shant shahbazian

The nature of the newly proposed two-positron bond in (PsH)2, which is composed of two protons, four electrons and two positrons, is considered in this contribution. The study is done at the multi-component-Hartree-Fock (MC-HF) and the Diffusion Monte Carlo (DMC) levels of theory by comparing ab initio data, analyzing the spatial structure of the DMC wavefunction, and applying the multi-component quantum theory of atoms in molecules and the two-component interacting quantum atoms energy partitioning schemes to the MC-HF wavefunction. The analysis demonstrates that (PsH)2 to a good approximation may be conceived of two slightly perturbed PsH atoms, bonded through a two-positron bond. In contrast to the usual two-electron bonds, the positron exchange phenomenon is quite marginal in the considered two-positron bond. The dominant stabilizing mechanism of bonding is a novel type of classical electrostatic interaction between the positrons, which are mainly localized between nuclei, and the surrounding electrons. To emphasize its uniqueness, this mechanism of bonding is proposed to be called gluonic which has also been previously identified as the main deriving mechanism behind formation of the one-positron bond in {H-,e+,H-]. We conclude that the studied two-positron bond should not be classified as a covalent bond and it must be seen as a brand-new type of bond, foreign to the electronic bonding modes discovered so far in the purely electronic systems.

The multi-component density functional theory is faced with the challenge of capturing various types of inter-and intra-particle exchange-correlation effects beyond those introduced by the conventional electronic exchange-correlation functionals. Herein, we focus on evaluating the electronproton/muon correlation functionals appearing in molecular/condensed-phase systems where a proton/muon is treated as a quantum particle on equal footing with electrons, beyond the Born-Oppenheimer paradigm. Five recently developed local correlation functionals, i.e., the epc series and eµc-1, are selected and their performances are analyzed by employing a two-particle model that includes an electron and a positively charged particle (PCP) with a variable mass, interacting through Coulombic forces, within a double harmonic trap. Using the Kohn-Sham (KS) inversion procedure, the exact two-component KS characterization of the model is deduced and its properties are compared to those derived from the considered functionals. The analysis demonstrates that these local functionals achieve their original parameterization objectives to reproduce the one-PCP densities and the electron-PCP correlation energies, but all fall short of reproducing the underlying PCP correlation potentials correctly. Moreover, a comprehensive error analysis reveals that the density-driven errors have a non-negligible contribution to the success of the considered functionals. Overall, the study shows the strengths as well as shortcomings of the considered functionals hopefully paving the way for designing more robust functionals in the future.

In [Phys. Rev. B 107, 094433 (2023)], Deng et al. have proposed an electron-muon correlation functional within the context of the two-component density functional theory (TC-DFT) for crystals/molecules containing positively charged muons. In order to verify its performance, we applied the functional in conjunction with the B3LYP, as a hybrid electronic exchange-correlation functional, to a benchmark set of molecules. The results demonstrate that the proposed functional is not capable of reproducing the correct one-muon densities as well as some other key properties like muon's kinetic energy, the total energies and the mean muonic bond lengths. Using the muonium atom in a double-harmonic trap as a model we also demonstrate that the successful reproduction of the electron-muon contact hyperfine coupling constants by Deng et al. is probably the result of error cancellations. We also discuss some theoretical intricacies with the very definition of the electron-muon correlation energy within the context of the TC-DFT that must be taken into account in future efforts to design electron-muon correlation functionals.

The proton between the two oxygen atoms of the malonaldehyde molecule experiences an effective double-well potential in which the proton’s wavefunction is delocalized between the two wells. Herein we employed the state-of-the-art multi-component quantum theory of atoms in molecules partitioning scheme to obtain the molecular structure, i.e. atoms in molecules and bonding network, from the superposed ab initio wavefunctions of malonaldehyde. In contrast to the familiar clamped-proton portrayal of malonaldehyde, in which the proton forms a hydrogen basin, for the superposed states the hydrogen basin disappears and two novel hybrid oxygen-hydrogen basins appear instead, with an even distribution of the proton population between the two basins. The interaction between the hybrid basins is stabilizing thanks to an unprecedented mechanism. This involves the stabilizing classical Coulomb interaction of the one-proton density in one of the basins with the one-electron density in the other basin. This stabilizing mechanism yields a bond foreign to the known bonding modes in chemistry.

It is well-known experimentally that the positively charged muon and the muonium atom may bind to molecules and solids, and through
muon’s magnetic interaction with unpaired electrons, valuable information on the local environment surrounding the muon is deduced.
Theoretical understanding of the structure and properties of resulting muonic species requires accurate and efficient quantum mechanical
computational methodologies. In this paper, the two-component density functional theory (TC-DFT), as a first principles method,
which treats electrons and the positive muon on an equal footing as quantum particles, is introduced and implemented computationally.
The main ingredient of this theory, apart from the electronic exchange–correlation functional, is the electron–positive muon
correlation functional that is foreign to the purely electronic DFT. A Wigner-type local electron–positive muon correlation functional,
termed eμc-1, is proposed in this paper and its capability is demonstrated through its computational application to a benchmark set
of muonic organic molecules. The TC-DFT equations containing eμc-1 are not only capable of predicting the muon’s binding site
correctly, but they also reproduce muon’s zero-point vibrational energies and the muonic densities much more accurately than the
TC-DFT equations lacking eμc-1. Thus, this study sets the stage for developing accurate electron–positive muon functionals, which
can be used within the context of the TC-DFT to elucidate the intricate interaction of the positive muon with complex molecular
systems.

Recently it has been proposed that the positron, the anti-particle analog of the electron, is capable of forming an anti-matter bond in a composite system of two hydride anions and a positron [Angew. Chem. Int. Ed. 57, 8859–8864 (2018)]. In order to dig into the nature of this novel bond the newly developed multi-component quantum theory of atoms in molecules (MC-QTAIM) is applied to this positronic system. The topological analysis reveals that this species is composed of two atoms in molecules, each containing a proton and half of the electronic and the positronic populations. Further analysis elucidates that the electron exchange phenomenon is virtually non-existent between the two atoms and no electronic covalent bond is conceivable in between. On the other hand, it is demonstrated that the positron density enclosed in each atom is capable of stabilizing interactions with the electron density of the neighboring atom. This electrostatic interaction suffices to make the whole system bonded against all dissociation channels. Thus, the positron indeed acts like an anti-matter glue between the two atoms.

Recently we have proposed an effective Hartree-Fock (EHF) theory for the electrons of the muonic molecules that is formally equivalent to the HF theory within the context of the Nuclear-Electronic Orbital theory [Phys. Chem. Chem. Phys. 20, 4466 (2018)]. In the present report we extend the muon-specific effective electronic structure theory beyond the EHF level by introducing the effective second order Møller-Plesset perturbation theory (EMP2) and the effective coupled-cluster theory at single and double excitation levels (ECCSD) as well as an improved version including perturbative triple excitations (ECCSD(T)). These theories incorporate electron-electron correlation into the effective paradigm and through their computational implementation, a diverse set of small muonic species is considered as a benchmark at these post-EHF levels. A comparative computational study on this set demonstrates that the muonic bond length is in general non-negligibly longer than corresponding hydrogenic analogs. Next, the developed post-EHF theories are applied for the muoniated N-Heterocyclic carbene/silylene/germylene and the muoniated triazolium cation revealing the relative stability of the sticking sites of the muon in each species. The computational results, in line with previously reported experimental data demonstrate that the muon generally prefers to attach to the divalent atom with carbeneic nature. A detailed comparison of these muonic adducts with the corresponding hydrogenic adducts reveals subtle differences that have already been overlooked.

A set of effective electronic-only Kohn-Sham (EKS) equations are derived for the muonic molecules (containing a positively charged muon), which are completely equivalent to the coupled electronic-muonic Kohn-Sham equations derived previously within the framework of the Nuclear-Electronic Orbital density functional theory (NEO-DFT).  The EKS equations contain effective non-coulombic external potentials depending on parameters describing muon’s vibration, which are optimized during the solution of the EKS equations making muon’s KS orbital reproducible.  It is demonstrated that the EKS equations are derivable from a certain class of effective electronic Hamiltonians through applying the usual Hohenberg-Kohn theorems revealing a “duality” between the NEO-DFT and the effective electronic-only DFT methodologies.  The EKS equations are computationally applied to a small set of muoniated organic radicals and it is demonstrated that a mean effective potential maybe derived for this class of muonic species while an electronic basis set is also designed for the muon.  These computational ingredients are then applied to muoniated ferrocenyl radicals, which had been previously detected experimentally through adding muonium atom to ferrocene.  In line with previous computational studies, from the six possible species the staggered conformer, where the muon is attached to the exo position of the cyclopentadienyl ring, is deduced to be the most stable ferrocenyl radical.

Equating (3, -1) critical points (CPs), derived from the topological analysis of the electron densities, to chemical bonds has triggered a lot of confusion in recent years. Part of this confusion stems from calling these CPs “bond” CPs (BCPs). While the origin of this terminology is traceable to the late seventies and beginning of eighties, when it sounded reasonable, new computational studies conducted on molecular electron densities cast serious doubt on the supposed universal equivalence between the chemical bonds and (3, -1) CPs. Herein, recent computational studies are briefly reviewed to demonstrate why (3, -1) CPs are not indicators of chemical bonds. It is discussed why this confusing terminology needs to be changed and reemphasized that (3, -1) CPs should be called “line” critical points (LCPs). The proposed terminology detaches the topological properties of molecular electron densities from any a priori chemical interpretation. Such detachment, if adopted by other authors, will hopefully prevent further misinterpretation of the data emerging from the quantum theory of atoms in molecules (QTAIM).

In a series of papers in the last ten years, various aspects of the mathematical foundations of the quantum theory of atoms in molecules have been considered by this author and his coworkers in some detail. Although these considerations answered part of the questions raised by some critics on the mathematical foundations of the quantum theory of atoms in molecules, however, during these studies new mathematical problems also emerged that were reviewed elsewhere [Int. J. Quantum Chem. 111, 4497 (2011)]. Beyond mathematical subtleties of the formalism that were the original motivation for initial exchanges and disputes, the questions raised by critics had a constructive effect and prompted the author to propose a novel extension of the theory, now called the multi-component quantum theory of atoms in molecules [Theor. Chem. Acc. 132, 1365 (2013)]. Taking this background into account, in this paper a new set of open problems is put forward that the author believes proper answers to these questions, may open new doors for future theoretical developments of the quantum theory of atoms in molecules. Accordingly, rather than emphasizing on the rigorous mathematical formulation the practical motivations behind proposing these questions are discussed in detail and the relevant literature are reviewed while when possible, evidence and routes to answers are also provided. The author hopes that proposing these open questions as a compact package may motivate more mathematically oriented people to participate in future developments of the quantum theory of atoms in molecules.

An effective set of the Hartree-Fock (HF) equations are derived for electrons of the muonic systems, i.e., molecules containing a positively charged muon, conceiving the muon as a quantum oscillator, which are completely equivalent to the usual two-component HF equations used to derive stationary states of the muonic molecules.  In these effective equations, a non-Coulombic potential is added to the orthodox coulomb and exchange potential energy terms, which describes the interaction of the muon and the electrons effectively and is optimized during the self-consistent field cycles. While in the two-component HF equations muon is treated as a quantum wave, in the effective HF equations it is absorbed into the effective potential and practically transformed into an effective potential field experienced by electrons.  The explicit form of the effective potential depends on the nature of muon’s vibrations and is derivable from the basis set used to expand the muonic spatial orbital. The resulting effective Hartree-Fock equations are implemented computationally and used successfully, as a proof of concept, in a series of the muonic molecules containing all atoms from the second and third rows of the Periodic Table.  To solve the algebraic version of the equations muon-specific gaussian basis sets are designed for both muon and surrounding electrons and it is demonstrated that the optimized exponents are quite distinct from those derived for the hydrogen isotopes.  The developed effective HF theory is quite general and in principle can be used for any muonic system while it is the starting point for a general effective electronic structure theory that incorporates various types of quantum correlations into the muonic systems beyond the HF equations.

The orthodox quantum theory of atoms in molecules (QTAIM) is based on the clamped nucleus paradigm and working solely with the electronic wavefunctions, so unable to include nuclear vibrations in the AIM analysis. On the other hand, the recently extended version of the QTAIM, called the multi-component QTAIM (MC-QTAIM), incorporates both electrons and quantum nuclei, i.e. those nuclei treated as quantum waves instead of clamped point charges, into the AIM analysis using non-adiabatic wavefunctions. Thus, the MC-QTAIM is the natural framework to incorporate the role of nuclear vibrations into the AIM analysis. In this study, within the context of the MC-QTAIM, the formalism of including nuclear vibrational energy in the atomic basin energy is developed in detail and its contribution is derived analytically using the recently proposed non-adiabatic Hartree product nuclear wavefunction. It is demonstrated that within the context of this wavefunction the quantum nuclei may be conceived pseudo-adiabatically as quantum oscillators and both isotropic harmonic and anisotropic anharmonic oscillator models are used to compute the zero-point nuclear vibrational energy contribution to the basin energies explicitly. Inspired by the results gained within the context of the MC-QTAIM analysis, a heuristic approach is proposed within the context of the orthodox QTAIM to include nuclear vibrational energy in the basin energy from the vibrational wavefunction derived adiabatically. The explicit calculation of the basin contribution of the zero-point vibrational energy using uncoupled harmonic oscillator model leads to results consistent with those derived from the MC-QTAIM.

A series of novel, but possibly synthetically accessible, rigid hydrocarbon structures are introduced computationally maintaining ultrashort non-bonded hydrogen-hydrogen (H…H) contacts, < 1.2 Å.  These are the shortest non-bonded reported H…H contacts bypassing previous world records of both recently experimentally observed, 1.56 Å, and computationally derived, 1.4 Å, H…H contacts in any stable molecular structure.

A new formula that relates the electron density at the nucleus of atoms,rho(0,Z), and the atomic number,Z, is proposed. This formula, rho(0,Z)=a(Z-bZ^(0.5))^3, contains two unknown parameters (a,b) that are derived using a least square regression to the ab initio derived rho(0,Z) of Koga dataset from He (Z=2) to Lr (Z=103) atoms (Theor Chim Acta 95, 113 (1997)). In comparison to the well-known formula, rho(0,Z)=aZ^b, used for the same purpose previously, the resulting new formula is capable of reproducing the ab initio rho(0,Z) dataset an order of magnitude more precisely without introducing more regression parameters. This new formula may be used to transform the equations that relate correlation energy of atoms and rho(0,Z) into simpler equations just containing the atomic number as a fundamental property of atoms.

It is customary to conceive the interactions of all the constituents of a molecular system, i.e. electrons and nuclei, as Coulombic. However, in a more detailed analysis one may always find small but non-negligible non-Coulombic interactions in molecular systems originating from the finite size of nuclei, magnetic interactions, etc. While such small modifications of the Coulombic interactions do not seem to alter the nature of a molecular system in real world seriously, they are a serious obstacle for quantum chemical theories and methodologies which their formalism is strictly confined to the Coulombic interactions. Although the quantum theory of atoms in molecules (QTAIM) has been formulated originally for the Coulombic systems, some recent studies have demonstrated that most of its theoretical ingredients are not sensitive to the explicit form of the potential energy operator. However, the Coulombic interactions have been explicitly assumed in the mathematical procedure that is used to introduce the basin energy of an atom in a molecule. In this study it is demonstrated that the mathematical procedure may be extended to encompass the set of the homogeneous potential energy functions thus relegating adherence to the Coulombic interactions to introduce the energy of a real-space subsystem. On the other hand, this extension opens the door for seeking novel real-space subsystems, apart from atoms in molecules, in non-Coulombic systems. These novel real-space subsystems, quite different from the atoms in molecules, call an extended formalism that goes beyond the orthodox QTAIM. Accordingly, based on a previous proposal the new formalism, which is not confined to the Coulombic systems nor to the atoms in molecules as the sole real-space subsystems, is termed the quantum theory of proper open subsystems (QTPOS) and its potential applications are detailed. The harmonic trap model, containing non-interacting fermions or bosons, is considered as an example for the QTPOS analysis. The QTPOS analysis of bosonic systems is particularly quite unprecedented not attempted before.

In this communication a systematic computational survey on some rigid hydrocarbon skeletons, e.g. half-cage pentacyclododecanes and tetracyclododecanes, and their chlorinated derivatives in order to seek for the so-called ultrashort "non-bonded" hydrogen-hydrogen contacts is done.  It is demonstrated that upon a proper choice and modifications of the main hydrocarbon backbones, and addition of some chlorine atoms instead of the original hydrogen atoms in parts of the employed hydrocarbons, the resulting strain triggers structural changes yielding ultrashort hydrogen-hydrogen contacts with inter-nuclear distances as small as 1.38 Å.  Such ultrashort contacts are clearly less than the world record of an ultrashort non-bonded hydrogen-hydrogen contact, 1.56 Å,  very recently realized experimentally by Pascal and coworkers in in,in-bis(hydrosilane) [J. Am. Chem. Soc. 135, 13235 (2013)].  The resulting computed structures as well as the developed methodology for structure design open the door for constructing a proper set of molecules for future studies on the nature of the so-called non-bonded hydrogen-hydrogen interactions that is now an active and controversial area of research.

In a recent paper [J. Organomet. Chem. (2013) doi: 10.1016 /j.jorganchem. 2013.03.047] analyzing the bonding mode of Trimethylenemethane (TMM) with some metal carbonyls, Mousavi and Frenking have declared the absence of bond paths, the so-called missed bond paths, between metal atoms and terminal carbon atoms in several complexes.  They inferred these missed bond paths based on two principles, first, the fact that both the molecular orbital diagrams and the energy decomposition analysis point to the presence of chemical bonds between the metal atoms and the terminal carbon atoms and second, the presupposition that the indicator of a chemical bond within the quantum theory of atoms in molecules (QTAIM) is a bond path.  They used these observations and concomitant interpretation to question the reliability of bonds paths as indicators of chemical bonds.  In this communication, it is first demonstrated that the presupposition of the equivalence of a bond path and a chemical bond within the context of the QTAIM is superficial and basically flawed which is not only against with the recent strict declaration on the contrary [R.F.W. Bader, J. Phys. Chem. A 113 (2009) 10396], but also in odd with the foundations of the QTAIM.  Then, it is demonstrated that the so-called missed bond paths indeed appear in molecular graphs of some non-equilibrium geometries that are energetically quite accessible at room temperatures.  To emphasize on the importance of this observation the term passionate neighbors is coined referring to the atomic basins that do not share an inter-atomic surface at the equilibrium geometry but are neighbors, share an inter-atomic surface, at non-equilibrium geometries accessible by nuclear vibrations.  Using the delocalization index as well as other evidence from previous literature it is demonstrated that the QTAIM analysis is indeed compatible with the presence of chemical bonds between iron metal and terminal carbons in (CO)3Fe-TMM complex.  This observation further demonstrates that a consistent bonding pattern is emerged from a combined careful QTAIM analysis and the other theoretical approaches used for the analysis of bonding modes in aforementioned complexes.  Finally, some general discussions are done to unravel the delicate relationship between the QTAIM proposed concepts, e.g. bond paths and molecular graphs, and some orthodox concepts of chemistry, e.g. chemical bonds and chemical structures, emphasizing that there is no one-to-one relationship between these two categorizes.

In his wonderful Facts and Mysteries, Martinus Veltman terminates a section with an anecdote: "When quarks were not immediately discovered after the introduction by Gell-Mann he took to calling them symbolic, saying they were indices. In the early seventies I met him at CERN and he again said something in that spirit. I then jumped up, coming down with some impact that made the floor tremble, and asked him: Do I look like a heap of indices? This visibly rattled him, and indeed after that he no more advocated this vision, at least not as far as I know" (See page 240 in (Veltman, 2003)).  Although it is probable that Murray Gell-Mann, the inventor of quarks, has changed his mind regarding the reality of his symbols after this tough conversation, even later in the start of eighties the reality of quarks, as basic constituents of protons and neutrons, was a matter of disputes and exchanges (Shrader-Frechette, 1982a,b; Albright, 1982, Gruender, 1982).  A generation later, all these sound strange for a student of particle physics; after all, isn't it true that matter is composed of atoms, atoms of electrons and nuclei, nuclei of nucleons, and the latter of quarks? How is it possible that tangible matter being composed of just symbols?  The fear of a generation calling non-real as real is now gone, making their mental constructs part of modern particle physics reality…

Recently, the author of this paper and his research team have extended the orthodox Quantum Theory of Atoms in Molecules(QTAIM) to a novel paradigm called the two-component QTAIM (TC-QTAIM). This extended framework enables one to incorporate nuclear dynamics into the AIM analysis as well as performing AIM analysis of the exotic species; positronic and muonic species are a few examples. In present paper, this framework has been reviewed, providing some computational examples with particular emphasis on origins and applications, in a non-technical language. The main questions, enigmas and basic ideas that finally yielded the TC-QTAIM are considered in chronological order to help the reader comprehend the intuition behind the math. Finally, it is demonstrated that the TC-QTAIM and its more refined versions are able to tackle problems inaccessible to the orthodox QTAIM.

""The mathematical foundations of the quantum theory of atoms in molecules (QTAIM) [1] was recently considered in some detail by our research group [2-8]. The main concern of those papers was the subsystem variational procedure (SVP) of the QTAIM as well as the very nature of the topological atoms. In a recent excellent contribution on the local kinetic energy [9], Ayers and coworkers described these works as "… at a level of mathematical rigor that most chemist will find reasonable". Whereas this statement is generally true, it seems that our previous contributions may also give some clues on the degree of mathematical soundness of the SVP beyond a "chemical level". Accordingly, this communication aims to clarify some probably less known points that emerge from our previous analysis and their implications on the mathematical rigor of the QTAIM.
""

The notion of Quasi-atoms is introduced within the context of the Quantum Theory of Atoms in Molecules.  Being a subset of the Quantum Divided Basins that were introduced previously, Quasi-atoms are the quantum subsystems which are practically indistinguishable from the topological atoms; thus, revealing the continuous evolution of quantum divided basins into topological atoms.  This indistinguishablility is rooted in the limited accuracy of chemical observations; they are not sensitive to discriminate a topological atom from its associated Quasi-atoms.  In this regard, it is disclosed that the set of quantum atoms is in a wide-range including members other than topological atoms; the Quasi-atoms are concrete examples.  Finally, the idea of the fuzzy set of atoms that is foreign to the disjoint partitioning schemes for which the orthodox QTAIM is a classic example is extended employing the set of Quasi-atoms.

The influence of electron density on the magnitude of non-nuclear magnetic shielding, NICS, is studied in detail by scanning the electron density vs. NICSzz (the out-of-plane component of NICS). This study sheds new light on the role of electron density on the magnitude of NICS. Scanning the electron density vs. NICSzz not only helps to discriminate the electronic ring currents operative in aromatic, nonaromatic and antiaromatic species, but also yields a measure to compare the strength of diatropic/paratropic currents in molecules with different ring sizes or different number of p electrons without relying on the methods of s–p separation.

The role of finite nuclear models is scrutinized within the context of the Quantum Theory of Atoms in Molecules.  It is demonstrated that the newly proposed analytic-algebraic definition of the topological atoms is consistently extendable to the cases where a finite nuclear model is employed to construct the molecular hamiltonian.  The whole variational procedure is reconsidered, and the insensitivity of final results relative to the employed finite nuclear models is explicitly demonstrated.  The analysis once again clearly demonstrates that the analytic-algebraic condition is an independent axiom that must be added to the subsystem variational procedure in order to construct the Quantum Theory of Atoms in Molecules.

The roots of the modern atomic theory of matter goes back to the down of 19th century chemistry,[1] and evolved through the introduction of the structural theory in the middle of the century, i.e. a chemical structure may be attributed to each molecule containing its atomic composition and the bonds between atoms.[2] In 20th century, thanks to the introduction of the quantum mechanics and the discovery of subatomic particles, the “phenomenological” atomic theory evolved into its final stage as seemingly an “inductive” theory based on handful of neat physical equations and principles. The triumphant atmosphere surrounded this achievement is best summarized by Paul Dirac as one of founding fathers of quantum mechanics: “The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble”.[3] In contrast to this initial optimism, a detailed scrutiny in following decades demonstrated that many useful concepts rooted in the structural theory, and in use by chemists, are not easily derivable from the quantum theory of the electronic structure. Even now, almost a century later, there is a hidden tension between certain aspects of the structural theory of chemistry and molecular quantum mechanics that is well documented by various scientists since the mid-seventies.[4–7] One of the main tensions is around the concept of “atoms in molecules”; while molecular quantum mechanics conceives a molecule as an electronic system belonging to a single Hilbert space with a basis of molecular quantum states, the structural theory portraits the same system composed of discernible atoms and bonds in real/3D space. These two views if not incompatible, are at least orthogonal, and in one sense, has the potential to undermine Dirac’s dream of “reducing” the structural theory of chemistry to underlying fundamental physics. In this talk I will try to consider this and similar tensions to convey the massage why there are serious problems in the reduction of the structural theory of chemistry to quantum mechanics. However, beyond these obstacles, I will try to demonstrate that the structural theory of chemistry, when mathematized properly, is extendable to non-electronic matter, e.g. molecules containing positrons or positively charge muons, as well as to exotic quantum superpositions of molecular states. The new mathematical formulation of the structural theory which relies on quantum mechanics, termed “multi-component quantum theory of atoms in molecules,[8–14] is worked out by our research group in the last decade and applied extensively to the positronic and the muonic molecular species.[15–19]  Particularly, we have succeeded to attribute chemical structures to the above mentioned exotic molecules, while we have proposed to add the positive muon into the periodic table.[16] Most recently, we analyzed the first proposed anti-matter bond, i.e. the positronic bond,[20] revealing the true nature of this novel type of bond.[19] A general description of our motivations and goals and a glimpse of mathematical formulation may be found in,[8] while for a philosophical discussion on the reality of atoms in molecules the following reference,[21] is recommendable.             
References
[1] A. J. Rocke, Chemical Atomism in the Nineteenth Century: From Dalton to Cannizzaro, Ohio State University Press, Columbus, 1984.
[2] A. J. Rocke, The Quiet Revolution: Hermann Kolbe and the Science of Organic Chemistry, University Of California Press, Berkeley, 1993.
[3] P. A. M. Dirac, Proc. R. Soc. Lond. Ser. A 1929, 123, 714–733.
[4] R. G. Woolley, Adv. Phys. 1976, 25, 27–52.
[5] H. Primas, Chemistry, Quantum Mechanics and Reductionism: Perspectives in Theoretical Chemistry, Springer Berlin Heidelberg, Berlin, Heidelberg, 1983.
[6] S. J. Weininger, J. Chem. Educ. 1984, 61, 939.
[7] B. T. Sutcliffe, R. G. Woolley, Phys. Chem. Chem. Phys. 2005, 7, 3664–3676.
[8] S. Shahbazian, Found. Chem. 2013, 15, 287–302.
[9] M. Goli, S. Shahbazian, Theor. Chem. Acc. 2012, 131, 1208.
[10] M. Goli, S. Shahbazian, Theor. Chem. Acc. 2013, 132, 1365.
[11] M. Goli, S. Shahbazian, Theor. Chem. Acc. 2013, 132, 1362.
[12] M. Goli, S. Shahbazian, Theor. Chem. Acc. 2013, 132, 1410.
[13] M. Goli, S. Shahbazian, Phys. Chem. Chem. Phys. 2015, 17, 245–255.
[14] M. Gharabaghi, S. Shahbazian, J. Chem. Phys. 2017, 146, 154106.
[15] M. Goli, S. Shahbazian, Phys. Chem. Chem. Phys. 2014, 16, 6602–6613.
[16] M. Goli, S. Shahbazian, Phys. Chem. Chem. Phys. 2015, 17, 7023–7037.
[17] M. Goli, S. Shahbazian, Chem. - Eur. J. 2016, 22, 2525–2531.
[18] M. Goli, S. Shahbazian, Int. J. Quantum Chem. 2011, 111, 1982–1998.
[19] M. Goli, S. Shahbazian, ChemPhysChem 2019, 20, 831–837.
[20] J. Charry, M. T. do N. Varella, A. Reyes, Angew. Chem. Int. Ed. 2018, 57, 8859–8864.
[21] S. Shahbazian, Found. Chem. 2014, 16, 77–84.

In a recent paper with the same title, I have reviewed recent computational evidence demonstrating that the so-called bond critical points emerging from the topological analysis of the electron density are not indicators of chemical bonds. In this talk I will consider the same evidence in more detail based on our recent computational studies. As a result of these evidence and the fact that there is no universal one-to-one equivalence between these critical points and the presence of chemical bond, based on a recent proposal, they are termed line critical points instead. This new terminology detaches the chemical interpretation from the topological nature of the critical points and hopefully prevents misinterpretation of the topological analysis. In a broader view, my talk is an attempt to reveal that seeking a neat and direct link between the topology of electron density and identity of bonds is a vain hope.

It is customary in ab initio electronic structure theory to employ the clamped nucleus model; treating electrons as quantum particles and nuclei as point charges. While this model works well in most cases, in the non-adiabatic processes, e.g., electron coupled proton transfer, or when light particles like muons or positrons are added to a molecule it is no longer legitimate to employ the model and the proton, muon or positron must be also considered as a quantum particle. This means that the whole arsenal of ab initio methodologies developed within context of the clamped nucleus model is of no use and novel methodologies must be developed for such situations. In the last two decades, many such methodologies have been developed that the Nuclear-Electronic Orbital methodology (usually called NEO) is a prime example. Like the usual ab initio methodologies, the NEO has a hierarchical structure and as a first step the NEO-Hartree-Fock equations are introduced while in next steps various types of correlations, i.e., electron-electron and electron-nucleus (or muon, or positron) are introduced. More recently it has been shown that the NEO-Hartree-Fock equations are hugely simplified if one uses a Hartree type wavefunction for the quantum nuclei and this simplification maybe extended also to the NEO-density functional theory. Very recently we have demonstrated that this simplified NEO-Hartree-Fock equations can be transformed into a new set of “effective” Hartree-Fock equations in which the nucleus/muon/positron disappears as a quantum particle while the external potential experienced by electrons becomes non-Coulombic. It has been shown that the same trick also works for the NEO-density functional theory equations and an effective density functional theory emerges from the transformation. In this talk, various aspects of this novel effective theory are discussed and potential applications are considered in some detail.

Recent advances in the field of the synthetic biology has far reaching consequences for the philosophy of biology and revive the long standing debate of vitalism versus materialism in a modern context. Can we conceive cells, and biological systems in general, as mere machines that one may manipulate them like every other physical system? Can we synthesis life or invent even new forms of life without any precedent in nature? The answer of some people active in this field of research seems to be affirmative in the light of new advances in the synthetic biology. In this lecture I will first consider the general view of physicists on what is a physical system, which includes a long tradition starting from Newton and his analysis of the solar system and how this evolves through time. Also, the synthetic chemistry is considered from historical viewpoint and its role on the materialization of the concept of chemical system is scrutinized. Then, it will discussed that to what extent recent advances in synthetic biology make the biological systems physical/chemical systems. The idea of synthetic life will be considered and particularly the recent experimental advances made by Craig Venter and his associates will be in focus. In the end, the general perspective that the synthetic biology is delivering is examined with an eye to its philosophical implications.

While there has been a large progress in development of ab initio methods trying to solve time-independent Schrödinger equation since the advent of quantum mechanics, less is known how “chemical observables” maybe extracted from the resulting ab initio wavefunctions. One of these chemical observables are “atoms in molecules” (AIM) that is the main element of the structural theory of chemistry. These lectures try to introduce an approach that aims to extract the AIM and their properties, which are usually conceived as “non-observables”, using an extension of quantum mechanics to real-space subsystems.

Lecture I: The orthodox quantum theory of atoms in molecules (QTAIM)

The quantum theory of atoms in molecules (QTAIM), introduced by Richard Bader and coworkers, yields the AIM through 3D partitioning of molecule. The resulting AIM have well-defined and universal boundaries and each AIM has concrete properties, e.g. energy or charge, which is a share of total molecular property. This is done extending the hypervirial theorem to real-space subsystems while through using the second-order density matrices and the fluctuation theory it is demonstrated that AIM are open subsystem. The required “input” of the QTAIM analysis is the ab initio electronic wavefunction of a molecule. The details of the theory is discussed in this lecture.         

Lecture II: The multi-component quantum theory of atoms in molecules (MC-QTAIM)

In contrast to its vast applications and widespread recognition, the orthodox QTAIM is tied to the clamped nucleus model assuming a molecule is composed of electrons as the sole quantum particles of system and the nuclei are treated as static point charges. This implies that the orthodox QTAIM is not applicable the exotic species like the positronic and the muonic molecules as well as molecular systems considered beyond the Born-Oppenheimer paradigm. Particularly, the intractability of the latter systems is a serious limitation taking into account that nowadays a large number of interesting phenomena in chemistry and biochemistry are tied to the quantum effects relevant to protons intrinsically beyond the Born-Oppenheimer paradigm. The common feature of all these cases is their “multi-component” nature, namely, the presence of various types of quantum particles in a molecule. To study these systems within the AIM paradigm, one must extend the orthodox formalism going beyond the orthodox “single-component” QTAIM. A new formalism is proposed termed as the multi-component quantum theory of atoms in molecules (MC-QTAIM). The foundations and some applications of the “extended” QTAIM are considered in this lecture.

This is a modified version of a one hour talk delivered in condensed matter branch of the Institute for theoretical physics and advanced mathematics at Tehran. It was also the basis of two other talks delivered at Brno in Czech Republic and at a conference in Austria

This is the first lecture of an undergraduate course on computational chemistry. The course is based mainly on the first three chapters of Errol Lewars book entitled "COMPUTATIONAL CHEMISTRY: Introduction to the Theory and Applications of Molecular and Quantum Mechanics".

This is the second lecture of an undergraduate course on computational chemistry. The course is based mainly on the first three chapters of Errol Lewars book entitled "COMPUTATIONAL CHEMISTRY: Introduction to the Theory and Applications of Molecular and Quantum Mechanics".

This is the third lecture of an undergraduate course on computational chemistry. The course is based mainly on the first three chapters of Errol Lewars book entitled "COMPUTATIONAL CHEMISTRY: Introduction to the Theory and Applications of Molecular and Quantum Mechanics".

This is the forth lecture of an undergraduate course on computational chemistry. The course is based mainly on the first three chapters of Errol Lewars book entitled "COMPUTATIONAL CHEMISTRY: Introduction to the Theory and Applications of Molecular and Quantum Mechanics".

This is the fifth lecture of an undergraduate course on computational chemistry. The course is based mainly on the first three chapters of Errol Lewars book entitled "COMPUTATIONAL CHEMISTRY: Introduction to the Theory and Applications of Molecular and Quantum Mechanics".

The quantum theory of atoms in molecules, QTAIM, is employed to identify AIM and quantify their interactions through the partitioning of molecule into atomic basins in the real space and it is confined only to the purely electronic systems composed of electrons as quantum particles and the nuclei as clamped point charges. The extended version of the QTAIM, called the multi-component QTAIM, MC-QTAIM, bypasses this border and makes it possible to identify AIM and quantify their interactions in systems composed of multiple quantum particles that electrons may or may not be one of their components opening a new door for the analysis of the exotic AIM and bonds. In this contribution, two conjectures, called Bader conjecture, BC, and extended Bader conjecture, EBC, are proposed as the cornerstones of the real-space partitioning of a molecule into atomic basins within the context of the QTAIM and the MC-QTAIM, respectively. A literature survey on various few-body quantum systems composed of quarks, nucleons, and elementary particles like muons and positrons is also done unraveling the fact that in all these diverse systems there are unambiguous cases of clusterizations. These clustered systems, irrespective to their components, behave as if they are molecules composed of some kind of atoms, instead of being an amorphous mixture of quantum particles. In the case of the muonic and the positronic molecules computational studies reveal that the AIM structures of these systems are well-captured by the EBC. Beyond identifying atomic basins, both QTAIM and MC-QTAIM attribute properties to AIM, which is their share from the molecular expectation values of quantum observables. It is demonstrated that not only the share from the average value of an observable may be attributed to an atomic basin, but also the fluctuation of each basin property is also quantifiable.

The concept of "atoms in molecules" (AIM) is one of the cornerstones of the structural theory of chemistry. However, in contrast to the free atoms, a comprehensive quantum mechanical theory of AIM, treating them as quantum particles or quantum subsystems, has never been proposed. Currently, the most satisfactory deduction of this concept is based on the "partitioning" methodologies that are trying to recover AIM from the ab initio wavefunctions. One of these methodologies is the quantum theory of AIM (QTAIM), which retrieves AIM by an exhaustive partitioning of the one-electron density into atomic basins in real space. The molecular properties are then partitioned into the basin and inter-basin contributions as the incarnation of the AIM properties and their interaction modes, respectively. The inputs of the QTAIM partitioning scheme are the electronic wavefunctions computed from the electronic Schrödinger equation, which is a "single-component" equation treating electrons as quantum particles and the nuclei as clamped point charges. A recently extended form of the QTAIM, called the multi-component QTAIM (MC-QTAIM), removes this restriction and enables AIM partitioning to be applied to the MC many-body quantum systems. This is done using MC wavefunctions as inputs that are derived from the MC Schrödinger equation in which there are two or more types of quantum particles. This opens the possibility for the AIM partitioning of molecular systems where certain nuclei, e.g. because of their non-adiabatic coupling to electrons, must be treated as quantum particles instead of clamped point charges. The same formalism allows the partitioning of exotic molecular systems in which there are other elementary particles like muons or positrons, in addition to electrons and nuclei. The application of the MC-QTAIM partitioning to such systems reveals that the positively charged muon may shape its atomic basin, i.e. an example of "exotic AIM", while a positron may act as an agent of bonding, i.e. an example of "exotic bonds".