The two-component quantum theory of atoms in molecules (TC-QTAIM): the unified theory of localization/delocalization of electrons, nuclei, and exotic elementary particles

Abstract

In this contribution, pursuing our research program extending the atoms in molecules analysis into unorthodox domains, another key ingredient of the two-component quantum theory of atoms in molecules (TC-QTAIM) namely, the theory of localization/delocalization of quantum particles, is disclosed. The unified proposed scheme is able not only to deal with the localization/delocalization of electrons in/between atomic basins, but also to treat nuclei as well as exotic particles like positrons and muons equally. Based on the general reduced second order density matrices for indistinguishable quantum particles, the quantum fluctuations of atomic basins are introduced and then used as a gauge to quantify the localization/delocalization introducing proper indexes. The explicit mass-dependence of the proposed indexes is demonstrated and it is shown that a single localization/delocalization index is capable of being used for all kind of quantum particles regardless of their masses or charge content. For various non-Born-Oppenhiemer (non-BO) wavefunctions, including Hartree-product as well as singlet and triplet determinants, the indices are calculated and then employed to rationalize the localization/delocalization of particles in a series of fourbody model systems consist of two electrons and two positively charged particles with variable mass. The ab initio FV-MC_MO derived non-BO wavefunctions for the four-body series are used for a comprehensive computational TC-QTAIM analysis, including topological analysis as well as basin integrations, in a wide mass regime, (m e stands for electron mass), disclosing various traits in these series of species that are unique to the TC-QTAIM. On the other hand, it is demonstrated that in the large mass extreme the TC-QTAIM analysis reduces to the one performed within context of the orthodox QTAIM with two clamped positive particles revealing the fact that the TC-QTAIM encompasses the orthodox QTAIM as an asymptote. Finally, it is concluded that the proposed localization/delocalization scheme is capable of quantifying quantum tunneling of nuclei for systems containing delocalized protons. Such capability promises novel applications for the TC-QTAIM as well as its extended multi-component version (MC-QTAIM) introduced recently.

Topological and AIM analyses beyond the Born–Oppenheimer paradigm: New opportunities

“…This contraction of the mean internuclear distances, which is a well known phenomenon [19][20][21][22][23], originates from the fact that energies in each class are also clearly correlated with the mass of hydrogen isotopes and are more negative for the heavier isotopes; the most negative energies correspond to the clamped nucleus limit. This is in line with previous studies [5,6,9,14] and is rationalized based on the virial theorem that is almost satisfied inspecting the computed virial ratios given in Table 1; according to this theorem, at the equilibrium state the total energy is just the minus sum of kinetic energies of all component bodies of a system [7]. Accordingly, as is also evident from Table 2, with increasing the mass of quantum nuclei the nuclear kinetic energy decreases, being zero for the clamped nucleus.…”

“…In order to fit our requirements, the original NEO package was modified and new features were added as detailed below. At the next stage the produced nBO wavefunctions were used for the MC-QTAIM analysis, encompassing both the topological analysis and the basin integrations, using procedures described fully in previous publications [5,9,12]. Finally, the AIMAll package was used to visualize the Molecular Graphs (MGs) [17].…”

“…The original formulation of the QTAIM was just confined within the Born-Oppenheimer (BO) paradigm, treating electrons as quantum waves and nuclei as clamped point charges, using the electronic wavefunctions as inputs [2]. The recently developed multi-component QTAIM (MC-QTAIM) goes beyond this paradigm and is capable of using non-adiabatic wavefunctions as inputs; treating nuclei as quantum waves instead of clamped nuclei [5][6][7][8][9][10]. Even more, this new formalism is capable of using the wavefunctions of the positronic and the muonic species as inputs yielding the atoms in molecules in these exotic species [11][12][13][14].…”

“…While in our previous computational studies only diatomic species were considered [5][6][7][8][9][10][11][12][13][14], in present contribution the first examples of the MC-QTAIM analysis of polyatomic species are considered in details assuming hydrogen nuclei as quantum waves. Our model systems include some basic hydrocarbons namely methane, ethylene, acetylene and benzene as well as their congeners containing deuterons and tritons instead of protons.…”

Chemical structure and reactivity by means of quantum chemical topology analysis

“…Otero de la Roza and Luaña [84] have discussed the rigorous characterization of the electron density Laplacian of crystals in terms of its topological properties, as well as these authors have also presented a program for real-space analysis of quantum chemical interactions in solids [85]. Very recently, Shahbazian and Goli [86][87][88] have reviewed the QTAIM framework, providing some computational examples with particular emphasis on origins and applications, while Martín-Pendás et al [89] have proved that QTAIM is a versatile tool to be applied to molecules in their electronic excited states, expanding the knowledge that the molecular orbital framework provides about electronic rearrangements.…”