An electron-preceding perspective on the deformation of materials

GBasis: A Python library for evaluating functions, functionals, and integrals expressed with Gaussian basis functions

GBasis is a free and open-source Python library for molecular property computations based on Gaussian basis functions in quantum chemistry. Specifically, GBasis allows one to evaluate functions expanded in Gaussian basis functions (including molecular orbitals, electron density, and reduced density matrices) and to compute functionals of Gaussian basis functions (overlap integrals, one-electron integrals, and two-electron integrals). Unique features of GBasis include supporting evaluation and analytical integration of arbitrary-order derivatives of the density (matrices), computation of a broad range of (screened) Coulomb interactions, and evaluation of overlap integrals of arbitrary numbers of Gaussians in arbitrarily high dimensions. For circumstances where the flexibility of GBasis is less important than high performance, a seamless Python interface to the Libcint C package is provided. GBasis is designed to be easy to use, maintain, and extend following many standards of sustainable software development, including code-quality assurance through continuous integration protocols, extensive testing, comprehensive documentation, up-to-date package management, and continuous delivery. This article marks the official release of the GBasis library, outlining its features, examples, and development.

An information-theoretic approach to basis-set fitting of electron densities and other non-negative functions

The numerical ill-conditioning associated with approximating an electron density with a convex sum of Gaussian or Slater-type functions is overcome by using the (extended) Kullback-Leibler divergence to measure the deviation between the target and approximate density. The optimized densities are non-negative and normalized, and they are accurate enough to be used in applications related to molecular similarity, the topology of the electron density, and numerical molecular integration. This robust, efficient, and general approach can be used to fit any non-negative normalized functions (e.g., the kinetic energy density and molecular electron density) to a convex sum of non-negative basis functions. We present a fixed-point iteration method for optimizing the Kullback-Leibler divergence and compare it to conventional gradient-based optimization methods. These algorithms are released through the free and open-source BFit package, which also includes a L2-norm squared optimization routine applicable to any square-integrable scalar function.

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.

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 T_σ(s) used to sample the U_σ-space cis- and trans-characteristics. The T_σ(s) were constructed by subjecting the C1-C2 BCP and N1-N2 BCP to torsions ± θ and summing all possible T_σ(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 T_σ(s) with cis- and trans-characteristics, respectively, based on the relative ease of motion of the electronic charge density ρ(r_b). Qualitative agreement is found with existing experimental data and predictions are made where experimental data is not available.

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.

New insights of QTAIM and stress tensor to finding non-competitive/competitive torquoselectivity of cyclobutene

This study aims to investigate the phenomenon of torquoselectivity through three thermal cyclobutene ring-opening reactions (N1-N3). This research focuses on the nature of the chemical bond, electronic reorganization, predicting non-competitive or competitive reactions, and torquoselectivity preference within Quantum Theory of Atoms in Molecules (QTAIM) and stress tensor frameworks. Various theoretical analyses for these reactions, such as metallicity ξ(r_b), ellipticity ε, total local energy density H(r_b), stress tensor polarizability ℙ_σ, stress tensor eigenvalue λ_3σ, and bond-path length, display differently for non-competitive and competitive reactions as well as for the conrotatory preferences either it is the transition state outward conrotatory (TS_out) or transition state inward conrotatory (TS_in) directions by presenting degeneracy or non-degeneracy in their results. The ellipticity profile provides the motion of the bond critical point locations due to the different substituents of cyclobutene. In agreement with experimental results, examinations demonstrated that N1 is a competitive reaction and N2-N3 are non-competitive reactions with TS_out and TS_in preference directions, respectively. The concordant results of QTAIM and stress tensor scalar and vectors with experimental results provide a better understanding of reaction mechanisms.

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 S_N 2 reaction and a chiral S_N 2 reaction. Both the achiral and chiral S_N 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.

Orbital-free quantum crystallography: view on forces in crystals

Quantum theory of atoms in molecules and the orbital-free density functional theory (DFT) are combined in this work to study the spatial distribution of electrostatic and quantum electronic forces acting in stable crystals. The electron distribution is determined by electrostatic electron mutual repulsion corrected for exchange and correlation, their attraction to nuclei and by electron kinetic energy. The latter defines the spread of permissible variations in the electron momentum resulting from the de Broglie relationship and uncertainty principle, as far as the limitations of Pauli principle and the presence of atomic nuclei and other electrons allow. All forces are expressed via kinetic and DFT potentials and then defined in terms of the experimental electron density and its derivatives; hence, this approach may be considered as orbital-free quantum crystallography. The net force acting on an electron in a crystal at equilibrium is zero everywhere, presenting a balance of the kinetic F kin( r ) and potential forces F ( r ). The critical points of both potentials are analyzed and they are recognized as the points at which forces F kin( r ) and F ( r ) individually are zero (the Lagrange points). The positions of these points in a crystal are described according to Wyckoff notations, while their types depend on the considered scalar field. It was found that F ( r ) force pushes electrons to the atomic nuclei, while the kinetic force F kin( r ) draws electrons from nuclei. This favors formation of electron concentration bridges between some of the nearest atoms. However, in a crystal at equilibrium, only kinetic potential v kin( r ) and corresponding force exhibit the electronic shells and atomic-like zero-flux basins around the nuclear attractors. The force-field approach and quantum topological theory of atoms in molecules are compared and their distinctions are clarified.

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.

Charge-Shift Bonding: A New and Unique Form of Bonding

Charge-shift bonds (CSBs) constitute a new class of bonds different than covalent/polar-covalent and ionic bonds. Bonding in CSBs does not arise from either the covalent or the ionic structures of the bond, but rather from the resonance interaction between the structures. This Essay describes the reasons why the CSB family was overlooked by valence-bond pioneers and then demonstrates that the unique status of CSBs is not theory-dependent. Thus, valence bond (VB), molecular orbital (MO), and energy decomposition analysis (EDA), as well as a variety of electron density theories all show the distinction of CSBs vis-à-vis covalent and ionic bonds. Furthermore, the covalent-ionic resonance energy can be quantified from experiment, and hence has the same essential status as resonance energies of organic molecules, e.g., benzene. The Essay ends by arguing that CSBs are a distinct family of bonding, with a potential to bring about a Renaissance in the mental map of the chemical bond, and to contribute to productive chemical diversity.

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.

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.

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.

Predictive methods for computational metalloenzyme redesign - a test case with carboxypeptidase A

Computational metalloenzyme design is a multi-scale problem. It requires treating the metal coordination quantum mechanically, extensive sampling of the protein backbone, and additionally accounting for the polarization of the active site by both the metal cation and the surrounding protein (a phenomenon called electrostatic preorganization). We bring together a combination of theoretical methods that jointly offer these desired qualities: QM/DMD for mixed quantum-classical dynamic sampling, quantum theory of atoms in molecules (QTAIM) for the assessment of electrostatic preorganization, and Density Functional Theory (DFT) for mechanistic studies. Within this suite of principally different methods, there are both complementarity of capabilities and cross-validation. Using these methods, predictions can be made regarding the relative activities of related enzymes, as we show on the native Zn²⁺-dependent carboxypeptidase A (CPA), and its mutant proteins, which are hypothesized to hydrolyze modified substrates. For the native CPA, we replicated the catalytic mechanism and the rate in close agreement with the experiment, giving validity to the QM/DMD predicted structure, the DFT mechanism, and the QTAIM assessment of catalytic activity. For most sequences of the modified substrate and tried CPA mutants, substantially worsened activity is predicted. However, for the substrate mutant that contains Asp instead of Phe at the C-terminus, one CPA mutant exhibits a reasonable activity, as predicted across the theoretical methods. CPA is a well-studied system, and here it serves as a testing ground for the offered methods.

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.

Quantified electrostatic preorganization in enzymes using the geometry of the electron charge density

Electrostatic preorganization is thought to be a principle factor responsible for the impressive catalytic capabilities of enzymes. The full protein structure is believed to facilitate catalysis by exerting a highly specific electrostatic field on the active site. Computationally determining the extent of electrostatic preorganization is a challenging process. We propose using the topology and geometry of the electron charge density in the enzyme's active site to asses the effects of electrostatic preorganization. In support of this approach we study the convergence of features of the charge density as the size of the active site model increases in Histone Deacetylase 8. The magnitude of charge density at critical points and most Bader atomic charges are found to converge quickly as more of the protein is included in the simulation. The exact position of critical points however, is found to converge more slowly and be strongly influenced by the protein residues that are further away from the active site. We conjecture that the positions of critical points are affected through perturbations to the wavefunctions in the active site caused by dipole moments from amino acid residues throughout the protein. We further hypothesize that electrostatic preorganization, from the point of view of charge density, can not be easily understood through the charges on atoms or the nature of the bonding interactions, but through the relative positions of critical points that are known to correlate with reactivity and reaction barriers.

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.

Theoretical study of lithium ionic conductors by electronic stress tensor density and electronic kinetic energy density

We analyze the electronic structure of lithium ionic conductors, Li3PO4 and Li3PS4, using the electronic stress tensor density and kinetic energy density with special focus on the ionic bonds among them. We find that, as long as we examine the pattern of the eigenvalues of the electronic stress tensor density, we cannot distinguish between the ionic bonds and bonds among metalloid atoms. We then show that they can be distinguished by looking at the morphology of the electronic interface, the zero surface of the electronic kinetic energy density. © 2016 Wiley Periodicals, Inc.

The influence of zero-flux surface motion on chemical reactivity

Motion of zero-flux surfaces when an electron is removed from an ICCF molecule.

Electronic stress tensor analysis of molecules in gas phase of CVD process for GeSbTe alloy

We analyze the electronic structure of molecules which may exist in gas phase of chemical vapor deposition process for GeSbTe alloy using the electronic stress tensor, with special focus on the chemical bonds between Ge, Sb, and Te atoms. We find that, from the viewpoint of the electronic stress tensor, they have intermediate properties between alkali metals and hydrocarbon molecules. We also study the correlation between the bond order which is defined based on the electronic stress tensor, and energy-related quantities. We find that the correlation with the bond dissociation energy is not so strong while one with the force constant is very strong. We interpret these results in terms of the energy density on the "Lagrange surface," which is considered to define the boundary surface of atoms in a molecule in the framework of the electronic stress tensor analysis.

A full topological analysis of unstable and metastable bond critical points

Researchers are developing conceptually based models linking the structure and dynamics of molecular charge density to certain properties. Here we report on our efforts to identify features within the charge density that are indicative of instability and metastability. Towards this, we use our extensions to the quantum theory of atoms in molecules that capitalize on a molecule's ridges to define a natural simplex over the charge density. The resulting simplicial complex can be represented at various levels by its 0-, 1-, and 2-skeleton (dependent sets of points, lines, and surfaces). We show that the geometry of these n-skeletons retains critical information regarding the structure and stability of molecular systems while greatly simplifying charge density analysis. As an example, we use our methods to uncover the fingerprints of instability and metastability in two much-discussed systems, that is, the di-benzene complex and the He and adamantane inclusion complex.

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

New insights into the double bond isomerization of fulvene in the ground and excited electronic states are provided by newly developed QTAIM and stress tensor tools. The S0 and S1 states follow the 'biradical' torsion model, but the double bond is stiffer in the S0 state; by contrast, the S2 state follows the 'zwitterionic' torsion. Differences are explained in terms of the ellipticity and bond critical point (BCP) stiffness for both QTAIM and the stress tensor. Overall, the wave-function based analysis is found to be in agreement with the work of Bonačić-Koutecký and Michl that the bond-twisted species can have biradical or zwitterionic character, depending on the state. Using QTAIM and the stress tensor a new understanding of bond torsion is revealed; the electronic charge density around the twisted bond is found not to rotate in concert with the nuclei of the rotated -CH2 methylene group. The ability to visualize how the bond stiffness varies between individual electronic states and how this correlates with the QTAIM and stress tensor bond stiffness is highlighted. In addition, the most and least preferred morphologies of bond-path torsion are visualized. Briefly we discuss the prospects for using this new QTAIM and stress tensor analysis for excited state chemistry.