Kristensen Kasper, Kauczor Joanna, Kjaergaard Thomas, Jørgensen Poul
Department of Chemistry, Lundbeck Foundation Center for Theoretical Chemistry, Aarhus University, Langelandsgade 140, DK-8000 Aarhus C, Denmark.
J Chem Phys. 2009 Jul 28;131(4):044112. doi: 10.1063/1.3173828.
We present a quasienergy-based formulation of damped response theory where a common effective lifetime parameter has been introduced for all excited states in terms of complex excitation energies. The introduction of finite excited state lifetimes leads to a set of (complex) damped response equations, which have the same form to all orders in the perturbation. An algorithm is presented for solving the damped response equations in Hartree-Fock theory and Kohn-Sham density functional theory. The use of the quasienergy formulation allows us to obtain directly the computationally simplest expressions for damped response functions by applying a set of response parameter elimination rules, which minimize the total number of damped response equations to be solved. In standard response theory broadened absorption spectra are obtained by ad hoc superimposing lineshape functions onto the absorption stick spectra, whereas an empirical lineshape function common to all excitations is an integrated part of damped response theory. By superimposing the lineshape functions inherent in damped response theory onto the stick spectra of standard response theory, we show that the absorption spectra obtained in standard and damped response theory calculations are identical. We demonstrate that damped response theory may be applied to obtain absorption spectra in all frequency ranges, also those that are not readily addressed using standard response theory. This makes damped response theory an effective tool, e.g., for determining absorption spectra for large molecules, where the density of the excited states may be very high, and where standard response theory therefore is not applicable in practice. A thorough comparison is given between our formulation of damped response theory and the formulation by Norman et al. [J. Chem. Phys. 123, 194103 (2005)].
我们提出了一种基于准能量的阻尼响应理论公式，其中针对所有激发态，根据复激发能引入了一个通用的有效寿命参数。有限激发态寿命的引入导致了一组（复）阻尼响应方程，这些方程在微扰的所有阶次上具有相同的形式。本文给出了一种在哈特里 - 福克理论和科恩 - Sham 密度泛函理论中求解阻尼响应方程的算法。使用准能量公式使我们能够通过应用一组响应参数消除规则，直接获得阻尼响应函数在计算上最简单的表达式，这些规则能使待求解的阻尼响应方程总数最小化。在标准响应理论中，通过将线形函数临时叠加到吸收棒状光谱上来获得展宽的吸收光谱，而所有激发态共有的经验线形函数是阻尼响应理论的一个组成部分。通过将阻尼响应理论中固有的线形函数叠加到标准响应理论的棒状光谱上，我们表明在标准和阻尼响应理论计算中获得的吸收光谱是相同的。我们证明了阻尼响应理论可用于获得所有频率范围内的吸收光谱，包括那些使用标准响应理论难以处理的频率范围。这使得阻尼响应理论成为一种有效的工具，例如，用于确定大分子的吸收光谱，在大分子中激发态密度可能非常高，因此标准响应理论在实际中不适用。我们对阻尼响应理论的公式与诺曼等人 [《化学物理杂志》123, 194103 (2005)] 的公式进行了全面比较。
