A general non-adiabatic quantum instanton approximation

Semiclassical Green's functions and an instanton formulation of electron-transfer rates in the nonadiabatic limit

We present semiclassical approximations to Green's functions of multidimensional systems, extending Gutzwiller's work to the classically forbidden region. Based on steepest-descent integrals over these functions, we derive an instanton method for computing the rate of nonadiabatic reactions, such as electron transfer, in the weak-coupling limit, where Fermi's golden-rule can be employed. This generalizes Marcus theory to systems for which the environment free-energy curves are not harmonic and where nuclear tunnelling plays a role. The derivation avoids using the Im F method or short-time appr…

Path integral evaluation of the kinetic isotope effects based on the quantum instanton approximation

A general method for computing kinetic isotope effects is described. The method uses the quantum-instanton approximation and is based on the thermodynamic integration with respect to the mass of the isotopes and on the path-integral Monte-Carlo evaluation of relevant thermodynamic quantities. The central ingredients of the method are the Monte-Carlo estimators for the logarithmic derivatives of the partition function and the delta-delta correlation function. Several alternative estimators for these quantities are described here and their merits are compared on the benchmark hydrogen-exchange r…

Exact non-adiabatic part of the Kohn-Sham potential and its fluidic approximation

We present a simple geometrical "fluidic" approximation to the non-adiabatic part of the Kohn-Sham potential, $v_{\mathrm{KS}}$, of time-dependent density functional theory. This part of $v_{\mathrm{KS}}$ is often crucial, but most practical functional approximations utilize an adiabatic approach based on ground-state DFT. For a variety of prototype systems, we calculate the exact time-dependent electron density, and find that the fluidic approximation corrects a large part of the error arising from the "exact adiabatic" approach, even when the system is evolving far from adiabatically.

Extending the random-phase approximation for electronic correlation energies: The renormalized adiabatic local density approximation

The adiabatic connection fluctuation-dissipation theorem with the random phase approximation (RPA) has recently been applied with success to obtain correlation energies of a variety of chemical and solid state systems. The main merit of this approach is the improved description of dispersive forces while chemical bond strengths and absolute correlation energies are systematically underestimated. In this work we extend the RPA by including a parameter-free renormalized version of the adiabatic local density (ALDA) exchange-correlation kernel. The renormalization consists of a (local) truncation…

含时密度泛函理论中的非绝热近似：进展与展望

Non-Adiabatic Approximations in Time-Dependent Density Functional Theory: Progress and Prospects

本文综述了含时密度泛函理论中非绝热（记忆依赖）交换关联泛函近似的研究进展、对计算的影响及开发实用精确泛函所面临的挑战。

Adiabatic approximation in open quantum systems

We generalize the standard quantum adiabatic approximation to the case of open quantum systems. We define the adiabatic limit of an open quantum system as the regime in which its dynamical superoperator can be decomposed in terms of independently evolving Jordan blocks. We then establish validity and invalidity conditions for this approximation and discuss their applicability to superoperators changing slowly in time. As an example, the adiabatic evolution of a two-level open system is analysed.

非绝热环聚合物瞬子速率理论：一种广义分界面方法

Nonadiabatic ring-polymer instanton rate theory: a generalised dividing-surface approach

本文提出一种广义非绝热环聚合物瞬子速率理论，通过可调分界面同时测量核坐标与电子态间的通量，桥接Born--Oppenheimer极限与Fermi黄金规则极限，在保持半经典精度的同时为非绝热反应提供新的机理视角。

Direct evaluation of the temperature dependence of the rate constant based on the quantum instanton approximation

A general method for the direct evaluation of the temperature dependence of the quantum-mechanical reaction rate constant in many-dimensional systems is described. The method is based on the quantum instanton approximation for the rate constant, thermodynamic integration with respect to the inverse temperature, and the path integral Monte Carlo evaluation. It can describe deviations from the Arrhenius law due to the coupling of rotations and vibrations, zero-point energy, tunneling, corner-cutting, and other nuclear quantum effects. The method is tested on the Eckart barrier and the full-dimen…

Dissipative Tunneling Rates through the Incorporation of First-Principles Electronic Friction in Instanton Rate Theory I: Theory

Reactions involving adsorbates on metallic surfaces and impurities in bulk metals are ubiquitous in a wide range of technological applications. The theoretical modelling of such reactions presents a formidable challenge for theory because nuclear quantum effects (NQEs) can play a prominent role and the coupling of the atomic motion with the electrons in the metal gives rise to important non-adiabatic effects (NAEs) that alter atomic dynamics. In this work, we derive a theoretical framework that captures both NQEs and NAEs and, due to its high efficiency, can be applied to first-principles calc…

Nonadiabatic time-dependent density-functional theory at the cost of adiabatic local density approximation

We propose a computationally efficient approach to the nonadiabatic time-dependent density functional theory (TDDFT) which is based on a representation of the frequency-dependent exchange correlation kernel as a response of a set of damped oscillators. The requirements to computational resources needed to implement our approach do not differ from those of the standard real-time TDDFT in the adiabatic local density approximation (ALDA). Thus, our result offers an exciting opportunity to take into account temporal nonlocality and memory effects in calculations with TDDFT in quantum chemistry and…