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Theoretical perspectives on non-Born–Oppenheimer effects in chemistry 化学中非玻恩-奥本海默效应的理论展望
Pub Date : 2022-03-28 DOI: 10.1098/rsta.2020.0377
S. Hammes‐Schiffer
The Born–Oppenheimer approximation, which assumes that the electrons respond instantaneously to the motion of the nuclei, breaks down for a wide range of chemical and biological processes. The rate constants of such nonadiabatic processes can be calculated using analytical theories, and the real-time nonequilibrium dynamics can be described using numerical atomistic simulations. The selection of an approach depends on the desired balance between accuracy and efficiency. The computational expense of generating potential energy surfaces on-the-fly often favours the use of approximate, robust and efficient methods such as trajectory surface hopping for large, complex systems. The development of formally exact non-Born–Oppenheimer methods and the exploration of well-defined approximations to such methods are critical for providing benchmarks and preparing for the next generation of faster computers. Thus, the parallel development of rigorous but computationally expensive methods and more approximate but computationally efficient methods is optimal. This Perspective briefly summarizes the available theoretical and computational non-Born–Oppenheimer methods and presents examples illustrating how analytical theories and nonadiabatic dynamics simulations can elucidate the fundamental principles of chemical and biological processes. These examples also highlight how theoretical calculations are able to guide the interpretation of experimental data and provide experimentally testable predictions for nonadiabatic processes. This article is part of the theme issue ‘Chemistry without the Born–Oppenheimer approximation’.
玻恩-奥本海默近似假设电子对原子核的运动作出即时反应,但在广泛的化学和生物过程中,这种近似被打破了。这种非绝热过程的速率常数可以用解析理论计算,非平衡动力学可以用数值原子模拟来描述。方法的选择取决于准确度和效率之间的理想平衡。动态生成势能曲面的计算费用往往倾向于使用近似、鲁棒和高效的方法,如大型复杂系统的轨迹表面跳变。正式精确的非born - oppenheimer方法的发展和对这些方法的定义良好的近似的探索对于提供基准和为下一代更快的计算机做准备至关重要。因此,并行开发严格但计算代价昂贵的方法和更近似但计算效率高的方法是最优的。本展望简要总结了现有的理论和计算非玻恩-奥本海默方法,并举例说明了分析理论和非绝热动力学模拟如何阐明化学和生物过程的基本原理。这些例子还强调了理论计算如何能够指导实验数据的解释,并为非绝热过程提供实验可测试的预测。这篇文章是主题问题“没有波恩-奥本海默近似的化学”的一部分。
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引用次数: 7
Quantum flux densities for electronic–nuclear motion: exact versus Born–Oppenheimer dynamics 电子-核运动的量子通量密度:精确与玻恩-奥本海默动力学
Pub Date : 2022-03-28 DOI: 10.1098/rsta.2020.0385
T. Schaupp, V. Engel
We study the coupled electronic–nuclear dynamics in a model system to compare numerically exact calculations of electronic and nuclear flux densities with those obtained from the Born–Oppenheimer (BO) approximation. Within the adiabatic expansion of the total wave function, we identify the terms which contribute to the flux densities. It is found that only off-diagonal elements that involve the interaction between different electronic states contribute to the electronic flux whereas in the nuclear case the major contribution belongs to the BO electronic state. New flux densities are introduced where in both, the electronic and the nuclear case, the main contribution is contained in the component corresponding to the BO state. As a consequence, they can be determined within the BO approximation, and an excellent agreement with the exact results is found. This article is part of the theme issue ‘Chemistry without the Born–Oppenheimer approximation’.
我们研究了一个模型系统中的耦合电子-核动力学,以比较电子和核通量密度的数值精确计算与从Born-Oppenheimer (BO)近似得到的结果。在总波函数的绝热展开中,我们确定了有助于通量密度的项。发现只有涉及不同电子态之间相互作用的非对角线元素对电子通量有贡献,而在核情况下,主要贡献属于BO电子态。引入了新的通量密度,在电子和核的情况下,主要贡献包含在对应于BO态的分量中。因此,它们可以在BO近似内确定,并且与精确结果非常吻合。这篇文章是主题问题“没有波恩-奥本海默近似的化学”的一部分。
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引用次数: 3
Mixed-quantum-classical or fully-quantized dynamics? A unified code to compare methods 混合量子经典动力学还是全量子化动力学?一个统一的代码来比较方法
Pub Date : 2022-03-28 DOI: 10.1098/rsta.2020.0386
J. Coonjobeeharry, K. E. Spinlove, C. Sanz Sanz, M. Sapunar, N. Došlić, G. Worth
Three methods for non-adiabatic dynamics are compared to highlight their capabilities. Multi-configurational time-dependent Hartree is a full grid-based solution to the time-dependent Schrödinger equation, variational multi-configurational Gaussian (vMCG) uses a less flexible but unrestricted Gaussian wavepacket basis, and trajectory surface hopping (TSH) replaces the nuclear wavepacket with a swarm of classical trajectories. Calculations with all methods using a model Hamiltonian were performed. The vMCG and TSH were also then run in a direct dynamics mode, with the potential energy surfaces calculated on-the-fly using quantum chemistry calculations. All dynamics calculations used the Quantics package, with the TSH calculations using a new interface to a surface hopping code. A novel approach to calculate adiabatic populations from grid-based quantum dynamics using a time-dependent discrete variable representation is presented, allowing a proper comparison of methods. This article is part of the theme issue ‘Chemistry without the Born–Oppenheimer approximation’.
比较了三种非绝热动力学方法,突出了它们的能力。多构型时变Hartree是时变Schrödinger方程的全网格解,变分多构型高斯(vMCG)使用不太灵活但不受限制的高斯波包基,弹道表面跳变(TSH)用一群经典轨迹代替核波包。使用模型哈密顿量进行了所有方法的计算。vMCG和TSH也在直接动力学模式下运行,并使用量子化学计算实时计算势能面。所有的动力学计算都使用了Quantics包,其中TSH计算使用了一个新的接口到一个表面跳码。提出了一种基于网格的量子动力学计算绝热种群的新方法,使用时变离散变量表示,允许对方法进行适当的比较。这篇文章是主题问题“没有波恩-奥本海默近似的化学”的一部分。
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引用次数: 7
Quantum dynamics with curvilinear coordinates: models and kinetic energy operator 曲线坐标下的量子动力学:模型和动能算子
Pub Date : 2022-03-28 DOI: 10.1098/rsta.2020.0388
Emanuele Marsili, F. Agostini, André Nauts, D. Lauvergnat
In order to simplify the numerical solution of the time-dependent or time-independent Schrödinger equations associated with atomic and molecular motions, the use of well-adapted coordinates is essential. Usually, this set of curvilinear coordinates leads to a Hamiltonian operator that is as separable as possible. Although their corresponding kinetic energy operator (KEO) expressions can be derived analytically for small systems or special kinds of coordinates, a numerical and exact approach allows one to compute them in terms of sophisticated curvilinear coordinates. Furthermore, the numerical approach enables one to easily define reduced-dimensionality or constrained models. We present here a recent implementation of this numerical approach that allows nested coordinate transformations, therefore leading to great flexibility in the definition of the curvilinear coordinates. Furthermore, this implementation has no limitations in terms of numbers of atoms or coordinate transformations. The quantum dynamics of the cis–trans photoisomerization of part of the retinal chromophore illustrates the construction of the coordinates and KEO part of a three-dimensional model. This article is part of the theme issue ‘Chemistry without the Born–Oppenheimer approximation’.
为了简化与原子和分子运动有关的时变或时变Schrödinger方程的数值解,必须使用适应良好的坐标。通常,这组曲线坐标会导致一个尽可能可分离的哈密顿算子。虽然它们对应的动能算符(KEO)表达式可以对小系统或特殊类型的坐标进行解析推导,但一种数值和精确的方法允许人们在复杂的曲线坐标中计算它们。此外,数值方法使人们能够轻松地定义降维或约束模型。我们在这里介绍了这种数值方法的最新实现,它允许嵌套坐标变换,因此在曲线坐标的定义中具有很大的灵活性。此外,该实现在原子数量或坐标转换方面没有限制。部分视网膜发色团的顺反光异构的量子动力学说明了三维模型的坐标和KEO部分的构建。这篇文章是主题问题“没有波恩-奥本海默近似的化学”的一部分。
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引用次数: 3
Non-Born–Oppenheimer effects in molecular photochemistry: an experimental perspective 分子光化学中的非玻恩-奥本海默效应:实验视角
Pub Date : 2022-03-28 DOI: 10.1098/rsta.2020.0376
M. Ashfold, Sang Kyu Kim
Non-adiabatic couplings between Born–Oppenheimer (BO)-derived potential energy surfaces are now recognized as pivotal in describing the non-radiative decay of electronically excited molecules following photon absorption. This opinion piece illustrates how non-BO effects provide photostability to many biomolecules when exposed to ultraviolet radiation, yet in many other cases are key to facilitating ‘reactive’ outcomes like isomerization and bond fission. The examples are presented in order of decreasing molecular complexity, spanning studies of organic sunscreen molecules in solution, through two families of heteroatom containing aromatic molecules and culminating with studies of isolated gas phase H2O molecules that afford some of the most detailed insights yet available into the cascade of non-adiabatic couplings that enable the evolution from photoexcited molecule to eventual products. This article is part of the theme issue 'Chemistry without the Born–Oppenheimer approximation'.
玻恩-奥本海默(BO)衍生势能面之间的非绝热耦合现在被认为是描述光子吸收后电子激发分子的非辐射衰变的关键。这篇观点文章阐述了非bo效应如何在暴露于紫外线辐射时为许多生物分子提供光稳定性,但在许多其他情况下,它是促进“反应性”结果(如异构化和键裂变)的关键。这些例子是按照分子复杂性的递减顺序呈现的,从溶液中的有机防晒分子的研究,到含芳香分子的两个杂原子家族,最后是分离的气相H2O分子的研究,这些研究提供了一些最详细的见解,这些见解可以用于非绝热耦合的级联,使从光激发分子到最终产物的进化。这篇文章是主题问题“没有波恩-奥本海默近似的化学”的一部分。
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引用次数: 5
The moving crude adiabatic alternative to the adiabatic representation in excited state dynamics 激发态动力学中绝热表示的移动粗绝热替代
Pub Date : 2022-03-28 DOI: 10.1098/rsta.2020.0379
Rosa Maskri, Loïc Joubert-Doriol
The choice of the electronic representation in on-the-fly quantum dynamics is crucial. The adiabatic representation is appealing since adiabatic states are readily available from quantum chemistry packages. The nuclear wavepackets are then expanded in a basis of Gaussian functions, which follow trajectories to explore the potential energy surfaces and approximate the potential using a local expansion of the adiabatic quantities. Nevertheless, the adiabatic representation is plagued with severe limitations when conical intersections are involved: the diagonal Born–Oppenheimer corrections (DBOCs) are non-integrable, and the geometric phase effect on the nuclear wavepackets cannot be accounted for unless a model is available. To circumvent these difficulties, the moving crude adiabatic (MCA) representation was proposed and successfully tested in low energy dynamics where the wavepacket skirts the conical intersection. We assess the MCA representation in the case of non-adiabatic transitions through conical intersections. First, we show that using a Gaussian basis in the adiabatic representation indeed exhibits the aforementioned difficulties with a special emphasis on the possibility to regularize the DBOC terms. Then, we show that MCA is indeed able to properly model non-adiabatic transitions. Tests are done on linear vibronic coupling models for the bis(methylene) adamantyl cation and the butatriene cation. This article is part of the theme issue ‘Chemistry without the Born–Oppenheimer approximation’.
在动态量子动力学中,电子表示的选择至关重要。绝热表示很有吸引力,因为绝热状态很容易从量子化学包中得到。然后,核波包在高斯函数的基础上展开,高斯函数沿着轨迹探索势能面,并使用绝热量的局部展开近似势能。然而,当涉及圆锥相交时,绝热表示受到严重限制:对角线Born-Oppenheimer校正(DBOCs)不可积,并且除非有可用的模型,否则无法解释核波包的几何相位效应。为了克服这些困难,提出了移动粗绝热(MCA)表示,并在低能动力学中成功地进行了测试,其中波包沿圆锥相交。我们评估了在非绝热过渡的情况下,通过锥形相交的MCA表示。首先,我们证明在绝热表示中使用高斯基确实表现出上述困难,特别强调了正则化DBOC项的可能性。然后,我们证明了MCA确实能够正确地模拟非绝热转变。对双(亚甲基)金刚烷基阳离子和丁腈基阳离子的线性振动耦合模型进行了试验。这篇文章是主题问题“没有波恩-奥本海默近似的化学”的一部分。
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引用次数: 13
On stable exponential cosmological solutions with two factor spaces in (1+ m + 2)-dimensional Einstein–Gauss–Bonnet model with Λ-term 具有Λ-term的(1+ m + 2)维Einstein-Gauss-Bonnet模型中具有两因子空间的稳定指数宇宙学解
Pub Date : 2022-03-14 DOI: 10.1098/rsta.2021.0177
V. Ivashchuk, A. A. Kobtsev
A (m+3)-dimensional Einstein–Gauss–Bonnet gravitational model including the Gauss–Bonnet term and the cosmological term Λ is considered. Exact solutions with exponential time dependence of two scale factors, governed by two Hubble-like parameters H>0 and h≠H, corresponding to factor spaces of dimensions m>2 and l=2, respectively, are found. Under certain restrictions on x=h/H, the stability of the solutions in a class of cosmological solutions with diagonal metrics is proved. A subclass of solutions with small enough variation of the effective gravitational constant G is considered and the stability of all solutions from this subclass is shown. This article is part of the theme issue ‘The future of mathematical cosmology, Volume 1’.
考虑了一个(m+3)维爱因斯坦-高斯-邦纳引力模型,其中包括高斯-邦纳项和宇宙学项Λ。得到了由两个类哈勃参数H>0和H≠H控制的两个尺度因子分别对应于维数m b> 2和l=2的因子空间的指数时间依赖的精确解。在x=h/ h的一定限制下,证明了一类具有对角度量的宇宙学解解的稳定性。考虑了有效引力常数G变化足够小的一类解,并证明了该类所有解的稳定性。本文是主题问题“数学宇宙学的未来,第一卷”的一部分。
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引用次数: 0
Cosmological milestones, conformal frameworks and quiescent cosmology 宇宙学里程碑,共形框架和静态宇宙学
Pub Date : 2022-03-14 DOI: 10.1098/rsta.2021.0172
S. Scott, Philip Threlfall
To understand the nature of the birth of our Universe and its eventual demise is a driving force in theoretical physics and astronomy and, indeed, for humanity. A zoo of definitions has appeared in the literature to catalogue different types of cosmological milestones such as ‘Big Bangs’, ‘Big Crunches’, ‘Big Rips’, ‘Sudden Singularities’, ‘Bounces’ and ‘Turnarounds’. Quiescent cosmology is the notion that the Universe commenced in a Big Bang that was highly regular and smooth, and evolved away from this initial isotropy and homogeneity due to gravitational attraction. The quiescent cosmology concept meshes well with Penrose’s ideas regarding gravitational entropy and the clumping of matter, and the associated Weyl Curvature Hypothesis. Conformal frameworks, such as the Isotropic Past Singularity (IPS), have been devised to encapsulate initial and final states for the Universe which are in accordance with these programmes. These geometric definitions are independent of models, coordinates and the equation of state of the source of the gravitational field. Much of the research on cosmological milestones has been focussed on the FRW solutions, many of which possess initial singularities which are isotropic Big Bangs. We analyse here the relationship between cosmological milestones and conformal frameworks for these solutions. We establish the general properties of FRW models which admit these conformal frameworks, including whether they satisfy various energy conditions, and are therefore physically reasonable. These results inform future development of the quiescent cosmology program. This article is part of the theme issue ‘The future of mathematical cosmology, Volume 1’.
了解宇宙诞生和最终消亡的本质是理论物理学和天文学的推动力,实际上也是人类的推动力。文献中出现了各种各样的定义,对不同类型的宇宙里程碑进行分类,如“大爆炸”、“大收缩”、“大撕裂”、“突然奇点”、“弹跳”和“逆转”。静态宇宙学认为,宇宙起源于一次高度规则和光滑的大爆炸,并在引力的作用下逐渐远离了最初的各向同性和均匀性。静止宇宙学的概念与彭罗斯关于引力熵和物质团块的观点以及相关的Weyl曲率假说非常吻合。共形框架,如各向同性过去奇点(IPS),已经被设计用来封装与这些程序相一致的宇宙的初始和最终状态。这些几何定义与引力场源的模型、坐标和状态方程无关。许多关于宇宙学里程碑的研究都集中在FRW解上,其中许多解具有初始奇点,即各向同性大爆炸。我们在此分析这些解的宇宙学里程碑和共形框架之间的关系。我们建立了承认这些共形框架的FRW模型的一般性质,包括它们是否满足各种能量条件,因此在物理上是合理的。这些结果为静态宇宙学计划的未来发展提供了信息。本文是主题问题“数学宇宙学的未来,第一卷”的一部分。
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引用次数: 0
Scientific advice for policymakers on climate change: the role of evidence synthesis 为气候变化政策制定者提供的科学建议:证据综合的作用
Pub Date : 2022-02-28 DOI: 10.1098/rsta.2021.0147
E. Surkovic, David Vigar
Science has a role to play in providing the evidence on both climate change and the solutions to it. In this paper, we look at the nature of expert advice to public policymakers and examine one approach to the synthesis of scientific evidence. We focus on a series of briefings for policymakers that summarize evidence from 12 areas of science and technology which are keys to accelerating progress towards net zero greenhouse gas emissions and resilience to climate change. This article is part of the theme issue ‘Developing resilient energy systems’.
在提供气候变化的证据和解决方案方面,科学可以发挥作用。在本文中,我们研究了专家向公共政策制定者提供建议的性质,并研究了一种综合科学证据的方法。我们的重点是为政策制定者提供的一系列简报,这些简报总结了来自12个科学和技术领域的证据,这些领域是加速实现温室气体净零排放和适应气候变化的关键。本文是“发展有弹性的能源系统”主题问题的一部分。
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引用次数: 1
Distributed renewable energy systems for resilient and sustainable development of remote and vulnerable communities 分布式可再生能源系统,促进偏远和脆弱社区的弹性和可持续发展
Pub Date : 2022-02-28 DOI: 10.1098/rsta.2021.0143
Tanvir Ahmad, Saddam Ali, Abdul Basit
More than 940 million people (13% of the world population) do not have any access to electricity. Most of these people live in rural and remote areas, where the lack of electricity access is significantly damaging the quality of life, economic development and the environment. Distributed energy systems (DESs) (based on clean energy technologies) for energy access offer a potentially important strategy for pursuing environment-friendly sustainable development and poverty alleviation; especially in rural and remote communities. DESs are also helpful in reducing deforestation and greenhouse gas (GHG) emissions as the fossil fuel-based energy production is among the largest contributors to GHG emissions. This paper presents the importance of energy access through DESs for resilient and sustainable development using two projects case studies from Pakistan. The first project case study is based on the Afghan refugee villages, where, currently, there is no electricity access. A baseline survey was conducted to assess the socio-economic conditions and energy demand of the refugees. This assessment is then used to devise clean energy solutions as per the local context. This project aims to improve the quality of life of the refugees by providing energy access. In the second case study, electricity access was provided to the local communities a few years ago. Analyses of primary data collected in this case study show that DES integrated with socio-economic and cultural systems can bring a significantly positive impact on the local communities, advancing all the sustainability development goals. This work concludes that DES can be significantly generative, if effectively integrated into socio-economic processes. This article is part of the theme issue ‘Developing resilient energy systems’.
超过9.4亿人(占世界人口的13%)没有任何电力供应。其中大多数人生活在农村和偏远地区,那里缺乏电力供应严重损害了生活质量、经济发展和环境。用于获得能源的分布式能源系统(以清洁能源技术为基础)为追求无害环境的可持续发展和减轻贫穷提供了一个潜在的重要战略;特别是在农村和偏远地区。由于以化石燃料为基础的能源生产是温室气体排放的最大来源之一,DESs还有助于减少森林砍伐和温室气体排放。本文通过对巴基斯坦两个项目的案例研究,介绍了通过发展经济手段获取能源对有复原力和可持续发展的重要性。第一个项目案例研究以阿富汗难民村庄为基础,那里目前没有电力供应。进行了一项基线调查,以评估难民的社会经济条件和能源需求。然后,根据当地情况,利用这一评估来设计清洁能源解决方案。该项目旨在通过提供能源来改善难民的生活质量。在第二个案例研究中,几年前向当地社区提供了电力。本案例研究收集的原始数据分析表明,与社会经济和文化系统相结合的生态环境可以给当地社区带来显著的积极影响,促进所有可持续发展目标的实现。这项工作的结论是,如果有效地将经济发展纳入社会经济进程,它可以产生巨大的影响。本文是“发展有弹性的能源系统”主题问题的一部分。
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引用次数: 2
期刊
Philosophical Transactions of the Royal Society A
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