Implementation of van der Waals Density Functional Approach to the Spin-Polarized System: Interaction Potential between Oxygen Molecules

H−T phase diagram of solid oxygen

“…The mechanism of the α-θ phase transition is explained in analogy with the O 2 -O 2 dimer, as follows. In zero field, the most stable alignment of the O 2 -O 2 dimer is H geometry where two molecules align rectangular-parallel [4][5][6][7]. The stability of the H geometry is owing to the maximized π orbital overlapping between the dimer, leading to larger AFM interaction.…”

“…However, when the magnetization of the dimer is saturated by an external field, AFM interaction is no longer favored and the molecules struggle to decrease it. For instance, if the molecules align in X geometry (crossed), overlap integral becomes zero due to the orthogonal geometry [4][5][6][7]. Namely, the O 2 -O 2 dimer can tune the exchange interaction by changing its alignment.…”

“…The exchange interaction between O 2 molecules contributes to condensation energy in addition to the van der Waals interaction. The strength of the exchange interaction greatly depends on the alignment of O 2 molecules [4][5][6][7], indicating that the packing structure of solid oxygen is tuned by its magnetic ground state. Moreover, solid oxygen is the only antiferromagnetic (AFM) insulator composed of single element [8].…”

Application of a Van Der Waals Density Functional to Small Molecular Complexes and Solids

“…Among others, the van der Waals density functional (vdW-DF) [2][3][4] developed by Langreth, Lundqvist, and co-workers has attracted much attention and applied a variety of systems [5], because it is able to describe the dispersion forces using only the charge density and density gradient as inputs, at a moderate computational cost with efficient algorithms [6][7][8] Following the proposal of vdW-DF for the general geometry by Dion et al, [3] several works [4,[9][10][11][12][13][14][15][16][17][18][19][20] have been done to improve the accuracy of vdW-DF as accuracy of the original one by Diotn et al is quite limited. Much effort has been devoted to develop better semilocal exchange functionals, as it is a dominate part of the total energy, and plays an important role in the interaction energy [9][10][11]20,45] .…”

“…The present author has proposed to use the exchange functional of Cooper (C09) [10] in conjunction with the nonlocal correlation functional for the second version of vdW-DF (vdW-DF2), which is dubbed vdW-DF2 C09 x (or vdW-DF2-C09), for an accurate calculation of the adsorption systems [13]. However, because the number of applications of vdW-DF2 C09 x is quite limited [13,19,[21][22][23][24], it is necessary to assess the accuracy of the functional for different systems and understand its applicability and limitation. This is particularly important for interfaces (for e.g., organic-inorganic interfaces), where different types of interactions come into play.…”