Competition Between Electronic and Mechanical Strain in Platinum-Metal-Directed Self-Assembled Macrocycles

Transcription

1 University of Colorado, Boulder CU Scholar Chemistry & Biochemistry Graduate Theses & Dissertations Chemistry & Biochemistry Spring Competition Between Electronic and Mechanical Strain in Platinum-Metal-Directed Self-Assembled Macrocycles Eric Anthony Buchanan University of Colorado Boulder, Follow this and additional works at: Part of the Physical Chemistry Commons Recommended Citation Buchanan, Eric Anthony, "Competition Between Electronic and Mechanical Strain in Platinum-Metal-Directed Self-Assembled Macrocycles" (2015). Chemistry & Biochemistry Graduate Theses & Dissertations This Thesis is brought to you for free and open access by Chemistry & Biochemistry at CU Scholar. It has been accepted for inclusion in Chemistry & Biochemistry Graduate Theses & Dissertations by an authorized administrator of CU Scholar. For more information, please contact

2 Competition between Electronic and Mechanical Strain in Platinum-Metal-Directed Self-Assembled Macrocycles by Eric A. Buchanan B.A., University of Texas, 2008 A thesis submitted to the Faculty of the Graduate School of the University of Colorado in partial fulfillment of the requirement for the degree of Master of Science Department of Chemistry and Biochemistry 2015

3 This thesis entitled: Competition between Electronic and Mechanical Strain in Platinum-Metal-Directed Self-Assembled Macrocycles written by Eric A. Buchanan has been approved for the Department of Chemistry and Biochemistry Josef Michl Robert Parson Date The final copy of this thesis has been examined by the signatories, and we Find that both the content and the form meet acceptable presentation standards Of scholarly work in the above mentioned discipline.

4 Buchanan, Eric A. (M.S., Chemistry and Biochemistry Department) Competition between Electronic and Mechanical Strain in Platinum-Metal-Directed Self-Assembled Macrocycles Thesis directed by Professor Josef Michl Ground state structures have been found using the density functional theory method PBE0/Def2-TZVPP//PBE0/Def2-SVP for the cis and trans isomers of platinum-metal-directed selfassemblies of four pyridine or acetylene terminated rods and four Pt(PR 3 ) 2 centers. The favored geometries are determined by a competition between ring strain and electronic strain at the Pt centers. The former generally grows and the latter decreases as the number of trans-pt centers is augmented. For cationic complexes containing two bipyridyl and two biphenyl rods, with a +1 charge on each Pt center, a puckered structure with all four Pt centers cis is found to be 37.6 kcal/mol lower in energy than the isomer with all four Pt centers trans. For neutral complexes with four biphenyl rods and neutral Pt centers, the highly ring-strained planar, circular all-trans isomer lies 17.2 kcal/mol below the square-shaped all-cis isomer. iii

5 Dedication I dedicate this thesis to my son, Jett, and my girlfriend, Rebecca. Without their patience and support, this work would not have been possible.

6 Acknowledgments I would like to express my gratitude to Prof. Josef Michl for his support, guidance, and supervision throughout this work. I am grateful for the guidance provided by Dr. Matthew Macleod on quantum theory and systems administration. support. I wish to express my appreciation to Dr. Cecile Givelet and RNDr. Jan Plutnar for their v

7 CONTENTS CHAPTER I. INTRODUCTION 1 Cyclic or Linear Oligomers 1 DFT Computations 3 II. COMPUTATIONAL DETAILS 4 III. RESULTS 5 Macrocycle Geometries 5 Electronic and Mechanical Strain 13 Fragment Structural Analysis 22 IV. DISCUSSION 28 V. CONCLUSION 32 BIBLIOGRAPHY 35 APPENDIX 37 vi

8 TABLES Table 1. Relative PBE0/Def2-TZVPP//PBE0/Def2-SVP Energies of Self-assembled Macrocycles 6 2. Relative PBE0/Def2-TZVPP Energies of Optimized Fragment Isomers Mechanical Strain in Fragments, PBE0/Def2-TZVPP//PBE0/Def2-SVP Relative Macrocycle Energies Calculated from Electronic and Mechanical Strain in Fragments Relative Electrostatic Interaction Between Fragments Using Mulliken and NBO Charge Distribution Analysis Relative Macrocycle Energies Calculated from Electronic and Mechanical Strain in Fragments with Corrections from Mulliken and NBO Charge Distribution Analysis Platinum Valence Angles for Neutral Macrocycles Platinum Valence Angles for Cationic Macrocycles 26 A1. Electrostatic Interaction between Fragments for Neutral Species Using Mulliken Charge Distribution Analysis 37 A2. Electrostatic Interaction between Fragments for Cationic Species Using Mulliken Charge Distribution Analysis 38 A3. Electrostatic Interaction between Fragments for Neutral Species Using NBO Charge Distribution Analysis 39 A4. Electrostatic Interaction between Fragments for Cationic Species Using NBO Charge Distribution Analysis 40 A5. PBE0/Def2-TZVPP Relative Energies of Optimized Dicationic Fragment Isomers 41 vii

9 FIGURES Figure 1. Platinum Atom Complexes 2 2. PBE0/Def2-SVP Structures of Neutral Macrocycles t 4 and c 1 t PBE0/Def2-SVP structures of Neutral Macrocycles ctct and cttc 8 4. PBE0/Def2-SVP structures of Neutral Macrocycles c 3 t and c PBE0/Def2-SVP structures of Cationic Macrocycles t 4 and c 1 t PBE0/Def2-SVP structures of Cationic Macrocycles ctct and ct:tc PBE0/Def2-SVP structures of Cationic Macrocycles c 3 t and c Optimized Geometries for Cis and Trans Isomers of Neutral and Cationic Fragments Valence Angles at Platinum Mechanical Strain (E strain ) vs. Ring Angle, á, for Fragments of Neutral Macrocycles Mechanical Strain (E strain ) vs. Ring Angle, á, for Fragments of Cationic Macrocycles 27 A1. Plot of Relative Complex Energies vs. Number of Cis Platinum Atoms for Neutral and Cationic Macrocycles 41 viii

10 I. Introduction Self-assembly of molecular rods and transition-metal connectors has been shown to be capable of synthesizing large, symmetric polygonal molecules. 1-8 These complexes have many possible applications such as molecular encapsulation 9 and catalysis. 10 Usually, transition-metaldirected self-assembly is carried out under equilibrium conditions and the reversibility of the assembly process results in fragile structures. 11 Covalent stabilization can convert the fragile structure of a self-assembled complex to a sturdier one by converting dative N Pt + bonds into covalent C-Pt bonds. Cyclic or Linear Oligomers In previous work, 12 a former group member, Alexandre Olive, started with terminally difunctionalized rod 1 and reported covalent stabilization synthesis of the covalent neutral macrocycle 2 (Figure 1). His interpretation of the 31 P NMR data was that all platinum atoms carried cis phosphine ligands in the starting rod 1, the cationic ( dative ) rectangular intermediate macrocycle 3, and the neutral ( covalent ) square macrocycle 2. His reasoning was that while rod 1 displayed a single 31 P peak with two Pt satellites, as would be expected for the trans isomer, the J P-Pt coupling constant (X = I: Hz; X = NO 3 : Hz) was too low for the trans isomer. He proposed that in 1 rapid intramolecular exchange of the phosphine ligands averaged the J P-Pt coupling constant for the phosphines cis and trans to the alkyl substituents and that the compound was the cis isomer. Rapid exchange was also suggested as the explanation for why only a singlet was observed for the 31 P signals in macrocycle 3 and that it, too, was cis and not trans. 1

11 1 2 Figure 1: Platinum atom complexes. All-cis isomers shown. 3 2

12 Another group member, Jan Plutnar, later proposed 13 that this was a misinterpretation of the 31 P NMR data. He believed that the proposed rapid exchange of the phosphine ligands was impossible and thought that the NMR data showed that the phosphines on the platinum atoms were in a trans orientation. He felt that cyclic products could not contain platinum atoms with trans phosphine ligands and proposed that no square or rectangular macrocycles have been synthesized, only linear oligomers. DFT Computations This controversy led us to the project described in the present thesis, a calculation of the optimized structures of the neutral and cationic macrocycles, with rather surprising results. After seeing our computational results and after further experimental analysis, Plutnar now agrees that the neutral macrocycle 2 indeed exists as a circular ring with all platinum atoms carrying trans phosphine ligands, but continues to feel that the cationic macrocycle 3 has never been prepared and that the isolated material is a mixture of linear oligomers. Our initial results were the optimized geometries of the all-trans and all-cis isomers of the neutral macrocycle 2. The results showed that the all-trans isomer of 2 was a circular ring and that it was 16 kcal/mol lower in energy than the all-cis isomer. This interesting result prompted us to investigate all the possible isomers of the neutral (2) and the cationic (3) macrocycle and to try and elucidate what factors determined whether the cis or trans isomer was favored. For the neutral macrocycle 2, there are 6 possible isomers: t 4, ct 3, ctct (where two trans platinum atoms are opposite to each other), cttc (where two trans platinum atoms are adjacent to each other), c 3 t, and c 4. In the cationic macrocycle 3, there is one more, because they contain two 3

13 different rods and allow two possible cttc isomers: one where a biphenyl rod is between the two adjacent trans platinum atoms, ct:tc, and one where a bipyridyl rod is between them, ct tc. This requires geometry optimizations for 13 complexes with 276 or 268 atoms for 2 and 3, respectively. The system size is reduced by 72 atoms by replacing the triethylphosphine with trimethylphosphine ligands. Optimized geometries for macrocycles with the two different phosphines were compared for the all-trans and all-cis macrocycles and were quite similar. Geometry optimizations of the other isomers were attempted with triethylphosphine ligands, but they failed to converge after months. To greatly reduce computation time, we decided to investigate complexes with trimethylphosphine ligands. The PBE0 14 functional was selected because of its accuracy in calculating optimized geometries of transition-metal complexes. 15 It has also been found to perform well in calculating energies. 16 Stuttgart-Dresden 17 type effective core potentials 18 (SDD) 17 outperform LANL2DZ 19 ECPs due to their more flexible valence basis on the metal 20 and perform well for transition-metal complex geometries when compared to all-electron results using ZORA. 15,21 II. Computational Details All density functional theory (DFT) computations were carried out with the PBE0 hybrid functional using the quantum chemistry program ORCA. 22 The Stuttgard ECP Def2-SD 23 was employed for platinum atoms along with the Ahlrichs-type valence basis sets designed to be used with Def2-SD ECPs: Def2-SVP 24 and Def2-TZVPP. 24,25 Rods and ligands used the corresponding all-electron basis sets. 25,26 SCF iterations used a size 2 integration grid while final energies evaluations used size 4. The RIJ-COSX 27,28 approximation to the Coulomb term was used in all DFT 4

14 calculations. Geometry optimizations for the macrocycles were performed with the Def2-SVP basis set while all single point energy calculations and geometry optimizations for fragments were carried out using the Def2-TZVPP basis. Charge distributions were obtained from Mulliken 29 and Natural Bond Orbital (NBO) 30,31 population analysis using the density matrix produced in PBE0/Def2-TZVPP calculations. Mulliken population analysis was performed by the ORCA program while NBO analysis was performed using the NBO 6.0 program 32 linked to ORCA. These charge distributions were used with the optimized macrocycle geometries to generate point charges and calculate classical electrostatic interactions between individual fragments in macrocycles: Here k e is the Coulomb constant, the first summation is over N point charges in one fragment, and the second summation runs over M point charges in a second fragment. Atomic units were used for these calculations. III. Results Macrocycle Geometries Ground state energies for the twelve neutral (2) and cationic (3) cis, trans isomers of platinum-metal-directed self-assembled macrocycles found are shown in Table 1. All six possible isomers were found for 2 while only six of the possible seven were found for 3. For the cationic isomer containing two cis and two trans platinum centers where similar centers are adjacent to each 5

15 other (cttc), only the isomer with adjacent centers connected by a biphenyl rod, ct:ct, was found. The geometry optimization of the isomer with similar centers connected by a bipyridyl rod, ct tc, repeatedly failed to converge, likely due to the mechanical strain between the two trans centers being too great because of the extreme curvature required. The neutral macrocycle 2 is generally destabilized as the number of cis centers increases. However, the isomer containing two cis and two trans platinum centers in which similar centers are opposite to each other (ctct) breaks this trend to the point of being nearly the most stable isomer. The trend is reversed in macrocycle 3, though again the energy of the ctct macrocycle is very near that of the lowest energy isomer. Figures 2 through 7 show the optimized structures of the twelve macrocycles. Front and right side views are provided to show the three-dimensional structure of the non-planar macrocycles. Table 1: Relative PBE0/Def2-TZVPP//PBE0/Def2-SVP Energies of Self-assembled Macrocycles. a COMPD. E rel E COMPD. rel (kcal/mol) (kcal/mol) Neutral (2) Cationic (3) t t ct ct ctct 0.4 ctct 0.4 cttc 9.8 ct:tc 13.8 c 3 t 11.4 c 3 t 3.0 c c a The energy of the most stable isomer is a.u. for 2 and a.u. for 3. 6

16 a) b) Figure 2: PBE0/Def2-SVP structures of 2 a) t 4 and b) ct 3. Fragments are labeled 1 to 4. 7

17 a) \ b) Figure 3: PBE0/Def2-SVP structures of 2 a) ctct and b) cttc. Fragments are labeled 1 to 4. 8

18 a) b) Figure 4: PBE0/Def2-SVP structures of 2 a) c 3 t and b) c 4. Fragments are labeled 1 to 4. 9

19 a) b) Figure 5: PBE0/Def2-SVP structures of 3 a) t 4 and b) ct 3. Fragments are labeled 1 to 4. 10

20 a) b) Figure 6: PBE0/Def2-SVP structures of 3 a) ctct and b) ct:ct. Fragments are labeled 1 to 4. 11

21 a) b) Figure 7: PBE0/Def2-SVP structures of 3 a) c 3 t and b) c 4. Fragments are labeled 1 to 4. 12

22 Eight of the twelve macrocycles are mostly planar. The exceptions are those shown in Figures 3b, 4a, 4b, and 7b. Interestingly, three of the four are neutral macrocycles 2, while only one is a macrocycle 3. The neutral macrocycle cttc deviates slightly from planarity but its cationic counterpart, ct:ct, is planar. The neutral macrocycles c 3 t and c 4 are both puckered; however, only c 4 is puckered among the cationic species. Rods connected to two cis platinum centers are the least bent and the least strained. The curvature of a rod generally increases with the number of trans platinum atoms to which it is connected. As the number of trans platinum atoms in a macrocycle increases, the mechanical strain also increases as a result of the curvature required to form the ring. Cis platinum atoms allow the rods to have much less distorted geometries and therefore less ring strain, but cis centers are only preferred over trans in the cationic macrocycles 3. Electronic and Mechanical Strain Platinum-based fragments of the macrocycles were investigated to elucidate the competition between mechanical and electronic strain. The fragments, which can be seen in Figure 8, consist of a platinum center with two trimethylphosphine ligands and one half of either two biphenyl rods for the neutral species or one half each of a biphenyl and a bipyridyl rod. The half-rods are made by cutting the central C-C bond in the rod and capping with a terminal hydrogen. Table 2 gives the relative energies of the cis and trans isomers of the fragments with all coordinates optimized. These structures are assumed to be the preferred structures for each fragment species. The trans isomer is the most stable for each species, with the cis isomer being electronically strained by 10.7 and 5.3 kcal/mol in the neutral and cationic fragments, respectively. By looking at the trans fragments for the two species and noting the lack of curvature in the two half-rods, it can be seen that the rods will 13

23 have to be bent to form the four fragment macrocycle, inducing a possibly large amount of mechanical strain into the ring. This leads to a competition between increasing mechanical strain with more trans character and increasing electronic strain with more cis centers. a) b) Figure 8: Optimized geometries for cis and trans isomers of a) neutral and b) cationic fragments. Table 2: Relative PBE0/Def2-TZVPP Energies of Optimized Fragment Isomers. a,b a See Figure 8. COMPD. E rel (kcal/mol) Neutral (2) trans 0.0 cis 10.7 Cationic (3) trans 0.0 cis 5.3 b The energy of the most stable isomer is a.u. for the neutral and a.u. for the cationic fragment. 14

24 To investigate the mechanical strain due to ring formation, we will again use platinum-based fragments as defined earlier and in Figure 8. Each macrocycle is divided into four fragments by cutting the central C-C bonds in the four rods and capping with terminal hydrogens. The numbers next to each platinum in Figures 2 through 7 correspond to the fragment number in Table 3. The energies, E strain, of each of the four fragments for each macrocycle, distorted to the geometries they have in the macrocycles shown in Figures 2 through 7, relative to the corresponding cis or trans fragment with all coordinates optimized (Figure 8), are shown in Table 3. The coordinates of these fragments are taken from the optimized macrocycle and have all atom positions constrained except for the two terminal hydrogens added. This provides an approximation to the mechanical strain induced by formation of the macrocyclic ring. Comparing Figures 2 through 7 with Table 3 shows that as the curvature of the rods increases, so does the mechanical strain. Cis fragments are typically strained by 1.0 to 3.5 kcal/mol while strain in trans fragments ranges from 4.5 to 17.0 kcal/mol. Mechanical strain is generally larger in cationic fragments than in their neutral counterparts. This is possibly due in part to the bipyridyl rods being shorter and therefore requiring more distortion to form the macrocycle ring than the biphenyl rods. The geometries of both the neutral and cationic ctct macrocycles allow the two trans centers to be only slightly curved, resulting in the lowest strain for trans fragments of any macrocycle. Increasing the number of trans fragments in a macrocycle generally increases the total strain, with ctct being the exception. Table 2 showed that trans fragments decrease electronic strain and this sets up the competition between mechanical strain induced by forming the ring and electronic strain in the platinum centers. As mechanical strain due to the presence of trans fragments is much greater in the cationic macrocycles 3 but electronic strain due to cis fragments is decreased, mechanical strain dominates electronic and the c 4 macrocycle is 15

25 the most stable. The opposite applies for the neutral macrocycles 2, resulting in electronic strain dominating mechanical and the t 4 macrocycle being preferred. 16

26 Table 3: Mechanical Strain in Fragments, PBE0/Def2-TZVPP//PBE0/Def2-SVP. COMPD. /Fragment E strain (kcal/mol) COMPD. /Fragment E strain (kcal/mol) Neutral (2) Cationic (3) t 4 t total 34.3 total 47.1 ct 3 ct total 27.6 total 35.5 ctct ctct total 13.0 total 15.7 cttc ct:tc total 22.4 total 25.6 c 3 t c 3 t total 13.1 total 15.6 c 4 c total 7.3 total

27 Using the electronic strain in cis and trans fragments given by Table 2 and the mechanical strain in each fragment at its macrocyclic geometry from Table 3, the total strain can be approximated for each macrocycle by summing the mechanical and electronic strain in all four fragments. Calculating the total strain in each macrocycle and subtracting the total strain of the most stable isomer for each species gives the relative total strain for each macrocycle, E strain, which is an approximation to its relative energy, E rel. The results of these calculations are shown in Table 4, where E rel is the relative, energy of a macrocycle from Table 1. Table 4: Relative Macrocycle Energies Calculated from Electronic and Mechanical Strain in Fragments. a COMPD. Erel Estrain Ä b a All values in kcal/mol. b Ä = E strain -E rel. Neutral (2) t ct ctct cttc c 3 t c Cationic (3) t ct ctct ct:tc c 3 t c

28 The difference Ä between E strain and E rel is given and shows that the relative energies of the neutral macrocycles 2 can be reproduced well by summing the total strain in the four fragments. The differences are almost all under 0.5 kcal/mol and the trend in relative isomer energies is reproduced. Unlike their neutral counterparts, the cationic macrocycles 3 are not well behaved. The differences between the relative total strains and the relative energies are large and increase with the number of trans fragments in the macrocycle. The trend in relative energies is mostly reproduced, but the ctct macrocycle is predicted to be the most stable. The large differences are believed to be due to electrostatic interactions among the four fragments in each macrocycle which are neglected in the calculation of E strain. This interaction should be much greater between cationic fragments in 3 than in neutral fragments in 2. To recover some of the missing interactions due to macrocycle fragmentation, the classical electrostatic interactions between each pair of fragments in each macrocycle were calculated for all neutral and cationic species using both Mulliken and NBO charge distributions. The charge distributions were used in conjunction with atom positions from the macrocycle geometries to generate point charges for the electrostatic interaction calculations. The electrostatic interaction energies between each fragment in each macrocycle are provided in appendices, Tables A1 through A4, and the relative electrostatic interaction energy for each macrocycle is given in Table 5. 19

29 Table 5: Relative Electrostatic Interaction Between Fragments Using Mulliken and NBO Charge Distribution Analysis. COMPD. E Mulliken E NBO (kcal/mol) (kcal/mol) Neutral (2) t ct ctct cttc c 3 t c Cationic (3) t ct ctct ct:tc c 3 t c In the neutral macrocycles 2, the interactions are small and have the same trend for each method, with E mulliken being 2 to 3 times larger than E NBO. The interactions are very large in the cationic macrocycles 3 as expected, and the two methods of charge distribution analysis do not produce the same trend, although the scale is similar. The difference between the two methods is the interaction energy for the cationic macrocycle ct:tc, with NBO analysis giving an energy that is 9.0 kcal/mol greater than that for Mulliken analysis. Table 6 gives E rel and E strain from Table 4 as well as E strain with electrostatic corrections from Mulliken and NBO charge distributions analysis for comparison. The difference Ä between E strain with and without electrostatic interaction corrections and E rel is given. 20

30 Table 6: Relative Macrocycle Energies Calculated from Electronic and Mechanical Strain in Fragments with Corrections from Mulliken and NBO Charge Distribution Analysis. a COMPD. E rel E strain E strain-mull. E strain-nbo Ä b Ä b Mulliken Ä b NBO Neutral (2) t ct ctct cttc c 3 t c total Cationic (3) t ct ctct cttc c 3 t c total a All values in kcal/mol. b Ä = E strain -E rel. In the neutral species 2, neither method of correction offers much improvement. The trends remain the same but the electrostatic correction is too large, especially when the Mulliken charge distribution is used. The cationic macrocycles 3 do benefit from electrostatic corrections. Both methods reduce the total difference Ä for all complexes by about 10.7 kcal/mol and both correctly identify the c 4 isomer as the lowest energy macrocycle. Both methods overestimate the interactions in the ctct macrocycle and predict it to be higher in energy than c 3 t; however, the NBO corrections correctly place cttc above ctct in energy. While neither correction reproduces the macrocycle energy trend faithfully, the NBO correction does better than the Mulliken correction. 21

31 Fragment Structural Analysis The mechanical strain in fragments of the macrocycles has been investigated, but so far the dependence of that strain on the geometry of the fragments has not. To determine which structural elements have the strongest influence on the mechanical strain in a fragment and to get a picture of a small region of the potential energy surface, the six valence angles at the platinum atoms were examined. Figure 9 shows the structure of the neutral and cationic fragments and defines all these valence angles. The ring angle between the two rods with the platinum atom at the vertex is labeled á. Tables 7 and 8 give E strain for each fragment for reference as well as values for all valence angles defined in Figure 9 in degrees for neutral and cationic macrocycles respectively. Values for the optimized, unstrained fragments from Figure 8 are provided at the bottom of each table. a) b) c) Figure 9: Valence angles at platinum. b) and c) show R for the neutral and cationic species respectively. 22

32 Table 7: Platinum Valence Angles for Neutral Macrocycles. a COMPD. b E strain /Fragment (kcal/mol) á c â ã ä å æ Neutral (2) t ct ctct cttc c 3 t c Optimized Fragemnt trans cis a Angles in degrees. b Fragment energies are relative to the respective optimized, unstrained cis or trans fragment. c The ring angle at the Pt atom. 23

33 The P-Pt-P angle â determines whether a fragment is cis or trans and the ring angle á can also be used to determine the isomerization of a fragment. Those with á and â near 90 are cis while those with them near 180 are trans. There are two classes of cis fragments: symmetric and asymmetric. Symmetric cis fragments have a plane of symmetry through the platinum atom bisecting the C-Pt-C and P-Pt-P (ring and ligand) angles. All symmetric cis fragments have angle pairs ä, and ã, æ differing by less than 1. For asymmetric cis fragments, these two angle pairs all differ by 5-6. All neutral cis fragments fall into one of these two categories. The optimized cis fragment is asymmetric; however, the angle pairs differ by only 1-2, so the two classes must result from the strain induced by forming the ring. Figure 10 shows plots of E strain for the fragments vs. á. Figure 10a shows a linear scaling of mechanical strain with ring angle for trans fragments instead of a parabolic curve with a minimum near 180 that would be expected. We do not know why this is. There appear to be two separate trends for the cis fragments and indeed when they are divided into symmetric and asymmetric, two parabolic trends emerge. Figure 10b shows only cis fragments, but divides them into symmetric and asymmetric conformers. The dependence of mechanical strain on platinum valence angles was investigated for each angle á through æ and for combinations of several angles included the sum of all angles. For the neutral macrocycles, all the plots were very similar, but the best fit came from just the ring angle á. 24

34 a) b) Figure 10: Mechanical strain (E strain) ) vs. ring angle á for fragments of neutral macrocycles. Plot a) includes all cis and trans fragments while b) includes only cis fragments. Trend line equations and R 2 values are provided in A1. 25

35 Table 8: Platinum Valence Angles for Cationic Macrocycles. a COMPD. b E strain /Fragment (kcal/mol) á c â ã ä å æ Cationic (3) t ct ctct cttc c 3 t c Optimized Fragment trans cis a Angles in degrees. b Fragment energies are relative to the respective optimized unstrained cis or trans fragment. c The ring angle. 26

36 The platinum valence angles do not offer the same insight for the cationic species as they do for the neutral. There are no patterns or subclasses of fragments that readily emerge from the data. Figure 11 shows the plot of E strain vs. the ring angle á. The only smooth trend is the relation of the ring angle of cis fragments to their mechanical strain. The cationic cis fragments are all asymmetric, but the angle pairs don t all differ by the same value as they did in the neutral fragments. The trans fragments appear to divide into two linear trends, indicating there may be two subclasses; however, there is no clear justification for separating them based on any of the platinum valence angles. Some plots of mechanical strain against the other valence angles are similar to the plot against ring angle while some are very different. The plot of E strain vs. ring angle does not give a smooth potential energy curve for the cationic species as it did for the neutral species because the relative energies of the fragments are incorrect due to the missing interactions between the fragments. As was seen previously, the cationic macrocycles do not exhibit simple trends upon fragment analysis. Figure 11: Mechanical strain (E strain ) vs. ring angle á for fragments of cationic macrocycles. Trend line equations and R 2 values are provided in A1. 27

37 IV. Discussion The trends in the relative energies of the macrocycles compared to the number of cis platinum atoms show very linear and somewhat linear scaling for the neutral and cationic species, respectively (Figure A6) if the ctct macrocycles are ignored. The geometries of the ctct macrocycles allow for greatly reduced mechanical strain around their two trans platinum atoms due to the small curvature required to form the ring as the two trans platinum atoms can be very close together. This allows for a very linear geometry compared to all the other macrocycles with trans platinum centers. That the energy scales linearly in neutral macrocycles with the number of cis platinum atoms, by 4.2 kcal/mol, indicates that the isomerization of one platinum atoms has very little effect on the rest of the macrocycle. The charge distribution analysis in Table 5, which shows that there is very little interaction between neutral fragments, supports this. The scaling of energy with the number of cis atoms in cationic macrocycles requires the addition of a second-order term, with a coefficient of 1.4 kcal/mol. The coefficient at the first-order term is kcal/mol and the y intercept for both is set to the energy of the t 4 macrocycle for each species. This indicates that the isomerization at one platinum atom has an effect on the rest of the macrocycle that is significant and non-linear. This is also supported by the charge distribution analysis in Table 5 and the large electrostatic interaction energies among the fragments in each macrocycle. The implication of this is that we can reduce the complexity of the system to one quarter by looking at fragments as defined in Figure 8. This allows us to separate the ring strain into its mechanical and electronic contributions much more easily than could be done for the macrocyclic complexes. We can calculate the average trans to cis isomerization energy to compare to Figure A1 by taking the difference of the average cis and trans fragment strain, excluding ctct fragments, and 28

38 adding the electronic strain. The result of this exercise for the neutral macrocycles 2 is 4.6 kcal/mol per cis platinum atom, which is in excellent agreement with the linear fit of 4.2 kcal/mol. This reinforces the proposal that the interactions among neutral fragments are weak. If the same is done for the cationic macrocycles, the average trans to cis isomerization energy is kcal/mol. This is far from the first-order term of the polynomial fit, kcal/mol. Again we see that we can accurately reproduce macrocycle relative energies in the neutral species by only considering their fragments and neglecting interactions among them while the same cannot be done in their cationic counterparts. By allowing all coordinates to be optimized, the fragments in Figure 8 have no mechanical strain that would be caused by the constraints of forming a ring and therefore the energy differences should just reflect the electronic strain caused by trans to cis isomerization. Table 2 shows that the relative stability of the trans isomer decreases as the fragment becomes positively charged and in fact Table A5 shows that in dicationic fragments, where both rods are represented with a pyridine group, the cis isomer is actually more stable than the trans by 2.2 kcal/mol. Trans isomers of platinum(ii) complexes are typically lower in energy than their cis counterparts in the gas phase due to the minimization of unfavorable ligand-ligand electrostatic interactions. 33 The electrostatic interaction within each fragment can be seen in Tables A1-A4 and shows that trans fragments have much lower electrostatic interaction energy than do cis for the neutral macrocycles 2. For the cationic macrocycles 3, the two isomers have effectively the same electrostatic interaction energy and the preference for the trans macrocycle is likely due to steric effects. 34 Comparing the energies at these optimized fragment geometries to those at the geometries in the macrocycles then tells us about the amount of mechanical strain required to form the ring. The total mechanical strain in the four 29

39 fragments in a macrocycle increases with the number of trans centers for both the neutral and cationic species. Again, the exception is with the ctct macrocycles due to their flattened geometries resulting from the two trans platinum atoms being so close together. The total mechanical strain in each macrocycle is also always greater in the cationic species. This is likely due to the bipyridyl rods being shorter than the biphenyl rods by two acetylenes requiring greater curvature in the rods of the cationic macrocycles. It should be noted though that these calculations analyzed mechanical strain in the fragments described in Figure 8, not in individual rods, and therefore no comment can be made on the relative stiffness of the biphenyl and bipyridyl rods, just on the relative stiffness of neutral and cationic fragments. The relative sum of the mechanical and electronic strain in all the fragments of each macrocycle reproduces the relative energies of the neutral macrocycles accurately. This justifies our method of separating mechanical and electronic strain and confirms the fact that the interactions among the fragments in the neutral macrocycles 2 are weak. The relative sums of the strain in the cationic fragments do not reproduce those in the cationic macrocycles 3 in any way. In fact, the summing of the relative strain does not even predict the c 4 macrocycle to have the lowest energy. We contribute this difference to the neglect of electrostatic interactions among the fragments. Adding a classical electrostatic correction does not improve matters for the neutral species, but using NBO charge distribution analysis, the trend in relative energy is mostly reproduced, except for the ctct macrocycle again, and the c 4 macrocycle is correctly identified as the most stable. The overestimation of the fragment interaction energy for the ctct macrocycle is understandable as the two trans fragments are much closer to each other than any two fragments in any of the other macrocycles. The use of point charges to represent the charge distribution is a poor approximation, 30

40 especially due to the fragments proximity to each other and the charges on the cationic species. The charge distributions are also calculated for each fragment in vacuum and not in the field of the other fragments in the macrocycle. Calculating the distribution in vacuum is consistent with the methodology of constructing the macrocycle energy from the relative energies of individual fragments, but introduces more approximations. Corrections based on NBO analysis gave better results, especially for the cationic species. Analysis of the six platinum valence angles is also instructive. If the six valence angles are thought of as the coordinates in a seven-dimensional potential energy plot, the potential energy curve with the ring angle á as the coordinate can be regarded as the potential energy surface resulting from varying the ring angle and allowing all other coordinates to optimize. It then makes sense that E strain is determined solely by whether a fragment is cis or trans and the ring angle, as the formation of the macrocycle only constrains the ring angle on the platinum atom. This high degree of correlation between mechanical strain and ring angle is seen in Figure 10 for the neutral species. The strain in the trans fragments scales linearly with the ring angle á while the two classes of cis fragments, symmetric and asymmetric, each correlate parabolically. We do not currently know why the trans fragments correlate linearly with á. As in other cases, the correlation breaks down somewhat for the cationic species (Figure 11). There is a very general trend that mechanical strain decreases as the ring angle approaches 180 in trans fragments. Surprisingly, the cis fragments have a nice parabolic correlation despite the inaccuracy in their energies. This is likely an artifact of luck. It has been shown that the neglect of the interactions among the fragments does not reproduce accurate energies and corrections are required. Including these interactions would shift all of the energies in the cationic species and may restore the linear correlation in the 31

41 trans fragments. The cis fragments would retain their parabolic correlation, though the shape of the well would very likely change. The fully optimized cis and trans fragments for each species should have their ring angle á at or at least near the minimum of their respective potential energy curves. For the cationic species, the ring angle of 85.8 in the cis fragments is located very near the minimum of the potential energy curve, though it is 2.0 kcal/mol lower in energy. However, as discussed previously, the energy scale for the cationic fragments is not very accurate. The lack of a well defined potential energy surface for the trans fragments prevents any comment on the ring angle of its fully optimized fragment. Regarding neutral fragments, the ring angle of 176 in the trans fragment sits at the bottom of the potential energy line as it should. It is difficult to comment on the fully optimized cis fragment as it is located on neither the symmetric nor asymmetric potential energy curves and is to the right of the minimum for both. It is therefore an unfavorable ring angle for a cis platinum atom when it is constrained to be in a ring. V. Conclusion The favored structure of the macrocycle (cis vs. trans phosphine ligands on platinum atoms) is determined by competition between electronic strain, for which trans isomers are favored, and mechanical strain, for which cis isomers are favored. In the neutral macrocycles 2, electronic strain prevails, all platinum atoms are trans, and the most stable isomer of the macrocycle is circular and planar. In the cationic macrocycles 3, mechanical strain prevails, all platinum atoms are cis, and the macrocycle is rectangular and puckered. As the charge on the platinum atom is increased, the trans isomer is destabilized relative to the cis isomer and is actually less favorable than the cis isomer in 32

42 the dicationic species where both rods are bipyridines. This work shows that for the neutral species there is little interaction among fragments when the macrocycles are fragmented in the manner described. This allows for reliable separation and analysis of mechanical and electronic strain providing an accurate method to predict the relative energies of macrocycles. Potential energy curves can be constructed for neutral fragments and could possibly be used to predict the approximate structures of macrocycles. There are exceptions when the macrocycle has a geometry which allows two platinum atoms to come very close to each other as in ctct. As the fragmentation method reduces the rather large system size of the complexes by 75%, it also allows for higher level, more accurate methods to be used. Properties such as NMR coupling constants could be predicted and compared to experimental results, which may not be possible if the large macrocycle has to be considered. Cationic macrocycles have interactions between fragments that are too large and the properties of macrocycles do not depend additively on the properties of fragments. Future work might involve applying the methods in this work to other transition metal complexes, especially those with available crystallographic data to check the accuracy of the predicted structures. Scalar relativistic all-electron treatment of the fragments would allow for accurate calculations of molecular properties such as electron density and NMR spectra and coupling constants. Calculating the J P-Pt coupling constants for complexes similar to the neutral fragments in this work where the J P-Pt coupling constants are known for the cis and trans isomers would allow for calibration of the calculated constants to compare with experimental data and better confirm that the observed isomer is indeed all-trans. This work provides evidence that the neutral macrocycle 2 has its phosphine ligands in the 33

43 trans orientation at all four platinum atoms and that the structure of the macrocycle is a ring. This is surprising and was not previously expected. Energetic properties of macrocycles depend additively on the properties of its fragments when there is weak interaction among the fragments as in the neutral species 2. 34

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46 Appendix Table A1: Electrostatic Interaction between Fragments for Neutral Species Using Mulliken Charge Distribution Analysis. COMPD. E rel /Fragment (kcal/mol) t total 0.0 ct total 1.1 ctct total 3.5 cttc total 2.1 c 3 t total 4.2 c total

47 Table A2: Electrostatic Interaction between Fragments for Cationic Species Using Mulliken Charge Distribution Analysis. COMPD. E rel /Fragment (kcal/mol) t total 30.7 ct total 21.5 ctct total 13.8 cttc total 0.4 c 3 t total 5.9 c total

48 Table A3: Electrostatic Interaction between Fragments for Neutral Species Using NBO Charge Distribution Analysis. COMPD. E rel /Fragment (kcal/mol) t total 0.0 ct total 0.3 ctct total 1.0 cttc total 0.8 c 3 t total 2.0 c total