Visualization of Orbitals (8) Probability Density Distribution in the Three Dimensional Representation of Hydrogen 1s - 6h Orbitals in a Spherical Glass Block

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  • TOKITA Sumio
    Saitama University (Emeritus), 255 Shimo-Ohkubo, Sakura-ku, Saitama, Saitama, 338-8570, Japan

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  • 電子を描く(8) – 球形彫刻とその特徴

Abstract

<p>A three dimensional representation of the probability density of a real hydrogen atomic orbital in a spherical glass block was developed. Different from a cubic medium in Figure 1 (a) or Figure 2 (a) on a previous paper [2], a spherical medium has no edge. This advantage is effective for the observation of n = 1, 2, …, l = n - 1, |m| = 2 orbitals. In the case of the fourth column in Figure 2 (a) [2], planar nodes containing z axis is clearly seen as is shown the one of them in the fourth column in Figure 1 (a) [2]. However, as for the pairing orbitals shown in the eighth column in Figure 2 (a) [2], it is difficult to observe planar nodes containing z axis because of the hindrance of edges (the plane x = y, or x = - y coalesces into edges parallel to the z axis). Another advantage of no edge effect lies on the total amount of the sculpture. As the one shape of the pairing orbitals transformed to the other by a proper rotation, 36 sculptures in Figure 1 (a) or 2 (a) are diminished to 21 patterns listed in Figure 3 (a) in a previous paper [2]. The greatest advantage of this sculpture in a spherical glass block lies in the appearance of the image of an absolute square of complex orbital in Figure 1 and 2 in a previous paper [1] by revolving a spherical glass block of the probability density of a real hydrogen atomic orbital. Figure 1 (a) shows a hydrogen 4f (zx2-zy2) (or 4f (xyz)) orbital, namely, an n = 4, l = 3, |m| = 2 orbital set on a plate for revolving. On revolving, the image of an n = 4, l = 3, m = 2 orbital of Figure 3 (a) on a previous paper [2] appears (Figure 1 (b, c)) .</p>

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