On the calculation of second order properties: An equation of motion approach
TL;DR: In this article, a general expression for polarisability calculation has been derived from the equation of motion method and different approximation methods can be deduced for different choices of ground state and excitation manifold.
Abstract: In the light of the equation of motion method a general expression for polarisability calculation has been derived. From this general expression, different approximation methods can be deduced for different choices of ground state and excitation manifold. Among these the coupled Hartree-Fock theory is the most extensively used one for polarisability calculations. It has also been shown that this theory has a simple relationship with random phase approximation.
Citations
More filters
01 Jan 1973
TL;DR: In this article, the Planck's radiation law and the Einstein coefficients were used to describe the atom-radiation interaction and the quantum mechanics of optical fluctuations and coherence, respectively.
Abstract: Preface 1. Planck's radiation law and the Einstein coefficients 2. Quantum mechanics of the atom-radiation interaction 3. Classical theory of optical fluctuations and coherence 4. Quantization of the radiation field 5. Single-mode quantum optics 6. Multimode and continuous-mode quantum optics 7. Optical generation, attenuation and amplification 8. Resonance fluorescence and light scattering 9. Nonlinear quantum optics Index
248 citations
TL;DR: The static polarizability of fifteen organic molecules (point group symmetry:C2v; number of electrons ≥ 26) have been theoretically calculated using the CNDO/S-CHFT scheme and the results have been compared with other available data.
Abstract: The static polarizability of fifteen organic molecules (point group symmetry:C2v; number of electrons ≥ 26) have been theoretically calculated using the CNDO/S-CHFT scheme and the results have been compared with other available data.
3 citations
References
More filters
Book•
01 Jan 1973
TL;DR: In this paper, the Planck's radiation law and the Einstein coefficients were used to describe the atom-radiation interaction and the quantum mechanics of optical fluctuations and coherence, respectively.
Abstract: Preface 1. Planck's radiation law and the Einstein coefficients 2. Quantum mechanics of the atom-radiation interaction 3. Classical theory of optical fluctuations and coherence 4. Quantization of the radiation field 5. Single-mode quantum optics 6. Multimode and continuous-mode quantum optics 7. Optical generation, attenuation and amplification 8. Resonance fluorescence and light scattering 9. Nonlinear quantum optics Index
3,038 citations
TL;DR: In this article, a method for the calculation of the matrix elements of the logarithm of an operator which gives the exact wavefunction when operating on the wavefunction in the one-electron approximation is proposed.
Abstract: A method is suggested for the calculation of the matrix elements of the logarithm of an operator which gives the exact wavefunction when operating on the wavefunction in the one‐electron approximation. The method is based on the use of the creation and annihilation operators, hole—particle formalism, Wick's theorem, and the technique of Feynman‐like diagrams. The connection of this method with the configuration‐interaction method as well as with the perturbation theory in the quantum‐field theoretical form is discussed. The method is applied to the simple models of nitrogen and benzene molecules. The results are compared with those obtained with the configuration‐interaction method considering all possible configurations within the chosen basis of one‐electron functions.
2,676 citations
01 Jan 1977
TL;DR: In this paper, the authors present a method for determining configuration interaction wave functions for the Electronic States of Atoms and Molecules: the Vector Method, which is a general computer program for ab initio calculations.
Abstract: 1. Gaussian Basis Sets for Molecular Calculations.- 2. The Floating Spherical Gaussian Orbital Method.- 3. The Multiconfiguration Self-Consistent Field Method.- 4. The Self-Consistent Field Equations for Generalized Valence Bond and Open-Shell Hartree-Fock Wave Functions.- 5. Pair Correlation Theories.- 6. The Method of Configuration Interaction.- 7. The Direct Configuration Interaction Method from Molecular Integrals.- 8. A New Method for Determining Configuration Interaction Wave Functions for the Electronic States of Atoms and Molecules: The Vector Method.- 9. The Equations of Motion Method: An Approach to the Dynamical Properties of Atoms and Molecules.- 10. POLYATOM: A General Computer Program for Ab Initio Calculations.- 11. Configuration Expansion by Means of Pseudonatural Orbitals.- Author Index.
1,817 citations
TL;DR: The equations-of-motion method is used in this paper to derive the random phase approximation (RPA) and the quasi-particle RPA (QRPA), and a higher RPA and QRPA are then derived to include these terms.
Abstract: 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.
852 citations
TL;DR: In this paper, it is shown that the Fock-Dirac density matrix can be computed in terms of the unperturbed Hamiltonian and density matrix, and the perturbation can be expressed as a series of series of perturbations.
Abstract: In Hartree-Fock theory and its various generalizations, it is customary to solve an eigenvalue problem involving an effective one-body Hamiltonian. The eigenvectors determine the Fock-Dirac density matrix, which also appears in the effective Hamiltonian, and solution proceeds iteratively until self-consistency is achieved.An alternative (necessary and sufficient) condition for a solution is that the density matrix ($\ensuremath{\rho}$) is idempotent and commutes with the Hamiltonian (h). The change in $\ensuremath{\rho}$, accompanying a change $\ensuremath{\Delta}$ in h, can then be expressed as a perturbation series. Formulas for the perturbation, to all orders, are obtained in terms of the unperturbed Hamiltonian and density matrix. It is also shown that the whole perturbation may be obtained directly, without separating the orders, and that the approach is related to earlier steepest-descent methods.
646 citations
Additional excerpts
...…(c.rr) either time-independent (Langhoff et al 1966) or time-dependent (McLachlan 1964; McLachlan and Ball 1964) versions and their variants (Langhoff et al 1972; McWeeny 1962; Dierksen and McWeeny 1966; Dodds et al 1977) have been the most extensively used ones for the polarisability calculations....
[...]