Parametrization of a Force Field for TeâN Secondary Bonding

DOI: 10.1021/cg100951y

Parametrization of a Force Field for Te-N Secondary Bonding Interactions and Its Application in the Design of Supramolecular Structures Based on Heterocyclic Building Blocks

2011, Vol. 11 668–677

Anthony F. Cozzolino and Ignacio Vargas-Baca* Department of Chemistry and Chemical Biology, McMaster University, 1280 Main Street West, Hamilton, Ontario L8S 4M1, Canada Received July 19, 2010; Revised Manuscript Received November 17, 2010

ABSTRACT: 1,2,5-Telluradiazole rings have a remarkably strong tendency toward association through Te-N secondary bonding interactions in the solid state. The reproducibility of the bond lengths and angles in the known crystal structures allowed the parametrization of an anharmonic force field to accommodate both the inter- and intramolecular Te-N bonds. The new parameters were tested against published crystal structures and were able to accurately reproduce the experimentally observed geometries. The incorporation of these parameters into a molecular mechanics force field enables the modeling of large and complex structures with significantly less computational effort than Hartree-Fock (HF) or density functional theory (DFT) methods. Simple modifications to the parameter set allowed the modeling of the structures of acyclic tellurium diamides. A series of 4,7-disubstituted benzo-2,1,3-telluradiazoles were modeled to probe the steric barrier of dimerization; only the groups with large spherical bulks such as t-butyl, trimethylsilyl, and adamantyl were able to destabilize the dimers. Modeling based on bifunctional building blocks suggests strategies for the construction of novel two- and three-dimensional supramolecular architectures.

Scheme 1. Formation of the [Te-N]2 Supramolecular Synthon

Introduction 1

Secondary bonding interactions (SBIs) bring together atoms, which had in principle previously satisfied their Lewisoctet valences, to distances that are shorter than the sum of van der Waals radii but much longer than the typical distance of the single hypervalent bond. Although SBIs centered on heavy main-group elements are recognized as a viable option in supramolecular chemistry,2-5 progress in this area has been contingent on the identification of the most efficient supramolecular synthons: the structural units which can be formed and/or assembled by synthetic operations involving intermolecular interactions.6 In this respect, the [Te-N]2 supramolecular synthon, the virtual four-membered ring formed when two 1,2,5-telluradiazoles associate through two simultaneous antiparallel Te-N SBIs (Scheme 1),7 is a good candidate because of its strength, directionality, reversibility, and the synthetic accessibility of the building blocks. This supramolecular synthon can be further strengthened by N-substitution of the building blocks.8-10 All the known crystal structures of the derivatives that are not N, N0 -disubstituted8 self-associate through the [Te-N]2 supramolecular synthon to form either dimers or ribbon polymers. Even in the case of the sterically encumbered phenanthro[9,10-c]-1,2,5-telluradiazole (1),11 the molecule undergoes significant geometrical distortion from planarity to alleviate repulsion and accommodate the formation of the supramolecular ribbon. Investigations in this area must address a fundamental question: what new supramolecular structures (and properties) would be available through the use of SBIs that are not attainable by the more conventional hydrogen bonding or *To whom correspondence should be addressed. Phone: 1-905-525-9140 x23497. Fax: 1-905-522-2509. E-mail: [email protected]. pubs.acs.org/crystal

Published on Web 01/19/2011

coordination of metal ions? In principle, the answer could be provided through a comprehensive research program involving the synthesis and characterization of multiple derivatives. This daunting task can be abbreviated with the use of modern computational methods, not to replace the experiments but to facilitate the process of design and identification of the systems that represent the most interesting synthetic targets. Density functional theory (DFT) has been a valuable tool for modeling the association of 1,2,5-telluradiazoles in the solid state using small models with up to six repeat units.7 Bond lengths and angles and even the degree of association are accurately reproduced or predicted, as has been shown in the cases of benzo-2,1,3-telluradiazole (2) and 4,7-dibromobenzo2,1,3-telluradiazole (3).2 There are, however, intrinsic limitations to quantum mechanical methods that hamper their application to the design of large supramolecular structures. For example, the contribution of dispersion forces cannot be accurately calculated even though there have been significant advances in the development of new hybrid meta exchangecorrelation functionals or functionals which include empirical corrections.12-15 The most important challenge to overcome in this respect would be the computational expense of modeling large systems. Molecular mechanics is a different method for molecular modeling which is applicable to a wide range of organic and biological supramolecular systems.16 The approach relies on evaluating the strain (the energetic cost of distorting the internal dimensions of a molecule from the ideal values) with simple harmonic or anharmonic functions that r 2011 American Chemical Society

Article

Crystal Growth & Design, Vol. 11, No. 3, 2011

669

Chart 1

constitute a force field. The application of molecular mechanics to heavy main group systems has been limited to a few cases. One of the reasons for this is that the great variety of oxidation states and coordination geometries available precludes the existence of a truly universal set of parameters. Force fields must therefore either have a large number of situation-specific atom types,17-21 or define sets of rules that quickly identify the type of structure and the corresponding set of parameters.22,23 The number of parameters available for main-group elements is rather small and those available apply only to strongly covalent bonds between atoms; SBIs are simply neglected within molecular mechanics. This report presents the parametrization of the MMX force field to account for supramolecular SBIs, the results from testing the parameter set against experimentally determined structures and the application of the method to envision new supramolecular structures based on the [Te-N]2 supramolecular synthon. Computational Details Density Functional Theory (DFT). Calculations were performed using the ADF DFT package (SCM, versions 2006.01 through 2009.01).24-26 The adiabatic local density approximation (ALDA) was used for the exchange-correlation kernel,27,28 and the differentiated static LDA expression was used with the Vosko-WilkNusair parametrization.29 The calculations of model geometries were gradient corrected with the exchange and correlation functionals of the gradient correction proposed by Perdew and Wang,30,31 which usually provide excellent reproduction of experimental geometries for heavy main-group systems.32 Geometry optimizations were conducted using a triple-ζ all-electron basis set with one set of polarization functions and applying the zeroth-order regular approximation (ZORA)26,33-36 with specially adapted basis sets. Symmetry constraints were used when a point group was applicable and in each case were followed by vibrational calculations37,38 to verify that all the computed frequencies were real and to provide force constants for selected vibrational modes. Molecular Mechanics. Model structures were optimized without any constraints using the MMX39 force field implemented within PCModel (Serena Software, version 9.10.0)40 with a custom set of parameters for 1,2,5-telluradiazoles described in this paper.

Results and Discussion Choice of Force Field and Parametrization. The MMX force field,39 an extension of Allinger’s MM2 force field,17,18

was selected for these investigations because it allows the use of anharmonic potentials which in principle are more accurate than harmonic potentials when bond lengths vary over a wide range, which is the case for Te-N SBIs (see below). The force field consists of bond-stretching, bond-angle bending, stretch-bending, torsion, and van der Waals potentials. In this model, the bond-stretching potential energy (eq 1) is a function of the interatomic distance (r), the force constant (Kr), and the equilibrium bond distance (req). Bending of a bond angle, including the out-of-plane angle for atoms bonded to three other atoms (eq 2) results in a potential energy contribution that is a function of the angle (θ), a force constant (Kθ), the equilibrium bond angle (θeq), and the sextet angle bending constant (S). The combination of changes in bond distances and angles yields a potential (eq 3) with its own force constant (Ksb). The torsion of a dihedral angle (j) is modeled with a periodic function (eq 4) where the location of the minimum or minima is defined by D1, D2, or D3 (generally 1, -1, and 1, respectively) and the force constants V1, V2, or V3. The van der Waals potential is calculated according to the Buckingham model (eq 5) as a function of the distance (rij) between a pair of atoms, their van der Waals radii (ri and rj), and three universally applied constants A, B, and C. Electrostatic contributions are modeled from charges (qi and qj), derived from bond dipoles moments (eq 6), which are separated by the distance rij in a medium of dielectric constant D. The tellurium parameters in the current version of the MMX force field are limited to those necessary for optimizing ditellurides with sp2 hybridized carbons attached to the tellurium atoms. With the exception of the van der Waals radii, none of the parameters supplied with MMX are appropriate for modeling telluriumnitrogen organic heterocycles, even less the [Te-N]2 supramolecular synthon. 7 ð1Þ E bond ¼ K r ðr - req Þ2 1 - 2ðr - req Þ þ ðr - req Þ2 3 E angle ¼ Eout- of- plane ¼

Kθ ðθ - θeq Þ2 ½1 þ Sðθ - θeq Þ4 2

E stretch bend ¼ K sb ðθ - θeq Þðr - req Þ

ð2Þ ð3Þ

670


Cozzolino and Vargas-Baca Table 3. Optimized MMX Stretch-Bend Parameters as Defined by eq 3 for 1,2,5-Telluradiazole Rings

Scheme 2. Numbering Scheme for the Definition of Parameters Used to Model a Supramolecular Ribbon of Benzo-2,1,3-telluradiazoles

out-of-plane angle

Kθ (kJ mol-1 deg-2)

C-N1-Te1-Te2 N1-Te1-N2-N3

57.28 57.28

Table 4. Optimized MMX Torsion Angle Parameters as Defined by eq 4 for 1,2,5-Telluradiazole Rings

Table 1. Optimized MMX Bond-Stretch Parameters as Defined by eq 1 for 1,2,5-Telluradiazole Rings bond

req (A˚)

Kr (kJ mol-1 A˚-2)

Te1-N1 (intramolecular) Te1-N3 (intermolecular)

2.021 2.700

1835 150.5

Table 2. Optimized MMX Bond Angle Bend Parameters as Defined by eq 2 for 1,2,5-Telluradiazole Rings bond angle

θeq (deg)

Kθ (kJ mol-1 deg-2)

N1-Te1-N2 Te1-N1-C C-N1-Te2 N1-Te1-N3 N1-Te2-N2 N1-Te1-N4 Te1-N1-Te2

83.3 110.8 141.0 153.3 136.7 70.0 110.0

0.0256 0.0825 0.0000 0.0000 0.0000 0.1466 0.1466

E torsion ¼

E vdW

V1 V2 ð1 þ D1 cos jÞ þ ð1 þ D2 cos 2jÞ 2 2 V3 þ ð1 þ D3 cos 3jÞ ð4Þ 2 ! 6 C ri þ r j - B=F ð5Þ ¼ Ae , F ¼ F rij Eelectrostatic ¼

qi qj Drij

ð6Þ

DFT investigations of the [Te-N]2 supramolecular synthon revealed that it is stabilized by electrostatic and orbital contributions.7 Given the features of the potential energy surface mapped by distortion of the virtual four-membered ring, the Te-N SBIs would be best modeled with the same potentials that apply to covalent bonds. In order to define all of the parameters necessary for isolated and associated 1,2,5-telluradiazoles, a distinction was made between internal (“covalent”) and external (SBI) parameters. This was enabled within MMX by adopting the numbering scheme shown in Scheme 2. The required internal parameters include those for the potentials of the Te1-N1 bond stretch, the N1-Te1-N2 and CdN1-Te1 angle bends, the out-of-plane bends, and the torsions within the five-membered ring. The external parameters correspond to the Te1-N3 SBI stretch as well as the bends, out-of-plane bends and torsions relevant to the [Te-N]2 supramolecular synthon. The number of crystallographically determined structures of 1,2,5-telluradiazole derivatives is too small to reliably parametrize the force field from experimental averages; instead, the behavior of the different components of the force field can be evaluated through more accurate DFT calculations. The optimal parameters were derived by mapping the force fields onto the DFT potential energy surfaces (PESs) as described below; their values are collected in Tables 1-4.

dihedral angle

V1 (kJ/mol)

D1

H-C-C-N1 H-C-N1-Te1 C-C-C-N1 C-C-N1-Te1 C-N1-Te1-N2 N1-C-C-N2 H-C-N1-Te2 C-C-N1-Te2 C-Ni-Tej-Nk Ni-Tej-Nk-Tel

42 42

-1 1

75a 84 84 84 42a 42 42

-1a -1 -1 -1 -1a cb cb

a

Values are given for V2 and D2. b j = 0°, c = 1; j = 180°; c = -1.

Equilibrium bond lengths and angles were taken directly from the DFT optimized geometries. The internal Te1-N1 bond stretching and the N1-Te-N2 bond angle bending force constants could ideally be obtained from DFT vibrational calculations. Each normal coordinate of these cyclic molecules, however, consists of a combination of correlated displacements of multiple atoms. Instead, the parameters were estimated from the vibrational calculations for acyclic compounds. Because the Te-N bond length in the 1,2,5telluradiazoles is intermediate between those of the unambiguous single and double Te-N bonds, both the diamino telluride (4) and tellurium diimide (5) were considered. The geometries of these molecules were optimized assuming C2v symmetry and their force constants were extracted from the calculation of the molecular vibrations. The optimized geometry of 4 was comparable to previously calculated structures41 as well as those of the monomeric di(bis(trimethylsilyl)amido)-42 (6) and bis(tert-butyl(trimethylsilyl)amido) tellurium43 (7) (see Table 5). Compared to the two experimental structures of the diamides, the Te-N bond length and the N-Te-N bond angle of 4 were overestimated by less than 0.05 A˚ and 3.1°, respectively. The DFT optimized geometry of 5 was comparable with a previously calculated structure41,44 as well as the tellurium diimide dimers (8,45 9,46 and 1047) (see Table 6); there are no known monomeric tellurium diimides. Compared to the experimental values, the TedN bond lengths were overestimated by less than 0.05 A˚. From the models of 4 and 5, the MMX force constants for intramolecular bond stretching and angle bending in the C2N2Te heterocycle were estimated by interpolation at the equilibrium Te1-N1 bond length and N1Te1-N2 angle (vide supra). The CdN1-Te1 bending potential was given the same force constant as the CdN-S bending already parametrized for MMX. Force constants for torsion potentials were adjusted until the torsion angles at the center of a 32-molecule ribbon of 1, the only telluradiazole ring known to significantly deviate from planarity, provided the closest match to the experimental values.11 These optimized torsion force constants for the telluradiazole ring were of the same order of magnitude as those used in MMX to model torsions in aromatic rings (V1 = 0 kJ/mol, V2 = 30.916 kJ/mol, and V3 = 4.184 kJ/mol).39 Experimental Te-N SBI distances vary from 2.825(8) and 2.842(8) A˚ in the ribbons of the sterically encumbered 111 to

Article


671

Table 5. Comparison of Selected Calculated and Experimental Bond Distances and Angles for 4 4

PW91a

HF44

MP244

B3LYP44

6 (exp)42

7 (exp)43

Te-N (A˚) N-H (A˚) N-Te-N (o) H-N-Te (o) H-N-H (o)

2.075 1.022 108.9 110.6 108.3

2.001 0.991 104.4 120.8 114.5

2.042 1.002 108.4 116.4 112.2

2.029 1.007 108.1 119.3 113.5

2.045(2)/ 2.054(2)

2.043(2)/ 2.050(2)

105.8(1)

105.7(1)

a

This work.

Table 6. Comparison of Selected Calculated and Experimental Bond Distances and Angles for 5 5

PW91a

B3PW9141

8 (exp)45

9 (exp)46

10 (exp)47

Te-N (A˚) N-H (A˚) N-Te-N (o) H-N-Te (o)

1.933 1.035 119.8 110.0

1.897 1.028 119.8 112.9

1.900(5)

1.88(1)

1.901(4)

a

This work.

Table 7. Comparison of Selected Calculated and Experimental Bond Distances and Angles for 2 and the Central Units in Models of Its Ribbon Polymer 2 (exp)2

2 (MMX)a

no. of units avg 1 6 1 6 20 2.003(7) 2.021 2.054 2.022 2.022 2.022 Te1-N1 (A˚) 1.32(1) 1.33 1.32 1.36 1.36 1.36 N1-C C-C 1.467(9) 1.482 1.481 1.478 1.478 1.478 2.701(7) 2.690 2.687 2.687 Te1-N3 (A˚) 88.2 83.1 86.1 86.0 86.0 N1-Te1-N2 (o) 83.8(3) 110.7(5) 105.9 110.4 108.9 109.0 109.0 Te1-N1-C o 69.9 70.0 70.0 N2-Te1-N3 ( ) 69.2(2) a

Figure 1. Potential energy curves for the in-plane dimerization through two simultaneous antiparallel Te-N SBIs as a function of the intermolecular distance modeled with DFT for 11 (;) and MMX for 2 (- - -).

2 (DFT)7

This work.

Figure 3. Comparison of π-stacking in the experimental crystal structure of 2 (yellow)2 with the MMX modeled structure (blue).

Figure 4. Comparison of the experimental crystal structure of 1 (yellow)11 with the MMX modeled structure (blue).

Scheme 3

Figure 2. Potential energy curves for the in-plane dimerization through two simultaneous antiparallel Te-N SBIs as a function of the intermolecular angle modeled with DFT for 11 (;) and MMX for 2 (- - -).

2.628(4) A˚ in the dimer of 4,6-di-t-butylbenzo-2,1,3-telluradiazole (12).47 Steric hindrance is likely a factor that influences the distance, but not the only one. The Te-N SBIs have a donor-acceptor character, and changes in the electronic density of the chalcogen influence the SBI length. The crystal structures of 3 and 3 3 DMSO show that formation of Te-O SBIs lengthens the Te-N SBIs from 2.697(8) to 2.744(4) A˚.2 Similarly, SBIs in ribbon polymers typically are ca. 0.1 A˚ longer than in dimers. Accurate modeling such

an effect is not possible with molecular mechanics; thus the equilibrium distance chosen for the MMX force field would necessarily be a compromise value. In the current parametrization, we chose the average of SBI distances in the crystal of 2, 2.700 A˚, which is intermediate between the two known

672


Cozzolino and Vargas-Baca

Table 8. Comparison of Selected Calculated and Experimental Bond Distances and Angles for 1 1 (exp)11 no. of units: Te1-N1 (A˚) N1-Te1-N2 (o) N1-Te1-N2-C (o) Te1-N1-C-C (o)b N1-C-C-N2 (o) C-C-C-C (o)c Te1-N3 (A˚) N2-Te1-N3 (o) N2-Te1-N3-Te2 (o) Te1-N3-Te2-N2(o) a

1 (MMX)a

2.023(6) 84.3(3) 2.5 6.6 9.4 16.3 2.825(8)/ 2.842(8) 70.7(3)/ 71.1(3) 0.0 0.0

1

2

4

8

16

32

2.021 81.9 0.0 0.0 0.0 0.0

2.021 83.2 0.0 0.0 0.0 0.0 2.822 73.2 0.0 0.0

2.021 86.6 5.6 5.0 6.8 5.4 2.866 71.9 0.3 0.2

2.021 87.2 4.3 12.1 17.5 14.1 2.875 70.9 0.1 0.1

2.021 87.2 4.8 13.5 19.6 15.9 2.888 70.4 0.0 0.0

2.022 87.2 4.9 13.6 19.8 16.0 2.890 70.4 0.2 0.2

Average values from the two central molecules. b Within the five-membered ring. c Sharing central C with N1-C-C-N2. Table 9. Calculated Structural and Energetic Parameters for the Dimers of 12 dimer structure

method MMX

DFT

dTe1-N3 (A˚) SBI aN2-Te1-N3 (°) aTe1-N3-Te2 (°) relative strain energy for the [Te-N]2 supramolecular synthon (kJ/mol) relative total strain energy (kJ/mol) dTe1-N3 (A˚) SBI aN2-Te1-N3 (°) aTe1-N3-Te2 (°) relative total energy (kJ/mol)

a

b

c

2.692 69.9 110.1 0.0 0 2.519 69.9 110.1 0

2.716/2.898 69.8/74.0 111.5/104.8 5.4 12.5 2.558/2.825 69.4/74.9 110.6/105.1 23.2

2.969 74.0 106.0 11.5 28.7 2.926 78.3 101.7 44.6

Table 10. Comparison of Selected Calculated and Experimental Bond Distances and Angles for 13 13 (exp)49 no. of units: Te1-N1 (A˚) N1-Te1-N2 (o) Te1-N3 (A˚) N2-Te1-N3 (o)

avg 2.050(2) 100.4(1) 2.959(2) 77.7(1)

13 (MMX) 1

6

12

2.026 101.5

2.027 105.7 2.850 70.8

2.027 105.7 2.850 70.8

extremes. The Te-N SBI stretching force constant was optimized by fitting to eq 1 the region of the DFT-calculated potential energy surface in which ΔE e 25 kJ/mol for two molecules of 11 displaced from their equilibrium position along a path parallel to the SBI axis without any geometry relaxation. The inverse of ΔEDFT was used as a weighing factor for this procedure. The force constant obtained in this manner was split equally between the two Te-N SBIs and refined fitting the MMX energy profile to the DFT calculation for 2. As this procedure accounts for the 1,4-nonbonded interactions, the Te-N bond dipole was set to 0 to exclude the explicit electrostatic interactions in the [Te-N]2 supramolecular synthon in the MMX forcefield. Figure 1 compares the DFT-calculated potential energy surface for 11 with the MMX potential energy profile for 2; the anharmonic curve follows the DFT calculation closely from 2.4 to 3.2 A˚, deviating by a maximum of -4.3 kJ/mol at 3.1 A˚. In a similar way, the N1-Te1-N4 and N2-Te1-N3 SBI angles were obtained from a DFT-optimized structure of 2, and the bending force constants were obtained by fitting to eq 2 the DFT potential energy surface calculated by sliding two telluradiazoles with respect to each other along a path parallel the N1-Te1 axis while keeping the Te1-N3 SBI distance constant. This parameter was refined by minimizing the weighted absolute differences between the MMX and DFT energies in the region where ΔE e 60 kJ/mol. Bending of each angle was assumed to contribute equally (1/4) to the

Figure 5. Comparison of the crystal structure of 13 (yellow)11 with the MMX modeled structure (blue).

Scheme 4

total potential; thus the force constants are identical. Figure 2 compares the DFT calculation with the optimized MMX potential model, where the maximum deviation between 100 and 120° is 6.3 kJ/mol at 120o. Validation of Parameters. The structures of systems for which the crystallographic determination is available were modeled in order to test the reliability of the structural predictions by MMX with the optimized set of force field parameters. It is not possible to perform such validation for an isolated molecule of a 1,2,5-telluradiazole because all the hitherto published structures correspond to molecules associated through either Te, N, or both, and DFT studies have shown that binding at these sites results in measurable structural reorganization.2,7,8 The crystal structure of 2 consists of supramolecular ribbons;2 the dimensions of the

Article


673

Table 11. Comparison of Selected MMX and DFT (in parentheses) Optimized Bond Distancesa and Angles,a MMX Strain Energiesa for the [Te-N]2 Supramolecular Synthon, Total MMX Strain Energies (minus EvdW contribution), and DFT Dimerization Energies for the Dimers of the Telluradiazoles 2, and 14-29 Te1-N3

Te1-N3-Te2

telluradiazole dimer

distance (A˚)

Ebond (kJ/mol)

angle (°)

22 142 152 162 172 182 192 202 212 222 232 242 252 262 272 282 292

2.693 (2.593) 2.689 (2.538) 2.728 (2.585) 2.744 (2.618) 2.758 (2.635) 2.728 (2.655) 2.738 (2.646) 2.770 (2.675) 2.996 (3.026) 2.872 (2.926) 2.749 (2.782) 2.777 (2.708) 2.814 (2.874) 2.713 (2.590) 2.707 (2.643) 2.706 (2.623) 2.710 (2.624)

0.00 0.00 0.05 0.13 0.22 0.06 0.10 0.32 4.04 1.62 0.16 0.38 0.78 0.01 0.00 0.00 0.01

110.1 (110.0) 109.9 (110.5) 108.9 (109.0) 108.3 (108.3) 107.7 (106.7) 108.9 (107.5) 108.7 (107.4) 108.0 (106.6) 105.7 (100.6) 105.8 (101.6) 105.8 (102.1) 107.8 (105.9) 102.8 (97.3) 109.3 (109.2) 109.4 (109.0) 109.6 (109.4) 109.1 (108.9)

a

[Te-N]2

MMX

DFT

Eangle (kJ/mol)

strain (kJ/mol)

total strain (kJ/mol)

ΔEdimer (kJ/mol)

0.00 0.00 0.09 0.21 0.38 0.09 0.13 0.30 1.38 1.27 1.35 0.37 3.89 0.04 0.03 0.01 0.04

0.01 0.00 0.46 1.10 1.98 0.48 0.72 1.82 13.58 8.32 5.73 2.23 17.11 0.19 0.12 0.05 0.19

-6.05 (0.00) -6.46(-0.23) -2.63 (0.82) 1.06 (2.08) 5.67 (4.18) -4.53 (0.72) -4.01 (0.83) 2.25 (5.74) 35.71 (23.28) 30.59 (23.42) 44.74 (13.62) -0.92 (6.13) 64.70 (43.75) -9.27 (10.32) -20.07 (0.14) -35.99 (0.95) -28.91 (-0.02)

-67.68 -84.00 -79.65 -76.77 -69.71 -61.82 -60.87 -59.50 -24.39 -26.21 -47.76 -53.91 -12.75 -67.47 -82.07 -80.70 -79.33

The average values are reported for the dimers of 23, 25, 28, and 29.

molecules and the supramolecular synthon have been previously modeled by DFT calculations using oligomers with two to six units.7 The same approach has been applied with molecular mechanics calculations. Table 7 summarizes these results and compares them to the experimental values. The most relevant dimensions are those of the molecules in the middle of the chain as they should most closely mimic the molecules within the crystal. The molecular mechanics parameters reproduce the bond lengths within 3σ of the experimental value and the bond angles within 1.2°. There is little change in the internal dimensions of the heterocycle from monomer to oligomer as the equilibrium bond distances and angles were obtained from the crystal structures and in this structure there is minimal structural distortion due to steric hindrance from neighboring molecules.2,7 In addition to computational expediency, one advantage of modeling supramolecular structures with molecular mechanics, as compared to the most commonly used density functionals, is the ability to approximate the contribution from dispersion forces with the simple van der Waals potential.48 This should in principle provide reasonable models of the stacking of the heterocycles. A model stack of four dimers of 2 was optimized from four different starting points with arbitrary initial spacing of parallel molecules. Each minimization led to the same structure which is displayed in Figure 3 along with the actual spacing of ribbon polymers from the crystal structure. The calculated interplanar spacing of 3.72 A˚ is in excellent agreement with the actual measurements from the crystal structure: 3.67(1) and 3.71(1) A˚.2 However, the vertical alignment of molecules on different planes calculated by MMX displays important differences from the arrangement of ribbons in the crystal structure. The crystal structure of 1,11 a twisted ribbon polymer, was useful for the evaluation of the dihedral parameters. The deviation from planarity of the ribbon polymer distorts the geometry of the five-membered heterocycle, causing puckering, while the virtual ring formed by the SBIs remains planar with 0° dihedral angles. Selected structural parameters are summarized in Table 8 and show that as the chain grows the intramolecular dimensions deviate from those in the modeled monomer and approach those found in the

Figure 6. Supramolecular sheet formed by association of 30.

Chart 2

crystal structure. Although the dihedral angles were difficult to reproduce with accuracy (a 10° deviation was obtained for

674



Figure 7. Optimized packing of 30 (a) monoclinic, (b) orthorhombic. Table 12. Predicted Crystallographic Parameters for the Optimized Packing of 30 polymorph

a

b

empirical formula crystal system space group a [A˚] b [A˚] c [A˚] β [°] Z F (calc) [g 3 cm-3]

C6H2N4Te2 monoclinic C2/c (No. 15) 10.40 7.68 5.51 93.53 2 2.91

C6H2N4Te2 orthorhombic C2221 (No. 20) 14.68 7.69 7.26 90 4 3.12

Chart 3

Figure 8. The two views of optimized two-dimensional array of 31.

the N1-C-C-N2 dihedral angle) the overall structure was well reproduced. The central pair of molecules in the 32 unit chain had an average deviation of 0.19 A˚ and a maximum deviation of 0.34 A˚ from the crystallographically determined positions (Figure 4). While the systems discussed up to this point are symmetrical and can only form one supermolecule, the dimer of 12 can adopt three different structures (Scheme 3). Their relative stability can be assessed by comparison of their strain energies, the energetic cost of displacing the internal molecular dimensions from the ideal equilibrium values. Table 9 presents relevant distances and angles calculated with MMX for the three possible structures as well as the strain energies (relative to the most stable isomer) and compares the results with those from DFT calculations. Under each approach, the supramolecular isomer a is the most stable; indeed this is only arrangement that is observed in the solid

state. 47 The trends in distances, angles, and energies are consistent between the DFT and MMX modeled structures, although there are differences of magnitude. For example, the Te-N SBI distances calculated by DFT are shorter than the MMX value, as expected from the choice of Te-N SBI equilibrium distance (vide supra). The MMX force field treats cyclic and acyclic systems separately; thus, the new parameter set could be adapted to model the extended structures assembled by acyclic diamino tellurides. Because there is an approximately 15° increase in the N-Te-N angles from the cyclic telluradiazoles to the acyclic tellurium diamides, additional parameters were created for the acyclic N-Te-N bond angle and force constant (100.3°, 0.09058 kJ mol-1 deg-2). The performance of the parameters for the diamino tellurides was evaluated by modeling ((CH3)2N)2Te49 (13) which forms a ribbon polymer through the [Te-N]2 supramolecular synthon. Comparison of the calculated and experimental structures (Table 10) reveals that although these parameters were not fully optimized they are capable of modeling the arrangement observed in the solid state (see Figure 5). Steric Limitation of Supramolecular Association. DFT calculations indicate that formation of SBIs has a definite effect

Article


675

Figure 9. Possible supramolecular assemblies of 31. (a, b) π-stacks of cyclic hexamers and (c, d) spiral chain.

Figure 10. Comparison of the MMX (blue) and DFT (yellow) minimized structures of a spiral assembly of 12 molecules of 31.

on the molecular and electronic structures (and consequently on the spectroscopic properties) of 1,2,5-telluradiazoles.7,50 However, such predictions remain unverified because there are no nonassociated examples of these rings which have been structurally authenticated. The N or Te atoms can be capped with Lewis acids8 or bases,2,9 respectively, but these are significant perturbations of the heterocycle. Instead, a monomeric species could be obtained by placing bulky groups at the 4 and 7 positions of benzo-2,1,3-telluradiazole. Moderate steric hindrance (Scheme 4a) does stabilize the dimers that are crystallographically characterized.2,47 It is therefore reasonable to expect that even bulkier groups would lead to monomeric telluradiazoles (Scheme 4b). In order to probe the effect of several bulky substituents and identify the group that is most appropriate to prevent association, the dimers of benzotelluradiazoles 2, and 14-29 were modeled using the optimized force field parameters and, for performance comparison, DFT. Table 11 contains the structural parameters and strain energies (calculated as the deviation from the equilibrium values for the bond distance, the bond angles and the dihedral angles) of the [Te-N]2 supramolecular synthons for the each of the optimized dimers. Also included are the differences of total strain energy between each dimer and its monomers with and without the van der Waals contribution, and the corresponding DFT dimerization energies. The MMX calculated SBI distances range from 2.693 to 2.996 A˚, and the DFT modeled distances range from 2.538 to 3.026 A˚. For the dimers with the least steric strain, the DFT calculated Te-N SBI distances are on average 0.10(3) A˚ shorter than the MMX minimized distances. The [Te-N]2 supramolecular synthon strain energies range from less than 0.01-17.11 kJ/mol, and the total strain energies with respect to the unperturbed monomers range from -35.99 to 64.70 kJ/mol (-0.2744.01 kJ/mol without the van der Waals contribution). There

Figure 11. The two views of the cyclic hexamer of 32.

is a nearly linear correlation (r = 0.94) between the MMX total strain energy and the DFT dimerization energy within the subset of alkyl and silyl substituents, but the trend is less defined with halogen and aryl substituents. Such a difference is understandable because MMX is unable to account for the effect of electronegative groups or the interaction between tellurium and aryl groups. Overall, however, the MMX approach does give results that are in reasonable agreement with the DFT calculations. The cases with the largest deviations from the equilibrium SBI distance are those of the molecules substituted with the t-butyl (21), trimethylsilyl (22), cyclohexyl (24), and 1-adamantyl (25) groups. Molecules with phenyl-based groups (26-29) do not display a significant change in the SBI distances because the aromatic rings can rotate to minimize repulsion. The MMX calculated Te1-N3-Te2 bond angles in the [Te-N]2 supramolecular synthon range from 102.8° to 110.1° (97.3-110.5° for DFT) with the most significant deviations observed in the molecules with the t-butyl (21), trimethylsilyl (22), trityl (23), and 1-adamantyl (25) substituents. To appropriately compare the stability of these model dimers, the strain on the [Te-N]2 supramolecular synthon must be combined with the strain on the remainder of the molecule. Analysis of the total strain energy indicates that the 1-adamantyl (25) substituent provides the most strain, followed by the trityl (23), t-butyl (21), and trimethylsilyl (22) substituents. The DFT calculations agree that these groups might permit the isolation of monomeric 1,2,5-telluradiazoles. Two-Dimensional Networks. Supramolecular arrays extending in a plane could be constructed from building blocks with more than one telluradiazole ring. There are examples related to this approach in the case of S-N and Se-N SBIs.51 The association of the bifunctional compounds 30

676



Figure 12. Spiral chains assembled by 32. (a, b) 5 units per turn and (c, d) 6 units per turn.

and 31 was modeled. Compound 30 formed a supramolecular sheet (Figure 6) that maximizes the number of Te-N SBIs with only a small strain energy on the [Te-N]2 supramolecular synthon: 0.00-0.05 kJ/mol on each of the N-Te-N SBI angles and 0.00-0.11 kJ/mol on the Te-N SBIs within a 12 molecule model. While the in-plane organization of the molecules is controlled by formation of the [Te-N]2 supramolecular synthon, π-stacking alone would define the arrangement in the third dimension; thus the whole structure is amenable to MMX optimization. Although such a crude approximation cannot replace a rigorous crystal optimization based on periodic potentials, it does provide an reasonable packing forecast. A second layer was initially placed eclipsing the first; optimization resulted in a shift in the center of mass by 3.9 A˚ along the molecular Te-Te axis (Figure 7) giving a van der Waals potential of -523 kJ/mol. In order to explore other stacking arrangements, the second layer was rotated by 45° and 90° before optimization. Both conditions led to structures with less favorable van der Waals interaction energies (-478 kJ/mol and -497 kJ/mol, respectively). From the most stable structure, two possible orientations were considered for the third sheet by either reversing (Figure 7a) or by repeating the interlayer shift (Figure 7b). From these large clusters, a unit cell can be approximated and the predicted space groups and crystallographic parameters for these arrangements are given in Table 12. The predicted densities are comparable to those experimentally determined for 2 (2.359 g 3 cm-3) and 3 (3.224 g 3 cm-3),2 which suggests that the predicted structures are realistic. The most stable of the possible two-dimensional (2D) arrangements obtained from compound 31 was a slightly puckered sheet (Figure 8) in which each molecule has one tetracoordinated and one tricoordinated Te atom participating, respectively, in two and one [Te-N]2 supramolecular synthons. Therefore, the structure features a combination of the dimer and the ribbon polymers motifs with their SBI axis at 120° from each other. Puckering is caused by the Te-H steric repulsion between neighboring molecules. The ribbons consist of two different supramolecular synthons: one that is almost planar (N-Te-N-Te torsion angle 1.8°) and significantly distorted (N-Te-N-Te torsion angle 6.4°). The N-Te-N-Te torsion angle between the tricoordinated Te centers is 2.4°. The distortion to the [Te-N]2 supramolecular synthon also impacts the Te-N SBI distances: 2.749 A˚ and 2.770-2.810 A˚ for the two different supramolecular synthons along the ribbons and 2.681 A˚ in the dimers. Modeling the π-stacking in this case was significantly complicated by the puckering and was not attempted.

Chains, Rings, and Spirals. MMX calculations showed that building block 31 is capable of assembling two arrangements in addition to the 2D array above-described: a cyclic hexamer with an optimized inner diameter of approximately 11 A˚, which can stack in a column (Figure 9), and a spiral with an inner diameter of 10 A˚ (Figure 9). The performance of MMX and DFT optimizations of such supermolecule was compared with a 12-molecule section; an overlay of the optimized models is provided in Figure 10. Differences of atomic coordinates between these models are on average 0.22(4) A˚ with a maximum of 0.34 A˚. The calculated interplanar separation along the spiral is greater in the DFT model (ex. 4.061 vs 3.676 A˚), likely due to the absence of van der Waals contributions in PW91. Also in this case, the DFT calculated Te-N SBIs are shorter than the MMX. The more flexible molecule 32 should facilitate the formation of similar planar chains, rings, and spirals. The calculated strain energy for a linear chain was 139 kJ/mol, irrespective of the model length. Rings of increasing size displayed a decrease of strain energy from 152 kJ/mol with four molecules, to 141 kJ/mol with five, 138 kJ/mol with six, and 139 kJ/mol with both seven and eight molecules. While the four- to six-membered rings were essentially planar, the larger rings were highly puckered. The six-membered ring, with a diameter of approximately 20 A˚ (Figure 11), is therefore the most stable because of the ca. 120° bite angle between the two telluradiazoles in 32. The stability of these rings was further tested by neglecting the SBIs of one supramolecular synthon for each model. The four- and five-membered rings did relax to the linear chain structure, but incipient spirals were obtained from the larger rings. While the seven- and eight-membered rings converged to columns of the same diameter, the five-membered ring gave a narrower structure. Longer models of the two spirals were then optimized (Figure 12); the strain energy was larger for the narrow spiral (115 kJ/mol) than for the wider structure (108 kJ/mol). Although the bite angle of the building block is likely to select the preferred size of the column, these results suggest that the diameter of such a structure could be influenced by environmental conditions such as the inclusion of a guest species within the spiral. In principle, the calculation of long spiral or linear supramolecular chains would be most appropriately done with a periodic force field; however, this approach would presume previous knowledge of the final structure. The identification of two spirals assembled by 32, with different diameters and periods, illustrates the importance of allowing the system to find the path to a minimum of potential energy without periodic constraints.

Article


Concluding Remarks. The experimental construction of supramolecular structures cannot be substituted by computational design, but the judicious use of modeling methods can foster progress at a rate faster than the pure synthetic approach would achieve on its own. Translation of the main features of DFT calculated potential energy surfaces onto the MMX force field afforded a set of parameters able to accurately model Te-N intramolecular bonds and supramolecular interactions in assemblies of building blocks that contain the 1,2,5-telluradiazole ring. The efficacy of this force field to reproduce the observed structural features in actual crystal structures of such systems was demonstrated even in a case that undergoes a significant distortion of molecular structure to accommodate the supramolecular interactions. The results are also comparable to those of DFT (GGA) calculations. Using this set of parameters to investigate the assembly of new supramolecular structures identified a number of molecular species that constitute appealing synthetic targets. Acknowledgment. We thank McMaster University, the Natural Sciences and Engineering Research Council of Canada, the Canada Foundation for Innovation, and the Ontario Innovation Trust for their financial support. This work was made possible by the facilities of the Shared Hierarchical Academic Research Computing Network (SHARCNET: www.sharcnet.ca) and Compute/Calcul Canada. We thank Dr. Kevin E. Gilbert (Serena Software) for valuable discussions regarding the structure of the MMX parameter files. Supporting Information Available: MMX parameters, example of input for 22, tables of optimized geometries of all structures, predicted crystallographic coordinates for two possible polymorphs of 30, selected geometric parameters for oligomers of 1 and 2. This information is available free of charge via the Internet at http:// pubs.acs.org/.

References (1) Alcock, N. W. Bonding and Structure, Structural Principles in Inorganic and Organic Cchemistry; Ellis Horwood: Cornwall, 1990; p 321. (2) Cozzolino, A. F.; Britten, J. F.; Vargas-Baca, I. Cryst. Growth Des 2006, 6, 181–186. (3) Gleiter, R.; Werz, D. B.; Rausch, B. J. Chem.;Eur. J. 2003, 9, 2676–2683. (4) Haiduc, I. Secondary Bonding. In Encyclopedia of Supramolecular Chemistry; Steed, J., Atwood, J., Eds.; Marcel Dekker, Inc.: New York, 2004; pp 1215-1224. (5) Starbuck, J.; Norman, N. C.; Orpen, A. G. New J. Chem. 1999, 23, 969–972. (6) Desiraju, G. R. Angew. Chem., Int. Ed. Engl. 1995, 34, 2311–2327. (7) Cozzolino, A. F.; Vargas-Baca, I.; Mansour, S.; Mahmoudkhani, A. H. J. Am. Chem. Soc. 2005, 40, 4966–4971. (8) Cozzolino, A. F.; Bain, A. D.; Hanhan, S.; Vargas-Baca, I. Chem. Commun. 2009, 4043–4045. (9) Dutton, J. L.; Ragogna, P. J. Inorg. Chem. 2009, 48, 1722–1730. (10) Risto, M.; Reed, R. W.; Robertson, C. M.; Oilunkaniemi, R.; Laitinen, R. S.; Oakley, R. T. Chem. Commun. 2008, 28, 3278–3280. (11) Neidlein, R.; Knecht, D.; Gieren, A.; Ruiz-Perez, C. Z. Naturforsch. B. 1987, 42, 84. (12) Zhao, Y.; Truhlar, D. G. Theor. Chem. Acc. 2008, 120, 215–241. (13) Zhao, Y.; Truhlar, D. G. J. Chem. Phys. 2006, 125. (14) Antony, J.; Grimme, S. Phys. Chem. Chem. Phys. 2006, 8, 5287–5293. (15) Grimme, S.; Antony, J.; Schwabe, T.; Muck-Lichtenfeld, C. Org. Biomol. Chem. 2007, 5, 741–758.

677

(16) Cornell, W. D.; Cieplak, P.; Bayly, C. I.; Gould, I. R.; Merz, K. M.; Ferguson, D. M.; Spellmeyer, D. C.; Fox, T.; Caldwell, J. W.; Kollman, P. A. J. Am. Chem. Soc. 1995, 117, 5179–5197. (17) Sprague, J. T.; Tai, J. C.; Yuh, Y.; Allinger, N. L. J. Comput. Chem. 1987, 8, 581–603. (18) Allinger, N. L. J. Am. Chem. Soc. 1977, 99, 8127–8134. (19) Allinger, N. L.; Allinger, J. A.; Yan, L. Q. THEOCHEM 1989, 60, 363–369. (20) Allinger, N. L.; Quinn, M. I.; Chen, K. S.; Thompson, B.; Frierson, M. R. J. Mol. Struct. 1989, 194, 1–18. (21) Allinger, N. L.; Yuh, Y. H.; Lii, J. H. J. Am. Chem. Soc. 1989, 111, 8551–8566. (22) Mayo, S. L.; Olafson, B. D.; Goddard, W. A. J. Phys. Chem. 1990, 94, 8897–8909. (23) Rappe, A. K.; Colwell, K. S.; Casewit, C. J. Inorg. Chem. 1993, 32, 3438–3450. (24) Te Velde, G.; Bickelhaupt, F. M.; Baerends, E. J.; Fonseca Guerra, C.; Van Gisbergen, S. J. A.; Snijders, J. G.; Ziegler, T. J. Comput. Chem. 2001, 22, 931–967. (25) Guerra, C. F.; Snijders, J. G.; Velde, G. t.; Baerends, E J Theor. Chem. Acc. 1998, 99, 391. (26) van Lenthe, E.; Snijders, J. G.; Baerends, E. J. J. Chem. Phys. 1996, 105, 6505–6516. (27) van Gisbergen, S. J. A.; Snijders, J. G.; Baerends, E. J. Phys. Rev. Lett. 1997, 78, 3097–3100. (28) van Gisbergen, S. J. A.; Snijders, J. G.; Baerends, E. J. J. Chem. Phys. 1998, 109, 10644–10656. (29) Vosko, S. H.; Wilk, L.; Nusair, M. Can. J. Phys. 1980, 58, 1200–11. (30) Perdew, J. P. Phys. Rev. B. 1986, 33, 8822. (31) Perdew, J. P.; Wang, Y. Phys. Rev. B. 1992, 45, 13244. (32) Leigh, W. J.; Harrington, C. R.; Vargas-Baca, I. J. Am. Chem. Soc. 2004, 126, 16105–16116. (33) van Lenthe, E.; Ehlers, A.; Baerends, E.-J. J. Chem. Phys. 1999, 110, 8943–8953. (34) van Lenthe, E.; Baerends, E. J.; Snijders, J. G. J. Chem. Phys. 1993, 99, 4597–610. (35) van Lenthe, E.; Baerends, E. J.; Snijders, J. G. J. Chem. Phys. 1994, 101, 9783–9792. (36) van Lenthe, E.; van Leeuwen, R.; Baerends, E. J.; Snijders, J. G. Int. J. Quantum Chem. 1996, 57, 281–93. (37) Fan, L. Y.; Ziegler, T. J. Phys. Chem. 1992, 96, 6937–6941. (38) Fan, L. Y.; Ziegler, T. J. Chem. Phys. 1992, 96, 9005–9012. (39) Gajewski, J. J.; Gilbert, K. E.; McKelvey, J. Advances in Molecular Modeling; JAI Press: New York, 1990; Vol. 2. (40) Gilbert, K. E. PCModel; Serena Software: Bloomington, NJ, 2004. (41) Schatte, G.; Chivers, T.; Tuononen, H. M.; Suontamo, R.; Laitinen, R.; Valkonen, J. Inorg. Chem. 2005, 44, 443–451. (42) Bjorgvinsson, M.; Roesky, H. W.; Pauer, F.; Stalke, D.; Sheldrick, G. M. Inorg. Chem. 1990, 29, 5140–5143. (43) Bjorgvinsson, M.; Roesky, H. W.; Pauer, F.; Stalke, D.; Sheldrick, G. M. Eur. J. Sol. State. Inor 1992, 29, 759–776. (44) Kontopoulos, C.; Sigalas, M. P. J. Mol. Struc.-Theochem 1999, 490, 125–131. (45) Chivers, T.; Gao, X. L.; Parvez, M. J. Chem. Soc., Chem. Commun. 1994, 2149–2150. (46) Chivers, T.; Gao, X. L.; Parvez, M. J. Am. Chem. Soc. 1995, 117, 2359–2360. (47) Chivers, T.; Gao, X. L.; Parvez, M. Inorg. Chem. 1996, 35, 9–15. (48) Important progress has been made towards accounting for the dispersion component with DFT functionals. For examples see (a) Grimme, S.; Antony, J.; Schwabe, T.; Muck-Lichtenfeld, C. Org. Biomol. Chem. 2007, 5, 741–758. (b) Zhao, Y.; Truhlar, D. G. Acc. Chem. Res. 2008, 41, 157–167. (49) Allan, R. E.; Gornitzka, H.; Karcher, J.; Paver, M. A.; Rennie, M.-A.; Russell, C. A.; Raithby, P. R.; Stalke, D.; Steiner, A.; Wright, D. S. J. Chem. Soc., Dalton Trans. 1996, 1727. (50) Cozzolino, A. F.; Whitfield, P. S.; Vargas-Baca, I. J. Am. Chem. Soc. 2010, 132, 17265-17270. (51) Suzuki, T.; Fujii, H.; Yamashita, Y.; Kabuto, C.; Tanaka, S.; Harasawa, M.; Mukai, T.; Miyashi, T. J. Am. Chem. Soc. 1992, 114, 3034.

Parametrization of a Force Field for TeâN Secondary Bonding

Recommend Documents

Parametrization of a Force Field for TeâN Secondary Bonding