Analytical First-Order Molecular Properties and Forces within the Adiabatic Connection Random Phase Approximation
Analytical First-Order Molecular Properties and Forces within the Adiabatic Connection Random Phase Approximation
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DOI：
10.1021/ct4008553
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发表时间：
2014-01-01
影响因子：
5.5
通讯作者：
Eshuis, Henk
中科院分区：
文献类型：
--
作者：
Burow, Asbjoern M.;Bates, Jefferson E.;Eshuis, Henk
随机相位近似（RPA）是在密度泛函理论的绝热连接涨落耗散定理框架内计算分子基态相关能的一种日益流行的方法。我们使用身份分辨率 (RI) 近似和虚频率积分，提出一阶 RPA 分子特性和核力的有效分析实现。我们方法的核心是分别在占据和虚拟参考轨道的酉变换下的变分 RPA 能量拉格朗日不变量。其构造需要解独立于扰动数量的单个耦合扰动 Kohn-Sham 方程。关于核位移和其他一阶特性（例如单粒子密度或偶极矩）的能量梯度是从拉格朗日的偏导数获得的。我们的 RPA 能量梯度实现与单点 RPA 能量计算一样，在系统规模 N 下表现出相同的 O(N(4)log N) 缩放。在典型应用中，计算相对于核位移的整个梯度向量的成本类似于单点 RPA 能量计算的 5 倍。用于频率积分的正交节点和权重的导数对于 RPA 梯度至关重要，其精度与 RPA 能量一致，可以包含在我们的方法中。 RPA 平衡结构的质量通过与共价主族化合物、wealdy 键合二聚体和过渡金属配合物的准确理论和实验数据进行比较来评估。 RPA 优于半局域泛函以及二阶 Moller-Plesset (MP2) 理论，后者对于过渡金属化合物严重失败。可极化分子和弱结合二聚体的偶极矩显示出类似的趋势。 RPA 谐波振动频率几乎相当于一组主族化合物的耦合簇单频、双频和微扰三频质量。与 Rekkedal 等人基于环耦合集群的实现相比。 [J。化学。物理。 2013, 139, 081101.]，我们的方法可以通过 N 的两倍更好地扩展，并支持半局部 Kohn-Sham 参考。后者对于 RPA 在小间隙系统中的良好性能至关重要。
The random phase approximation (RPA) is an increasingly popular method for computing molecular ground-state correlation energies within the adiabatic connection fluctuation dissipation theorem framework of density functional theory. We present an efficient analytical implementation of first-order RPA molecular properties and nuclear forces using the resolution-of-the-identity (RI) approximation and imaginary frequency integration. The centerpiece of our approach is a variational RPA energy Lagrangian invariant under unitary transformations of occupied and virtual reference orbitals, respectively. Its construction requires the solution of a single coupled-perturbed Kohn-Sham equation independent of the number of perturbations. Energy gradients with respect to nuclear displacements and other first-order properties such as one-particle densities or dipole moments are obtained from partial derivatives of the Lagrangian. Our RPA energy gradient implementation exhibits the same O(N(4)log N) scaling with system size N as a single-point RPA energy calculation. In typical applications, the cost for computing the entire gradient vector with respect to nuclear displacements is similar to 5 times that of a single-point RPA energy calculation. Derivatives of the quadrature nodes and weights used for frequency integration are essential for RPA gradients with an accuracy consistent with RPA energies and can be included in our approach. The quality of RPA equilibrium structures is assessed by comparison to accurate theoretical and experimental data for covalent main group compounds, wealdy bonded dimers, and transition metal complexes. RPA outperforms semilocal functionals as well as second-order Moller-Plesset (MP2) theory, which fails badly for the transition metal compounds. Dipole moments of polarizable molecules and weakly bound dimers show a similar trend. RPA harmonic vibrational frequencies are nearly of coupled cluster singles, doubles, and perturbative triples quality for a set of main group compounds. Compared to the ring-coupled cluster based implementation of Rekkedal et al. [J. Chem. Phys. 2013, 139, 081101.], our method scales better by two powers of N and supports a semilocal Kohn-Sham reference. The latter is essential for the good performance of RPA in small-gap systems.