N8–C1–H27 33%, N8–C1–H26 13%, N8–C1–H27 13% C12–O11–H40 54%, N8–C1–C2–H36 10%, N8–C1–C2–H28 9% N8–C1–C2–H28 22%, N8–C1–C2–H36 22%, C12–O11–H40 11%, C1–C2–C3–H37 9% C2–C3–C4–H38 34%, C2–C3–C4–H30 30%, C3–C4–H30 11%, C12–C13–C14–H23 36%, C14–O19–H35 36% C13–O18–H22 31%,O11–C12–C13–H21 28%, C12–C13–H21 13% C2–C3–H37 22%, C3–C4–C5–H31 16% N8–C1–H27 36%, O11–N8–C1–H27 15%, N8–C1–H26 12% C3–C4–C5–H31 26%, C5–N9–H32 9% C1–C2–H36 15%, C3–C4–H38 14%, C1–C2–H28 13%, C4–C5–H31 11%, C3–C4–H30 10% C2–C3–H37 13%, C3–C4–H38 9%, C3–C4–H30 8%, C4–C5–H31 6%, C2–C3–H29 6%, C1–C2–H28 5% N8–C1–H26 18%, C2–C3–H29 18%, C1–N8–H39 8% C1–C2–H36 5%, N8–C1–H27 5% C15–O20–H34 26%, C2–C3–H37 9%, C13–C14–H23 7%, C2–C3–H29 5% C6–O10–H24 25%, N8–C1–H26 14%, C15–O20–H34 9% O11–C12–C13–H21 24%, C13–C14–H23 18%, C14–O19–H35 18%, C13–O18–H22 15%

␯OH(A) Overtones Overtones Overtones ␯OH(hydrogen bond) Overtones ␯OH(B) ␯CO ␯CO ␦NH ␯CO ␦NH ␦NH ␦CH ␦CH ␦OH ␦CH, ␦OH(O11–H40) ␦CH ␦CH, ␦OH(O19–H35) ␦OH(O18–H22) ␦CH ␦CH ␳CH ␳CH ␳CH ␳CH ␦OH, ␳CH ␦OH(O10–H24) ␳CH

M. Drozd, M.K. Marchewka / Spectrochimica Acta Part A 64 (2006) 6–23

19

Table 7 (Continued ) Scaled theoretical frequency

Theoretical intensity (km/mol)

Experimental Relative frequency experimental intensity

1301

51

1296 1290

28 70

1267

75

1258

176

1250

34

1239

20

1206

130

1290

0.72

1194

1

1138

0.75

1183

3

1122 1267

0.83 0.78

1167 1160

13 25

1253 1219

0.8 0.74

1138

40

1170

0.67

1107 1097 1085 1077

248 118 5 9

1155

0.74

1075

0.85

1068

24

1050

191

1043

0.59

1012

12

1027

0.57

1003

48

979

26

1015 1003 966

0.57 0.61 0.49

954

13

948 937

0.5 0.5

926 908 883

31 90 2

911 889

0.45 0.56

875 859

17 9

865

0.49

824

15

816 806

3 4

844 812

0.59 0.43

781 745

36 10

793

0.47

PED %

Assignment

C3–C4–H30 17%, C1–C2–H28 16%, C2–C3–H37 5%, C1–C2–H36 4% C4–C5–H31 17%, C2–C3–H29 15%, C1–C2–H36 7% C15–O20–H34 22%, C12–C13–H21 14%, C13–C14–H23 11%, C13–O18–H22 8% O11–C12–C13–H21 31%, C13–C14–H23 14%, C12–C13–C14–H23 14%, C14–O19–H35 13%, C13–O18–H22 9% C13–C14–H23 18%, O11–C12 16%, C12–C13–C14–H23 8%, C14–O19–H35 6% C4–C5–H31 12%, C3–C4–H38 11%, C3–C4–C5–H31 10%, C12–C13–C14–H23 6%, C1–C2–H36 5% C1–C2–H36 9%, C3–C4–H38 8%, C2–C3–H37 6%, C2–C3–H29 6%, C4–C5–H31 6%, C1–N8–H25 5%, C5–N9–H32 5%, N8–C1–H27 5% C12–C13–H21 37%, O11–C12 25%, C15–O20 7%, C15–O20–H34 5%, C13–O18–H22 5% C5–N9–H32 20%, C4–C5–H31 13%, C5–N9–H33 12%, C3–C4–H30 7%

␳CH

C6–O10–H24 14%, C3–C4–C5–H31 12%, C6–O10 12%, O17–C12–O11–H40 11%, C5–N9–H33 9% O17–C12–O11–H40 19%, C15–O20 16%, C6–O10 9% O17–C12–O11–H40 20%, C15–O20 17%, C15–O20–H34 9%, C12–C13–C14–H23 8%, C6–O10 6%, C6–O10–H24 5% O17–C12–O11–H40 29%, C6–O10 10%, C3–C2–C1–N8 5%, C2–C3–C4–H30 5%, C3–C4–C5–H31 4%, C6–O10–H24 4%, C1–C2–C3–H29 4%, C2–C3–C4–H38 4% C13–O18 57%, C14–O19 10%, O11–C12 4%, C13–C14 4% C14–O19 57%, C13–O18 9%, C15–O20 8% C2–C3 20%, C2–C1–N8–O118%, C1–C2–C3 8% C1–C2 12%, C5–N911%, C1–N8–H25 10%, C1–N8 8%, C4–C5 6%, C1–C2–H36 6%, C3–C4–H38 6%, C5–N9–H33 6% C3–C4 27%, C4–C5 22%, C6–O10 7%, C2–C3 6%, C1–N8 6%, C1–C2 5%, C5–N9 5% C1–N8 18%, C4–C5–N9–H32 13%, C5–N9–H33 12%,C5–N9–H32 7%, C4–C5–N9–H33 6% C1–N8–H25 21%, C1–C2 8%, C1–C2–H28 8%, C2–C3 4%, C4–C5 4% C2–C3 22%, C1–N813%, C3–C4 12%, C5–N9 11%, C4–C5 3% C3–C4 16%, C1–N8–H39 10%, C5–N9 9%, C2–C3 9%, C2–C1–N8–H25 8%, C1–N8–H25 6%, C2–C1–N8–H39 6% C12–C13 16%, C14–C15 15%, C13–C14 13%, C12–C13–C14 6%, C13–C14–C15 5% C5–C6 11%, C4–C5 10%, C5–N9 9%, C1–C2 5%, C3–C4 5% C1–N8 32%,C5–N9 13%, C1–C2 11%, C4–C5 3% C13–C14 33%, C13–C14–C15–O20 11%, C12–C13–C14 9%, N8–O11–C12–O17 9%, C13–C14–C15–O16 8%, O11–C12–C13–C14 7% C14–C15 22%, C12–C13 19% C1–C2 14%, O11–N8–C1–H26 14%, O11–N8–C1–H27 8%, C2–C3 8% C14–C15–O20–H34 26%, C13–C14–C15–O20 14% N8–O11–C12–C13 11% C1–N8 8%, C5–N9 8%, N8–C1–C2–H36 6%, N8–C1–C2–H28 6% C5–C6 12%, C4–C5–C6–O7 11%, C6–O10 6%, C3–C4–C5–C6 5%, C13–C14–C15–O20 4%, O11–C12–C13–C14 4% C14–C15–O20–H34 56%, O11–C12–C13–C14 22% C5–C6–O7 14%, C4–C5–C6–O7 12%, C5–C6 11%, C5–C6–O10 6%, C4–C5–C6–O10 5%, C4–C5 4%, C1–C2 3%

␳CH ␳CH, ␦OH(O20–H34) ␳CH, ␦OH ␳CH ␳CH ␳CH ␳CH, ␯s CO ␳CH, ␳NH ␳NH ␯s CO, ␳NH, ␳CH ␯s CO ␯s CO ␯s CO, ␳CH ␯s CO ␯s CO(pure) ␯CC, ␳NH ␯CC, ␯CN ␯CC, ␳NH ␯CC, ␳NH ␳NH, ␯CC ␯CN, ␯CC ␯CN ␯CC, ␻NH ␯CC ␯CC ␯CN, ␯CC ␯CC ␯CC ␯CC, ␻NH ␥OH(O20–H34) , ␻NH ␯CN, ␶CH ␦CO ␥OH(O20–H34) , ␦CC ␦CO

20

M. Drozd, M.K. Marchewka / Spectrochimica Acta Part A 64 (2006) 6–23

Table 7 (Continued ) Scaled theoretical frequency 734

Theoretical intensity (km/mol) 11

Experimental Relative frequency experimental intensity

PED %

Assignment

778

0.37

O11–C12–O17 25%, C14–C15–O16 11%, C13–C14 9%, C14–C15–O20 8%, O11–C12 8%, C15–O20 6%, C14–C15 3%

␦CO

740 723N 701

0.48 0.77

C1–C2–C3–H37 16%, C1–C2–C3–H29 14%, N8–C1–C2–H28 8%, N8–C1–C2–H36 8%, C2–C3–C4–H30 5% C5–C6–O10–H24 84% C14–C15–O16 25%, O11–C12–O17 15%, C12–C13–C14–O19 9%, C15–O20 8%, C13–C14–C15–O16 6%, O11–C12 5%, C14–O19 4%,C13–O18 3% N8–O11–C12–O17 17%, O11–C12–C13–O18 16%, C13–C14–O19 13%, C14–C15–O16 11%, C14–C15–O20 8% C13–C14 23% C13–C14–C15–O16 15%, N8–O11–C12–O17 11%, O11–C12–O17 8%, C13–C14–C15–O20 7% C5–C6–O10 26%, C4–C5–N9 22%, C3–C4–C5 8%, C2–C3–C4 6% C5–C6–O7 32%, C5–C6 14%, C4–C5–C6–O10 9%, C4–C5–C6 9%, C4–C5–C6–O7 8%, C3–C4–C5 7%, C1–C2–C3 5% O11–C12–C13 20%, C2–C1–N8 11%, C14–C15–O20 10%, C12–C13–O18 8%

␶CH

711

2

691 675

79 22

662

0.53

609

28

652

0.51

592

20

627

0.46

570

2

596

0.59

529

12

557

0.44

515

11

515

0.56

514

8

495 464

0.4 0.61

481 448

4 26

430

0.37

433 376

27 20

365

1

359 327

0 41

318

8

309

22

284

7

263 243

37 2

234

5

205

3

184 160

3 4

151

3

136

35

118

10

102

15

92

7

C5–C6–O7 13%, C3–C4–C5–N9 10%, C4–C5–N9 10%, C3–C4–C5–C6 9% C2–C1–N8 27% C14–C15–O20 21%, C13–C14–O19–H35 15%, C13–C14–O19 14% C13–C14–O19–H35 61%, C12–C13–O18–H22 14% C4–C5–N9–H33 24%, C4–C5–N9–H32 17%, C3–C4–C5 13%, C2–C1–N8–O11 9%, C2–C1–N8–H25 5%, C2–C3–C4 4%, C2–C1–N8–H39 4% C2–C1–N8–H39 21%, C2–C1–N8–H25 20%, C1–C2–C3 7%, C4–C5–N9–H32 6%, C4–C5–N9–H33 5%, C2–C3–C4 4% C4–C5–N9 47%, C3–C4–C5–N9 20% C12–C13–O18 28%, O11–C12–C13 15%, C12–C13–O18–H22 10%, C13–C14–O19–H35 6% C2–C1–N8 14%, C1–C2–C3 13%, C14–C15–O16 8%, C13–C14–O19 6%, C12–C13–C14 5%, O11–C12–C13 5% C12–C13–C14–O19 26%, C14–C15–O16 22%, C2–C1–N8 13%, C1–C2–C3 7%, C14–C15–O20 7%, C13–C14–O19 4% C5–C6–O10 25%, C3–C4–C5–C6 19%, C2–C3–C4 10%, C3–C4–C5–N9 9%, C5–C6–O7 7%, C4–C5–C6 6%, C3–C4–C5 5% N8–O11 18%, O11–C12–C13–O18 17%, C13–C14–O19 15% O11–C12–C13–O18 29%, C13–C14–O19 17%, N8–O11 13%, O11–C12–C13 9% C4–C5–C6 47%, C2–C3–C4 17%, C1–C2–C3 7%, C3–C4–C5–C6 6%, C3–C4–C5 3% C3–C4–C5–N9 32%, C1–C2–C3 19%, C2–C3–C4 19%, C3–C2–C1–N8 17%, C3–C4–C5 15% C13–C14–C15 26%, C2–C1–N8–O11 18%, C12–C13–C14 7% C3–C2–C1–N8 46%, C13–C14–C15 24%, C13–C14–C15–O20 16%, C12–C13–C14 13% C12–C13–C14 19%, C2–C3–C4–C5 12%, C2–C1–N8–O111%, C3–C2–C1–N8 10% C12–C13–O18–H22 22%, C13–C14–C15–O16 22%, C1–N8–O11–C12 12%, C13–C14–C15–O20 10% N8–O11–C12–C13 38%, C3–C2–C1–N8 32%, O11–C12–C13–C14 29% C2–C1–N8–O11 39%, O11–C12–C13–C14 34%, C1–C2–C3–C4 29% C2–C3–C4–C5 42%, N8–O11–C12 16%, C3–C4–C5–C6 11%, C4–C5–C6 8%, C3–C4–C5 6%

␥OH(O10–H24) ␦CO ␥CO ␥CO ␥CO, ␥CN ␥CO ␥CO, ␥NH ␻CN ␻CN ␻CO, ␥OH(O19–H35) ␥OH(O18–H22) ␶NH ␶NH Skl. CCC Skl. CCC ␶NH, Skl. CCC, ␥CO Skl. CCO Skl. CCO, Skl. CCC

Skl. CCO Skl. CCO Skl. CCC Skl. CCN Mix internal vibrations

M. Drozd, M.K. Marchewka / Spectrochimica Acta Part A 64 (2006) 6–23

21

Table 7 (Continued ) Scaled theoretical frequency

Theoretical intensity (km/mol)

86 79

2 1

72 56

3 4

51

1

36

12

25 11 −69

5 1 53

Experimental frequency

Relative experimental intensity

PED %

Assignment

C1–C2–C3–C4 55%, C1–N8–O11 31% C2–C1–N8–O11 36%, C3–C2–C1–N8 32%, C3–C4–C5–C6 30%, N8–O11–C12 22% C12–C13–C14–C15 76%, C12–C13–C14–O19 11% N8–O11–C12 41%, C4–C5–C6–O10 35%, N8–O11–C12–C13 10%, C1–C2–C3–C4 10% C2–C1–N8–O11 49%, C4–C5–C6–O10 22%, C12–C13–C14–O19 5% O11–C12–C13–C14 41%, C2–C3–C4–C5 25%, N8–O11–C12 15%, C1–N8–O11 15% C1–N8–O11–C12 85%, C2–C3–C4–C5 14% N8–O11–C12–C13 48%, C2–C1–N8–O11 41%, C1–N8–O11 12%

␯: stretching, s: symmetric, as: antisymmetric, ␦: scissoring (symmetric in-plane), ␳: rocking (antisymmetric in-plane), ␻: wagging (symmetric out-of-plane), ␶: twisting (antisymmetric out-of-plane), tors: torsional, N: nujol, skl.: skeletal.

noticed at lower frequencies at 309, 284 and 243 cm−1 , but clear-cut interpretation of results seems to be very difficult because the bands are strongly mixed. 3.4.4. O–H vibrations According to PED calculation, the bands at 3482, 3444, 3404 and 3192 cm−1 were assigned to ␯OH vibrations. Of course, these calculations are in good agreement with theoretical calculated structure with the one hydrogen bond ˚ For hydrogen O(10)–H(24)···O(20) with distance 3.73 A. bonds with similar distance the bands arising from stretching vibrations should be noticed in the range of 3450–3300 cm−1 . Surprisingly, the band originating from hydrogen bond O(11)–H(40) which is involved in short hydrogen bond ˚ is noticed at 2415 cm−1 . (2.68 A) The bands corresponding to in-plane deformation vibrations of hydrogen bonds are observed at 1469, 1463 cm−1 (O(11)–H(40)), 1419 cm−1 (O(19)–H(35), 1409 cm−1 (O(18)–H(22)), 1320, 1316 cm−1 (O(10)–H(24)), −1 1290 cm (O(20)–H(34)) and 1267 cm−1 . The out-of-plane deformation vibrations for theoretical molecule are noticed at 824 cm−1 (O(20)–H(34)), 781, 691 cm−1 (O(10)–H(24)) and at lower frequencies: 448 cm−1 (O(19)–H(35) and 433 cm−1 (O(18)–H(22)). The verification of these calculated values as well as comparison with experimental data are quite difficult. In real crystal two hydrogen bonds are observed: one is strong with ˚ while the second is a longer and equal to distance 2.54 A ˚ It is clear that calculated values of frequencies noticed 2.74 A. for bands arising from vibrations of hydrogen bonds are different than that in the case of real crystal. It seems to be clear that for the shorter O–H···O hydrogen bond the broad band with three components A, B and C arising from stretching vibrations of the hydrogen bond should be observed. The B and C components are identified at 2727 and 1940 cm−1 , respectively. Of course, this broad shape and sub-maxima are not reflected in DFT harmonic approximation.

The bands arising from deformation vibrations of above mentioned hydrogen bonds are expected in the range of 1300–800 cm−1 . According to PED calculation and literature data the reliable assignment of bands originating from ␦OH vibration seems to be possible. Thus, the weak band at 1313 cm−1 was assigned to in-plane deformation vibrations of OH groups. The calculated frequencies of bands arising from this type of vibrations are in the wide range, but four values seems to be adequate (1320, 1316, 1290 and 1267 cm−1 ). The out-of-plane bending modes (␥OH) could be identified in powder IR spectra in the range 950–750 cm−1 . In real infrared spectrum the weak bands at 937 and 911 cm−1 are observed. These bands may correspond to ␥OH but this assignment seems to be uncertain. In this case, the calculated frequencies are in poor agreement with experimental data. Of course, it is not surprise because the calculated lengths of hydrogen bonds are different than in real crystal. On the other hand, it is interesting that frequencies of bands originating from ␥OH vibrations seem to be more sensitive and depending on length of hydrogen bonds stronger than frequencies of bands assigned to in-plane deformation vibrations of OH group. 3.4.5. N–H vibrations In the real crystal six N–H···O hydrogen bonds were detected. The lengths of these bonds are in the range ˚ It is characteristic that three protons con2.7022–3.0329 A. nected with N(9*) atoms are involved in these interaction (the N(9*)–H is involved in the bifurcated hydrogen bonds), whereas only two hydrogen atoms from second NH3 group (N(8*) nitrogen atom) make typical hydrogen bonds. In theoretical molecule three hydrogen bonds are noticed only. In first, the H(34) atom is involved, whereas in other hydrogen bonds the protons H(32) and H(40) are involved. The stretching and bending vibrations of the NH3 group in real may be considered as vibrations of the N–H···O hydrogen

22

M. Drozd, M.K. Marchewka / Spectrochimica Acta Part A 64 (2006) 6–23

bonds. In the IR spectrum of the investigated crystal one can notice a broad band with additional structure at ca. 3245 and 3165 cm−1 . This antisymmetric band should be assigned to ␯NH of the N–H···O hydrogen bond. ˚ The longest N···O distance is equal to 3.03 A (N2–H2C···O1C), therefore, the vibrations of the NH3 group may be considered as antisymmetric (␯as NH3 ) and symmetric (␯s NH3 ). The band arising from (␯as NH3 ) is noticed at 3326 cm−1 . The band of symmetric stretching vibrations of this group is invisible in IR spectrum measured as nujol mulls. Similar situation is observed in theoretical calculation. The bands observed at 3266 cm−1 should be assigned to antisymmetric stretching vibrations of NH3 group. The band originating from ␯s NH3 is observed at 3173 cm−1 . The bands noticed at 3245 and 3165 cm−1 are assigned to stretching vibrations of N–H···O bonds. It is worthwhile mentioning here that in the case of these bonds the very good agreement between experimental and theoretical frequencies is observed. Of course, in calculation the scaling factor (0.92) was used. The other bands in experimental spectrum (till ca. 2000 cm−1 ) are typical for the N–H···O hydrogen bonds. They arise from overtones. It is clear that these bands are not presents in theoretical calculation, because the harmonic approximation is used. The PED analysis shows that the bands arising from deformation in-plane vibrations of the amino group should be observed at 1649 and 1623 cm−1 . The counterparts of these bands are noticed in real spectrum at 1648, 1582 and 1506 cm−1 . In both spectra, the intensities of these bands are weak. The region of rocking vibrations of NH3 group exhibits in experimental IR spectrum (1200–1100 cm−1 ) a lot of bands. The assignment of these bands without PED analysis is difficult. The theoretical approach shows that two complex bands at 1194, 1183, 1085, 1068, 1050 and 1012 cm−1 should be assigned partially to out-of-plane deformation vibrations of NH3 groups. On the basis of this analysis, the two bands in real spectrum (at 1138 and 1122 cm−1 ) were noticed as arising from ␳NH3 group. According to PED analysis the bands observed at 979 and 824 cm−1 were assigned partially to ␻NH3 vibrations. The clear-cut assignment of them in experimental infrared spectrum is very difficult. The bands observed at 966 cm−1 should be assigned to this type of vibrations. The PED calculations show that participation of ␶NH3 vibrations is observed in experimental spectrum in the band at 515 cm−1 . The other bands which should be assigned to ␶NH3 vibrations are noticed at 376, 365 and 318 cm−1 . This region is not present in real IR spectrum and comparison of calculated frequencies with experimental one is not possible. The participation of N–H···O deformation vibrations is observed in bands arising from skeletal vibrations of investigated molecule. The low frequency bands noticed at 102, 86, 79, 56, 51 and 36 cm−1 originate partially from this type of vibration.

3.4.6. C–N vibrations According to theoretical calculation the bands derived from stretching vibration of C–N bonds are noticed in the range 1077–816 cm−1 . The vibrations of C(1)–N(8) bond are involving in bands at 1050 cm−1 , whereas in the bands at 1077, 1003, 979, 908 and 916 cm−1 both C(1)–H(8) and C(5)–N(9) bonds are participated. As bands originating from this type of vibration in IR experimental spectrum the bands at 1003, 889 and 844 cm−1 were proposed. Surprisingly, the bands arising from deformation vibrations of CCN groups are noticed at higher frequencies than that taken from the literature data [30]. Our calculations show that these bands should be observed at 570, 514 and 481 cm−1 . The calculated intensities of these bands are small. The first band is mixed strongly, whereas the others have “pure” character. On the basis of these calculation and literature data the bands at 464 and 430 cm−1 were assigned to the deformation vibrations of CCN groups, but this assignment seems to be an open question. The detailed PED analysis suggests strongly that in low frequency bands observed at 205, 160, 151, 118, 79 and 11 cm−1 the medium participation of the deformation vibration of CCN takes place.

4. Conclusions (1) For the l-lysine × tartaric acid complex the equilibrium geometry was calculated. One negative (imaginary) frequency obtained in DFT calculation of vibrational spectrum suggest strongly, that in geometry approach the equilibrium transition state was determined. (2) Analysis of calculated geometry parameters and comparison with crystallographic data is very helpful in determination of unambiguous position of atoms in future X-ray studies. (3) According to our theoretical studies the postulated (by previous crystallographic study) disorder in tartaric acid molecule seems to be questionable. (4) The Lowdin charges analysis shows that negative charge in investigated molecule is de-localized between nitrogen, oxygen and carbon atoms. The positive charges are localized on the all hydrogen atoms and on three carbon atoms from carboxylic groups. Surprisingly, the Mulliken population analysis in the case of investigated complex suggests wrong values of electrostatic charges. (5) The obtained values of hyperpolarizability, β, seem to be too small than experimental values. The relatively big value of second hyperpolarizability, γ, shows that l-lysine × tartaric acid complex can be used as third harmonic light generator. (6) Almost all bands of the infrared spectra were assigned on the basis of potential energy distribution analysis. In spite of the good agreement for frequencies in general, the greatest discrepancies were observed for bands aris-

M. Drozd, M.K. Marchewka / Spectrochimica Acta Part A 64 (2006) 6–23

ing from out-of-plane deformation vibrations of hydrogen bonds. This discrepancy can result from the limitation followed from the isolated molecule model used in this theoretical approach. These calculations ignore intermolecular couplings that may occur in the solid state.

Acknowledgments The work was financially supported by Ministry of Science and Information Society Technologies (Project No. 3 T09A 121 28). The calculations were performed on the computers of Wrocław Supercomputer and Networking Center.

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