Electronic and Crystal Packing Effects in Terms of Static and Kinetic Force Field Features: Picolinic Acid N-Oxide and Methimazole

Abstract

Herein, we experimentally obtained and studied the inner-crystal scalar potential fields and the associated vector force fields of static and kinetic nature in picolinic acid N-oxide (PANO) and methimazole. The “through-bond” and “through-space” electronic effects were defined and distinguished via the vector fields and concurred with the penetration of the electron contributor’s electrostatic and kinetic force field pseudoatoms (φes- and φ k -basins) into the occupier’s chemical atom (ρ-basin). A special focus was given to the dipolar N+–O– bond as well as to the thioamide N–CS and carboxylic OC–OH fragments. An unusual way of interatomic charge transfer was revealed between two nonbonded hydrogen atoms [COO−]H···H[−C] in the PANO crystal. The experimental electric and kinetic force fields in the molecular crystals were compared to the theoretical ones for the free molecules and hydrogen-bonded associates, which helped figure out the natural consequences of the crystal packing effect. As expected, the appearance of neighboring attractors in a dense crystal packing requires zero-flux surfaces (ZFSs) emerging in the vector fields and the compression of the outer force field pseudoatoms of a molecule. We proposed to consider a ZFS in the kinetic force field to be a turning surface for electrons in the sense that an electron passed through the boundary is immediately affected by the redirected force attributed to another attractor. The strengthening and noticeable increase observed in the covalency of the intramolecular hydrogen bond O–H···O in the PANO crystal is a direct consequence of such compression of the hydrogen atom and pseudoatoms by the inner-crystal environment. The Pauli and fermionic scalar and vector fields were applied to locate electron lone pairs and describe their involvement in noncovalent interactions within the donor–acceptor mechanism.

Unified Picture of Interatomic Interactions, Structures, and Chemical Reactions by Means of Electrostatic and Kinetic Force Density Fields: Appel’s Salt and Its Ion Pairs

“…In quantum chemistry, instead of the more common energy (bonding) approach, chemical interactions and structures can be described in terms of the force (binding) approach, − that is by means of the Hellmann–Feynman , and Ehrenfest forces acting on nuclei and electrons, respectively, as well as of Hellmann–Slater molecular virial theorem , connecting bonding and binding approaches. On the other hand, in the local form, forces acting on electrons are expressed in terms of force density fields in crystals , or in molecules and associates . Namely, since there are potential fields φ i ( r ) in an electron–nuclear system {φ W ( r ) is the bosonic or von Weizsäcker potential, , φ P ( r ) is the Pauli potential that is the fermionic correction to φ W ( r ), φ k ( r ) = φ W ( r ) + φ P ( r ) is the total kinetic potential, φ es ( r ) is the electrostatic potential, φ x ( r ) is the exchange–correlation potential, and φ em ( r ) = −φ es ( r ) + φ x ( r ) is the total static potential or the potential acting on an electron in a molecule (PAEM) , }, each of these scalar fields can be associated with the corresponding vector force field scriptF ( r ) = prefix− normal∇ φ normale normalm ( r ) , F es ( r ) = ∇φ es ( r ), or F i ( r ) = −∇φ i ( r ) acting on a unit negative charge .…”

“…Namely, since there are potential fields φ i ( r ) in an electron–nuclear system {φ W ( r ) is the bosonic or von Weizsäcker potential, , φ P ( r ) is the Pauli potential that is the fermionic correction to φ W ( r ), φ k ( r ) = φ W ( r ) + φ P ( r ) is the total kinetic potential, φ es ( r ) is the electrostatic potential, φ x ( r ) is the exchange–correlation potential, and φ em ( r ) = −φ es ( r ) + φ x ( r ) is the total static potential or the potential acting on an electron in a molecule (PAEM) , }, each of these scalar fields can be associated with the corresponding vector force field scriptF ( r ) = prefix− normal∇ φ normale normalm ( r ) , F es ( r ) = ∇φ es ( r ), or F i ( r ) = −∇φ i ( r ) acting on a unit negative charge . The homotropic total static force or the force acting on an electron in a molecule (FAEM), scriptF ( r ) = boldF normale normals ( r ) + boldF x ( r ) , is driven by the structural confinements and draws electrons to the respective atomic nucleus, − ,, while the heterotropic kinetic force F k ( r ) = F W ( r ) + F P ( r ) is driven by the quantum-mechanical electron motion and pushes electrons away from the nucleus so as to compensate for the former one, that is boldF k ( r ) = prefix− scriptF ( r ) at the ground-state condition −∇μ( r ) = 0 {μ( r ) is the electronic chemical potential}. − , …”

“…These fragments are called the potential-based φ es - and φ k -basins or, if each of them includes a joint nucleus, the electrostatic and kinetic force-field pseudoatoms, or F es - and F k -pseudoatoms for short. The ZFSs U (Ω) and P (Ω) that demarcate potential-based basins or pseudoatoms are defined by the zero-flux conditions: − ,, boldF es ( r ) · boldn ( r ) = normal∇ φ normale normals ( r ) · boldn ( r ) = 0 , ∀ boldr ∈ U ( Ω , r U ) boldF k ( r ) · boldn ( r ) = prefix− normal∇ φ k ( r ) · boldn ( r ) = 0 , ∀ boldr ∈ P ( Ω , r P ) where n ( r ) is the outward-directed vector normal to the inter-pseudoatomic surface. Like the QTAIM, a pair of neighboring nuclei can be connected in the φ es ( r ) or φ k ( r ) scalar field through a binding internuclear line or φ-path, the analogue of a bond ρ-path.…”

“…Our attention is now drawn to the newly developing orbital-free force density field approach that is grounded on the mechanical concept of binding rather than that on the energetical concept of bonding. This approach is built on the assertion that (i) the appearance of localized pseudoatoms characterized by shape and charge and of ZFSs delimiting them, , (ii) the mutual compression of force-field pseudoatoms of the same type, (iii) the penetration of a bonded atom into neighboring force-field pseudoatoms, ,, and (iv) the occurrence of a saddle equilibrium point between two force-field attractors connected through a binding φ-path , are all the inherent consequences of the emergence and existence of any many-electron multinuclear system and reflect the mutual influence of all atoms in a system. Therefore, for a chemical system under statistical equilibrium, they elucidate the chemical bonding or interactions.…”

“…It is worth noting that the FAEM scriptF ( r ) and Ehrenfest force density frakturH ( r ) exhibit similar behavior, topology, and physical meaning, , but scriptF ( r ) , as well as the other abovementioned force fields F i ( r ), is accessible from experimental ED distributions in crystals applying the ideas of the orbital-free density functional theory (OF DFT). , In particular, the behavior of FAEM scriptF ( r ) and kinetic force F k ( r ) in crystals obtained from experimental data has recently been described in detail on the several examples. − ,,, The behavior of frakturH ( r ) in calculated systems has also been the subject of fruitful research. − …”