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DFT study and IR spectra of hexaphenoxycyclotriphosphazene G0c′ generation phosphorus dendrimer
Chemical Physics 330 (2006) 349–354 www.elsevier.com/locate/chemphys
DFT study and IR spectra of hexaphenoxycyclotriphosphazene G00c generation phosphorus dendrimer V.L. Furer
a,*
, I.I. Vandyukova c, C. Padie b, J.P. Majoral b, A.M. Caminade b, V.I. Kovalenko c,*
a Kazan State Architect and Civil Engineering University, Zelenaya, 1, Kazan 420043, Russia Laboratorie de Chimie de Coordination, CNRS, 205 route de Narbonne, 31077 Toulouse Cedex 4, France A.E. Arbuzov Institute of Organic and Physical Chemistry, Russian Academy of Science, Arbuzov Street, 8, 420088 Kazan, Russia b
c
Received 26 May 2006; accepted 11 August 2006 Available online 16 August 2006
Abstract The infrared (150–3500 cm1) spectra have been recorded for hexaphenoxycyclotriphosphazene [NP(OPh)2]3 and all-D isotope specie. These compounds include a cyclotriphosphazene core and terminal phenoxy groups of elementoorganic dendrimers. The structural optimization and normal mode analysis are performed for elementoorganic dendrimer on the basis of the ab initio density functional theory. It is found that the dendrimer exists in a single stable conformation with slightly non-planar cyclotriphosphazene core. Relying on DFT calculations a complete vibrational assignment is proposed for different parts of the studied dendrimers. The softness of sulphur atom in the thiophosphoryl core to nucleophilic attack is higher than the softness of the atoms of the cyclotriphosphazene core. The reactivity of the core is less than that of terminal groups. Ó 2006 Elsevier B.V. All rights reserved. Keywords: Phosphorus-containing dendrimers; IR spectra; Normal vibrations; DFT
1. Introduction Dendritic-type architectures are frequently encountered in the biological world, such as the branches and roots of plants [1–3]. Dendrimers constitute a small-scale artificial model of these natural dendritic architectures [4–6]. The three structural components of dendrimers, namely an interior core, repeating branching units radially attached to the core, and functional terminal groups attached to the outermost branching units, can be tuned at will [2]. A fine control of the overall size (the generation), shape, and properties of the dendrimer, creating special three-dimen-
* Corresponding authors. Tel.: +7 8432 104737; fax: +7 8432 387972 (V.L. Furer); tel.: +7 8432 732283; fax: +7 8432 732253 (V.I. Kovalenko). E-mail addresses: [email protected] (V.L. Furer), [email protected] (V.I. Kovalenko).
0301-0104/$ - see front matter Ó 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.chemphys.2006.08.009
sional environments, can be achieved [2]. To yield a better understanding of the properties imparted by each component to the whole structure and the influence of each part on the others, it is highly desirable to introduce the quantum density functional theory (DFT) studies of electronic structure of low-generation dendrimers. The preparation and IR and Raman spectra of phosphorus dendrimers with thiophosphoryl core built up to 12th generation with terminal aldehyde and P–Cl groups were reported [7–10]. Considering the size of dendrimer molecules the difficulty arises in spectral interpretation, and, therefore, DFT calculations would help facilitate spectral assignment. In this paper we report the IR spectra study combined with DFT calculations of hexaphenoxycyclotriphosphazene ðG00c -H Þ and all-D isotope specie ðG00c -DÞ which is the zero generation phosphorus dendrimer built from cyclotriphosphazene core. These dendrimers have ‘‘spheri-
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V.L. Furer et al. / Chemical Physics 330 (2006) 349–354
cal’’ architecture and optimal occupation of space as compared with ‘‘conical’’ architecture of dendrimers with thiophosphoryl core. This work is an extension of the spectroscopic and quantum chemical studies concerning the structure and reactivity of phosphorus dendrimers. During full optimization we were able to find local minimum conformer of G00c -H and G00c -D molecules and their IR spectra using DFT techniques. The values of calculated geometric parameters were compared with precise molecular structure derived by the X-ray analysis [11]. Thus the main aim of this work was to obtain the characteristic spectral features of structural parts of dendrimer: a cyclotriphosphazenic core and terminal phenoxy groups based on ab initio quantum chemical analysis. The results that emerge from such an analysis contribute to the understanding of the structure, dynamics and properties of dendrimers. 2. Experimental The synthesis and main characteristics of the studied phosphorus dendrimer were described earlier [3,8]. The G00c -H molecules contain the following parts of dendrimers: a hexafunctional core (NP)3 and phenoxy fragments –O– C6H5 as the end-groups (Fig. 1). In all-D isotope specie ðG00c -DÞ the terminal groups were –O–C6D5. IR spectra in the region 3500–150 cm1 were recorded on an IFS-113v Bruker FTIR-spectrophotometer with a 4 cm1 resolution.
3. Computational method Calculations of IR spectra of dendrimers G00c -H and were carried out using the gradient-correlated density functional theory with Perdew–Burke–Ernzerhof exchange-correlation functional (DFT/PBE) [12]. This functional is very satisfactory from the theoretical point of view, because it verifies many of the exact conditions for the exchange-correlation hole and it does not contain any fitting parameters [13]. The binding energies, geometries and dynamical properties of different molecules calculated with PBE functional show the best agreement with experiment [14,15]. Calculations were performed using three exponential basis with two polarizing functions (TZ2P) [16]. This basis set was chosen in order to obtain the most advantageous relation of accuracy and computation time [16]. Its peculiarity is that the same set of exponents is used for all values of angle moment in atom [16]. The program PRIRODA was used to perform DFT calculations [16]. All stationary points were characterized as minima by analysis of Hessian matrices. The software package SHRINK was used for transformation of quantum mechanical Cartesian force constants to the matrix in redundant internal coordinates and calculation of potential energy distribution [17]. No scaling procedure of frequencies or force constants was applied. Recently, we checked the selected functional and basis set by calculation of geometry and IR spectra of dendrimers [18,19]. G00c -D
Fig. 1. Optimized geometry and atom numbering for G00c -H .
V.L. Furer et al. / Chemical Physics 330 (2006) 349–354
The minima of the potential surface were found by relaxing the geometric parameters with standard optimization methods. IR spectra were generated from a list of frequencies and intensities using Gaussian band shape and half-width r of 10 cm1 for each of N vibration modes calculated. The intensity of each band is Ak in km/mol: ( ) 2 N X Ak ðm m0 Þ pffiffiffiffiffiffi exp IðmÞ ¼ 2r2 2pr k An assignment of bands was fulfilled on the basis of calculated potential energy distribution (PED). The electronic chemical potential, the chemical hardness and softness were obtained from the expressions l (IE + EA)/2, g (IE EA) and S = 1/2g, in terms of the first vertical ionization energy IE and electron affinity EA, respectively [20]. The Fukui functions fkþ ðrÞ ¼ ½qk ðN þ 1Þ qk ðN Þ for nucleophilic attack, and fk ðrÞ ¼ ½qk ðN Þ qk ðN 1Þ for electrophilic attack, where qk is the electronic population of atom k in the molecule, N the number of electrons, were calculated. The local softness is obtained by projecting the global quantity onto any
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atomic centre k in the molecule by using the Fukui funcþ tion: sþ k ¼ Sf k , sk ¼ Sf k . The Fukui function and local softness for each reactive atom were calculated using Hirshfeld population analysis [21]. 4. Results and discussion The geometric parameters of G00c -H in crystalline state were defined by the X-ray diffraction method [11]. Three main features of this compound can be emphasized. The cyclotriphosphazene ring is slightly non-planar, with two˚ in opposite directions nitrogen atoms displaced by 0.15 A from the plane of the other four (three phosphorus and one nitrogen) atoms [14]. The conformations of the phenoxy groups are different at the three phosphorus atoms, and there are small deviations among chemically equivalent angles [11]. There are no differences among chemically equivalent bond lengths [11]. Although the comparison between gas phase and condensed phase structures is not direct, we can observe a reasonable agreement between theoretical calculations and
Table 1 ˚ ) and bond angles (°) of G0 -H Experimental and calculated bond distances (A 0c Experimental [9] Bond distances P(1)–N(1) P(1)–N(3) P(2)–N(1) P(2)–N(2) P(3)–N(2) P(3)–N(3) C(1)–O(1) C(13)–O(3) C(25)–O(5) Angles N(1)–P(1)–N(3) N(1)–P(2)–N(2) N(2)–P(3)–N(3) P(1)–N(1)–P(2) P(2)–N(2)–P(3) P(1)–N(3)–P(3) O(1)–P(1)–O(2) O(3)–P(2)–O(4) O(5)–P(3)–O(6) P(1)–O(1)–C(1) P(1)–O(2)–C(7) P(2)–O(3)–C(13) P(2)–O(4)–C(19) P(3)–O(5)–C(25) Dihedral angles P(1)–N(1)–P(2)–N(2) N(1)–P(2)–N(2)–P(3) P(2)–N(2)–P(3)–N(3) P(1)–N(3)–P(3)–N(2) P(3)–N(3)–P(1)–N(1) P(2)–N(1)–P(1)–N(3) N(1)–P(1)–O(1)–C(1) N(1)–P(1)–O(2)–C(7) N(2)–P(2)–O(3)–C(13)
Calculated 1.574 1.581 1.572 1.573 1.574 1.575 1.395 1.409 1.407
1.610 1.611 1.611 1.609 1.608 1.611 1.399 1.410 1.400
117.3 117.9 116.6 121.3 122.4 122.1 100.1 100.1 94.1 128.7 123.5 121.3 124.8 120.8
119.9 120.2 119.8 119.8 120.0 120.1 104.5 104.3 104.1 126.7 126.3 121.0 126.6 126.6
4.3 11.8 4.8 9.9 16.6 9.3 174.7 20.6 168.8
2.3 0.7 0.3 1.5 3.1 3.6 173.4 60.8 47.3
Experimental [9] P(1)–O(1) P(1)–O(2) P(2)–O(3) P(2)–O(4) P(3)–O(5) P(3)–O(6) C(7)–O(2) C(19)–O(4) C(31)–O(6)
Calculated 1.583 1.576 1.583 1.578 1.584 1.585 1.412 1.406 1.406
1.635 1.633 1.635 1.637 1.633 1.637 1.400 1.396 1.400
O(1)–P(1)–N(3) O(2)–P(1)–N(3) O(1)–P(1)–N(1) O(2)–P(1)–N(1) O(3)–P(2)–N(1) O(4)–P(2)–N(1) O(3)–P(2)–N(2) O(4)–P(2)–N(2) O(5)–P(3)–N(2) O(6)–P(3)–N(2) O(5)–P(3)–N(3) O(6)–P(3)–N(3) P(3)–O(6)–C(31)
110.9 110.2 106.6 110.3 112.5 109.2 104.6 110.9 112.0 109.9 109.8 112.2 120.0
112.0 103.7 103.9 111.9 104.4 111.9 111.4 103.6 104.0 111.9 112.3 103.8 125.9
P(1)–O(1)–C(1)–C(2) P(1)–O(2)–C(7)–C(8) P(2)–O(3)–C(13)–C(14) P(2)–O(4)–C(19)–C(20) P(3)–O(5)–C(25)–C(26) P(3)–O(6)–C(31)–C(32) N(2)–P(2)–O(4)–C(19) N(3)–P(3)–O(5)–C(25) N(3)–P(3)–O(6)–C(31)
172.8 59.7 80.8 110.0 74.9 101.0 111.0 55.3 78.0
176.1 166.0 96.2 0.8 11.6 19.0 1.0 56.1 169.3
V.L. Furer et al. / Chemical Physics 330 (2006) 349–354
experimental X-ray diffraction data for the crystal phase of G00c -H [11] (Table 1). Full optimization yielded the conformer of G00c -H with slightly non-planar cyclotriphosphazene ring. The calculated dihedral angles of cyclotriphosphazene ring are less than 4°. Our data correspond to recent ab initio calculations of phosphazenes [22]. It was shown that most of cyclotriphosphazene derivatives have planar ring conformations [22]. The conformations of the phenoxy groups are different at the three phosphorus atoms for theoretical structure and in the crystalline state. These deviations may be ascribed to intermo˚) lecular steric effect. The calculated bond distances (in A 1.610 (P–N), 1.634 (P–O), 1.400 (C–O) correspond well to the experimental values 1.575, 1.582, 1.406. The theoretical bond angles (in degrees) NPN (119.9), PNP (120.0), OPO (104.5), OPN (112.0), POC (125.9) are also in close agreement with the experimental values 117.3, 121.3, 100.1, 110.9, 120.0. DFT total energy calculations reveal G00c -H molecules to have only one of low-energy stable conformation. No evidence of metastable conformations, which have a similar energy were found. The barrier to rotation of benzene rings around CO bond is about 10 kcal/mol and a flip process in the seemed not to be noticeable. The concept of using dendrimers as new types of carriers of active substances was propounded until the very beginning of the research in the field of dendrimers chemistry [1–3]. In order to evaluate the interactions between dendrimers and various active substances such as drugs, pesticides, perfumes etc., we calculated electronic density spatial distribution for the core and terminal groups. From our calculations it follows that the studied phosphorus-containing dendrimers incorporate strong P–N polar bonds in the core with Hirshfeld atomic charges (in au) on atoms N (0.31) and P (0.48). The oxygen atoms of the terminal group also have negative charges 0.13. Thus there are active sites for reaction and interaction inside dendrimer. The experimental and calculated IR spectra of G00c -H and G00c -D are represented at Fig. 2 and in Tables 2 and 3. The intense bands at 1589, 1487 cm1 in the IR spectra of G00c -H refer to CCar stretch and CCH bending vibrations of aromatic ring. The corresponding bands at 1557, 1370 cm1 in the IR spectra of G00c -D are due to CCar stretch and CCD bending vibrations. The rather weak band at 1455 cm1 in the IR spectra of G00c -H corresponds to CCar stretch and CCH bending vibrations of aromatic ring. The strong band at 1269 cm1 in the IR spectra of G00c -H is due to P–N and C–O stretching vibrations. The strong bands at 1248, 1240 cm1 in the IR spectra of G00c -D are also connected with P–N and C–O stretching vibrations. The very strong and complex bands in the experimental IR spectra of G00c -H at 1192, 1180, 1164 cm1 and the intense band at 1138 cm1 in the IR spectra G00c -D refer to C–O and P–N stretch. The weak in the IR spectra of G00c -H bands at 1070, 1023, 1006 cm1 are assigned to
CCH bending and CCar stretching vibrations of aromatic ring. The weak band at 1041 cm1 in the IR spectra of G00c -D was assigned to CCD bend.
4
3 Extinction
352
2
1
400
600
800
1000
1200
1400
1600
Wavenumber/cm-1 Fig. 2. Theoretical (1,3) and experimental (2,4) IR spectra of G00c -H (1,2) and G00c -D (3,4).
Table 2 Experimental and corresponded calculated frequencies m (cm1) and intensity I (km/mol) of bands in the IR spectra of G00c -H Experiment
Calculation, assignment
m
m
I
PED
1589 1487 1455 1269 1192 1180 1164 1070 1023 1006 947 906 883 815 781 726 690 616 585 573 556 531 502 433
1590 1482 1449 1233 1184 1181 1165 1076 1027 1007 950 902 859 805 773 730 706 613 584 564 556 540 496 422
39.3 186.3 2.3 114.7 248.2 282.2 129.5 14.3 34.3 10.6 5.7 277.0 395.5 1.3 1.3 23.2 85.0 4.0 0.8 1.6 32.7 1.2 92.0 25.8
69 59 62 42 45 43 64 52 56 65 56 58 34 95 25 71 33 66 23 26 29 31 36 21
m(CCar), 23 d(CCH) d(CCH), 36 m(CCar) d(CCH), 35 m(CCar) m(PN), 30 m(CO), 8 m(CCar) m(CO), 23 d(CCH), 18 m(CCar) m(CO), 23 d(CCH), 17 m(CCar) d(CCH), 15 m(CO), 14 m(CCar) d(CCH), 44 m(CCar) m(CCar), 39 d(CCH) d(CCH), 31 m(CCar) m(PO), 17 m(CCar), 10 m(PN) m(PO), 15 m(CO), 12 m(CCar) m(PN), 14 m(PO), 11 m(CO) q(CH) m(PN), 19 m(CO), 8 m(PO) q(CH), 9 m(PO) m(PO), 16 d(CCC), 12 m(CO) d(CCC), 24 d(CCH) d(POC), 18 d(CCC), 7 d(PNP) d(POC), 22 d(CCC) d(POC), 15 d(CCC), 6 d(OCC) d(CCC), 12 d(POC) v(CC), 9 v(PO), 9 v(PN) d(OCC), 14 v(PO), 8 d(PNP)
V.L. Furer et al. / Chemical Physics 330 (2006) 349–354 Table 3 Experimental and corresponded calculated frequencies m (cm1) and intensity I (km/mol) of bands in the IR spectra of G00c -D Experiment
Calculation, assignment
m
m
I
PED
1557 1370 1248 1240 1138 1041 970 939 921 887 858 841 807 779 716 704 638 568 536 521 500 476 448
1557 1368 1209 1206 1121 1031 971 936 902 897 856 844 800 779 711 681 625 553 534 526 516 471 448 403
27.2 166.7 566.0 584.0 1761.9 13.6 14.5 4.4 594.7 205.6 50.9 62.8 200.9 3.2 49.7 37.3 3.5 22.9 13.2 0.1 8.2 116.7 150.2 11.2
75 43 69 68 41 81 20 47 55 51 71 82 52 89 22 25 90 50 24 29 31 26 14 25
m(CCar), 10 d(CCD) m(CCar), 26 d(CCD), 21 m(CO) m(PN), 9 m(CO), 5 m(CCar) m(PN), 12 m(CO), 6 m(CCar) m(CO), 22 m(PN), 10 m(CCar) d(CCD) d(CCC), 17 m(CCar), 9 m(PO) m(PO), 37 m(CCar), 9 m(PN) m(PO), 25 m(CCar), 11 m(CO) m(PO), 27 m(CCar), 13 m(CO) d(CCD), 11 m(PO), 6 m(CCar) d(CCD), 11 m(CCar) d(CCD), 14 m(CCar), 13 m(PO) q(CD) m(PO), 12 m(CO), 11 d(CCC) m(PO), 14 m(CO), 12 d(CCC) q(CD) q(CD), 12 d(CCC), 10 m(PO) d(CCC), 16 d(POC), 7 d(OCC) d(CCC), 13 d(OCC), 12 d(POC) q(CD), 18 d(CCC), 12 d(POC) d(NPO), 25 v(PN), 11 d(POC) d(PNP), 14 v(PO), 13 d(CCC) d(OCC), 12 v(PO), 11 d(PNP)
The strong bands at 947, 883 cm1 in the IR spectra of and the intense bands at 939, 887 cm1 in the IR spectra of G00c -D were assigned to P–O stretch. The medium-intensity bands at 781, 690 cm1 in the IR spectra of G00c -H refer to P–N, C–O and P–O stretch. The band at 726 cm1 in the IR spectra of G00c -H refer to CH out-of-plane bending vibrations. The band at 616 cm1 in the IR spectra of G00c -H is connected with CCC and CCH bending vibrations. The bands at 586, 573, 556, 531, 433 cm1 in the IR spectra of G00c -H are assigned to POC and CCC bending vibrations. The band at 502 cm1 in the IR spectra of G00c -H refers to torsion around CC bond. Thus the dendrimer core (NP)3, reveal itself by band at 1269 cm1 in the IR spectra of G00c -H assigned to P–N stretch. In the IR spectra of G00c -D this band is located at 1240 cm1. The phenoxy terminal groups are characterized by the well-defined bands at 1487, 1589 cm1 in the experimental IR spectra of G00c -H and by bands at 1370, 1557 cm1 in the IR spectra of G00c -D. The reactivity of the end groups of these dendrimers is amongst the most versatile and the most widely studied [3]. A huge number of reactions on the end groups of the studied dendrimes have been carried out [3]. For instance, dendrimers having three or even four different types of end groups simultaneously have been described, for the first time [3]. This very special and so far unique type of functionalization was called ‘‘multiplurifunctionalization’’ [3]. In this work we try to characterize the reactivity of dendrimer G00c -H with phenoxy end groups by means of global G00c -H ,
353
Table 4 Global reactivity descriptors of G00c -H Ionization energy, eV
Electron affinity, eV
Chemical potential, eV
Global softness, au
5.789
1.383
3.586
3.086
Table 5 Local reactivity descriptors (au) of G00c -H Atom
P N O C H
Electronic population
Fukui function
Local softness
qk(N 1)
qk(N)
qk(N + 1)
fk
fkþ
s k
sþ k
14.510 7.307 8.126 5.920 0.941
14.516 7.314 8.135 5.931 0.950
14.519 7.307 8.137 5.935 0.960
0.006 0.007 0.009 0.011 0.009
0.003 0.007 0.002 0.004 0.010
0.019 0.022 0.028 0.034 0.028
0.009 0.022 0.006 0.012 0.031
and local reactivity descriptors (Tables 4 and 5). The ionization energy IE, affinity EA, the global softness and reactivity of dendrimer G00c -H and G1 are very similar to the corresponding values of dendrimers G1 and G01 with thiophosphoryl core and terminal PCl2 and aldehyde groups [21,22]. The local softness of the G00c -H and G01 are quite different. The softness of sulphur atom in the thiophosphoryl core to nucleophilic attack is higher than the softness of the atoms of the cyclotriphosphazene core. We found that the softness values of atoms of the terminal S@PCl2 and aldehyde groups in the G1 and G01 are higher, than softness of atoms of phenoxy end group in G00c -H . The most reactive place is located in the terminal groups in dendrimers G1 and G01 , the core P@S bond is less active. In G00c -H the reactivity of the core is also less than that of terminal groups. The intensity of the most prominent bands in the IR spectra of G00c -H and G00c -D is reproduced by our calculations. The calculated absorption curves of G00c -H and G00c -D as a whole corresponds to the experimental IR spectra in the wide frequency region. Thus the employed DFT method enables one to calculate the structure, charges on atoms, and reproduce the experimental IR spectra of the phosphorus dendrimer with cyclotriphosphazene core and phenoxy end groups. References [1] F. Vogtle, S. Gestermann, R. Hesse, H. Schwierz, B. Windisch, Progr. Polym. Sci. 25 (2000) 987. [2] J. Leclaire, R. Gagiral, S. Fery-Forgues, Y. Coppel, B. Donnadieu, A.M. Caminade, J.P. Majoral, J. Am. Chem. Soc. 127 (2005) 15762. [3] J.P. Majoral, A.M. Caminade, V. Maraval, Chem. Commun. (2002) 2929. [4] J.M.J. Frechet, D.A. Tomalia, Dendrimers and Other Dendritic Polymers, Wiley, New York, 2002. [5] D.K. Smith, Tetrahedron 59 (2003) 3797. [6] S.C. Zimmerman, L.J. Lawless, Top. Curr. Chem. 217 (2001) 95. [7] A.M. Caminade, J.P. Majoral, Progr. Polym. Sci. 30 (2005) 491. [8] A.M. Caminade, J.P. Majoral, in: M. Gleria, R. de Jaeger (Eds.), Phosphazenes: a Worldwide Insight, NOVA Science Publishers, New York, 2004, p. 713 (Chapter 30).
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DFT study and IR spectra of hexaphenoxycyclotriphosphazene G00c generation phosphorus dendrimer V.L. Furer
a,*
, I.I. Vandyukova c, C. Padie b, J.P. Majoral b, A.M. Caminade b, V.I. Kovalenko c,*
a Kazan State Architect and Civil Engineering University, Zelenaya, 1, Kazan 420043, Russia Laboratorie de Chimie de Coordination, CNRS, 205 route de Narbonne, 31077 Toulouse Cedex 4, France A.E. Arbuzov Institute of Organic and Physical Chemistry, Russian Academy of Science, Arbuzov Street, 8, 420088 Kazan, Russia b
c
Received 26 May 2006; accepted 11 August 2006 Available online 16 August 2006
Abstract The infrared (150–3500 cm1) spectra have been recorded for hexaphenoxycyclotriphosphazene [NP(OPh)2]3 and all-D isotope specie. These compounds include a cyclotriphosphazene core and terminal phenoxy groups of elementoorganic dendrimers. The structural optimization and normal mode analysis are performed for elementoorganic dendrimer on the basis of the ab initio density functional theory. It is found that the dendrimer exists in a single stable conformation with slightly non-planar cyclotriphosphazene core. Relying on DFT calculations a complete vibrational assignment is proposed for different parts of the studied dendrimers. The softness of sulphur atom in the thiophosphoryl core to nucleophilic attack is higher than the softness of the atoms of the cyclotriphosphazene core. The reactivity of the core is less than that of terminal groups. Ó 2006 Elsevier B.V. All rights reserved. Keywords: Phosphorus-containing dendrimers; IR spectra; Normal vibrations; DFT
1. Introduction Dendritic-type architectures are frequently encountered in the biological world, such as the branches and roots of plants [1–3]. Dendrimers constitute a small-scale artificial model of these natural dendritic architectures [4–6]. The three structural components of dendrimers, namely an interior core, repeating branching units radially attached to the core, and functional terminal groups attached to the outermost branching units, can be tuned at will [2]. A fine control of the overall size (the generation), shape, and properties of the dendrimer, creating special three-dimen-
* Corresponding authors. Tel.: +7 8432 104737; fax: +7 8432 387972 (V.L. Furer); tel.: +7 8432 732283; fax: +7 8432 732253 (V.I. Kovalenko). E-mail addresses: [email protected] (V.L. Furer), [email protected] (V.I. Kovalenko).
0301-0104/$ - see front matter Ó 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.chemphys.2006.08.009
sional environments, can be achieved [2]. To yield a better understanding of the properties imparted by each component to the whole structure and the influence of each part on the others, it is highly desirable to introduce the quantum density functional theory (DFT) studies of electronic structure of low-generation dendrimers. The preparation and IR and Raman spectra of phosphorus dendrimers with thiophosphoryl core built up to 12th generation with terminal aldehyde and P–Cl groups were reported [7–10]. Considering the size of dendrimer molecules the difficulty arises in spectral interpretation, and, therefore, DFT calculations would help facilitate spectral assignment. In this paper we report the IR spectra study combined with DFT calculations of hexaphenoxycyclotriphosphazene ðG00c -H Þ and all-D isotope specie ðG00c -DÞ which is the zero generation phosphorus dendrimer built from cyclotriphosphazene core. These dendrimers have ‘‘spheri-
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cal’’ architecture and optimal occupation of space as compared with ‘‘conical’’ architecture of dendrimers with thiophosphoryl core. This work is an extension of the spectroscopic and quantum chemical studies concerning the structure and reactivity of phosphorus dendrimers. During full optimization we were able to find local minimum conformer of G00c -H and G00c -D molecules and their IR spectra using DFT techniques. The values of calculated geometric parameters were compared with precise molecular structure derived by the X-ray analysis [11]. Thus the main aim of this work was to obtain the characteristic spectral features of structural parts of dendrimer: a cyclotriphosphazenic core and terminal phenoxy groups based on ab initio quantum chemical analysis. The results that emerge from such an analysis contribute to the understanding of the structure, dynamics and properties of dendrimers. 2. Experimental The synthesis and main characteristics of the studied phosphorus dendrimer were described earlier [3,8]. The G00c -H molecules contain the following parts of dendrimers: a hexafunctional core (NP)3 and phenoxy fragments –O– C6H5 as the end-groups (Fig. 1). In all-D isotope specie ðG00c -DÞ the terminal groups were –O–C6D5. IR spectra in the region 3500–150 cm1 were recorded on an IFS-113v Bruker FTIR-spectrophotometer with a 4 cm1 resolution.
3. Computational method Calculations of IR spectra of dendrimers G00c -H and were carried out using the gradient-correlated density functional theory with Perdew–Burke–Ernzerhof exchange-correlation functional (DFT/PBE) [12]. This functional is very satisfactory from the theoretical point of view, because it verifies many of the exact conditions for the exchange-correlation hole and it does not contain any fitting parameters [13]. The binding energies, geometries and dynamical properties of different molecules calculated with PBE functional show the best agreement with experiment [14,15]. Calculations were performed using three exponential basis with two polarizing functions (TZ2P) [16]. This basis set was chosen in order to obtain the most advantageous relation of accuracy and computation time [16]. Its peculiarity is that the same set of exponents is used for all values of angle moment in atom [16]. The program PRIRODA was used to perform DFT calculations [16]. All stationary points were characterized as minima by analysis of Hessian matrices. The software package SHRINK was used for transformation of quantum mechanical Cartesian force constants to the matrix in redundant internal coordinates and calculation of potential energy distribution [17]. No scaling procedure of frequencies or force constants was applied. Recently, we checked the selected functional and basis set by calculation of geometry and IR spectra of dendrimers [18,19]. G00c -D
Fig. 1. Optimized geometry and atom numbering for G00c -H .
V.L. Furer et al. / Chemical Physics 330 (2006) 349–354
The minima of the potential surface were found by relaxing the geometric parameters with standard optimization methods. IR spectra were generated from a list of frequencies and intensities using Gaussian band shape and half-width r of 10 cm1 for each of N vibration modes calculated. The intensity of each band is Ak in km/mol: ( ) 2 N X Ak ðm m0 Þ pffiffiffiffiffiffi exp IðmÞ ¼ 2r2 2pr k An assignment of bands was fulfilled on the basis of calculated potential energy distribution (PED). The electronic chemical potential, the chemical hardness and softness were obtained from the expressions l (IE + EA)/2, g (IE EA) and S = 1/2g, in terms of the first vertical ionization energy IE and electron affinity EA, respectively [20]. The Fukui functions fkþ ðrÞ ¼ ½qk ðN þ 1Þ qk ðN Þ for nucleophilic attack, and fk ðrÞ ¼ ½qk ðN Þ qk ðN 1Þ for electrophilic attack, where qk is the electronic population of atom k in the molecule, N the number of electrons, were calculated. The local softness is obtained by projecting the global quantity onto any
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atomic centre k in the molecule by using the Fukui funcþ tion: sþ k ¼ Sf k , sk ¼ Sf k . The Fukui function and local softness for each reactive atom were calculated using Hirshfeld population analysis [21]. 4. Results and discussion The geometric parameters of G00c -H in crystalline state were defined by the X-ray diffraction method [11]. Three main features of this compound can be emphasized. The cyclotriphosphazene ring is slightly non-planar, with two˚ in opposite directions nitrogen atoms displaced by 0.15 A from the plane of the other four (three phosphorus and one nitrogen) atoms [14]. The conformations of the phenoxy groups are different at the three phosphorus atoms, and there are small deviations among chemically equivalent angles [11]. There are no differences among chemically equivalent bond lengths [11]. Although the comparison between gas phase and condensed phase structures is not direct, we can observe a reasonable agreement between theoretical calculations and
Table 1 ˚ ) and bond angles (°) of G0 -H Experimental and calculated bond distances (A 0c Experimental [9] Bond distances P(1)–N(1) P(1)–N(3) P(2)–N(1) P(2)–N(2) P(3)–N(2) P(3)–N(3) C(1)–O(1) C(13)–O(3) C(25)–O(5) Angles N(1)–P(1)–N(3) N(1)–P(2)–N(2) N(2)–P(3)–N(3) P(1)–N(1)–P(2) P(2)–N(2)–P(3) P(1)–N(3)–P(3) O(1)–P(1)–O(2) O(3)–P(2)–O(4) O(5)–P(3)–O(6) P(1)–O(1)–C(1) P(1)–O(2)–C(7) P(2)–O(3)–C(13) P(2)–O(4)–C(19) P(3)–O(5)–C(25) Dihedral angles P(1)–N(1)–P(2)–N(2) N(1)–P(2)–N(2)–P(3) P(2)–N(2)–P(3)–N(3) P(1)–N(3)–P(3)–N(2) P(3)–N(3)–P(1)–N(1) P(2)–N(1)–P(1)–N(3) N(1)–P(1)–O(1)–C(1) N(1)–P(1)–O(2)–C(7) N(2)–P(2)–O(3)–C(13)
Calculated 1.574 1.581 1.572 1.573 1.574 1.575 1.395 1.409 1.407
1.610 1.611 1.611 1.609 1.608 1.611 1.399 1.410 1.400
117.3 117.9 116.6 121.3 122.4 122.1 100.1 100.1 94.1 128.7 123.5 121.3 124.8 120.8
119.9 120.2 119.8 119.8 120.0 120.1 104.5 104.3 104.1 126.7 126.3 121.0 126.6 126.6
4.3 11.8 4.8 9.9 16.6 9.3 174.7 20.6 168.8
2.3 0.7 0.3 1.5 3.1 3.6 173.4 60.8 47.3
Experimental [9] P(1)–O(1) P(1)–O(2) P(2)–O(3) P(2)–O(4) P(3)–O(5) P(3)–O(6) C(7)–O(2) C(19)–O(4) C(31)–O(6)
Calculated 1.583 1.576 1.583 1.578 1.584 1.585 1.412 1.406 1.406
1.635 1.633 1.635 1.637 1.633 1.637 1.400 1.396 1.400
O(1)–P(1)–N(3) O(2)–P(1)–N(3) O(1)–P(1)–N(1) O(2)–P(1)–N(1) O(3)–P(2)–N(1) O(4)–P(2)–N(1) O(3)–P(2)–N(2) O(4)–P(2)–N(2) O(5)–P(3)–N(2) O(6)–P(3)–N(2) O(5)–P(3)–N(3) O(6)–P(3)–N(3) P(3)–O(6)–C(31)
110.9 110.2 106.6 110.3 112.5 109.2 104.6 110.9 112.0 109.9 109.8 112.2 120.0
112.0 103.7 103.9 111.9 104.4 111.9 111.4 103.6 104.0 111.9 112.3 103.8 125.9
P(1)–O(1)–C(1)–C(2) P(1)–O(2)–C(7)–C(8) P(2)–O(3)–C(13)–C(14) P(2)–O(4)–C(19)–C(20) P(3)–O(5)–C(25)–C(26) P(3)–O(6)–C(31)–C(32) N(2)–P(2)–O(4)–C(19) N(3)–P(3)–O(5)–C(25) N(3)–P(3)–O(6)–C(31)
172.8 59.7 80.8 110.0 74.9 101.0 111.0 55.3 78.0
176.1 166.0 96.2 0.8 11.6 19.0 1.0 56.1 169.3
V.L. Furer et al. / Chemical Physics 330 (2006) 349–354
experimental X-ray diffraction data for the crystal phase of G00c -H [11] (Table 1). Full optimization yielded the conformer of G00c -H with slightly non-planar cyclotriphosphazene ring. The calculated dihedral angles of cyclotriphosphazene ring are less than 4°. Our data correspond to recent ab initio calculations of phosphazenes [22]. It was shown that most of cyclotriphosphazene derivatives have planar ring conformations [22]. The conformations of the phenoxy groups are different at the three phosphorus atoms for theoretical structure and in the crystalline state. These deviations may be ascribed to intermo˚) lecular steric effect. The calculated bond distances (in A 1.610 (P–N), 1.634 (P–O), 1.400 (C–O) correspond well to the experimental values 1.575, 1.582, 1.406. The theoretical bond angles (in degrees) NPN (119.9), PNP (120.0), OPO (104.5), OPN (112.0), POC (125.9) are also in close agreement with the experimental values 117.3, 121.3, 100.1, 110.9, 120.0. DFT total energy calculations reveal G00c -H molecules to have only one of low-energy stable conformation. No evidence of metastable conformations, which have a similar energy were found. The barrier to rotation of benzene rings around CO bond is about 10 kcal/mol and a flip process in the seemed not to be noticeable. The concept of using dendrimers as new types of carriers of active substances was propounded until the very beginning of the research in the field of dendrimers chemistry [1–3]. In order to evaluate the interactions between dendrimers and various active substances such as drugs, pesticides, perfumes etc., we calculated electronic density spatial distribution for the core and terminal groups. From our calculations it follows that the studied phosphorus-containing dendrimers incorporate strong P–N polar bonds in the core with Hirshfeld atomic charges (in au) on atoms N (0.31) and P (0.48). The oxygen atoms of the terminal group also have negative charges 0.13. Thus there are active sites for reaction and interaction inside dendrimer. The experimental and calculated IR spectra of G00c -H and G00c -D are represented at Fig. 2 and in Tables 2 and 3. The intense bands at 1589, 1487 cm1 in the IR spectra of G00c -H refer to CCar stretch and CCH bending vibrations of aromatic ring. The corresponding bands at 1557, 1370 cm1 in the IR spectra of G00c -D are due to CCar stretch and CCD bending vibrations. The rather weak band at 1455 cm1 in the IR spectra of G00c -H corresponds to CCar stretch and CCH bending vibrations of aromatic ring. The strong band at 1269 cm1 in the IR spectra of G00c -H is due to P–N and C–O stretching vibrations. The strong bands at 1248, 1240 cm1 in the IR spectra of G00c -D are also connected with P–N and C–O stretching vibrations. The very strong and complex bands in the experimental IR spectra of G00c -H at 1192, 1180, 1164 cm1 and the intense band at 1138 cm1 in the IR spectra G00c -D refer to C–O and P–N stretch. The weak in the IR spectra of G00c -H bands at 1070, 1023, 1006 cm1 are assigned to
CCH bending and CCar stretching vibrations of aromatic ring. The weak band at 1041 cm1 in the IR spectra of G00c -D was assigned to CCD bend.
4
3 Extinction
352
2
1
400
600
800
1000
1200
1400
1600
Wavenumber/cm-1 Fig. 2. Theoretical (1,3) and experimental (2,4) IR spectra of G00c -H (1,2) and G00c -D (3,4).
Table 2 Experimental and corresponded calculated frequencies m (cm1) and intensity I (km/mol) of bands in the IR spectra of G00c -H Experiment
Calculation, assignment
m
m
I
PED
1589 1487 1455 1269 1192 1180 1164 1070 1023 1006 947 906 883 815 781 726 690 616 585 573 556 531 502 433
1590 1482 1449 1233 1184 1181 1165 1076 1027 1007 950 902 859 805 773 730 706 613 584 564 556 540 496 422
39.3 186.3 2.3 114.7 248.2 282.2 129.5 14.3 34.3 10.6 5.7 277.0 395.5 1.3 1.3 23.2 85.0 4.0 0.8 1.6 32.7 1.2 92.0 25.8
69 59 62 42 45 43 64 52 56 65 56 58 34 95 25 71 33 66 23 26 29 31 36 21
m(CCar), 23 d(CCH) d(CCH), 36 m(CCar) d(CCH), 35 m(CCar) m(PN), 30 m(CO), 8 m(CCar) m(CO), 23 d(CCH), 18 m(CCar) m(CO), 23 d(CCH), 17 m(CCar) d(CCH), 15 m(CO), 14 m(CCar) d(CCH), 44 m(CCar) m(CCar), 39 d(CCH) d(CCH), 31 m(CCar) m(PO), 17 m(CCar), 10 m(PN) m(PO), 15 m(CO), 12 m(CCar) m(PN), 14 m(PO), 11 m(CO) q(CH) m(PN), 19 m(CO), 8 m(PO) q(CH), 9 m(PO) m(PO), 16 d(CCC), 12 m(CO) d(CCC), 24 d(CCH) d(POC), 18 d(CCC), 7 d(PNP) d(POC), 22 d(CCC) d(POC), 15 d(CCC), 6 d(OCC) d(CCC), 12 d(POC) v(CC), 9 v(PO), 9 v(PN) d(OCC), 14 v(PO), 8 d(PNP)
V.L. Furer et al. / Chemical Physics 330 (2006) 349–354 Table 3 Experimental and corresponded calculated frequencies m (cm1) and intensity I (km/mol) of bands in the IR spectra of G00c -D Experiment
Calculation, assignment
m
m
I
PED
1557 1370 1248 1240 1138 1041 970 939 921 887 858 841 807 779 716 704 638 568 536 521 500 476 448
1557 1368 1209 1206 1121 1031 971 936 902 897 856 844 800 779 711 681 625 553 534 526 516 471 448 403
27.2 166.7 566.0 584.0 1761.9 13.6 14.5 4.4 594.7 205.6 50.9 62.8 200.9 3.2 49.7 37.3 3.5 22.9 13.2 0.1 8.2 116.7 150.2 11.2
75 43 69 68 41 81 20 47 55 51 71 82 52 89 22 25 90 50 24 29 31 26 14 25
m(CCar), 10 d(CCD) m(CCar), 26 d(CCD), 21 m(CO) m(PN), 9 m(CO), 5 m(CCar) m(PN), 12 m(CO), 6 m(CCar) m(CO), 22 m(PN), 10 m(CCar) d(CCD) d(CCC), 17 m(CCar), 9 m(PO) m(PO), 37 m(CCar), 9 m(PN) m(PO), 25 m(CCar), 11 m(CO) m(PO), 27 m(CCar), 13 m(CO) d(CCD), 11 m(PO), 6 m(CCar) d(CCD), 11 m(CCar) d(CCD), 14 m(CCar), 13 m(PO) q(CD) m(PO), 12 m(CO), 11 d(CCC) m(PO), 14 m(CO), 12 d(CCC) q(CD) q(CD), 12 d(CCC), 10 m(PO) d(CCC), 16 d(POC), 7 d(OCC) d(CCC), 13 d(OCC), 12 d(POC) q(CD), 18 d(CCC), 12 d(POC) d(NPO), 25 v(PN), 11 d(POC) d(PNP), 14 v(PO), 13 d(CCC) d(OCC), 12 v(PO), 11 d(PNP)
The strong bands at 947, 883 cm1 in the IR spectra of and the intense bands at 939, 887 cm1 in the IR spectra of G00c -D were assigned to P–O stretch. The medium-intensity bands at 781, 690 cm1 in the IR spectra of G00c -H refer to P–N, C–O and P–O stretch. The band at 726 cm1 in the IR spectra of G00c -H refer to CH out-of-plane bending vibrations. The band at 616 cm1 in the IR spectra of G00c -H is connected with CCC and CCH bending vibrations. The bands at 586, 573, 556, 531, 433 cm1 in the IR spectra of G00c -H are assigned to POC and CCC bending vibrations. The band at 502 cm1 in the IR spectra of G00c -H refers to torsion around CC bond. Thus the dendrimer core (NP)3, reveal itself by band at 1269 cm1 in the IR spectra of G00c -H assigned to P–N stretch. In the IR spectra of G00c -D this band is located at 1240 cm1. The phenoxy terminal groups are characterized by the well-defined bands at 1487, 1589 cm1 in the experimental IR spectra of G00c -H and by bands at 1370, 1557 cm1 in the IR spectra of G00c -D. The reactivity of the end groups of these dendrimers is amongst the most versatile and the most widely studied [3]. A huge number of reactions on the end groups of the studied dendrimes have been carried out [3]. For instance, dendrimers having three or even four different types of end groups simultaneously have been described, for the first time [3]. This very special and so far unique type of functionalization was called ‘‘multiplurifunctionalization’’ [3]. In this work we try to characterize the reactivity of dendrimer G00c -H with phenoxy end groups by means of global G00c -H ,
353
Table 4 Global reactivity descriptors of G00c -H Ionization energy, eV
Electron affinity, eV
Chemical potential, eV
Global softness, au
5.789
1.383
3.586
3.086
Table 5 Local reactivity descriptors (au) of G00c -H Atom
P N O C H
Electronic population
Fukui function
Local softness
qk(N 1)
qk(N)
qk(N + 1)
fk
fkþ
s k
sþ k
14.510 7.307 8.126 5.920 0.941
14.516 7.314 8.135 5.931 0.950
14.519 7.307 8.137 5.935 0.960
0.006 0.007 0.009 0.011 0.009
0.003 0.007 0.002 0.004 0.010
0.019 0.022 0.028 0.034 0.028
0.009 0.022 0.006 0.012 0.031
and local reactivity descriptors (Tables 4 and 5). The ionization energy IE, affinity EA, the global softness and reactivity of dendrimer G00c -H and G1 are very similar to the corresponding values of dendrimers G1 and G01 with thiophosphoryl core and terminal PCl2 and aldehyde groups [21,22]. The local softness of the G00c -H and G01 are quite different. The softness of sulphur atom in the thiophosphoryl core to nucleophilic attack is higher than the softness of the atoms of the cyclotriphosphazene core. We found that the softness values of atoms of the terminal S@PCl2 and aldehyde groups in the G1 and G01 are higher, than softness of atoms of phenoxy end group in G00c -H . The most reactive place is located in the terminal groups in dendrimers G1 and G01 , the core P@S bond is less active. In G00c -H the reactivity of the core is also less than that of terminal groups. The intensity of the most prominent bands in the IR spectra of G00c -H and G00c -D is reproduced by our calculations. The calculated absorption curves of G00c -H and G00c -D as a whole corresponds to the experimental IR spectra in the wide frequency region. Thus the employed DFT method enables one to calculate the structure, charges on atoms, and reproduce the experimental IR spectra of the phosphorus dendrimer with cyclotriphosphazene core and phenoxy end groups. References [1] F. Vogtle, S. Gestermann, R. Hesse, H. Schwierz, B. Windisch, Progr. Polym. Sci. 25 (2000) 987. [2] J. Leclaire, R. Gagiral, S. Fery-Forgues, Y. Coppel, B. Donnadieu, A.M. Caminade, J.P. Majoral, J. Am. Chem. Soc. 127 (2005) 15762. [3] J.P. Majoral, A.M. Caminade, V. Maraval, Chem. Commun. (2002) 2929. [4] J.M.J. Frechet, D.A. Tomalia, Dendrimers and Other Dendritic Polymers, Wiley, New York, 2002. [5] D.K. Smith, Tetrahedron 59 (2003) 3797. [6] S.C. Zimmerman, L.J. Lawless, Top. Curr. Chem. 217 (2001) 95. [7] A.M. Caminade, J.P. Majoral, Progr. Polym. Sci. 30 (2005) 491. [8] A.M. Caminade, J.P. Majoral, in: M. Gleria, R. de Jaeger (Eds.), Phosphazenes: a Worldwide Insight, NOVA Science Publishers, New York, 2004, p. 713 (Chapter 30).
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