Response of the mechanical and chiral character of ethane to ultra-fast laser pulses.

A pair of simulated left and right circularly polarized ultra-fast laser pulses of duration 20 femtoseconds that induce a mixture of excited states are applied to ethane. The response of the electron dynamics is investigated within the next generation quantum theory of atoms in molecules (NG-QTAIM) using third-generation eigenvector-trajectories which are introduced in this work. This enables an analysis of the mechanical and chiral properties of the electron dynamics of ethane without needing to subject the C-C bond to external torsions as was the case for second-generation eigenvector-trajectories. The mechanical properties, in particular, the bond-flexing and bond-torsion were found to increase depending on the plane of the applied laser pulses. The bond-flexing and bond-torsion, depending on the plane of polarization, increases or decreases after the laser pulses are switched off. This is explainable in terms of directionally-dependent effects of the long-lasting superpositions of excited states. The chiral properties correspond to the ethane molecule being classified as formally achiral consistent with previous NG-QTAIM investigations. Future planned investigations using ultra-fast circularly polarized lasers are briefly discussed.

Tools for overcoming reliance on energy-based measures in chemistry: a tutorial review.

The vast majority of literature in the chemical sciences describes fundamental chemical and physical phenomena using scalar measures, such as the energy, even though many phenomena are beyond the scope of scalar-based considerations. This problem exists no matter how accurately the associated energies are calculated. The solution that is explained in this work is to remove the reliance on scalar quantum chemical measures and instead utilize the vector-based and full symmetry-breaking nature of next generation quantum theory of atoms in molecules (NG-QTAIM). The connection with experiment on neutral chiral molecules is explained. A selection of non-energy-based explanations are provided: the functioning of molecular devices, why the cis-effect is the exception rather than the rule, stereochemical phenomena including chiral discrimination, quantifying chiral character of formally achiral molecules, mixed S and R stereoisomer character and the effect of an applied electric field. Current and future developments along with suggestions for future avenues of investigation are discussed. This tutorial review provides the practical details required to implement NG-QTAIM for a range of phenomena that are not accessible with energy-based measures. Step-by-step worked examples are included with data sets and instructions for use of commercial and open-source software along with examples of how to interpret the results.

Scoring molecular wires subject to an ultrafast laser pulse for molecular electronic devices.

A nonionizing ultrafast laser pulse of 20-fs duration with a peak amplitude electric-field ±E = 200 × 10-4 a.u. was simulated. It was applied to the ethene molecule to consider its effect on the electron dynamics, both during the application of the laser pulse and for up to 100 fs after the pulse was switched off. Four laser pulse frequencies ω = 0.2692, 0.2808, 0.2830, and 0.2900 a.u. were chosen to correspond to excitation energies mid-way between the (S1 ,S2 ), (S2 ,S3 ), (S3 ,S4 ) and (S4 ,S5 ) electronic states, respectively. Scalar quantum theory of atoms in molecules (QTAIM) was used to quantify the shifts of the C1C2 bond critical points (BCPs). Depending on the frequencies ω selected, the C1C2 BCP shifts were up to 5.8 times higher after the pulse was switched off compared with a static E-field with the same magnitude. Next generation QTAIM (NG-QTAIM) was used to visualize and quantify the directional chemical character. In particular, polarization effects and bond strengths, in the form of bond-rigidity vs. bond-flexibility, were found, for some laser pulse frequencies, to increase after the laser pulse was switched off. Our analysis demonstrates that NG-QTAIM, in partnership with ultrafast laser irradiation, is useful as a tool in the emerging field of ultrafast electron dynamics, which will be essential for the design, and control of molecular electronic devices.

Next generation quantum theory of atoms in molecules for the design of emitters exhibiting thermally activated delayed fluorescence with laser irradiation.

The effect of a static electric (E)-field and an unchirped and chirped laser pulse field on the cycl[3.3.3]azine molecule was investigated using next-generation quantum theory of atoms in molecules (NG-QTAIM). Despite the magnitude of the E-field of the laser pulses being an order of magnitude lower than for the static E-field, the variation of the energy gap between the lowest lying singlet (S1 ) and triplet (T1 ) excited states was orders of magnitude greater for the laser pulse than for the static E-field. Insights into the response of the electronic structure were captured by NG-QTAIM, where differences in the inverted singlet-triplet gap due to the laser pulses were significant larger compared to those induced by the static E-field. The response of the S1 and T1 excited states, as determined by NG-QTAIM, switched discontinuously between weak and strong chemical character for the static E-field. In contrast, the response to the laser pulses, determined by NG-QTAIM, is to induce a continuous range of chemical character, indicating the unique ability of the laser pulses to induce polarization effects in the form of "mixed" bond types. Our analysis demonstrates that NG-QTAIM is a useful tool for understanding the response to laser irradiation of the lowest-lying singlet S1 and triplet T1 excited states of emitters exhibiting thermally activated delayed fluorescence. The chirped laser pulse led to more frequent instances of the desired outcome of an inverted singlet-triplet gap than the unchirped pulse, indicating its usefulness as a tool to design more efficient organic light-emitting diode devices.

The Cis-Effect Explained Using Next-Generation QTAIM.

We used next-generation QTAIM (NG-QTAIM) to explain the cis-effect for two families of molecules: C2X2 (X = H, F, Cl) and N2X2 (X = H, F, Cl). We explained why the cis-effect is the exception rather than the rule. This was undertaken by tracking the motion of the bond critical point (BCP) of the stress tensor trajectories Tσ(s) used to sample the Uσ-space cis- and trans-characteristics. The Tσ(s) were constructed by subjecting the C1-C2 BCP and N1-N2 BCP to torsions ± θ and summing all possible Tσ(s) from the bonding environment. During this process, care was taken to fully account for multi-reference effects. We associated bond-bending and bond-twisting components of the Tσ(s) with cis- and trans-characteristics, respectively, based on the relative ease of motion of the electronic charge density ρ(rb). Qualitative agreement is found with existing experimental data and predictions are made where experimental data is not available.

Chirality without Stereoisomers: Insight from the Helical Response of Bond Electrons.

The association between molecular chirality and helical characteristics known as the chirality-helicity equivalence is determined for the first time by quantifying a chirality-helicity measure consistent with photoexcitation circular dichroism experiments. This is demonstrated using a formally achiral SN 2 reaction and a chiral SN 2 reaction. Both the achiral and chiral SN 2 reactions possess significant values of the chirality-helicity measure and display a Walden inversion, i. e. an inversion of the chirality between the reactant and product. We also track the chirality-helicity measure along the reaction path and discover the presence of chirality at the transition state and two intermediate structures for both reactions. We demonstrate the need for the chirality-helicity measure to differentiate between steric effects due to eclipsed conformations and chiral behaviors in formally achiral species. We explain the significance of this work for asymmetric synthetic reactions including the intermediate structures where the Cahn-Ingold-Prelog (CIP) rules cannot be used.

Next-generation QTAIM for scoring molecular wires in E-fields for molecular electronic devices.

The effect of a varying, directional E x , E y , and E z electric field on the ethene molecule was investigated using next-generation quantum theory of atoms in molecules (QTAIM). Despite using low E-field strengths that are within the realm of experiment and do not measurably alter the molecular geometry, significant changes to the QTAIM properties were observed. Using conventional QTAIM, the shifting of the C─C and C─H bond critical points (BCPs) demonstrates polarization through an interchange in the size of the atoms involved in a bond, since a BCP is located on the boundary between a pair of bonded atoms. Next-generation QTAIM, however, demonstrates the polarization effect more directly with a change in morphology of the 3-D envelope around the BCP. Modest increases of ≈ 2% in the ellipticity ε of the BCP were uncovered when the C─C bond was aligned parallel or anti-parallel to the applied E x -field. Significant asymmetries were found in the response of the next-generation QTAIM 3-D paths of the C─H bonds to the applied E-field. When the E-field coincided with the C─C bond, the BCP moved in response and was accompanied by the envelope constructed from 3-D next-generation paths. The response displayed a polarization effect that increased with increasing magnitude of the E x -field parallel and anti-parallel to the C─C bond. Our analysis demonstrates that next-generation QTAIM is a useful tool for understanding the response of molecules to E-fields, for example, for the screening of molecular wires for the design of molecular electronic devices. © 2019 Wiley Periodicals, Inc.

3-D bond-paths of QTAIM and the stress tensor in neutral lithium clusters, Lim (m = 2-5), presented on the Ehrenfest force molecular graph.

In this investigation we set out to understand the origins of non-nuclear attractors (NNAs) found for neutral lithium clusters Lim (m = 2-5) on the QTAIM molecular graph but not on the Ehrenfest force F(r) molecular graph. Therefore, we pursued the stress tensor σ(r) without using the dependency on the QTAIM partitioning, since previously σ(r) was only calculated within the QTAIM partitioning, to see if any indication of NNA character can be determined. Because the stress tensor σ(r) lacks an associated scalar- or vector-field as is the case for QTAIM and the Ehrenfest F(r) partitioning schemes respectively, a stress tensor σ(r) partitioning scheme cannot be constructed. Therefore, to overcome this difficulty we use next generation QTAIM, constructed from the most preferred directions of electronic charge density accumulation, to calculate the stress tensor σ(r) 3-D bond-paths on the Ehrenfest force F(r) molecular graph. Using next generation 3-D bond-paths within the Ehrenfest force F(r) partitioning, we can classify the degree of NNA character in the absence of NNAs. A much higher degree of NNA character is found to be present for the stress tensor σ(r) 3-D bond-paths than for the corresponding QTAIM or Ehrenfest force F(r) 3-D bond-paths. The stabilizing effect of the NNA is demonstrated by undertaking Li2 bond-path compression and stretching distortions sufficient to cause the annihilation of the NNA. The compression and stretching distortions also lead to a large increase in the 3-D bond-path asymmetry and persistent bond-path torsion respectively.

Intramolecular mode coupling of the isotopomers of water: a non-scalar charge density-derived perspective.

The H2O/D2O/HDO isotopomers of water are presented in terms that enable bond-flexing, bond-twist and bond-anharmonicity to be quantified during the bending (Q1), symmetric-stretch (Q2) and anti-symmetric-stretch (Q3) normal modes of vibration. Bond-flexing was detected by the presence of curved bonding and the bond-anharmonicity was detected by the presence of motion of the bond critical point (BCP) relative to the oxygen atom. These 2-D scalar measures are unable to fully describe the 3-D nature of the normal modes of vibration and therefore any susceptibility towards normal mode coupling, or to fully distinguish the three isotopomers. To detect bond-twist a vector-based measure was used, in the form of the bond critical point (BCP) trajectory, constructed in terms of preferred directions of electronic motion, defined by the variation of the position of the BCP during the normal modes of vibration. The BCP trajectories describe the coupling of the intramolecular bending and symmetric-stretch normal modes as well as distinguishing all three isotopomers within the harmonic approximation. The coupling of the bending and symmetric-stretch normal modes are suggested to be facilitated by the absence of bond-twist that would disrupt the coupling between Sigma O-H bonds and hydrogen-bonding. Partial coupling was found for the mixed isotopomer HDO.

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.

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.

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.

Non-nuclear attractors in small charged lithium clusters, Limq (m = 2-5, q = ±1), with QTAIM and the Ehrenfest force partitioning.

In this investigation we explore the function and existence of the non-nuclear attractor (NNA) for a series of small charged lithium clusters Limq (m = 2-5, q = ±1) using QTAIM and the Ehrenfest force F(r) partitioning schemes. The NNAs were found to be present in all of the Limq (m = 2-5, q = ±1) clusters for QTAIM, in contrast none were found for F(r). We discovered that the anionic and cationic lithium dimers are limiting cases for minimal and maximal impact of the NNA related to the relative sparseness of total charge density ρ(r) distributions respectively. Evidence is found that the NNA in the anionic dimer is in the process of being annihilated by two neighboring BCPs. We provide a measure of the size of the NNA and find for Limq (m = 2-5, q = ±1) that larger NNAs correlate with increased Li-Li separations. The NNA was determined to be a persistent feature by varying the Li separations for the cationic and anionic dimers. Very large Li separations failed to induce an NNA in the F(r) anionic dimer and therefore we conclude that F(r) is unable to detect NNAs. The metallicity ξ(rb) was also used to measure the sparseness of the distribution of ρ(r) and significant metallic character, on the basis of ξ(rb) > 1, was present for QTAIM but not for F(r), providing further evidence that F(r) cannot detect NNAs. Advantages of the use of Ehrenfest force F(r) partitioning scheme are discussed that include the design of nano-devices through tuning of the Ehrenfest potential VF(b) by the application of external forces such as a constant electric or strain field.

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.

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.

Distinguishing and quantifying the torquoselectivity in competitive ring-opening reactions using the stress tensor and QTAIM.

Currently the theories to explain and predict the classification of the electronic reorganization due to the torquoselectivity of a ring-opening reaction cannot accommodate the directional character of the reaction pathway; the torquoselectivity is a type of stereoselectivity and therefore is dependent on the pathway. Therefore, in this investigation we introduced new measures from quantum theory of atoms in molecules and the stress tensor to clearly distinguish and quantify the transition states of the inward (TSIC) and outward (TSOC) conrotations of competitive ring-opening reactions of 3-(trifluoromethyl)cyclobut-1-ene and 1-cyano-1-methylcyclobutene. We find the metallicity ξ(rb ) of the ring-opening bond does not occur exactly at the transition state in agreement with transition state theory. The vector-based stress tensor response ßσ was used to distinguish the effect of the CN, CH3 , and CF3 groups on the TSIC and TSOC paths that was consistent with the ellipticity ε, the total local energy density H(rb ) and the stress tensor stiffness Sσ . We determine the directional properties of the TSIC and TSOC ring-opening reactions by constructing a stress tensor UσTS space with trajectories TσTS (s) with length l in real space, longer l correlated with the lowest density functional theory-evaluated total energy barrier and hence will be more thermodynamically favored. © 2016 Wiley Periodicals, Inc.

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.

QTAIM and stress tensor interpretation of the (H2 O)5 potential energy surface.

Using the quantum theory of atoms in molecules a near complete combined directed spanning quantum topology phase diagram (QTPD) was constructed from the nine (H2 O)5 reaction-pathways and five unique Poincaré-Hopf solutions that were found after an extensive search of the MP2 potential energy surface. Two new energy minima that were predicted from earlier work are found and include the first (H2 O)5 conformer with a 3-DQT quantum topology. The stress tensor Poincaré-Hopf relation indicated a preference for 2-DQT (H2 O)5 topologies as well as the presence of coupling between shared-shell OH BCPs to the hydrogen-bond BCPs that share an H NCP. The complexity of the near complete combined QTPD was explained in terms of the O…O bonding interactions that were found in six of the nine (H2 O)5 reaction-pathways and for all points of the combined QTPD. The stabilizing role of the O…O bonding interactions from the values of the total local energy density was explored. © 2016 Wiley Periodicals, Inc.

Electronic stress as a guiding force for chemical bonding.

In the electron-preceding picture of chemical change, the paramount problem is identifying favorable changes in electronic structure. The electronic stress tensor provides this information; its eigenvectors represent electronic normal modes, pointing the way towards energetically favorable (or unfavorable) chemical rearrangements. The resulting method is well founded in both density functional theory and the quantum theory of atoms in molecules (QTAIM). Stress tensor analysis is a natural way to extend the QTAIM to address chemical reactivity. The definition and basic properties of the electronic stress tensor are reviewed and the inherent ambiguity of the stress tensor is discussed. Extending previous work in which the stress tensor was used to analyze hydrogen-bonding patterns, this work focuses on chemical bonding patterns in organic reactions. Other related material (charge-shift bonding, links to the second-density-derivative tensor) is summarized and reviewed. The stress tensor provides a multifaceted characterization of bonding and can be used to predict and describe bond formation and migration.