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Journal of the Mexican Chemical Society

versión impresa ISSN 1870-249X

J. Mex. Chem. Soc vol.58 no.1 Ciudad de México ene./mar. 2014




The Rhodathiabenzene and Rhodaoxabenzene: Structure and Bonding and Density Functional Calculations


Reza Ghiasi,1* and Mozhdeh Abdoli2


1 Department of Chemistry, East Tehran Branch, Islamic Azad University, Qiam Dasht, Tehran, Iran.

2 Department of Chemistry, Saveh Branch, Islamic Azad University, Saveh, Iran.


Received November 27, 2012.
Accepted September 24, 2013.



The electronic structure and properties of the rhodathiabenzene and rhodaoxabenzne isomers have been investigated using the hybrid density functional mpw1pw91 theory. The energetic aspect shows that I-isomer is the most stable isomer. Molecular orbital analysis shows linear correlation between hardness and anisotropic polarizability values of rhodaoxabenzene isomers. These calculations indicate a linear relation between ΣBOR (sum of Wiberg indices in ring) and relative energy for rhodathiabenzene. The atoms in molecule analysis indicates a correlation between r(Rh-X; X=C, S, P, O) bonds and the electron density of bond critical point in all species.

Key words: Metallabenzenes, Rhodaoxabenzene, Rhodathiabenzene, Quantum theory atoms in molecules (QTAIM), Wiberg bond index.



Se han investigado la estructura electrónica y propiedades de isomeros del rodatiabenceno y del rodaoxabenceno usando el funcional híbrido mPW1PW91. El aspecto energético muestra que el isomero-l es el más estable. El análisis de orbitales moleculares muestra una correlación lineal entre la dureza y la anisotropía de la polarizabilidad de los isómeros del rodaoxabenceno. Estos cálculos indican una relación lineal entre ΣBOR (la suma de los índices de Wiberg en el anillo) y la energia relativa para el rodatiabenceno. El analisis de atomos en moléculas indica una correlación entre las distancias de enlace r (Rh-X; X=C, S, P, O) y la densidad electrónica en el punto crítico de enlace de todas las especies.

Palabras clave: Metalbencenos, rodaoxabenceno, rodatiabenceno, teoría cuántica de átomos en moléculas (QTAIM), índice de enlace de Wiberg.



Metallabenzenes are organic/transition-metal “hybrids” which own aromatic properties. They have been shown to reveal many similarities to heterobenzenes: downfield chemical shifts for ring protons, planarity of the six membered metallacycle, no alternation of bond lengths, and even electrophilic aromatic substitution [1-11]. There is now an extensive amount of relevant synthetic, structural, spectral, computational, and reactivity data for metallabenzenes. Chen et al. [12] and Bianchini et al. [13, 14] have independently synthesized iridathiabenzenes via insertion of iridium into C-S bonds of thiophene. The rhodium analogue has been similarly generated in a thiophene ringopening reaction [15]. As with other 4d transition metals, uncoordinated rhodabenzenes are probably unstable. The inability to isolate a rhodabenzene is congruent with the DFT calculations reported by van der Boom, Martin, and co-workers [16].

In the present study, the stability, geometries and properties of Rhodaoxabenzene, and Rhodathiabenzene isomers are investigated theoretically. The analysis of quantum theory atoms in molecules has been used for providing valuable information on bonding characters.


Computational Method

All calculations were carried out with the Gaussian 2003 suite of program [17] using the standard 6-31G(d,p) basis set calculations of systems contain C, H, O, S and P (Method 1) [18, 19]. Also, for calculation of polariazability and hyperpolarizability values 6-311+G(d,p)basis has been used (Method 2) [20].

For Rh element standard LANL2DZ basis set [21-23] are used and Rh described by effective core potential (ECP) of Wadt and Hay pseudopotential [24] with a doublet-ξ valance using the LANL2DZ. Geometry optimization was performed utilizing one parameter hybrid functional with modified Perdew-Wang exchange and correlation (mpw1pw91) [25]. A vibrational analysis was performed at each stationary point found, that confirm its identity as an energy minimum.

Geometries were optimized at this level of theory without any symmetry constraints followed by the calculations of the first order hyperpolarizabilities. The total static first hyperpolarizability j) was obtained from the relation (equation 1):

upon calculating the individual static components (equation 2)


Due to the Kleinman symmetry (equation 3) [26]:

one finally obtains the equation that has been employed (equation 4 ):

The isotropic polarizability is calculated as the mean value as given in the following equation [27]

and the polarizability anisotropy invariant is:

The AIM2000 program was used for topological analysis of electron density [28]. The following characteristics of ring critical points (RCPs) are taken into account: density at RCP (ρ(rc)), its Laplacian (∇2(rc)).


Result and Discussion

Energetic criteria

Absolute energy and relative energy values of the heterocyclic rhodabenzene (Fig. 1) are presented in Table 1. The relative energies values show that stability of the possible isomers decrease in the following trend:


This trend shows that I- isomers are more stable than other isomers.




Polarizabilities describe the response of a system in an applied electric field [30]. They determine not only the strength of molecular interactions (such as the long range intermolecular induction, dispersion forces, etc.) as well as the cross sections of different scattering and collision processes, but also the nonlinear optical properties of the system [31].

The calculated isotropic and anisotropy polarizability values indicate these values decrease when heteroatom is X=O.

(Table 2). Thus, the larger isotropic polarizability of X=S rings resulting in the stronger response of external field.

It is well known that a general characteristic required for basis sets to perform well for polarizability calculations is that they should contain diffuse functions (Method 2) [32, 33]. These values are more than method 1. Again, the calculated isotropic and anisotropy polarizability values are more in X=S rings (Table 2).


Molecular structural parameters

The selected structural parameters have been gathered for rhodaoxabenzene and rhodathiabenzene isomers in Table 3. These values show that Rh-C, RhS, RhPapical, and RhPbasal bond lengths are compatible with experimental data for similar compounds [15, 16]. These bond lengths are indicative of structural aromaticity. The structural analysis in I-isomer (most stable isomer) shows that:

Rh-P distances: Rh-Pbasal bonds are larger than Rh-Papical bonds.

Rh-S distances: The Rh-S bond (2.31 Å) is shorter than Rh-SH (2.41 Å). These trends reveal important π-bonding between these ring atoms.

CC distances: the CC bond distances analysis presents the C2-C3 bond is shorter than C3-C4 bond. This shows that resonance structure (II) has a greater contribution to the bonding picture (Fig. 2).


Wiberg bond index matrix in the NAO basis

Wiberg indices are electronic parameters related to the electron density between atoms. They can be obtained from a natural population analysis and provide an indication of the bond strength [34]. These values have been computed for rings atoms (Table 4). The bond delocalization can also be found from the calculated bond indices. The C-/C bond indices are comparable to the calculated those for benzene (1.462). The bond indices of Rh-C single, and double bond are got from the results of calculated model complexes trans-[Rh(SH)2(CH3)(PH3)2] and trans- [Rh(SH)2(=CH2)(PH3)2]-which are optimized at mpw1pw91 level and using the same basis sets as the context. The Rh-C5 bond indexes are intermediate between calculated Rh-C single and double bond indices (X=O: 0.595 and 1.194; X=S: 0.5689 and 1.174, respectively).

These values indicated good linear relation between ΣBOR with relative energy for rhodathiabenzene (Fig. 3).


Frontier orbital energies and chemical hardness

The frontier orbital energies, HOMO-LUMO gap energy, hardness, chemical potential, and electrophilicity of all complexes computed are given in the Table 5. To evaluate the hardness and chemical potential of these complexes, these values can be calculated from the HOMO and LUMO orbital energies using the following approximate expressions:

Where μ is the chemical potential (the negative of the electronegativity), and η is the hardness [35, 36]. To evaluate the electrophilicity of these complexes, we have calculated the electrophilicity index, ω, for each complex measured according to Parr, Szentpaly, and Liu [37] using the expression:

These values show that most stable isomer has maximum hardness in rhodathiabenzene complex, as expected from the principles of minimum energy and minimum polarizability in most cases. Furthermore, the hardness and chemical potential values of rhodathiabenzene complexes are higher than rhodoxa-benzens complexes (except in V-isomer). The values of electrophilicity index in Table 5 indicate a higher electrophilcity in rhodathiabenzen.

Fig. 4. confirms the linear behavior between αanisotropic 1/3 and 1/(2η) values for rhodaoxabenzene isomers [38].



Since even a small absorption at the operating wavelength of optic devices can be detrimental, it is important to make NLO chromophores as transparent as possible without compromising the molecule’s non-linearity. The first static hyperpolarizability (βtot) values for the molecules are shown in Table 6. The results show that the magnitude of the first hyperpolarizability tensor of all molecules is rather small. The V- isomer has the most βtot values. On the other hand, we calculated hyperpolarizability values with diffuse functions for nonmetal elements (Method 2). These values are more than method 1. Again, the most βtot value has been shown for V- isomer.


AIM analysis

It has been proved that the AIM-based analysis of electron density can provide valuable information on many physical and chemical properties of molecular systems [39-43].

Table 7 indicates ∇2p values of Rh-C, Rh-O, Rh-S, and Rh-PH3 bonds at corresponding BCPs are positive, as it was found for closed-shell interactions. On the other hand, the H(p) values are negative, as found for shared interactions. This is in agreement with observations made for the Ti-C bonds in titanium complexes [44] and transition metal carbonyl clusters [45], in the case when the metal-ligand bonding has a characteristic that represents a mix of the closed-shell and shared parameters. The strong polar character is also revealed by the large G(rb)/ρ(rb) ratio and atomic charges, while the covalence is manifested by large and negative H(rb)/ρ((rb) (Table 7).

Moreover, the H(p) values are more negative for Rh-C1 and Rh-C5 bonds in rhodaoxabenzene, which is directly connected with relative greater predominance of |V(p)| magnitude over the G(ρ) magnitude. This suggests a more covalent character of the Rh-C1 and Rh-C5 bonds of rhodaoxabenzene as compared with the rhodathiabenzene. Furthermore, Rh-C bonds have more negative H(p) values rather than Rh-S, Rh-O and Rh-P bonds. Generally, when the value of |H(p)| are greater (with negative sign), there is more covalent character of the bond.

The ρ(3,+1) and ∇2ρ(3,+1) values have been gathered in Table 1. There is a good linear relationship between ρ(3,+1) and relative energies in rhodaoxabenzene isomers (R2 = 0.985). The most stable isomers has minimum ρ(3,+1) and ∇2ρ(3,+1) values.

The results from QTAIM calculations may also explain the fact that the calculated Rh-Pbasal bonds are slightly longer than the remaining Rh-Paxial bonds (Table 7). The QTAIM calculations show that the electron density on RCP of Rh-Paxial bond is larger, in comparison to Rh-Pbasal.



In this paper, an attempt has been made to examine the structure, bonding and stabilization of rhodathiabenzene and rho-daoxabenzene isomers with the hybrid density functional mp-w1pw91 theory. Calculations illustrate:

1. Energetic criteria suggest that I- isomer enjoys conspicuous stabilization in rhodathiabenzene and rhoda-oxabenzene isomers.

2. Bond lengths and wiberg index values the six mem-bered metallacyles indicate to some amount aromatic properties.

3. The frontier orbitals investigation exhibited that most stable isomer has maximum hardness in rhodathia-benzene complex, as expected from the principles of minimum energy and minimum polarizability in most cases.

4. Quantum theory atoms in molecules (QTAIM) exemplify Rh-C, Rh-S, Rh-P, and Rh-O bonding. This analysis showed that metal-ligand bonding has a characteristic that signifies a mix of the closed-shell and shared parameters.



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