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Hamiltonian Matrix (hamiltonian + matrix)
Selected AbstractsEfficient generation of Heisenberg Hamiltonian matrices for VB calculations of potential energy surfacesINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 3 2009A. M. Tokmachev Abstract The spin-Hamiltonian valence bond theory relies upon covalent configurations formed by singly occupied orbitals differing by their spin counterparts. This theory has been proven to be successful in studying potential energy surfaces of the ground and lowest excited states in organic molecules when used as a part of the hybrid molecular mechanics,valence bond method. The method allows one to consider systems with large active spaces formed by n electrons in n orbitals and relies upon a specially proposed graphical unitary group approach. At the same time, the restriction of the equality of the numbers of electrons and orbitals in the active space is too severe: it excludes from the consideration a lot of interesting applications. We can mention here carbocations and systems with heteroatoms. Moreover, the structure of the method makes it difficult to study charge-transfer excited states because they are formed by ionic configurations. In the present work we tackle these problems by significant extension of the spin-Hamiltonian approach. We consider (i) more general active space formed by n ± m electrons in n orbitals and (ii) states with the charge transfer. The main problem addressed is the generation of Hamiltonian matrices for these general cases. We propose a scheme combining operators of electron exchange and hopping, generating all nonzero matrix elements step-by-step. This scheme provides a very efficient way to generate the Hamiltonians, thus extending the applicability of spin-Hamiltonian valence bond theory. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009 [source] Spin-adapted states: A basis for quantum dot structure calculationINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 1 2006R. D. Muhandiramge Abstract The exact diagonalization method using a spin-adapted basis is employed to calculate the electronic structure of a multi-electron quantum dot. By isolating spin and orbital angular momentum eigenstates, we have significantly reduced the size of the matrices required in comparison with the standard configuration interaction method. A novel approach to the simplification of the interaction integrals that arise in the calculation is also presented, which allows exact evaluation of the Hamiltonian matrix required in the calculations. This Mathematica package permits accurate calculation of energy levels and wave functions for both ground and excited states of multiple electrons confined in a circular quantum dot. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006 [source] Variational treatment of the vibrational Hamiltonian for NH3 and H2NOJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 5 2002Philippe Marsal Abstract The full vibrational Hamiltonian for the inversion of NH3 and H2NO has been diagonalized in a basis set that is the direct product of functions of the inversion coordinate and of harmonic vibrational functions independent of this inversion coordinate. The kinetic part of the Hamiltonian matrix is constructed with the use of the closure relation for these vibrational functions. The method is tested with the potential function which is supposed to be harmonic for the vibrations orthogonal to the inversion coordinate: the first computed levels are in good agreement with experimental levels for NH3. For higher levels, anharmonic terms should be included. © 2002 Wiley Periodicals, Inc. J Comput Chem 23: 541,547, 2002; DOI 10.1002/jcc.10033 [source] Systematic Study of Selected Diagonalization Methods for Configuration Interaction MatricesJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 13 2001Matthew L. Leininger Abstract Several modifications to the Davidson algorithm are systematically explored to establish their performance for an assortment of configuration interaction (CI) computations. The combination of a generalized Davidson method, a periodic two-vector subspace collapse, and a blocked Davidson approach for multiple roots is determined to retain the convergence characteristics of the full subspace method. This approach permits the efficient computation of wave functions for large-scale CI matrices by eliminating the need to ever store more than three expansion vectors (bi) and associated matrix-vector products (,i), thereby dramatically reducing the I/O requirements relative to the full subspace scheme. The minimal-storage, single-vector method of Olsen is found to be a reasonable alternative for obtaining energies of well-behaved systems to within ,Eh accuracy, although it typically requires around 50% more iterations and at times is too inefficient to yield high accuracy (ca. 10,10Eh) for very large CI problems. Several approximations to the diagonal elements of the CI Hamiltonian matrix are found to allow simple on-the-fly computation of the preconditioning matrix, to maintain the spin symmetry of the determinant-based wave function, and to preserve the convergence characteristics of the diagonalization procedure. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1574,1589, 2001 [source] | ||||||||||