Electronic Rearrangements during the Inversion of Lead

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Electronic Rearrangements during the Inversion of Lead Phthalocyanine Anton Sergeevich Nizovtsev, and Svetlana G. Kozlova J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/jp3108107 • Publication Date (Web): 17 Dec 2012 Downloaded from http://pubs.acs.org on December 17, 2012

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The Journal of Physical Chemistry

Electronic rearrangements during the inversion of lead phthalocyanine Anton S. Nizovtseva,* and Svetlana G. Kozlovaa,b,c a

Nikolaev Institute of Inorganic Chemistry, Siberian Branch of the Russian Academy of Sciences, Acad. Lavrentiev Ave. 3, 630090, Novosibirsk, Russian Federation

b

c

Novosibirsk State University, Pirogova Str. 2, 630090, Novosibirsk, Russian Federation

Boreskov Institute of Catalysis, Siberian Branch of the Russian Academy of Sciences, Acad. Lavrentiev Ave. 5, 630090, Novosibirsk, Russian Federation

* Corresponding author. E-mail address: [email protected] (A. S. Nizovtsev)

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Abstract The mechanism of inversion of lead phthalocyanine (PbPc), possessing a shuttlecock shape, was studied in detail within the bonding evolution theory framework. We have found that reaction pathway calculated using hybrid density functional theory (DFT) method, B3LYP, consists of five structural stability domains which are connected by four bifurcation points. Reorganization of Pb’s basins with pronounced role of core ones is the basis of the catastrophes identified, whereas basins belonging to other atoms are almost not involved in the electronic structure changing. These results provide the new topological picture of processes underlying the conformational transitions of shuttlecock shaped metal phthalocyanines adsorbed on surfaces.

Keywords: molecular switch, reaction mechanism, electronic structure, bonding evolution theory, ELF


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Introduction Constructing of controlled nanodevices is an actual challenge attracting attention of many researchers around the world.1 Substrates suitable as active components are intensively searched. It has been earlier studied that systems based on the shuttlecock shaped metal phthalocyanines (MPc, M=Ge, Sn, Pb) have a promising properties.2-20 In contrast to the most MPc, these molecules are characterized by non-planar structure: the central atom comes out from the phthalocyanine macrocycle plane and causes its distortion, so that the molecule takes shape of shuttlecock. It allows MPc (M=Sn, Pb) to adsorb on different surfaces3,12,13 in two conformations, – with central atom directed toward (MPc↓) the surface or away from (MPc↑) one. Transition between conformations can occur under influence of external factors, particularly, electric field, generated on the scanning tunneling microscope (STM) tip.3 This fact together with thermal and chemical stability and unique electrophysical properties of shuttlecock shaped MPc as well as its ability to form well-ordered structures on different solid surfaces2 opens up wide possibilities for developing molecular machines, sensors and switches on their basis. However, principles of molecular devices’ working often remain unsolved, preventing to control the processes of interest in full and narrowing the range of potential applications. The first step to understanding the mechanism of transition between MPc↑ and MPc↓ conformations, which can be the case both for a single molecule and for the densely-packed layers adsorbed on solid surfaces, is the detailed study of MPc’s inversion, – the elementary act underlying the molecular switches. Recent DFT calculations of isolated molecules showed that the inversion mechanism of shuttlecock shaped MPc’s depends on the nature of central atom.16 For GePc and SnPc transition between conformations appears to carry out through D4h planar structure, while the PbPc inversion proceeds via a transition state (TS) with C2h symmetry. However, the description of the reaction from the energetic point of view may be insufficient to establish its electronic mechanism in detail.



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A considerable advantage over orbital-based techniques has bonding evolution theory (BET),21 consisting of the topological analysis of electron localization function (ELF, η(r))22-24 and catastrophe theory by Thom,25 within which one can trace the electronic structure evolution during the reaction. Topological analysis of ELF gradient field26 provides a partition of molecular space into basins of attractors corresponding to chemically meaningful concepts such as atomic cores (core basins, C(A), surrounding nuclei of element A with atomic number Z>2), bonds and lone pairs (valence basins: V(A) – monosynaptic basin, V(A,B) – disynaptic basin, etc.). Valence basins are represented by valence shell electrons of atoms in molecular systems and labeled according to their synaptic order,27 i.e. the number of core basins with which they share a boundary. Quantitative characteristic of the method is the population of ELF basin by electrons ( N ), which is calculated by integration of the electron density ( ρ (r ) ) over the ELF basin’s volume ( Ω ):

N (Ω i ) = ∫ ρ (r )dr . Ωi

Thus, within a single elementary act in BET approach one can determine the sequence of elementary chemical events (bond forming/breaking processes, electronic density redistribution, creation/annihilation of lone pairs etc.), analyzing the ELF topology in the points along the reaction path, and classify topology change taking place in catastrophes or, in other words, bifurcations on catastrophe theory. As a result, detailed information about the electronic reaction mechanism can be obtained. It is worth to note that in spite of this methodology has been successfully applied for studying organic reactions,28,29 reactions involving metal compounds hardly been studied.30-34 Here, we investigate MPc inversion by the PbPc example in terms of electronic density rearrangement to shed some light on features of reaction mechanism, in particular, we study an elementary act PbPc↑ → PbPc↓ by using BET at the current level, in which the evolution of the basins’ number is only considered.


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Computational details Geometric parameters of species under study were fully optimized in the gas phase within spin-restricted DFT formalism35,36 using hybrid B3LYP functional37-39 with all-electron Dunning’s correlation-consistent basis set of double-zeta quality, cc-pVDZ,40 on H, C and N atoms and cc-pVDZ-PP41 set on Pb in conjunction with appropriate relativistic effective core potential (RECP),42 replacing 60 core electrons (next, such combinations will be abbreviated as VnZ, n=D in this case). It was previously shown that B3LYP functional is capable to reproduce experimental structural parameters of PbPc with a good accuracy.17,19 All the following singlepoint calculations were carried out with B3LYP/VDZ geometries. Zero-point vibrational energies (EZPE) were computed from the B3LYP/VDZ harmonic vibrational frequencies without scaling factors. The thermal correction to the enthalpy (ETC) was calculated within rigid-rotor-harmonic-oscillator approximation and used for obtaining reaction enthalpies at 298 K. Stationary points were characterized by their harmonic vibrational frequencies as minima or saddle point (number of imaginary frequencies was equal to 0 and 1 for local minima and transition state, respectively). Minimum energy path was constructed at B3LYP/VDZ level in mass-weighted coordinates without symmetry constrains by employing intrinsic reaction coordinate (IRC)43-45 algorithm with step size of 0.2 amu1/2bohr. IRC calculations were carried out in one direction due to symmetry of the system. In order to achieve clear description of electron localization in the core region, all topological calculations were carried out on wavefunctions generated from all-electron computations. For that, ZORA-B3LYP/TZP level was used taking into account scalar relativistic effects;45-49 core potential was not used, the numerical integrals were evaluated with an accuracy of 8 significant digits. Topological calculations were performed with DGrid.51 The ELF basin populations were preliminary calculated for a rectangular parallelepipedic grid with a mesh size of 0.08 bohr, and 5 ACS Paragon Plus Environment


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then recomputed in the points of interest using a mesh size of 0.05 bohr. In order to increase the accuracy of basin integration electron density grid was refined throughout with the precision of 0.1 e. 51b Synapticity of the ELF basins was defined by inspection of the corresponding zero-flux surfaces and was checked by analysis of critical points at ELF gradient field. Also, we performed single-point calculations by using meta hybrid M0552 and M0653,54 functionals specially developed for calculations of compounds containing metals. Ultrafine grid was used in these DFT calculations. The ZORA-B3LYP/TZP computations were performed with the use of ADF2010 program,55-57 while the remaining computations were carried out in Gaussian09.58 cc-pVnZ-PP basis sets were taken from the EMSL database.59 All species were considered in their ground states.

Results and discussion Inversion of PbPc. A number of experimental6-13,15,19 and theoretical works6,14-20 was devoted to PbPc. In particular, it was experimentally established that PbPc crystallizes in a monoclinic8 and triclinic forms,9 and in PbPc thin films under external electric field the switching between two states is observed, their electrical resistance being differed by ten orders of magnitude.11 Furthermore, a variety of quantum chemical techniques were used to calculate the molecular structure of PbPc14,15 and its charge distribution,16,17 infrared and Raman spectra,16 electronic absorption spectra,18,19 electronic spectra in a valence and core region.15 We should also mention the recent work of Baran and Larsson,16 in which the energy barrier for PbPc inversion was calculated at B3LYP/TZVPP2 level. According to ref 16, ionization of the molecular system should promote transition between PbPc↑ and PbPc↓ conformations as confirmed by a characteristic change in the structure of single molecule ionized. To the same conclusion Wang and coworkers came,3 selectively modifying SnPc individual molecules within the thin films adsorbed on Ag(111) using STM. It is essential that electrons must be removed from the HOMO-1 upon ionization. 6 ACS Paragon Plus Environment

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In order to apply BET to the PbPc inversion, first, we have localized stationary points on the potential energy surface (PES). The atomic labelling is given in Figure 1. The most relevant geometric parameters are the distance between Pb and isoindole nitrogens (r(Pb-N2), r(Pb-N4)), the distance between Pb and the center of plane formed by four isoindole nitrogens (r(Pb-X)) and also the distance between X and the closest nitrogens (r(X-N2), r(X-N4)). The sum of r(X-N2) and r(X-N4) is suitable for determining the size of Pc cavity. Figure 1 One can assume that PbPc inversion proceeds via planar TS by passing of Pb atom through the Pc cavity. In this case a movement of the metal to the molecular center, expressed in decreasing of r(Pb-X) distance up to 0 Å, and consistent straightening of isoindole subunits should take place. Thus, initial molecule with C4v symmetry should turn into a TS with D4h one. However, this way does not happen for free PbPc molecule as it was previously established.16 More favorable inversion mechanism is to proceed a reaction bypassing C2h-symmetry TS (Figure 1), in which pairs of isoindole fragments are twisted in different directions. Indeed, our calculations at B3LYP/VDZ theoretical level confirmed these results. Structural and energetic properties of PbPc (C4v symmetry) and desired TS (C2h symmetry) localized are shown in Tables 1-2. The imaginary vibrational frequency of TS (ν≠=186i cm-1) corresponds to a vertical displacement of Pb atom together with distortion of isoindole fragments, proving a direct TS accordance to the elementary act considered. We have also succeeded in locating a flat PbPc form. It is turned out to be fifth order saddle point without a certain physical meaning because it has five imaginary frequencies, which is in line with ref 16. Nevertheless, the electronic structure of flat PbPc is of interest since under the experimental conditions structural changes of the initial substrate are likely to become possible, leading, in particular, to a flat configuration. Thus, it would be rather useful to explore the electron distribution in PbPc (D4h). Table 1 7 ACS Paragon Plus Environment


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Table 2 In fact, at B3LYP/VDZ level ∆H 0Ο of inversion barrier is 94.3 kcal/mol, whereas for the transition from PbPc to PbPc (D4h) ∆H 0Ο equals to 111.1 kcal/mol as it can be seen from Table 2. A significant difference in energy (16.8 kcal/mol) makes the latter process less probable. Anyway, the values calculated are too large to observe these processes under experimental conditions. At the same time, a set of factors such as interaction with the substrate, ionization, electronic excitation and collective effects may lead to the realization of both inversion mechanisms. Therefore, despite the reactions are simple models, their detailed study allows us to approach to understanding the phenomena underlying the real processes. This fact grants the meaning to such studies. As the reaction proceeds geometric parameters are changed (Table 1). Distortion of aromatic groups reduces r(Pb-N2) and r(Pb-N4) bond lengths in TS by 0.112 Å in comparison with PbPc. Due to this, a larger cavity is formed in the center of molecule, ∆r(X-N2)=∆r(XN4)=0.261 Å, facilitating to bulk lead atom to go through Pc window. It should be noted that r(X-N2) and r(X-N4) distances in PbPc (D4h) and TS are almost identical (2.282 Å vs. 2.241 Å).

It is interesting to compare the recently published geometric parameters16 and those were obtained in present work. The most important interatomic distances of PbPc, TS and PbPc (D4h) are collected in Table 1. The values are agreed with each other within 0.03 Å (for r(N2-C2) in TS difference is 0.078 Å, but it seems to be caused by a misprint in ref 16). Thus, the B3LYP/VDZ method is capable to reproduce the structural parameters of the compounds reasonably. To check accuracy of quantum chemical approach proposed we have performed singlepoint calculations using both a larger basis set (triple-zeta instead of double-zeta) and advanced functionals (M05, M06). The values obtained for the barrier height and the energy of PbPc → PbPc (D4h) process are presented in Table 2. As one can see from the Table the basis set extension from VDZ to VTZ in B3LYP approximation has a little (less than 1 kcal/mol) 8 ACS Paragon Plus Environment

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energetic effect for both processes, but all-electron ZORA-B3LYP/TZP calculation lowers E of barrier slightly stronger, by 1.7 kcal/mol, while energy of PbPc planarization is almost identical compared to B3LYP/VDZ calculations. The use of recently proposed M05 and M06 functionals, specifically designed for the calculation of metal compounds, revealed no significant differences between the results also: an inversion barrier is almost the same for all DFT methods, the electronic energy of PbPc → PbPc (D4h) process greater by 2.4 and 3.4 kcal/mol for M05 and M06, respectively, compared to B3LYP/VTZ. As for the comparison the results obtained with the previous data, despite the geometry optimization in ref 16 was performed in a more flexible basis set the energy of processes being considered agrees well with each other. Thus, the using of all-electron ZORA-B3LYP/TZP method for wave function generating and the subsequent topological calculations is justified. ELF topological analysis of stationary points. ELF isosurface for PbPc (Figure 2) reveals valence monosynaptic basin on Pb, V1(Pb), with a population of about two electrons (Table 1), corresponding to lone pair localized on Pb atom in terms of the Lewis theory. While for the other structures, TS and planar PbPc, two valence monosynaptic basins are observed on Pb with population less than one electron (0.32 and 0.52, respectively) that seems to be formed from the initial Pb lone pair of PbPc. Figure 2. It is interesting to note the organization of Pb core basins in PbPc (Figure 3), which features can be identified owing to all-electron basis set using. Four, C2(Pb)-C5(Pb), from five basins are symmetrically arranged and possess the similar population (mean value is 4.66 e), while the fifth one, C1(Pb), is located directly under V1(Pb) and has a rather low population (1.29 e).

Figure 3. The valence electrons of lead (6s6p) are mainly distributed between V1(Pb) nonbonding basin and four disynaptic ones between Pb and nitrogens adjacent to it (V(Pb,N2), V(Pb,N4) and 9 ACS Paragon Plus Environment


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also symmetric V(Pb,N2'), V(Pb,N4')). These disynaptic basins share a boundaries with the corresponding core basins belonging to nitrogens and lead as confirmed by presence of (3,–1) critical points in regions under consideration. In terms of ELF the disynaptic basin implies the covalent character of the bonding between two atoms. So, one can expect some extent of covalency in the Pb–N bonds. Indeed, summing up populations of all core basins and valence monosynaptic one of Pb and deducting result from the overall number of electrons in Pb atom, i.e. 82 e, one can obtain that Pb donates 0.37 e to the each of four equivalent nitrogen lone pairs, thus forming disynaptic basins. This simple estimate shows that contribution of Pb to the electronic population of V(Pb,N2) and similar disynaptic basins is around 12 %. Core basins C1-5(Pb) are mostly formed by penultimate shell electrons (n=5) of lead with a relatively small contribution of valence (0.62 e) and, interestingly, N-shell electrons (1.29 e). The latter is the reason why the total number of Pb’s electrons populating basins with its participation, excepting C(Pb), is equal to 23.29, rather than 22 which might correspond to the sum of electrons from valence (n=6) and penultimate (n=5) shells. Another situation takes place in TS and PbPc in flat conformation. Appearance of the second monosynaptic basin V2(Pb) is accompanied by the reorganization of the core basins leading to forming of a new C6(Pb) one. It should be emphasized that the contribution of the valence electrons of Pb in its core basins increases to 1.53 e and 1.82 e for PbPc (D4h) and TS, respectively. It is important that the amount of electrons in all lead basins except for C(Pb) exceeds 22, thus indicating the presence of electrons lying at deeper atomic level as compared with n=5. The metal charge is determined by the number of electrons donated to the adjacent nitrogen atoms. Considering that, we obtain q(Pb) is equal to +1.49, +1.54 and +1.44 in PbPc, TS and PbPc (D4h), respectively. So, as TS reaching, charge of Pb is slightly increased, whereas for the planar PbPc charge of the central atom is somewhat decreased. Both the charge values and their changes are consistent with that of previously computed by NBO scheme.16 Atomic 10 ACS Paragon Plus Environment

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charges confirm the constancy of Pb oxidation state at the stationary points in contrast to the closely-related GePc and SnPc molecules, which are characterized by changing in the oxidation level of the metal during their inversion (MII↔MIV). Thus, in all cases a [PbIIPc2–] situation is realized as shown previously.16 Bifurcation points along reaction coordinate. From the perspective of BET at current level elementary reactions can be divided into pliomorphic (∆µ>0), miomorphic (∆µ

Electronic Rearrangements during the Inversion of Lead

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