Homodesmotic Reactions Research Articles

Accurate Ring Strain Energy Calculations on Saturated Three-Membered Heterocycles with One Group 13-16 Element.

Accurate ring strain energy (RSE) data for parent (CH2)2X rings are reported, where X are group 13-16 elements (El) in their lowest oxidation state, from the second to the sixth row, with their covalence completed by bonds to H. They are obtained from appropriate homodesmotic and hyper-homodesmotic reactions at different levels up to the CCSD(T) level, thus providing a benchmark of high-quality reference RSE values, as well as acceptably accurate faster lower-level options. Derivatives of indium, thallium, and lead cannot be properly described by a three-member ring connectivity, because they display a unique donor-acceptor structure from an ethylene π(C═C) orbital to an empty p orbital of a metallylene subunit. The RSE of groups 13 and 14 heterocycles increases on descending in the group (except for Ga and Ge), while it decreases for groups 15 and 16. The latter is presumably due to a strain-releasing mechanism favored by the increase of p-character at the sp3-type atomic orbital used by El in the endocyclic El-C bonds, %p(El)El-C, originated by the tendency of the El lone pairs in groups 15-16 to increase their s-character. This strain-releasing mechanism does not exist in heavier tetrels, which keep almost unchanged the p-character in the endocyclic bonds at El, whereas for triels the p-character is still lower owing to their sp2-like hybridization. Remarkable linear correlations were found between the RSE and either the above-mentioned %p(El)El-C, the distal C-C bond distance or the relaxed force constants for the endocyclic bond angles.

Complete set of homodesmotic reactions for the analysis of non-valence effects in the three-to-six-membered cyclic organic compounds

Graph theory based method is proposed for constructing a complete set of homodesmotic reactions (HDR) for studying the molecular energy of organic compounds. The efficiency of the method is shown by the example of ring strain energy Es calculation for a test set of 65 cyclic compounds. The absolute enthalpies of the cycles as well as of reference compounds used in HDRs were calculated using the composite methods G3 and G4. Depending on the structure of the studied cyclic compound, the thermal effect of HDR was shown to be a combination of uncompensated non-valence effects: ring strain, gauche interaction, hydrogen bonding, as well as difference in far environment of atoms, which is observed as the effect of small molecules. Within the framework of a complete set of HDRs, it is possible to separate all of these effects and determine Es free from secondary interactions. The obtained Es set allows tracing its relation with different structural factors such as cycle size, presence of hetero- or sp2-hybridized atoms in the cycle, effect of the substituent etc.

A theoretical study on the strain energy of helicene-containing carbon nanobelts.

In this study, the theoretical analysis of the strain energy of helicene-containing carbon nanobelts is reported. It was found that the combined method of linear regression analysis and suitable homodesmotic reactions can successfully estimate the strain energies of various helicene-containing carbon nanobelts including previously synthesized chiral (18,12) carbon nanobelts.

Theoretical Studies of Structures and Conformational Analysis of Anthracene-2,7-diyl Cyclic Oligomers

Abstract The structures and conformation of anthracene-2,7-diyl cyclic oligomers were investigated by DFT calculations. The energy minimum and transition state structures of the oligomers ranging from pentamer to nonamer were optimized at the M05-2X/6-31G(d) level. The mechanisms of conformational interconversion were analyzed on the basis of the calculated structures and the thermodynamic energies. The number of structures and the conformational flexibility rapidly increased with increasing ring size. In the stable structures, the dihedral angles between the anthracene units were ca. ±40° or ±140°, and the obtuse angles appeared only in large oligomers. We estimated the cavity size of the cyclic oligomers from the calculated structures and their strain energies by thermochemical calculations of the homodesmotic reactions.

The CBS values of ΔfHo298.15 and So298.15 of the phenoxy radicals, formed by abstraction of H atom from the components of surrogate bio-oil

In the present work, the standard thermochemical properties of the most thermochemically stable radicals, produced by abstraction of the hydrogen atom from 2,4-dimethylphenol (2,4-xylenol), 2-methoxy-4-methylphenol, 3-methoxy-4-formylphenol (vanillin), are determined using the results of RO/CBS-4M and RO/CBS-QB3 calculations. It is found that the formation of phenoxy radicals is the most thermochemically favorable pathway for the H atom abstraction from the considered compounds.The consistent values of the standard enthalpies of formation of the most thermochemically stable structures are determined using the RO/CBS-4M and RO/CBS-QB3 thermochemistry of the homodesmotic reactions, as well as using the correction dependencies.The values of the standard entropies of these compounds, calculated in the present work, are also reported.

Novel photoresponsive cyclicparaphenylenediazenes: structure, strain energy, cis-trans isomerization, and electronic properties.

A series of cis-trans isomers of cyclicparaphenylenediazenes (CPPDs) have been designed to explore their potential applications in solar thermal fuels and photoswitchable devices. In this work, three isomers of cis-trans-[3]CPPD, seven isomers of cis-trans-[4]CPPD, eleven isomers of cis-trans-[5]CPPD, and sixteen isomers of cis-trans-[6]CPPD have been proposed using density functional theory (DFT) at the B3LYP/6-31+G(d,p) level of theory. The stability of these CPPDs has been quantified by the homodesmotic reaction approach. Strain energies (SE) indicate that 3-cct, 4-ctct-anti, 5-cctct-anti, and 6-cttttc-anti are stable molecules in their respective CPPDs. The SE and heats of formation of cis-trans-CPPDs were also compared with those of all-cis-CPPDs and all-trans-CPPD isomers. The calculations suggest that cis-trans-CPPDs are more stable than all-cis and all-trans-CPPDs. The SE and also suggest that 3-cct, 4-ctct-anti, 5-cctct-anti, and 6-cttttc-anti are important candidates for laboratory test. The calculated highest occupied molecular orbital (HOMO) to the lowest unoccupied molecular orbital (LUMO) energy gaps of cis-trans-CPPDs indicate that these oligomers are potential materials for the construction of solar cells. Time-dependent (TD) DFT calculations of CPPDs show a characteristic peak in the range of 450 nm to 600 nm, which is consistent with previous studies. The predicted structures, and thermochemical and electronic properties can be a good starting point for the synthesis of CPPD-based photoswitchable and solar fuel cell devices.

Tuning the Circumference of Six-Porphyrin Nanorings

Most macrocycles are made from a simple repeat unit, resulting in high symmetry. Breaking this symmetry allows fine-tuning of the circumference, providing better control of the host–guest behavior and electronic structure. Here, we present the template-directed synthesis of two unsymmetrical cyclic porphyrin hexamers with both ethyne (C2) and butadiyne (C4) links, and we compare these nanorings with the symmetrical analogues with six ethyne or six butadiyne links. Inserting two extra carbon atoms into the smaller nanoring causes a spectacular change in binding behavior: the template affinity increases by a factor of 3 × 109, to a value of ca. 1038 M–1, and the mean effective molarity is ca. 830 M. In contrast, removing two carbon atoms from the largest nanoring results in almost no change in its template-affinity. The strain in these nanorings is 90–130 kJ mol–1, as estimated both from DFT calculation of homodesmotic reactions and from comparing template affinities of linear and cyclic oligomers. Breaking the symmetry has little effect on the absorption and fluorescence behavior of the nanorings: the low radiative rates that are characteristic of a circular delocalized S1 excited state are preserved in the low-symmetry macrocycles.

Theoretical studies on a new series of 1,2,3,4-tetrazine 1,3-dioxide annulation with an imidazole ring or oxazole ring.

To continue our previous work, the structure and some properties of a new series of 1,2,3,4-tetrazine 1,3-dioxides annulated with an imidazole ring or oxazole ring were studied in this paper. Four imidazolo-v-tetrazine 1,3-dioxides (ITDOs) I1-I4 and eight oxazolo-v-tetrazine 1,3-dioxides (OTDOs) O1-O8 were designed. We employed the density functional theory (DFT) in B3LYP/6-311++G(d,p) to study their geometrical structures and the homodesmotic reaction method to calculate the enthalpies of formation. Detonation properties and stabilities were also studied. Generally speaking, ITDOs and OTDOs have more preferable stabilities than TTDOs or pyrazolo-TDOs. I3, I4, O1, and O2 were found to be comparable to the energy level of RDX; O5 and O6 are even as powerful as HMX. The stabilities analysis in this paper can also prove that the five-membered ring deformation and the steric hindrance change caused by the different substituents will affect the stabilities of the structures of 1,2,3,4-tetrazine 1,3-dioxides annulated with a five-membered nitrogen-rich heterocycle. Other factors, such as the position of the electron-withdrawing substituents or the position of coordinated oxygen atom, are worthwhile to investigate in future work.

The Use of D Index in the Estimation of Aromaticity: The Case of Cycloparaphenylene

Cycloparaphenylenes are important compounds for their photophysical and electronic properties. The curved structure of these compounds induces an alteration of the aromatic character of these compounds. D values have been used to describe the aromatic character of compounds from [5]- to [10]cycloparaphenylene. D values are compared with HOMED and with the strain energy are obtained by using an homodesmotic reaction.

Quantum Chemical Calculations on CHOP Derivatives-Spanning the Chemical Space of Phosphinidenes, Phosphaketenes, Oxaphosphirenes, and COP- Isomers.

After many decades of intense research in low-coordinate phosphorus chemistry, the advent of Na[OCP] brought new stimuli to the field of CHOP isomers and derivatives thereof. The present theoretical study at the CCSD(T)/def2-TZVPP level describes the chemical space of CHOP isomers in terms of structures and potential energy surfaces, using oxaphosphirene as the starting point, but also covering substituted derivatives and COP− isomers. Bonding properties of the P–C, P–O, and C–O bonds in all neutral and anionic isomeric species are discussed on the basis of theoretical calculations using various bond strengths descriptors such as WBI and MBO, but also the Lagrangian kinetic energy density per electron as well as relaxed force constants. Ring strain energies of the superstrained 1H-oxaphosphirene and its barely strained oxaphosphirane-3-ylidene isomer were comparatively evaluated with homodesmotic and hyperhomodesmotic reactions. Furthermore, first time calculation of the ring strain energy of an anionic ring is described for the case of oxaphosphirenide.

The s‐homodesmotic method for the computation of conventional strain energies of bicyclic systems and individual rings within these systems

AbstractThe s‐homodesmotic method for computing conventional strain energies (CSE) has been extended for the first time to bicyclic systems and to individual rings within these systems. Unique isodesmic, homodesmotic, and hyperhomodesmotic reactions originate from the s‐homodesmotic method. These are used to investigate 12 bicyclic systems comprising cyclopropane and cyclobutane and how the CSE of each system compares to the sum of the individual rings within each. Equilibrium geometries, harmonic vibrational frequencies, and the corresponding electronic energies and zero point vibrational energy corrections are computed for all relevant molecules using second‐order perturbation theory and density functional theory (B3LYP) with the correlation consistent basis sets cc‐pVDZ and cc‐pVTZ. Single‐point CCSD(T) energies are computed at the MP2/cc‐pVTZ optimized geometries to ascertain the importance of higher order correlation effects. Results indicate that CSEs are additive when the two rings are separated by one or two bonds and somewhat additive in other cases.

Polyazulenes and Polynaphthalenes: Prediction and Computational Study

AbstractThe geometries, the electronic structures and the aromaticity of the [n]‐azulene and [n]‐naphthalene polymers were studied, by using the Density Functional Theory (DFT) and the Møller–Plesset (MP2) Pertubation Theory, for the different multiplicities (M=2S+1): singlet (S=0, closed and open shell), triplet (S=1) and quintet (S=2). The ground‐states of the [n]‐azulene polymers were a singlet (closed shell) for any values of n (n≤10). The ground‐states of the [n]‐naphthalene polymers were a singlet (closed shell) for n≤6 and triplet for 7≤n≤10. The electric dipole moment of the odd [n]‐azulene polymers varied with the length of the polymer chain, while exhibiting a local minimum for [5]‐azulene. The dipole of the even [n]‐azulene and the (even and odd) [n]‐naphthalene polymers were null by symmetry. The HOMO‐LUMO gap was estimated at 0.70 eV for [n]‐azulene polymers with large chain. All of the polymers had electronic transition peaks in the visible region and their maximum was red‐shifted for the increasing chains. The nucleus independent chemical shift (NICS) calculations have shown that ring tension was an important factor in the aromaticity loss, as shown, for example, for the flat, the cycle, and the Möbius strip [20]‐polymers. The Aromatic Stabilization Energies (ASEs) that were based on the homodesmotic and isodesmic reactions were also obtained.

Determining the Basis of Homodesmotic Reactions of Cyclic Organic Compounds by Means of Graph Theory

Comparative calculations based on the use of a homodesmotic reaction (HDR)—an isodesmic process with the additional requirement for group balance—is used to analyze the thermochemical characteristics of cyclic organic compounds exemplified by bicyclo[2.1.0]pentene-2. To avoid confusion in selecting HDRs, an algorithm is developed for determining the HDR basis, i.e., the set of all possible independent homodesmotic reactions. The algorithm for constructing the set of HDRs is based on an analysis and transformations of the bond graph of groups for the investigated chemical compound. The use of graph theory allows us to automate the procedure for deriving the basis of homodesmotic reactions, and to obtain a visual geometric interpretation of the basis, which is important for subsequent physicochemical analysis. The energetics of bicyclo[2.1.0]pentene-2 is investigated using the proposed approach, and the independent basis of HDRs is found to include 19 formal transformations. Standard enthalpies for the test compound and the participants of homodesmotic reactions are calculated using the G3 composite approach. Thermochemical analysis of the obtained data allows us to determine the standard enthalpy of formation of the bicycle (ΔfH° = 336.4 kJ/mol) and value ΔfH° of a number of cyclic and acyclic alkenes and alkadienes that are products of theoretical decomposition of the test compound. The proposed method is shown to be extremely effective in analyzing the effects of nonbonded interactions in the structure of organic molecules. The ring strain energy of the bicycle is calculated or the test compound: ES = 295.2± 2.2 kJ/mol.

Analysis of the Nucleus-Independent Chemical Shifts of [10]Cyclophenacene: Is It an Aromatic or Antiaromatic Molecule?

[10]Cyclophenacene is an important synthetic target that shows a pair of nucleus-independent chemical shift (NICS) values for the center of mass and six-membered rings typical of an aromatic species. This is found in contrast with the global paratropic current density induced by a magnetic field parallel to the main symmetry axis. This apparent contradiction has been analyzed by studying the tensor character of the magnetic response. It turns out that the molecule displays two characters, one paratropic (antiaromatic) and another one diatropic (aromatic), depending on the orientation of the inducing magnetic field. The paratropic response, which cannot be recognized from the NICS values, is associated with a well-defined destabilization of the belt closure, as witnessed by homodesmotic reactions. A scalar measure of magnetic aromaticity, the field-independent current strength, has been introduced, which allows us to reach the conclusion that [10]cyclophenacene is indeed an aromatic molecule, although it is significantly affected by the paratropic response.

Distorted naphthalenes and azulenes

The molecular structures and relative energies of various methyl and tert-butyl substituted naphthalenes and azulenes have been studied by DFT method ωB97XD/6-311(d, p) with dispersion correction. The relative energies of molecules and effects of steric repulsion, strain and ring distortion were estimated via the appropriate homodesmotic and isodesmic reactions. The calculated standard reaction enthalpies allowed us to estimate the magnitude of various nonbonding intramolecular interactions. The introduction of bulky tert-butyl substituents leads to significant distortions of naphthalene and azulene rings. The aromaticity of the rings had been estimated using HOMA indices. For the most distorted aromatic rings it was found that the net destabilization is more pronounced in octa-tert-butylnaphthalene than in the octa-tert-butylazulene even though the structural distortions of the rings were smaller in the former.

Coexistence of Normal and Auxetic Behavior in a Thermally and Chemically Stable sp3 Nanothread: Poly[5]asterane

A one-dimensional nanostructure with sp3 -hybridized carbon atoms, namely, poly[5]asterane (PA), is predicted by means of electronic structure calculations and reactive molecular dynamics simulations. Thermochemical analysis based on homodesmotic reactions showed that the formation of poly[5]asterane is more favorable than that of polytriangulane and comparable to that of polytwistane. A plane-wave DFT approach gave a computed Young's modulus of about 0.84 TPa, which is quite promising and comparable to those of other sp3 -hybridized nanothreads. Simulations of the desorption of hydrogen atoms from PA showed a high activation energy (Ea ≈52 kcal mol-1 ), which again indicates substantial chemical stability. Interestingly, PA was shown to exhibit auxetic behavior (negative Poisson's ratio). Thus, PA is advocated as a new mechanically and chemically stable nanothread with exotic auxetic behavior.

Theoretical thermochemical studies of phenylacetylene scaffolds

Phenylacetylene scaffolds are known to be an important component in electronic devices, but their thermochemistry has not been studied so far. In this paper, we systematically calculate the strain energies (SE) and the standard enthalpies of formation (ΔfH298°) of sixteen linear polyynes-substituted benzene (PSB) and seven cyclic[n]orthophenyleneacetylenes ([n]COPAs) (n=2–8). The geometries and vibrational frequencies of PSB were calculated at B3LYP/6–31+G(d,p), mPW1PW91/6–31+G(d,p), and M06-2X/6–31+G(d,p) levels of theory and for [n]COPAs, mPW1PW91/6-31G(d) was used. Isodesmic and homodesmotic reactions approach were used to calculate SE and ΔfH298°. The results show that ΔfH298°of PSB increases steadily with the increasing the numbers of CC linkage, and endothermicΔfH298°of these molecules are indicative of an acetylene substituent strain. The SE per-unit monomer (SE/n), and ΔfH298°per-unit monomer (ΔfH298°/n) of [n]COPAs were calculated and results were compared with its meta and para counterpart. In addition, electronic properties such as HOMO, LUMO and HOMO-LUMO energy gap were calculated.

Performance of DFT, MP2, and composite ab initio methods for the prediction of enthalpies of formations of CHON compounds using isodesmic reactions

This paper assesses the performance of quantum chemical models with regard to the calculation of enthalpy of formation of CHON molecules using isodesmic reactions. The high accuracy of prediction of enthalpy of formation of CHON compounds can be achieved by the combination of isodesmic reaction scheme with composite ab initio methods. The best composite methods, such as G4, G4MP2, CBS-QB3, and CBS-APNO, can attain near chemical accuracy or better depending on reaction type. Other composite methods yield the same accuracy only in conjunction with isodesmic or homodesmotic reactions. The DFT and MP2 methods lead to good results if they are used with homodesmotic reactions. For CHO compounds, all composite methods demonstrate the high accuracy not only with isodesmic and homodesmotic reactions, but also with isogyric reactions. Moreover, the DFT and MP2 methods can also yield a high accuracy estimate of the enthalpy of formation when they are used with isodesmic or homodesmotic reactions. Four composite methods (G4, G3, CBS-APNO, and CBS-QB3) employed in conjunction with 45 isogyric reactions yield the enthalpy of formation of hydrazine (97.7±2.0kJ/mol) in agreement with the best approximating to CCSD(T)/CBS energy, thus calling into question the usually quoted experimental value of 95.5kJ/mol.

Prediction of heat of formation for exo-Dicyclopentadiene

Dicyclopentadiene (DCPD) is an organic compound with two structural isomers, the exo and endo isomers. There have been several thermal runaway accidents related to this hazardous compound. It is well known that heat of formation is one of the most important parameters to investigate thermal runaway reactions. The heat of formation for the endo isomer has been characterized via computational and experimental studies. However, there is no thorough computational or experimental study on the heat of formation for the exo isomer. In this work, computational chemistry methods with homodesmotic reaction schemes were proposed to predict the heat of formation for the exo isomer. First, the computational methodology was validated by comparing predicted results of the endo isomer with its existing experimental value (42.2 ± 0.6 kcal/mol). The results from high level ab-initio, density functional theory, and composite methods were shown in a good agreement with the experimental value. The same methodology was then applied to predict the heat of formation for the exo isomer. The energy difference of heat of formation between two isomers was estimated at 0.7 ± 0.1 kcal/mol based on various computational methods. Therefore, combining the experimental and computational data, the predicted heat of formation for the exo isomer is 41.5 ± 0.6 kcal/mol. This work could provide reliable thermochemical data for inherently safer design of any processes involving DCPD.

Can Strained Hydrocarbons Be "Forced" To Be Stable?

Many strained hydrocarbons are prone to isomerization, dimerization, and trimerization under normal laboratory conditions. Here we investigate a method to stabilize angle-strained cycloalkynes by applying a mechanical pulling force to the carbon atoms adjacent to the triple bond, which partially linearizes the C≡C-C bond angles. We discuss various methods of applying such pulling forces, including photoswitches and incorporation into additional strained macrocycles. We use the computational JEDI (Judgement of Energy DIstribution) analysis to quantify the distribution of energy in strained cycloheptyne and judge the change in stability upon application of an external force via isodesmic and homodesmotic reactions. We find that cycloheptyne can indeed be stabilized by external forces. However, the force generated by photoswitches during isomerization is too low to lead to a significant stabilization of the molecule. Hence, stronger forces are needed, which can be achieved by incorporating cycloheptyne into a second strained macrocycle.