Energy Decomposition Analysis Coupled with Natural Orbitals for Chemical Valence and Nucleus-Independent Chemical Shift Analysis of Bonding, Stability, and Aromaticity of Functionalized Fulvenes: A Bonding Insight.

The Donor base ligand-stabilized cyclopentadienyl-carbene compounds L-C5H4 (L = H2C, aAAC; (CO2Me)2C, Py; aNHC, NHC, PPh3; SNHC; aAAC = acyclic alkyl(amino) carbene, aNHC = acyclic N-hetero cyclic carbene, NHC = cyclic N-hetero cyclic carbene, SNHC = saturated N-hetero cyclic carbene, Py = pyridine) (1a-1d, 2a-2c, 3) have been theoretically investigated by energy decomposition analysis coupled with natural orbitals for chemical valence calculation. Among all these compounds, aNHC=C5H4 (2a) and Ph3P=C5H4 (2c) had been reported five decades ago. The bonding analysis of compounds with the general formula L=C5H4 (1a-1d) [L = (H2C, aAAC, (CO2Me)2C, Py] showed that they possess one electron-sharing σ bond and electron-sharing π bond between L and C5H4 neutral fragments in their triplet states as expected. Interestingly, the bonding scenarios have completely changed for L = aNHC, NHC, PPh3, SNHC. The aNHC analogue (2a) prefers to form one electron-sharing σ bond (CL-CC5H4) and dative π bond (CL ← CC5H4) between cationic (aNHC)+ and anionic C5H4 - fragments in their doublet states. Similar bonding scenarios have been observed for NHC (2b) and PPh3 (2c) (PL-CC5H4, PL ← CC5H4) analogues. In contrast, the SNHC and C5H4 neutral fragments of SNHC=C5H4 (3) prefer to form a dative σ bond (CSNHC → CC5H4) and a dative π bond (CSNHC ← CC5H4) in their singlet states. The pyridine analogue 1d is quite different from 2c from the bonding and aromaticity point of view. The nucleus-independent chemical shifts of all the abovementioned species (1-3) corresponding to aromaticity have been computed using the gauge-independent atomic orbital approach.

Introduction

Tclass="Chemical">he formatioclass="Chemical">n of cclass="Chemical">n class="Chemical">hemical bonds is one of the uttermost important stabilization forces because of which the atoms/ions/molecules can come close to each other leading to formation of the ingredients of life to the building blocks of megastructures of our universe.[1] The first chemical bond of the universe was a weak dative bond (He → H+) between He and H atoms of helium hydride (HeH+).[1d] Inorganic and organic chemistry started much earlier in space than those on Earth. Up in deep interstellar space, highly polar five-membered ring cyanocyclopentadiene (1-cyano-1,3-cyclopentadiene) has been very recently detected from a combination of laboratory rotational spectroscopy and a sensitive spectral line survey in the radio band toward the starless cloud core.[1e] Cyclopentadiene and cyclopentadienyl rings are among the classic examples of ligands to the chemists. They are regularly utilized in the laboratory for different means.[2−6] Substituted cyclopentadienes/cyclopentadienyls (Cp) are utilized as ligand/groups in different areas of chemistry.[2] They are utilized in organometallic chemistry for the preparation of the catalysts to carry out organic transformations.[3] They have been employed as stabilizing ligand compounds of metalloids and complexes with metal ions and in different oxidation states.[2,4] Some of these functionalized Cp containing molecules/complexes are highly fluorescent,[5] or metal–Cp complexes can display extremely slow relaxation of magnetization.[6] The functionalization of cyclopentadiene/cyclopentadienyl rings with different substituents is very beneficial and demanding. Moreover, the introduction of the imidazolium group might induce ionic liquid properties since imidazolium salts are employed as an ionic liquid for many chemical reactions. Functionalization of cyclopentadiene/cyclopentadienyl rings with aliphatic groups of axially bis-ligated Dy-cation efficiently prevents[6] zero-field quantum tunneling via the prevention of intermolecular magnetic interaction (dipolar Cp···Cp interactions).[7] Thus, functionalization of Cp rings with a donor–acceptor neutral ligand [Ph3P[8a] and C(NMe2)2],[8b] which started way back in the 1950s, seems to have attracted synthetic chemists till today.[8c−8k] The functionalization of the Cp ring with mono- and bis-NHC carbenes (NHC = N-hetero cyclic carbene) started over a decade ago.[8c,8d,8k] Recent synthetic progress of functionalization of Cp with different carbenes showed that the accumulation of electron densities on the Cp ring is extremely high. The bis-NHC functionalization of Cp leads to the formation of ionic compounds of [(NHC)2Cp]+ X– salts, which rapidly exchange H with D when they have been reacted with D2O.[8k] The Cp-stabilized half sandwich and sandwich complexes of metalloid and metals have attracted chemists over the past decades.[2−8] The detailed bonding analysis of Cp-functionalized organic molecules is rarely reported.

Giclass="Chemical">lclass="Chemical">n class="Chemical">bert Lewis introduced the Lewis electron pair approach for chemical bonding in 1916. His concept of the cubic electron rule was elaborately popularized by Langmuir in 1919. Langmuir also introduced the octet, 18 e, and 32 e rules and coined the term “covalent bonding” in 1919–1921. Sidgwick suggested an arrow formalism for the coordinate bond in the 1920s. These developments are even before modern quantum theory of bonding. In 1927, Heitler and London explained the physical origin of chemical bonding in H2, utilizing quantum theory by Heisenberg and Schrödinger. Century-long efforts finally shed light on different bonding scenarios (Scheme ). The bonding model of Gilbert Lewis has been slightly modified over the years. The rules for using Lewis structures have slightly changed with the flow of time. However, the essential common features of chemical bonding remain the same until today.[9] Even after a century, chemists like to display the bonding scenarios as a Lewis electron pair. A few decades later, Fukui’s frontier molecular orbital (FMO) theory and Woodward and Hoffmann’s orbital symmetry rules for pericyclic reactions are significant additions to the bonding and reactivity of organic molecules.[9]

Scheme 1

Representative Types of σ (a–c), π (e–f), Ionic (d), and Charge Shift Bonds (g)

See reference (12) for undisputed use of arrows for dative bonds.

See reference (12) for unclass="Chemical">disputeclass="Chemical">n class="Chemical">d use of arrows for dative bonds.

Tclass="Chemical">he C atom is at tclass="Chemical">n class="Chemical">he heart of organic chemistry. Tetravalent and trivalent C compounds most commonly satisfy the octet rule. Carbene with (divalent C atoms) six valence electrons has also been very familiar to organic chemists for over two decades due to its application in metal-free catalysis and also inmetal ion employed catalysis. A less familiar divalent zero-valence C(0)-atom[10] stabilized by two donor ligands Ph3P (carbodiphosphane; Scheme , A) was synthesized six decades ago.[10a] The NHC analogue is called carbodicarbene [L2C(0); L = Ph3P, NHC].[10c] This monoatomic C(0) of A possesses two pairs of electrons that are donatable to the acceptor molecules (Scheme , B and C), which is remarkable. Theoretical calculations[10b] showed that the central C(0) of A has been stabilized by donor–acceptor σ and π bonds [L → C, L ← C] with the excited singlet C(0).[10e] Very recently, a linear C3 unit of (L)2C3 stabilized by the formation of one electron-sharing σ bond, dative σ bond [C3– with (L)2+; L = Ph3P, NHC; doublet states], and two dative π bonds (L ← C) has been reported.[11] The arrows for dative bonds were originally used by Sidgwick in 1923.[12a] The use of arrow for a dative bond has been undisputed[12b−12d] which was originally envisioned by Sidgwick nearly a century ago.[12a] The same arrow formalism, which was suggested for divalent carbon(0) compounds L → C ← L, was suggested already by Varshavskii in 1980.[13] In past four decades, the quatum chemical calculations on the different aspects of chemical bonding have been significant. Different types of chemical bonds are summarized in Scheme with examples.

Scheme 2

Donor Ligand-Stabilized C(0) Atom in the Excited Singlet State: Carbodiphosphane L2C(0) (A); and Monoatomic C(0) Center Acting as Ligands: L2C(0) → BR3 (B) and L2C(0) → (BR3)2 (C) [L = Ph3P]

Black and pink arrows represent (→) dative σ bond and dative π bond (R = H).

Bclass="Chemical">lack aclass="Chemical">nclass="Chemical">n class="Chemical">d pink arrows represent (→) dative σ bond and dative π bond (R = H).

class="Chemical">Here, we report tclass="Chemical">n class="Chemical">he theoretical calculations on the stability and bonding of a donor ligand-stabilized C5H4 unit having a general formula of (L)C5H4 (Scheme ). Our EDA-NOCV analysis shows three different bonding scenarios in these seemingly similar-looking molecules (L)C5H4 (1–3) [L = H2C (1a), aAAC (1b), (CO2Me)2C (1c), Py (1d); aNHC (2a), NHC (2b), PPh3 (2c); SNHC (3)]. In addition, the computed NICS values have revealed the effect of chemical bonding on the aromaticity of five-membered C5H4 rings of all compounds (1–3).

Computational Methods

Geometry optimizations anclass="Chemical">d vibratioclass="Chemical">naclass="Chemical">n class="Chemical">l frequency calculations of compounds (L)C5H4 (1–3) [L = H2C (1a), aAAC (1b), (CO2Me)2C (1c), Py (1d); aNHC (2a), NHC (2b), PPh3 (2c); SNHC (3)] in singlet and triplet electronic states have been carried out at the BP86-D3(BJ)/def2-TZVPP level in the gas phase.[14] The absence of imaginary frequencies assures the minima on the potential energy surface. All the calculations have been performed using the Gaussian 16 program package.[15] Natural bond orbital (NBO)[16] calculations have been performed using the NBO 6.0 program[17] to evaluate partial charges, Wiberg bond indices (WBI),[18] and natural bond orbitals. The nature of the bond in L–C5H4 compounds was analyzed by energy decomposition analysis (EDA)[19] coupled with natural orbitals for chemical valence (NOCV)[20] using the ADF 2018.105 program package.[21] EDA-NOCV calculations were carried out at the BP86-D3(BJ)/TZ2P[22] level using the geometries optimized at the BP86-D3(BJ)/def2-TZVPP level. The EDA-NOCV method involves the decomposition of the intrinsic interaction energy (ΔEint) between two fragments into four energy components as follows:[23]where the electrostatic, ΔEelstat term originates from the quasi-classical electrostatic interaction between the unperturbed charge distributions of the prepared fragments and the Pauli repulsion, ΔEPauli (repulsion energy due to the interactions of the same spins between the fragments) is the energy change associated with the transformation from the superposition of the unperturbed electron densities of the isolated fragments to the wavefunction, which properly obeys the Pauli principle through explicit anti-symmetrization and renormalization of the production of the wavefunction. The dispersion interaction, ΔEdisp (equivalent to attractive forces due to instantaneous fluctuation of electron clouds in the fragment before and after bond formation) is also obtained as we used D3(BJ). The orbital term, ΔEorb comes from (constructive interference during spatial mixing of orbitals of the fragments) the mixing of orbitals, charge transfer, and polarization between the isolated fragments. This can be further divided into contributions from each irreducible representation of the point group of an interacting system as follows:

Tclass="Chemical">he combiclass="Chemical">neclass="Chemical">n class="Chemical">d EDA-NOCV method is able to partition the total orbital interactions into pairwise contributions of the orbital interactions, which are important in providing a complete picture of the bonding. The charge deformation Δρ(r), which comes from the mixing of the orbital pairs ψ(r) and ψ–(r) of the interacting fragments, gives the magnitude and the shape of the charge flow due to the orbital interactions (eq ), and the associated orbital energy, ΔEorb presents the amount of orbital energy coming from such interaction (eq ).

Reaclass="Chemical">ders are furtclass="Chemical">n class="Chemical">her referred to the recent review articles to know more about the EDA-NOCV method and its application.[23] A thorough depiction of the EDA-NOCV approach and the meaning of each parameter is given in recent reviews/books.[9,16] Also, a very recent report related to eq has been critically discussed by different researchers.[24]

Results and Discussion

Tclass="Chemical">he optimizeclass="Chemical">n class="Chemical">d geometries of compounds (L)C5H4 (1–3) [L = H2C (1a), aAAC (1b), (CO2Me)2C (1c), Py (1d); aNHC (2a), NHC (2b), PPh3 (2c); SNHC (3)] in singlet ground states are shown in Figure and Scheme . The compounds were found to be stable in singlet states than in their triplet states by 28.1–55.1 kcal/mol (Figure S1). The C–CL bond lengths in these compounds are in the range of 1.349–1.402 Å, which is close to the typical C=C bond length in ethylene (1.34 Å)/benzene (1.39 Å) and less than the sp2–sp2 carbon single bond distance (1.48 Å), suggesting a double bond character of the C–CL bond.[8c,8k] This C–CL bond length varies in the order 1a < 1c < 3 < 2a < 1b < 2b. The increase in C–CL bond distance is attributed to the steric crowding of the ligand or due to Pauli repulsion energy.[9] The CCP–N bond length in 1d (1.386 Å) is significantly longer than the C=N double bond of imine (1.279 Å) and close to C–N bond lengths in pyridine (1.35 Å), indicating a partial double bond character. Meanwhile, the CCP–P bond length in 2c (1.711 Å) is very close to the value (1.6993 (5) Å) reported for the ylide Ph3P=CH–Ph,[25a] significantly shorter than the typical C–P single bond distance (1.81–1.84 Å) and close to the C–P partial double bond lengths (1.698–1.703 Å) in phosphinidenide anion.[25b] Geometrical parameters of the compounds 1a, 1d, 2a, 2b, and 2c, calculated at the BP86-D3(BJ)/def2-T-ZVPP level correlated well with the experimental values reported by Mueller-Westerhoff,[8b] Kunz et.al,[8c] Ramirez et.al,[8a] and Lloyd et al.[26] The C1–C′–CL bond angles in compounds 1a to 3 are in the range of 121.4–126.8°. The torsion angles show that the C5H4 unit and the ligand lie in the same plane in 1a and 1c, while they deviate from the plane in all other compounds.

Figure 1

Optimized singlet state geometries of (L)C5H4 compounds (1–3) (L = CH2, aAAC, C(CO2Me)2, pyridine, aNHC, NHCDip, PPh3, SNHCDip) at the BP86-D3(BJ)/def2-TZVPP level of theory.

Scheme 3

Cyclopentadienyl-Carbene/Phosphene Compounds L–C5H4 (L = CH2, aAAC, C(CO2Me)2, Pyridine, aNHC, NHCDip, PPh3, SNHCDip) (1a-1d, 2a-2c, 3)

See reference (8) for relevant previously reported compounds.

Optimizeclass="Chemical">d class="Chemical">n class="Chemical">singlet state geometries of (L)C5H4 compounds (1–3) (L = CH2, aAAC, C(CO2Me)2, pyridine, aNHC, NHCDip, PPh3, SNHCDip) at the BP86-D3(BJ)/def2-TZVPP level of theory.

See reference (8) for reclass="Chemical">levaclass="Chemical">nt previousclass="Chemical">n class="Chemical">ly reported compounds.

Tclass="Chemical">he tclass="Chemical">n class="Chemical">hermodynamic stability of L–C5H4 compounds has been assessed from the dissociation of L–C5H4 into C5H4 and L units (L = CH2, aAAC, C(CO2Me)2, pyridine, aNHC, NHCDip, PPh3, SNHCDip). The bond dissociation energy (BDE) values (Table S1) were calculated at 0 K and the change in Gibbs free energy at 298 K (ΔG298). The De values of the compounds 1a to 3 vary from 81.6 to 190 kcal/mol, depending on the ligand L. Among all the ligands, the CH2 ligand in 1a is strongly bound to C5H4 (De= 190 kcal/mol) followed by C(CO2Me) (De= 156.9 kcal/mol), while pyridine (De= 81.6 kcal/mol) is comparatively weakly bound followed by PPh3 (De= 92.2 kcal/mol). The bond dissociation energies of carbene ligands (L = aAAC, aNHC, NHC, SNHC) lie in between, with SNHC having higher bond strength (De= 132.7 kcal/mol) followed by aAAC (De= 129.4 kcal/mol), aNHC (De= 128.3 kcal/mol), and NHC (De= 128.0 kcal/mol). In general, the bond energy of a coordinate/dative single bond is lower than that of an electron-sharing single bond.[12b−12d]

Tclass="Chemical">he class="Chemical">n class="Chemical">dissociation of L–C5H4 is significantly endergonic at room temperature with endergonicity (ΔG298) values ranging from 64.9 to 171.7 kcal/mol. Substantially high dissociation energies and reasonably high endergonicity ascertain the thermodynamic stability of L–C5H4 compounds. Another stability parameter that indicates the electronic stability is the HOMO–LUMO energy gap (ΔH-L). High ΔH-L denotes higher electronic stability and less reactivity. The L–C5H4 compounds exhibit a high HUMO–LUMO energy gap (40.1–63.5 kcal/mol) indicating their electronic stability.

We have empclass="Chemical">loyeclass="Chemical">n class="Chemical">d various methods to analyze the bonding situation in L–C5H4 compounds, 1a to 3 [L = H2C (1a), aAAC (1b), (CO2Me)2C (1c), Py (1d); aNHC (2a), NHC (2b), PPh3 (2c); SNHC (3)]. The NBO results from Table shows σ and π occupancies of 1.97–1.99 and 1.66–1.81 e, respectively for L–C5H4 bonds in almost all compounds except 1d and 2c, where only σ occupancies are prominent. The σ and π bonds are almost equally polarized with a slight inclination toward the C5H4 ring in compounds 1a, 1b, and 1c, whereas in compounds 2a, 2b, and 3, σ bonds are almost equally polarized and π bonds are more polarized toward the C5H4 ring. The CC5H4–NPy σ bond of 1d is more polarized toward N. The CC5H4–PPPh3 σ bond of 2c is more polarized toward the C5H4 ring. NBO analysis shows an accumulation of charge on the C5H4 ring in all compounds except compound 1c. The slightly positive charge on the C5H4 ring in 1c is due to the electron-withdrawing effect of two CO2Me groups in the ligand part. The Wiberg bond indices (WBI) values of 1.34–1.77 support the partial double bond character in all compounds except 1d and 2c. The WBI values of 1.07 (1d) and 1.14 (2c) indicate a very weak partial double bond character in 1d and 2c. These compounds[8a−8c] are reported to be very polar (dipole moment >7 D).[8c] The HOMO of almost all compounds is mainly the π* MOs of the C5H4 ring, while HOMO-1 indicates L–CCp π interactions except for compound 1d, where the HOMO indicates L–CC5H4 π interactions and HOMO-1 represents the π* MO of the C5H4 ring (Figure S2). The quantum theory of atoms in molecules (QTAIM) calculations have been carried out to further explore the bonding pattern in L–C5H4 compounds. The results from Table shows the ellipticity values of 0.229–0.265 for L–C5H4 bond in compounds 1a to 3. The ellipticity (εBCP = λ1/λ2 – 1) is a measure of the bond order, and in general, the εBCP of a single and triple bond is close to zero because of the cylindrical contours of electron density, ρ, while for a double bond, the value is greater than zero.[27] This is due to the asymmetric distribution of electron density, ρ perpendicular to the bond path for a double bond. The ellipticity values of current compounds under study are deviated from the cylindrical contours, indicating the double bond character with reasonable π contribution, and are in good agreement with WBI values. The (3, −1) bond critical points (BCPs) of the L–C5H4 bond in compounds 1a to 3 are characterized with reasonably high negative Laplacian ∇2ρ(r) and total energy density H(r) along with considerable local electron densities ρ(r) of 0.193–0.342 a.u., indicating open-shell interactions. The disparity in electron density, ρ(r) and total energy density, H(r) in all compounds except 1d and 2c can be attributed to C–CL bond lengths. The local electron density, ρ(r) and total energy density, H(r) at the BCP (Table) decrease with an increase in C–CL bond length (Figure ). Thus, the compounds with shorter C–CL bond length shows higher electron density, ρ(r) and total energy density, H(r). The Laplacian of electron density contour plots shows that the BCPs (green dots) are located at the center of the bond path for compounds 1a, 1b, and 1c, whereas it is slightly polarized toward the C5H4 ring in compounds 2a, 2b, and 3. In 1d, the BCP is polarized toward the C5H4 ring, and in 2c, it is polarized toward the P atom (Figure S3). The εBCP value (0.229) of 2c is significantly lower than that of the reported ylide Ph3P=CH–Ph (0.510).[25a] The η value determines the covalency of the bond: an η value greater than 1.0 indicates the covalent nature of the bond and a value less than 1.0 indicates a closed-shell nature. The η values of 1.413–2.253 suggest that the L–C5H4 bond is more covalent in compounds 1a to 3. The AIM analysis of the current systems under study shows a reasonably high negative Laplacian of electron density and a lowering in potential energy, which supports covalent bonding and rules out the possibility of charge shift bonding.

Table 1

NBO Results of the (L)C5H4 Compounds [L = H2C (1a), aAAC (1b), (CO2Me)2C (1c), Py (1d); aNHC (2a), NHC (2b), PPh3 (2c); SNHC (3)] at the BP86/def2-TZVPP Level of Theorya

compound	bond	ON	L-C1 polarization and hybridization (%)		WBI	q (C5H4)
1a	CL–C1 σ	1.99	CL: 48.1 s(39.9), p(60.1)	CCp: 51.9 s(38.3), p(61.7)	1.77	–0.126
	CL–C1 π	1.81	CL: 48.1 s(0.3), p(99.7)	CCp: 51.9 s(0.5), p(99.5)
1b	CL–C1 σ	1.97	CL: 49.1 s(37.2), p(62.8)	CCp: 50.9 s(36.8), p(63.2)	1.46	–0.371
	CL–C1 π	1.69	CL: 43.6 s(0.2), p(99.8)	CCp: 56.4 s(0.1), p(99.9)
1c	CL–C1 σ	1.98	CL: 50.5 s(41.0), p(59.0)	CCp: 49.5 s(36.9), p(63.1)	1.64	0.021
	CL–C1 π	1.75	CL: 51.5 s(0.1), p(99.9)	CCp: 48.5 s(0.1), p(99.9)
1d	CL–N σ	1.98	N: 63.5 s(35.4), p(64.6)	CCp: 36.5 s(29.1), p(70.9	1.14	–0.238
2a	CL–C1 σ	1.97	CL: 50.7 s(40.1), p(59.9)	CCP: 49.3 s(34.4), p(65.6)	1.34	–0.470
	CL–C1 π	1.66	CL: 41.7 s(0.1), p(99.9)	CCp: 58.3 s(0.1), p(99.9)
2b	CL–C1 σ	1.97	CL: 50.7 s(40.1), p(59.9)	CCp: 49.3 s(34.4), p(65.6)	1.34	–0.470
	CL–C1 π	1.66	CL: 41.7 s(0.1), p(99.9)	CCp: 58.3 s(0.1), p(99.9)
2c	CL–P σ	1.97	P: 41.6 s(30.5), p(69.5)	CCp: 58.4 s(31.0), p(69.0)	1.07	–0.915
3	CL–C1 σ	1.97	CL: 50.9 s(41.9), p(58.1)	CCp: 49.1 s(34.7), p(65.3)	1.35	–0.472
	CL–C1 π	1.67	CL: 40.7 s(0.1), p(99.9)	CCp: 59.3 s(0.1), p(99.9)

Occupation number, ON, polarization and hybridization of the L–C5H4 bonds, and partial charges, q.

Table 2

QTAIM Results of the (L)C5H4 Compounds [L = H2C (1a), aAAC (1b), (CO2Me)2C (1c), Py (1d); aNHC (2a), NHC (2b), PPh3 (2c); SNHC (3)]

molecule	bonds	ρ(r)	∇2ρ(r)	H(r)	V(r)	G(r)	ε	η
1a	CL-CCp	0.342	–1.025	–0.388	–0.518	0.130	0.255	2.253
1b	CL-CCp	0.309	–0.863	–0.324	–0.433	0.109	0.252	1.961
1c	CL-CCp	0.332	–0.967	–0.369	–0.495	0.126	0.254	2.158
1d	N-CCp	0.291	–0.670	–0.635	–0.702	0.267	0.265	1.412
2a	CL-CCp	0.310	–0.878	–0.331	–0.442	0.111	0.261	2.042
2b	CL-CCp	0.302	–0.846	–0.326	–0.441	0.114	0.249	2.077
2c	P-CCp	0.193	–0.088	–0.193	–0.365	0.171	0.229	0.664
3	CL-CCp	0.307	–0.871	–0.334	–0.451	0.116	0.262	2.102

Occupation numclass="Chemical">ber, ON, poclass="Chemical">n class="Chemical">larization and hybridization of the L–C5H4 bonds, and partial charges, q.

It shouclass="Chemical">lclass="Chemical">n class="Chemical">d be noted that NBO and QTAIM methods cannot distinguish the dative or electron sharing interactions and hence the classification of L–C5H4 bonds as dative or electron sharing remains elusive. In this regard, the acumen of energy decomposition analysis–natural orbitals for chemical valence (EDA–NOCV) is helpful to give a detailed insight into the nature of the chemical bonds of L–C5H4 compounds [L = H2C (1a), aAAC (1b), (CO2Me)2C (1c), Py (1d); aNHC (2a), NHC (2b), PPh3 (2c); SNHC (3)] by its ability to provide the best bonding model to represent the overall bonding situation in the molecule. The bonding model with the lowest ΔEorb is contemplated as the best bonding representation since it needs the least change in the electronic charge of the fragments to make the electronic structure of the compound.[28]

We have conclass="Chemical">siclass="Chemical">n class="Chemical">dered four different bonding possibilities (Scheme ) by varying the electronic states of interacting fragments L and C5H4, to give the best description of the L–C5H4 bonds in the compounds 1a to 3 [L = H2C (1a), aAAC (1b), (CO2Me)2C (1c), Py (1d); aNHC (2a), NHC (2b), PPh3 (2c); SNHC (3)]. These are (a) neutral L and C5H4 fragments in their electronic triplet states forming electron-sharing σ and π bonds, (b) singly charged [L]+ and [C5H4]− fragments in their electronic doublet states, which would interact to form electron-sharing σ and dative π bonds, (c) neutral L and C5H4 fragments in their electronic singlet states forming both σ and π dative bonds, and finally (d) singly charged [L]+ and [C5H4]− fragments in their electronic doublet states interacting to form σ dative and π electron-sharing bonds. Table shows the numerical results of all possible bonding situations with different fragmentation modes. Based on the lowest ΔEorb value, compounds 1a to 3 can be categorized with three different bonding patterns. Compounds 1a to 1d prefer to form electron-sharing σ and π bonds (L=C5H4) resulting from the interaction of neutral L and C5H4 fragments in their electronic triplet, whereas compounds 2a to 2c choose to form electron-sharing σ (L–C5H4) and dative π (L ← C5H4) bonds with the interaction of [L]+ and [C5H4]−fragments in their electronic doublet states. In contrast, compound 3 prefers to form dative σ (L → C5H4) and dative π bonds (L ← C5H4) with the interaction of neutral L and C5H4 fragments in their electronic singlet states (Scheme ). Dative bonds are represented with arrows (→) according to the DCD model,[29] and this helps in distinguishing dative bonds from electron-sharing bonds.[12]

Scheme 4

Bonding Possibilities of L–C5H4 Compounds (L = CH2, aAAC, C(CO2Me)2, Pyridine, aNHC, NHCDip, PPh3, SNHCDip) (1a-d, 2a-c, 3)

Table 3

EDA-NOCV Results of L-C5H4 Bonds of (L)C5H4 Compounds (L = CH2, aAAC, C(CO2Me)2, Pyridine, aNHC, NHCDip, PPh3, SNHCDip) Using Four Different Sets of Fragments with Different Charges and Electronic States (S = Singlet, D = Doublet, T = Triplet) and Associated Bond Types at the BP86-D3(BJ)/TZ2P Levelb

D = dative bond; E = electron-sharing bond.

Energies are in kcal/mol. The most favorable fragmentation scheme and bond type are given by the smallest ΔEorb value written in red.

Scheme 5

The Best Bonding Scenarios of (L)C5H4 Compounds 1a–b, 2a–c, 3 (L = H2C, aAAC; (CO2Me)2C, Py; aNHC, NHCDip, PPh3; SNHCDip) at the BP86-D3(BJ)/TZ2P Level of Theory

The arrow represents covalent dative bond.

Tclass="Chemical">he arrow represeclass="Chemical">nts covaclass="Chemical">n class="Chemical">lent dative bond.

class="Chemical">D = class="Chemical">n class="Chemical">dative bond; E = electron-sharing bond.

Energies are in kcaclass="Chemical">l/moclass="Chemical">n class="Chemical">l. The most favorable fragmentation scheme and bond type are given by the smallest ΔEorb value written in red.

Tclass="Chemical">he class="Chemical">n class="Chemical">detailed EDA-NOCV results of the most appropriate bonding possibility showing pairwise orbital interactions are given in Tables and 5. The intrinsic interaction energy (ΔEint) denotes the overall strength of the bond, and ΔEint values of the eight compounds vary in the order of1c < 1b < 1d < 1a < 3 < 2a < 2c < 2b. The intrinsic strength, ΔEint values of almost all compounds except compound 1a are significantly larger than the bond dissociation energies, which might be due to the larger preparative energies (ΔEprep) of the fragments. The preparative energies originate from the changes in the geometry of the fragments from their equilibrium structure to the geometry in the compound and from the electronic excitation to a reference state. The high intrinsic interaction energies of compounds despite large Pauli repulsion energies can be attributed to the high orbital and electrostatic contributions. The total orbital (covalent) interactions (ΔEorb) contribute 50.4–62.1% to the total attractive interactions. This is in accord with the negative Laplacian and total energy densities of QTAIM calculations. The remaining contributions come from electrostatic (36.9–48.4%) and dispersion (0.5–3.6%) interactions. The electrostatic contribution is higher in compounds 2a to 3 compared to compounds 1a to 1d. The breakdown of ΔEorb into pairwise contributions further sheds light on the strength and type of interactions. The deformation densities and associated molecular orbitals as shown in Figures and 3 and Figures S4–S8 help in visualizing the direction of charge flow and shape of interacting MOs of the ligands and C5H4 fragments.

Table 4

EDA-NOCV Results at the BP86-D3(BJ)/TZ2P Level of L-C5H4 Bonds of (L)C5H4 Compounds (L = CH2 (1a) aAAC (1b), C(CO2Me)2 (1c) Py (1d)) Compounds Using Neutral L and Cp in the Electronic Triplet (T) States as Interacting Fragmentsc

energy	interactionc	CH2 (T) + C5H4 (T) 1a	aAAC (T) + C5H4 (T) 1b	C(CO2Me)2 (T) + C5H4 (T) 1c	Py (T) + C5H4 (T) 1d
ΔEint		–181.5	–175.1	–172.0	–175.8
ΔEPauli		305.8	412.9	384.8	417.8
ΔEdispa		–2.7 (0.5%)	–11.3 (2%)	–6.8 (1.2%)	–5.6 (1%)
ΔEelstata		–192.6 (39.5%)	–247.3 (42%)	–218.3 (39.2%)	–219.0 (36.9%)
ΔEorba		–291.9 (60%)	–329.3 (56%)	–331.8 (59.6%)	–369.0 (62.1%)
ΔEorb(1)b	L-C5H4 σ e– sharing	–207.6 (71.1%)	–200.3 (60.8%)	–230.6 (69.5%)	–275.3 (74.6%)
ΔEorb(2)b	L-C5H4 π e– sharing	–66.2 (22.6%)	–93.0 (28.2%)	–68.7 (20.7%)	–53.5 (14.5%)
ΔEorb(3)b	L ← C5H4 π back donation	–7.7 (2.6%)
	L-C5H4 σ polarization		–18.8 (5.7%)	–15.9 (4.8%)	–18.8 (5.1%)
ΔEorb(4)b	L ← C5H4 σ back donation	–4.2 (1.4%)
	L ← C5H4 π back donation		–8.2 (2.5%)	–10.2 (3.1%)	–8.7 (2.3%)
ΔEorb(5)b	L → C5H4 π donation				–6.6 (1.8%)
ΔEorb(rest)b		–6.2 (2.1%)	–9.0 (2.7%)	–6.4 (1.9%)	–6.1 (1.6%)

The values in parentheses show the contribution to the total attractive interaction ΔEelstat + ΔEorb + ΔEdisp.

The values in parentheses show the contribution to the total orbital interaction ΔEorb.

Energies are in kcal/mol.

Table 5

EDA-NOCV Results at the BP86-D3(BJ)/TZ2P Level of L-C5H4 Bonds of (L)C5H4 Compounds (L = aNHC (2a), NHCDip (2b) PPh3 (2c), SNHCDip (3)) Using Singly Charged [L]+ and [C5H4]− in the Electronic Doublet (D) States as Interacting Fragments for L = aNHC, NHCDip, PPh3 and Neutral L and C5H4 in the Electronic Singlet (T) States as Interacting Fragments for L = SNHCDipc

Energy	Interactionc	[aNHC]+ (D) + [C5H4]− (D) 2a	[NHC]+ (D) + [C5H4]− (D) 2b	[PPh3]+ (D) + [C5H4]− (D) 2c	SNHC (S) + C5H4 (S) 3
ΔEint		–249.2	–293.1	–263.7	–182.3
ΔEPauli		450.2	464.3	375.5	367.7
ΔEdispa		–8.2 (1.2%)	–16.5 (2.2%)	–12.3 (2%)	–20.0 (3.6%)
ΔEelstata		–338.1 (48.4%)	–326.9 (43.1%)	–298.6 (46.7%)	–209.9 (38.2%)
ΔEorba		–352.1 (50.4%)	–414.3 (54.7%)	–328.2 (51.3%)	–320.1 (58.2%)
ΔEorb(1)b	L-C5H4 σ e– sharing	–248.9 (70.7%)	–265.8 (64.1%)	–197.2 (60%)
	L → C5H4 σ donation				–243.1 (76.0%)
ΔEorb(2)b	L ← C5H4 π back donation	–62.4 (17.7%)	–69.5 (16.7%)	–54.0 (16.4%)	–43.8 (13.7%)
ΔEorb(3)b	L → C5H4 σ donation	–21.2 (6.0%)	–33.4 (8.0%)
	L ← C5H4 σ back donation			–18.9 (5.6%)	–11.9 (3.7%)
ΔEorb(4)b	L ← C5H4 π back donation	–9.2 (2.6%)	–17.4 (4.2%)	15.0 (4.6%)
ΔEorb(5)b	C5H4 π polarization		–5.4 (1.3%)	–11.4 (3.5%)
ΔEorb(6)b	C5H4 π polarization			–5.8 (1.7%)
ΔEorb(rest)b		–10.4 (3.0%)	–22.8 (5.5%)	–25.9 (7.9%)	–21.3 (6.6%)

The values in parentheses show the contribution to the total attractive interaction ΔEelstat + ΔEorb + ΔEdisp.

The values in parentheses show the contribution to the total orbital interaction ΔEorb.

Energies are in kcal/mol.

Figure 2

Shape of the deformation densities, Δρ(1)–(4) that correspond to ΔEorb(1)–(4), and the associated MOs of CH2–C5H4 (1a ) and the fragment orbitals of CH2 and C5H4 in the triplet state at the BP86-D3(BJ)/TZ2P level. Isosurface values are 0.003 a.u. for Δρ(1)–(4). The eigenvalues, |νn| give the size of the charge migration in e. The direction of the charge flow of the deformation densities is red → blue.

Figure 3

Shape of the deformation densities, Δρ(1)–(4) that correspond to ΔEorb(1)–(4), and the associated MOs of aNHC-C5H4 (2a) and the fragment orbitals of aNHC and C5H4 in the triplet state at the BP86-D3(BJ)/TZ2P level. Isosurface values are 0.003 a.u. for Δρ(1)–(4). The eigenvalues, |νn| give the size of the charge migration in e. The direction of the charge flow of the deformation densities is red → blue.

Shape of tclass="Chemical">he class="Chemical">n class="Chemical">deformation densities, Δρ(1)–(4) that correspond to ΔEorb(1)–(4), and the associated MOs of CH2–C5H4 (1a ) and the fragment orbitals of CH2 and C5H4 in the triplet state at the BP86-D3(BJ)/TZ2P level. Isosurface values are 0.003 a.u. for Δρ(1)–(4). The eigenvalues, |νn| give the size of the charge migration in e. The direction of the charge flow of the deformation densities is red → blue.

Shape of tclass="Chemical">he class="Chemical">n class="Chemical">deformation densities, Δρ(1)–(4) that correspond to ΔEorb(1)–(4), and the associated MOs of aNHC-C5H4 (2a) and the fragment orbitals of aNHC and C5H4 in the triplet state at the BP86-D3(BJ)/TZ2P level. Isosurface values are 0.003 a.u. for Δρ(1)–(4). The eigenvalues, |νn| give the size of the charge migration in e. The direction of the charge flow of the deformation densities is red → blue.

Tclass="Chemical">he vaclass="Chemical">n class="Chemical">lues in parentheses show the contribution to the total attractive interaction ΔEelstat + ΔEorb + ΔEdisp.

Tclass="Chemical">he vaclass="Chemical">n class="Chemical">lues in parentheses show the contribution to the total orbital interaction ΔEorb.

Energies are in kcan class="Chemical">l/moclass="Chemical">n class="Chemical">l.

Tclass="Chemical">he vaclass="Chemical">n class="Chemical">lues in parentheses show the contribution to the total attractive interaction ΔEelstat + ΔEorb + ΔEdisp.

Tclass="Chemical">he vaclass="Chemical">n class="Chemical">lues in parentheses show the contribution to the total orbital interaction ΔEorb.

Energies are in kcan class="Chemical">l/moclass="Chemical">n class="Chemical">l.

Tclass="Chemical">he resuclass="Chemical">n class="Chemical">lts from Table illustrates four pairwise contributions for compounds 1a to 1c and five pairwise interactions for compound 1d (Figure , Figures S4–S6). The strongest orbital interaction, ΔEorb(1) arise from the electron sharing σ interactions between unpaired electrons in the SOMO of the fragments and contributes 60.8–74.6% of total orbital interactions. ΔEorb(2) represents the electron-sharing π interactions between unpaired electrons in the SOMO of the fragments and contributes 14.5–28.2% of the total orbital interactions. There are other weak π interactions and ΔEorb(5) in 1d coming from the π back donation from filled orbitals of C5H4 into vacant orbitals of ligands (L ← C5H4) as represented by ΔEorb(3) in 1a, ΔEorb(4) in 1b to 1d, and π donation from the ligand to C5H4 (L → C5H4). These weak π interactions provide 2.5–3.1% to the total orbital interactions. Collectively, the relative strength of π interactions is much smaller than the σ interactions. The strength of π interactions of compounds 1a to 1d varies in the order of ligand as pyridine (1d) < C(CO2Me)2 (1c) < CH2 (1a) < aAAC (1b) according to the π accepting ability of the ligand. ΔEorb (3) represents σ polarization in compounds 1b to 1d and contributes 4.8 to 5.7% to the total orbital interactions. The detailed EDA-NOCV analysis of pyridine analogues (1d) shows that the bonding scenario is not as simple as it shows in its structure. Pyridine units like to form a bond with C5H4 units in 1d when both fragments are in triplet states. The π-bonding overlap between Py and C5H4 units is very weak. This π bond might be due to the dipolar interactions between one unpaired electron in each unit with opposite spins.

Tabclass="Chemical">le shows tclass="Chemical">n class="Chemical">he detailed EDA-NOCV results of compounds 2a to 2c, which prefers to form electron-sharing σ and dative π bonds, and compound 3, which prefers both σ and π dative bonds. The results indicate four pairwise interactions for compounds 2a and 3, five pairwise interactions for 2b, and six pairwise interactions for 2c (Figure , Figures S7 and S8). In compounds 2a to 2c, the strongest interaction, ΔEorb (1) providing 60–70.7% to the total orbital interactions comes from the electron-sharing σ interaction. The weaker ΔEorb(2) (16.4–17.7%) and ΔEorb(4) (2.6–4.6%) are due to π back donation (L ← C5H4) from filled HOMO, HOMO-1, and HOMO-3 to the vacant LUMO and high lying LUMOs of ligands L (L = aNHC (2a), NHC (2b), PPh3 (2c)), respectively. The relative contribution due to electron-sharing σ interactions is much higher than the π interactions. The dative π interactions of compounds 2a to 2c are weaker compared to those of 1a to 1d. ΔEorb(3) (5.6–8%) represents ligand (aNHC (2a), NHC (2b)) to C5H4 σ donation (L → C5H4) from the HOMO and HOMO-1 of ligands to LUMO+6 of C5H4 in compounds 2a and 2b, whereas in compound 2c, it represents C5H4 to ligand (L) σ back donation (L ← C5H4) from the SOMO to LUMO+7 of ligand PPh3. The other weak ΔEorb(5) (1.3–3.5%) in compounds 2b and 2c and ΔEorb(6) (1.7%) in compound 2c are due to π polarizations. The ΔEorb (1) of compound 3 arise from the σ donation (L → C5H4) from the HOMO of ligand (SNHC) to LUMO of C5H4 and contributes 76% to the total orbital interactions. The ΔEorb(2) (13.7%) and ΔEorb(3) (3.7%) come from the weak π back donation and σ back donation from C5H4 to ligand SNHC (L ← C5H4), respectively (Figure ). Compound 1d and 2c are completely different from the bonding point of view.

Figure 4

Shape of the deformation densities Δρ(1)–(3) that correspond to ΔEorb(1)–(3), and the associated MOs of SNHC- C5H4 (3) and the fragment orbitals of SNHC and C5H4 in the triplet state at the BP86-D3(BJ)/TZ2P level. Isosurface values are 0.003 a.u. for Δρ(1)–(3). The eigenvalues, |νn| give the size of the charge migration in e. The direction of the charge flow of the deformation densities is red → blue.

Shape of tclass="Chemical">he class="Chemical">n class="Chemical">deformation densities Δρ(1)–(3) that correspond to ΔEorb(1)–(3), and the associated MOs of SNHC- C5H4 (3) and the fragment orbitals of SNHC and C5H4 in the triplet state at the BP86-D3(BJ)/TZ2P level. Isosurface values are 0.003 a.u. for Δρ(1)–(3). The eigenvalues, |νn| give the size of the charge migration in e. The direction of the charge flow of the deformation densities is red → blue.

We have caclass="Chemical">lcuclass="Chemical">n class="Chemical">lated magnetic nucleus-independent chemical shifts (NICS), introduced by Schleyer et al.,[30] to measure the aromaticity of the five-membered Cp ring in L–C5H4 compounds (1–3) using the gauge-independent atomic orbital (GIAO) approach at the BP86/def2-TZVPP level on the geometries optimized at the BP86-D3(BJ)/def2-TZVPP level. The NICS method qualitatively and quantitatively describes the aromaticity, antiaromaticity, and nonaromaticity of ring systems and is considered as the most authentic probe of aromaticity due to its efficacy. NICS values calculated at the geometric centers of the ring are termed as NICS(0) and the values calculated at 1 Å above the plane of the ring are designated as NICS(1) (Table ). Negative NICS values indicate aromaticity, and positive NICS values denote antiaromaticity, while values close to zero represent nonaromaticity. NICS(0) is considered as a measure of σ + π-electron delocalization and NICS(1) represents π-electron delocalization.[31] The positive NICS(0) and negative NICS(1) values of compound 1a indicate the σ antiaromaticity and π aromaticity of the C5H4 ring. The positive NICS(0) and NICS(1) values of compound 1c denotes σ and π antiaromaticity of the C5H4 ring. This is due to the electron-withdrawing effect of carboxyl groups of the ligand. The negative NICS(0) and NICS(1) values in all other compounds (1b, 1d, 2a, 2b, 2c, and 3) indicates high σ and π aromaticity of the C5H4 ring in these systems and the aromaticity varies in the order 1d < 1b < 2a < 3 < 2b < 2c. Compound 2c shows high aromaticity, while compound 1d shows the least aromaticity among all compounds although 1d possesses a very high dipole moment.[8b,8c]

Table 6

NICS Results of L-C5H4 Compounds at the BP86/def2-TZVPP Level

compound	NICS(0)	NICS(1)
1a	+1.518	–2.033
1b	–4.087	–5.940
1c	+4.157	+0.345
1d	–0.670	–2.770
2a	–6.101	–6.351
2b	–8.201	–7.639
2c	–8.877	–8.076
3	–7.638	–7.585

Summary and Conclusions

In this work, we report tclass="Chemical">he quaclass="Chemical">ntum cclass="Chemical">n class="Chemical">hemical calculations of eight experimentally reported and not yet modeled L-C5H4 compounds (L = CH2, aAAC, C(CO2Me)2, pyridine, aNHC, NHCDip, PPh3, SNHCDip). The calculations suggest singlet ground-state geometries with reasonably high thermodynamic and electronic stabilities. The bonding analysis of L-C5H4 bonds by NBO, QTAIM, and EDA-NOCV methods nicely complement each other. EDA-NOCV calculations predict three different best bonding patterns under which the eight L-C5H4 compounds can be categorized. Compounds 1a to 1d prefer to form electron-sharing (L-C5H4) σ and π bonds with the interaction between L and C5H4 fragments in their electronic triplet states. Meanwhile, compounds 2a to 2c favors electron-sharing σ (L–Cp) and dative π bonds (L → C5H4) with the interaction of singly charged [L]+ and [C5H4]− fragments in an electronic doublet state. On the other hand, compound 3 chooses to form dative σ (L → C5H4) and dative π bonds (L ← C5H4) with the interaction of neutral L and C5H4 fragments in their electronic singlet states. The calculated NICS values suggest the σ and π aromatic character of the C5H4 ring for almost all compounds except 1a and 1c. The computed values suggest σ antiaromaticity and π aromaticity of the C5H4 ring for 1a and σ and π antiaromaticity of C5H4 the ring for 1c. Overall, the detailed theoretical analysis of the current study throws light on the bonding and aromaticity of otherwise some of the well-known ligand-stabilized C5H4 ring compounds.