Hartree-Fock calculations, molecules

Even Hartree-Fock calculations are diflTicult and expensive to apply to large molecules. As a result, fiirther simplifications are often made. Parts of the Fock operator are ignored or replaced by parameters chosen by some sort of statistical procedure to account, in an average way, for the known properties of selected... 

A simple example would be in a study of a diatomic molecule that in a Hartree-Fock calculation has a bonded cr orbital as the highest occupied MO (HOMO) and a a lowest unoccupied MO (LUMO). A CASSCF calculation would then use the two a electrons and set up four CSFs with single and double excitations from the HOMO into the a orbital. This allows the bond dissociation to be described correctly, with different amounts of the neutral atoms, ion pair, and bonded pair controlled by the Cl coefficients, with the optimal shapes of the orbitals also being found. For more complicated systems... 

A Hbasis functions provides K molecular orbitals, but lUJiW of these will not be occupied by smy electrons they are the virtual spin orbitals. If u c were to add an electron to one of these virtual orbitals then this should provide a means of calculating the electron affinity of the system. Electron affinities predicted by Konpman s theorem are always positive when Hartree-Fock calculations are used, because fhe irtucil orbitals always have a positive energy. However, it is observed experimentally that many neutral molecules will accept an electron to form a stable anion and so have negative electron affinities. This can be understood if one realises that electron correlation uDiild be expected to add to the error due to the frozen orbital approximation, rather ihan to counteract it as for ionisation potentials. 

The application of density functional theory to isolated, organic molecules is still in relative infancy compared with the use of Hartree-Fock methods. There continues to be a steady stream of publications designed to assess the performance of the various approaches to DFT. As we have discussed there is a plethora of ways in which density functional theory can be implemented with different functional forms for the basis set (Gaussians, Slater type orbitals, or numerical), different expressions for the exchange and correlation contributions within the local density approximation, different expressions for the gradient corrections and different ways to solve the Kohn-Sham equations to achieve self-consistency. This contrasts with the situation for Hartree-Fock calculations, wlrich mostly use one of a series of tried and tested Gaussian basis sets and where there is a substantial body of literature to help choose the most appropriate method for incorporating post-Hartree-Fock methods, should that be desired. 

Here we give the molecule specification in Cartesian coordinates. The route section specifies a single point energy calculation at the Hartree-Fock level, using the 6-31G(d) basis set. We ve specified a restricted Hartree-Fock calculation (via the R prepended to the HF procedure keyword) because this is a closed shell system. We ve also requested that information about the molecular orbitals be included in the output with Pop=Reg. 

Notice that NewZMat has set up a Hartree-Fock calculation by default, using the 6-31G(d) basis set. The molecule specification in the generated file is also in Z-matrix format rather than Cartesian coordinates. You can now edit this file to modify the procedure, basis set, and type of run desired. We won t bother running this file, since it is the same job as the one we just completed. 

Force Constants and Dipole-Moment Derivatives of Molecules from Perturbed Hartree-Fock Calculations I J. Gerratt and I. M. Mills Journal of Physical Chemistry 49 (1968) 1719... 

Scheme 83 and crystallographically characterized. With 2.942(2) A the Ti-Ti distance in the molecule is fairly short, and ab initio unrestricted Hartree-Fock calculations suggested the presence of a Ti-Ti bonding interaction. 

Rotational Barrier in Ethylene. It is well known that the rotational barrier of the ethylene molecule cannot be adequately described by a single reference Hartree-Fock calculation SCF calculations on this level resulted in values of 126 kcal/mole (30) and 129 kcal/mole (31) whereas the experimental value is 65 kcal/mole (32). Open-shell ab initio calculations of double zeta+polarization quality give the more acceptable value of 48 kcal/mole (33). Inclusion of correlation such as in CEPA calculations yield theoretical results within the experimental error bar (34), albeit at a considerable computational cost. 

During this process the atomic charges for the adsorbed molecules were taken from a Mulliken analysis of a DZP basis set Hartree Fock calculation (using CADPAC on the MOPAC (PM3) optimized molecular structure. Table 3 gives the cation charges for the sulfoxide group and C2 for each cation. In both cases the sulfur and transferred proton are positively charged but at sulfur the... 

Five large basis sets have been employed in the present study of benzene basis set 1, which has been taken from Sadlej s tables [37], is a ( ()s6pAdl6sAp) contracted to 5s >p2dl >s2p and contains 210 CGTOs. It has been previously adopted by us in a near Hartree-Fock calculation of electric dipole polarizability of benzene molecule [38]. According to our experience, Sadlej s basis sets [37] provide accurate estimates of first-, second-, and third-order electric properties of large molecules [39]. 

In view of the impracticability of the Hartree-Fock calculation for common molecules, the LCAO MO spatial functions may be used in place of Hartree-Fock ones. The MO s a and b are given by... 

For most molecules studied, modest Hartree-Fock calculations yield remarkably accurate barriers that allow confident prediction of the lowest energy conformer in the S0 and D0 states. The simplest level of theory that predicts barriers in good agreement with experiment is HF/6-31G for the closed-shell S0 state (Hartree-Fock theory) and UHF/6-31G for the open-shell D0 state (unrestricted Hartree-Fock theory). The 6-31G basis set has double-zeta quality, with split valence plus d-type polarization on heavy atoms. This is quite modest by current standards. Nevertheless, such calculations reproduce experimental barrier heights within 10%. 

Poly(2,5-pyridyl) commonly know as poly(pyridine) has been the subject of considerable research effort as it luminesces in the blue region of the spectrum and may have uses in light emitting diodes (LEDs). Vaschetto and co-workers [103] reported a series of calculations on the molecule and its oligomers. The calculations included both the B3LYP and B3P88 density functions, Hartree-Fock calculations and a periodic solid-state DFT calculation using linear muffin tintype orbitals (LMTO). 

How does a rigorously calculated electrostatic potential depend upon the computational level at which was obtained p(r) Most ab initio calculations of V(r) for reasonably sized molecules are based on self-consistent field (SCF) or near Hartree-Fock wavefunctions and therefore do not reflect electron correlation in the computation of p(r). It is true that the availability of supercomputers and high-powered work stations has made post-Hartree-Fock calculations of V(r) (which include electron correlation) a realistic possibility even for molecules with 5 to 10 first-row atoms however, there is reason to believe that such computational levels are usually not necessary and not warranted. The Mpller-Plesset theorem states that properties computed from Hartree-Fock wave functions using one-electron operators, as is T(r), are correct through first order (Mpller and Plesset 1934) any errors are no more than second-order effects. 

Suhai128 investigated water dimer and an infinite chain of hydrogen-bonded water molecules by means of the DFT and post-Hartree-Fock calculations. For the infinite system, the DFT(BLYP), MP2, and MP4 binding energies were within 0.2 kcal/mol, whereas the corresponding interatomic distances were within 0.04 A. A similar agreement was reported for water dimer. 

Hamiltonian equations, 627-628 II electronic states, 632-633 triatomic molecules, 587-598 minimal models, 615-618 Hartree-Fock calculations ... 

The difficulties encountered in the calculation of magnetic properties are illustrated by a series of Hartree-Fock calculations of the indirect spin-spin coupling constant of the molecule at the experimental geometry... 

Values of the MacLaurin coefficients computed from good, self-consistent-field wavefunctions have been reported [355] for 125 linear molecules and molecular ions. Only type I and II momentum densities were found for these molecules, and they corresponded to negative and positive values of IIq(O), respectively. An analysis in terms of molecular orbital contributions was made, and periodic trends were examined [355]. The qualitative results of that work [355] are correct but recent, purely numerical, Hartree-Fock calculations [356] for 78 diatomic molecules have demonstrated that the highly regarded wavefunctions of Cade, Huo, and Wahl [357-359] are not accurate for IIo(O) and especially IIo(O). These problems can be traced to a lack of sufficiently diffuse functions in their large basis sets of Slater-type functions. 

Applications based on the even-tempered prescription (1) have shown that it can lead to atomic and diatomic Hartree-Fock ground state energies of an accuracy approaching that achieved in numerical Hartree-Fock calculations [4] It is conjectured that a comparable accuracy can be achieved for small polyatomic molecules [12], [13] by constructing basis sets according to the prescription established for diatomic molecules. Similar procedures can... 

One-center expansion was first applied to whole molecules by Desclaux Pyykko in relativistic and nonrelativistic Hartree-Fock calculations for the series CH4 to PbH4 [81] and then in the Dirac-Fock calculations of CuH, AgH and AuH [82] and other molecules [83]. A large bond length contraction due to the relativistic effects was estimated. However, the accuracy of such calculations is limited in practice because the orbitals of the hydrogen atom are reexpanded on a heavy nucleus in the entire coordinate space. It is notable that the RFCP and one-center expansion approaches were considered earlier as alternatives to each other [84, 85]. 

Atomic charges on the guest molecules were obtained from first principles Hartree-Fock calculations, fitting the electrostatic potential surface (EPS), then scaled up or down in order to reproduce the experimental dipole moments. Table 2 gives partial charges of typical molecules considered in our work. 

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