Laboratory of Computational and Structural Physical Chemistry, Chemistry Department, West University of Timişoara, Pestalozzi Street No.16, Timişoara, RO-300115, Romania.
Int J Mol Sci. 2009 Nov 10;10(11):4816-4940. doi: 10.3390/ijms10114816.
The density matrix theory, the ancestor of density functional theory, provides the immediate framework for Path Integral (PI) development, allowing the canonical density be extended for the many-electronic systems through the density functional closure relationship. Yet, the use of path integral formalism for electronic density prescription presents several advantages: assures the inner quantum mechanical description of the system by parameterized paths; averages the quantum fluctuations; behaves as the propagator for time-space evolution of quantum information; resembles Schrödinger equation; allows quantum statistical description of the system through partition function computing. In this framework, four levels of path integral formalism were presented: the Feynman quantum mechanical, the semiclassical, the Feynman-Kleinert effective classical, and the Fokker-Planck non-equilibrium ones. In each case the density matrix or/and the canonical density were rigorously defined and presented. The practical specializations for quantum free and harmonic motions, for statistical high and low temperature limits, the smearing justification for the Bohr's quantum stability postulate with the paradigmatic Hydrogen atomic excursion, along the quantum chemical calculation of semiclassical electronegativity and hardness, of chemical action and Mulliken electronegativity, as well as by the Markovian generalizations of Becke-Edgecombe electronic focalization functions - all advocate for the reliability of assuming PI formalism of quantum mechanics as a versatile one, suited for analytically and/or computationally modeling of a variety of fundamental physical and chemical reactivity concepts characterizing the (density driving) many-electronic systems.
密度矩阵理论是密度泛函理论的前身，为路径积分（PI）的发展提供了直接的框架，允许通过密度泛函封闭关系将正则密度扩展到多电子系统。然而，路径积分形式用于电子密度规定具有几个优点：通过参数化路径确保系统的内部量子力学描述；平均量子涨落；作为量子信息时空演化的传播子；类似于薛定谔方程；允许通过计算配分函数对系统进行量子统计描述。在这个框架中，提出了路径积分形式的四个层次：费曼量子力学、半经典、费曼-克莱因特有效经典和福克-普朗克非平衡。在每种情况下，都严格定义并呈现了密度矩阵或/和正则密度。量子自由和调和运动的实用专门化，统计高温和低温极限，玻尔量子稳定性假设的扩展合理性，以及氢原子激发的范例，沿着半经典电负性和硬度、化学作用和 Mulliken 电负性的量子化学计算，以及贝克-边缘科电子聚焦函数的马尔可夫推广——所有这些都支持将量子力学的 PI 形式作为一种通用的形式，适用于分析和/或计算建模各种基本物理和化学反应性概念的可靠性，这些概念描述了（密度驱动）多电子系统。
