Equal Bond Lengths Research Articles

Aided design and molecular regulatory mechanism of non-fused ring acceptors in the framework of A-D1-D2-A molecular systems

Non-fused ring acceptors (NFRAs) have garnered significant attention due to their low cost, ease of synthesis, and high efficiency. Molecules with asymmetric structures can improve molecular stacking and effectively reduce non-radiative energy loss. So, the asymmetric A-D1-D2-A series NFRAs (DPCT-4F and DPCT-4Cl) were selected as the research objects, and four acceptors (DPCT-D1∼DPCT-D4) were designed using end-capped modification strategies. Theoretical simulations were conducted on the ground and excited state characteristics of DPCT series molecules, and the electron mobility of the dimers formed by these acceptors was calculated. It was found that the simulated energy levels, energy gaps, absorption spectra and open-circuit voltages of original molecules are consistent with the trends in the experiment, ensuring the accuracy of the calculation method. Moreover, the nearly equal bond lengths of the developed compounds and the original molecules at the corresponding positions indicate that end-capping modification strategies have little effect on the molecular bond lengths. However, the instability of C-C single bond results in an increased dihedral angle between dipyran and cyclopentadithiophene. Among these designed molecules, DPCT-D1 and DPCT-D2, modified with -CN/-NO2 functional groups, outperform the reference molecules regarding energy gap, molecular descriptors, absorption spectrum, and exciton binding energy. This demonstrates the superiority of functional group substitution strategies with strong electron-withdrawing ability. Introducing thiophene units enables DPCT-D4 molecule to achieve a higher open-circuit voltage, dipole moment and light capture ability. Additionally, all the designed molecules exhibit higher electron mobility than DPCT-4F. DPCT-D1 shows even higher mobility than the better-performing reference molecule DPCT-4Cl due to its greater electronic coupling strength and lower reorganization energy. Overall, most tailored molecules, particularly DPCT-D1, exhibit superior performance in most critical parameters compared to the reference molecules, demonstrating the design strategy's effectiveness and offering worthwhile theoretical instruction for developing high-performance acceptors.

Front Cover: Protonated Ethylene Carbonate: A Highly Resonance‐Stabilized Cation (ChemistryOpen 12/2021)

The Front Cover shows the crystal structure of the salt of protonated ethylene carbonate [C3H5O3][Sb2F11]. Protonated ethylene carbonate was synthesized by reacting the neutral compound in the superacidic system HF/SbF5 at low temperature. Interestingly, the single-crystal X-ray structure analysis revealed a planar CO3 moiety with nearly equal CO bond lengths. Further theoretical investigations of the cation led to the result, that it contains a remarkably delocalized 6π-electron system. On the cover this resonance stabilization is highlighted by p-orbitals on the CO3 moiety. More information can be found in the Research Article by Stefanie Beck et al.

Protonated Ethylene Carbonate: A Highly Resonance-Stabilized Cation.

Invited for this month's cover picture is the group of Prof. Andreas J. Kornath at the LMU in Munich (Germany). The cover picture shows the crystal structure of the salt of protonated ethylene carbonate [C3 H5 O3 ][Sb2 F11 ]. Protonated ethylene carbonate was synthesized by reacting the neutral compound in the superacidic system HF/SbF5 at low temperature. Interestingly, the single-crystal X-ray structure analysis revealed a planar CO3 moiety with nearly equal CO bond lengths. Further theoretical investigations of the cation led to the result, that it contains a remarkably delocalized 6π-electron system. On the cover this resonance stabilization is highlighted by p-orbitals on the CO3 moiety. Read the full text of their Research Article at 10.1002/open.202100229.

Structures of molecular complexes of SbCl5 with pyridine and acetonitrile: equal bond lengths, different stability

Molecular structure of crystalline complex SbCl5 • Py was determined for the first time and the structure of the complex SbCl5 • AN was refined by means of single crystal X-ray diffraction analysis. It is shown that donor-acceptor Sb–N bond lengths for these complexes are equal within the experimental error. Quantum chemical calculations of the complexes in the gas phase reveal that the energies of the donor-acceptor bond Sb–N are 88 and 180 kJ mol−1 for SbCl5 • AN and SbCl5 • Py, respectively. It is established that the length of the donor-acceptor bond Sb–N in the crystal cannot serve as a measure of its strength.

Bis[μ-O-isopropyl (4-ethoxyphenyl)dithiophosphonato-κ2S:S′]bis{[O-isopropyl (4-ethoxyphenyl)dithiophosphonato-κ2S,S′]mercury(II)}

The title compound, [Hg2(C11H16O2PS2)4], is a dinuclear complex with a distorted tetra­hedral geometry around each HgII atom. Although the two HgII atoms are surrounded by the same ligand, two different coordination modes are observed: one is chelating and the other bridging. The Hg—S bonds form two distinct pairs of long and short bonds. One pair includes both chelating and bridging Hg—S bonds with approximately equal bond lengths of 2.4042 (8) and 2.3997 (7) Å, respectively. The other pair is significantly longer at 2.9361 (9) and 2.8105 (8) Å, respectively. This pattern forms a center of inversion through the mol­ecule with an equal and opposite effect occurring at the other HgII atom. The S—Hg—S angles vary widely from 76.26 (2) to 154.65 (3)°, indicative of a distorted tetra­hedral arrangement of the S atoms around the HgII atom. The P—S bond lengths are 1.9681 (10) and 2.0519 (11)°, clearly indicating partial double-bond character in the former. The mol­ecule contains an inversion center situated between the two HgII atoms.

Structures, Energetics, and Aromaticities of the Tetrasilacyclobutadiene Dianion and Related Compounds: (Si4H4)2–, (Si4H4)2–·2Li+, [Si4(SiH3)4]2–·2Li+, [Si4(SiH3)4]2–·2Na+, and [Si4(SiH3)4]2–·2K+

In light of the important recent synthesis of a stable tetrasilacyclobutadiene dianion compound by Sekiguchi and co-workers and the absence of theoretical studies, ab initio methods have been used to investigate this dianion and a number of related species. These theoretical methods predict multiple minima for each compound, and most minima contain folded and bicyclic silicon rings. For (Si(4)H(4))(2-), (Si(4)H(4))(2-)·2Li(+), [Si(4)(SiH(3))(4)](2-)·2Li(+), [Si(4)(SiH(3))(4)](2-)·2Na(+), and [Si(4)(SiH(3))(4)](2-)·2K(+), respectively, the energetically lowest-lying structures are designated A-3 (C(2v) symmetry), B-8 (C(1) symmetry), C-1 (C(2) symmetry), D-1 (C(2) symmetry), and E-1 (C(2h) symmetry). None of these structures satisfies both the ring planarity and the cyclic bond equalization criteria of aromaticity. However, all of the representative NICS values of these lowest-lying structures are negative, indicating some aromatic character. Especially, structures C-1 and D-1 of C(2) symmetry effectively satisfy the criteria of aromaticity due to the slightly trapezoidal silicon rings, which are nearly planar with nearly equal bond lengths. SiH(3) substitution for hydrogen in (Si(4)H(4))(2-)·2Li(+) significantly reduces the degree of aromaticity, as reflected in the substantially smaller NICS absolute values for [Si(4)(SiH(3))(4)](2-)·2Li(+) than those of (Si(4)H(4))(2-) and (Si(4)H(4))(2-)·2Li(+). The aromaticity is further weakened in [Si(4)(SiH(3))(4)](2-)·2Na(+) and [Si(4)(SiH(3))(4)](2-)·2K(+) by replacing lithium with the sodium and potassium cations.

Thermodynamics of the rupture in a Morse lattice

The rupture of a Morse lattice is considered in the present paper. The critical rupture force F cr is found to decrease with the number of particles N as F cr ~ 1/ $\sqrt{N}$ . The partition function is obtained for two states of the lattice – with all equal bond lengths and one broken bond. In the first case an accurate expressions for thermodynamic parameters are obtained, and thermodynamic expressions are derived in the harmonic approximation in the latter case. The analytical predictions are confirmed by extensive MD simulations. Cis-trans isomerization is considered as an example. Volume fractions of trans- and cis-isomers versus number of monomer units N are found depending on the torsion stiffnesses.

Ideal Polyhedral Model for Boron Nanotubes with Distinct Bond Lengths

In this Article, we extend both the rolled-up model and the polyhedral geometric model for single-walled boron nanotubes with equal bond lengths to the corresponding models but having distinct bond lengths. The boron nanotubes considered here are assumed to be formed by sp2 hybridization and π-bonds and may have as many as three different bond lengths, and the nanotube lattice is assumed to comprise a triangular pattern. Beginning with the two postulates that all equivalent bond lengths lying on the same helix are equal and that all of the atoms are equidistant from a common axis of symmetry, we derive exact formulas for the geometric parameters such as chiral angles, bond angles, radius, and unit cell length. Results for both the rolled-up model and the prior geometric model are shown to emerge from the new geometric model in the limit of large radius and in the limit of equal bond lengths, respectively. Numerical results for the new polyhedral model are related to existing numerical results for a novel boron nanotube structure, which involves 1/9 of the atoms missing. This novel structure is believed to be more energetically favorable than the conventional model.

Silicon nanotubes with distinct bond lengths

In this paper, we extend both the rolled-up and the polyhedral models for single-walled silicon nanotubes with equal bond lengths to models having distinct bond lengths. The silicon nanotubes considered here are assumed to be formed by sp3 hybridization with different bond lengths so that the nanotube lattice is assumed to comprise only skew rhombi. Beginning with the three postulates that all bonds lying on the same helix are equal, all adjacent bond angles are equal, and all atoms are equidistant from a common axis of symmetry, we derive exact formulae for the polyhedral geometric parameters such as chiral angles, bond angles, radius and unit cell length. The polyhedral model presented here with distinct bond lengths includes both the rolled-up model with distinct bond lengths which arises from the first term of an asymptotic expansion, and an existing polyhedral model of the authors which assumes equal bond lengths. Finally, some molecular dynamics simulations are undertaken for comparison with the geometric model. These simulations start with equal bond lengths and then stabilize in such a way that two distinct bond lengths emerge.

Nonempirical studies of the electronic properties of highly conducting polymers

We present ab initio calculations on the electronic structure of highly conducting polymers. A Hartree-Fock study of the lithium doping of all-trans polyacetylene demonstrates that the bond alternation, present in the undoped chain is dramatically reduced as the charge transfer from the lithium atom increases. At ˜0.1e transferred per CH unit, we predict equal bond lengths. The relationship of these results to the soliton model for polyacetylene is discussed. Nonempirical effective Hamiltonian calculations on undoped polyacetylene, polydiacetylene, poly (p-phenylene) and derivatives including poly (p-phenylene sulfide) are described. These calculations provide reliable bandwidths and ionization potentials. The ionization potential results are in good agreement with experimental estimates; the bandwidth results yield a satisfying qualitative correlation to the conductivities obtained on doping for the various systems considered.

The thermodynamic characteristics of the rupture of a Morse lattice

We consider the thermodynamic characteristics of the rupture of a one-dimensional lattice with the Morse interaction potential between neighboring particles. The description is given in terms of the Gibbs canonical distribution. Equations for partition functions corresponding to states with equal bond lengths and one broken bond were obtained in the quasi-harmonic low-temperature approximation. The ratios between these partition functions allow lattice lifetimes in both states to be estimated. The approximation used corresponds to a substantially truncated phase space volume, when states other than those in the immediate vicinity of potential energy minima are excluded from consideration. Nevertheless, satisfactory agreement between analytic equations and molecular dynamics simulation results was obtained for the number of particles in the Morse lattice N = 10.

Theoretical Study of BeN Linear Chains: Optimized Geometries and Harmonic Frequencies.

The electronic structure of linear beryllium chains has been theoretically studied at an ab initio level. By using a CAS-SCF approach, geometries have been optimized and harmonic frequencies computed. The optimized geometries present almost equal bond lengths, while all the harmonic frequencies are real. This fact indicates the presence of a local minimum, at this level of theory, having a linear geometry. The energy splitting between the singlet ground state, (1)Σg, and the quasi-degenerated excited triplet, (3)Σu, has been computed at CAS-SCF and MR-CI level. It was found that the splitting goes exponentially to zero as the number of atoms in the chain is increased.

Structure of chiral single-walled carbon nanotubes under hydrostatic pressure

Abstract We investigate the structural parameters, i.e., bond lengths and bond angles of chiral tubes of various chiralities using a procedure based on helical and rotational symmetries and Tersoff potential. The results indicate that at ambient conditions, there are equal bond lengths and three unequal bond angles in the structure of chiral tubes. This bond length depends significantly on the chirality and insignificantly on the tube radius. Length of the tubes does not play very significant role on bond length and bond angles. These C–C bonds were recalculated under hydrostatic pressure. The bond length compresses with pressure while the bond angles remain practically unchanged. We also carry out analysis regarding the cross sectional shape of chiral tubes and its pressure dependence. It is found that at some pressures, transition from circular to oval cross section takes place. The transition pressure is found to strongly depend on the radius and chirality of tube. At this transition, corresponding to given elliptical cross section, the bond length for all chiral tubes of various chiralities and radius approaches nearly a fixed value of 1.434 A.

A study of the ground and excited states of Al3 and Al3−. I. 488 nm anion photoelectron spectrum

The vibrationally resolved, 488 nm anion photoelectron spectrum of aluminum trimer displays transitions from two electronic states of Al(3)(-) to four states of Al(3). Franck-Condon analyses of the spectra in the independent harmonic oscillator, parallel mode approximation provide information concerning equilibrium bond length and bond angle differences among the observed states. The electron affinity of Al(3) is measured to be 1.916+/-0.004 eV. In the X (2)A(1)(') Al(3) ground state, fundamental symmetric stretching (nu(1)) and bending (nu(2)) vibrational frequencies are 357+/-10 and 240+/-10 cm(-1). In the X (1)A(1)(') Al(3)(-) ground state, these values are 365+/-15 and 257+/-15 cm(-1), and the equilibrium bond lengths are the same as those of Al(3) to within 0.02 A. The transition between the Al(3)(-) and Al(3) ground states displays only weak activity in the bending mode, consistent with essentially D(3h) structures for both states. An excited (3)B(2) Al(3)(-) state at 0.409+/-0.004 eV (T(0)) has vibrational frequencies of 330+/-20 (nu(1)) and 200+/-10 cm(-1) (nu(2)). This C(2v) state has a 65+/-1 degree apex bond angle and its two equal bond lengths are within 0.01 A of the ground state value. Liquid nitrogen cooling of the downstream portion of the approximately 60 cm long, 0.4-0.7 Torr flow tube anion source increases the observed relative population of this excited triplet state among the sampled anions, evidently slowing its relaxation to the singlet ground state. A (2)A(2)(") excited state of Al(3) lies 0.192+/-0.004 eV above the ground state and has frequencies of 315+/-15 (nu(1)) and 197+/-10 cm(-1) (nu(2)) and bonds 0.10+/-0.03 A longer than in the ground state. A (4)A(2) Al(3) excited state at 0.300+/-0.004 eV displays 315+/-15 (nu(1)) and 140+/-10 cm(-1) (nu(2)) vibrational frequencies. The Franck-Condon analysis of this state, which is accessed only from the (3)B(2) anion, indicates a C(2v) structure with a 69+/-2 degree apex bond angle and bonds 0.06+/-0.02 A longer than in the ground state. A (2)B(2) Al(3) excited state at 0.706+/-0.005 eV is also accessed from the (3)B(2) anion. The lack of vibrational features observable over overlapping transitions indicates similar structures for the (2)B(2) and (3)B(2) states. Primary stretching force constants (mdyn/A) are reported for the Al(3)(-) (0.70+/-0.06) and Al(3) (0.63+/-0.04) ground states and for three excited states. In the following paper, computational predictions for the ground and excited states of Al(3)(-) and Al(3) are reported and compared with these results.

Mathematical aspects of vacuum energy on quantum graphs

We use quantum graphs as a model to study various mathematical aspects of the vacuum energy, such as convergence of periodic path expansions, consistency among different methods (trace formulae versus method of images) and the possible connection with the underlying classical dynamics. In our study we derive an expansion for the vacuum energy in terms of periodic paths on the graph and prove its convergence and smooth dependence on the bond lengths of the graph. For an important special case of graphs with equal bond lengths, we derive a simpler explicit formula. With minor changes this formula also applies to graphs with rational (up to a common factor) bond lengths. The main results are derived using the trace formula. We also discuss an alternative approach using the method of images and prove that the results are consistent. This may have important consequences for other systems, since the method of images, unlike the trace formula, includes a sum over special ‘bounce paths’. We succeed in showing that in our model bounce paths do not contribute to the vacuum energy. Finally, we discuss the proposed possible link between the magnitude of the vacuum energy and the type (chaotic versus integrable) of the underlying classical dynamics. Within a random matrix model we calculate the variance of the vacuum energy over several ensembles and find evidence that the level repulsion leads to suppression of the vacuum energy.

Geometric Model for Boron Nitride Nanotubes Incorporating Curvature

The conventional rolled-up model of nanotubes does not apply to the very small radii tubes, for which curvature effects become significant. Here, an existing geometric model for carbon nanotubes that has been proposed by the authors, which accommodates this deficiency and is based on the exact polyhedral cylindrical structure, is extended to a nanotube structure involving two species of atoms in equal proportion, and, in particular, boron nitride nanotubes. This generalization allows the principle features to be included as the fundamental assumptions of the model, such as equal bond length but distinct bond angles and radii between the two species. Working from five simple geometric assumptions, expressions are derived for the various structural parameters such as radii and bond angles for the two species for specific values of the chiral vector numbers (n, m). The new model incorporates an additional constant of proportionality (τ), which we assume applies to all nanotubes comprising the same elements a...

DOUBLE FJORD MOTIF IN OVERCROWDED LARGE POLYCYCLIC AROMATIC HYDROCARBONS: THE CONFORMATIONAL SPACE OF HEXABENZO[a,cd,f,j,lm,o]PERYLENE

The overcrowded large polycyclic aromatic hydrocarbon (LPAH) hexabenzo[a,cd,f,j,lm,o]perylene (HBP) was subjected to a theoretical study. The ab-initio Hartree-Fock (HF) and the density functional theory (DFT) B3LYP methods were employed to calculate energies and geometries of the stationary point conformations of HBP. The global minimum was found to be the twisted t-D 2 ; the local minimum anti-folded a-C 2h was 20.5 kJ/mol higher in energy (B3LYP/6-31G(d)). Thus, only t-D 2 -HBP exists at room temperature in solution. The enantiomerization of HBP proceeds via a pathway that connects the chiral t-D 2 to the achiral a-C 2h through a chiral twisted-folded transition state, tf-C 1 . The energy barrier for enantiomerization was 134.4 kJ/mol. The central benzene ring F of t -D 2 is highly distorted from planarity (torsion angles of 15.4° and −30.5°), and has a remarkable resemblance to the twist angle of the central ene in the parent BAE bifluorenylidene (32°). Yet, nucleus-independent chemical shift (NICS) values, calculated at GIAO-B3LYP/6-31G(d)//B3LYP/6-31G(d) and the almost equal bond lengths (ca. 142 pm) of the central ring are indicative of the aromatic character of this ring. The NICS values are also indicative of the aromatic character of the peripheral rings and the central rings of the two minima and the transition state, consistent with the Clar picture.

Electrochemical synthesis and characterization of conducting polymers using room temperature melt as an electrolyte

Aromatic monomers can be polymerised using the chloroaluminate room temperature melt obtained by mixing 1:2 ratio of cetyl pyridinium chloride and anhydrous aluminium chloride miscible in all proportions with organic solvents as an electrolyte. The chloroaluminate (AlCl 4 −) anion generated in this melt having a tetrahedral symmetry with equal bond lengths and bond angles is the dopant to stabilize macrocation generated near the vicinity of anode to yield better conducting and better ordered electronically conducting free standing polymer film. In this communication, we discuss the polymers derived from benzene and pyrrole and their characterization by various techniques.

Effect of electron-phonon coupling on the conductance of a one-dimensional molecular wire

The effect of inelastic scattering, particularly that of the electron-phonon interactions, on the current-voltage characteristics of a one-dimensional tight-binding molecular wire has been investigated. The wire has been modeled using the Su-Schreiffer-Heeger Hamiltonian and we compute the current using the Landauer's scattering formalism. Our calculations show that the presence of strong electron-lattice coupling in the wire can induce regions of negative differential resistance (NDR) in the I-V curves. The reasons for this can be traced back to the quasidegeneracy in few of the low-energy molecular levels in the presence of electron-phonon coupling and an external applied bias. The molecular levels become highly delocalized at the critical bias at which the NDR is seen, corresponding to the vanishing of the electron-phonon coupling with equal bond lengths.

Aromaticity of four-membered-ring 6pi-electron systems: N2S2 and Li2C4H4.

N(2)S(2) is a four-membered-ring system with 6pi electrons. While earlier proposals considered N(2)S(2) to be aromatic, recent electronic structure calculations claimed that N(2)S(2) is a singlet diradical. Our careful reexamination does not support this assertion. N(2)S(2) is closed shell and aromatic since it satisfies all three generally accepted criteria for aromaticity: energetic (stability), structural (planarity with equal bond lengths), and magnetic (negative nucleus-independent chemical shift due to the pi electrons). These characteristics as well as the electronic structure of N(2)S(2) are compared with those for an isoelectronic pi system, Li(2)C(4)H(4), motivated by theoretical and recent experimental investigations that confirmed its aromaticity. However, N(2)S(2) and Li(2)C(4)H(4) are both essentially 2pi-electron aromatic systems with a formal N-S (C-C) bond order of 1.25 even though they both have 6pi electrons. This is because four of the six pi electrons occupy the nonbonding pi HOMOs and only two electrons participate effectively in the aromatic stabilization. However, wave function analysis shows relatively large LUMO occupation numbers; this antibonding effect can be said to reduce the aromatic character by approximately 7% and 4% for N(2)S(2) and Li(2)C(4)H(4), respectively.