Hartree-Fock direct

Tel. 412-621-2050, fax 412-621-3563, e-mail info gaussian.com Gaussian 92. Ab initio molecular orbital calculations (Hartree-Fock, Direct HF, Moller-Plesset, Cl, Reaction Field Theory, electrostatic potential-derived charges, vibrational frequencies, etc.). Input and output of molecular structures in formats of many other molecular modeling systems. Browse for archival storage of computed results. VAX, Cray, DEC-RISC (Ultrix), Fujitsu (UXP/M), Kubota, IBM RS/6000, Multiflow, Silicon Graphics, Sun, and other versions. Gaussian 90 for Convex, FPS-500, Fujitsu (MSP), IBM (VM, MVS), HP-700, and NEC SX/3 systems. 

Direct dynamics attempts to break this bottleneck in the study of MD, retaining the accuracy of the full electronic PES without the need for an analytic fit of data. The first studies in this field used semiclassical methods with semiempirical [66,67] or simple Hartree-Fock [68] wave functions to heat the electrons. These first studies used what is called BO dynamics, evaluating the PES at each step from the elech onic wave function obtained by solution of the electronic structure problem. An alternative, the Ehrenfest dynamics method, is to propagate the electronic wave function at the same time as the nuclei. Although early direct dynamics studies using this method [69-71] restricted themselves to adiabatic problems, the method can incorporate non-adiabatic effects directly in the electionic wave function. 

To use direct dynamics for the study of non-adiabatic systems it is necessary to be able to efficiently and accurately calculate electronic wave functions for excited states. In recent years, density functional theory (DFT) has been gaining ground over traditional Hartree-Fock based SCF calculations for the treatment of the ground state of large molecules. Recent advances mean that so-called time-dependent DFT methods are now also being applied to excited states. Even so, at present, the best general methods for the treatment of the photochemistry of polyatomic organic molecules are MCSCF methods, of which the CASSCF method is particularly powerful. 

Boys and Cook refer to these properties as primary properties because their electronic contributions can be obtained directly from the electronic wavefunction As a matter of interest, they also classified the electronic energy as a primary property. It can t be calculated as the expectation value of a sum of true one-electron operators, but the Hartree-Fock operator is sometimes written as a sum of pseudo one-electron operators, which include the average effects of the other electrons. 

Although a calculation of the wave function response can be avoided for the first derivative, it is necessary for second (and higher) derivatives. Eq. (10.29) gives directly an equation for determining the (first-order) response, which is structurally the same as eq. (10.36). For an HF wave function, an equation of the change in the MO coefficients may also be formulated from the Hartree-Fock equation, eq. (3.50). 

The ab initio methods used by most investigators include Hartree-Fock (FFF) and Density Functional Theory (DFT) [6, 7]. An ab initio method typically uses one of many basis sets for the solution of a particular problem. These basis sets are discussed in considerable detail in references [1] and [8]. DFT is based on the proof that the ground state electronic energy is determined completely by the electron density [9]. Thus, there is a direct relationship between electron density and the energy of a system. DFT calculations are extremely popular, as they provide reliable molecular structures and are considerably faster than FFF methods where correlation corrections (MP2) are included. Although intermolecular interactions in ion-pairs are dominated by dispersion interactions, DFT (B3LYP) theory lacks this term [10-14]. FFowever, DFT theory is quite successful in representing molecular structure, which is usually a primary concern. 

Thus, the combined experimental and theoretical results indicate that the chemical shift observed for the S(2p) core level, of about 1.6 eV, should be due to a secondary effect from the attachment of Al atoms to the adjacent carbon atoms. Indeed, this is fully consistent with tib initio Hartree-Fock ASCF calculations of the chemical shifts in aluminum-oligolhiophene complexes 187], From calculations on a AI2/a-3T complex, where the two AI atoms are attached to the a-car-bons on the central thiophene unit, the chemical shift of the S(2p) level for the central sulfur atom is found to be 1.65 eV, which is in close agreement with the experimental value of about 1.6 eV [84]. It should be pointed out that although several different Al-lhiophene complexes were tested in the ASCF calculations, no stable structure, where an Al atom binds directly to a S atom, was found [87]. 

The second-order density matrix is in the Hartree-Fock approximation given by Eqs. 11.44 and 11.53, and we obtain directly... 

An Application of the Half-Projected Hartree-Fock Model to the Direct Determination of the Lowest Singlet and Triplet Excited States of Molecular Systems... 

In addition, since the HPHF wavefunction exhibits a two-determinantal form, this model can be used to describe singlet excited states or triplet excited states in which the projection of the spin momentum Ms=0. The HPHF approximation appears thus as a simple method for the direct determination of excited states (with Afs=0)such as the usual Unrestricted Hartree Fock model does for determining triplet excited states with Ms = 1. 

It may be concluded thus that the Half-Projected Hartree-Fock model proposed more than two decades ago for introducing some correlation effects in the ground state wave-function [1,2], could be employed advantageously for the direct determination of the lowest triplet and singlet excited states, in which Ms = 0. This procedure could be especially suitable for the singlet excited states of medium size molecules for which no other efficient procedure exists. 

An application of the half-projected Hartree-Fock model to the direct... 

This can only be true if p2 (xj, Xj) = 0. In other words, this result tells us that the probability of finding two electrons with the same spin at the same point in space is exactly zero. Hence, electrons of like spin do not move independently from each other. It is important to realize that this kind of correlation is in no way connected to the charge of the electrons but is a direct consequence of the Pauli principle. It applies equally well to neutral fermions and - also this is very important to keep in mind - does not hold if the two electrons have different spin. This effect is known as exchange or Fermi correlation. As we will show below, this kind of correlation is included in the Hartree-Fock approach due to the antisymmetry of a Slater determinant and therefore has nothing to do with the correlation energy E discussed in the previous chapter. 

Rubio J, Povill A, Malrieu J-P, Reinhardt PJ (1997) Direct determination of localized Hartree-Fock orbitals as a step toward Nscaling procedures. J Chem Phys 107 10044... 

Experimentally determined maximum absolute ionization cross sections for the inert gases and a range of small molecules are compared with the predictions of DM, BEB, and EM calculations in Table 1. Atomic orbital coefficients for the DM calculations were determined at the Hartree-Fock level and the EM cross sections are volume averaged for calculations carried out at the HF/6-31G level. Hie same data are plotted in Figure 5 with the calculated values on the ordinate and the experimental result on the abscissa. The heavy line represents a direct correspondence between experiment and theory. Although the ab initio EM method performs well for the calculation of qm and Em,T,17 the DM and BEB methods allow for the calculation of the cross section as a function of the electron energy, i.e. the ionization... 

Barone, V. and C. Adamo. 1994. Theoretical study of direct and water-assisted isomerization of formaldehyde radical cation. A comparison between density functional and post-Hartree-Fock approaches. Chem. Phys. Lett. 224, 432. 

---