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Quantum Theory for Chemical Applications最新文献

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Approximate Molecular Orbital Theory: The Hückel/Tight-binding Model 近似分子轨道理论:h<s:1> ckel/紧密结合模型
Quantum Theory for Chemical Applications Pub Date : 2020-12-21 DOI: 10.1093/OSO/9780190920807.003.0012
J. Autschbach
{"title":"Approximate Molecular Orbital Theory: The Hückel/Tight-binding Model","authors":"J. Autschbach","doi":"10.1093/OSO/9780190920807.003.0012","DOIUrl":"https://doi.org/10.1093/OSO/9780190920807.003.0012","url":null,"abstract":"Huckel molecular orbital (HMO) theory is a simple approximate parameterized molecular orbital (MO) theory that has been very successful in organic chemistry and other fields. This chapter introduces the approximations made in HMO theory, and then treats as examples ethane, hetratriene and other linear polyenes, and benzene and other cyclic polyenes. The pi binding energy of benzene is particularly large according to HMO theory, rationalizing the special ‘aromatic’ behaviour of benzene. But there is a lot more to benzene than that. It is shown that the pi bond framework of benzene would rather prefer a structure with alternating single and double C-C bonds, rather than the actually observed 6-fold symmetric structure where all C-C bonds are equivalent. The observed benzene structure is a result of a delicate balance between the tendencies of the pi framework to create bond length alternation, and the sigma framework to resist bond length alternation.","PeriodicalId":207760,"journal":{"name":"Quantum Theory for Chemical Applications","volume":"20 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":"114191288","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
Quantized Rotational Motion in a Plane 平面上的量子化旋转运动
Quantum Theory for Chemical Applications Pub Date : 2020-12-21 DOI: 10.1093/OSO/9780190920807.003.0015
J. Autschbach
{"title":"Quantized Rotational Motion in a Plane","authors":"J. Autschbach","doi":"10.1093/OSO/9780190920807.003.0015","DOIUrl":"https://doi.org/10.1093/OSO/9780190920807.003.0015","url":null,"abstract":"The angular momentum for the simplified case of a particle rotating in a fixed plane is treated. The ‘perimeter model’ is the analogue of the one-dimensional particle in a box (PiaB), with the particle moving on a circle with fixed radius. This requires cyclic – or periodic – boundary conditions. It is shown that the quantum perimeter model results can be obtained by re-interpreting the coordinate of the linear PiaB and by considering the periodic boundary conditions. The eigenvalue pattern leads to a 4n+2 Huckel rule. Next, the chapter discusses hindered rotations, such as the rotation of a methyl group around a C-C bond. The solutions to the hindered rotation problem combine features of the harmonic oscillator at low energies, with features of the perimeter model at high energies.","PeriodicalId":207760,"journal":{"name":"Quantum Theory for Chemical Applications","volume":"36 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":"124996416","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
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
{"title":"Many-electron Systems and the Pauli Principle","authors":"J. Autschbach","doi":"10.1093/OSO/9780190920807.003.0007","DOIUrl":"https://doi.org/10.1093/OSO/9780190920807.003.0007","url":null,"abstract":"It is shown how the quantum Hamiltonian for a general molecule is set up, using the ‘quantum recipe’ of chapter 3. In the most restrictive Born Oppenheimer approximation, the nuclei are held fixed and the Schrodinger equation (SE) is set up for the electrons only. The wavefunction depends on the positions and spin projections of all electrons. The electron spin projection is introduced heuristically as another two-valued electron degree of freedom. The electronic SE cannot be solved exactly, and (spin-) orbitals are introduced to construct an approximate wavefunction. The Pauli principle demands that a many-electron wavefunction is antisymmetric upon the exchange of electron labels, which leads to the construction of the approximate orbital-model wavefunction as a Slater determinant rather than a simple Hartree product. The orbital model wavefunction does not describe the Coulomb electron correlation, but it incorporates the (Fermi) correlation leading to the Pauli exclusion.","PeriodicalId":207760,"journal":{"name":"Quantum Theory for Chemical Applications","volume":"102 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":"122433529","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
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
Hydrogen-like Atoms 所以原子
Quantum Theory for Chemical Applications Pub Date : 2020-12-21 DOI: 10.1093/OSO/9780190920807.003.0017
J. Autschbach
{"title":"Hydrogen-like Atoms","authors":"J. Autschbach","doi":"10.1093/OSO/9780190920807.003.0017","DOIUrl":"https://doi.org/10.1093/OSO/9780190920807.003.0017","url":null,"abstract":"This chapter shows how the electronic Schrodinger equation (SE) is solved for a hydrogen-like atom, i.e. an electron moving in the field of a fixed point-like nucleus with charge number Z. The hydrogen atom corresponds to Z = 1. The potential in atomic units is –Z/r, with r being the distance of the electron from the nucleus. The SE is not separable in Cartesian coordinates, but in spherical polar coordinates it separates into a radial equation and an angular momentum equation. The bound states have a total energy of –Z2/(2n2), with n = nr + ℓ being the principal quantum number (q.n.), ℓ = 0,1,2,… the angular momentum q.n., and nr = 1,2,3,… being a radial q.n. Each state for a given ℓ is 2ℓ+1-fold degenerate, with the components labelled by the projection q.n. mℓ. The wavefunctions for mℓ ≠ 0 are complex, but real linear combinations can be formed. This gives the atomic orbitals known from general and organic chemistry. Different ways of visualizing the real wavefunctions are discussed, e.g. as iso-surfaces.","PeriodicalId":207760,"journal":{"name":"Quantum Theory for Chemical Applications","volume":"29 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":"121845950","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
Particle in a Cylinder, in a Sphere, and on a Helix 在圆柱体、球体和螺旋上的粒子
Quantum Theory for Chemical Applications Pub Date : 2020-12-21 DOI: 10.1093/OSO/9780190920807.003.0018
J. Autschbach
{"title":"Particle in a Cylinder, in a Sphere, and on a Helix","authors":"J. Autschbach","doi":"10.1093/OSO/9780190920807.003.0018","DOIUrl":"https://doi.org/10.1093/OSO/9780190920807.003.0018","url":null,"abstract":"The particle in a box from an earlier chapter is useful as a model to treat the electron motion in linear molecular ‘wires’, rectangular surfaces, and cuboid nano-particles. In this chapter, similar models are developed for spherical and cylindrical nano-particles, and helical nano-wires. Applications of these models that have been reported in the literature are discussed. For example, the particle in a cylinder model has been applied to treat the absorption spectra of silver nano-rods. The particle in a sphere model can be used tom rationalize the occurrence of sodium nano-clusters with certain ‘magic’ numbers of Na atoms. The model also explains the behaviour of potassium under high pressure, where the element starts to behave like a transition metal. The particle on a helix has been used to rationalize the optical activity of helical pi-conjugated molecules.","PeriodicalId":207760,"journal":{"name":"Quantum Theory for Chemical Applications","volume":"7 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":"126107003","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
Classical Mechanics According to Newton and Hamilton 根据牛顿和汉密尔顿的经典力学
Quantum Theory for Chemical Applications Pub Date : 2020-12-21 DOI: 10.1093/OSO/9780190920807.003.0002
J. Autschbach
{"title":"Classical Mechanics According to Newton and Hamilton","authors":"J. Autschbach","doi":"10.1093/OSO/9780190920807.003.0002","DOIUrl":"https://doi.org/10.1093/OSO/9780190920807.003.0002","url":null,"abstract":"This chapter introduces classical mechanics, starting with the familiar definitions of position, momentum, velocity, acceleration force, kinetic, potential, and total energy. It is shown how the Newton equation of motion is solved for the one-dimensional harmonic oscillator, which is a point mass oscillating around the position x = 0 driven by a force that is proportional to x (Hooke’s law). Next, the minimal action principle, the Lagrange equation of motion, and the classical Hamilton function (Hamiltonian) and conjugated variables are introduced. The chapter also discusses angular momentum and rotational motion.","PeriodicalId":207760,"journal":{"name":"Quantum Theory for Chemical Applications","volume":"2 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":"128419967","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
Orbital-based Descriptions of Electron Configurations, Ionization, Excitation, and Bonding 基于轨道的电子构型、电离、激发和成键描述
Quantum Theory for Chemical Applications Pub Date : 2020-12-21 DOI: 10.1093/OSO/9780190920807.003.0010
J. Autschbach
{"title":"Orbital-based Descriptions of Electron Configurations, Ionization, Excitation, and Bonding","authors":"J. Autschbach","doi":"10.1093/OSO/9780190920807.003.0010","DOIUrl":"https://doi.org/10.1093/OSO/9780190920807.003.0010","url":null,"abstract":"This chapter deals with quantitative aspects of molecular orbital (MO) theory: Construction of an orbital diagram, bonding and antibonding overlap, Koopmans’ theorem, orbital energies versus total energies, an explanation of the unintuitive ground state electron configurations seen for some neutral transition metals, and a discussion of orbital energy gaps versus electronic excitations and other observable energy gaps. Localized MOs show the chemical bonds expected from the Lewis structure more readily than the canonical orbitals obtained from solving the SCF equations. It is shown that the delocalization of localized, not the canonical, MOs shows whether a system is delocalized. Algorithms by which to obtain localized MOs are sketched.","PeriodicalId":207760,"journal":{"name":"Quantum Theory for Chemical Applications","volume":"103 1 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":"131240813","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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