In 2012 Lange et al. suggested a distinct bonding mechanism: perpendicular paramagnetic bonding, generated by the stabilization of antibonding orbitals in their perpendicular orientation relative to an external magnetic field. The perpendicular paramagnetic bonding explains the bonding of H2 in the 3Σu+(1σg1σu*) triplet state and of He2 in the 1Σg+(1σg21σu*2) singlet state, as well as their preferred perpendicular orientation in the external field. In this paper, the culture of quantum chemistry and life in Norway are also briefly touched upon.
An anion (negative ion) such as O2−, which is stable in a molecule/solid, sometimes cannot bind an attached electron in a vacuum and emits an electron. To describe an anion, the author previously developed the SIWB (surrounding or solid Coulomb-potential-induced well for basis set) method for a linear combination of atomic orbitals (LCAO) calculated numerically in a discrete variational (DV) density functional theory (DFT). For the generation of basis atomic orbitals, the DV method usually adds a well potential to the potential for electrons to stabilize the electrons. There was no reasonable method for determining the depth and radius of the well and the usual well depth has a relatively deep value of about −1 Eh independent of electron attachment tendency. In contrast, the SIWB method adds a well potential solely for generating and improving anion basis atomic orbital functions and uniquely determines the depth and radius of the well, which is relatively shallow, considering the Coulomb potential arising from the surrounding nuclei and electron cloud in a molecule/solid. This article aims to attempt calculations for the one-electron wave function of a molecule including an anion using the finite element method, which adopts a basis set localized in a small region on a space lattice that is suitable for the wave function behavior of an anion. The finite element results were compared not only to results from the usual LCAO method with a relatively deep well (denoted as LCAO−N), but also to those from the improved LCAO method with the SIWB scheme (denoted as LCAO−SIWB). It emerged from the present study that the finite element results for the anion are consistent with the LCAO−SIWB results.
The 1/Nπ relationship states that the reorganization energy λ of a molecule associated with charge transport is inversely proportional to the number Nπ of sites or π electrons involved in a π state of the molecule: λ∝1/Nπ. We investigated the fundamental question of how λ is influenced by Nπ, from the perspective of the vibronic coupling density. Vibronic coupling density analysis showed that symmetric distribution of the electron-density difference Δρ is essential for this relationship. The relationship can be more precisely rephrased as the size of the vibronic coupling constant is inversely proportional to the square-root of the number of sites over which Δρ is delocalized. Our findings provide not only a fundamental understanding of the 1/Nπ relationship, but also a practical approach to the molecular design of functional materials through controlling Δρ and vibronic couplings.
1s電子により結合を形成するH2+， H2， HeH+， He2+， He22+について，平衡核間距離とポテンシャルエネルギー曲面，および軌道相互作用を解析した．平衡核間距離は，UMP2/6–311++G**レベルでそれぞれ1.0496，0.738，0.785，1.086，0.712 Å (1 Å = 1−10m)であり，それぞれの大小関係を電子反発と軌道相互作用で説明することができた．但しHe2+の核間距離がHe22+より長いのは，He22+の反結合性軌道に電子が入ったためと考えられるが，H2+より短いので，Heの1sの半径がHのそれに比べて短いことに起因している可能性もある．