Today, coupled-cluster theory offers the most accurate results among the practical ab initio electronic-structure theories applicable to moderate-sized molecules. Though it was originally proposed for problems in physics, it has seen its greatest development in chemistry, enabling an extensive range of applications to molecular structure, excited states, properties, and all kinds of spectroscopy. In this review, the essential aspects of the theory are explained and illustrated with informative numerical results.

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Coupled-cluster theory in quantum chemistry

The Theory of Matrices. By F R. Gantmacher. Two volumes, pp. 374 and 276. 1959. (Translated from the Russian by K. A. Hirsch; Chelsea Publishing Company, New York)

저작근 근전도에 관한 정상교합자와 ii급 부정교합자의 비교 연구

Metric affine gauge theory of gravity: Field equations, Noether identities, world spinors, and breaking of dilation invariance

The jellium model of simple metal clusters has enjoyed remarkable empirical success, leading to many theoretical questions. In this review, we first survey the hierarchy of theoretical approximations leading to the model. We then describe the jellium model in detail, including various extensions. One important and useful approximation is the local-density approximation to exchange and correlation effects, which greatly simplifies self-consistent calculations of the electronic structure. Another valuable tool is the semiclassical approximation to the single-particle density matrix, which gives a theoretical framework to connect the properties of large clusters with the bulk and macroscopic surface properties. The physical properties discussed in this review are the ground-state binding energies, the ionization potentials, and the dipole polarizabilities. We also treat the collective electronic excitations from the point of view of the cluster response, including some useful sum rules.

/pdf/the-physics-of-simple-metal-clusters-self-consistent-jellium-3u9wf8r66h.pdf

The physics of simple metal clusters: self-consistent jellium model and semiclassical approaches

This paper presents the equations-of-motion method as a useful and flexible tool in the study of nuclear spectroscopy. It is partly a review, but also it introduces a new and much more powerful equations-of-motion technique which supercedes the older linearization methods. The older methods worked with operator equations. To obtain closed expressions they had to be linearized in a rather arbitrary manner. The present approach works with the ground-state expectation of operator equations and thereby avoids all problems of linearization. Thus, like the Green's function method, the equations-of-motion method becomes potentially exact. It has many advantages over Green's function methods, however, among which are its greater compactness, simplicity, and the physical insight it yields.The method is first applied to rederive the random phase approximation (RPA) and the quasi-particle RPA (QRPA) and to show precisely what terms they neglect. It is demonstrated that some of these terms have coherent phases. A higher RPA and QRPA are then derived to include these terms. The corrections have some interesting effects: notably, there is a reduction of the effective interaction strength and a stabilization of the nucleus against sudden phase transitions. The equations-of-motion method is also used to generalize, in a very simple and natural way, the Hartree-Fock (HF) and Hartree-Bogolyubov (HB) concepts of independent particles and quasi-particles to nonsimple ground states.The equations-of-motion method is presented as a simple extension of the shell model to the treatment of excitationg of a correlated ground state. By concentrating on the quantities of direct physical interest, the complexity of workins with correlated wavefunctions is avoided.

Equations-of-Motion Method and the Extended Shell Model

This articles reviews the development of a microscopic theory of nuclear collective structure as a submodel of the nuclear-shell model. It starts by showing how the so-called geometrical (Bohr-Mottelson-Frankfurt) collective model must be augmented by the addition of vortex spin degrees of freedom to make it compatible with the shell model. A unified symplectic model emerges that can be applied both with phenomenological and microscopic interactions. Examples are given of both kinds of calculation. It is shown how the full shell model space can be expressed in an Sp(3R) contains/implies U(3) basis in which form it naturally factors into collective and intrinsic subspaces. In this way, the collective content of a shell model state becomes immediately apparent. Thus a shell model interpretation is given of collective states, including the low-lying rotational bands, the so-called beta and gamma vibrations and the giant monopole and quadrupole resonances.

https://iopscience.iop.org/article/10.1088/0034-4885/48/10/003/pdf

Microscopic theory of the nuclear collective model

A microscopic model is presented which provides a practical means for selecting the states necessary for the development of nuclear collective rotational and quadrupole vibrational motions in a shell-model calculation. The model is based on the noncompact Sp(3,R) algebra and is a natural generalization of Elliott's SU(3) model to include many major shells. (AIP)

Nuclear Sp(3,R) model

Phenomenological Models: General Trends and Coupling Schemes The Collective Vibrational Model The Unified Model for Vibrations The Vibrating Potential Model The E1 Photoresonance The Collective Rotational Model The Unified Model for Rotations The Moment of Inertia Microscopic Theories: Hartree?Fock Self-Consistent Field Theory: Spherical Nuclei Hartree?Fock Self-Consistent Field Theory: Deformed Nuclei Pairing-Force Theory The Tamm?Dancoff Approximation or Simple Particle?Hole Theory An Equations-of-Motion Method The Random Phase Approximation or Sophisticated Particle-Hole Theory Time-Dependent Hartree?Fock (TDHF) Theory The Microscopic Foundations of the Unified Vibrational Model Concluding Remarks.

David J Rowe

Papers

Equations-of-Motion Method and the Extended Shell Model

Microscopic theory of the nuclear collective model

Nuclear Sp(3,R) model

Nuclear Collective Motion: Models and Theory

On the algebraic formulation of collective models III. The symplectic shell model of collective motion