The Face-to-Face σ-Hole···σ-Hole Stacking Interactions: Structures, Energies, and Nature

The existence of the π···π stacking interaction is well-known. Similarly, it is reasonable to assume the existence of the σ-hole···σ-hole stacking interaction. In this work, the structures, energies, and nature of the face-to-face σ-hole···σ-hole stacking interactions in the crystal structures have been investigated in detail by the quantum chemical calculations. The calculated results clearly show that the face-to-face σ-hole···σ-hole stacking interactions exist and have unique properties, although their strengths are not very significant. The energy component analysis reveals that, unlike many other dispersion-dominated noncovalent interactions in which the induction energies always play minor roles for their stabilities, for the face-to-face σ-hole···σ-hole stacking interaction the contribution of the induction energy to the total attractive energy is close to or even larger than that of the electrostatic energy. The structures, energies, and nature of the face-to-face σ-hole···σ-hole stacking interactions confined in small spaces have also been theoretically simulated. One of the important findings is that encapsulation of the complex bound by the face-to-face σ-hole···σ-hole stacking interaction can tune the electronic properties of the container.

Electrostatics, Charge Transfer, and the Nature of the Halide-Water Hydrogen Bond

Binary halide–water complexes X^–(H₂O) are examined by means of symmetry-adapted perturbation theory, using charge-constrained promolecular reference densities to extract a meaningful charge-transfer component from the induction energy. As is known, the X^–(H₂O) potential energy surface (for X = F, Cl, Br, or I) is characterized by symmetric left and right hydrogen bonds separated by a <i>C_2v</i>-symmetric saddle point, with a tunneling barrier height that is < 2 kcal/mol except in the case of F^–(H₂O). Our analysis demonstrates that the charge-transfer energy is correspondingly small (< 2 kcal/mol except for X = F), considerably smaller than the electrostatic interaction energy. Nevertheless, charge transfer plays a crucial role determining the conformational preferences of X^–(H₂O) and provides a driving force for the formation of quasi-linear X^...H–O hydrogen bonds. Charge-transfer energies correlate well with measured O–H vibrational redshifts for both halide–water complexes as well as OH^–(H₂O) and NO₂^–(H₂O), providing some indication of a general mechanism. <br>

Electrostatics, Charge Transfer, and the Nature of the Halide-Water Hydrogen Bond

Binary halide–water complexes X^–(H₂O) are examined by means of symmetry-adapted perturbation theory, using charge-constrained promolecular reference densities to extract a meaningful charge-transfer component from the induction energy. As is known, the X^–(H₂O) potential energy surface (for X = F, Cl, Br, or I) is characterized by symmetric left and right hydrogen bonds separated by a <i>C_2v</i>-symmetric saddle point, with a tunneling barrier height that is < 2 kcal/mol except in the case of F^–(H₂O). Our analysis demonstrates that the charge-transfer energy is correspondingly small (< 2 kcal/mol except for X = F), considerably smaller than the electrostatic interaction energy. Nevertheless, charge transfer plays a crucial role determining the conformational preferences of X^–(H₂O) and provides a driving force for the formation of quasi-linear X^...H–O hydrogen bonds. Charge-transfer energies correlate well with measured O–H vibrational redshifts for both halide–water complexes as well as OH^–(H₂O) and NO₂^–(H₂O), providing some indication of a general mechanism. <br>

Average value of the shape and direction factor in the equation of refractive index

The theoretical calculation of the refractive indices is of great significance for the developments of new optical materials. The calculation method of refractive index, which was deduced from the electron-cloud-conductor model, contains the shape and direction factor [Formula: see text]. [Formula: see text] affects the electromagnetic-induction energy absorbed by the electron clouds, thereby influencing the refractive indices. It is not yet known how to calculate [Formula: see text] value of non-spherical electron clouds. In this paper, [Formula: see text] value is derived by imaginatively dividing the electron cloud into numerous little volume elements and then regrouping them. This paper proves that [Formula: see text] when molecules’ spatial orientations distribute randomly. The calculations of the refractive indices of several substances validate this equation. This result will help to promote the application of the calculation method of refractive index.