Hartree-Fock perturbation

Pisani C, Doves R and Nada R 1990 Ab initio Hartree-Fock perturbed-cluster treatment of local defects in crystals J. Chem. Phys. 92 7448... 

These compounds have been the subject of several theoretical [7,11,13,20)] and experimental[21] studies. Ward and Elliott [20] measured the dynamic y hyperpolarizability of butadiene and hexatriene in the vapour phase by means of the dc-SHG technique. Waite and Papadopoulos[7,ll] computed static y values, using a Mac Weeny type Coupled Hartree-Fock Perturbation Theory (CHFPT) in the CNDO approximation, and an extended basis set. Kurtz [15] evaluated by means of a finite perturbation technique at the MNDO level [17] and using the AMI [22] and PM3[23] parametrizations, the mean y values of a series of polyenes containing from 2 to 11 unit cells. At the ab initio level, Hurst et al. [13] and Chopra et al. [20] studied basis sets effects on and y. It appeared that diffuse orbitals must be included in the basis set in order to describe correctly the external part of the molecules which is the most sensitive to the electrical perturbation and to ensure the obtention of accurate values of the calculated properties. 

Bernardi, F., Bottom, 1997, Polar Effect in Hydrogen Abstraction Reactions from Halo-Substituted Methanes by Methyl Radical A Comparison Between Hartree-Fock, Perturbation, and Density Functional Theories , J. Phys. Chem., 101, 1912. 

JHC735>. The polarizability and hyperpolarizability of 1,2,3-triazole have been computed by the Hartree-Fock perturbation theory on an extended basis CNDO method <90JPC1755>. 

The abstract of Russian work on the application of Hartree-Fock perturbation theory to the calculation of 7r-electron ring currents in inter alia pyrrole, indole, indolizine and carbazole reports agreement between calculated and experimental HNMR shifts... 

The basic computational method is that of coupled Hartree-Fock perturbation theory (14). At present we prefer the GIAO implementation mentioned above because of its computational efficiency and ease of use, but we have previously used a common gauge-origin method as implemented in the software SYSMO (15) as well as the random-phase approximation, localized orbital (RPA LORG) approach as implemented in the software RPAC (16). 

Polarizability will be dealt with first because it is the easiest of the three properties to calculate and has certainly received the most attention. Many of the conclusions also apply to x and a, which are dealt with in much less detail. In each section we have tried to pick out the most important methods and consider them in detail at the expense of the less useful methods. Thus, for example, although the variational technique of Karplus and Kolker is simpler than the other uncoupled Hartree-Fock perturbation methods, it is not a very useful technique for calculating polarizabilities. It is very useful for calculations of magnetic susceptibility, however, where many other techniques are inappropriate. 

More recently, Caves and Karplus71 have used diagrammatic techniques to investigate Hartree-Fock perturbation theory. They developed a double perturbation expansion in the perturbing field and the difference between the true electron repulsion potential and the Hartree-Fock potential, V. This is compared with a solution of the coupled Hartree-Fock equations. In their interesting analysis they show that the CPHF equations include all terms first order in V and some types of terms up to infinite order. They propose an alternative iteration procedure which sums an additional set of diagrams and thus should give results more accurate than the CPHF scheme. Calculations on Ha and Be confirmed these conclusions. 

After some sparse papers published by different authors in the 1970s (see e.g. refs. 111-113), in 1987 Tossel et al.114 performed ab initio CHFPT (coupled Hartree-Fock perturbation theory) calculations of Gd and ap/ the diamagnetic and... 

Coupled Hartree-Fock perturbation theory has been used to calculate the polarizability of a pair of He atoms as a function of R. However, the authors conclude that further work is needed, including electron correlation.100... 

Bernardi F, Bottoni A. Polar effect in hydrogen abstraction reactions from halo-substituted methanes by methyl radical a comparison between Hartree-Fock, perturbation, and density functional theories. J Phys Chem A 1997 101(10) 1912—1919. 

There are also properties for which the magnitude is dependent upon transition intensity and for which accurate results can be obtained only with perturbation theory examples occur in currently much studied areas like NMR spectroscopy (described in Chapter 2), but also involve other properties like magnetic susceptibilities and refractive indices, which are not much studied from an electronic structure point of view (although we would argue that, due to advances in theory, such experimental techniques are ripe for further exploration). Within a Hartree-Fock approach the perturbation of a molecule by electric or magnetic fields can be calculated at a number of levels of theory. Coupled Hartree-Fock perturbation theory (Lipscomb, 1966 Ditchfield, 1974), which arrives at a self-... 

Table 5.4. Calculated NMR shieldings (cr, a , and q°) for linear (SiHjljO, SiHjOAlH,, SiHjOH, SiHjOMg, and PH3OAIH3 units obtained from Hartree-Fock perturbation theory (sp O 3d, T 3d basis)...

T. J. Lee and D. Jayatilaka, Chem. Phys. Lett., 201, 1 (1993). An Open-Shell Restricted Hartree-Fock Perturbation Theory Based on Symmetric Spin Orbitals. 

Various forms of Hartree-Fock perturbation theory have been applied to the calculation of nitrogen screening constants within the framework of Ramsey s treatment. These avoid the difficulties associated with the infinite summation over excited states by restricting the summation to states described by the molecular orbitals used in the calculation. (11-14)... 

Langhoff, P.W., Karplus, M., Hurst, R.P. Approximations to Hartree-Fock perturbation theory.. 1. Chem. Phys. 44, 505-514 (1966)... 

The electrostatic potential V(r) is the first order contribution to the interaction energy. The second order contribution P(r), which is commonly referred to as a polarization correction to the electrostatic potential, is defined within the imcoupled Hartree-Fock perturbation theory by [41]... 

Eq. (6.72), we note that the matrix elements, which appear in the numerator of the second-order energy, now have four indices instead of two. This is an immediate result of the two-particle nature of the perturbation. Therefore, it is reasonable to expect that the diagrams which represent Hartree-Fock perturbation theory have dots with two lines going in and two lines coming out. This is in fact the case. To obtain the diagrams that contribute to the nth-order energy we connect n vertically ordered dots in all possible ways, such that... 

Table 6.2 contains all second- and third-order Goldstone diagrams in Hartree-Fock perturbation theory. They have been evaluated using the following rules ... 

Now the expression (19) is an uncoupled formulation of the polarizability. We can replace it by a polarizability derived from coupled Hartree-Fock perturbation theory, which is more accurate, because it takes account of the reorganisation of the electron distribution in a self-consistent manner. Better still would be to evaluate the monomer polarizability by a method that takes account of electron correlation as well . But whatever the level of calculation, we can once again perform a much better calculation of the monomer property than is possible for the dimer. In this way we arrive at a description of the induction energy that is far more accurate than we can obtain through either intermolecular perturbation theory, where the perturbation is treated in an uncoupled fashion, or from a supermolecule calculation, where the size of the basis is limited by the need to perform calculations at a large number of points on the potential energy surface. 

P. W. Langhoff, M. Karplus, and R. P. Hurst, J. Chem. Phys., 44, 505 (1966). Approximations to Hartree-Fock Perturbation Theory. 

Keywords Excited states Constrained Hartree-Fock Perturbation theory Double core hole states Frozen orbitals... 

Lee, T. J., 8c Jayatilaka, D. (1993). An open-shell restricted Hartree-Fock perturbation theory based on symmetric spin orbitals. Chemical... 

Measured by using EDXD and calculated by using Coulomb Hartree-Fock perturbed ion, GGA, and LDA methods [10]. 

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