# & RECENT CONTRIBUTIONS

Chérif F. Matta

Dept. of Chemistry & Physics, Mount Saint Vincent University.

Updated: 1 June 2020   – – – – – – – – – –   Copyright © 2020 by Chérif F. Matta

## PREAMBLE

This research programme is in theoretical and computational (bio)chemistry and (bio)physics. The focus of this research programme is primarily on the analysis of the electron density with a particular interest in problems of biology and of material science amenable to the methods of theoretical analysis. There are five overlapping research thrusts outlined below (the reader can consult the cited references for details).

## CONTENTS

 1 Electron localization-delocalization matrices (LDMs). 2 Mitochondrial biophysics. 3 Molecules in external electric fields: 3.1    Molecules in static electric fields. 3.2    Molecules in time-varying (laser) fields. 4 Quantum Crystallography. 5 Other interests: 5.1    Design of new tunable crystalline materials. 5.2    Recoil energy and chemical yield in nuclear reactions. 5.3    Electronic basis of bioisosterism & lock-and key complementarity. 5.4    Excited states electron densities in QTAIM. 6 Closing remarks. 7 Acknowledgements. 8 References.

## MAIN CURRENT LINES OF RESEARCH

### 1. Electron Localization-Delocalization Matrices (LDMs)

A localization-delocalization matrix  (also called “ζ-matrix”)  was proposed in 2014 [1] as a representation of a molecule as a network of electron delocalization pathways [2,3]. The idea is to bridge the strengths of quantum chemistry (electronic structure calculations) [4-6] expressed in Bader’s Quantum Theory of Atoms in Molecules (QTAIM) [7-9] and Chemical Graph Theory (CGT) [10-15]. (Fig. 1).

An LDM is constructed from the numbers of shared electrons between every pair of atoms in a molecule calculated with the QTAIM framework. The localization-delocalization matrices are then manipulated by the tools of chemical graph theory to extract matrix invariants (independent on the (arbitrary) numbering of the atoms). The invariants are then used as predictive descriptors [16] in quantitative structure/property to activity (QSAR/QSPR) modeling and were shown accurate an widely applicable.

Fig. 1         Localization-delocalization matrices (LDMs) as a bridge between Bader’s Quantum Theory of Atoms in Molecules (QTAIM) and Chemical Group Theory (CGT) (top). The figure contrasts the conventional chemical view of a molecule (bottom, left) as an incomplete and discrete/sharp (all-or-none) graph (incomplete in the sense that edges connect only those atoms that chemically-bonded) with the localization-delocalization complete and fuzzy graph (bottom right) where every pair of atoms in a molecule are connected by a continuously variable electron delocalization communication channel.

More specifically, an LDM is composed of the complete set of localization indices [17], {Λ(Ωi)}, along the diagonal, and the complete set of the delocalization indices [17] divided by 2, {δ(Ωij)/2 = δ(Ωji)/2, ij}, as the off-diagonal elements. These two sets of indices provide a bookkeeping of the whereabouts of the N electron population of the molecule. An LI counts the number of electrons localized within an atomic basin while a DI counts the number of electrons shared between two basins. Accordingly, the molecular LDM is defined [1]:

##### Eq.(1)

where the sum of any column or row yields an atomic population by virtue of Bader’s summation rule (the first equality in Eq. (2):

Eq.(2)

Eq. (2) describes how an atomic population arises from a localized contribution (electrons exchanging with one another within the same atom) and a delocalized contribution from electrons shared, i.e. exchanging, between a given atom and every other atom in the molecule.

Correspondingly, the number of electrons in the molecule (N) can be expressed as the sum of a localized and a delocalizaed population:

Eq.(3)

where

Eq.(4)

and

Eq.(5)

Thus, an LDM carries a considerable amount of information about the molecular electron distribution at an atomic and diatomic resolution (Fig. 2). The information coded in an LDM include the fuzzy molecular graph when the molecule is viewed as a network of “exchange channels [18]” (with those coinciding with bond paths being generally dominant “privileged exchange channels” [18]).

Fig. 2         Information coded in an LDM.

Given the information contained tacitly within an LDM, it is unsurprising that LDMs are good predictors of molecular properties in QSAR/QSPR studies [1,3,19-25]. Instead of thousands of descriptors tailored for restricted ranges of properties [16], LDMs have been shown capable of predicting thermodynamic properties such as boiling points of isomers (sensitive to the degree of molecular branching which is hard to quantify) – see example in Fig. 3, enthalpies of vaporization, heats of combustions, enthalpies of formation, total energies [1], pKa‘s [23], aromaticity of rings-in-molecules (RIMs) [21], UV lmax‘s [23], mosquito repellency [22], stress corrosion cracking inhibitors’ activities [3,19]. LDMs can also be used as an additional measure of the quality of a basis set [19,20].

Fig. 3         Correlation of the boiling points (BPs) of the five isomers of hexane (C6H14) with the Frobenius distance of their LDMs from the LDM of the most branched isomer, 2,2-dimethylbutane [2].

## 2. Mitochondrial Biophysics

The interest of this group into mitochondrial biophysics started from the serendipitous realization of the similarity of the working of the kidney and of a mitochondrion – from the point of view of information theory, while teaching a class on biochemistry by the author.

Following the lead of Johnson and Knudsen’s work on the thermodynamics of the kidney (an entire organ acting as a sorting machine) [27-29] we applied their approach, not to an organ but rather to a cell organelle’s constituent, namely, ATP synthase [30-32]. Our work led to the finding that the thermodynamic efficiency of mitochondrial ATP synthase may have been underestimated by as much as 30% in standard biochemistry textbook, if one considers “in principle unavoidable” dissipation of free energy as useful work without which no sorting action is possible. Stated differently, this underestimation of efficiency results from overlooking the free-energy dissipation necessarily associated with every act of “sorting”. Every time an ion is “selected” for transport through a membrane, a minimum of kTln2 must be dissipated as demonstrated through Shannon Information Theory [33,34]). We have argued that the kidney and mitochondrial ATP synthase are two realizations of Maxwell demon [35-44], one is in the form of an entire organ and the latter in the form of a sorting molecular machine [30-32].

Besides an additional term in Mitchell’s theory equation, there are other consequences of this essential dissipation of energy – as depicted in Fig. 4. Thus, a term is proposed to be added to Mitchell’s chemiosmotic equation to account for the energy cost of sorting of protons by ATP synthase (Fig. 4). Further, considerations of the quantum mechanical (Heisenberg) uncertainty in this light leads to an expression for the uncertainty in the time of the measurement (or sorting act) which is inversely proportional to the temperature at which the measurement occurs [30]. Finally, because of Einstein’s famous energy-mass equivalence, an almost imperceptible mass is predicted to accompany every bit of information accumulated. A terabyte at room temperature is equivalent to 250 yoktograms, that is, approximately the rest mass of 150 protons.

Fig. 4         Three consequences of accounting for the minimal energy cost of information: On Mitchell’s chemiosmotic theory’s central equation (by adding the last information-theoretic term (top)), on a minimal quantum uncertainty of the time of performing a binary selection (bottom, left), and on a predicted tiny mass associated with every bit of information (bottom, right).

This work sparked our generalized interest in mitochondrial biophysics. That coincided with reports in 2018 – based on temperature-sensitive fluorescent probes – that mitochondria might be much hotter than previously assumed, with temperatures reaching perhaps as high as 50 oC [45]. Fahimi et al. have examined the possible revisions to textbook mitochondrial thermodynamics if these claims are confirmed, and we found that even if the mitochondrion was as hot as claimed, i.e. operating at 50 oC, the effect on the thermodynamics and on its Carnot efficiency would constitute  only a slight perturbation [46]. Meanwhile, there could be more drastic effects on the kinetics the Krebs’ tricarboxylic acid Cycle and of the electron transport reactions in view of the exponential dependence of rate constants on the absolute temperature [46]. The image constructed from different pieces of the jigsaw  suggest that mitochondria are probably “hotter” indeed but to a lower degree than initially suggested by Chétien et al. [46].

Among “circumstantial evidence” for a hotter mitochondrion is their abundance with heat shock proteins. Indeed, biological, evolutionary, and bioinformatics considerations by Nasr et al. indicate that mitochondrial heat shock proteins (mHsps) may have been particularly abundant in mitochondria to protect against the deleterious effects of its hotter environment [47], a fact qualitatively aligned with the primary conclusion of Chétien et al. [45]. Such deleterious heating effects include the possibility of reaching melting temperatures of some mitochondrial proteins and/or nucleic acids and, simultaneously, the heat-induced increased production of reactive oxygen species [47]. (Fig. 5). Among the circumstantial evidence we have gathered are the presence of significantly higher incidence of purine tracts in the mitochondrial nucleic acids compared with their nuclear counterparts, the high concentrations of “compatible solutes” in mitochondria, and the compatibility of the higher mitochondrial temperature with endosybmiosis theory [47]. These findings reinforce the claims of a “hot mitochondrion” but do not necessarily endorse the magnitude of the mitochondrial temperature, 50 oC, claimed by Chrétien et al. [46].

Fig. 5         Mitochondrial heat shock proteins (mHsps) as structural protectants in the “hot” mitochondrion. mHsps can contribute at maintaining the structural stability of mitochondrial nucleic acids and proteins and in the protection against the temperature-enhanced production of reactive oxygen species (ROS).

## 3. Molecules in External Electric Fields

### 3.1 Molecules in Static Electric Fields

In 2013, Solati-Hashjin and Matta proposed a “field-perturbed Morse potential” to predict the effects of external static electric fields on bond lengths and on vibrational spectra (vibrational Stark effect) in diatomics solely from the field-free properties of the molecule [48]. Our model has been validated numerically by comparison with the results of brute force calculations including a field term in the Hamiltonian. The importance of this undertaking has been underscored in L. Piela’s Ideas in Quantum Chemistry [6]:

The problem is how to compute the molecular properties in the electric field from the properties of the isolated molecule and the characteristics of the applied field”.

Our field-perturbed Morse potential has been inspired by (but differs from) Delley’s earlier work [49]. The Morse potential is generalized by the inclusion of field-terms [48]:

Eq.(6)

where E is the electric field strength, μ0 and a//0 are the field-free molecular dipole moment and the longitudinal element of the polarizability tensor.

The field-perturbed Morse potential yields the following equations that predict bond lengths and vibrational frequencies of diatomic molecules in the presence of an external static electric field from their field-free values [48]:

Eq.(7)

##### Eq.(8)

where R0 and ν0 are the field-free equilibrium bond length and harmonic frequency, RE and νE are the corresponding values under an external electric field E, and r is the inter-nuclear separation. The effect of external fields on some homonuclear and heteronuclear diatomics is displayed in Fig. 6.

The negative or positive signs of the dipole terms in Eqs. (7) and (8) correspond, respectively, to parallel and antiparallel orientations of the permanent molecular dipole moment (if it exists) with respect to the field. For molecules without a permanent dipole, the dipolar term vanishes and the response to the field is totally determined by the polarizability term. These equations reproduce the results of direct calculations with explicit treatment of the field-effects [48].

More recently, we extended this study to trace molecular changes to their atomic contributions based on QTAIM [50]. It is found that atoms in molecules in external fields often exhibit a “compensatory response” whereby the changes in the properties of one atoms cancels to a large extent the changes induced in its bonding partner [50].

Our Eq. (8) was used by Grabowsky, Warneke, et al. to explain their discovery of a highly electrophilic behavior of an anion [51]. Noble gases, Ng = Xe, Kr, were found to be bound by 80-100 kJ/mol to boron-chlorine anionic complexes [[B12Cl12]2-, [B12Cl11]-, and [C6H5]+] at room temperature via a B-Ng bond. The local electrophilicity of these anions was determined by the vibrational Stark-shift experienced by a physisorbed CO reporter molecule to these anionic clusters [51]. Grabowsky, Warneke, et al. established the presence of fields ~ 109 – 1010 V.m-1 directed as in cations in certain regions acting as sources of field lines around these complexes. (See Table 1 of Ref. [51]).

A different aspect of imposed external fields is their effects on kinetics. Arabi and Matta developed a protocol to study the kinetics of proton transfer reactions that include tunneling corrections under strong external field that likely occur in the biological microenvironment [52-54]. (Fig. 5). The class of double proton transfer reactions, when they occur in a DNA base pairs, is known as the Löwdin mechanism of spontaneous and induced mutation [55-57]. Our protocol has been used by other research groups to examine, for example, (a) the kinetics of Löwdin mechanism mutation in external electric fields of intensities typical of the microenvironment of nucleic acids (|E| ~108 – 109 V/m) [58-61] (b) the double proton transfer in non-natural nucleic acid base pairs [62-65], (c) the kinetics of enzyme-catalyzed reactions in the natural electric fields in enzyme active sites [66-68]. Together with our work on the field-effects on chemical bonds [48], this research may have inspired the possible use of STM electric fields to manipulate nanoscale supramolecular assembly on surfaces [69].

Fig. 6         The change in the equilibrium bond lengths (BLs), DR (in Å), as a function of the strength of the electric field (E) for homo-nuclear diatomics (top, left), and as functions of the field strength and direction for hetero-nuclear diatiomics (bottom, left). The change in harmonic frequencies in cm–1 (Dν) as functions of field strength for the homonuclear diatomics (top, right) and as functions of field strength and direction for the heteronuclear diatomics (bottom, right).

Fig. 7         (Left) Acceleration of the double proton transfer reaction in the formic acid dimer by an electric field measured by the rate constant (after quantum tunneling correction) as a function of field strength at room temperature [52]. The field is parallel to the z-direction. (Right) An example of the modeled Löwdin mechanism of mutations illustrated for an adenine-thymine base pair.

Using molecular dynamics (MD) simulations, Kandezi, Lakmehsari, and Matta have shown that an external field can enhance the ion selectivity of boron- and nitrogen-doped graphene sheets through the differential field-effects on the hydration shells of the ions [70].

### 3.2 Molecules and Reactions in Laser Fields

Bandrauk et al. demonstrated that the intensity and phase of a plane polarized, phase-stabilized, two-color laser pulses can be tuned to invert the potential energy surface (PES) for co-linear collisions of methane with halogens [71,72] and metal ions [73] [X• + CH4 –> HX + •CH3, (X = F, Cl, Li)]. In this way, a transition state on the PES can be converted to a radiation-stabilized bound state. (Fig. 8).

The effective potential of the field-molecule system as a function of the reaction coordinate (s) can be approximated as [72,73]:

Eq.(9)

$\mu _z$ and $\alpha _{zz}$ are the components of the dipole moment and of the polarizability tensor element parallel to the C3 axis, E0 is the amplitude and  the phase of the electric component of the electromagnetic field.

The parallel (z) components of the dipole moment and zz polarizability tensor element of the X• + CH4 reacting system is found to exhibit sharp peaks near the transition state (TS). Thus, and through Eq. (9), one can anticipate a maximal effect of the field on the reaction near the TS where the field-molecule interaction is maximal through the interferences of the second and third terms. The phase and the intensity of the field can, hence, be adjusted to eliminate or even invert the potential barrier converting a TS into a bound state. (Fig. 8).

We examined atomically-decomposed dipole moment surfaces to pinpoint those atoms responsible of the dipole moment peak near the transition state and found that the halogen is the principal contributor. Hence, the nature of the halogen atom is that what determines the response of this reaction to an external laser field [71].

Fig. 8         Energy profile along the reaction coordinate, for a 3.0 x 1013 W.cm-2 laser pulse along the long axis of a radiation-aligned Cl+CH4 system plus the dipole moment and polarizability contributions. Field-induced bound states are shown to have a deep minimum at Φ = π at this field intensity.

## 4. Quantum Crystallography

“Quantum Crystallography (QCr)” [74-86] aims at extracting entire density matrices (not only electron densities), or wavefunctions [82,87-89], that are consistent simultaneously with crystallographic X-ray diffraction data and with the underlying quantum mechanical mathematical structure (Fig. 9). QCr ensures the derivability of the observed electron density from an underlying properly antisymmetrized wavefunction that is consistent with the observed structure factors simultaneously.

In principle, QCr enables us to extract information insofar unavailable from traditional X-ray diffraction experiments. These properties can include momentum densities, and, importantly, energies [84]. The injection of quantum mechanics during the refinement of crystallographic data ensures the satisfaction of the obtained densities to the basic rules of quantum mechanics such as N-representatbility – not typically guaranteed in the usual post-experiment refinement. Thus, QCr allows the crystallographer to obtain much more information than the electron density or molecular geometry, information available already in the X-ray data.

One approach to QCr within a single-determinental approach is through the imposition of the property of a projector on a matrix P, expressed in a given molecular orbital basis by ensuring its idempotency, i.e., that Pn = P (n, any integer). The trace of P is the number of doubly occupied orbitals for a closed-shell system and P = CCS, a matrix product where C is the matrix of coefficients of the LCAO in a particular orbital basis and S is the overlap matrix. The projector property of P is imposed via the Clinton’s equations iterative process (the Clinton equations appear in the lower right corner of Fig. 9). Because overlap dies out quickly in space, one can construct an approximate solution to the Schrӧdinger equation from properly selected fragments termed “kernels”. This led to the development of the Kernel Energy Method (or KEM) of Lulu Huang, Lou Massa, and Jerome Karle [90].

Fig. 9         Main steps of quantum crystallography in conjunction with the kernel energy method (KEM).

The KEM fragmentation scheme allows one to estimate the properties of a large molecule from single and double fragments (kernels). The double fragments account for the “two-fragments” interactions between every pair of single kernels in the molecule. The properties of the full molecule is then estimated after accounting for the double counting associated with representing the single kernels again in the double kernels (see Fig. 10).

Fig. 10       An illustration of a large molecule broken into three single kernels and three double kernels.

The form of the constitutive equation of the KEM method is general and, while written below for the total energy and the electron density, it can be written to approximate QTAIM atomic charges [91], Interacting Quantum Atoms [92-94] energy components [95], the molecular dipole moment components [96], the energy or the dipole moment response to external fields [96] (Fig. 11), and the molecular electrostatic potential. The same mathematical form has also been proposed for the approximate reconstruction of one-body and two-body reduced density matrices [84,85,91,97], and has yielded good approximations to the energy [98] and to the electron localization-delocalization matrices (LDMs) of a finite graphene nanoribbon [24].

The KEM approximates the total energy E (in vacuum, in a solvent reaction field, or in an external electric field) as:

Eq. (10)

where EKEM is the KEM approximation to the total energy of the full system, Eij is the energy of the ijth double kernel, Ek is the energy of the kth single kernel, i, j, and k are running integer indices, and n is the number of single kernels.

The electron density of the full molecule, in its turn, can be approximated as [24,96]:

Eq. (11)

where ρij and ρk are the electron densities of the ijth double kernel and of the kth single kernel, respectively, and r is a position vector.

With an approximate KEM density, the molecular electrostatic potential V can be reconstructed using the charges Zi (in atomic units) and positions (Ri) of the nuclei [99]:

##### Eq. (12)

where the ith term in the first sum must be eliminated when Ri = r. Alternatively, VKEM(r) can be reconstructed from the molecular ESP calculated for the kernel fragments on a point-by-point basis using an equation of the same form of Eq. (11).

Fig. 11       (Left) A finite graphene nanoribbon under an external uniform electric field reconstructed from KEM fragments. (The arrow in the middle (antiparallel to the x-axis) depicts the permanent dipole moment). (Middle) Comparison of field-induced changes in the total energy of the nanoribbon calculated directly for the intact molecule and from the KEM approximation as a function of the field’s strength. (Right) Comparison of field-induced changes in the principal (y-) component of the dipole moment of the nanoribbon calculated directly for the intact molecule and from the KEM approximation as a function of the field’s strength.

## 5. Other Interests

### 5.1. Design of New Tunable Crystalline Materials

We have recently started to investigate the design of new materials by means of periodic density functional theory (DFT) [100-102] electronic structure calculations. In a study by Azzouz et al., we predicted that alloys with the composition NaYS1.33Te0.67 and NaYS0.67Te1.33 have exciton binding energies of 9.78 meV for and 6.06 meV – which are of the order of the thermal energy at room temperature. This result suggests an easily dissociable electron-hole pair suggesting that alloys of the type NaYS2(1−x)Te2x  may be promising for visible photocatalytic devices since our calculations established that they absorb in the visible part of the spectrum [103].

In another study, we showed that compounds of the type RbLnSe2 (Ln = Ce, Pr, Nd, Gd) are semiconductor in character. These compounds exhibit two different spin band gaps. In the case of RbNdSe2 and RbGdSe2, the band gaps and also their calculated bulk mechanical and elastic properties suggest their potential use in a future photo-response and/or spintronic application [104].

Periodic DFT calculations by Azzouz et al. showed that the previously synthesized RbCeTe2 crystal [105] exhibits a ferromagnetic electronic structure [106]. Our DFT calculations on the crystal of this telluride under a uniformly-applied external hydrostatic pressure have further shown this crystal to be highly deformable as indicated by the significant anisotropies of the pressure-response of its elastic constants Cij, its Young’s modulus, and its Poisson ratio [106]. As a result of this anisotropy, the electronic structure of RbCeTe2 exhibits a dramatic spin-phase transition under the relatively moderate pressure of 10 GPa. At this pressure, the α-spin band gap closes completely leaving a relatively large β-spin gap, suggesting a pressure-induced switching of the electronic structure that may be exploited in spintronic applications.  (Fig. 12).

Fig. 12       Calculated spin-polarized band structure of RbCeTe2 (a) at no external hydrostatic pressure and (b) at 10 GPa of external pressure. Alpha (α)-spin and beta (β)-spin at the right and left panels, respectively.

### 5.2. Recoil Energy & Chemical Yield in Nuclear Reactions

The question of the fate of a compound that undergoes a nuclear transformation has been addressed by computational quantum chemistry in 2014 [107]. This study presents a mathematical model to predict the primary retention yield following a nuclear decay event (the primary retention yield is the fraction of molecules that survive the nuclear recoil following – in this case – a β-decay event). The primary retention yield can be obtained by the fraction of nuclear transmutation events that will result in an angle equal to or less than a critical value θcritical between the ejected β-electron and the accompanying antineutrino as a function of a maximal allowed recoil energy Erecoil (set for example as the bond dissociation energy (BDE) of the weakest bond in the compound). Thus, from mass and linear momentum conservation arguments [108] we derived the formula [107]:

Eq. (13)

where the imposed upper bounds on the recoil energy, Erecoil, is converted into maximum allowable angular deviations from p between the directions of the ejected β-electron and the accompanying antineutrino that will result in an Erecoil that does not exceed the imposed upper bound, and where the max(Ee) is the highest energy of the ejected β-electrons. The angular bounds can be converted into fractions of ejected β-electrons that leave the residual nucleus with a recoil energy less than or equal to the chosen upper bound (Fig. 13).

Fig 13        (a) The abscissa represents the deviations of the angle θ from p (in o) between the trajectories of the ejected β-electron and the antineutrino the three values of the experimentally-observed max(Ee) for an upper bond rupture threshold Erecoil = 20 kcal/mol. Each curve delimits a region contained to the left of the curve and which corresponds to energies of recoil £ to 20 kcal/mol and areas to its right that correspond to angular deviations greater than the critical values would result in bond rupture. (b) The abscissa represents the percent fraction of nuclei that will survive a decay event with the ejection of a β-particle given in the ordinate axis.

### 5.3 The Electronic Basis of Bioisosterism and Lock-and Key Complementarity

A long standing problem is to explain why there exist structurally and chemically very different bioisosteric groups that are interchangeable in a drug with little effect on the drug’s pharmacological profile. For a particular pair of bioisosteres, the tetrazole and carboxylate anions, Matta, Arabi, and Weaver found that they exhibit an identical topology and a very similar topography of their electrostatic potential irrespective of the capping group [109,110] (Fig. 14). Curiously, and despite of the different chemical nature of these two bioisosteres, their average electron densities are almost identical [109,110]. Similar results were also observed for the bioisosteric couple methylsquarate and carboxylic acid [111] and were further by Arabi to a larger group of bioisosteres [112].

Fig. 14       The two bioisosteres carboxylate and tertrazole anions and a cartoon of the region of a receptor complementary to the –COO and −CN4 regions. Isosurfaces of the electrostatic potential (ESP): Pink for ESP > 0, violet for ESP < 0, and the displayed isosurfaces are (in atomic units) ±0.250 for CH3-COO- and ±0.275 for CH3-CN4-. The distance matrix of the four minima in the ESP of each bioisostere is given at the bottom.

Castanedo et al. performed a comprehensive potential semi-empirical energy surface scans followed by statistical mechanical analysis and ending up with molecular DFT calculations to test the hypothesis of whether direct complexation between a carcinogen and a protective agent may explain the effect of the latter [113]. These calculations have indeed confirmed that a number of phenolic compounds present in the extract of the Cuban plant Phyllanthus orbicularis K form stable complexes with several environmental mutagens of the aromatic amines class explaining away the known experimental genoprotective properties of this plant extract [113]. The lock and key complementarity of the mutagens with the protective phenols is clear from an examination of their electrostatic potentials and the weak bonding patterns connecting every pair that was studied.

### 5.4 Excited StatesElectron Densities in QTAIM

Terrabuio et al. examined the structures and electron densities of difluorodiazirine in the ground and two low-lying excited states [114,115] and that of carbon monoxide (CO) [116] to explain their unexpected dipole moments in their ground and low-lying excited states. This has been achieved by decomposing the molecular dipole moment into atomic polarization (AP) and inter-atomic charge transfer (CT) contributions according to the quantum theory of atoms in molecules (QTAIM) [7,117-119] (Fig. 15).

It has long been known, for example, that a large but opposite AP and CT contributions essentially cancel in the ground state (S0) of CO’s ([119] and references therein). In the lowest triplet (T1) and singlet (S1) excited states, however, this balance is disturbed resulting in significant dipole moments mainly driven by an induced charge transfer from O to C [116]. (Fig. 15). The reduction in the intensity of the vibrational stretching band is shown to result mainly from changes in the atomic charges as well, although other contributions become more significant in the vibrations of excited states but largely cancel.

Fig. 13       The dipole moment of CO shown to arise from two terms: A charge transfer term and an atomic polarization (deformation) term expressed in an origin independent manner.

## 6. Closing Remarks about Matta’s Research Programme/Group

This Research Programme is problem- and hypothesis-driven. The choice of topics and problems is not dictated by the comfort zone of the “easily accessible” technology. Quite the contrary. We seek challenges, we seek to explore unbeaten paths, and we encourage unconventionality. We learn techniques and expand our repertoire as needed by the problem at hand. If an immediate expertise is needed and is deemed too far from ours, we collaborate.

Students are encouraged to actualize their potential by following their dreams and special interests. We encourage “dreamers”. Student members of the Group have a major say in the type of problems we study which explains the diversity of the problems we attack. This thematic diversity reflects an underlying diversity in the composition of our Group members backgrounds’ as engineers, biologists, pharmacists, physicists, mathematicians, physicians, and of course chemists.

Besides the thematic and training diversity, we are equally passionate about Equity, Diversity, and Inclusion (EDI). Everyone and anyone are welcome to the Matta Group. We particularly welcome women, visible and religious minorities of any national origin, aboriginal persons, members of the LGBT community, persons of any age, and persons with disabilities. The Group has had a history of inclusion in this sense having been enriched from present and past members from Algeria, Brazil, Canada, China, Cuba, Egypt, Iran, Lebanon, Saudi Arabia, Ukraine, USA, and Zambia.

## Acknowledgements

The author is extremely grateful to his collaborators, students, co-workers, and colleagues nationally and internationally – too numerous to list. Funding for this research has been obtained from the Natural Sciences and Engineering Research Council of Canada (NSERC), the Canada Foundation for Innovation (CFI), the Academy of Scientific Research and Technology (of Egypt), and Mount Saint Vincent University. The author is also grateful to Dalhousie University, Université Laval, Saint Mary’s University, and Zewail City for Science and Technology for Adjunct Faculty appointments that greatly facilitated this research through expanding the colleagues basis, access to students and trainees, and through the generous sharing of their resources.

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[103] Azzouz L , Halit M, Charifi Z, Matta CF. Tellurium doping and the structural, electronic and optical properties of NaYS2(1-x)Te2x alloys. ACS Omega 4, 11320-11331 (2019).

[104] Azzouz L , Halit M, Charifi Z, Baaziz H, Rérat M, Denawi H, Matta CF. Magnetic semiconductor properties of RbLnSe2 (Ln = Ce, Pr, Nd, Gd): A density functional study. J. Mag. Mag. Mater. 501, Art#166448 (pp.1-8) (2020).

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[106] Azzouz L , Halit M, Denawi H, Charifi Z, Baaziz H, Rérat M, Matta CF. RbCeTe2 crystal under pressure: Spin-phase transitions and response properties. Submitted, in peer review (2020).

[107] Timm M, Matta CF. Primary retention following nuclear recoil in β-decay: Proposed Synthesis of a metastable rare gas oxide (38ArO4) from (38ClO4) and the evolution of chemical bonding over the nuclear transmutation reaction path. Appl. Rad. Isotopes 94, 206-215 (2014).

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[109] Matta CF , Arabi AA, Weaver DF. The bioisosteric similarity of the tetrazole and carboxylate anions: Clues from the topologies of the electrostatic potential and of the electron density. Eur. J. Med. Chem. 45, 1868-1872 (2010).

[110] Matta CF, Arabi AA. Electron-density descriptors as predictors in quantitative structureactivity/property relationships and drug design. Future Med. Chem. 3, 969-994 (2011).

[111] Arabi AA , Matta CF. Bioisosteric groups in methylsquarate and carboxylic acid: The similarities of their electrostatic potentials and average electron densities. Future Med. Chem. 8, 361-371 (2016).

[112] Arabi AA. Atomic and molecular properties of nonclassical bioisosteric replacements of the carboxylic acid group. Future Med. Chem. In press (DOI: 10.4155/fmc-2019-0278) (2020).

[113] Castanedo LAM, Lamar AS, Boado CM, de la Nuez Veulens A, Matta CF. Genoprotection by complexation: The case of Phyllanthus orbicularis K extract. Comput. Theor. Chem. 1164, Art.#112555 (pp. 1-9) (2019).

[114] Terrabuio LA, Haiduke RLA, Matta CF. Difluorodiazirine (CF2N2): A comparative quantum mechanical study of the first triplet and first singlet excited states. Chem. Phys. Lett. 655-656, 92-102 (2016).

[115] Terrabuio LA, Haiduke RLA, Matta CF. Difluorodiazirine (CF2N2): A quantum mechanical study of the electron density and of the electrostatic potential in the ground and excited electronic states. Theor. Chem. Acc. 135, 1-18 (2016).

[116] Terrabuio LA, da Silva NA, Haiduke RLA, Matta CF. Real space atomic decomposition of fundamental properties of carbon monoxide in the ground and two low-lying excited electronic states. Mol. Phys. 115, 1955-1965 (2017).

[117] Bader RFW. Dielectric polarization: A problem in the physics of an open system. Mol. Phys. 100, 3333-3344 (2002).

[118] Bader RFW, Matta CF. Properties of atoms in crystals: Dielectric polarization. Int. J. Quantum Chem. 85, 592-607 (2001).

[119] Matta CF, Gillespie RJ. Understanding and interpreting electron density distributions. J. Chem. Educ. 79, 1141-1152 (2002).

(Updated: 1 June 2020)