Gaussian, Inc., 340 Quinnipiac Street Building 40, Wallingford, Connecticut 06492, USA.
J Chem Phys. 2010 Mar 21;132(11):114110. doi: 10.1063/1.3359469.
Continuum solvation models are appealing because of the simplified yet accurate description they provide of the solvent effect on a solute, described either by quantum mechanical or classical methods. The polarizable continuum model (PCM) family of solvation models is among the most widely used, although their application has been hampered by discontinuities and singularities arising from the discretization of the integral equations at the solute-solvent interface. In this contribution we introduce a continuous surface charge (CSC) approach that leads to a smooth and robust formalism for the PCM models. We start from the scheme proposed over ten years ago by York and Karplus and we generalize it in various ways, including the extension to analytic second derivatives with respect to atomic positions. We propose an optimal discrete representation of the integral operators required for the determination of the apparent surface charge. We achieve a clear separation between "model" and "cavity" which, together with simple generalizations of modern integral codes, is all that is required for an extensible and efficient implementation of the PCM models. Following this approach we are now able to introduce solvent effects on energies, structures, and vibrational frequencies (analytical first and second derivatives with respect to atomic coordinates), magnetic properties (derivatives with respect of magnetic field using GIAOs), and in the calculation more complex properties like frequency-dependent Raman activities, vibrational circular dichroism, and Raman optical activity.
连续溶剂化模型之所以吸引人，是因为它们对溶质的溶剂效应提供了简化而准确的描述，可以用量子力学或经典方法来描述。尽管可极化连续体模型（PCM）溶剂化模型家族是应用最广泛的模型之一，但由于在溶质-溶剂界面上积分方程的离散化会产生不连续性和奇点，它们的应用受到了阻碍。在本研究中，我们引入了连续表面电荷（CSC）方法，为 PCM 模型提供了一种平滑且稳健的形式。我们从 York 和 Karplus 十多年前提出的方案开始，并以各种方式对其进行了推广，包括对原子位置的二阶导数进行解析扩展。我们提出了一种确定表观表面电荷所需积分算子的最佳离散表示。我们实现了“模型”和“腔”之间的清晰分离，这与现代积分代码的简单推广一起，是实现 PCM 模型可扩展和高效实现所需的全部内容。采用这种方法，我们现在能够在能量、结构和振动频率（原子坐标的一阶和二阶导数）、磁性质（使用 GIAO 相对于磁场的导数）以及更复杂的性质（如频率相关拉曼活性、振动圆二色性和拉曼光学活性）上引入溶剂效应。
