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首页> 外文期刊>The journal of physical chemistry, A. Molecules, spectroscopy, kinetics, environment, & general theory >Polar Coordinate Representation of H_b(r_c)versus(h~2/8m)~2ρ_b(r_c)at BCP in AIM Analysis:Classification and Evaluation of Weak to Strong Interactions
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Polar Coordinate Representation of H_b(r_c)versus(h~2/8m)~2ρ_b(r_c)at BCP in AIM Analysis:Classification and Evaluation of Weak to Strong Interactions

机译：AIM分析中BCP的H_b（r_c）对（h〜2 / 8m）〜2ρ_b（r_c）的极坐标表示：弱相互作用到强相互作用的分类和评估

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Polar coordinate (R,θ) representation is proposed for the plot of H_versus (h~2/8m)?~2ρ_b(r_c) in AIM analysisto classify, evaluate, and understand weak to strong interactions in a unified way and in more detail; H_b(r_c)and ?~2ρ_b(r_c) are total electron energy densities and the Laplacian of ρ_atbond critical points (BCPs: c),respectively, where ρ_b(r_c) are electron densities at r_c. Both thex-and y-axes of the plot are expressed in thecommon unit of energy since H_b(r_c) = G_b(r_c) + V_b(c)and(h~2/8m)~2ρ_b(c)=?H_c)-V_r_c)/2 (=G_r_c) +V_b(r_c)/2), whereG_c)andV_arekinetic energy densities and potential densities, respectively.Data employed for the plot are calculated at BCPs for full-optimized structures and optimized structures withthe fixed distances (r) of r = r_o+wa_o,wherer_oare the full-optimized distances,a_ois Bohr radius, andw = ±0.1 and ±0.2. The plot draws a helical stream starting from near origin (H_=(h~2/8m)?~2ρ_b(r_c) =0) for very weak interactions and turns to the right as interactions become stronger. The helical stream is welldescribed by the polar coordinate representation with (R, θ); R is given in the energy unit, and θ in degreesis measured from the y-axis. The ratio of V_b(r_c)/G_c) (= k)controls θ,of which an acceptable range in theplot is 45.0 <θ < 206.6°. Each plot for an interaction gives a curve, which supplies important information.It is expressed by θ_p and k_p; θ_pcorresponds to the tangent line measured from y-direction, and k_pis thecurvature of the plot at w = 0. The polar coordinate (R, θ) representation with (θ_p, k_p) helps us to classify,evaluate, and understand the nature of weak to strong interactions in a unified way.
机译：针对AIM分析中H_versus（h〜2 / 8m）？〜2ρ_b（r_c）的图提出了极坐标（R，θ）表示法，以统一，更详细地分类，评估和理解弱到强相互作用。 H_b（r_c）和？〜2ρ_b（r_c）分别是总电子能量密度和ρ_atbond临界点（BCPs：c）的拉普拉斯算子，其中ρ_b（r_c）是r_c处的电子密度。由于H_b（r_c）= G_b（r_c）+ V_b（c）和（h〜2 / 8m）〜2ρ_b（c）=？H_c）-，因此图的x轴和y轴均以公共能量单位表示。 V_r_c）/ 2（= G_r_c）+ V_b（r_c）/ 2），其中G_c）和V_arekinetic能量密度和势能密度。在BCP上针对固定距离（r r = r_o + wa_o的），其中r_o是完全优化的距离，a_ois玻尔半径，w =±0.1和±0.2。对于非常弱的相互作用，该图绘制了一个从近原点（H _ =（h〜2 / 8m）？〜2ρ_b（r_c）= 0）开始的螺旋流，并随着相互作用的增强而向右旋转。螺旋流由极坐标表示为（R，θ）很好地描述; R以能量单位给出，θ角度是从y轴测量的。 V_b（r_c）/ G_c）的比率（= k）控制θ，在图中可接受的范围是45.0 <θ<206.6°。每个交互图都给出一条曲线，该曲线可提供重要信息。它由θ_p和k_p表示; θ_p对应于从y方向测量的切线，并且k_pis是曲线在w = 0时的曲率。极坐标（R，θ）表示为（θ_p，k_p）有助于我们分类，评估和理解弱项的性质以统一的方式进行强大的互动。

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