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A comparison is made of the accuracy with which the total electronic energy can be calculated by using the finite basis set approach (the algebraic approximation) and the finite difference method in calculations employing the Hartree-Fock model for the open shell ground (X[sup 2]Σ[sup +]) states of the fluorides BaF and YbF. The convergence of the calculations carried out within the algebraic approximation is monitored by employing systematically constructed basis sets of increasing size. The difference between the finite basis set and finite difference Hartree-Fock energies is 2.6 µE[sub h] for BaF and 2.8 µE[sub h] for YbF. Dipole moments determined within the algebraic approximation are also compared with the corresponding finite difference expectation values. [ABSTRACT FROM AUTHOR]

The local orbital energy function is used to assess the quality of approximate Hartree-Fock orbitals obtained by invoking the algebraic approximation and using a finite basis set expansion. Systematic sequences of distributed universal even-tempered basis sets of sphericalharmonic Gaussian-type functions are used to generate orbitals for which the corresponding total Hartree-Fock energy approaches the 1 μ E [sub h] level of accuracy. A pilot study of the behaviour of the local energy function is made for the hydrogenic atom described by a sequence of even-tempered Gaussian basis sets. The results of prototype calculations for the Hartree-Fock ground state of the BF molecule at its equilibrium geometry are presented. Sequences of calculations which use atom-centred basis sets are investigated as well as sequences which also include bond centred functions. The effects of the bond centred functions on the local orbital energy function are analysed. The local orbital energy function is seen as a measure of the quality of calculations carried out within the matrix Hartree-Fock approximation which can be employed in cases where the corresponding finite difference Hartree-Fock results are not available. [ABSTRACT FROM AUTHOR]

A comparison is made of the accuracy with which the total electronic energy can be calculated by using either the finite basis set approach (the algebraic approximation) or finite difference methods in calculations employing the restricted Hartree-Fock model for the open-shell ground (X[sup 2] Sigma+) states of the Group IIa fluorides BeF, MgF, CaF and SrF. The convergence of the calculations carried out within the algebraic approximation is monitored by employing systematically constructed basis sets of increasing size. By using two different grids, the accuracy of the finite difference calculations has been estimated to be of the order of 10-2 muE[sub h] . The average difference between the finite basis set and finite difference total Hartree-Fock energies is 2.75 muE[sub h] . Dipole moments determined within the algebraic approximation are also compared with the corresponding finite difference expectation values. [ABSTRACT FROM AUTHOR]

A comparison is made of the accuracy with which the total electronic energy can be calculated by using either the finite basis set approach (the algebraic approximation) or finite difference methods in calculations employing the Hartree-Fock model for the open shell ground (X 2zeta +) states of the 13-electron systems BeF, BO, CN and N+2. The convergence of the calculations carried out within the algebraic approximation is monitored by employing systematically constructed basis sets of increasing size. The accuracy of the finite difference calculations is assessed by employing two grids of different sizes, one of 32617 points and the other of 132385 points. The total Hartree-Fock energies supported by these two grids differ by less than 0.05mu Eh. The average difference between the finite basis set and finite difference Hartreeh Fock energies is 1.3mu Eh. Dipole moments determined within the algebraic approximation are compared with the corresponding finite difference expectation values for the neutral species. [ABSTRACT FROM AUTHOR]

A comparison is made of the finite basis set approach (the algebraic approximation) and finite difference methods in calculations using the Hartree-Fock model for the ground (X1Sigma+) states of the heaviest Group IIIb fluorides: indium fluoride and thallium fluoride molecules. The XF molecules, X = In, Tl, are considered as a prototype for systems containing increasingly heavy atoms and a number of electrons. New finite difference Hartree-Fock calculations for the GaF ground state improve upon earlier results. The convergence of the calculations carried out within the algebraic approximation is monitored by employing systematically constructed basis sets of increasing size. The dependence of the finite difference calculations on the numerical grid employed is discussed. For the InF molecule, the total Hartree-Fock energy obtained with a grid of 595 595 points lies 15 mu E below the finite basis set energy. For the ground h state of TlF the finite basis set energy lies about 61 mu E above the converged finite difference result obtained on a grid of 595 595 points. For the TlF molecule, the matrix element required to evaluate the electric dipole moment volume interaction for the elementary particles in the Tl nucleus is evaluated from the finite difference Hartree-Fock wavefunction. [ABSTRACT FROM AUTHOR]

The orbital amplitude difference function is used to assess the quality of Hartree-Fock orbitals obtained by invoking the algebraic approximation for the BF ground-state. Systematic sequences of even-tempered, spherical-harmonic Gaussian-type basis functions are used to generate orbitals for which the corresponding total Hartree-Fock energy approaches the 1 mu E level of accuracy. Exact orbitals are obtained from finite difference calculations using h a grid based on spheroidal coordinates. The finite basis set approximations for the orbital are discretized. The accuracy of the discretization is assessed. For each occupied orbital a discretized representation of the orbital amplitude difference function is generated and analysed. [ABSTRACT FROM AUTHOR]

The article presents a study that focuses on the development of oar-boat-rower system model for the optimization of rowing performance. It cites the establishment of the model with parameters from mechanics, hydrodynamics and biomechanics. It also indicates the use of the model in evaluating the performance sensitivity to the parameters.