The response of the electronic structure to electronic excitation and double bond torsion in fulvene: a combined QTAIM, stress tensor and MO perspective

Warning! The negative divergence of the stress-tensor does not always yield the Ehrenfest force

It has been assumed that the negative divergence of all stress tensors in common use yields the same force. This work finds that this is untrue, and, in fact, can vary wildly. We demonstrate this for the hydrogen atom, the one-particle isotropic harmonic oscillator, and a particle in an infinite spherical well where the exact density, pair-density, and the first order reduced density matrix are known for ground and excited states without any approximation. The Ehrenfest stress-tensor is introduced as any stress-tensor whose negative divergence will yield the corresponding Ehrenfest force for the same system when the exact wave-function is utilized. Stress-tensors within the literature are examined to show those that are Ehrenfest stress-tensors. Those that differ are demonstrated by how they differ within an exact formulation. The proof that the negative divergence of an Ehrenfest stress-tensor yields the Ehrenfest force is summarized.

Anticancer Activities of Re(I) Tricarbonyl and Its Imidazole-Based Ligands: Insight from a Theoretical Approach

Rhenium complexes have been observed experimentally to exhibit good inhibitory activity against malignant cells. Hence, our motivation is to explore this activity from a theoretical perspective. In the present study, density functional theory (DFT) and in silico molecular docking approaches were utilized to unravel the unique properties of metal-based rhenium tricarbonyl complexes as effective anticancer drugs. All DFT calculations and geometric optimizations were conducted using the well-established hybrid functional B3LYP-GD(BJ)/Gen/6-311++G(d,p)/LanL2DZ computational method. The FT-IR spectroscopic characterization of the complexes: fac-[Re(Pico)(CO)₃(Pz)] (R1), fac-[Re(Pico)(CO)₃(Py)] (R2), fac-[Re(Dfpc)(CO)₃(H₂O)] (R3), fac-[Re(Dfpc)(CO)₃(Pz)] (R4), fac-[Re(Dfpc)(CO)₃(Py)] (R5), fac-[Re(Tfpc)(CO)₃(H₂O)] (R6), fac-[Re(Tfpc)(CO)₃(Py)] (R7), and fac-[Re(Tfpc)(CO)₃(Im)] (R8) was explored. To gain insights into the electronic structural properties, bioactivity, and stability of these complexes, the highest occupied molecular orbital-lowest unoccupied molecular orbital analysis, binding energy, and topological analysis based on quantum theory of atoms-in-molecules were considered. The anticancer activities of the complexes were measured via in silico molecular docking against human BCL-2 protein (IG5M) and proapoptotic (agonist) BAX 1 protein (450O). The results showed that the studied complexes exhibited good binding affinity (-3.25 to -10.16 kcal/mol) and could cause significant disruption of the normal physiological functions of the studied proteins. The results of DFT calculations also showed that the studied complexes exhibited good stability and are suitable candidates for the development of anticancer agents.

EDA-NOCV analysis of carbene-borylene bonded dinitrogen complexes for deeper bonding insight: A fair comparison with a metal-dinitrogen system

Binding of dinitrogen (N₂ ) to a transition metal center (M) and followed by its activation under milder conditions is no longer impossible; rather, it is routinely studied in laboratories by transition metal complexes. In contrast, binding of N₂ by main group elements has been a challenge for decades, until very recently, an exotic cAAC-borylene (cAAC = cyclic alkyl(amino) carbene) species showed similar binding affinity to kinetically inert and non-polar dinitrogen (N₂ ) gas under ambient conditions. Since then, N₂ binding by short lived borylene species has made a captivating news in different journals for its unusual features and future prospects. Herein, we carried out different types of DFT calculations, including EDA-NOCV analysis of the relevant cAAC-boron-dinitrogen complexes and their precursors, to shed light on the deeper insight of the bonding secret (EDA-NOCV = energy decomposition analysis coupled with natural orbital for chemical valence). The hidden bonding aspects have been uncovered and are presented in details. Additionally, similar calculations have been carried out in comparison with a selected stable dinitrogen bridged-diiron(I) complex. Singlet cAAC ligand is known to be an exotic stable species which, combined with the BAr group, produces an intermediate singlet electron-deficient (cAAC)(BAr) species possessing a high lying HOMO suitable for overlapping with the high lying π*-orbital of N₂ via effective π-backdonation. The BN₂ interaction energy has been compared with that of the FeN₂ bond. Our thorough bonding analysis might answer the unasked questions of experimental chemists about how boron compounds could mimic the transition metal of dinitrogen binding and activation, uncovering hidden bonding aspects. Importantly, Pauling repulsion energy also plays a crucial role and decides the binding efficiency in terms of intrinsic interaction energy between the boron-center and the N₂ ligand.

Bonding and stability of dinitrogen-bonded donor base-stabilized Si(0)/Ge(0) species [(cAACMe-Si/Ge)2(N2)]: EDA-NOCV analysis

Recently, dinitrogen (N₂) binding and its activation have been achieved by non-metal compounds like intermediate cAAC-borylene as (cAAC)₂(B-Dur)₂(N₂) [cAAC = cyclic alkyl(amino) carbene; Dur = aryl group, 2,3,5,6-tetramethylphenyl; B-Dur = borylene]. It has attracted a lot of scientific attention from different research areas because of its future prospects as a potent species towards the metal free reduction of N₂ into ammonia (NH₃) under mild conditions. Two (cAAC)(B-Dur) units, each of which possesses six valence electrons around the B-centre, are shown to accept σ-donations from the N₂ ligand (B ← N₂). Two B-Dur further provide π-backdonations (B → N₂) to a central N₂ ligand to strengthen the B–N₂–B bond, providing maximum stability to the compound (cAAC)₂(B-Dur)₂(N₂) since the summation of each pair wise interaction accounted for the total stabilization energy of the molecule. (cAAC)(B-Dur) unit is isolobal to cAAC–E (E = Si, Ge) fragment. Herein, we report on the stability and bonding of cAAC–E bonded N₂-complex (cAAC–E)₂(N₂) (1–2; Si, Ge) by NBO, QTAIM and EDA-NOCV analyses (EDA-NOCV = energy decomposition analysis coupled with natural orbital for chemical valence; QTAIM = quantum theory of atoms in molecule). Our calculation suggested that syntheses of elusive (cAAC–E)₂(N₂) (1–2; Si, Ge) species may be possible with cAAC ligands having bulky substitutions adjacent to the C_cAAC atom by preventing the homo-dimerization of two (cAAC)(E) units which can lead to the formation of (cAAC–E)₂. The formation of E Created by potrace 1.16, written by Peter Selinger 2001-2019 ]]> E bond is thermodynamically more favourable (E = Si, Ge) over binding energy of N₂ inbetween two cAAC–E units.

Dinitrogen (N₂) binding and its activation have been achieved by non-metal compounds like intermediate cAACborylene with the general formula of (cAAC)₂(B-Dur)₂(N₂) [cAAC = cyclic alkyl(amino)carbene; Dur = aryl group, 2,3,5,6-tetramethylphenyl; B-Dur = aryl-borylene].

Interatomic exchange-correlation interaction energy from a measure of quantum theory of atoms in molecules topological bonding: A diatomic case

The potential relations between the measure of topological interatomic bonding-integrals of electron density with respect to internuclear axis over the corresponding quantum theory of atoms in molecules (QTAIM)-defined interatomic surface (IAS)-and interatomic exchange-correlation contributions from the interacting quantum atoms approach are discussed. The quantum chemical computations of 38 equilibrium diatomic systems at different levels of theory (HF, MP2, MP4SDQ, and CCSD) are invoked to support abstract considerations. Parameters of excellent correlations between IAS integrals and interatomic exchange-correlation energy are found by the optimization. The performance of these trends depends on the accuracy of the electronic correlation treatment. The resulting trends are a unique feature of equilibrium states, whereas more complicated dependencies are explored for several systems at non-equilibrium conditions. The relations of established trends with other IAS-based estimations of strength of bonding interactions between topological atoms and issues explored for multiatomic systems are briefly discussed.

Stress Tensor Eigenvector Following with Next-Generation Quantum Theory of Atoms in Molecules: Excited State Photochemical Reaction Path from Benzene to Benzvalene

In this investigation, we considered both the scalar and 3-D vector-based measures of bonding using next generation quantum theory of atoms in molecules (QTAIM), constructed from the preferred direction of electronic charge density accumulation, to better understand the photochemical reaction associated with of the formation of benzvalene from benzene. The formation of benzvalene from benzene resulted in two additional C-C bonds forming compared with the benzene. The creation of the additional C-C bonds was explained in terms of an increasing the favorability of the reaction process by maximizing the bonding density. The topological instability of the benzvalene structure was determined using the scalar and vector-based measures to explain the short chemical half-life of benzvalene in terms of the competition between the formation of unstable new C-C bonding that also destabilizes nearest neighbor C-C bonds. The explosive character of benzvalene is indicated by the unusual tendency of the C-C bonds to rupture as easily as weak bonding. The topological instability of the short strong C-C bonds was explained by the existence of measures from conventional and next generation QTAIM that previously have only been observed in weak interactions; such measures included twisted 3-D bonding descriptors.

An overview of the cycloaddition chemistry of fulvenes and emerging applications

The unusual electronic properties and unique reactivity of fulvenes have interested researchers for over a century. The propensity to form dipolar structures at relatively low temperatures and to participate as various components in cycloaddition reactions, often highly selectively, makes them ideal for the synthesis of complex polycyclic carbon scaffolds. As a result, fulvene cycloaddition chemistry has been employed extensively for the synthesis of natural products. More recently, fulvene cycloaddition chemistry has also found application to other areas including materials chemistry and dynamic combinatorial chemistry. This highlight article discusses the unusual properties of fulvenes and their varied cycloaddition chemistry, focussing on applications in organic and natural synthesis, dynamic combinatorial chemistry and materials chemistry, including dynamers, hydrogels and charge transfer complexes. Tables providing comprehensive directories of fulvene cycloaddition chemistry are provided, including fulvene intramolecular and intermolecular cycloadditions complete with reactant partners and their resulting cyclic adducts, which provide a useful reference source for synthetic chemists working with fulvenes and complex polycyclic scaffolds.

Halogen and Hydrogen Bonding in Halogenabenzene/NH3 Complexes Compared Using Next-Generation QTAIM

Next-generation quantum theory of atoms in molecules (QTAIM) was used to investigate the competition between hydrogen bonding and halogen bonding for the recently proposed (Y = Br, I, At)/halogenabenzene/NH3 complex. Differences between using the SR-ZORA Hamiltonian and effective core potentials (ECPs) to account for relativistic effects with increased atomic mass demonstrated that next-generation QTAIM is a much more responsive tool than conventional QTAIM. Subtle details of the competition between halogen bonding and hydrogen bonding were observed, indicating a mixed chemical character shown in the 3-D paths constructed from the bond-path framework set B. In addition, the use of SR-ZORA reduced or entirely removed spurious features of B on the site of the halogen atoms.

The destabilization of hydrogen bonds in an external E-field for improved switch performance

The effect of an electric field on a recently proposed molecular switch based on a quinone analogue was investigated using next-generation quantum theory of atoms in molecules (QTAIM) methodology. The reversal of a homogenous external electric field was demonstrated to improve the "OFF" functioning of the switch. This was achieved by destabilization of the H atom participating in the tautomerization process along the hydrogen bond that defines the switch. The "ON" functioning of the switch, from the position of the tautomerization barrier, is also improved by the reversal of the homogenous external electric field: this result was previously inaccessible. The "ON" and "OFF" functioning of the switch was visualized in terms of the response of the most preferred directions of motion of the electronic charge density to the applied external field. All measures from QTAIM and the stress tensor provide consistent results for the factors affecting the "ON" and "OFF" switch performance. Our analysis therefore demonstrates use for future design of molecular electronic devices. © 2019 Wiley Periodicals, Inc.

Exploration of the forbidden regions of the Ramachandran plot (ϕ-ψ) with QTAIM

A new QTAIM interpretation of the Ramachandran plot is formulated from the most and least facile eigenvectors of the second-derivative matrix of the electron density with a set of 29 magainin-2 peptide conformers. The presence of QTAIM eigenvectors associated with the most and least preferred directions of electronic charge density explained the role of hydrogen bonding, HH contacts and the glycine amino acid monomer in peptide folding. The highest degree of occupation of the QTAIM interpreted Ramachandran plot was found for the glycine amino acid monomer compared with the remaining backbone peptide bonds. The mobility of the QTAIM eigenvectors of the glycine amino acid monomer was higher than for the other amino acids and was comparable to that of the hydrogen bonding, explaining the flexibility of the magainin-2 backbone. We experimented with a variety of hybrid QTAIM-Ramachandran plots to highlight and explain why the glycine amino acid monomer largely occupies the 'forbidden' region on the Ramachandran plot. In addition, the new hybrid QTAIM-Ramachandran plots contained recognizable regions that can be associated with concepts familiar from the conventional Ramachandran plot whilst retaining the character of the QTAIM most and least preferred regions.

A new twist in the photophysics of the GFP chromophore: a volume-conserving molecular torsion couple

Dynamics of a nonplanar GFP chromophore are studied experimentally and theoretically. Coupled torsional motion is responsible for the ultrafast decay.

The simple structure of the chromophore of the green fluorescent protein (GFP), a phenol and an imidazolone ring linked by a methyne bridge, supports an exceptionally diverse range of excited state phenomena. Here we describe experimentally and theoretically the photochemistry of a novel sterically crowded nonplanar derivative of the GFP chromophore. It undergoes an excited state isomerization reaction accompanied by an exceptionally fast (sub 100 fs) excited state decay. The decay dynamics are essentially independent of solvent polarity and viscosity. Excited state structural dynamics are probed by high level quantum chemical calculations revealing that the fast decay is due to a conical intersection characterized by a twist of the rings and pyramidalization of the methyne bridge carbon. The intersection can be accessed without a barrier from the pre-twisted Franck–Condon structure, and the lack of viscosity dependence is due to the fact that the rings twist in the same direction, giving rise to a volume-conserving decay coordinate. Moreover, the rotation of the phenyl, methyl and imidazolone groups is coupled in the sterically crowded structure, with the methyl group translating the rotation of one ring to the next. As a consequence, the excited state dynamics can be viewed as a torsional couple, where the absorbed photon energy leads to conversion of the out-of-plane orientation from one ring to the other in a volume conserving fashion. A similar modification of the range of methyne dyes may provide a new family of devices for molecular machines, specifically torsional couples.

Theoretical study of non-Hammett vs. Hammett behaviour in the thermolysis and photolysis of arylchlorodiazirines

Calculations show that the different Hammett behaviour of arylchlorodiazirines is due to different mechanisms in the ground and excited state.

QTAIM and Stress Tensor Characterization of Intramolecular Interactions Along Dynamics Trajectories of a Light-Driven Rotary Molecular Motor

A quantum theory of atoms in molecules (QTAIM) and stress tensor analysis was applied to analyze intramolecular interactions influencing the photoisomerization dynamics of a light-driven rotary molecular motor. For selected nonadiabatic molecular dynamics trajectories characterized by markedly different S₁ state lifetimes, the electron densities were obtained using the ensemble density functional theory method. The analysis revealed that torsional motion of the molecular motor blades from the Franck-Condon point to the S₁ energy minimum and the S₁/S₀ conical intersection is controlled by two factors: greater numbers of intramolecular bonds before the hop-time and unusually strongly coupled bonds between the atoms of the rotor and the stator blades. This results in the effective stalling of the progress along the torsional path for an extended period of time. This finding suggests a possibility of chemical tuning of the speed of photoisomerization of molecular motors and related molecular switches by reshaping their molecular backbones to decrease or increase the degree of coupling and numbers of intramolecular bond critical points as revealed by the QTAIM/stress tensor analysis of the electron density. Additionally, the stress tensor scalar and vector analysis was found to provide new methods to follow the trajectories, and from this, new insight was gained into the behavior of the S₁ state in the vicinity of the conical intersection.

Proton-Gated Photoisomerization of Amino-Substituted Dibenzofulvene Rotors

Derivatives of 9-(2,2,2-triphenylethylidene)-fluorene (TEF) undergo E/Z photoisomerization and are candidates for light-powered molecular actuators and switches. The 2-substituted derivatives bearing an amino group (ATEF) or a dimethylamino group (DTEF) are weakly photoactive in the absence of acids, but protonation increases photoisomerization quantum yields by factors of 30-60. Such compounds may be useful for incorporation into pH-switchable photoactive devices.

A QTAIM and stress tensor investigation of the torsion path of a light-driven fluorene molecular rotary motor

The utility of the QTAIM/stress tensor analysis method for characterizing the photoisomerization of light driven molecular rotary machines is investigated on the example of the torsion path in fluorene molecular motor. The scalar and vector descriptors of QTAIM/stress tensor reveal additional information on the bonding interactions between the rotating units of the motor, which cannot be obtained from the analysis of the ground and excited state potential energy surfaces. The topological features of the fluorene motor molecular graph display that, upon the photoexcitation a certain increase in the torsional stiffness of the rotating bond can be attributed to the increasing topological stability of the rotor carbon atom attached to the rotation axle. The established variations in the torsional stiffness of the rotating bond may cause transfer of certain fraction of the torsional energy to other internal degrees of freedom, such as the pyramidalization distortion. © 2016 Wiley Periodicals, Inc.

A stress tensor and QTAIM perspective on the substituent effects of biphenyl subjected to torsion

The Quantum Theory of Atoms in Molecules (QTAIM) defines quantities in 3D space that can be easily obtained from routine quantum chemical calculations. The present investigation shows that local properties can be related quantitatively to measures traditionally connected to experimental data, such as Hammett constants. We consider the specific case of substituted biphenyl to quantify the effects of a torsion φ, 0.0° ≤ φ ≤ 180.0°, of the C-C bond linking the two phenyl rings for C12 H9 -x, where x = N(CH3 )2 , NH2 , CH3 , CHO, CN, NO2, on the entire molecule. QTAIM interpreted Hammett constants, aΔH(rb ) are introduced and constructed using the difference between the H(rb ) value of C12 H9 -x and the C12 H9 -H, biphenyl which is the reference molecule, with a constant of proportionality a. This investigation unexpectedly yields very good or good agreement for the x groups with the Hammett para-, meta-, and ortho-substituent constants and is checked against para-substituted benzene. We then proceed to present the interpreted substituent constants of seven new biphenyl substituent groups, where tabulated Hammett substituent constant values are not available; y = SiH3 , ZnCl, COOCH3 , SO2 NH2 , SO2 OH, COCl, CB3 . Consistency is found for the QTAIM interpreted biphenyl substituent constants of the seven new groups y independently using the stress tensor polarizability Pσ . In addition, a selection of future applications is discussed that highlight the usefulness of this approach. © 2016 Wiley Periodicals, Inc.

Synthesis and Photoisomerization of Substituted Dibenzofulvene Molecular Rotors

The synthesis, spectral and structural characterization, and photoisomerization of a family of 2-substituted dibenzofulvene molecular actuators based on (2,2,2-triphenylethylidene)fluorene (TEF) are reported. The 2-substituted species investigated are nitro (NTEF), cyano (CTEF), and iodo (ITEF). X-ray structures of these three compounds and three intermediates were determined to assign alkene configuration and investigate the effects of the 2-substituents on steric gearing. The addition-elimination reaction of Z-9 with trityl anion to form Z-10 proceeded with complete retention of configuration. Rates of photoisomerization were measured at irradiation wavelengths between 266-355 nm in acetonitrile/dioxane solutions at room temperature. Photoisomerization quantum yields (φ) were calculated by means of a mathematical model that accounts for a certain degree of photodecomposition in the cases of CTEF and ITEF. Quantum yields vary significantly with substituent, having maximum values of φ=0.26 for NTEF, 0.39 for CTEF, and 0.50 for ITEF. NTEF is photochemically robust and has a large quantum yield for photoisomerization in the near-UV, making it a particularly promising drive rotor moiety for light-powered molecular devices.

Seeking small molecules for singlet fission: a heteroatom substitution strategy

We design theoretically small molecule candidates for singlet fission chromophores, aiming to achieve a balance between sufficient diradical character and kinetic persistence. We develop a perturbation strategy based on the captodative effect to introduce diradical character into small π-systems. Specifically, this can be accomplished by replacing pairs of not necessarily adjacent C atoms with isoelectronic and isosteric pairs of B and N atoms. Three rules of thumb emerge from our studies to aid further design: (i) Lewis structures provide insight into likely diradical character; (ii) formal radical centers of the diradical must be well-separated; (iii) stabilization of radical centers by a donor (N) and an acceptor (B) is essential. Following the rules, we propose candidate molecules. Employing reliable multireference calculations for excited states, we identify three likely candidate molecules for SF chromophores. These include a benzene, a napthalene, and an azulene, where four C atoms are replaced by a pair of B and a pair of N atoms.

Photochemistry and photophysics at extended seams of conical intersection

The role of extended seams of conical intersection in excited-state mechanisms is reviewed. Seams are crossings of the potential energy surface in many dimensions where the decay from the excited to the ground state can occur, and the extended seam is composed of different segments lying along a reaction coordinate. Every segment is associated with a different primary photoproduct, which gives rise to competing pathways. This idea is first illustrated for fulvene and ethylene, and then it is used to explain more complex cases such as the dependence of the isomerisation of retinal chromophore isomers on the protein environment, the dependence of the efficiency of the azobenzene photochemical switch on the wavelength of irradiation and the direction of the isomerisation, and the coexistence of different mechanisms in the photo-induced Wolff rearrangement of diazonaphthoquinone. The role of extended seams in the photophysics of the DNA nucleobases and the relationship between two-state seams and three-state crossings is also discussed. As an outlook, the design of optical control strategies based on the passage of the excited molecule through the seam is considered, and it is shown how the excited-state lifetime of fulvene can be modulated by shaping the energy of the seam.