Journal ArticleDOI
Unitary Group Approach to the Many-Electron Correlation Problem via Graphical Methods of Spin Algebras
Josef Paldus,M. J. Boyle +1 more
TLDR
In this paper, a simple and efficient algorithm for the calculation of two-electron matrix elements of spin-independent Hamiltonians needed in the unitary group configuration interaction (shell model) approach is presented.Abstract:
The various existing approaches for the evaluation of matrix elements of unitary group generators and their products with respect to the basis of electronic Gelfand states or the corresponding Yamanouchi-Kotani states are interrelated, and their desirable features combined, yielding a direct algorithm for the evaluation of matrix elements of products of two generators and, consequently, a simple and efficient algorithm for the calculation of two-electron matrix elements of spin-independent Hamiltonians needed in the unitary group configuration interaction (shell model) approach. Moreover, this algorithm is compatible with the efficient generation and representation scheme for electronic Gelfand states based on the distinct row table concept. Diagrammatic techniques based on the time-independent Wick theorem and graphical methods of spin algebras are used to derive the required factors for both one and two-generator (or electron) matrix elements for three different phase conventions and several possible simplifications in the evaluation of the two-electron part of the Hamiltonian matrix are outlined.read more
Citations
More filters
Book ChapterDOI
The Complete Active Space Self‐Consistent Field Method and its Applications in Electronic Structure Calculations
Journal ArticleDOI
The complete active space SCF (CASSCF) method in a Newton–Raphson formulation with application to the HNO molecule
Abstract: The complete active space (CAS) SCF method is presented in detail with special emphasis on computational aspects. The CASSCF wave function is formed from a complete distribution of a number of active electrons in a set of active orbitals, which in general constitute a subset of the total occupied space. In contrast to other MCSCF schemes, a CASSCF calculation involves no selection of individual configurations, and the wave function therefore typically consists of a large number of terms. The largest case treated here includes 10 416 spin and space adapted configurations. To be able to treat such large CI expansions, a density‐matrix oriented formalism is used. The Newton–Raphson scheme is applied to calculate the orbital rotations, and the secular problem is solved with recent developments of CI techniques. The applicability of the method is demonstrated in calculations on the HNO molecule in ground and excited states, using a triple‐zeta basis and different sizes of the active space. With a reasonable choice of active space, the calculations converge in 6–10 iterations. This is true also for states which are not the lowest state of the symmetry in question. The equilibrium geometry for the ground state is RNO=1.215(1.212) A, RNH =1.079(1.063) A, ϑHNO=108.8(108.6) °, the experimental values given in parenthesis for comparison. The best estimates for the transition energies to the lowest 3A″ and 1A″ states are 0.67(0.85) eV and 1.52(1.63) eV, respectively. The results obtained indicate that the choice of active space may be crucial for the convergence properties of CASSCF calculations.
Journal Article
A critical assessment of coupled cluster method in quantum chemistry
Josef Paldus,Xiangzhu Li +1 more
Book ChapterDOI
Use of Cluster Expansion Methods in the Open-Shell Correlation Problem
Debashis Mukherjee,Sourav Pal +1 more
TL;DR: The open-shell many-body perturbation theory (MBPT) and the propagator or the Green's function methods have now developed into vast computational technology, generating softwares that are cost-effective and competitive with the CI-based codes as mentioned in this paper.
Journal ArticleDOI
The direct CI method
V. R. Saunders,J.H. van Lenthe +1 more
TL;DR: A thorough analysis of the direct CI method as applied to the case of a general set of reference configurations coupled to all single and double substitutions is presented in this article, where a variety of procedures are presented together with rules to enable the selection of the most favorable under a given circumstance.
References
More filters
Journal ArticleDOI
Group theoretical approach to the configuration interaction and perturbation theory calculations for atomic and molecular systems
TL;DR: In this paper, a formalism for the generation of spin-symmetry adapted configuration interaction (CI) matrices of the N −electron atomic or molecular systems, described by nonrelativistic spin-independent Hamiltonians, is presented.
Book ChapterDOI
Time-Independent Diagrammatic Approach to Perturbation Theory of Fermion Systems
Josef Paldus,J. Čížek +1 more
TL;DR: In this article, a diagrammatic approach to perturbation theory of fermion systems is presented, and the second and third-order excitation energy contributions are given in a simple way without the involvement of the Green function formalism.
Journal ArticleDOI
Application of unitary group methods to configuration interaction calculations
Dermot Hegarty,Michael A. Robb +1 more
TL;DR: In this article, a computational approach to the direct configuration interaction method is described using the calculus of the generators of the unitary group and the simple structure of the generator matrices within the harmonic excitation level scheme is exploited to give a computational method that is competitive with traditional approaches.
Journal ArticleDOI
The graphical unitary group approach to the electron correlation problem. Methods and preliminary applications
TL;DR: In this paper, the graphical unitary group approach (GUGA) was developed into an extraordinarily powerful theoretical method for solving the upper walk problem, the restriction of configuration space employed to the multireference interacting space and the restructuring of the Hamiltonian in terms of loop types.
Journal ArticleDOI
Correlation problems in atomic and molecular systems. V. Spin‐adapted coupled cluster many‐electron theory
TL;DR: In this article, the graphical techniques of spin algebras are combined with a diagrammatic approach based on the time independent Wick theorem to yield the spin-adapted form of the coupled cluster theory.