arXiv subjects

Shant Shahbazian

Publications and source records attributed to Shant Shahbazian.

At least 19 recordsLinked to original sources

arXiv2026

The two-positron gluic bond as a manifestation of "super" van der Waals interactions

Recently, it has been demonstrated theoretically that the interaction of two PsH atoms, each being a stable bound state of a hydrogen atom and a positronium atom, is attractive, leading to the formation of a molecular complex denoted as (PsH)2. However, the physical nature of this interaction has remained elusive. In the present study, we show that the stabilizing mechanism is entirely encoded in the quantum correlations between the two positrons and, to a lesser extent, in the electron-positron correlations. Notably, the interaction cannot be recovered at the mean-field (Hartree-Fock) level, nor by computational models that include only electron-electron correlation effects. Accordingly, the bond formed between PsH units, termed here a two-positron gluic bond to emphasize its fundamentally distinct character from the two-positron covalent bonds present in pure antimatter molecules, emerges only when matter and antimatter particles form a common bound state. When classified within the framework of known bonding mechanisms, this gluic bond falls into the category of stabilizing dispersion interactions, giving rise to a van der Waals complex. However, its remarkably large bond dissociation energy, compared with those of strongly bonded van der Waals complexes of similar size, reveals an anomalously strong interaction. For this reason, we propose that (PsH)2 is most appropriately described as a "super" van der Waals complex stabilized by a "super" van der Waals bond.

physics.chem-ph↗

arXiv2025

Exotic Harmonium Model: Exploring Correlation Effects of Attractive Coulomb Interaction

Simple few-body systems often serve as theoretical laboratories across various branches of theoretical physics. A prominent example is the two-electron Harmonium model, which has been widely studied over the past three decades to gain insights into the nature of the electron-electron correlations in many-electron quantum systems. Building on our previous work [Phys. Rev. B 108, 245155 (2023)], we introduce an analogous model consisting of an electron and a positively charged particle (PCP) with variable mass, interacting via Coulomb forces while confined by external harmonic potentials. Termed the exotic Harmonium model, this provides insights into the electron-PCP correlations, a cornerstone of the emerging field of the ab initio study of multi-component many-body quantum systems. Through a systematic exploration of the parameter space and numerical solutions of the corresponding Schrödinger equation, we identify two extreme regimes: the atom-like and the particle-in-trap-like behavior. The electron-PCP correlation dominates in the atom-like regime, significantly influencing physical observables, while its role diminishes in the particle-in-trap-like limit. Between these two extremes lies a complex intermediate regime that challenges qualitative interpretation. Overall, the exotic Harmonium model offers a powerful framework to unravel the electron-PCP correlations across diverse systems, spanning particles of varying masses and conditions, from ambient to high-pressure environments.

quant-ph↗

arXiv2024

Comment on "Two-component density functional theory study of quantized muons in solids"

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.

cond-mat.other↗

arXiv2023

Quantifying errors of the electron-proton/muon correlation functionals through the Kohn-Sham inversion of a two-component model system

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 electron-proton/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 e$μ$c-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.

physics.atm-clus↗

arXiv2023

On the nature of the two-positron bond: Evidence for a novel bond type

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.

physics.chem-ph↗

arXiv2023

The MC-QTAIM analysis reveals an exotic bond in the coherently quantum superposed Malonaldehyde

The proton between the two oxygen atoms of the malonaldehyde molecule experiences an effective double-well potential in which the proton 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.

physics.chem-ph↗

arXiv2022

The conceptual and mathematical foundations of the MC-QTAIM

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 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 (WF). 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. The inputs of the QTAIM partitioning scheme are the electronic WF computed from the electronic Schrodinger equation (SE), which is basically a single-component equation treating electrons as quantum particles and the nuclei as clamped point charges (CPC). 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 quantum systems. This is done using MC-WF as inputs that are derived from the MC-SE 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 CPC. 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 own atomic basin, i.e. an example of exotic AIM, while positron may act as an agent of bonding, i.e. an example of exotic bonds.

physics.chem-ph↗

arXiv2022

The MC-QTAIM: A framework for extending the atoms in molecules analysis beyond purely electronic systems

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.

physics.atm-clus↗

arXiv2022

Two-component density functional theory for muonic molecules: Inclusion of the electron-positive muon correlation functional

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 which is foreign to the purely electronic DFT. A Wigner-type local electron-positive muon correlation functional, termed e$μ$c-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 e$μ$c-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 e$μ$c-1. Thus, this study set 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.

physics.chem-ph↗

arXiv2019

On the nature of the positronic bond

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 (2018)]. In order to dig into the nature of this novel bond the newly developed multi-component quantum theory of atoms in molecules 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.

physics.atm-clus↗

arXiv2018

Developing effective electronic-only coupled-cluster and Muller-Plesset perturbation theories for the muonic molecules

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 Muller-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.

physics.atm-clus↗

arXiv2018

Revisiting the foundations of the quantum theory of atoms in molecules: Some open problems

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 details. 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, new mathematical problems also emerged during these studies 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 and its multi-component version.

physics.chem-ph↗

arXiv2018

Effective electronic-only Kohn-Sham equations for the muonic molecules

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 vibration, which are optimized during the solution of the EKS equations making muon 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.

physics.atm-clus↗

arXiv2017

Toward a muon-specific electronic structure theory: Effective electronic Hartree-Fock equations for the muonic 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 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.

physics.atm-clus↗

arXiv2017

Extending the topological analysis and seeking the real-space subsystems in non-Coulombic systems with homogeneous potential energy functions

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 apart from basin energy of an atom in a molecule, its theoretical ingredients are not sensitive to the explicit form of the potential energy operator. In this study, it is demonstrated that the basin energy may be defined not only for coulombic systems but for all real-space subsystems of those systems that are described by any member of the set of the homogeneous potential energy functions. 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 call for an extended formalism that goes beyond the orthodox QTAIM, which is not confined to the Coulombic systems nor to the atoms in molecules as the sole real-space subsystems. It is termed the quantum theory of real-space open subsystems (QTROS) and its potential applications are detailed. The harmonic trap model, containing non-interacting fermions or bosons, is considered as an example for the QTROS analysis. The QTROS analysis of bosonic systems is particularly quite unprecedented, not attempted before.

physics.chem-ph↗

arXiv2017

Incorporating nuclear vibrational energies into the -atom in molecules- analysis: An analytical study

The quantum theory of atoms in molecules (QTAIM) is based on the clamped nucleus paradigm and solely working with the electronic wavefunctions, so does not 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 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.

physics.chem-ph↗

arXiv2016

Some implications of the Hartree product treatment of the quantum nuclei in the ab initio Nuclear-electronic orbital methodology

In this letter the conceptual and computational implications of the Hartree product type nuclear wavefunction introduced recently within the context of the ab initio non-Born-Oppenheimer Nuclear-electronic orbital (NEO) methodology are considered. It is demonstrated that this wavefunction may imply a pseudo-adiabatic separation of the nuclei and electrons and each nucleus is conceived as a quantum oscillator while a non-Coulombic effective Hamiltonian is deduced for electrons. Using the variational principle this Hamiltonian is employed to derive a modified set of single-component Hartree-Fock equations which are equivalent to the multi-component version derived previously within the context of the NEO and, easy to be implemented computationally.

physics.chem-ph↗

arXiv2015

Revisiting the Z-dependence of the electron density at the nuclei

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.

physics.chem-ph↗