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541.
Ruben Pauncz 《International journal of quantum chemistry》1984,25(4):707-713
A new derivation is given for the Waller–Hartree–Fock double-determinantal spatial wave function. One starts from the single-determinant wave function in which a orbitals are doubly occupied, and decomposes it into a sum of products of spatial and spin functions. The spatial product of the first genealogical spin eigenfunction is a double-determinantal function. The derivation is based on the simple form of U1?(P) when the representation matrix is obtained from the genealogical spin eigenfunction. 相似文献
542.
Equations for the Missing Boundary Values in the Hamiltonian Formulation of Optimal Control Problems
Vicente Costanza Pablo S. Rivadeneira Ruben D. Spies 《Journal of Optimization Theory and Applications》2011,149(1):26-46
Partial differential equations for the unknown final state and initial costate arising in the Hamiltonian formulation of regular
optimal control problems with a quadratic final penalty are found. It is shown that the missing boundary conditions for Hamilton’s
canonical ordinary differential equations satisfy a system of first-order quasilinear vector partial differential equations
(PDEs), when the functional dependence of the H-optimal control in phase-space variables is explicitly known. Their solutions are computed in the context of nonlinear systems
with ℝ
n
-valued states. No special restrictions are imposed on the form of the Lagrangian cost term. Having calculated the initial
values of the costates, the optimal control can then be constructed from on-line integration of the corresponding 2n-dimensional Hamilton ordinary differential equations (ODEs). The off-line procedure requires finding two auxiliary n×n matrices that generalize those appearing in the solution of the differential Riccati equation (DRE) associated with the linear-quadratic
regulator (LQR) problem. In all equations, the independent variables are the finite time-horizon duration T and the final-penalty matrix coefficient S, so their solutions give information on a whole two-parameter family of control problems, which can be used for design purposes.
The mathematical treatment takes advantage from the symplectic structure of the Hamiltonian formalism, which allows one to
reformulate Bellman’s conjectures concerning the “invariant-embedding” methodology for two-point boundary-value problems.
Results for LQR problems are tested against solutions of the associated differential Riccati equation, and the attributes
of the two approaches are illustrated and discussed. Also, nonlinear problems are numerically solved and compared against
those obtained by using shooting techniques. 相似文献
543.
The use of different spin functions in the AMO method was investigated for benzene, the ring of six H atoms, and fulvene. The additional improvement in the energy obtained by the use of a linear combination of different spin functions is quite small for the singlet ground state. It is pointed out that there are great differences in energy between functions having the same spatial function but different spin functions. 相似文献
544.
Divergente Koordinationschemie: Parallele Synthese von [2×2]‐Eisen(II)‐Gitterkomplextautokonformeren
545.
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549.
The static dipole polarizabilities of Ne, CO, N2, F2, HF, H2O, HCN, and C2H2 (acetylene) have been determined close to the Full-CI limit along with an asymptotically complete basis set (CBS), according to the principles of a Focal Point Analysis. For this purpose the results of Finite Field calculations up to the level of Coupled Cluster theory including Single, Double, Triple, Quadruple and perturbative Pentuple excitations [CCSDTQ(P)] were used, in conjunction with suited extrapolations of energies obtained using augmented and doubly-augmented Dunning's correlation consistent polarized valence basis sets of improving quality. The polarizability characteristics of C2H4 (ethylene) and C2H6 (ethane) have been determined on the same grounds at the CCSDTQ level in the CBS limit. Comparison is made with results obtained using lower levels in electronic correlation, or taking into account the relaxation of the molecular structure due to an adiabatic polarization process. Vibrational corrections to electronic polarizabilities have been empirically estimated according to Born–Oppenheimer Molecular Dynamical simulations employing Density Functional Theory. Confrontation with experiment ultimately indicates relative accuracies of the order of 1 to 2%. 相似文献
550.