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Reliable Structures and Energetics for Two New Delocalized Pбббp PAPER www.rsc.org/pccp | Physical Chemistry Chemical Physics Reliable structures and energetics for two new delocalized pÁÁÁp prototypes: cyanogen dimer and diacetylene dimerwz Brian W. Hopkins, Adel M. ElSohly and Gregory S. Tschumper* Received 22nd November 2006, Accepted 3rd January 2007 First published as an Advance Article on the web 7th February 2007 DOI: 10.1039/b616878g Two new prototype delocalized pÁÁÁp complexes are introduced: the dimers of cyanogen, (NRC–CRN)2, and diacetylene, (HCRC–CRCH)2. These dimers have properties similar to larger delocalized pÁÁÁp systems such as benzene dimer but are small enough that they can be probed in far greater detail with high accuracy electronic structure methods. Parallel-slipped and T-shaped structures of both cyanogen dimer and diacetylene dimer have been optimized with 15 different procedures. The effects of basis set size, theoretical method, counterpoise correction, and the rigid monomer approximation on the structure and energetics of each dimer have been examined. MP2 and CCSD(T) optimized geometries for all four dimer structures are reported, as well as estimates of the CCSD(T) complete basis set (CBS) interaction energy for every optimized geometry. The data reported here suggest that future optimizations of delocalized pÁÁÁp clusters should be carried out with basis sets of triple-z quality. Larger basis sets and the expensive counterpoise correction to the molecular geometry are not necessary. The rigid monomer approximation has very little effect on structure and energetics of these dimers and may be used without consequence. Due to a consistent cancellation of errors, optimization with the MP2 method leads to CCSD(T)/CBS interaction energies that are within 0.2 kcal molÀ1 of those for structures optimized with the CCSD(T) method. Future studies that aim to resolve structures separated by a few tenths of a kcal molÀ1 should consider the effects of optimization with the CCSD(T) method. 1. Introduction dimer, is much too large to study at this level of detail. Hence, much work has been carried out to develop less demanding Complexes of molecules with delocalized (conjugated) p elec- electronic structure techniques that can accurately describe tron clouds are exceptionally difficult to study even in com- this type of non-covalent interaction.12–14 If we are to gain an 1–10 parison with other van der Waals complexes. In fact, a understanding of the detailed physics of conjugated pÁÁÁp recent invited article in this journal presented a benchmark systems, we will need a newer, smaller prototype system that database of weakly bound complexes and highlighted the need can be examined in more detail than is possible for benzene to move beyond the MP2 level of theory when the dispersion dimer. 9 contribution to binding becomes significant. Consider, for Cyanogen (NRC–CRN) is one of the smallest known example, the dimers listed in Table 1. MP2 and CCSD(T) closed-shell, neutral, conjugated molecules. As such, its dimer interaction energies are quite similar for (N2)2 and (C2H2)2 is an ideal prototype for conjugated pÁÁÁp interactions. Un- while MP2 tends to substantially overestimate the attractive fortunately, little is known about the (NRC–CRN)2 system. forces of pÁÁÁp stacking in complexes with delocalized p The first theoretical work on cyanogen dimer dates to 1984, electron clouds. Recent work has suggested that highly accu- when Hasanein and Evans studied nine dimer structures at the rate studies of these complexes require correlated methods that HF level of theory and with an empirical atom–atom potential 11 include the effects of quadruple excitations. For instance, the method.15 Unfortunately, the HF level of theory was demon- inclusion of perturbative approximations to quadruple excita- strably inadequate for describing the system; five of the nine tions increases the binding energy in the cyanogen dimer HF potential curves plotted by Hasanein and Evans were parallel-slipped and T-shaped configurations by 0.10 and purely repulsive. Because dispersion forces are extremely im- À1 11 0.07 kcal mol , respectively. This represents a considerable portant in the binding of p-type dimers, MP2 theory may be obstacle since the classic prototype pÁÁÁp system, benzene considered the lowest level of theory that can reasonably be expected to describe their structure and energetics. For this Department of Chemistry and Biochemistry, University of Mississippi, reason, neither Hartree Fock nor density functional methods University, MS 38677-1848, USA. E-mail: [email protected] have been employed in this study. w The HTML version of this article has been enhanced with colour In 1991, molecular beam electric resonance spectroscopy images. 16 z Electronic supplementary information (ESI) available: Cartesian performed by Klemperer and coworkers indicated a coordinates for all optimized structures. See DOI: 10.1039/b616878g T-shaped (NRC–CRN)2 structure in C2v symmetry. No 1550 | Phys.Chem.Chem.Phys., 2007, 9, 1550–1558 This journal is c the Owner Societies 2007 Table 1 Results of previous studies that demonstrate the difference metry; a T-shaped transition state in C2v symmetry; and a 27 between MP2 and CCSD(T) p ÁÁÁ p stacking interaction energies in stacked second-order saddle point in D2h symmetry. In the parallel-slipped systems with and without delocalized p electron same work, Karpfen examined the acetylene dimer in con- clouds. All energies are in kcal molÀ1 siderably more detail; this included performing optimizations Interaction energies with larger basis sets and computing single-point interaction energies at the MP4, CCSD, and CCSD(T) levels of theory. System MP2 CCSD(T) These calculations on acetylene dimer showed virtually no a Nitrogen dimer À0.58 À0.51 change in the dimer structure with increasing basis set size, and Acetylene dimera À1.99 À1.72 b only minute changes in the interaction energy of (C H ) were Benzene dimer À4.95 À2.78 2 2 2 Pyrrole dimerc À0.63 þ0.45 observed as more sophisticated treatments of electron correla- Pyrimidine dimerc À3.87 À2.64 tion were applied. Karpfen therefore concluded that the more c Triazine dimer À3.77 À2.79 rigorous theoretical treatment was not necessary for the study a Ref. 11. b Ref. 4. c Ref. 3. of the larger diacetylene complex. These results, however, are not really applicable to the dimer of diacetylene. As seen in Table 1, interactions between molecules with delocalized or conjugated p electron clouds are fundamentally different from other structures were observed in the experiment. Subse- those in small pÁÁÁp prototypes like acetylene dimer or the quently the group of de Almeida examined T-shaped, linear, dimer of molecular nitrogen. MP2 calculations are known to and parallel structures at the HF level of theory.17 Important give accurate results for simple pÁÁÁp systems.3,11 For con- nonplanar structures (including some of those studied by jugated systems, however, the results of MP2 calculations are Hasanein and Evans) were neglected entirely by de Almeida erroneous, often overstating the binding energy of conjugated et al., and the work went on to conclude that the T-shaped pÁÁÁp complexes by as much as 100%.1,3,9,28,29 structure was the global minimum on the dimer potential Despite its well known tendency to overestimate the stability energy surface. of stacked, delocalized pÁÁÁp complexes, the MP2 method Interestingly, despite the similarity of their methods, the HF continues to be used for geometry optimizations of dimers results of the de Almeida and Evans studies disagree with bound by delocalized pÁÁÁp interactions. The effect of using respect to the nature of the end-to-end linear structure. Using MP2 optimized geometries on the energetics of these types of the 6-31G basis, Evans’s HF calculations show a purely dimers is not well known, as most delocalized pÁÁÁp complexes repulsive potential curve as the molecules approach end-to- are much too large to optimize with more accurate theoretical end. By contrast, de Almeida’s HF/4-31G calculations do methods. Only recently has this effect been examined when identify an end-to-end linear stationary point on the dimer Sherill and co-workers estimated CCSD(T) optimized struc- surface. This disagreement may be due to the rigid monomer tures of the benzene dimer by using MP2 potential energy approximation, which was employed by Evans but not by de curves that had been corrected for the difference between MP2 Almeida. Such a result is notable in that it highlights the and CCSD(T) interaction energies and found that changes to sensitivity of the dimer surface to subtle geometrical effects; their best estimates of the interaction energies were on the because the minima are very shallow, even slight changes in order of 0.2 kcal molÀ1.7 The fact remains, however, that it is theoretical methods can qualitatively change the nature of the currently unknown exactly which theoretical methods are potential energy surface (PES). adequate to study the shape of such a surface. The thrust of The dimer of diacetylene (HCRC–CRCH) has been this work aims to determine how the energetics of delocalized studied somewhat more thoroughly.18 Diacetylene is the smal- pÁÁÁp systems are affected by geometrical perturbations intro- lest of the polyynes thought to be of value as molecular ‘‘rods’’ duced when popular approximations are implemented during in the construction of nanoscale molecular machines.19 The optimization procedures (e.g., smaller basis set, lower theore- interaction between diacetylene units has already been used in tical method, counterpoise correction, rigid monomer approx- the construction of a ‘‘molecular zipper’’ by Shu et al.20 In imation). Having identified the most reliable procedures for addition to their importance in the construction of nano- the characterization of pÁÁÁp interactions, detailed character- materials, both polyacetylenes and cyanopolyacetylenes are izations of the PESs of these new prototypes will soon be known to be present in extraterrestrial space.21–25 These presented.
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