Attosecond science is an emerging topic, where chirality plays a central role. Here, we demonstrate subjecting iodoacetylene, a geometrically achiral molecule, to a pair of simulated nonionizing ultrafast circularly polarized laser pulses at the highest time resolution to date, by 2 orders of magnitude (3.87 attoseconds), of the continuously valued S and R electronic chirality assignments. We partner with the only vector-based quantum chemical physics theory enabling full symmetry-breaking with electronic and nuclear dynamics simulations: the former does not require charge density differences or special symmetry positions. The resulting "easy" and "hard" directions of the total electronic charge density motion are quantified as a cardioid-like morphology for the duration of the simulated laser pulses and toroidal afterward. Future research directions include determination of the underlying mechanism governing chiral-induced spin selectivity, in addition to application to chiral spin-selective phenomena in opto-spintronics and exotic superconductors, partnered with orbital-free density functional theory (OF-DFT).

We investigated crystalline Im-3m H3S at 200 GPa, a pressure regime where H3S is generally considered to be an exotic superconductor. Simulated circularly polarized 10 femtosecond (fs) laser pulses were applied and we quantified the effects on the electron dynamics during the application of "pump" and candidate "probe" laser pulses to discover optimal "probe" laser pulses. This is undertaken for the first application of Next Generation Quantum Theory of Atoms in Molecules (NG-QTAIM) using the Hessian of the "spin-up" and "spin-down" contributions to the total electronic charge density ρ(r). The optimal "probe" pulse was found to possess a peak electric field E = 10.0 × 10-4 a.u. compared with the "pump" pulse of E = 200.0 × 10-4 a.u. Separately considering the spin-up and spin-down contributions doubles the values of the chirality-helicity Chelicity function relative to that of the total charge density contribution for the H-H bonding for the application of the "pump" laser pulse. Within the NG-QTAIM interpretation, a combination of highly responsive and coherent behaviors is associated with superconductivity. These behaviors were discovered from the very high values of the Chelicity function, near-linear scaling of the bond-flexing F and bond-chirality C values with peak E-field and all instances of the H-H bonding possessing R electronic chirality assignments. The "pump" pulse was found to magnify the effects associated with superconductivity within the NG-QTAIM interpretation. Future applications are discussed including chiral spin selective phenomena and exotic high temperature superconductivity where phonons do not play a significant role.

We investigated Im-3m H3S at 200 GPa, a pressure regime where crystalline H3S is widely considered to be a superconductor. Simulated circularly polarized 10 femtosecond (fs) laser pulses were applied and we quantified the effects on the electron dynamics both during the application of the ultra-fast laser pulse and 5.0 fs after the pulse was switched off. In addition, the carrier-envelope phase (CEP) angle ϕ, which quantifies the relationship between the time-varying direction of electric (E)-field and the amplitude envelope, is employed to control the time evolution of the wavefunction ψ(r). This is undertaken for the first application of Next Generation Quantum Theory of Atoms in Molecules (NG-QTAIM) to the solid state. Ultra-fast phenomena related to superconductivity are discovered in the form of a geometric Berry phase angle associated with the H--H bonding in addition to very high values of the chirality–helicity function that correspond to values normally found in chiral molecules. Future applications are discussed, including chiral spin selective phenomena in addition to high-temperature superconductivity and organic superconductors where phonons do not play a significant role.

Simulated circularly -polarized 10 fs laser pulses that induce a mixture of excited states are applied to ethane. Additionally, the carrier -envelope phase (CEP) angle 0 , that quantifies the relationship between the time -varying direction of electric ( E ) -field and the amplitude envelope was used to manipulate the mechanical and chiral properties of ethane using Next Generation Quantum Theory of Atoms in Molecules (NG-QTAIM). The chirality assignments were reversed from S to R as the CEP angle 0 was increased from 0 = 0.0 degrees to 0 = 180 degrees . A one-to-one mapping between the CEP angle 0 and NG-QTAIM trajectories was discovered.

We investigate the construction of an ultra-fast laser probe to determine the response of the electron dynamics of ethane using next generation QTAIM (NG-QTAIM). This is undertaken by applying a pair of simulated left and right circularly polarized ultra-fast laser pulses of duration 10 fs. A proportional increase in the C-C BCP bond strain with peak electric field was discovered. NG-QTAIM was used to identify a characteristic morphology associated with ultra-fast laser probes. Candidate ultra-fast laser probes were selected on the basis of the ground state population remaining undisturbed at a time t = 15 fs.

The electron density determines all properties of a system of nuclei and electrons. It is both computable and observable. Its topology allows gaining insight into the mechanisms of bonding and other phenomena in a way that is complementary to and beyond that available from the molecular orbital picture and the formal oxidation state (FOS) formalism. The ability to derive mechanistic insight from electron density is also important with methods where orbitals are not available, such as orbital-free density functional theory (OF-DFT). While density topology-based analyses such as QTAIM (quantum theory of atoms-in-molecules) have been widely used, novel, vector-based techniques recently emerged such as next-generation (NG) QTAIM. Density-dependent quantities are also actively used in machine learning (ML)-based methods, in particular, for ML DFT functional development, including machine-learnt kinetic energy functionals. We review QTAIM and its recent extensions such as NG-QTAIM and localization-delocalization matrices (LDM) and their uses in the analysis of bonding, conformations, mechanisms of redox reactions excitations, as well as ultrafast phenomena. We review recent research showing that direct density analysis can circumvent certain pitfalls of the FOS formalism, in particular in the description of anionic redox, and of the widely used (spherically) projected density of states analysis. We discuss uses of density-based quantities for the construction of DFT functionals and prospects of applications of analyses of density topology to get mechanistic insight with OF-DFT and recently developed time-dependent OF-DFT.

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.

In this chapter we build on the work of Chap. 6 that introduced the eigenvector-Space Trajectories $${\mathsf{T}}$$ i(s); i = {σ, ρ, F} including chiral discrimination and apply to stereochemistry with the stress tensor trajectory $${\mathsf{T}}$$ σ(s) and the Hessian of ρ(r) trajectories $${\mathsf{T}}$$ (s).

The calculation of wavefunctionsWavefunction is central to the implementation of both scalar and vector-based quantum theory of atoms in molecules (QTAIM)Quantum theory of atoms in molecules (QTAIM) and will be overviewed in this chapter and forms the basis for the rest of this book.

This chapter bridges conventional QTAIM, developments of which were covered in Chap. 2 and Next Generation QTAIMNext Generation QTAIM (NG-QTAIM) that is presented in Chap. 4 and the subsequent chapters.

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.

In this chapter we present the NG-QTAIM representation of the chemical bond, the bond-path framework set $$\mathsf{B}$$ . The bond-path framework set $$\mathsf{B}$$ is constructed from the e1 and e2 eigenvectors, in contrast to conventional (scalar) QTAIM that is only constructed using the e3 eigenvector. Consequently, $$\mathsf{B}$$ is much more sensitive to changes in the distribution of the total electronic charge density distribution ρ(r) than is the case for the QTAIM bond-path. In Sect. 4.1 we outline the construction of the bond-path framework set $$\mathsf{B}$$ and briefly include some of the possible geometrical properties of $$\mathsf{B}$$ . The procedure to calculate the precession $$\mathsf{K}$$ of $$\mathsf{B}$$ is described in Sect. 4.2. In Sect. 4.3 we consider the applications of $$\mathsf{B}$$ that highlight the sensitivity to changes in ρ(r). This includes the infrared active modes of benzene in Sects. 4.3.1–4.3.3. The treatment of strained and unusual bonding environments is accommodated in Sect. 4.4. The provision for including multi-electronic statesMulti-electronic state is detailed in Sect. 4.5. The summary of the chapter is presented in Sect. 4.6 by outlining benefits, limitations and suggestions for further investigations of the ideas introduced. Further reading materials are provided in Sect. 4.7.

In this chapter we build on the NG-QTAIM representation of the chemical bond presented in Chap. 4 , the bond-path framework set $$\mathsf{B}$$ . The bond-path framework set $$\mathsf{B}$$ was constructed to be applicable for use with the stress tensor σ(r) and Ehrenfest Force F(r). In Sect. 5.1 we outline the basics of the stress tensor σ(r), explaining its relationship to the Hessian of ρ(r) partitioning and construction of the stress tensor bond-path framework set $$\mathsf{B}$$ σ. In Sect. 5.1.1 we provide an example using the torsion of etheneEthene to compare the used in the Hessian of ρ(r) bond-path framework set $$\mathsf{B}$$ and stress tensor bond-path framework set $$\mathsf{B}$$ σ. In Sect. 5.1.2 we consider the mixed bonding character of halogen-bonding and hydrogen-bonding in halogenabenzene and include consideration of relativistic effects. The photochemical reaction path from benzene to benzvalene was investigated and $$\mathsf{B}$$ σ was particularly useful at explaining the explosive nature of benzvalene. In Sect. 5.2 the Ehrenfest Force F(r) partitioning was outlined including the implementation details. In Sects. 5.2.1–5.2.2 examples including small lithiumLithium and water clusters are examined. The Ehrenfest Force F(r) precessions $$\mathsf{K}$$ ʹF and $$\mathsf{K}$$ F corresponding to the Ehrenfest Force F(r) are explained in Sect. 5.3. In Sect. 5.3.1 Ehrenfest Force F(r) precessions $$\mathsf{K}$$ ʹF and $$\mathsf{K}$$ F are applied to small water clusters. The summary of the chapter was presented in Sect. 5.4 by outlining benefits, limitations and suggestions for further investigations of the ideas introduced. Further reading materials are provided in Sect. 5.5.

The consideration of chemical bonding is traditionally based on the use of scalar measures and in this chapter we explore, starting from the framework of the quantum theory of atoms in molecules (QTAIM), how far we can usefully proceed with scalar chemical measures. We demonstrate that Euclidian geometry should not be used to quantify the geometry of molecules since they are quantum mechanical objects and doing so reduces the understanding of the molecular dimensionality to comparison with macroscopic objects. Various formalisms of the QTPD are introduced with examples. We pursue the total local energy density H(rb) as a measure of the presence of covalent bonding in strengthening weak interactions such as hydrogen-bonding and discuss the limitations of the use within scalar QTAIM. We created a real-space understanding of bond metallicity for use with molecules, clusters and solids that is particularly useful for strained and unusual bonding environments.

In this investigation, we seek to understand the role of non-nuclear attractors (NNAs) of the neutral Li-2 dimer subjected to an electric (+/- E) field that is directed parallel (+/- E-x) and perpendicular (+/- E-y) to the bond-path. The +/- E-x-fields and +/- E-y-fields are separately applied to the Li-2 molecular graph until the bond ruptures. The next generation quantum theory of atoms in molecules (NG-QTAIM) interpretation of bonding was constructed with the stress tensor sigma(r) eigenvectors on the Hessian of rho(r) molecular graph. The asymmetry induced by both the +/- E-y-field and +/- E-x-field was detected in terms of the rotation of the orthogonal triad of stress tensor sigma(r) eigenvectors {(e) under bar (1 sigma), (e) under bar (2 sigma), (e) under bar (3 sigma)} relative to the Cartesian coordinate frame. The orthogonal triad of Hessian of rho(r) eigenvectors {(e) under bar (1), (e) under bar (2), (e) under bar (3)} however, were only able to detect rotation induced by the high degree of asymmetry present for bent bond-paths induced by the +/- E-y-fields. Larger movement of the NNAs along the bond-path correlated with greater bond critical point (BCP) bond metallicity xi(r(b)). The effect of applying the +/- E-x-field was compared with unpublished results on neutral Li-2 subject to a stretching distortion. The lack of NNA motion along the bond-path for the stretching distortion correlated with a lower degree of bond metallicity xi(r(b)). The stress tensor sigma(r) eigenvectors have a unique ability to detect rotation relative to the Cartesian coordinate frame for high bond-path symmetry occurring for the bond-stretching distortion and application of the +/- E-x-field. Suggestions for future work are provided.

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.

In this chapter we firstly provide the theoretical background Eigenvector-space trajectories $$\mathsf{T}$$ i(s) and the corresponding numerical considerations including the associated QuantVec software required for their construction in Sects. 6.1 and 6.2 respectively. In Sect. 6.3 we provide an application of the $$\mathsf{T}$$ i(s) based on QTAIM, i.e. using the Hessian of ρ(r) for the normal modes of vibration analysis of isotope effects and bond coupling of deuterium in water. An NG-QTAIM normal mode analysis of benzene is used as an application of $$\mathsf{T}$$ i(s) using the stress tensor σ(r) to provide the dynamic couplingDynamic coupling of the C-H bonds and C-C bonds in Sect. 6.4.1. The coupling of covalent (sigma) OH and hydrogen-bonds on the (H2O)5 MP2 potential energy surface is examined in Sect. 6.4.2. In Sect. 6.4.3 the first of two iso-energetic phenomena is considered, that of the prediction of the flip rearrangement in the water pentamerWater pentamer. The second of two iso-energetic phenomena: prediction of torquoselectivity in competitive ring-opening reactionsCompetitive ring-opening reaction is presented in Sect. 6.4.4. In Sect. 6.5 we provide an application of the $$\mathsf{T}$$ i(s) to predict the photochemical ring-opening reactions of oxiraneOxirane with the Ehrenfest ForceEhrenfest Force trajectory F(r) where consistency with a hybrid $$\mathsf{T}$$ Fσ(s) Ehrenfest Force F(r) and stress tensor σ(r) is found. In Sect. 6.6 we conclude by summarizing the importance of directional quantum chemical measures for providing new insight into investigations of normal modes analysis, ring-opening reactions and isoenergetic phenomena.

Example dataset for NG-QTAIM eigenvector following trajectories: the F-NAIBP molecular rotary motor.

In this chapter we use the work of Chaps. 4 – 6 that introduced the bond-path framework set B and stress tensor trajectory Tσ(s). In Sect. 8.1 we introduce background to molecular devices and the role of NG-QTAIM. The molecular devices with the greatest degree of nuclear motion, the molecular rotary motorsMolecular rotary motor are presented in Sect. 8.2.