اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدTowards a formal definition of static and dynamic electronic correlations
249
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Some of the most spectacular failures of density-functional and Hartree-Fock theories are related to an incorrect description of the so-called static electron correlation. Motivated by recent progress on the N-representability problem of the one-body density matrix for pure states, we propose a way to quantify the static contribution to the electronic correlation. By studying several molecular systems we show that our proposal correlates well with our intuition of static and dynamic electron correlation. Our results bring out the paramount importance of the occupancy of the highest occupied natural spin-orbital in such quantification.
قيم البحث
اقرأ أيضاً
We introduce, analyze, and compare two novel methods of Single Photon Cooling that generically cool and compress molecular gases. The first method compresses the molecular gas density by three orders of magnitude and increases collision frequency in
trapped samples. The second method compresses the phase space density of the gas by at least two orders of magnitude. Designed with combinations of electric and magnetic fields these methods cool the molecules from ~100mK to 1mK using a single irreversible state change. They can be regarded as generic cooling schemes applicable to any molecule with a magnetic and electric dipole moment. The high efficiency calculated, compared to schemes involving cycling, is a result of cooling the molecules with a single step.
Multi-configurational approaches yield universal wave function parameterizations that can qualitatively well describe electronic structures along reaction pathways. For quantitative results, multi-reference perturbation theory is required to capture
dynamic electron correlation from the otherwise neglected virtual orbitals. Still, the overall accuracy suffers from the finite size and choice of the active orbital space and peculiarities of the perturbation theory. Fortunately, the electronic wave functions at equilibrium structures of reactants and products can often be well described by single-reference methods and hence are accessible to accurate coupled cluster calculations. Here, we calculate the heterolytic double dissociation energy of four 3d-metallocenes with the complete active space self-consistent field method and compare to highly accurate coupled cluster data. Our coupled cluster data are well within the experimental error bars. This accuracy can also be approached by complete active space calculations with an orbital selection based on information entropy measures. The entropy based active space selection is discussed in detail. We find a very subtle balance between static and dynamic electron correlation effects that emphasizes the need for algorithmic active space selection and that differs significantly from restricted active space results for identical active spaces reported in the literature.
This thesis contributes to the formalisation of the notion of an agent within the class of finite multivariate Markov chains. Agents are seen as entities that act, perceive, and are goal-directed. We present a new measure that can be used to identi
fy entities (called $iota$-entities), some general requirements for entities in multivariate Markov chains, as well as formal definitions of actions and perceptions suitable for such entities. The intuition behind $iota$-entities is that entities are spatiotemporal patterns for which every part makes every other part more probable. The measure, complete local integration (CLI), is formally investigated in general Bayesian networks. It is based on the specific local integration (SLI) which is measured with respect to a partition. CLI is the minimum value of SLI over all partitions. We prove that $iota$-entities are blocks in specific partitions of the global trajectory. These partitions are the finest partitions that achieve a given SLI value. We also establish the transformation behaviour of SLI under permutations of nodes in the network. We go on to present three conditions on general definitions of entities. These are not fulfilled by sets of random variables i.e. the perception-action loop, which is often used to model agents, is too restrictive. We propose that any general entity definition should in effect specify a subset (called an an entity-set) of the set of all spatiotemporal patterns of a given multivariate Markov chain. The set of $iota$-entities is such a set. Importantly the perception-action loop also induces an entity-set. We then propose formal definitions of actions and perceptions for arbitrary entity-sets. These specialise to standard notions in case of the perception-action loop entity-set. Finally we look at some very simple examples.
Leveraging hypergraph structures to model advanced processes has gained much attention over the last few years in many areas, ranging from protein-interaction in computational biology to image retrieval using machine learning. Hypergraph models can p
rovide a more accurate representation of the underlying processes while reducing the overall number of links compared to regular representations. However, interactive visualization methods for hypergraphs and hypergraph-based models have rarely been explored or systematically analyzed. This paper reviews the existing research landscape for hypergraph and hypergraph model visualizations and assesses the currently employed techniques. We provide an overview and a categorization of proposed approaches, focusing on performance, scalability, interaction support, successful evaluation, and the ability to represent different underlying data structures, including a recent demand for a temporal representation of interaction networks and their improvements beyond graph-based methods. Lastly, we discuss the strengths and weaknesses of the approaches and give an insight into the future challenges arising in this emerging research field.
We study theoretically and experimentally the electronic relaxation of NO2 molecules excited by absorption of one ~400 nm pump photon. Semi-classical simulations based on trajectory surface hopping calculations are performed. They predict fast oscill
ations of the electronic character around the intersection of the ground and first excited diabatic states. An experiment based on high-order harmonic transient grating spectroscopy reveals dynamics occuring on the same timescale. A systematic study of the detected transient is conducted to investigate the possible influence of the pump intensity, pump wavelength, and rotational temperature of the molecules. The quantitative agreement between measured and predicted dynamics shows that, in NO2, high harmonic transient grating spectroscopy encodes vibrational dynamics underlying the electronic relaxation.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
