Pawłowski Filip, Olsen Jeppe, Jørgensen Poul
qLEAP Center for Theoretical Chemistry, Department of Chemistry, Aarhus University, Langelandsgade 140, DK-8000 Aarhus C, Denmark.
J Chem Phys. 2015 Mar 21;142(11):114109. doi: 10.1063/1.4913364.
The time-dependent Schrödinger equation for a time-periodic perturbation is recasted into a Hermitian eigenvalue equation, where the quasi-energy is an eigenvalue and the time-periodic regular wave function an eigenstate. From this Hermitian eigenvalue equation, a rigorous and transparent formulation of response function theory is developed where (i) molecular properties are defined as derivatives of the quasi-energy with respect to perturbation strengths, (ii) the quasi-energy can be determined from the time-periodic regular wave function using a variational principle or via projection, and (iii) the parametrization of the unperturbed state can differ from the parametrization of the time evolution of this state. This development brings the definition of molecular properties and their determination on par for static and time-periodic perturbations and removes inaccuracies and inconsistencies of previous response function theory formulations. The development where the parametrization of the unperturbed state and its time evolution may differ also extends the range of the wave function models for which response functions can be determined. The simplicity and universality of the presented formulation is illustrated by applying it to the configuration interaction (CI) and the coupled cluster (CC) wave function models and by introducing a new model-the coupled cluster configuration interaction (CC-CI) model-where a coupled cluster exponential parametrization is used for the unperturbed state and a linear parametrization for its time evolution. For static perturbations, the CC-CI response functions are shown to be the analytical analogues of the static molecular properties obtained from finite field equation-of-motion coupled cluster (EOMCC) energy calculations. The structural similarities and differences between the CI, CC, and CC-CI response functions are also discussed with emphasis on linear versus non-linear parametrizations and the size-extensivity of the obtained molecular properties.
对于时间周期微扰的含时薛定谔方程被重新表述为一个厄米特本征值方程，其中准能量是本征值，时间周期正则波函数是本征态。基于这个厄米特本征值方程，发展出了一种严格且清晰的响应函数理论表述，其中：(i) 分子性质被定义为准能量相对于微扰强度的导数；(ii) 准能量可以使用变分原理或通过投影从时间周期正则波函数中确定；(iii) 未微扰态的参数化可以与该态时间演化的参数化不同。这一发展使得分子性质的定义及其对于静态和时间周期微扰的确定处于同等地位，并消除了先前响应函数理论表述中的不准确和不一致之处。未微扰态及其时间演化的参数化可以不同这一发展也扩展了能够确定响应函数的波函数模型的范围。通过将其应用于组态相互作用（CI）和耦合簇（CC）波函数模型，并引入一个新模型——耦合簇组态相互作用（CC - CI）模型（其中未微扰态使用耦合簇指数参数化，其时间演化使用线性参数化），说明了所提出表述的简单性和通用性。对于静态微扰，CC - CI响应函数被证明是从有限场运动方程耦合簇（EOMCC）能量计算中获得的静态分子性质的解析类似物。还讨论了CI、CC和CC - CI响应函数之间的结构异同，重点在于线性与非线性参数化以及所获得分子性质的尺寸扩展性。
