Chemical Modelling: Volume 14 - Rilegato

Duarte, Helio Anderson; De Abreu, Heitor Avelino; Benavides-Riveros, Carlos L.

Rilegato

ISBN 10: 1788010043 ISBN 13: 9781788010047

Casa editrice: Royal Society of Chemistry, 2018

Riassunto

Chemical modelling covers a wide range of hot topics and active areas in computational chemistry and related fields. With the increase in volume, velocity and variety of information, researchers can find it difficult to keep up to date with the literature in these areas. Containing both comprehensive and critical reviews, this book is the first stop for any materials scientist, biochemist, chemist or molecular physicist wishing to acquaint themselves with major developments in the applications and theory of chemical modelling.

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Dalla quarta di copertina

Chemical modelling covers a wide range of hot topics and active areas in computational chemistry and related fields. With the increase in volume, velocity and variety of information, researchers can find it difficult to keep up to date with the literature in these areas. Containing both comprehensive and critical reviews, this book is the first stop for any materials scientist, biochemist, chemist or molecular physicist wishing to acquaint themselves with major developments in the applications and theory of chemical modelling.

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Chemical Modelling Volume 14

By J.-O. Joswig, M. Springborg

The Royal Society of Chemistry

Copyright © 2018 The Royal Society of Chemistry
All rights reserved.

ISBN: 978-1-78801-004-7

Contents

Preface Michael Springborg and Jan-Ole Joswig, v, 
Theoretical studies as a tool for understanding the aromatic character of porphyrinoid compounds Heike Fliegl, Rashid Valiev, Fabio Pichierri and Dage Sundholm, 1, 
Atomistic modeling for molecular electronics and spintronics: successes and challenges Carmen Herrmann, 43, 
Recent progress on fermionic exchange symmetry Carlos L. Benavides-Riveros, 71, 
Dynamics and electronic structure of atomic clusters Patricio Fuentalba, Roberto Donoso and Carlos Cárdenas, 107, 
Clusters as catalysts: advantages and challenges Shuchi Gupta, Navjot Kaur, Indu Kumari and Neetu Goel, 126, 
Modeling the oxidation mechanism of pyrite and arsenopyrite – connection to acid rock drainage Hélio Anderson Duarte, Egon Campos Dos Santos, Juliana Cecília de Mendonça Silva, Guilherme Ferreira de Lima and Heitor Avelino de Abreu, 162, 
Energetic processing of PAHs: isomerisation and dissociation Aude Simon and Mathias Rapacioli, 195, 
From graphene to borophene the fascinating 2D materials Ihsan Boustani, 217, 

CHAPTER 1

Theoretical studies as a tool for understanding the aromatic character of porphyrinoid compounds

Heike Fliegl, Rashid Valiev, Fabio Pichierric and Dage Sundholm

DOI: 10.1039/9781788010719-00001

1 Introduction

The scientific interest in porphyrinoid based materials is steady growing, since porphyrinoids are not only of biological relevance, but they also show interesting spectroscopic properties that link them to many possible applications such as near infrared dyes, photovoltaic dyes, field-effect transistors, nonlinear optical materials and nanoelectronic devices. Biomedical applications of porphyrinoids are of particular importance specially for photomedical applications in cancer treatment, such as photodynamic therapy, multimodal imaging, drug delivery and biosensing. Porphyrinoids show also an ability to form complexes with metals with unusual oxidation states and are therefore relevant for catalysis.

The classic porphyrin molecule can formally be regarded as four pyrrole rings connected to each other by methin bridges. Depending on the localization of the two inner pyrrolic hydrogen atoms the molecule is labeled cis- or trans-porphyrin. However, at room temperature the inner hydrogens generally move around inside the porphyrin ring. The more general term porphyrinoids is used for a class of molecules that share the classical porphyrin structure for the macroring but differ for example by bearing various substituents or heteroatoms. Classic porphyrins, chlorins and bacteriochlorins are aromatic molecules satisfying Hückel's (4n + 2) p-electron count rule for aromaticity. There is no doubt that aromaticity is an important concept in chemistry albeit it is still not fully understood and thus continuously under debate. Theoretical calculations have shown that the aromatic pathways of classic porphyrins and porphyrinoids can differ, even though they have an almost the same degree of aromaticity.

Structural modifications of porphyrinoids can be readily achieved experimentally by using organometallic approaches. See for example different routes for synthesis of expanded porphyrins, contracted porphyrins and corroles with aromatic as well as antiaromatic character. In particular, synthesis of Ni(II)–norcorrole has recently received attention, since it is air and water stable and is therefore a suitable cathode-active material in battery applications. Antiaromatic Ni(II)–norcorrole shows an order of magnitude higher electrical conductance as compared to a similar aromatic Ni(II)–porphyrin complex, making the molecule highly attractive as component material for future molecular electronic devices.

Experimental and computational studies show that aromatic pathways of non-classical porphyrins such as carbaporphyrins, where one pyrrolic nitrogen has been replaced by carbon and carbathiaporphyrins, where one pyrrolic nitrogen has been replaced by carbon and another one by sulfur, differ from that of classic porphyrins. The existence of antiaromatic isophlorins was predicted by Woodward already in 196044 and synthesized in 2008 by Reddy and Anand. Isophlorins are examples of air-stable antiaromatic porphyrinoids, which have been obtained by replacing an inner pyrrolic nitrogen atom by another heteroatom such as sulfur or oxygen.

Considering the link between porphyrinoids and various applications of them, it is useful to have a deep understanding of their electronic structure and magnetic properties, in particular when aiming at a tailored design of porphyrin based materials with desired properties. By controlling the number of p electrons that participate in the electron delocalization pathway, one can also adjust the electronic and spectroscopic properties of the porphyrinoids. Through the control of the number of p electrons, the (anti)aromatic character and aromatic pathway can be tuned. However, the electron mobility pathways are not easily experimentally accessible, whereas calculated current densities provide accurate information about the current flow in the molecules when they are exposed to an external magnetic field.

In the present review, we give a brief overview over different computational methods that are currently employed for assessing the degree of aromaticity of porphyrinoids with the main focus on current density calculations and studies performed by us and our coworkers. We decided to avoid the discussion of nucleus independent chemical shift (NICS) studies, because NICS studies have been recently reviewed. However, some advantages and disadvantages of the NICS approaches are briefly discussed. Links between computational studies and experimental works are highlighted. The present review is structured as follows. A number of experimental methods motivating computational studies are briefly sketched in Section 2. In Section 3, we give an overview of some of the available theoretical methods that are used as aromaticity indicators. Recent applications on porphyrinoids and porphyrin based molecules are discussed in Section 4. An outlook is given in Section 5.

2 Experimental methods

Experimentally, aromaticity is related to energetic stabilizations, equalizations of bond lengths, preferred substitution reactions, and magnetic properties that differ from those of nonaromatic molecules. Typical spectroscopic techniques that have been used for characterizing porphyrinoids are nuclear magnetic resonance (NMR), ultraviolet (UV) absorption, magnetic circular dichroism (MCD), electronic circular dichroism (ECD), photoelectron (PE), two-photon absorption (TPA) spectroscopies as well as cyclovoltametric (CV) measurements to mention only the most commonly applied ones.

In the context of aromaticity studies, it is widely accepted that experimental proton nuclear magnetic resonance (1H NMR) chemical shifts predict concordant degrees of aromaticity. The 1H NMR spectra show specific features such as a deshielding and downfield shift for the resonances of the protons that are attached to the exterior part of an aromatic ring. The influence of the aromaticity on the 1H NMR chemical shifts can be explained with the so called ring-current effect. Ring shaped molecules such as porphyrins sustain magnetically induced currents when being exposed to an external magnetic field as it is the case for an NMR experiment. These ring currents generate an induced magnetic field that is oriented opposed to the external field in the case of an aromatic molecule. Typically, electrons that circle the classical (diatropic) direction are dominant in aromatic molecules, whereas the situation in antiaromatic molecules is reversed and ring currents that circle in the nonclassical (paratropic) direction dominate. Albeit ring currents have not yet been measured directly they can indirectly be determined through measurements of 1H NMR chemical shifts as pointed out above and by measuring magnetizabilities, see Section 3 for more details. Thus, computational aromaticity studies often adopt the magnetic criterion, since these properties are easier accessible and more robust as compared to estimates of aromatic stabilization energies (ASE) using a series of calculations of homodesmic reaction energies. Knowledge of the pattern of magnetically induced currents leads to a deeper understanding of aromatic properties, which complements interpretations of experimental 1H NMR spectra. It is also possible to detect magnetic dipole electronic transitions between electronic states experimentally. Magnetically induced currents can in principle be detected in neutron scattering experiments.

The UV/Vis absorption spectrum of porphyrins shows also characteristic features depending on their aromatic character. For example, the absorption spectrum of free-base porphyrin consists of weak Qx and Qy bands that appear in the red part of the visible region. It has been shown theoretically that further peaks appearing in the Q-band region of the absorption spectrum of porphyrin are due to vibronic progression of S0 -> S1 and S0 -> S2 electronic transitions, while the strong Soret Bx and By bands are typically broad peaks without any fine structure in the violet region. The S0 -. S1–S4 transitions of the classic porphyrins can be explained by employing Gouterman's four-orbitals model. The characteristic absorption features of free-base porphyrin can also be applied to other porphyrinoids. In this context one often refers to Soret-like and Q-like bands. While aromatic porphyrinoids have strong Soret-like bands and small Q-like bands, antiaromatic porphyrinoids can be identified by the ill-defined Soret-like bands and the absence of Q-like bands.

In the past, magnetic circular dichroism (MCD) spectroscopy has proven to be very useful for assessing the Q bands of various porphyrinoids. While the Soret bands are electric dipole allowed transitions, the Q bands are formally electric dipole forbidden and appear only weakly, even though the intensity of the Q bands are significantly enhanced by vibronic coupling effects of Herzberg–Teller type. However, the transitions responsible for the Q bands are of HOMO to LUMO type, which implies a change in the orbital angular momentum that makes them detectable via MCD spectroscopy. Both Soret and Q bands are magnetic dipole allowed transitions and can be related to the Faraday B term in MCD theory. MCD spectra depend on the aromatic or antiaromatic character of the porphyrinoid. For example, the negative-to-positive MCD signals around the Q and Soret bands are typical for aromatic porphyrinoids of lower molecular symmetry, while antiaromatic porphyrinoids show only very weak formally forbidden bands in the low energy region together with a clear Faraday B term. Depending on whether the investigated porphyrinoid is aromatic or antiaromatic, the (4n + 2)- or the (4n)-electron perimeter model developed by Michl et al. is a useful theoretical tool for estimating the shape of the MCD spectra at the four most prominent lowenergy bands. The relation between spectroscopic and structural properties of phthalocyanines based on frontier molecular orbital arguments has recently been reviewed and will not be discussed further in the present review.

Two-photon absorption measurements (TPA) have also been used for assigning molecular aromaticity, because it is empirically known that larger TPA cross sections are observed for aromatic molecules as compared to their antiaromatic congener species. Antiaromatic species are spectroscopically often characterized by broad absorption bands, very weak or no fluorescence activity, small TPA cross sections, ultrashort excited-state lifetimes, the presence of a low-lying optically dark state, and strong paratropic ring currents.

3 Theoretical characterizations

There are numerous aromaticity indices and criteria available and discussing all of them is beyond the scope of the present review. Instead we give in Table 1 a brief overview of the most commonly applied criteria for assessing the aromatic character of general molecules and porphyrinoids. The aromaticity criteria is related to the p electron count of a molecule and it can be separated into energetic, geometric, magnetic, spectroscopic and optical criteria.

3.1 HOMA

A popular structural criterion for aromaticity is the bond-length alternation HOMA (harmonic oscillator model of aromaticity) index defined as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

The constants aCC, aCN, RCC,opt, and RCN,opt can be found in ref. 114. The number of bonds forming the respective ring is labeled as n. As a rule, for aromatic rings with little bond-length alternation, the HOMA index is about 1, while very small and negative HOMA values indicate that the ring consists of localized single and double bonds implying that they are non- or antiaromatic. Typically, the HOMA value is calculated along an anticipated delocalization pathway. However, the HOMA value is an indicative quantity and not a quantitative one, see for example ref. 116.

3.2 ACID

The anisotropy of the magnetically induced current-density tensor (ACID) method was initially developed for constructing a scalar function that can be used for computationally assessing the degree of electron delocalization in a molecule. The ACID function is constructed using the anisotropic part of the current susceptibility tensor, which is also the key quantity in current density studies. The ACID function is a scalar function similar to the electron density having the advantage that it is independent of the direction of the external field and it is easy to visualize.

However, the simplifications used for obtaining the ACID function come at the cost of loosing information by contracting the current density, which is a vector quantity. Another drawback is that ACID functions calculated using the commonly used implementation suffer from a very slow basis set convergence, because ordinary basis functions are employed. The slow basis-set convergence affects the accuracy and reliability of the approach. Recently, Fliegl et al. implemented a method to calculate ACID functions using London orbitals in the GIMIC code. The use of gauge-including atomic orbitals (GIAO) a.k.a London atomic orbitals (LAO) leads to a fast basis set convergence of the current density and consequently also of the ACID function. The GIAO-ACID method was tested on free-base trans-porphyrin. The isosurfaces of the ACID function for trans-porphyrin with two different isovalues are shown in Fig. 1 illustrating that visual inspection of the ACID function may lead to different interpretations regarding the electron mobility pathways depending on which isosurface is chosen.

3.3 NICS

ACID functions are often calculated in combination with nucleus independent chemical shift (NICS) values. Current pathways in porphyrins have been investigated using this combination. NICS values are obtained by placing a dummy atom (probe) in the center of a molecular ring or above or below it. The negative isotropic shielding constant i.e. the magnetic response calculated in the probe is the NICS value. Several NICS approaches such as using the isotropic shielding constant or taking only the zz component of the shielding tensor into account are used. More sofisticated approaches such as calculating a set of NICS values along the symmetry axis of molecules or scanning the magnetic response in two or three dimensions are also employed. Is a common misconception that NICS and current density calculations are identical approaches by referring to the Biot–Savart relation. A series of different studies has shown that current strength susceptibilities obtained from magnetic shielding data depend on the assumed current-pathway model. This explains why shielding based approaches lead to significant uncertainties in ring-current strength susceptibilities, current pathways, and consequently in the degree of aromaticity, specially when complicated molecules are investigated. This has been pointed out by several research groups. Explicit current density calculations are more reliable as compared to NICS calculations. Calculated current densities provide deeper insights in particular when studying complicated ring systems.

3.4 Current density

When a molecule is exposed to an external magnetic field the electrons are forced to move, which is giving rise to the so called magnetically induced current density that induces a magnetic response. In case of aromatic molecules, the induced magnetic field is oriented in the opposite direction to the applied external field weakening the effect of the external magnetic field as in the classical case. For antiaromatic molecules, the induced magnetic field is aligned in the same direction as the applied one leading locally to a strengthening of the magnetic field.

(Continues...)

Excerpted from Chemical Modelling Volume 14 by J.-O. Joswig, M. Springborg. Copyright © 2018 The Royal Society of Chemistry. Excerpted by permission of The Royal Society of Chemistry.
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Dettagli dell'edizione

• Editore: Royal Society of Chemistry
• Data di pubblicazione: 2018
• Lingua: Inglese
• ISBN 10: 1788010043
• ISBN 13: 9781788010047
• Rilegatura: Copertina rigida
• Numero di pagine: 254
• Redattore: Springborg Michael, Joswig Jan-ole
• Contatto del produttore: non disponibile
• Persona responsabile: non disponibile