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Quantum Mechanical Calculation of the Optical Absorption of Silver and Gold Nanoparticles by Density Functional Theory | Science Publications

机译：密度泛函理论计算银和金纳米粒子的光吸收率的量子力学计算科学出版物

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> Problem statement: Metal nanoparticles confine the motion of conduction electrons and exhibit a strong optical absorption of electromagnetic radiation in the UV-vis-NIR region. The absorption is classically derived from the collective oscillations of free electrons in a metallic nanostructure as a consequence of incident electromagnetic radiation polarizing the particle optically embedded in a dielectric matrix. These oscillations, known as the localized surface Plasmon resonance has been modelled by Gustav Mie in 1908 using the Maxwell's equations. Nevertheless, the electrodynamics approach cannot account for the electronic transitions often displayed in experiment as a broad UV-vis optical absorption spectrum originated from the conduction electrons of metal nanoparticles. A quantum mechanical approach is required to address the optical absorption spectra of metal nanoparticles systemically. Approach: In this study, an attempt was made to calculate the optical absorption spectra of conduction electrons of metal nanoparticle quantum mechanically using the density functional theory. The particle was an isolated spherical metal nanoparticle containing N atoms confined in a face-centered cubic lattice structure. When light strikes the particle, the occupied ground-state conduction electrons absorbed the energy and excite to the unoccupied higher energy-state of the conduction band. In this development, we used time-independent Schrodinger equation for the ground-state energy of Thomas-Fermi-Dirac-Weizsacker atomic model for the total energy functional and the density function in the Euler-Lagrange equation is algebraically substituted with the absorption function. The total energy functional was computed numerically for silver and gold nanoparticles at various diameters. Results: The results showed broad absorption spectra derived from the occupied ground-state conduction electrons at the orbital {n = 5 and l = 0 or 5s} for silver and {n = 6 and l = 0 or 6s} for gold, which excite to the unoccupied higher energy of conduction band at the orbital {n≥6 and l = 0 or 1} for silver and {n≥7 and l = 0 or 1} for gold. A nonlinear red-shift of the absorption peak λmax, appearing at 404.79, 408.36, 412.55, 415.73, 418.42 and 420.96 nm for silver and at 510.28, 520.91, 533.11, 542.35, 549.74 and 556.04 nm for gold when the particle diameter varies at 4, 5, 7, 10, 15 and 25 nm respectively. The quantum confinement effect of the conduction bands is stronger for silver and gold nanoparticles of less than about 20 nm in diameter. Conclusion: The optical absorption spectra of silver and gold nanoparticles have been successfully calculated using a quantum treatment and this calculation could be extended to other transition metal nanoparticles of interest in nanoscience and nanotechnology.
机译： > 问题陈述：金属纳米粒子限制了传导电子的运动，并在UV-vis-NIR区域表现出对电磁辐射的强光吸收。吸收是经典地源自金属纳米结构中自由电子的集体振荡，这是入射电磁辐射使光学嵌入电介质基体中的粒子极化的结果。古斯塔夫·米（Gustav Mie）在1908年使用麦克斯韦（Maxwell）方程对这些振荡进行了建模，称为局部表面等离振子共振。然而，电动力学方法不能解释在实验中经常显示的电子跃迁，因为它是源自金属纳米粒子的传导电子的宽广的可见光吸收光谱。需要量子力学方法来系统地解决金属纳米颗粒的光吸收光谱。 方法：在这项研究中，尝试使用密度泛函理论以机械方式计算金属纳米粒子量子的导电电子的光吸收谱。该粒子是包含限制在面心立方晶格结构中的N原子的孤立球形金属纳米粒子。当光撞击粒子时，占据的基态传导电子吸收能量并激发到未占据的导带高能态。在这项研究中，我们将时间无关的Schrodinger方程用于Thomas-Fermi-Dirac-Weizsacker原子模型的基态能量，用于总能量函数，并将Euler-Lagrange方程中的密度函数代入吸收函数。对于各种直径的银和金纳米颗粒，通过数值计算了总能量函数。 结果：结果表明，银的{n = 6和l = 0或6时，在轨道{n = 5和l = 0或5s}处，占据的基态传导电子所产生的宽吸收光谱。对于金为6s}，在银{n≥7且l = 0或1}时激发{n≥6且l = 0或1}轨道上未占用的更高的导带能量。吸收峰λ max 的非线性红移，出现在404.79、408.36、412.55、415.73、418.42和420.96 nm（对于银）和510.28、520.91、533.11、542.35、549.74和556.04 nm。粒径分别在4、5、7、10、15和25 nm时变化的金。对于直径小于约20nm的银和金纳米颗粒，导带的量子约束作用更强。 结论：使用量子处理已成功计算了银和金纳米颗粒的光吸收光谱，该计算可扩展到纳米科学和纳米技术中感兴趣的其他过渡金属纳米颗粒。

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