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Quantum Theory for Chemical Applications最新文献

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Many-electron Systems and the Pauli Principle 多电子系统和泡利原理
Quantum Theory for Chemical Applications Pub Date : 2020-12-21 DOI: 10.1093/OSO/9780190920807.003.0007
J. Autschbach
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引用次数: 0
Static Perturbation Theory and Derivative Properties 静态摄动理论及其导数性质
Quantum Theory for Chemical Applications Pub Date : 2020-12-21 DOI: 10.1093/OSO/9780190920807.003.0022
J. Autschbach
{"title":"Static Perturbation Theory and Derivative Properties","authors":"J. Autschbach","doi":"10.1093/OSO/9780190920807.003.0022","DOIUrl":"https://doi.org/10.1093/OSO/9780190920807.003.0022","url":null,"abstract":"Perturbation theory (PT) is a method by which the energies and wavefunctions of a system of interest are expressed in terms of the known solutions of a presumably simpler reference system. The Rayleigh-Schrodinger expressions for the wavefunctions and energies of exact states are derived up to 3rd and 4th order, respectively. A simple application deals with substitution effects on the absorption color of organic chromophores. The Moller-Plesset correlation energy is derived in 2nd order (MP2). It is then shown how bi-linear perturbations associated with the electric and magnetic field operators of chapter 21 define properties such as polarizability, magnetizability or susceptibility, nuclear magnetic resonance shielding and spin-spin coupling, harmonic nuclear vibrational frequencies, and many other properties. The bi-linear magnetic perturbation energy is derived for paramagnetic systems with low-energy thermally populated degenerate states. The chapter concludes with a description of derivative techniques for approximate quantum chemical methods.","PeriodicalId":207760,"journal":{"name":"Quantum Theory for Chemical Applications","volume":"88 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125756145","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Recap: Molecular Orbitals and Common Misconceptions 概述:分子轨道和常见的误解
Quantum Theory for Chemical Applications Pub Date : 2020-12-21 DOI: 10.1093/OSO/9780190920807.003.0011
J. Autschbach
{"title":"Recap: Molecular Orbitals and Common Misconceptions","authors":"J. Autschbach","doi":"10.1093/OSO/9780190920807.003.0011","DOIUrl":"https://doi.org/10.1093/OSO/9780190920807.003.0011","url":null,"abstract":"This chapter recapitulates the series of approximations that lead to the commonly used description of the electronic structure of molecules in terms of molecular orbitals (MOs), which in turn are usually expressed as linear combination of atomic orbital-like basis functions. Next, a number of common misconceptions about orbitals are discussed, such that the reader is aware of not only what electron orbitals are but also what they are not.","PeriodicalId":207760,"journal":{"name":"Quantum Theory for Chemical Applications","volume":"91 6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116250025","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Hydrogen-like Atomic Wavefunctions: A First Sketch 类氢原子波函数:初步草图
Quantum Theory for Chemical Applications Pub Date : 2020-12-21 DOI: 10.1093/OSO/9780190920807.003.0006
J. Autschbach
{"title":"Hydrogen-like Atomic Wavefunctions: A First Sketch","authors":"J. Autschbach","doi":"10.1093/OSO/9780190920807.003.0006","DOIUrl":"https://doi.org/10.1093/OSO/9780190920807.003.0006","url":null,"abstract":"This chapter reiterates the quantum numbers for atomic orbitals, known from general chemistry, and places them into the context developed so far. It is sketched how the Schrodinger equation (SE) for the hydrogen atom hydrogen-like systems (one electron plus a nucleus of charge Z) is set up. When the nucleus is treated as a fixed point charge, the SE is only for the electron. The solutions of the SE can be obtained by switching to spherical polar coordinates, such that the variables are separable in terms of the electron distance from the nucleus, r, and two angles. The kinetic energy of the electron then has a radial component, and an angular component. The latter is associated with the angular momentum quantum number, which is codified by the letters s, p, d, f, and so forth. A step by step solution of the SE is provided later, in chapter 19.","PeriodicalId":207760,"journal":{"name":"Quantum Theory for Chemical Applications","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128350079","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The One-electron Quantum Hamiltonian in the Presence of EM Fields 电磁场下的单电子量子哈密顿量
Quantum Theory for Chemical Applications Pub Date : 2020-12-21 DOI: 10.1093/OSO/9780190920807.003.0021
J. Autschbach
{"title":"The One-electron Quantum Hamiltonian in the Presence of EM Fields","authors":"J. Autschbach","doi":"10.1093/OSO/9780190920807.003.0021","DOIUrl":"https://doi.org/10.1093/OSO/9780190920807.003.0021","url":null,"abstract":"The interaction between atoms or molecules and electromagnetic (EM) fields underlies all spectroscopic techniques and a great variety of desirable molecular properties. EM fields and EM waves are introduced via the famous Maxwell equations. The scalar and vector potential are defined, and the gauge freedom is outlined. The Coulomb gauge is adopted. The classical Hamiltonian for a charged particle in an EM field is derived, and from this the ‘minimal substitution’ rules for incorporating the fields in the quantum Hamiltonian are obtained. The operators describing the interaction of an electron with static electric and magnetic fields, including the magnetic fields from nuclear spins, are derived, followed by the derivation of the interaction between an electron and an EM wave.","PeriodicalId":207760,"journal":{"name":"Quantum Theory for Chemical Applications","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125495271","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Quantum Recipe 量子配方
Quantum Theory for Chemical Applications Pub Date : 2019-03-19 DOI: 10.2307/j.ctvc77hrx.5
J. Autschbach
{"title":"The Quantum Recipe","authors":"J. Autschbach","doi":"10.2307/j.ctvc77hrx.5","DOIUrl":"https://doi.org/10.2307/j.ctvc77hrx.5","url":null,"abstract":"Introduction of the postulates of quantum mechanics: Wavefunctions, operators, observables, commutating operators, expectation values, probabilities, Heisenberg uncertainty. The postulates are then used to set up a ‘quantum recipe’, i.e. a straightforward recipe by which to write down the (nonrelativistic) quantum Hamiltonian of a system of particles. This chapter also discusses the representation of quantum operators as matrices, in reference to a set of ‘basis’ functions, and the variation principle. The idea of a particle trajectory must be abandoned in quantum mechanics. Observable properties of a particle correspond to eigenvalues of the associated quantum operators. The chapter concludes with a brief discussion of the Schrodinger’s cat paradox, quantum entanglement, and other oddities.","PeriodicalId":207760,"journal":{"name":"Quantum Theory for Chemical Applications","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125463986","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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