Hamiltonian theories

Baer R and Kosloff R 1997 Quantum dissipative dynamics of adsorbates near metal surfaces a surrogate Hamiltonian theory applied to hydrogen on nickel J. Chem. Rhys. 106 8862... 

In another promising method, based on the effective Hamiltonian theory used in quantum chemistry [19], the protein is divided into blocks that comprise one or more residues. The Hessian is then projected into the subspace defined by the rigid-body motions of these blocks. The resulting low frequency modes are then perturbed by the higher... 

For the sake of completeness we note that spin-Hamiltonian theory (Pake and Esde 1973 95) states that any interaction of the form Bb Ss P is allowed to occur, i.e.,... 

Average or effective Hamiltonian theory, as introduced to NMR spectroscopy by Waugh and coworkers [55] in the late 1960s, has in all respects been the most important design tool for development of dipolar recoupling experiments (and many other important experiments). In a very simple and transparent manner, this method facilitates delineation of the impact of advanced rf irradiation schemes on the internal nuclear spin Hamiltonians. This impact is evaluated in an ordered fashion, enabling direct focus on the most important terms and, in the refinement process, the less dominant albeit still important terms in a prioritized manner. 

IIOb — 0. if is not self-commuting at all times and effective Hamiltonian theory is therefore applied to gain physical insight. 

The Intermediate Hamiltonian Theory is a generalization of the Effective Hamiltonian Theory. The full Cl space of Slater determinants can be divided into three parts,... 

C. Valdemoro, M. P. de Lara-Castells, R. Bochicchio, and E. Perez-Romero, A relevant space within the spin-adapted reduced Hamiltonian theory. 1. Study of the BH molecule. Int. J. Quantum Chem. 65, 97 (1997). 

First, we note that the determination of the exact many-particle operator U is equivalent to solving for the full interacting wavefunction ik. Consequently, some approximation must be made. The ansatz of Eq. (2) recalls perturbation theory, since (as contrasted with the most general variational approach) the target state is parameterized in terms of a reference iko- A perturbative construction of U is used in the effective valence shell Hamiltonian theory of Freed and the generalized Van Vleck theory of Kirtman. However, a more general way forward, which is not restricted to low order, is to determine U (and the associated amplitudes in A) directly. In our CT theory, we adopt the projection technique as used in coupled-cluster theory [17]. By projecting onto excited determinants, we obtain a set of nonlinear amplitude equations, namely,... 

The problem of estimating crystal field parameters can be solved by considering the CFT/LFT as a special case of the effective Hamiltonian theory for one group of electrons of the whole A -electronic system in the presence of other groups of electrons. The standard CFT ignores all electrons outside the d-shell and takes into account only the symmetry of the external field and the electron-electron interaction inside the d-shell. The sequential deduction of the effective Hamiltonian for the d-shell, carried out in the work [133] is based on representation of the wave function of TMC as an antisymmetrized product of group functions of d-electrons and other (valence) electrons of a complex. This allows to express the CFT s (LFT s or AOM s) parameters through characteristics of electronic structure of the environment of the metal ion. Further we shall characterize the effective Hamiltonian of crystal field (EHCF) method and its numerical results. 

Focussing on the HOMO s and the LUMO e+, DFT yields the KS eigenvectors u, and U- (equation (A.3)). Effective Hamiltonian theory [15] allows to reduce the size of matrix V to 2 X 2. Choosing the latter sub-matrix U, written in the subspace... 

Unlike the theory discussed in Chapter 3, which relies on VB structures that are eigenfunctions of both the Sz and S2 operators, Heisenberg—Hamiltonian theory uses, as basis functions, VB determinants that are eigenfunctions of the Sz operator only. The reader has by now some background on the VB... 

This theory also possesses an ab initio based quantitative version (10,19), in which the parameters are geometry dependent and fitted on accurately calculated potential surfaces of ethylene. Despite its simplicity, the spin-Hamiltonian theory has proven itself to be accurate for predicting ground state, as well as excited state, properties and transition energies. 

The inclusion of average Hamiltonian theory derived pulse sequence building blocks specifically designed for the measurement of RDCs is highly desirable. The homonuclear dipolar decoupling sequences used in ref. 190 lead to the less complex multiplet structures observed in isotropic samples with the chemical shift resolution reduced by a factor of 2-3, depending on the multiple pulse... 

Briefly, the aim of Lie transformations in Hamiltonian theory is to generate a symplectic (that is, canonical) change of variables depending on a small parameter as the general solution of a Hamiltonian system of differential equations. The method was first proposed by Deprit [75] (we follow the presentation in Ref. 76) and can be stated as follows. 

The outline of the review is as follows in the next section (Sect. 2) we introduce the basic ideas of effective Hamiltonian theory based on the use of projection operators. The effective Hamiltonian (1-5) for the ligand field problem is constructed in several steps first by analogy with r-electron theory we use the group product function method of Lykos and Parr to define a set of n-electron wavefimctions which define a subspace of the full -particle Hilbert space in which we can give a detailed analysis of the Schrodinger equation for the full molecular Hamiltonian H (Sect. 3 and 4). This subspace consists of fully antisymmetrized product wavefimctions composed of a fixed ground state wavefunction, for the electrons in the molecule other than the electrons which are placed in states, constructed out of pure d-orbitals on the... 

The renormalized theory of the effective Hamiltonian implied by the restriction to some subspace S of the full Hilbert space also imposes a requirement for renonnalisation of expectation values of other operators (Freed ). Suppose that we have some operator B and we require its expectation value in a state 0 of the full Schrddinger Eq. (2-2) in complete analogy with the effective Hamiltonian theory described above we define an effective operator B by the requirement that its expectation value in a state A ) in the subspace should equal the exact expectation value (c.f. Eq. (2-4)),... 

Important guidelines for the construction of a multiple-pulse sequence with desired properties are provided by average Hamiltonian theory (see Section IV). The effective Hamiltonian created by the sequence must meet a number of criteria (see Section IX). Most importantly, spins with different resonance frequencies, that is, with different offsets and Vj from a given carrier frequency, must effectively be energy matched in order to allow Hartmann-Hahn transfer. This can be achieved if the derivative of the effective field with respect to offset vanishes, which is identical to the Waugh criterion for efficient heteronuclear decoupling... 

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